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REMAL Sylvie SupAgro 3A

Spécialisation: Production Végétale Durable

Mémoire de fin d’études :

Conceptual and numerical evaluation of a plot scale, process-based

model of coffee agroforestry systems in Central America: CAF2007

Photo: M. Van Oijen

Supervisor: Bruno Rapidel, CIRAD in CATIE

Tutor: Aurélie Metay, Supagro Montpellier

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ACKNOWLEDGMENTS

First of all, I would like to thank my tutor, Dr. Jacques Wery (UMR SYSTEM/ CIRAD

Montpellier) and my supervisor, Dr. Bruno Rapidel (UMR SYSTEM/ CIRAD at CATIE Turrialba) for giving me the opportunity to do this very interesting internship for UMR SYSTEM/ CIRAD Montpellier in collaboration with CEH Edinburgh and CATIE Turrialba, in three beautiful countries, Scotland, Costa Rica and Nicaragua.

I would like to address a special thank to my other supervisors, Dr. Marie-Ange Ngo Bieng (UMR SYSTEM/ CIRAD Montpellier) and Dr. Marcel van Oijen (CEH Edinburgh), for their advice, guidance and help in the achievement of this work.

I also would like to express my gratitude to Dr. Elias de Melo (CATIE Turrialba), and Dr.

Jeremy Haggar (CATIE Nicaragua) and their colleagues Luis Romero and Elvin Navarette for learning me a lot on coffee agroforestry systems and for accompanying me during my field work. Without their help, this study would not have been possible, I am very grateful for that.

I also would like to acknowledge Dr. Aurélie Metay and Dr. Anne Mérot from UMR

SYSTEM/ INRA Montpellier and Dr. Olivier Roupsard and Dr. Jacques Avelino from CIRAD at CATIE, for their support and for being valuable sources of ideas and knowledge.

I can’t forget to thank the support staff and students of CATIE in Turrialba and Managua for always helping me while needed.

Finally, special thanks are addressed to Bruno and all my family for providing me moral support, for always being there for me and helping me staying strong face to adversity.

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SYNOPSIS ACKNOWLEDGMENTS ................................................................................................................................................................ 2

SYNOPSIS .................................................................................................................................................................................... 3

ABBREVIATIONS.......................................................................................................................................................................... 4

LIST OF TABLES AND FIGURES..................................................................................................................................................... 5

LIST OF APPENDICES................................................................................................................................................................... 6

I- Introduction ....................................................................................................................................................................... 7

1- Context and aim of this study .......................................................................................................................... 7

2- Interest and stake of coffee AFS in Central America .............................................................................. 7

3- Interests of modeling for evaluation of systems performance ............................................................... 8

4- CAF2007, a process-based model of coffee agroforestry systems in Central America.................... 9

5- Objectives of the study .................................................................................................................................. 10

II- Material and methods ........................................................................................................................................... 11

1- Conceptual evaluation of CAF2007 .................................................................................................................... 11

2- Numerical evaluation of CAF2007...................................................................................................................... 12

A - Experimental design ............................................................................................................................................ 12

B - Choice of the plots............................................................................................................................................... 14

C - Data collect ........................................................................................................................................................... 15

D - Sensitivity analysis of CAF2007 ...................................................................................................................... 17

E - Evaluation of CAF2007 ....................................................................................................................................... 17

III- Results and discussion ........................................................................................................................................... 18

1- Conceptual evaluation of CAF2007 .................................................................................................................... 18

a- Effect of tree shading on coffee reproductive dynamics....................................................................... 18

b- Coffee carbon production and allocation ..................................................................................................... 20

c- Coffee agroforestry systems water dynamics........................................................................................... 23

d- Coffee agroforestry systems nitrogen dynamics ...................................................................................... 25

e- Conclusion............................................................................................................................................................ 27

2- Numerical evaluation of CAF2007...................................................................................................................... 28

A - Data collect ........................................................................................................................................................... 28

B - Sensitivity analysis of CAF2007....................................................................................................................... 32

C – Numerical evaluation of CAF2007.................................................................................................................... 33

IV- Conclusion and perspectives ................................................................................................................................ 37

BIBLIOGRPAHY.......................................................................................................................................................................... 38

ABSTRACT ................................................................................................................................................................................. 41

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ABBREVIATIONS

APES: Agricultural Production and Externalities Simulator CABI: Canadian Agency for International development CAF2007: Coffee AgroForestry 2007 CASCA: Coffee Agroforestry Systems in Central America CATIE: Centro Agronómico Tropical de Investigación y Enseñanza CEH: Centre of Ecology and Hydrology CIRAD: Centre International de Recherche Agronomique pour le Développement Hi-sAFe: Hi-silvoarable AgroForestry for Europe INCAE: Instituto Centroamericano de Administración de Empresas LAI: Leaf Area Index PAR: Photosynthetically active radiation PROMECAFE: Programa Cooperativo Regional para el Desarrollo Tecnológico de la Cafeicultura en Centroamérica, Panamá, República Dominicana and Jamaica RRMSE: Relative Root Mean Square Error SEAMLESS: System for Environmental and Agriculture Modeling, Linking European Science and Society SLA: Specific Leaf Area UMR SYSTEM: Unité Mixte de Recherche, Fonctionnement et conduite des systèmes de culture tropicaux et méditerranéens UNA: Universidad Nacional Agraria, Nicaragua WaNuLCAS: Water, Nutrient and Light Capture in Agroforestry System

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LIST OF TABLES AND FIGURES

Figure 1: Map of the coffee producing countries in Central America…………………..…………….7

Figure 2: Conceptual scheme of CAF2007 (Marcel Van Oijen, submitted)……………………….....10 Figure 3: Technical itinerary in coffee agroforestry trials in Turrialba and Masatepe……………..…13 Figure 4: The five coffee phenological stages (Rebolledo, 2008)…………………………..……...…19

Figure 5: Carbon conversion and allocation diagram, academic source (Rebolledo, 2008).................22

Figure 6: Scheme of calculation of coffee leaves, woody parts, roots and fruits sink strengths and their respective fractions of carbon allocation in CAF2007………………………………………...………22 Figure 7: Boxplot of observed yields in function of the treatment. ………………..…………………29 Figure 8: Graphic representing mean of yields in function of interaction between the level of input (MGT) and the subplot on abscissa (PLOT)…………………………………….……………………..30 Figure 9: Annual coffee yields in Turrialba………………………………………………….……30 Figure 10: Annual coffee yields in Masatepe………………………………………………………... 31 Figure 11: Differences between simulated and observed coffee yields for both modeling…………..35

Table 1: Tree species used in shade combinations in: a) Turrialba, Costa Rica.........................................................................................................................12 b) Masatepe, Nicaragua..........................................................................................................................12

Table 2: Input levels for nutrient and pest management in coffee systems experiments.....................13 Table 3: Main plot and subplot treatments combinations in a) Turrialba, Costa Rica..........................................................................................................................14 b) Masatepe, Nicaragua..........................................................................................................................14 Table 4: Initial state variables required by CAF2007 and their default value......................................16

Table 5: The 7 outputs, out of the 32 existing, chosen for the sensitivity analysis………………..…..17 Table 6: Observed coffee annual yields (tDM/ha/y) in Turrialba and Masatepe………………………....29 Table 7: Measured Specific Leaf Area and default data included in CAF2007……………..………..32 Table 8: Relative roots mean square errors calculated for each subplot, in both modeling situations: model with default setting of parameters (DEF) and model with measured initial state and management variables and Specific Leaf Area (MES). ………………………………..……………...33 Table 9: Average of RRMSE calculated for both situations, for different factors: the localization, level of inputs, crossing of localization/level of inputs, type of combination……………………………….33

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LIST OF APPENDICES

APPENDIX 1: Description of the structure of CAF2007, a dynamic model for coffee agroforestry systems

APPENDIX 2: Technical manual of CAF2007

APPENDIX 3: Parameters of CAF2007

APPENDIX 4: Processes identified in conceptual evaluation of CAF2007, subsystems involved,

ideal set of data needed and involved parameters involved in each one

APPENDIX 5: Table of parameters involved for model initialization

APPENDIX 6: Coefficients of variation obtained for the model inputs and for each of the 7 chosen outputs APPENDIX 7 : Observed and simulated coffee annual yields in both modelling situations

APPENDIX 8: Simulated vs. Observed coffee annual yields

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I- Introduction 1- Context and aim of this study

Coffee (Coffea arabica, L.) is a plant native from Ethiopia where it grows under highlands forests. In Central America (fig.1), it is commonly grown at altitude between 600 and 2500 m, often in association with shade trees. Its cultivation, mainly destined to exportation, contributes to income of about 265 000 producers (Muschler and Beer, 1999). The tendency of the thirty last years has been the modernization of the culture with intensified cultural practices such as fertilization, use of herbicides and pesticides and growing of more productive varieties and, in Costa Rica, reduced shading. However, the 1999’s world overproduction had led to the collapse of coffee prices. Intensification of coffee production systems was no longer attractive, and the interest of producers’ for shade-grown coffee increased again (Da Matta, 2004; Albertin and Nair, 2004).

Figure 1: Map of the coffee producing countries in Central America. In green are presented countries producing coffea arabica and in yellow, countries producing coffea arabica and robusta.

Few modeling tools are available to synthesize existing knowledge and to help predicting

the effects of shade trees on coffee productivity and profitability. During the CASCA project (set up in 2001 and carried out by CIRAD, CATIE, CEH, PROMECAFE and UNA), a dynamic process-based numeric model of coffee AFS in Central America, CAF2007, was developed by Marcel Van Oijen from the Center of Ecology and Hydrology in Edinburgh. The objective of this project was to reduce vulnerability of producers face to coffee prices fluctuations. Thus, the model is expected to be used to design, in collaboration with farmers, competitive, sustainable and diversified management strategies for AFS. However, this model has not been validated and thus its potential use is still limited.

2- Interest and stake of coffee AFS in Central America In Central America, coffee is grown under full sun or under shade depending on the type

of farm (commercial vs. smallholder farms, conventional vs. organic farms…). In Costa Rica, 40% of all cultivations represent coffee monoculture and 60% represent coffee agoforestry systems with legume or timber trees (Hergoualc’h, 2008). In monoculture, coffee is generally managed intensively and production levels are higher (Da Matta, 2004). Many traditional coffee agroforestry systems include legume ‘service’ trees and/or valuable fast-growing timber trees as part of the shade canopy (Somarriba et al., 2001). Although production levels are lower in agroforestry systems, sustainability of the plantations is very often enhanced (Malézieux et al., 2009; van Noordwijk et al. 2003). Moreover, those types of systems provide more stable income.

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However, the use of shade tree still generates debates in the coffee community (Da Matta, 2004), since almost the inception of coffee cultivation in Central America.

Several benefits of the introduction of shade trees in coffee plantation have been reported.

The use of shade trees permits to attenuate extreme temperatures in both air and soil (Rebodello, 2008; Albertin and Nair, 2004; Malézieux et al., 2009), improves soil fertility through the incorporation of organic matter from leaf litter and pruning and through N-fixation capacity of some legume species (Remal and Perrin, 2009; Rebolledo, 2008). It also regulates coffee light transmission and so increase longevity of coffee plantation by reducing “die-backs” (Albertin and Nair, 2004; Robolledo, 2008) and if well managed, might meliorate system water dynamics. Introduction of shade trees also improve control of weeds, and some disease and pests (Albertin and Nair, 2004) and also improves coffee quality (Muschler, 2001). Finally, coffee agroforestry systems can contribute to biodiversity conservation (Harvey and González Vilalobos, 2007), enhance farmers’ income through tree productions such as fruits, timber and services such as carbon sequestration (Nair et al. 2009) and reduction negative impacts of coffee production to environment, such as ground water contamination by fertilizers and agrochemicals (Beer et al. 1998).

Nevertheless, coffee agroforestry systems also present some disadvantages. The introduction of shade trees in coffee plantation has been shown to reduce coffee productivity above a certain shading threshold (Albertin and Nair, 2004). For example, while a high competition for resources (soil nutrients, water and light) occurs between coffee and shade tree species, coffee yield is reduced. Shade trees can also increase the incidence of some pests and diseases through increased humidity rate (Beer et al. 1998).

The final balance between benefits (positive impacts on environments) and disadvantages

(productivity loss) of the introduction of shade trees species in coffee plantation is site-specific as depending on climate, soils, management practices, and shade tree species. The intensification of agrosystems have shown such limits in terms of environmental, economic and social sustainability that there is an increasing interest in valorizing eco-services that can be provided by agrosystems for the society. In this context, there is a need for better understanding of agroforestry systems’ functioning to help producers adapting their systems to benefit from other opportunities. The final balance needs to be quantified for establishing the best management practices as well as for designing new coffee production systems.

3- Interests of modeling for evaluation of systems performance

Research works have permitted to identify environmental factors, management strategies and plants characteristics that affect coffee growth and yields such as the amount of radiation, the shade tree density etc. However estimations of these factors are site-specific and more often qualitative than quantitative and few studies have compared systems’ performance through different climate and soil conditions (Van Oijen et al., submitted). Moreover, the coffee AFS systems present an important heterogeneity in Central America (Somarriba et al., 2001). Thus, it remains difficult to extrapolate obtained results from one site to other sites.

A way to integrate coffee AFS knowledge in order to quantify the systems’ performances in different conditions is to build crop models.

Crop models are mathematical models which represent the growth and development of a crop interacting with its environment and management. In mechanistic models, dynamical biophysical processes are described through a set of equations. Those types of models are more and more developed by researchers in order to simulate the dynamical evolution of agroforestry systems where more processes are involved as results of species interactions within the

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association which can include shade trees in interaction with annual or perennial crops (Malézieux et al., 2008).

Crops models are often used as diagnostic tool as they can lead to a better understanding

of systems’ biophysical evolution and to identification of points that need to be clarified by experimentation (Boote et al. 1996). As a predictive tool, crops models permit to test effects of different factors on productivity and environmental impacts of the systems. For example, in the case of coffee agroforestry systems where management of shade trees species need to be improved to increase their sustainability (Beer et al. 1998; Somarriba et al., 2001 ; Klein et al. 2003 ; Klein et al. 2002; ), analyzing quantified responses of a model to different management options can be a good way to enhance benefits and minimize negative effects of the systems. Moreover, taken into account more global issues, such as climate change, model use can be a useful tool to predict how it can impact on crops systems (Rapidel, 2008). Finally, the use of crops modeling tools also permits to reduce costs of experimentations’ setting up in terms of time and money.

In order to quantify services that can be provided by coffee agroforestry systems, and

taken into account potential uses of crops systems mechanistic models, which are becoming simpler to parameterize and provide more robust prediction (Van Oijen et al., submitted), such a tool can be very useful. The CASCA project had provided scientific bases for a better management of coffee agroforestry systems, a promotion of coffee quality and an improvement of producers’ incomes from this crop. During this project, the first numeric model has been developed to simulate coffee agroforestry systems’ productivity and environmental impacts by Marcel Van Oijen, the model CAF2007.

4- CAF2007, a process-based model of coffee agroforestry systems in

Central America

CAF2007 is a process-based model developed to simulate the biophysical evolution of coffee agroforestry systems in Central America, in response to their given environment and management. Although his model has been developed with a huge bibliographic work, it has not been validated for the moment (Van Oijen et al. submitted).

For its elaboration, simple algorithms existing in crop or forestry models have been used.

CAF2007 has been kept simple but can be further made more complex thanks to experimental investigation (Van Oijen et al. submitted).

CAF2007 focused on the main factors affecting coffee productivity taking into account

effects of presence of shade trees. Processes described in the model and variables calculated are presented in the conceptual scheme of the model (fig.2). The detailed description of the structure of the model and a technical manual for its use are available in appendix 1 and 2. The list of parameters included in CAF2007 is available in appendix 2.

In CAF2007, weeds, diseases and pests development are not taken into account because

their effects are regarded as less important, than other environmental non biotic factors, excepted for some diseases. Air pollution and soil toxicity which are difficult to simulate are also not taken into account.

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Figure 2: Conceptual scheme of CAF2007 (Marcel Van Oijen, 2008). The model is composed of two parts: one where coffee is grown under full sun (sunlit part) and one where it is grown under shade trees (shaded part). The two parts are interacting at a daily step. Three compartments are considered: the shade trees in the shaded part, the coffee in shade or sun and the soil under trees or under coffee in sun. The processes described are listed in the left boxes. The daily step state variables calculated for each compartment are listed in the right boxes. The upper boxes represent the climate and the shade tree, coffee and soil management. Both have an influence on both parts of the model.

5- Objectives of the study

In 2007, the Mesoamerican Scientific Partnership Platform for Agroforestry Systems with Perennials Crops has been built up between CIRAD, CATIE, INCAE, Bioversity, CABI and Promecafé. The general objective of this scientific partnership platform is to contribute to maintaining and increasing the competitiveness and sustainability of the agricultural sector of Mesoamerica through the quantification, valuing and development of the potential products and environmental services of agroforestry systems with several perennial crops, including coffee. Within this perspective, CAF2007 will be used to evaluate effects of climatic change on systems productivity and also as a helping tool to develop innovations in coffee agroforestry systems.

The objectives of the present study are (i) to do a conceptual evaluation of the CAF2007

model by identifying the main biophysical processes which need to be well simulated, and (ii) to evaluate its capacity to simulate coffee agroforestry systems’ productivity by confronting simulations using data from two long-term experiments in Central America. The first part of this study, the conceptual evaluation, is based on literature review. The second part, the numerical evaluation of the model, first includes the elaboration of the database before presenting the model evaluation.

Management Climate

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II- Material and methods

1- Conceptual evaluation of CAF2007 We first performed a conceptual evaluation of CAF2007, which means that it has been

tested for its capacity to well describe the main biophysical processes involved in coffee agroforestry systems. This step was important to test if the model can be used to simulate effects of coffee agroforestry systems’ management on their productivity but also on social and environmental services. By doing that, we could highlight some critical points and particularities of the model that could be further improved, focusing on coffee productivity.

CAF2007 was confronted to the existing experts’ knowledge on these systems. In a

previous study, Rebolledo (2008) have collected knowledge from researchers, farmers, technicians, and processors in tree Costa Rican coffee productive zones. During interviews, reproductive coffee phenological stages were identified as well as environmental factors affecting coffee yield elaboration and quality at each of those stages. This knowledge was then processed to produce conceptual models, which synthesize the information from these different sources and permit to compare them. Diagrams were obtained thanks to the AKT software and were compared to CAF2007. Based on this work and on a complementary literature review, we could identify the main biophysical processes that characterize the behavior of coffee agroforestry systems in Central America. We choose to focus on processes involving interactions between coffee and tree for light, water and nitrogen, and on the effects of those interactions on coffee productivity. We then have checked how these processes have been implemented or not in CAF2007 and if yes, in which way and in which subsystem.

Although no comparable model exist for coffee agroforestry systems, process-based

models do exist, which simulate other agroforestry systems involving annual crops. The challenges that agroforestry systems pose to modelers are of similar nature across different agrosystems involving crops association. They particularly concern implementation of plants growth and development taking into account interactions between the associated species for the above and belowground resources (Malézieux et al. 2009). Therefore, we continued the conceptual evaluation by comparing the biophysical processes’ implementation and focus of three other existing agroforestry models:

- APES model, which simulates temperate annual crops systems but also vineyard in

association with grass. This model was developed within the European project SEAMLESS for integrating analysis of impacts on systems’ sustainability and multi-functionality (Donatelli et al., submitted, Aurélie Metay et Eric Casellas, personal communication).

- Hi-sAFe model, which simulates temperate systems involving annual crops and trees. This model has been developed within the European project SAFE to predict evolution of intercrops’ productivity and trees’ growth and estimate the environmental budget of the systems in terms of carbon, nitrogen and water (Dupraz et al., 2004; Lecomte I. 2006, Grégoire Talbot, personnal communication).

- WaNuLCAS model, which simulates a lot of different types of systems involving perennials or annuals crops and trees. This model has been performed to evaluate systems’ sustainability and profitability, focusing on belowground interactions (Van Noordwijk and Lusiana, 1999).

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Among the biophysical processes, we chose to focus the comparison on the models’ implementation of:

- Plants’ phenological development, taking into account interactions between species. - Plants’ growth and calculation light interception, carbon assimilation and allocation to

harvested organs, including plants’ reserves dynamics, particularly for perennials crops as they are more likely to develop a strategy of reserves accumulation during their cycle.

- Inter-specific competition for below-ground resources, in particular water and nitrogen, with a regard on relative environmental impacts, in particular N-leaching, run-off and soil erosion.

2- Numerical evaluation of CAF2007

A literature review done by Marcel Van Oijen (Van Oijen, submitted) gives an overview of available quantitative data on coffee agroforestry systems for diverse combinations and localizations in Central America. A first model parameters’ calibration has been done from this review although information on climate, shade trees and coffee plants were limited.

In our study, we chose to work with data sets from two long-term trials established in 2000 by CATIE in two different agroecological zones, in Costa Rica and Nicaragua, in order to compare coffee agroecosystem performance under full sun, legume and non-legume shade types, and intensive and moderate, conventional and organic inputs.

A- Experimental design

The first trial is situated in a low (685 meters above sea level) humid tropical zone (3200 mm annual rainfall), in CATIE in Turrialba in Costa Rica and the other one in a low (455 meters above sea level) but more arid zone in Masatepe in Nicaragua (1470 mm annual rainfall) with a marked 6-month dry season (less than 50 mm per month). In both trials, main treatment plots are different shade tree combinations with subplots for input levels for nutrient and pest management. However shade trees species, which are the most common species used in association with coffee, differ between both sites (tab 1). Each trial has a full-sun treatment and different combinations of shade tree species to represent a gradient of nitrogen fixation and contrasting combinations of evergreen/deciduous and canopy type. Four inputs treatments have been implemented: two levels of organic management and two level of conventional management (tab.2).

Table 1: Tree species used in shade combinations in: a) Turrialba, Costa Rica

Species phenology canopy shape N-fixing use Terminalia amazonia (TA) evergreen high compact No timber Chloroleucon eurycyclum (CE) evergreen high spreading Yes timber Erythrina poepiggiana (EP) evergreen low compact Yes service b) Masatepe, Nicaragua

Species Phenology canopy shape N-fixing use Simarouba glauca (SG) Evergreen high narrow No timber Tabebuia rosea (TR) Deciduous high narrow No timber Samanea saman (SS) Evergreen high spreading Yes timber Inga laurina (IL) Evergreen low spreading Yes service

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Table 2: Input levels for nutrient and pest management in coffee systems experiments Input type Organic Organic Chemical Chemical Name of

treatment Moderate Organic Intensive Organic Moderate

Conventional Intensive

Conventional

Type of soil amendments

Coffee wastes

Coffee wastes, chicken manure,

ground rock minerals

Chemical fertilizer at half rate

Chemical fertilizer at recommended rates for full sun coffee

Disease management

None Use of botanical and

mineral foliar applications

Use of infrequent commercial fungicide

applications

Regular use of commercial fungicides

Insect pest management

Gleaning of berries after harvest

Manual practices and use of botanical and

biological applications

Manual practices and infrequent use of

commercial insecticides

Regular use of commercial insecticides

Weed management

2-4 routine machete weedings per year

Manual selective weed management between row and

clean within row area

Selective weed management between row and clean within row area with manual

and herbicide

Maintain bare soil with herbicides

Organic and conventional fertilizer rates changed over time depending on the whether

during coffee growth phase (first 2 years) or productive phase, and subsequently adjusted based on the results of soils analysis and changes in soil fertility. Those rates were around 150 kgN/ha/y for the moderate conventional inputs level, around 300 kgN/ha/y for the intensive conventional one, around 9 t/ha of coffee pulp for modertae organic one adding 7 t/ha of chicken manure for intensive organic one (J. Haggar and E. de Melo, personnal communication). Figure 3 represents the annual technical itinerary developed in both trails.

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

Coffee floweringCoffee harvesting

Coffee Pruning

Shade tree pruning/thinning EP and TA IL EP

Fertilization

Weeds and pests control

Figure 3: Technical itinerary in coffee agroforestry trials in Turrialba (red) and in Masatepe (green). Coffee flowering period is also indicated.

Main plots and subplots treatments combinations are presented in Table 3. Three replicas

were established at each site forming a randomized block design with shade as main treatments and inputs as subtreatments within shade. Subplot size varied between 500-600 m2, with measurement plots of 225-300m2 (minimum of 24 shade trees and 100 coffee plants). The full experiment covers 6 ha in Costa Rica and 3 ha in Nicaragua.

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Table 3: Main plot and subplot treatments combinations in

a) Costa Rica Main plot Full sun

FS Erythrina

EP Terminalia

TA Chloroleucon

CE Terminalia Chloroleucon

CETA

Terminalia Erythrina

EPTA

Chloroleucon Erythrina

CEEP Subplot IC, MC IC, MC,

IO, MO IC, MC, IO, MO

MC, IO MC, IO MC, IO IC, MC, IO, MO

b) Nicaragua Main plot treatments

Full sun FS

Simarouba, Tabebuia

SGTR

Tabebuia, Samanea

SSTR

Simarouba, Inga

ILSG

Inga Samanea

SSIL Subplot treatments

IC, MC IC, MC, IO, MO MC, IO MC, IO IC, MC, IO, MO

Coffee was planted at 4000 plants per hectare in Nicaragua and 8000 plants per hectare in

Costa Rica, the latter was achieved by planting two plants per planting hole – a common practice in Costa Rica. Coffee bushes were selectively prunned after each harvest in order to decrease the amount of old branches and stimulate the production of new productive tissues. Shade trees were planted at 667 trees per ha in Nicaragua and 417 trees per ha in Costa Rica, 4 times their expected final density, and have been reduced by 50% by two thinnings. In Nicaragua the legume timber tree originally selected and planted was Enterolobium cyclocarpum, however, after two years tree growth was very low and variable, thus it was considered necessary to replace it with Samanea saman, which was planted in 2002.

In Costa Rica Erythrina shade trees are generally pruned two times each year leaving only the main trunk to a heigth of about 1.5 – 2.0 meters. However, based on recent studies in Costa Rica (Muschler, 2001) of the effect of shade levels on coffee quality, Erythrina management was varied by treatment. In the IC treatment, Erythrina is pruned completely twice a year, one time after coffee flowering and one after harvesting. However, in all the other treatments with Erythrina, a minimum of three branches were left for partial shade cover after each of the two annual prunings. Temporary shade was not initially included in the establishment strategy in Costa Rica. However, temporary shade of Ricinus was incorporated after coffee planting to suppress weed growth and to improve coffee plant survival during transplanting.

In Nicaragua the initial establishment plan included the use of temporary shade for all treatments with permanent shade. Ricinus comunis was the non-N fixing species, while Cajanus cajan was the N-fixing species. Temporary shade was planted between every coffee plant and then thinned to provide biomass for soil improvement and to achieve shade to suppress weeds and diminish light intensity for young recently planted coffee plants. Timber species are pruned to achieve a marketable main trunk, removing lower branches, while Inga is pruned once per year for more uniform shade distribution.

Both sites, localized in different climatic zones, present also different coffee, shade trees and soil management. These contrasts represent an interest in the present study which final objective is to test the performance of the model to be used as a diagnotic and predictive tool for coffee agoforestry systems in different environmental and management conditions.

B - Choice of the plots

As the model CAF2007 takes only N-mineral fertilization into account, we first chose to work with data from subplots managed with conventional fertilizers: Intensive Conventional and Medio Conventional. Moreover, the model can include only one shade tree species in association with coffee, so that we have eliminated combinations involving more than one species in Turrialba. In Masatepe, all the combinations involve two shade tree species. However we chose to work with data from subplots including Samanea saman, as it was planted in 2002 and until

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the year 2006, as trees were too well developed after to consider only one species. We also ignored the presence of temporary shade at trials establishments as we couldn’t implement it in the model. This could lead to problems while evaluating the model; simulated yields might be lower because it will not take into account the fact that this presence improves the establishment of the coffee plant and soil fertility.

In Turrialba we have collected data from subplots with both levels of conventional managements (IC and AC) for full-sun plots and combinations with the N-fixing species Erythrina poepiggiana also present in CAF2007 and with the timber tree species Terminalia amazonia, as this species is of the same gender than Terminalia ivorensis, already present in the model. In Nicaragua, we also collected data from subplots with conventional management levels for the full-sun plots and for the combination with the N-fixing tree species Inga laurina in association with Samanea saman which has been ignored. This species was compared to Inga densiflora, the only species of same gender included in the model.

We finally worked on 5 treatments for two level of inputs; 6 subplots in Turrialba and 4 in Masatepe. This leads to the possibility to test the model in 10 different situations in terms of climate but also coffee, tree and soil management.

C - Data collect Climatic data The first step to compare model outputs with observed data from the chosen subplots was

to collect climatic data since trials establishment in 2000. CAF2007 requires six daily weather data (appendix1); daily maximum and minimum temperature (°C), wind speed (m/s), photosynthetic active rate (MJ/m-²), vapor pressure (kPa) and rain (mm).

Model initialization We then selected the data needed to initialize the model with a maximum of subplot-

specific initial state variables. As presented in table 4, the model requires 4 state variable for shade tree, 4 for coffee and 7 for soil.

Management The model also requires 3 parameters for coffee management; the first day of pruning, the

interval between two pruning and the fraction of pruned biomass, 6 parameters for shade tree management; the first day of pruning, the interval between two pruning, the fraction of pruned biomass, the two dates of thinning, the fraction of thinned biomass, and the initial tree density, and 4 parameters for soil fertility management; the three dates of fertilizer application, and the application rates.

Coffee yields We also needed to have annual coffee yields in both sites in order to compare them with

simulations. The model calculates annual yields in tons of coffee beans cry matter per hectare while they are measured in Costa Rica in the local volume unit cajuelas of green coffee at a humidity rate of 12% per subplot per year and in Nicaragua in kilograms of coffee berries at a humidity rate of 12% per subplot per year. Thus, data needed to be converted in order to allow a comparison.

Other data Finally, we searched for more data in all the other studies made by researchers and

students on the subplots in order to have a maximum of data to compare with the model outputs, such as the carbon biomass after a pruning, the tree height, the shade area, the quantity of carbon into the soil.

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Table 4: Initial state variables required by CAF2007 and their default value

Parameter Identifier Unit Default data

Initial C biomass in branches CB0T kg C m-2 0,10

Initial C biomass in leaves CL0T kg C m-2 0,05

Initial C biomass in roots CR0T kg C m-2 0,20 Tree

Initial C biomass in stems CS0T kg C m-2 0,10

Initial biomass leaves CL0 kg C m-2 0,05

Initial biomass storage organs CP0 kg C m-2 0,00

Initial biomass roots CR0 kg C m-2 0,05 Coffee

Initial biomass stems plus branches CW0 kg C m-2 0,05

Initial amount of litter CLITT0 kg C m-2 0.33

Initial concentration of C in organic matter CSOM0 kg C m-2 11,00

Initial fraction of the soil organic matter which is unstable

FCSOMF0 - 0,64

Initial C/N ratio in litter CNLITT0 kg C kg-1 N 17,00

Initial C/N ratio in unstable organic matter CNSOMF0 kg C kg-1 N 12,00

Initial values NMIN NMIN0 kg N m-2 0,001

Soil

Initial C/N ratio in stable organic matter CNSOMS0 kg C kg-1 N 11,00

Measurement of Specific Leaf Area A parameter has been directly measured in the trials during the study, the Specific Leaf

Area of each shade tree species and the maximum and minimum Specific Leaf Area of coffee. In the model, growth organs rates are calculated in term of carbon biomass. This parameter permits to calculate daily coffee and shade tree leaf area index from the leaf biomass. Those latter variables contribute to determine the carbon coffee production and also the effect of tree shading on coffee. So it was interesting to obtain the values of theses parameters for each treatment where we choose to calibrate and test the model.

To measure specific leaf area of shade tree species, for each treatment, we collected five leaves per branch and one branch per tree for 5 shade trees. To measure maximum and minimum specific leaf area of coffee, young, mature and old leaves were collected separately. For each treatment and each leaves category we selected ten plants and took five leaves per plant. This measurement has been done for both sites.

Leaf areas were measured and leaves were dried at 60°C during two days and then weighted. The specific leaf area of each tree species present in the chosen treatment and both maximum and minimum specific leaf area of coffee were determined.

Literature review As we have already noticed before, a previous literature review has been done by Marcel

Van Oijen during the model construction. For some parameters, data were found available in some studies. Although those data are sometimes very contrasting, they constitute a good reference for the model elaboration (Marcel Van Oijen, personal communication).

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D - Sensitivity analysis of CAF2007

Local sensitivity analysis was performed in order to have an idea of the sensitivity of the

model outputs to the variation of parameters values. Sensitivity analysis permits to investigate how the variation in the outputs of a model can be attributed to variation in the inputs. Thus, this method can be used to do a diagnostic of a model to understand how the model’s outputs respond to changes in the inputs which are the initial state variables and parameters. By doing this analysis, we could determine factors that mostly contribute to the outputs’ variability (Satelli et al., 2000; Monod et al., 2006).

We varied the value parameter by parameter and checked the obtained seven chosen outputs of the model listed in Table 5. These outputs were chosen according to the objective of the model to be used to assess agroforestry systems productivity and environmental impacts for different management and climatic conditions. We defined a minimum and a maximum value for each parameter according to literature review done by Marcel van Oijen and discussion with experts. Table 5: The 7 outputs, out of the 32 existing, chosen for the sensitivity analysis

Output Unit Average coffee productivity ton DM ha-1

Average wood productivity m3 ha-1 y-1 Average N-emission kg N ha-1 y-1 Average N-leaching

kg N ha-1 y-1

Average C-sequestration on-site t C ha-1 y-1

Average C-soil run-off t C ha-1 y-1 Average water drainage mm d-1

We then wrote scripts (see appendix 2) to generate outputs for each value with a fixed

interval for each parameter. The 7 outputs values obtained for each value of each parameter were saved and coefficients of variation have been calculated for each one and each parameter. The coefficient of variation is unitless and thus can be compared relatively. Results were interpreted to have an idea of the most sensitive outputs and the most influent factors in the model.

E- Evaluation of CAF2007

Evaluation was performed for both moderate and intensive conventional inputs levels in order to test the capacity of the model to simulate effects of nitrogen limiting-factor on systems’ productivity. Model’s outputs were generated with default data inputs and with collected data to test the model’s need for site-specific inputs data for being more performing.

To compare CAF2007 with data, we edited graphs of model annual coffee yield predictions versus observed value, of differences between measured and calculated values against measured values because they are easier to evaluate and compare. To measure agreement between measured and calculated values, we also calculated the relative root mean square error, or 'general standard deviation’, whose advantage is to be unitless and thus easier to compare (Mayer and Butler, 1993). All those methods are very often used for crops models’ evaluation (Mérot et al., 2008; Wallach, 2006).

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The relative root mean square error (RRMSE) is given by:

RRMSE = √ ((∑ (Yi-yi) ²)/N)/Ῡ Where:

- Yi is the observed annual coffee yields for the year i - yi the simulated annual coffee yields for the year i - N is the number of year of simulation - Ῡ is the average of Yi values

More the value of RRMSE is high; more model simulations are different from

observations, which mean that model doesn’t predict well the annual coffee yield of the system. On the contrary, more this value is low, more model simulations are closed to observations and the model is considered more reliable. This value has been used to compare the performance of the model to simulate the coffee productivity among the different subplots.

III- Results and discussion

1- Conceptual evaluation of CAF2007 As a result of the conceptual evaluation, four biophysical processes were identified

important to be correctly simulated by the model; (i) the effect of shading on reproductive dynamics, (ii) the coffee carbon production and organs allocation, (iii) nitrogen dynamics and (iv) water dynamics. These processes were chosen because they involve interactions between species for light, water and nitrogen and contribute to explain the observed variations in coffee yields and thus need to be well implemented in CAF2007.

a- Effect of tree shading on coffee reproductive dynamics The first critical we pointed deals with coffee phenology and particularly its reproductive

stages because it has been shown that effects of environmental factors on the reproductive stages contribute to determine the final coffee yields (Rebolledo, 2008). Moreover, the reproductive cycle of coffee plant takes place 8 to 10 months per year (Frank, 2005). In her study, M. Rebolledo listed 5 coffee phenological stages (fig.4) and reported the effects of environmental factors on each of those stages by processing conceptual models.

It has been observed that sufficient period and intensity of radiation, temperature or water stress followed by a sufficient amount of rain contribute to determine coffee flowering activation and intensity (Rebolledo, 2008; Franck, 2005; Drinnan and Menzel, 1994). This process is very specific to coffee. Intensity of flowering (amount of fertile flowers), and so potential productivity of coffee plants, is also governed by the amount of vegetative nodes produced the preceding year. During fruits growth, vegetative growth can also takes place leading to higher competition for carbon between fruits and leaves. This phenomenon is at the origin of the “tired” status of the coffee plant. Radiation, temperatures, wind and amounts of rain can also have effects on fruits growth and maturation. (Rebolledo, 2008; Kanten and Vaast, 2006; Drinnan and Menzel, 1995).

Tree shading has an influence on environmental factors controlling coffee reproductive dynamics by modifying microclimate. A study made in different coffee agroforestry systems in Perez Zeledon, Costa Rica reported different impacts of shade trees on coffee vegetative and reproductive growth according to the species (Terminalia ivoriensis, Eucalyptus degupta and Erythrina poepigiana) (Angrand et al., 2004). The vegetative growth was enhanced in all

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agroforestry systems compared with full sun system and the higher increase was obtained under Terminalia ivoriensis. However, flowers number per productive node was higher in full sun compared to the three agroforestry systems because of their buffering effect on coffee water and temperature stress which determine flowering intensity. However, the number of fruit number per productive node was higher in agroforesty systems than in full sun because of the higher fruit falling rate in full sun system.

Figure 4: The five coffee phenological stages (Rebolledo, 2008) Another study, made in 1997 by Estivariz Coca in the region of Turrialba, Costa Rica

compared coffee flowering and production under homogeneous and heterogeneous shade of Erythrina poeppigiana and at different distances from shade trees. In this study, the light was the only production-limiting factor. The homogeneous shade was provided by tall trees which selectively pruned allowed 40 to 60% of the photosynthetically active radiation (PAR). The heterogeneous shade was provided by trees drastically pruned to allow more than 80% of the PAR. There were no significant differences among the number of flowers and fruits between both shades. In fact, the flowering peaks were more related to precipitation and temperature patterns of the studied site. However, the conversion rate from flower to fruit was lower under homogeneous shade. Homogeneous shade also slew down the vegetative growth and so the potential coffee production compared to heterogeneous shade. Moreover, the morphological variables of shade trees (crown diameter, height and productive basal area) were correlated to coffee production. Distance to the nearest tree did not show a significant effect on flowering and on potential production. These results indicate that the effects of shade trees on coffee reproductive dynamics can vary according to the shade trees species and the intensity of shading.

In CAF2007, the different 5 phenological stages listed in the conceptual model

(Rebolledo, 2008) have not been implemented. Although the coffee phenology module is more empirical, it stays specific to coffee production systems. Two key phenological events are taken into account:

- the flowering starting day which is simulated as the first day of the year with a fixed minimum amount of rain. This implementation seems to be concordant with

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observations in coffee plantations in Central America (Rebolledo, 2008; Franck et al., 2006; Estivariz Coca, 1997)

- the day of fruits maturation which is also the harvesting day. It is determined by a fixed sum of temperature (Franck et al., 2006), without taken into account effects of amounts of radiation and rains, and forced to happen before the end of the year if the fixed temperature sum is not reached. This is also relevant with observations because farmers try also to avoid this overlap by pruning trees to accelerate fruits maturation (Rebolledo, 2008).

This implementation differs from the three numeric models where annuals and perennials crops’ phenological stages involved in both vegetative and reproductive growth are determined by temperature sum and are taken into account for calculation of crops growth rates (appendix 1).

The intensity of coffee flowering, which represents the potential production, is taken into account in the model while calculating the fruit sink strength directly at the flowering starting day. This sink strength is then used to calculate fraction of carbon allocated to coffee beans. The fruit sink strength increases with the average of photosynthetically active radiation of the previous thirty days. This is in concordance with the conceptual model where flowering intensity is increased by an irradiative stress. However, water and temperature stress also previously reported are not taken into account in the model to calculate this strength.

This implementation is original compared to the other numeric models. In the model Hi-

safe for example, grains yield is calculated with a harvesting rate that increases linearly with the temperature sum during the grains filling stage. In the model APES, the biomass is distributed in the storage organs according to allocations tables at each phenological stage. In CAF2007, calculation of flowering intensity is function of radiation experienced by coffee around flowering. Nevertheless, by calculating the sink strength directly, all the other environmental factors, such as wind and temperature, influencing amounts of fertile flowers and fruits reported in the conceptual model are ignored. Moreover, the fact that only one day of flowering and harvesting is simulated seems not realistic as it doesn’t consider the coffee flowering waves. In fact, crazy flowering happens when flowers open on different times and leads to delayed time of fruits maturation.

b- Coffee carbon production and allocation

An interest was also given to the implementation of coffee carbon production and

particularly its allocation in the model. Photosynthesis depends on factors such as radiation, temperature, CO2 atmospheric

concentration, water and nutrients availability, fruits load, leaf age, and plant genotype. Moreover, it has been shown that stomata limitations reduce photosynthetic activity. Carbon assimilation can be affected by microclimate, when the effect of fruits as a sink is eliminated. As a result from the modification of carbon assimilation, a seasonal pattern has been proposed: roots development during the dry season and aerial development during the rainy season (Rebolledo, 2008).

In the conceptual model (fig. 5), high amount of radiation increases the flowering intensity so that the fruits demand for carbon can become higher than the leaves demand. Thus, it is sometimes difficult for coffee plants to response to the high demand level for carbon and allocation very often favors to fruits, causing “die-back” of coffee plants. The bi-annual effect observed on coffee yields can be explained by this carbon competition. A good production one year is often fallowed by a poor one because an important fraction of the carbon has been allocated to the fruits and thus the vegetative organs are not enough strong to permit high production levels the following year. This effect is limited in agroforestry systems because of the

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lower fruit sink strength compared to source strengths. Thus, shade can improve longevity and stability of coffee plantations.

Furthermore, in 2006, Frank et al. have shown that there is a source–sink down-regulation of carbon assimilation rate. In fact, when fruit demand is high, carbon assimilation rate is increased. This is explained because assimilated sugars are exported from leaves to fruits. When this demand is low, sugars are accumulated in leaves reducing carbon assimilation rate by feed-back. Thus, this mechanism can limit coffee photosynthesis, especially when plants are grown in agroforestry systems and carry low fruit loads. Coffee carbon assimilation rate decreasing with light intensity have also been explained in other studies as an adaptative strategy of coffee as a shade plant (Da Matta, 2005; Van Oijen, 2004). Coffee plants can also constitute reserves of carbon as starch which can be mobilized when fruits demand is higher than photosynthetic capacity (Rebolledo, 2008).

According to these studies, it seems important to check if the bi-annual dynamics, reserves dynamics and effects of fruit sink strength on carbon assimilation rate are taken into account in CAF2007 in yields calculation.

In CAF2007, light interception is modeled by Beer’s law with a constant light extinction

coefficient as fallowing:

PAR intercepted= PAR* (1-exp (-KEXT*LAI)) Where:

- PAR is the photosynthetically active radiation - KEXT is a fixed coffee light extinction coefficient - LAI is the coffee leaf area index

Assimilate production of carbon is then calculated by multiplying the PAR intercepted by

coffee with the light-use efficiency (LUE). LUE is computed from atmospheric CO2 concentration, temperature, light intensity, upper leaves RUBISCO content, and coffee light extinction coefficient and photoperiod duration. LUE decreases with light intensity which is consistent with high rates of photosynthesis observed at low light intensity. Carbon assimilation rate is also modulated by a water stress factor and decreases in case of drought. It is hampered if insufficient nitrogen is available to maintain fixed N/C ratios. Temperature and radiation, which affect carbon assimilation rate, are reduced with the presence of shade trees. Water and nutrients availability are also modified through the coffee/tree competition for both resources.

Fractions of carbon allocated to coffee leaves, woody parts, roots and fruits are calculated from the sink strength of each organ (fig. 6). Woody parts, leaves and roots sink strengths are fixed as parameters in the model. However, roots sink strength is modulated by a water stress factor (TranF) and increases in case of drought. Leaves sink strength is enhanced during first weeks of reproductive growth. To reproduce the effect of competition for carbon between fruits and leaves, fruit sink strength is calculated taking into account coffee Leaf Area Index.

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Figure 5: Carbon conversion and allocation diagram, academic source (Rebolledo, 2008)

Figure 6: Scheme of calculation of coffee leaves, woody parts, roots and fruits sink strengths (respectively SINKL, SINKW, SINKR, SINKP) and their respective fractions of carbon allocation (FCL, FCW, FCR, FCP) in CAF2007. White boxes are fixed parameters given as inputs, blue boxes are inputs coming from other subsystems, and yellow boxes are calculations.

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These implementations reflect the seasonal pattern mentioned above. Moreover, productive bi-annual pattern resulting from carbon competition between leaves and fruits is also implemented in CAF2007 by activating four parameters. Three of them are involved in the calculation of both leaves and fruits sink strengths and one in the calculation of leaves senescence rate in function of fruit growth rate. However, reserves dynamic are not taken into account in CAF2007, neither effect of fruit sink strength on carbon assimilation rate.

In all the other numeric models, light interception is also computed by Beer’s law with some differences in the architectural design. Potential carbon growth rate is also function of environmental factors (radiation and temperature) and limited by water and nitrogen availability. Nevertheless, in the other models, it also depends on the phenologoical stages. In CAF2007, carbon growth rate is calculated independently from phenological stages; assimilated carbon is allocated in each organ, adding fruits after flowering activation. In APES, contrary to other models, effects of diseases and non biotic factors such as wind and froze on growth rate can also be simulated. Carbon is allocated to the different organs at each phenological stage according to allocations tables, which differs from CAF2007 where fractions are calculated from organs sink strengths.

Although the model seems to well describe carbon production and allocation, taking into

account fruits/ leaves competition and effects of shade trees, the fact that some processes involved, such as reserves dynamics, are not implemented in CAF2007 can lead to problems to simulate the bi-annuality of coffee yields and trade-off and between productivity and longevity of coffee plantations. Moreover, shade trees can have large effects on all these processes by modifying coffee plants microclimate. Thus, it could be interesting to confront the processes of carbon biomass production and allocation under sun and different shade trees species against experimental data.

c- Coffee agroforestry systems water dynamics

The amount of water available for coffee plants development depends on: (i) rain amount and atmospheric humidity (the sources), (ii) the different uses of this water in plants’ transpiration, soil evaporation, drainage and runoff (the sinks).

In Central America, two seasons are defined: a dry and a rainy season. The dry season which causes a drop in soil water is necessary to induce coffee flowering that is then activated by rain (Carr, 2001). However, if this season is too long, it can result in lower coffee production (Coste, 1968). In contrast, a better soil water status resulting from higher amount of rain increases the coffee water status. However higher temperature, radiation and wind speed lead to higher coffee transpiration rate, decreasing coffee water status (Rebolledo, 2008). Atmospheric humidity also influences coffee growth. In fact, stomatal limitations are induced by higher leaf temperature and vapor pressure deficit during the dry season, resulting in decreased coffee transpiration and photosynthetic activity (Carr, 2001; Coste, 1968). Moreover water dynamics impact on coffee beans yields and quality; bean size as well as fruit growth can be increased by improved soil water status and the need for irrigation varies depending on the rainfall distribution, the severity of the dry season, and soil type and depth (Carr 2001).

Many effects of shade trees on coffee agroforestry systems water dynamics have been reported. The presence of shade trees buffers microclimatic conditions and is assumed to reduce coffee water stress (Rebolledo, 2008) although in cases of more arid climatic conditions, it can increase this stress through water competition between coffee and tree (van Kanten and Vaast, 2006; Coste 1968). In a study made in 4-year-old coffee agroforestry systems in sub-optimal ecological conditions of Costa Rica, the presence of three shade trees species (Eucalyptus deglupa, Terminalia ivorensis and Erythrina poepiggiana) improved water status of the coffee

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plant although it also increases the total water consumption of the system (van Kanten and Vaast, 2006). Measured transpiration rates of coffee and shade trees appeared to follow the seasonal pattern and to depend on vapor pressure more than on photosynthetic photon flux density and potential evapo-transpiration. In fact, during the dry period, higher vapor pressure deficit limited coffee transpiration. Water flows are also modified by the introduction of shade trees in coffee plantations. Agroforestry systems displayed smaller total annual throughfall and larger annual stemflow compared to monoculture (Siles et al. submitted). Authors also show that with shade tree inclusion, the total rainfall interception was larger than in monoculture as a result of larger canopy storage capacity and surface of evaporation in agroforestry than in monoculture.

According to those studies, the first important point to underline is that coffee plants are not only sensitive to soil humidity but also very sensitive to atmospheric humidity (van Kanten and Vaast, 2006; Carr, 2001). Thus, we can wonder if both type of water stress experienced by coffee leaves and roots are implemented in CAF2007. Moreover, the presence of shade trees modifies systems’ total evapo-transpiration but also soil water infiltration, drainage and run-off, so that it can be interesting to see in which conditions a better soil and coffee water status can be improved or not by the presence of shade trees in the model.

In CAF2007, two processes are simulated to characterize soil water status; soil

evaporation, plants transpiration, drainage and run-off. Water sharing depends on coffee and tree demand (potential transpiration), on soil water availability and on water stress sensibility of both species. CAF2007 gives an important place to systems’ water dynamics for coffee yields elaboration. In fact, the ratio of current transpiration of the plant to its potential one (TranF) is a water stress factor very often used in the model. It is used to calculate coffee LAI, roots growth rate but also leaves senescence. Water dynamics are described in two main subsystems of the model; the belowground resources subsystem where current soil evaporation and transpiration rate coffee and tree are calculated and the soil subsystem in which runoff and drainage are simulated.

The potential evapo-transpiration rate is computed for coffee and tree following Penman equation in function of climatic variables (temperature, wind speed, vapor pressure, radiation and rain) and LAI which is used to calculate amount of rain intercepted by the plant. The intercepted water reduces transpiration demand and evaporates the same day. Although the Penman-Montheith equation permits to take into account stomatal conductance to calculate reference evapo-transpiration rate, it has not been chosen in CAF2007 because of the unreliability of results obtained during model’s building (Marcel van Oijen, personal communication). Nevertheless, this implementation is in contradiction with literature which underlines that coffee transpiration rate is also affected by water stress perceived not only by coffee roots but also by coffee leaves. Then, actual coffee and tree evapo-transpiration rates are deduced from potential ones, modulated by water availability into soil depth explored by coffee roots and a parameter that represents plant’ sensibility to drought. Thus the water stress factor TranF only takes into account water stress perceived by coffee roots.

Runoff is modeled proportional to the daily rain not intercepted by the canopy, increasing from zero on flat soil to complete run-off on vertical soil. Run-off also decreases with higher total LAI, which describes the reduction of rain falling impacts on surface run-off in agroforestry systems. Drainage is calculated as the last term of water balance (i.e. soil water content plus rain minus water losses by evapo-transpiration, interception and run-off) and thus is also reduce by the presence of shade trees. Nevertheless, it is well known that both processes also involve soil’s characteristics such as texture, porosity, hydraulic conductivity and depth (Roupsard Olivier, personal communication). However in CAF2007, it was a choice to keep the soil as a simple one-layer model of fixed depth to avoid lack of information on those parameters (van Oijen et al., submitted).

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In the model WaNuLCAs, water dynamics implementation is more complex. The soil is described in two dimensions and composed of 16 compartments according to depth and distance to coffee plants and shade trees. The sharing is based on roots density, demand and supply by diffusion. Potential water absorption of each plant is calculated based on matrix flux for given roots density and soil water content. The model Hi-sAFe also integrates spatial heterogeneity of hydraulic soil conditions by roots voxels (3D). Water sharing is based on demand calculated with Penman-Monteith equation for tree and with K-ETP equation for the crops. Competition is than based on matrix flux taking into account roots lengths. Vertical flows are derived from the model STICS for water infiltration, evaporation and drainage. Run-off is a constant proportion of rain amount.

In APES four processes are implemented to describe soil water status: water distribution into the soil, soil evaporation, plants absorption and soil cultural practices. Soil depth is taken into account with parameters to describe hydraulic properties. The amount of water absorbed at each layer by each species is function of plants demand, soil description and roots distribution in the different layers. Water sharing is the same as in the model Hi-sAFe.

By comparison, water dynamics seem to be computed in a more simple way in CAF2007,

without taking into account stomatal conductance to simulate plants transpiration, soil and roots spatial heterogeneity to simulate horizontal and vertical flows. Thus, subsystems involved in water dynamics in CAF2007 should be further tested as they can have important influences on the other connected subsystems.

d- Coffee agroforestry systems nitrogen dynamics Finally, coffee agroforestry systems’ nitrogen dynamics are also investigated as a

competition for this resource can appear between involved species, resulting in lower coffee productivity. Coffee is a crop very sensitive to nitrogen fertilization (Harmand et al. 2007) and it has been shown that in organic systems, yields are lower because of a lack of N-fertilization (Elias de Melo and Jeremy Haggar, personal communication). Moreover, a good N-nutrition enhances coffee carbon assimilation rate, resulting in increased vegetative growth and so in coffee productivity the following year (Rebolledo, 2008).

In Central America, coffee is very often over fertilized ( Hergoualc’h et al., 2008; Van Oijen, submitted) which leads to overproduction. Moreover, filtering soils reduce fertilization efficiency by increasing losses by leaching. Thus, nitrogen fertilization also creates a risk of water contamination through nitrate-leaching. Introduction of shade trees in coffee plantations may increase N-accumulation in litter and permanent biomass and so limit this risk from excessive fertilization (Harmand et al. 2007).

N-fixing shade trees species also provide nitrogen through atmospheric N-fixation (Perrin et Remal, 2009). However pruning and fertilization are practices that contribute to reduce the N-fixation capacity of the shade trees (Rebolledo, 2008; Perrin and Remal, 2009). The presence of N2 fixing shade trees, as well as the addition of nitrogen fertilizers, can increase N20 emissions, because of the higher nitrogen inputs in litter and potential nitrogen soil mineralization rate (Hergoualc’h at al., 2008).

Based on these observations, we can wonder if CAF2007 can reproduce coffee sensitivity to nitrogen fertilization, shade trees effects on nitrogen recycling and fixation, and if this recycling allows a better nitrogen efficiency.

In CAF2007, nitrogen dynamics are implemented in two main subsystems: the soil subsystem to simulate nitrogen mineralization and the belowground resources subsystem to calculate nitrogen supply for both species (appendix 1). The soil C and N resource subsystem is composed of a single chain of decomposition of materials that contain both C and N. The chain consists of four subsystems representing four different soil pools: litter, fast degrading soil

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organic matter, slowly degrading, and mineralized material. In each pool, degradation of added carbon material (coming from coffee/tree pruning, thinning, organs senescence, or degradation of previous pool) is calculated with a fixed turn-over. Then, daily degraded carbon material is split with fixed ratios between respiration and degradation in the next pool (respectively 25% and 75% for litter, and 97% and 3% for fast degrading soil organic matter). The model keeps track of the amounts of C and N in the different pools. The decomposition steps for both elements are linked: in each pool, the rate of N degraded depends on the rate of C degraded.

N-uptake is then limited by either demand from the plants or supply from the soil. The N-supply follows a Michaelis-Menten function of soil mineral N concentration and is proportional to roots biomass. N-demand is the sum of organ-specific multiplications of N/C ratios with carbon growth rates.

The facts that in CAF2007 the N and C mineralization rates of soil organic matter do not take into account soil temperature and moisture, that the relative losses of C and N in soil compartment are assumed equal, and that every removed biomass from coffee/tree pruning and thinning are re-integrated to the soil and not exported for timber or firewood can be controversial. Moreover, soil N-mineralization and N-allocation in the different plants’ organs are also strongly governed by C dynamics through the use of organs-specific N/C ratios for which information is limited (van Oijen et al., submitted).

The fact that nitrogen sharing of between both species depends on relative demand, relative roots density and on uptake capacity of both species, is common for all numeric models. Nevertheless, while in CAF2007 soil is represented as a unique layer with two compartments: shaded or not, in Hi-sAFe, soil is 3-dimensional and in WaNulCAS 2-dimensional. In the other models, potential uptakes are also function of diffusion speed from soil to roots, adding that in WanulCAS, this potential uptake cannot be superior to the one in monoculture. Thus, the Michaelis-Menten equation for N-supply calculation is specific to CAF2007. Moreover, in WaNulcas, biologic fixation is also included and demand is calculated from an empirical relation between absorption and biomass production in non-limiting condition. In Hi-sAFe and APES, demand is calculated according to optimal quantity in the different crops’ organs. So, the calculation of demand based on carbon growth rates is also specific to CAF2007. All these specificities in implementation of N relations in CAF2007 should be further numerically tested for their impacts on productivity and environment.

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e- Conclusion

Each of the four processes has been replaced in the conceptual models elaborated by

Maria Rebolledo in 2008, in the conceptual schemes of CAF2007 but also of the other numeric models to underline similarities and differences. We chose those processes because performance of agroforestry systems depends on the interactions between tree and annual or perennial crop and more particularly on the competition for resources between both. All the compared numerical models simulate biophysical evolution of agroforestry systems, taking into account their characteristics and insisting on these interactions. However, the sharing processes of the above (light) and the belowground (nutrients and water) resources, are the most important but difficult to implement (Malézieux et al., 2009 ). Moreover, because coffee is a perennial crop, those interactions have to be considered in long-time period for coffee agroforestry system. That is why we conducted the conceptual evaluation having a particular interest for the implementation of those interactions in CAF2007. As a result, we found that:

- Coffee phenology implementation in CAF2007 is not function of thermal time but is more specific to coffee with two key phonological events: flowering activation and fruits maturation. Flowering is activated by a fixed amount of rain, and its intensity depends on radiation. However, water and temperature stress are not taken into account for the calculation of coffee flowering activation and intensity.

- Coffee carbon production is simulated taking into account all the factors cited in the literature except effect of fruit load which explains the buffering effect of shade trees on productive bi-annual pattern. Implementation of carbon allocation in organs is not based on allocation tables and is kept simpler than in reality. Nevertheless, the competition between vegetative and reproductive growth during season can be activated in the model with a specific set of parameters.

- Water relations are also implemented in a simpler way than the reality and than in the other numerical models (soil is represented as a homogeneous layer), without taking into account stomatal conductance, though it is important to determine coffee water consumption.

- Nitrogen relations are also kept simple compared to reality and other numeric models. Soil is decomposed in 4 pools of organic matter degradation, which is calculated based on fixed turn-over for each pool ignoring effect of soil temperature and moisture. N-dynamics are also strongly related to C-dynamics which supposes that N/C ratios in coffee plants are maintained constant, which is an important assumption of the model.

Table presented in appendix 4 recapitulates the four processes we identified that should

be tested numerically, the subsystems involved in each process in CAF2007, the ideal set of data needed to test the process and the name of parameters involved in each one. To test those processes, it would be interesting to disconnect each subsystems involved in CAF2007 to avoid the other effects caused by the numerous links existing between variables and parameters which may reduce the efficiency of an evaluation. However, those modules are not easy to disconnect, and needed data set for testing were not available. Thus, it has not been possible yet to test those processes numerically and a global numerical evaluation of the model has been performed.

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2- Numerical evaluation of CAF2007

A - Data collect Climatic data Climatic data were easy to collect from Turrialba trial as a meteorological station is

located and managed by CATIE. However, for Masatepe, only 2,8 years of radiation were available. Missing-years data were generated based on the empirical distribution of available time series with the software Infostat and the statistic Fisher test was performed to ensure the variances equality between years (p-value>0,05).

Model initialization Determination of initial state variables for coffee and tree was not possible as they have

not been measured at the establishment of experiments so that we kept working with the default data. However, in Masatepe we measured the carbon content in shade trees organs biomass from five plants collected in a nursery at the stage of implantation. The plants were dried and the different parts were then weighted separately.

The table of all parameters values for the model initialisation is presented in appendix 5. For each treatment the values obtained are mean of their three replicates. Initial state variables for soil were determined from data sets coming from studies in both sites.

Management The management parameters are also included. Coffee is assumed to reach its full

productivity the third year after its plantation and to necessitate one year to reach this productivity after being pruned. First coffee pruning is done earlier in Turrialba than in Masatepe. This could be explained by the arid climate in Masatepe, which contributes to slow down the growth. In both site, coffee is pruned each year after harvest. The fraction of biomass which is pruned varies each year according to the potential productivity of each plant. However, the model takes into account the same rate for each year. Thus, we calculated the mean for this fraction among years which has been found higher in Turrialba than in Costa Rica.

Management of shade trees depends on the species. In Turrialba, Erythrina poepiggiana is pruned twice a year since the first year while the first pruning of Terminalia amazonia happened only the sixth year. Fraction of pruned biomass was assumed to be 20% higher for IC treatment than for MC treatment with Erythrina while equal in both treatments with Terminalia. In Masatepe, Inga glauca has been pruned since the fifth year and the fraction of pruned biomass assumed to be equal in both treatments. Two tree thinning has been done recently two times in both sites at a rate of 50%.

N-fertilizers are applied three times a year in both sites at a rate of 300 kgN/ha/year for the intensive conventional treatment and at a rate of 150 kgN/ha/year for the medio conventional treatment.

Coffee yields Coffee annual yields have been collected for the three replicates of each subplot, averages

are presented in Table 6 for each subplot. In the figure 7, we plotted those yields for each treatment. Coffee yields are generally higher with the intensive conventional management than with the moderate one. This confirms the above mentioned sensitivity of coffee for N-fertilization.

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Table 6: Observed coffee annual yields (tDM/ha/y) in Turrialba and Masatepe Masatepe Turrialba Full Sun Inga Full Sun Erythrina Terminalia

year IC MC IC MC IC MC IC MC IC MC 2000 0 0 0 0 0 0 0 0 0 0 2001 0 0 0 0 0 0 0 0 0 0 2002 0 0 0 0 0,47 0,68 0,36 0,17 0,29 0,09 2003 0,24 0,26 0,10 0,07 2,77 2,30 2,27 1,56 2,09 1,78 2004 1,10 0,37 0,47 0,60 0,80 0,70 1,05 0,74 1,03 0,51 2005 1,60 0,58 1,02 0,58 2,45 2,00 2,21 1,58 2,38 1,83 2006 1,99 1,69 1,23 1,14 0,88 0,42 0,75 0,10 0,34 0,13 2007 1,09 1,06 0,93 0,72 2,74 2,72 2,32 1,26 1,56 1,54 2008 0,85 0,50 0,65 0,33 0,91 0,50 1,21 0,67 0,46 0,31 Mean 0,76 0,50 0,49 0,38 1,23 1,04 1,13 0,68 0,91 0,69

Figure 7: Boxplot of observed yields in function of the treatment. M: Masatepe, T: Turrialba, FS: Full Sun, IG: Inga laurina, EP: Erythrina poepiggiana, TT: Turrialba-Terminalia amazonia, IC: Intensive Conventional, MC: Moderate Conventional.

We also represented the interaction between level of inputs and subplot in figure 8. As a result, we can see that:

- Coffee yields are higher with a higher level of fertilization, but also that - Coffee yields are higher under full sun than under shade. - Coffee yields are higher in Turrialba than in Masatepe, where arid climatic conditions

are less favorable for coffee production.

We then performed a multi-factorial analysis of variances with the statistics software R and found that there were no significativity of the interaction between the inputs level, the subplot and the year to explain coffee yields (p-val>0,05). That means that there is no simultaneous effect of these three factors on coffee yields. Thus, we then test the effect of each factor and found that coffee yields variation is not explained by the level of inputs (p-val>0,05), but more by the subplot and by the year (p-val<0,05). Although it has been reported that coffee is sensitive to fertilization, in this study we couldn’t confirm statistically this hypothesis. In fact, the presence and type of shade tree species and climatic conditions are more likely to explain variability of coffee productivity.

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Figure 8: Graphic representing mean of yields in function of interaction between the level of input (MGT) and the subplot on abscissa (PLOT).

Finally, we plotted coffee yields obtained in each subplot in function of years (fig. 9 and 10). While in Turrialba, the bi-annual pattern of coffee productivity, mentioned in literature, is well defined, in Masatepe, it is not. This can be explained because in Masatepe yields are generally lower (p-val<0,05), and thus the effect of competition for carbon between vegetative and reproductive growth is less pronounced.

Figure 9: Annual coffee yields in Turrialba. IC: Intensive Conventional, MC: Moderate Conventional, TFS: Turrialba-Full Sun, TEP: Turrialba-Erythrina poepiggiana, TT: Turrialba, Terminalia amazonia.

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Figure 10: Annual coffee yields in Masatepe MFS: Masatepe-Full Sun, MIG: Masatepe-Inga laurina, IC: Intensive Conventional, MC: Moderate Conventional, MFS

Moreover, in Turrialba, yields are higher under Erythrina than Terminalia with the intensive conventional management. This can be explained by the N-fixing capacity of Erythrina. However for the moderate conventional management, decreased coffee yields are not different under both species, underlying that N-fixation by Erythrina was not sufficient to contribute to increase yields. This might be explained because in the moderate conventional treatment, Erythrina was pruned twice per year to remove some branches so as to provide a constant shade, possibly reducing coffee production when shade cover was high. This is contrary to the traditional management of pollarding the tree twice per year removing all branches, which was implemented for the intensive conventional treatment. With this type of management, shade is more reduced at important coffee stages of yields elaboration (before flowering to increase flowering intensity and after to increase fruits growth). In Masatepe, Inga shade systems had lower coffee productivity compared to full sun systems. This can also be linked to higher shade levels during the dry season.

Measurement of Specific Leaf Area

Specific Leaf Area (SLA) is used in the model to calculate LAI from leaves carbon biomass. We measured this parameter for coffee and the three shade trees species involved in the chosen subplots. Results are shown in table 7.

For coffee, the maximum specific leaf area was obtained for leaves collected under shade and the minimum for leaves collected under full sun. The observed difference of SLA between shade and full sun systems can be due to the fact that under shade, leaf area is more extended in order to increase light interception compared to full sun system (data not shown). Also under full sun, SLA was found higher for young leaves than mature and old ones and under shade, however no differences were observed between leaves age under shade (data not shown).

Compared to default data included in the model from literature review, both measured coffee SLAMAX and FSLAMIN were quite similar. Nevertheless, thanks to these measurements, we could adjust values of SLA for Terminalia and Inga, as default data were higher than measurements. This could be because except for Erythrina poepiggiana, species included in the model are different from those in both trials even though from the same gender.

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Table 7: Measured Specific Leaf Area and default data included in CAF2007 Parameter measured data default data

SLAMAX_Coffea (m2/kg C) 27,61 27

FSLAMIN_Coffea (-) 0,68 0,64

SLAT _Erythrina (m2/kg C) 38,82 38

SLAT _Terminalia (m2/kg C) 18,16 32

SLAT_Inga (m2/kg C) 26,15 39

B - Sensitivity analysis of CAF2007 We performed the sensitivity analysis to have an idea of sensitivity of model’s responses

to inputs’ uncertainty. Coefficients of variations obtained for each parameter for each of the 7 chosen outputs are shown in Table 1, 2, 3 and 4 of appendix 6. If read in line, these tables give information on the parameters that have influence on each output while when read in column, they give an idea of the most sensitive outputs to the uncertainty of a given parameter.

CAF2007 seems not to be sensitive to initial state values for coffee and tree, which is an advantage because those values are not often available. However, uncertainty of initial state values for the soil compartment affects more the different outputs, meaning that those values have to be well entered in the model to interpret model’s response (tab. 1, appendix 6).

The two outputs which are the most sensitive to variation of tree parameters are the tree wood volume and the carbon sequestration (tab. 2, appendix 6). In fact, all the parameters used to simulate tree growth and allocation into the woody parts, have an influence on tree wood volume, as well as on carbon sequestration because in the model pruned and thinned tree material is degraded into the soil.

Coffee yield, soil carbon sequestration and run-off are the three outputs which vary the most when we vary coffee parameters (tab. 3, appendix 6). Coffee yield is relatively more sensitive to parameters used to calculate coffee carbon production and allocation into the different organs. Carbon sequestration is sensitive to parameters affecting coffee growth rates and allocation into organs which are not exported. Nevertheless, the fact that it is less sensitive to woody part carbon sink strength was not expected. Run-off is also sensitive to coffee parameters which are involved in the calculation of LAI. Drainage, tree wood, N-leaching and N-emission are relatively less sensitive to coffee parameters.

Except drainage, all the outputs are very sensitive to soil parameters (tab. 4, appendix 6). Fraction of soil water content at field capacity has a great influence on all the outputs. This can be explained as it is used to calculate water dynamics in the systems. For the same reason, fraction of soil water content at wilting point also impacts on different outputs. Efficiency of organic matter degradation, time constant for unstable organic matter decomposition, ratio of runoff in bulk soil are also important parameters for all outputs. Gaseous N-emission, N-leaching and run-off are also governed by parameters specific to their calculation.

This analysis also permits to select important parameters that need to be further well

calibrated as having more important impacts on the model outputs (Makowski et al. 2006). Those parameters are those with high coefficients of variation values for several outputs. In the other way, uncertainty of some parameters has very low impact on these outputs and thus need less to be accurately determined.

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C – Numerical evaluation of CAF2007

To do the numerical evaluation of CAF2007, we first run the model with the default

settings of parameters (appendix 3). Then, we run the model with collected data for soil, management for each subplot (see appendix 4). Obtained simulated coffee annual yields were compared with observed ones for both modeling situations and relative root mean square errors were calculated (tab. 8). Table 9 presents averages of RRMSE calculated according to different factors: localization, level of inputs, crossing of localization/level of inputs and type of combination.

Table 8: Relative roots mean square errors calculated for each subplot, in both modeling

situations: model with default setting of parameters (DEF) and model with measured initial state and management variables and Specific Leaf Area (MES).

SUBPLOT RRMSE- DEF RRMSE- MES T-MC-EP 1,1985 0,6223 T-MC-TA 1,0977 0,9666 T-MC-FS 1,3458 0,9657 T-IC-EP 0,8657 0,4799 T-IC-TA 1,0300 0,9068 T-IC-FS 1,0658 0,6780

M-MC-IL 1,8535 2,1847 M-MC-FS 1,6549 1,4601 M-IC-IL 1,6770 1,7161 M-IC-FS 1,2419 0,6183

T: Turrialba, M: Masatepe, MC: Moderate conventional, IC: Intensive Conventional, EP : Erythrina poepiggiana, TA : Terminalia amazonia, IL: Inga laurina, FS: Full sun.

Table 9: Average of RRMSE calculated for both situations, for different factors: the

localization, level of inputs, crossing of localization/level of inputs, type of combination.

FACTOR RRMSE- DEF RRMSE- MES T 1,1006 0,7699 M 1,6068 1,4948

MC 1,4301 1,2399 IC 1,1761 0,8798

T-MC 1,2140 0,8515 T-IC 0,9479 0,6934

M-MC 1,7542 1,8224 M-IC 1,4594 1,1672 EP 1,0321 0,5511 TA 1,0639 0,9367 IL 1,7653 1,9504

M-FS 1,4484 1,0392 T-FS 1,2058 0,8219 FS 1,3271 0,9305

T: Turrialba, M: Masatepe, MC: Moderate conventional, IC: Intensive Conventional, EP : Erythrina poepiggiana, TA : Terminalia amazonia, IL: Inga laurina, FS: Full sun.

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In figures 1 to 5 of appendix 7, we plotted observed coffee annual yields and simulated one for each combination for both modeling situations. These plots first reveal that with the default settings of inputs, simulated yields become very low the third productive year. This can be explained because in this simulation coffee is drastically pruned every five years although it is really pruned annually since the first year after plantation. This contributes to explain the higher values of RRMSE obtained for this modeling situation compared with those obtained for simulations with collected data (tab. 8 and 9).

Except in Masatepe under Inga laurina, running the model with collected data gives

lower differences between observed and simulated yields and thus lower values of RRMSE than running the model with default settings of inputs in all combinations (fig. 11 and tab. 9). Thus, variables of management and initial soil carbon and nitrogen composition need to be well implemented in the model to give better predictions. Nevertheless, implementation of management stays simpler in the model than in reality. In fact, each coffee plant is pruned annually after harvesting with a variable intensity function of its productivity the previous year, while in the model fraction of pruned biomass stays constant among years.

The bi-annual pattern of coffee yields observed in Turrialba is not reproduced by the

model (fig. 1 to 3, appendix 7). This might be explained by the fact that pruning intensity is constant among years, as well as by the fact that reserves dynamics are not included in the model. Thus, the effect of pruning intensity on coffee plants production and reserves accumulation for the following year is ignored. The four parameters implemented to describe this bi-annual pattern has been activated but yields were found very low and thus RRMSE were very high (data not shown), suggesting that these parameters need to be more accurately calibrated to simulate the pattern.

Except in Turrialba with the shade tree species Erythrina poepiggiana, in all other

combinations efficiency of N-fertilization is underestimated (fig. 1 to 5, appendix 7) by the model and values of RRMSE are higher with the moderate conventional level of N-fertilization than with the intensive level (tab.9). This suggest that implementation of N-relations in the model should be revised. However, the fact that effect of N-fertilization on simulated yields of coffee is better simulated under Erythrina poepiggiana also suggests that the model can be improved by a better calibration of shade trees parameters. In fact, the coffee agroforestry system involving Erythrina poepiggiana has been well documented compared to other species of the experiments (van Oijen et al., submitted). Moreover, the other shade trees species are not included in the model and we worked with species of the same gender, which can have led to a greater source of error and thus higher RRMSE values compared to those of Erythrina poepiggiana (fig. 11 and tab. 9). The species-specific parameters are related to C and N tree dynamics (see tab.4, appendix 3), so they can have an important influence on C and N soil recycling. Thus, before changing implementation of N-relations in the model, a calibration of shade tree species parameters should be performed.

In both modeling situations, RRMSE were found higher for Masatepe than for Turrialba

(tab. 9). The model, run with collected data inputs in Masatepe, over-estimates coffee yields under full sun and under Inga laurina during the first productive years (fig. 4 and 5, appendix 7 and 8). In fact, implantation of coffee plants was difficult in Masatepe and it took some years for coffee plants to be well developed (Haggar Jeremy, personal communication) and this has not been reflected by simulations.

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Figure 11: Differences between simulated and observed coffee yields for both modeling situations. DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

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This result also suggests that the model is more adapted for simulations of coffee agroforestry systems in humid zones than in arid ones with longer dry season. This can be due to the model simplicity for its implementation of water dynamics. Besides, the sensitivity analysis has shown the importance of soil parameters for calculation of final coffee bean annual yields, underlying that CAF2007 need at least to be well informed for these parameters values. Fraction of soil water content at field capacity, which has an influence on several outputs (appendix 6), depends on soil structure which varies among sites (Haggar, personal communication).

Moreover, the fact that the model doesn’t take into account stomatal conductance to

simulate plants’ transpiration and photosynthetic activity, can contribute to explain the difference between both sites. In fact, through the conceptual evaluation, this factor has been shown to be important for calculation of water relations in coffee agroforestry systems. In Masatepe, climate is more arid than in Turrialba so that stomatal limitations of coffee growth might be more important than in Turrialba. Thus, by ignoring this process, CAF2007 might over-estimate yields in drier climatic conditions.

In appendix 8, we plotted simulated yields against observed yields and traced the line

y=x for each treatment. Globally model under-estimates yields in Turrialba with a better prediction of coffee yields under full sun than under shade trees species (fig. 1 to 3 appendix 8). However RRMSE value is higher than under Eryhthrina poepiggina (tab. 9) because of the accentuated bi-annual pattern under full sun. By contrast, model over-estimates yields in Masatepe (fig 4 and 5, appendix 8) with higher values of RRMSE under Inga laurina than under full sun.

To conclude, we can say that model is more performing to simulate coffee

agroforestry systems in Turrialba, under full sun and under the shade tree species Erythrina poepiggiana. This might be explained because model’s parameters estimation from literature was more precise for those situations, suggesting that parameters should be calibrated more precisely. Moreover, the fact that simulations were closer to observations when model was run with collected initial values of C an N soil composition and management for each subplot suggests that this model needs site-specific inputs values.

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IV- Conclusion and perspectives

To participate to continuation of CAF2007 elaboration, its conceptual evaluation was

done, based on literature review and collected knowledge from experts on coffee agroforestry systems in Central America. We found the model simple, however specific to those systems, taking into account characteristics of coffee as a shade plant as well as interactions between coffee and tree. Nevertheless, some critical points can be improved in the model as they have been shown to be important to evaluate systems’ productivity and environmental impacts. We advice to further test numerically four processes described by the model: coffee phenology, coffee carbon production and allocation, water and nitrogen dynamics in the systems. For this evaluation, subsystems need to be isolated in the model and data might be collected from two short-term experimentations in Costa Rica: Aquiares and Perez Celedon.

We then tested the model globally for it capacity to well simulate coffee productivity

using data from two long-term experiments in two contrasted agro-ecological zones: Turrialba and Masatepe. From these experiments, we found that coffee yields were higher with a higher level of fertilization, and under full sun than under shade. Bi-annual pattern of coffee productivity was more pronounced in Turrialba than in Masatepe. Coffee productivity was also higher in Turrialba than in Masatepe, where arid climatic conditions are less favorable for coffee production. The presence and type of shade tree species and climatic conditions were more likely to explain variability of coffee productivity.

We calculated relative roots mean square error between observed and simulated coffee

annual yields for two modeling situations: with default settings of inputs and with collected data from experiments. From this comparison, we show that CAF2007 needs site-specific values as inputs to give better predictions. Moreover, CAF200 seems to be more performing to simulate coffee agroforestry systems in humid tropical zones than in more arid ones. This confirms that the model needs to be more precisely tested for its implementation of systems’ water dynamics. Moreover, efficiency of N-fertilization was under-estimated by the model. That also reveals that N-relations might also be improved in the model.

Lowest values of RRMSE were found for coffee production under full sun and

Erythrina poepiggiana, suggesting that information on parameters for those two situations were more adequate. Nevertheless, CAF2007 doesn’t reproduce bi-annual pattern of coffee productivity as it doesn’t include neither reserves dynamics, neither year-specific management. Thus, the fact that overbearing exhausts coffee’s reserves and limits the production of leaves, leading to poor crop the next year, which allows an excessive foliage to form which, in turn, permits an intensive flowering and hence a good yield (Da Matta et al., 2004), cannot be described by the model.

Finally, the high values of RRMSE found for other shade trees combinations as well as

the sensitivity analysis also suggest that CAF2007 needs to be more precisely calibrated. Data have already been collected from both sites to perform automatic calibration through Bayesian method to quantify the model uncertainties (van Oijen et al., submitted). Parameters to include for this calibration can be selected according to three criteria: (i) from the literature review, (ii) the conceptual evaluation to select parameters which are involved in the four identified processes and (iii), from the sensitivity analysis which permits to screen important parameters from all the parameters set.

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Remal Sylvie, MSc. Thesis, Appendices 1

APPENDICES

APPENDIX 1: Description of the structure of CAF2007, a dynamic model for coffee agroforestry systems……………………………………………………………………………………………………..….2 APPENDIX 2: Technical manual of CAF2007…………………………………………………………..…17

APPENDIX 3: Parameters of CAF2007…………………………………………………………………….25

APPENDIX 4: Processes identified in conceptual evaluation of CAF2007, subsystems involved, ideal set of

data needed and involved parameters involved in each one…………………………………………………29

APPENDIX 5: Table of parameters involved for model initialization……………………………………...30

APPENDIX 6: Coefficients of variation obtained for the model inputs and for each of the 7 chosen outputs………………………………………………………………………………………………………..32 APPENDIX 7 : Observed and simulated coffee annual yields in both modelling situations…………..…34

APPENDIX 8: Simulated vs. Observed coffee annual yields……………………………………………..37

Remal Sylvie, MSc. Thesis, Appendices 2

APPENDIX 1:

Description of the structure of CAF2007, a dynamic model for coffee agroforestry systems

Sylvie Remal (CIRAD Montpellier), Marie Ange Ngo Bieng (CIRAD-Montpellier) & Marcel van Oijen

(CEH-Edinburgh)

Image of the top-level of the Simulink CAF 2007 model

Remal Sylvie, MSc. Thesis, Appendices 3

INTRODUCTION This paper describes structure and functioning of the modular model CAF2007 (Van Oijen et al., submitted). CAF2007 is a dynamic plot-scale process-based model for coffee agroforestry systems. The model divides the land into two main areas, an area where coffee is grown under full sun and the other where coffee is under shade trees. As both areas are interacting together, the resource balance in each area is influenced by modifications in the other one. The shaded part of the field increases in size, and the full-sun part decreases, when the tree crowns expand. This change can continue until the whole field is shaded. Conversely, the shaded area decreases each time trees are pruned or thinned. Because all state variables in the model are expressed with regard to either shaded or un-shaded ground area, they need to be recalculated whenever the shaded area changes in size (Van Oijen et al., submitted). Each area is composed of different compartments. The aim of this paper is to describe in detail what is included in each of those compartments.

Remal Sylvie, MSc. Thesis, Appendices 4

I-The sun part of the field

This part represents the fraction of the field where coffee is not under shade and so where there are no interactions with trees. In this part we can distinguish two components: the coffee and the soil. The model also includes compartments in which the interactions between aboveground and belowground resources are calculated.

A- The soil compartment

This component is composed of two sub-systems: one for the water resource and one for C and N contents in the soil.

Remal Sylvie, MSc. Thesis, Appendices 5

1- The water resource subsystem

The water resource subsystem is used to calculate vertical and horizontal water flows into the soil. The change in soil water content at each step is the result of water gain from rainfall minus water losses by rainfall interception by coffee, by transpiration, evaporation, drainage and run-off. It is also affected positively or negatively by the change in fraction of the field which is under shade. The water losses: - by transpiration and evaporation: calculated from their potential rates (Penman equation) modulated by a deficit or excess of soil water content. The potential rates of transpiration and evaporation are calculated as functions of temperature, vapour pressure, radiation, wind speed, LAI, and the amount of rain intercepted by foliage. - by interception of rain: calculated as the minimum of rainfall amount and LAI times rain interception capacity. - by drainage and run-off: calculated from the soil water content, the amount of rain, amount of rain intercepted by coffee, leaf area index of coffee, slope, run-off rate, root depth, water content in field capacity, water content in saturation, evaporation and transpiration rates. Run-off is modelled as proportional to the daily rain not intercepted by the canopy, increasing from zero on flat soil to complete run-off on vertical soil. Drainage is the result of the difference between soil water content and water availability at field capacity plus gain from rain and minus losses by interception, run-off, evaporation and transpiration rates. Outputs of this subsystem: Soil water content (m3 m-3), amount of drained water (mm d-1), water lost by run-off (mm d-1). 2-The C and N resource subsystem This subsystem simulates the breakdown of organic material in the soil. It is composed of a single chain of decomposition of materials that contain both C and N. The chain consists of four subsystems representing four different soil pools: litter, fast degrading soil organic matter (SOM), slowly degrading SOM, and mineralised material. The model keeps track of the amounts of C and N in the different pools. The decomposition steps for both elements are linked: in each pool, the rate of N degraded depends on the rate of C degraded.

Remal Sylvie, MSc. Thesis, Appendices 6

The inputs for the first C pool (litter, CLITT) are: amounts of C in pruned coffee leaves and woody parts and in senescent leaves. The amount of C in this pool is modified by the dynamics of shading and by C losses due to run-off and turnover. Of the daily turnover of C in this pool (sCLITT), 25% C is lost as CO2 by respiration and 75% goes to the next pool in the chain (CSOMF). For the other pools of the decomposition chain, the fluxes are calculated similarly. For the second pool (fast degrading soil organic matter, CSOMF), the inputs are the amount of non-respired C in the first pool and the amount of C in senescent roots. Of the daily turnover of C in this pool (sCSOMF), 97% C is lost as CO2 by respiration and 3% goes to the next pool (CSOMS). For the third pool (slowly degrading soil organic matter, CSOMS), which is the last stage of degradation, the only input is the non-respired output of the second pool. All turnover of C in this pool leads to mineral carbon (CO2) which leaves the system as respiration. The last compartment in the chain (bottom-left box in the figure above) calculates the total respiratory loss of carbon from all previous pools, i.e. the rate of production of CO2. The model does not keep track of the amount of CO2 in the soil. In parallel, the N pools involve the same steps in the chain of degradation, but with some differences. The N contained in the litter pool is calculated from the N/C ratios of each part of the plants. The N lost by turnover is the result of a simple assumption that the relative losses of C and N in a pool are equal. The same percentages for shifting these losses from turnover between respiration and the next following pool are applied. The fourth pool represents the mineral N that is available for uptake by the plants. This amount is calculated from the mineralisation in the previous pools, fertilisation minus losses by coffee uptake, N-leaching and gaseous emission of N. N-leaching in the un-shaded part is a function of the water drainage rate, the overall concentration of mineral N in soil and a constant ratio of mineral N concentration in drained water to this overall concentration. N-emission is proportional to the mineral N content of the soil, a constant N-emission rate from soil and to the relative water content of the soil. Main outputs of the C and N resource subsystem: N or C soil organic content in litter and both other organic matter pools (kg m-2), soil mineral content (kg m-2), N-leaching rate (kg N m-2 d-1), N-emission rate (kg N m-2 d-1).

Remal Sylvie, MSc. Thesis, Appendices 7

B- Belowground resources compartment

This subsystem is set up to calculate how much water and N the soil can supply for uptake by coffee. It is composed of three different boxes. The first box uses the Penman equation to calculate the potential rates of soil evaporation and coffee transpiration, in dependence of the weather conditions, as described previously. In the second box, the actual rates of transpiration by coffee and evaporation from soil are calculated. The inputs to this calculation are potential evapotranspiration, root depth, a constant transpiration coefficient and soil water content. The outputs of this box are the actual rates of soil evaporation and plant transpiration (mm d-1), the transpiration ratio (fraction of potential transpiration rate that is actually realised), and the relative water content (m3 m-3). The third box calculates N-supply. It represents how much N the soil can deliver per day to the coffee. N-supply follows a Michaelis-Menten curve using two constants, a maximum uptake rate by the plant which is proportional to root biomass (expressed as amount of carbon in roots), and the Km-factor, i.e. the mineral N content at which supply is half of this maximum rate. The final N-supply is the minimum of this calculation and soil mineral N divided by the time step of the model, to prevent the model from calculating an uptake rate that exceeds the availability of N in the soil. The inputs used in this box are the mineral N content in the soil, which is calculated in the soil subsystem, and the C content in roots. The output of this third box is the N-supply (kg N m-2 d-1). C- Coffee compartment This subsystem computes some physiological and phenological characteristics of the coffee plant, allowing assessing the growth and production of this plant in this compartment. It is composed of 6 boxes.

Remal Sylvie, MSc. Thesis, Appendices 8

1- Phenology

The box “phenology” computes a state variable characterising the development stage of the coffee (DVS). It is a continuous variable going from 0 to 1, 0 representing the vegetative stage and 1 the mature stage. This DVS is computed from the number of degree-days. The compartment is an empirical part of the model; the physiological development depends on a number of (degrees) days which are modulated by important periods: the vegetative stage, during 3 years after the beginning of planting; the time between start and full productivity, the time between pruning and full productivity, the first time of pruning coffee, and the daily temperature sum. From the start (DVS = 0, i.e. vegetative stage), the key physiological stage is: the reproductive stage which may start after the 3 years, and be composed of 2 key events: the flowering activation and bean maturation stages. The flowering stage is activated if the plant is still in the vegetative stage, is sensitive to rain and if there is a daily rain amount superior to RAINHI, a threshold rain amount (evaluated with observations). Bean maturation, and harvest, takes place a fixed number of degree-days later. The main output of this phenology box is the (daily) state variable quantifying the development stage of the coffee (phenological development stage of the coffee, corresponding to a number of degree-days). As described, it is assumed that the coffee will reach maturation (DVS=1) at a fixed total number of degree-days. However, this stage is forced to completion within the same calendar year as flowering, to ensure that harvesting happens once a year. Another key assumption in the model is that there is one date of flowering and thus one day for maturation in each part of the field (corresponding to harvesting day). At this harvesting day, the carbon content in reproductive organs (beans) is reset to zero.

2- Growth The box growth computes coffee growth from above- and belowground resources and phenological stage. Growth consists of an amount of C (and N) accumulated daily from C source and demand (sink strength) of each organ. The source strength (potential amount of C which can be assimilated by photosynthesis) is computed from the PAR intercepted by the coffee, the light-use efficiency (computed from the atmospheric CO2,

Remal Sylvie, MSc. Thesis, Appendices 9

temperature, the photoperiod-average of PAR, the light extinction coefficient, and leaf RUBISCO content. Photosynthesis is also modulated by the water status in soil (as expressed in the ratio of actual to potential transpiration rate, the so-called ‘transpiration realisation factor’) and is assumed to be zero at days of pruning (the “NOPRUN” variable =0). Finally, the assimilated carbon is modulated by constant growth efficiency. The sink strength of growth, i.e. the C and N demand by each organ, is calculated for leaves, woody part, roots and storage organs (beans). As specified in the paper (Van Oijen et al., submitted) the C fractions allocated in these different parts are constant, but modulated by the availability of water and N in the soil. There is a functional equilibrium between aboveground and belowground organs: deficiency of water or N leads to an allocation as a priority to roots. The potential amount of C in each part is computed by multiplying the sink strength of each one with the source strength (C assimilated by photosynthesis), and the potential amount of N in each part is derived from this potential amount of C, according to an organ-specific N/C ratio. These potential amounts of C and N are modulated by the N supply and N demand to determine actual N-uptake. Actual C growth rate of the coffee plant is then calculated as the sum of the C growth rates in the different organs. The allocation is also modified by the phenological stage, with an allocation as a priority to bean during the maturation stage.

3- Biomass The biomass box computes the amounts of C and N in leaves (thus N/C ratio in leaves), and of C in woody parts, roots and in storage organs. The calculations for the different organs are similar apart from differences in the processes that lead to loss of biomass. The amount of C and N in leaves part is computed from their growth rate, modified by changes in the shaded area and by losses from senescence and pruning. The amount of C in woody parts increases due to growth, modified by the dynamics of the shaded area of the field, and minus the loss by pruning. C in roots changes with growth, shaded area dynamics and senescence. And finally, the amount of C in storage organs is computed from its growth, with a gain from the dynamic changes of the shaded part of the field, minus the loss by harvest.

4- Foliage The “foliage” box calculates the dynamics of LAI of coffee. Growth rate of LAI is the product of the specific leaf area (which depends on leaf N-content) and leaf growth rate of C. The dynamic change of the shaded part of the field is added minus the losses by senescence and pruning.

5- Senescence The “senescence” box computes the losses of C and N in leaves, and thereby the reduction of LAI and of C in roots due to “natural death”. The inputs are the amount of C and N in leaves and of C in roots, computed in the “biomass” box, the LAI from the “foliage” box, the transpiration realisation computed in the “belowground resources” compartment and the growth rate of C in storage organs computed in the “growth” box. The losses of C in root are computed from the turn-over of C in roots (TCCR). The losses in leaves are computed from their amount of C and N and the LAI, the transpiration realisation, the maximum turn-over rate of leaves and the competitive effect of allocation of C to reproductive organs.

6- Pruning and harvesting The amounts of harvested and pruned products are computed in the box “Pruning and harvesting”. The pruned LAI, C and N are computed from the LAI, the amount of biomass (C and N in leaves, C in wood) removed by pruning, which depends on the parameterisation of the fraction that is removed. Coffee yield is represented by the amount of C in the storage organs removed at harvest, which happens when the coffee reaches maturity (the harvested rate for N is computed from the harvested rate for C, according to the N/C ratio of storage organs) and takes into account the gain from the yield in the shaded part of the field becoming sunny. The model also calculates cumulative bean yield, i.e. the sum of yields over the number of years of simulation, NYEARS.

Remal Sylvie, MSc. Thesis, Appendices 10

To summarize, the coffee compartment computes at a daily time step the changes (variations, increase or decrease) of some state variables characterizing coffee development and growth, taking into account the management. The main outputs of this compartment are: LAI (m²m-²), (amount of) N in leaves (kg N m-²), (amount of) C in leaves, woody parts, roots and storage organs (depending on the development stage) (kg C m-²). These variables (relative to C) allow quantifying the yield (kg dry matter m-²). D- Aboveground resources compartment

This compartment computes the average light intensity during the photoperiod (PARav, MJ PAR m-2 d-1) and total light interception by coffee (PARint, MJ PAR m-2 d-1) from the total daily PAR, the photoperiod length, the LAI and the light extinction coefficient. Light interception by coffee is modelled by Beer’s law with a constant light extinction coefficient. Photoperiod mean PAR is calculated by dividing total daily PAR by day length. II- The shade part of the field

This part of the model represents the fraction of the field where coffee is under shade, and is in interaction with shade trees. Thus, in this part, we can distinguish one more component than in the sun part: trees, plus one more compartment “Shade” which quantifies the shade effects of trees on microclimate and soil. Therefore, there appear new interactions in the simulation of aboveground and belowground resources.

Remal Sylvie, MSc. Thesis, Appendices 11

A- Tree compartment

The tree compartment is based on the BASic FORest simulator (BASFOR, Van Oijen). It is composed of 5 subsystems: Tree morphology, Biomass allocation, Tree growth and N-uptake, Net primary production, N and C content in tree. There are six state variables: C in leaves, branches, stems and roots, nitrogen in leaves and tree density. N contents are calculated through fixed organ-specific N/C ratios. Phenological stages are not taken into account, as the trees are grown only to provide shade for coffee and timber for some tree species: fruit trees are not simulated 1- Morphology Morphological variables (LAI, crown area index and height) are calculated as functions of the biomass variables (amount of C in leaves, branches and stems). Leaf area index (LAI) is calculated from C content in leaves, specific leaf area constant and the crown area of the trees. The crown area index of individual trees (CA, m2 tree-1) is calculated from the C content in branches, tree density, and an allometric constant linking CA to the amount of C in branches. Height is computed from C content in stem, tree density, and an allometric constant linking height to this C content. Inputs of this subsystem: Carbon in leaves, in branches and stem, tree density Outputs of this subsystem: crown area index of individual trees and of all trees (m2 m-2)), leaf area index (m2 m-2) and height (m). 2- Allocation This box computes the C allocated in each compartment of trees (branches, leaves, stems and roots). The allocation to leaves is computed from the LAI, the maximum LAI (LAIMAX) and the N/C ratio in leaves. Allocation to leaves decreases when LAI approaches the value of LAIMAX. The fraction of carbon allocated to leaves is determined by a constant maximum C content in leaves modulated by 3 reduction factors to take into account the current LAI of tree (fGILAI), the functional equilibrium between leaves and roots in case of N-deficiency (fGIN) and water stress (ratio of current transpiration/potential transpiration, as calculated in the Belowground resources subsystem). The fractions of C allocated to branches and stem are constants. Adding the C content in leaves, branches and stem and subtracting the sum from one gives the fraction allocated to roots. Thefractions of C allocated to leaves, branches, stem and roots constitute the outputs of this subsystem (kg kg-1). 3- NPPmaxN This compartment has been implemented to simulate the net primary productivity of trees without N deficiency. Tree growth rate is calculated by multiplying light interception with a light-use efficiency (LUEt) which is calculated more simply than the LUE of the coffee plants, not involving the Farquhar equations. LUEt follows an optimum curve with respect to temperature and, as for coffee, decreases proportionally to the ratio of actual and Penman potential transpiration. CO2-effects are modelled empirically using the concept of the biotic growth factor β which assumes proportionality between growth enhancement by elevated CO2 and the logarithm of the ratio of elevated to default atmospheric CO2 concentration (Van Oijen, submitted). The PAR absorbed per unit of crown-covered area is a function of the total daily PAR and the LAI of the tree. It is calculated by multiplication of PAR absorbed per crown-covered area with projected crown area of trees. The net primary productivity is then the product of PAR absorbed and tree light-use efficiency, offset by a constant respiration/photosynthesis ratio. Inputs of this subsystem: total daily PAR, tree species-specific potential light-use efficiency, atmospheric CO2 concentration, temperature and the ratio of actual to potential transpiration.

Remal Sylvie, MSc. Thesis, Appendices 12

Outputs of this subsystem: the net primary productivity (kg C m-2 d-1) and the PAR absorbed per crown-covered area (MJ PAR m-2 d-1). 4- Tree growth and N uptake In this subsystem, there are two boxes. The first is for the calculation of nitrogen demand by organs. This box has as inputs the net primary productivity NPPmaxN and the fraction of C allocated to each organ type coming from the Allocation subsystem. The product of NPPmaxN and allocation fractions gives the potential growth rates of all organs in terms of C. N-demand of each organ is calculated by multiplying its potential C-growth rate with an organ-specific N/C ratio. The sum of the N-demands is the total tree N demand. Then, in the second box, N-uptake is calculated with as inputs the N- demand by the trees, N-supply by the soil, which comes from the belowground resources subsystem and the shaded area index. The actual N-uptake by trees is the minimum of N-demand and N-supply. .Finally, actual C growth rates of the different organs are calculated from their N/C ratios. Root growth is modulated by the N uptake by tree, according to the functional equilibrium: when the N-content of the leaves is high, root growth is reduced. The outputs of this box are the N growth rates of leaves, the C growth rates of leaves, branches, stem and roots and Nuptake by trees (kg m-2 d-1). 5- C and N in tree This subsystem has as inputs the previous growth rates. For the different organs, the N and C content is modulated by the different forms of management applied to trees, such as thinning and pruning. The carbon content and the carbon which is removed from tree organs are the outputs. For the leaves, the nitrogen content and the nitrogen removed is also calculated through N/C ratio. The global variables obtained in the tree compartment are tree height, carbon content in trees and in stem volume (calculated from stem C by division by wood density in kg C m-3).

B- Shading

This compartment has been build to simulate the effects of shading on the system. The total daily PAR in shade is calculated according to crown area index multiplied with shade projection to give the shade area index, the PAR absorbed by crown and the total daily PAR. The temperature under shade is also modulated by a constant maximum temperature variation which can occur in such systems. The shade area index is also used to calculate the fraction of the field area which moves from the sunny to the shaded part or vice-versa (Van Oijen submitted, see appendix 1).

Remal Sylvie, MSc. Thesis, Appendices 13

C- Above ground resources compartment

As for the sunny part of the field, coffee light interception is modelled by Beer’s law with a constant light extinction coefficient. However the PAR taken into account is the one calculated for the shade part of the field. D- Soil compartment

The soil compartment of the shade part is composed of the same subsystems as those of the sun part of the field. However, the presence of shade trees modifies some processes. The soil water resource subsystem is the same; water content of the soil, run-off and drainage are calculated similarly under shade or not, with the addition of rain intercepted by tree and tree transpiration rate for calculating water losses. In the C and N soil contents subsystem, the same soil pools are involved; litter, fast and slowly degraded organic matter and mineral pool. However in the shade part of the field, the amount of C in leaves and branches removed from the tree, which is modelled in the Tree compartment, is added for calculation of C amount in litter. The amount of C lost by tree roots is added for the calculation of C content in the fast degrading organic matter pool. In the last C pools, the calculations are the same as for the field un-shaded part. Also, to calculate the amount of N in the litter, the N content of removed leaves and branches of the tree are taken into account. The amount of N lost by tree roots is calculated with the N/C ratio of tree roots and then added for the calculation of N content in the fast degrading organic matter pool. The N content in the stable organic matter pool is calculated similarly as for the un-shaded part of the field. Finally, N-uptake by trees, which is calculated in the Tree compartment, contributes to depletion of the mineral N pool. However, for N-fixing tree species, atmospheric N-fixation, calculated as the product of tree roots' C growth rate and a fixed specific N-fixation capacity, can contribute to increase in this pool.

Remal Sylvie, MSc. Thesis, Appendices 14

D- Belowground resources compartment

Penman potential evapotranspiration rate, water soil status and soil N supply are all influenced by the shade tree entrance in the system. In this part of the field, global daily radiation is first intercepted by the trees. Then, the potential transpiration rate of the trees is calculated with the Penman equation, involving climate variables and tree LAI. The potential transpiration rate of the coffee plants is then calculated as in the non-shaded part of the field, but radiation and temperature are lowered by the shading and the amount of rain that reaches the soil is reduced by interception by tree leaves. In the Water resources subsystem, a second box has been added to simulate the rates of actual soil evaporation and tree transpiration, in the same way as for the coffee. The outputs are the soil evaporation rate under coffee, the transpiration rate of coffee and tree and the relative soil water content. Finally in the subsystem implemented to calculate N-supply for plants, N-supply for coffee is calculated as in the non-shaded part. In parallel, the N-supply for tree is calculated in the same way, in dependence of C in roots, and following a Michaelis-Menten equation. E- Coffee compartment This compartment remains the same as in the sun part of the field. However, the availability of resources is changed by the presence of shade trees (see the Belowground and Aboveground resources compartments). III- Some key assumptions of the model: 1- N-uptake by coffee is proportional to C content in root biomass. 2- Organic C and N decomposition rate in soil does not depend on soil temperature and water content. 3- Relative losses of C and N in a soil pool are equal. 4- Coffee plants reach maturation stage at a fixed total number of degree-days. 5- Flowering happens once in both parts of the field. 6- The relative sink strengths of leaves and beans changes with the developmental stage. 7- Photosynthesis is interrupted during pruning days. IV- Inputs and outputs of the model: A-Inputs: The inputs of the general model are of different type: - 6 daily weather variables: Tmin (°C), Tmax (°C), wind speed (m s-1), vapour pressure (kPa), precipitation (mm d-1), and radiation (MJ m-2 d-1) - 7 initial state variables for coffee: Carbon in leaves, woody parts, roots and reproductive organs (kg C m-2), Nitrogen in leaves (kg N m-2), LAI (m2 m-2) and phenological stage (dimensionless).

Remal Sylvie, MSc. Thesis, Appendices 15

- 6 initial state variables for trees: Carbon in leaves, branches, stems and roots (kg C m-2), Nitrogen in leaves (kg N m-2) and tree density (m-2). - 8 initial state variables for soil: carbon and nitrogen in litter, unstable and stable organic matter (kg C m-2, kg N m-2), mineral nitrogen (kg N m-2) and water content (kg m-2, assumed equivalent to mm water) - 28 parameters for coffee - 32 parameters for trees - 3 parameters for site, - 4 parameters for atmospheric conditions and weather - 15 parameters for soil - 12 parameters for management - 4 parameters for run control B-Outputs: There are 32 standard outputs produced by model. However, it is possible to add new outputs or to remove some of them.

Output Unit Cumulative bean yield ton DM ha-1 Carbon content of coffee plants ton C ha-1 LAI of coffee plants m2 m-2 Carbon content of trees ton C ha-1 Standing wood volume of tree m3 ha-1 Carbon content of soil ton C ha-1 Water content of soil mm average Mineral N concentration in soil water mg N l-1 H2O average Rain mm d-1 average Rain Interception by coffee mm d-1 average Rain Interception by Tree mm d-1 average Runoff mm d-1 average Drainage mm d-1 average Evaporation from the soil surface mm d-1 average Transpiration by coffee mm d-1 average Transpiration by tree mm d-1 average N-fertilisation rate kg N ha-1 y-1 average N-fixation rate by trees kg N ha-1 y-1 average N-mineralisation rate kg N ha-1 y-1 average N-leaching rate kg N ha-1 y-1 average N-emisission rate from soil surface kg N ha-1 y-1 average N-uptake rate by coffee kg N ha-1 y-1 average N- uptake rate by tree kg N ha-1 y-1 average N loss from coffee plants kg N ha-1 y-1 average N loss from trees kg N ha-1 y-1 average N loss from soil kg N ha-1 y-1 LAI of tree m2 m-2 crown area Shade Area index m2 shade m-2 total N content of products of coffee kg N ha-1 y-1 N content of products of tree kg N ha-1 y-1 Volume of tree products m3 ha-1 y-1 Carbon loss from soil (C erosion) ton C ha-1 y-1

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APPENDIX 2

Technical manual for CAF2007.mdl

April 2009

1. MATLAB and Simulink The coffee agroforestry model CAF2007 is written in Simulink, which is a graphical-modelling tool. Simulink is an add-on to MATLAB, so MATLAB needs to be installed first. CAF2007 has been tested using MATLAB/Simulink version R2007a. Older and newer versions may work as well. 2. Running the model We can run the model in two very different ways: (1) in Simulink, using buttons on the screen, (2) in MATLAB, using the command sim(‘caf2007’). In both cases, model output will become available in the MATLAB ‘Workspace’. The output consists of only two structures: the vector (one-dimensional array) tout and the matrix (two-dimensional array) yout. The results can be analysed, plotted or written to external files (usually CSV-files or Excel-files). The vector tout contains the time axis, i.e. the day-numbers. The columns of yout contain the time series for all output variables, 32 in total. To have a quick idea of the results of the model, one can type, in the Workspace, plot(tout,yout). That will show all 32 output variables in the same graph. The variables are numbered in the order in which they appear in the Simulink subsystem ‘Outputs’. Their names can also be found in the initialise_caf2007.m file. It is also possible to plot just one variable, or a small number of them. Then type, for example, plot(tout,yout(:,1)), to show the results for the first variable which is production of beans. 3. Essential files CAF2007 comes in a subdirectory with 64 files. To run the model, only the following 8 files are essential:

1. caf2007.mdl 2. CRI11_98_04.txt 3. freadweathern.m 4. initialise_caf2007.m 5. maInit.m 6. parameters_plant_coffee.m 7. parameters_plant_tree.m 8. parameters_site.m

The first file, caf2007.mdl, is the Simulink-model file. It will never be necessary to look inside that file. The file will change if you change the structure of the model, but you do that interactively, using the graphical modelling system of Simulink. You won’t need to edit the model-file directly. The second file, CRI11_98_04.txt, has the default weather data for the model, which are from Turrialba, Costa Rica.

The other six files are so-called “m-files” which contain MATLAB code to do various things. The most important one is initialise_caf2007.m. That file sets the default choices for weather data (the file mentioned above), for the parameter values of coffee, trees and soil, and it also gives the list of names and units of the output variables. It does most of those things by calling four other m-files in the list of eight: freadweathern.m, parameters_plant_coffee.m, parameters_plant_tree.m and parameters_site.m. The last file in the list, maInit.m, is essential because the model uses it in the calculation of some the output variables, to calculate time-averages.

If you have MATLAB/Simulink plus those 8 files on your computer, you can run the model. However, the model will then look ugly on the screen and model use will altogether be a bit awkward.

Remal Sylvie, MSc. Thesis, Appendices 17

4. Image files The four files bgclouds.jpg, coffee.jpg, coffee&tree.jpg, volcanic_soil_profile.jpg are image-files that make the top-level of the Simulink model (i.e. what you see on your screen when you open the model) look nicer. The create a new subsystem with its own picture, it is easiest to copy any other subsystem that already has a picture, replace the contents of the subsystem as desired, and change the appearance of the subsystem-block by right-clicking on it, followed by Edit Mask. Then modify the line where the existing jpg-file is called . 5. Using Simulink: the top-level of the model When we double-click on the caf2007.mdl file in Windows, MATLAB/Simulink will start up and we see the top-level of the model on the screen:

Every rectangular box on the screen is a so-called “subsystem” of the model. The structure of the CAF2007 model itself consists of all visible subsystems except the three in the top-left corner. Model structure can be inspected by clicking on any of those 13 subsystems, but that is documented elsewhere – here we only discuss the three subsystems for handling the model. The subsystem in the corner is a ‘Model Info’ block which shows when the model was last modified. The next two are for run control and model output, and are discussed in more detail in the next sections. 6. Using Simulink: the buttons in subsystem “RUN CONTROL” The easiest way to use the model is to (1) start it up in Simulink, (2) click on the RC (‘RUN CONTROL’) subsystem and (3) use the buttons in there. Each button, when double-clicked, runs a bit of MATLAB-code. The following table lists all 20 buttons, explains what they do and how they work. [Note that the functionality of each button can also be inspected in Simulink itself, by right-clicking on them, selecting ‘Block Properties’ → ‘Callbacks’ → ‘OpenFcn’.]

Remal Sylvie, MSc. Thesis, Appendices 18

Table 1. The RUN-CONTROL system: explanation of the buttons. Button What does it do? How does it work?

Resets the model. Default values for parameters and weather are restored, according to the commands in the m-file ‘initialise_caf2007.m’.

The m-file initialise_caf2007.m is executed.

Removes shade trees from the model. The parameter TREEDENS0 is set to 0.

Opens a menu where each of the 124 parameters of the model can be changed.

The m-file change_parameter.m is executed.

Opens a menu where one of six pre-defined shade-tree species can be selected.

The m-file change_tree_species.m is executed, which then calls the parameter-file of the selected species.

Makes four parameter changes, compared to default, that lead to a biennial bean yield pattern.

The m-file change_parameter_BE.m is executed.

Takes model output and calculates annual yields and coefficients of biennial growth.

The m-file calcBE_nyears.m is executed.

Allows selecting an FAO long-term weather file (App. B), which must be in the working directory. Option to generate daily varying rain.

The m-file change_FAOweather.m is executed.

Plots two years of the currently selected weather.

The m-file show_weather_2years.m is executed.

Runs the model and plots all 32 output variables in the colour of the subsystem box itself. If repeated, the new lines will be added to the existing figure.

Executes the following code: sim( bdroot ) ; t = tout/365+STYEAR ; y=yout; figure(101) ; fshow_y(t,y,1:ny,yNameList,'k-') ;

Plots six key output variables in a separate figure. Left button: continuous lines. Right: dashed.

Executes the following code: figure(102); fshow_y(t,y,[1,3,5,27,6,7],yNameList,'k-') ;

Shows a bar chart with all components of the water balance of the system (means over whole period).

The m-file show_balance_water.m is executed.

Shows a bar chart with all components of the total-N balance of the system (means over whole period).

The m-file show_balance_Nsys.m is executed.

Shows a bar chart with all components of the total-N balance of the soil (means over whole period).

The m-file show_balance_Nsoil.m is executed.

Shows a bar chart with all components of the mineral-N balance of the soil (means over whole period).

The m-file show_balance_Nmin.m is executed.

Runs the model for 2×2 levels of CO2 and fertilisation, and plots results for 18 output variables in two graphs.

The m-file testCO2N.m is executed.

Writes summary output (15 output variables) to the EXCEL-file res.xls.

The m-file res_EXCEL.m is executed.

Remal Sylvie, MSc. Thesis, Appendices 19

7. Running the model in batch-mode, using a script-file The model can also be run non-interactively using a script-file. Script-files are MATLAB m-files with code for running the model, and they can be very useful for sensitivity analysis. The following are some hopefully self-explanatory examples:

% All examples run the model and write results to E XCEL model = 'caf2007' ; % EXAMPLE 1 initialise_caf2007 ; sim(model) ; calcOutputs7 ; xlswrite( 'TESTFILE' , { 'YIELD' } , 'EXAMPLE1' , 'A1' ) ; xlswrite( 'TESTFILE' , outputs7(1) , 'EXAMPLE1' , 'A2' ) ; % EXAMPLE 2: Does exactly the same as EXAMPLE 1 (ex cept that it writes to % a different worksheet of the same EXCEL-workbook) initialise_caf2007 ; sim(model) ; calcOutputs7 ; fresFile( 'TESTFILE' , 'EXAMPLE2' , 1 , 'YIELD' , outputs7(1) ) ; % EXAMPLE 3 initialise_caf2007 ; for i = 1:9 KEXT = 0.2+0.1*i; sim(model) ; calcOutputs7 ; fresFile( 'TESTFILE' , 'EXAMPLE3' , i , 'YIELD' , outputs7(1) ) ; end % EXAMPLE 4: same as EXAMPLE 3 but with more inform ation written to the % EXCEL-file initialise_caf2007 ; xlswrite( 'TESTFILE' , { 'YIELD' } , 'EXAMPLE4' , 'A2' ) ; for i = 1:9 KEXT = 0.2+0.1*i; sim(model) ; calcOutputs7 ; fresFile( 'TESTFILE' , 'EXAMPLE4' , i+1 , [ 'KEXT=' ,num2str(KEXT)] , ... outputs7(1) ) ; end % EXAMPLE 5: same as EXAMPLE 4 + autres variables initialise_caf2007 ; xlswrite( 'TESTFILE' , { 'YIELD' } , 'EXAMPLE5' , 'A2' ) ; xlswrite( 'TESTFILE' , { 'NLEACHING' } , 'EXAMPLE5' , 'A3' ) ; for i = 1:9 KEXT = 0.2+0.1*i; sim(model) ; calcOutputs7 ; fresFile( 'TESTFILE' , 'EXAMPLE5' , i+1 , [ 'KEXT=' ,num2str(KEXT)] , ... outputs7(1) ) ; fresFileRow( 'TESTFILE' , 'EXAMPLE5' , 3, i+1 , outputs7(4) ) ; end % EXAMPLE 6: same as EXAMPLE 4 but with all output 7 variables initialise_caf2007 ; xlswrite( 'TESTFILE' , { 'YIELD' } , 'EXAMPLE6' , 'A2' ) ; for i = 1:9 KEXT = 0.2+0.1*i; sim(model) ; calcOutputs7 ; fresFile( 'TESTFILE' , 'EXAMPLE6' , i+1 , [ 'KEXT=' ,num2str(KEXT)] , ... outputs7 ) ; end % EXAMPLE 7: same as EXAMPLE 6 but with all daily o utput for LAI initialise_caf2007 ; xlswrite( 'TESTFILE' , { 'YIELD' } , 'EXAMPLE7' , 'A2' ) ; for i = 1:9 KEXT = 0.2+0.1*i; sim(model) ; calcOutputs7 ; fresFile( 'TESTFILE' , 'EXAMPLE7' , i+1 , [ 'KEXT=' ,num2str(KEXT)] , ... yout(:,3)' ) ; end % EXAMPLE 8: same as EXAMPLE 7 but with all daily o utput for LAI for only % 365 days initialise_caf2007 ; xlswrite( 'TESTFILE' , { 'YIELD' } , 'EXAMPLE8' , 'A2' ) ; for i = 1:9 KEXT = 0.2+0.1*i; sim(model) ; calcOutputs7 ; fresFile( 'TESTFILE' , 'EXAMPLE8' , i+1 , [ 'KEXT=' ,num2str(KEXT)] , ... yout(1:365,3)' ) ; end

Remal Sylvie, MSc. Thesis, Appendices 20

8. Existing script-files in the CAF2007 subdirectory Four examples of script-files are included in the CAF2007 directory. Two of the script files (script_CAF_FAO...) are still under development and should not be used yet. The simplest script file is script_CAF_SingleFactors.m. It begins by running the model using the default settings. Then the script-file calls another m-file (calcOutputs7.m) to process the model results, i.e. to calculate seven key outputs (average production of coffee and wood, emission and leaching of N, sequestration and run-off of C and drainage loss of water). These seven outputs are written to the EXCEL-file res1.xls (by means of the m-file fresFile.m). The script-file then repeats all that for 22 other runs, each different from the default in one single way (one different parameter value, or different tree species).

The file script_tradeoffs8_2007.m runs nine different sensitivity analyses (SA) of the model. Each SA is bifactorial, i.e. two different parameters are changed. After each SA, a number of graphs are sent to the screen. The following SA are carried out (n = number of parameter combinations):

• SA 1 (n=22): CO2A = {380,760} × NFERTMULT = {0.00,0.15, … 1.50} • SA 2 (n=22): NFERTMULT = {0,1.5} × TREEDENS0 = {0,000.005, … 0.050} • SA 3 (n=22): NFERTMULT = {0,1.5} × SLOPE = {0,5, … 50} • SA 4 (n=22): RAINMULT = {1,0.5} × TPLUS = {-10,-8, … 10} • SA 5 (n=22): CO2A = {380,760} × TPLUS = {-10,-8, … 10} • SA 6 (n=8): DAYTHINT(1) = {-1,2000} × DAYPRUNTI = {182,365,548,731} • SA 7 (n=6): DAYPRUNC0 = {1825,9999}× DAYPRUNCI = {1095,1460,1825} • SA 8 (n=24): Tree species = {1,2,…6} × DAYPRUNTI = {182,365,548,731} • SA 9 (n=4): NFERTMULT = {0.5,1} × TREEDENS0 = {0,0.025}

Many of the m-files in the model directory are called by script_tradeoffs8_2007.m to carry out these SA-runs. This includes the 16 m-files whose names begin with “runModel2series…”. 9. Writing a new script-file The easiest way to create a new script-file is to copy an example from section 7 above, or the file script_CAF_SingleFactors.m, rename the copy (any name is allowed, but for clarity include the phrase “script” in the name) and start modifying it. Note that the script file can make us of all the m-files that are already available. This includes the m-files that are called when you use Simulink interactively, i.e. the m-files mentioned in the last column of Table 1. Another idea is to try out new statements in the MATLAB Workspace first, before copying them into the new script-file.

Remal Sylvie, MSc. Thesis, Appendices 21

10. FAQ - How can we create a new “Run Control” button? Copy an existing button, right-click on it and edit it. - How can we create a new subsystem? Copy an existing subsystem, double-click on it and modify its contents as desired. - How can we create a new output variable, from a variable calculated during the simulation? You will need a ‘Goto’ as well as a ‘From’ block to do this. In the part of the model where the variable of interest is calculated, add the Goto block and link the variable to it. Add the From block to the ‘Extra’-subsystem, which is the last one in the top-level subsystem ‘Outputs’. Link the From block as the last entry to the vertical (‘Mux’) bar on the right. After you have done that, the new variable will become available after the simulation as the 33rd output variable, i.e. the 33rd column of ‘yout’. - How can we write daily values of an output variable to an EXCEL-file? Say your variable is column 23 of yout. Then use the MATLAB command xlswrite to write yout(:,23) to an EXCEL-file - How can we run a part of a script? Either comment-out the part of the script you don’t want (by selecting the lines and pressing Ctrl-R), or select the part you want to run and press F9. - How can we follow the evolution of a simulation? CAF2009 is very fast, so we normally do not want to follow the progress of a single simulation. However, it is possible to do so by adding a ‘Scope’-block to the model and feeding the output variable in which we are interested into the Scope. If we want to follow the progress of a large sequence of multiple simulations, we can add a ‘disp’-statement to the script-file, to display, for example, the run-number. - How can we stop a simulation? Press Ctrl-C. - How can we modify a susbsystem? Use the graphical editing that Simulink provides. It is not possible to change code using a text-editor. - How can we define a new routine to export results to EXCEL and call it from a script? Use the MATLAB-command ‘xlswrite’ in the script, or modify and rename an existing m-file for writing to EXCEL, such as ‘fresxls.m’. - How can we create a new figure from a script? Use the ‘plot’-command in the script. For example, after any line in the script where the model is being run (‘sim(model)’), we can add a line ‘plot(tout,yout)’ to plot results. - What is a “asv file”? An “asv file” is the previous version of a file modified in the MATLAB-editor.

Remal Sylvie, MSc. Thesis, Appendices 22

Appendix A. Files in the CAF2007-subdirectory Most files are explained above; further explanation will follow in future versions of this document. bgclouds.jpg caf2007.mdl calcBE_nyears.m calcOutputs7.m change_FAOweather.m change_parameter_BE.m change_parameter.m change_tree_species.m coffee.jpg coffee&tree.jpg CRI11_98_04.txt freadweatherFAO.m freadweatherFAOrainvar.m freadweathern.m fresFAOxls.m fresFile.m fresxls.m fshow_y.m initialise_caf2007.m listStateVariables.m maInit.m parameters_plant_coffee.m parameters_plant_tree_Cordia.m parameters_plant_tree_Erythrina.m parameters_plant_tree_Eucalyptus.m parameters_plant_tree_Gliricidia.m parameters_plant_tree_Inga.m parameters_plant_tree.m parameters_plant_tree_Terminalia.m parameters_site.m plotdouble.m README_CoffeeMar2007.doc res1Table.xls res1.xls res_EXCEL.m resFAOfigs.xls runModel2seriesFigCsoilLeaching.m runModel2seriesFigNminSERIES1.m runModel2seriesFigNsoilSERIES1.m runModel2seriesFigNsysSERIES1.m runModel2seriesFigSoilCloss.m runModel2seriesFigWaterSERIES1.m runModel2seriesFigYieldVol.m runModel2series.m runModel2seriesTreeSpeciesFigCsoilLeaching.m runModel2seriesTreeSpeciesFigNminSERIES1.m runModel2seriesTreeSpeciesFigNsoilSERIES1.m runModel2seriesTreeSpeciesFigNsysSERIES1.m runModel2seriesTreeSpeciesFigSoilCloss.m runModel2seriesTreeSpeciesFigWaterSERIES1.m runModel2seriesTreeSpeciesFigYieldVol.m runModel2seriesTreeSpecies.m runModelTreeSpecies.m script_CAF_FAOweathertest2.m script_CAF_FAOweathertest_rainMA.m script_CAF_SingleFactors.m script_tradeoffs8_2007.m show_balance_Nmin.m show_balance_Nsoil.m show_balance_Nsys.m show_balance_water.m show_weather_2years.m testCO2N.m volcanic_soil_profile.jpg

Remal Sylvie, MSc. Thesis, Appendices 23

Appendix B. FAO weather data files Filename Country Station Location Latitude Longitude Altitude CRI3.AVG Costa Rica 3 Pacayas 09 55 N 083 49 W 1735 m. CRI4.AVG Costa Rica 4 Coliblanco 09 57 N 083 48 W 2200 m. CRI5.AVG Costa Rica 5 Fabio Baudrit 10 01 N 084 16 W 840 m. CRI7.AVG Costa Rica 7 San Jose 09 55 N 084 04 W 1171 m. CRI11.AVG Costa Rica 11 Turrialba Iica 09 53 N 083 38 W 602 m. CRI12.AVG Costa Rica 12 San Isidro Gener. 09 21 N 083 42 W 702 m. CRI14.AVG Costa Rica 14 Ciudad Quesada 10 19 N 084 25 W 650 m. GTM2.AVG Guatemala 2 Santa Margarita 14 30 N 091 00 W 1099 m. GTM3.AVG Guatemala 3 Pena Plata 14 27 N 091 04 W 619 m. GTM5.AVG Guatemala 5 Cuilapa 14 15 N 090 18 W 892 m. GTM6.AVG Guatemala 6 La Morena 14 09 N 090 21 W 739 m. GTM7.AVG Guatemala 7 Huenuetenango 15 19 N 091 28 W 1901 m. GTM8.AVG Guatemala 8 Montelimar 14 55 N 092 01 W 759 m. GTM11.AVG Guatemala 11 Coban 15 29 N 090 19 W 1316 m. GTM13.AVG Guatemala 13 Sanarate 14 46 N 090 12 W 811 m. GTM14.AVG Guatemala 14 La Moka 14 45 N 091 45 W 1079 m. GTM15.AVG Guatemala 15 Beliz 14 39 N 090 37 W 839 m. GTM16.AVG Guatemala 16 Labor Ovalle 14 51 N 091 30 W 2399 m. GTM19.AVG Guatemala 19 Guatemala C.-o.n. 14 35 N 090 31 W 1502 m. GTM20.AVG Guatemala 20 Patzulin 14 39 N 091 25 W 1199 m. GTM21.AVG Guatemala 21 Castaneda 14 37 N 089 25 W 649 m. GTM22.AVG Guatemala 22 El Pito Chocola 14 36 N 091 24 W 970 m. GTM23.AVG Guatemala 23 Florencia 14 33 N 090 40 W 1979 m. NIC1.AVG Nicaragua 1 Managua 12 07 N 086 11 W 53 m.

Remal Sylvie, MSc. Thesis, Appendices 24

APPENDIX 3 : Parameters of CAF2007

Table 1: Parameters for coffee

Parameter Identifier Unit Default Subsystem involving the

parameter Initial development stage DVS0 - 0 Coffee/Phenology Initial biomass leaves CL0 kg C m-2 0,05 Coffee/Biomass Initial biomass storage organs CP0 kg C m-2 0 Coffee/Biomass Initial biomass roots CR0 kg C m-2 0,05 Coffee/Biomass Initial biomass stems plus branches CW0 kg C m-2 0,05 Coffee/Biomass

Carbon concentration in bean dry matter CCONC kg C kg-1

DM 0,47 Outputs

Time between start and full productivity DAYSPLNOP

d 900 Coffee/Phenology

Time between pruning and full productivity DAYSPRNOP

d 365 Coffee/Growth/Sink strenghts

Base temperature for maturation TMATB degC 10 Coffee/Phenology Thermal time to maturation TMATT degC 2780 Coffee/Phenology Maximum specific leaf area SLAMAX m2 kg-1 C 27 Coffee/Foliage Lower bound of the range of SLA expressed as the fraction of the maximum

FSLAMIN - 0,64 Coffee/Foliage

N/C ratio leaves (maximum) NCLMAX kg N kg-1 C 0,06 Coffee/Growth/Gcoffee&Nupt

Coffee/Growth/NdemandOrgans

Lower bound of the range of N/C ratio leaves expressed as the fraction of the maximum

FNCLMIN - 0,64 Coffee/Growth/Gcoffee&Nupt

Coffee/Growth/NdemandOrgans

N/C ratio storage organs NCP kg N kg-1 C 0,033 Coffee/Growth/Gcoffee&Nupt

N/C ratio roots NCR kg N kg-1 C 0,045 Coffee/Growth/NdemandOrgans

Coffee/Prunning&Harvesting

N/C ratio stems and branches NCW kg N kg-1 C 0,006 Coffee/Growth/NdemandOrgans

Coffee/Soil/C&Nsoil/NLITT Minimum of daily rain that triggers flowering after the start of the new year

RAINHI mm d-1 10 Coffee/Phenology

Maximum lifespan of leaves TCCLMAX d 650 Coffee/Senescence Lower bound of range of leaves lifespan expressed as the ratio of maximum

FTCCLMIN - 0,64 Coffee/Senescence

Light extinction coefficient KEXT m2 m-2 0,76 Coffee/Growth/Source

strenght/LUECO2 Average lifespan of roots TCCR d 2000 Coffee/Senescence Rain interception capacity KRNINTC mm 0,25 Belowground Resources/PET

Km for N-uptake KNMIN kg N m-2 0,036 Belowground Resources/Nsupply Vmax for N-uptake KNUPT kg N m-2 d-1 0,002 Belowground Resources/Nsupply

Rubisco content RUBISC g m-2 0,54 Coffee/Growth/Source

strenght/LUECO2 Sink strength for leaves SINKL - 1,2 Coffee/Growth/Sink strenghts Sink strength for storage organs SINKPMAX - 3,6 Coffee/Growth/Sink strenghts Sink strength for roots SINKR - 2,5 Coffee/Growth/Sink strenghts

Sink strength for stems plus branches SINKW - 2,1 Coffee/Growth/Sink strenghts

Transpiration coefficient TRANCO mm d-1 7,1 Belowground

Resources/Water/Etcoffee Growth efficiency YG kg C kg-1 C 0,74 Coffee/Growth/Source strenght ajustement senescence de feuille en fonction de la croissance des fruits

KTCCLGCP m2 d kg-1 0 Coffee/Senescence

Parameter for calculation of storage organs sink strenght KSINKPLAI m2 m-2 99 Coffee/Growth/Sink strenghts/

Seasonal start of bean sink

Parameter for calculation of storage organs sink strenght KSINKPPAR m2 d MJ-1 0,55 Coffee/Growth/Sink strenghts/

Seasonal start of bean sink Phenological stage activating competition for C allocation DVSSINKL - 0,4 Coffee/Growth/Sink strenghts Parameter for calculation of competition for C allocation KSINKLDVS - 0 Coffee/Growth/Sink strenghts

Remal Sylvie, MSc. Thesis, Appendices 25

Table 2. Parameters trees Parameter Identifier Unit Default Subsystem involving the parameter Initial C biomass in branches CB0T kg C m-2 0,1 Trees/C&Ntree/CBT Initial C biomass in leaves CL0T kg C m-2 0,05 Trees/C&Ntree/CLT Initial C biomass in roots CR0T kg C m-2 0,2 Trees/C&Ntree/CRT Initial C biomass in stems CS0T kg C m-2 0,1 Trees/C&Ntree/CST C Allocation to branches FB kg C kg-1 0,23 Trees/Allocation C Maximum Allocation to leaves FLMAX kg C kg-1 0,3 Trees/Allocation C Allocation to stems FS kg C kg-1 0,28 Trees/Allocation N-fixation capacity KNFIX kg N kg-1 C 0,019 Soil2/C&Nsoil/NMIN Rain interception capacity KRNINTCT mm (m2 m-2)-1 0,25 Belowground Resources2/PETtr

N/C ratio leaves (maximum) NCLMAXT kg N kg-1 C 0,089 Trees/Allocation

Growth/Gtree&Nupt Growth/NdemandOrgans

N/C ratio leaves (minimum) FNCLMINT kg N kg-1 C 0,68 Trees/Allocation

N/C ratio roots NCRT kg N kg-1 C 0,042 Trees/Growth/NdemandOrgans

Soil/C&Nsoil/NSOMF

N/C ratio stems and branches NCWT kg N kg-1 C 0,0068 Soil/C&Nsoil/NLITT Trees/C&Ntree/CST

Trees/Gtree&Nupt/NdemandOrgans

Maximum LAI LAIMAXT m 2 m-2 5,6 Trees/Allocation

Specific Leaf Area SLAT m2 kg-1 C 32 Trees/Morphology

Life time of C in branches TCCBT d 2000 Trees/C&Ntree/CBT Maximum life time of C in leaves TCCLMAXT d 800 Trees/C&Ntree/CLT Fraction of minimum life time of C in leaves FTCCLMINT - 0,1 Trees/C&Ntree/CLT Life time of C in roots TCCRT d 4800 Trees/C&Ntree/CRT

Wood density WOODDEN

S kg C m-3 200 Outputs

Biotic growth factor BETA - 0,5 Trees/NPP (NMAX)

Respiration/photosynthesis ratio GAMMA kg kg-1 0,55 Trees/NPP (NMAX)

Light extinction coefficient KEXTT m2 m-2 0,7 Trees/NPP (NMAX)

Light use efficiency LUET kg C MJ-1

PAR 0,00087

Trees/NPP (NMAX) Trees/NPP (NMAX)/ Gain1

Allometric constant linking C biomass in branches to crown area

KCA m2 17 Trees/Morphology

Allometric constant linking C biomass in branches to crown area

KCAEXP - 0,38 Trees/Morphology

Allometric constant linking C biomass in stem to heigh, à 1kg de biomasset

KH m 5,1 Trees/Morphology

Allometric constant linking C biomass in stem to height

KHEXP - 0,31 Trees/Morphology

N-uptake: Minimum N uptake capacity KNMINT kg N m-2 0,0082 Belowground Resources2/Nsupply

N-uptake: N-uptake rate KNUPTT kg N m-2 d-1 0,0013 Belowground Resources2/Nsupply

Shade projection SHADEPROJ m2 m-2 1,2 shading

Maximum temperature difference provided by tree shading

TDIFFMAX ºC 4 shading

Optimum temperature for C assimilation TOPTT ºC 22 Trees/C&Ntree/NPP (Nmax) Total temperature for C assimilation TTOLT ºC 10 Trees/C&Ntree/NPP (Nmax) Transpiration coefficient TRANCOT - 5,9 Belowground Resources/Water

Remal Sylvie, MSc. Thesis, Appendices 26

Table 3. Parameters site, soil, atmosphere and management

Parameter Identifier Unit Default Subsystem involving the parameter Altitude ALT m 1171 - Latitude LAT ºN 9,92 Weather - Trees/Morphology

CO2 concentration of the atmosphere CO2A ppm 380 Coffee/Growth/Source strenght/LUECO2 -

Trees/NPP Slope SLOPE % 5 Soil/Water/Runoff&Drainage Initial amount of litter CLITT0 kg C m-2 0,33 Soil/C&Nsoil/NLITT - CLITT

Initial concentration of organic matter CSOM0 kg C m-2 11 Soil/C&Nsoil/CSOMF-CSOMS-NSOMF-

NSOMS Initial fraction of the soil organic matter which is unstable

FCSOMF0 - 0,64 Soil/C&Nsoil/CSOMF-CSOMS-NSOMF-

NSOMS Initial C/N ratio in litter CNLITT0 kg C kg-1 N 17 Soil/C&Nsoil/NLITT Initial C/N ratio in unstable organic matter CNSOMF0 kg C kg-1 N 12 Soil/C&Nsoil/NSOMF Initial C/N ratio in stable organic matter CNSOMS0 kg C kg-1 N 11 Soil/C&Nsoil/NSOMS Initial values NMIN NMIN0 kg N m-2 0,001 Soil/C&Nsoil/NMIN Pruning coffee: first time DAYPRUNC0 d 1825 Management - Plant/Growth/Sink strenght Pruning coffee: interval DAYPRUNCI d 1825 Management/Coffee Pruning trees: first time DAYPRUNT0 d 182 Management/Tree Pruning trees: interval DAYPRUNTI d 365 Management/Tree Thinning trees: first and second times DAYTHINT d [-1,1000] Management/Tree First day of fertilization DOYFERT(1 d 15 Management/Soil Second day of fertilization DOYFERT(2 d 136 Management/Soil Third day of fertilization DOYFERT(3 d 228 Management/Soil

Pruning coffee: fraction removed FRPRUNC kg kg-1 0,95 Coffee/Growth/Sink strenghts Coffee/Prunning&Harvesting

Pruning trees: fraction removed FRPRUNT kg kg-1 0,5 Management/Tree Thinning trees: fraction removed FRTHINT # #-1 0,5 Management/Tree Fertilization rate NFERT kg N ha-1 [100,100,100] Management/Soil

Initial tree density TREEDENS0 # m-2 0,025 Management/Tree

Trees/C&Ntree Fraction of water content at air dryness FWCAD - 0,01 Belowground Resources/Water Fraction of water content at wilting point FWCWP - 0,41 Belowground Resources/Water

Fraction of water content at field capacity FWCFC - 0,65 Belowground Resources/Water Soil/Water/Runoff&Drainage

Fraction of water content at water saturation FWCWET - 0,87 Belowground Resources/Water

Water content at saturation WCST m3 m-3 0,63 Belowground Resources/Water Soil/Water/Runoff&Drainage

Rooting depth ROOTD m 1 Belowground Resources/Water

Efficiency of organic matter transformation FSOMFSOMS kg kg-1 0,03 Soil/C&Nsoil/CSOMF Soil/C&Nsoil/NSOMF

Efficiency of litter transformation FLITTSOMF kg kg-1 0,75 Soil/C&Nsoil/NLITT Soil/C&Nsoil/CLITT

N-emission rate constant from soil at field capacity KNEMIT kg N kg-1 N

d-1 0,0006 Soil/C&Nsoil/NMIN

Ratio of NMIN in drainage to bulk soil RNLEACH kg N kg-1 N 1 Soil/C&Nsoil/NMIN

Ratio of runoff in bulk soil RRUNBULK kg kg-1 0,05

Soil/C&Nsoil/CLITT/Soil loss Soil/C&Nsoil/CSOMF/Soil loss Soil/C&Nsoil/NLITT/Soil loss

Soil/C&Nsoil/NSOMF/Soil loss Run-off constant, protection by LAI KRUNOFF m2 m-2 0,5 Soil/Water/Runoff&Drainage Time constant for litter decomposition TCLITT d 500 Soil/C&Nsoil/CLITT

Time constant for unstable organic matter decomposition

TCSOMF d 7500 Soil/C&Nsoil/CSOMF

Time constant for stable organic matter decomposition

TCSOMS d 25000 Soil/C&Nsoil/CSOMS

Multiplier for external N-inputs NFERTMULT - 1 Management/Soil

Multiplier for radiation I0MULT - 1 Weather

Multiplier for rain RAINMULT - 1 Weather

Addition-constant for temperature TPLUS ºC 0 Weather

Remal Sylvie, MSc. Thesis, Appendices 27

Table 4: Parameters for each tree species included in the model

Biophysical process Parameters Description Units Generic shade tree

Cordia alliodora

Erythrina poepiggiana

Eucalyptus deglupans

Gliricidia sepium

Inga densiflora

Terminalia ivorensis

N-fixation KNFIX N-fixation capacity kg N kg-1

C 0.019 0 0.019 0 0.019 0.019 0

Wood density WOODDENS Wood density kg C m-3 200 215 125 250 225 200 185

T-sensitivity TOPTT Optimum temperature for C

assimilation ºC 22 22 22 22 22 22 22

TTOLT Total temperature ?? ºC 10 10 10 10 10 10 10 Leaf-fall at drought TRANCOT Transpiration coefficient - 5.9 4 8 4 2 8 2

TCCLMAXT Maximum life time of C in

leaves d 800 730 365 800 365 800 800

FTCCLMINT Fraction of minimum life time

of C in leaves - 0,1 0,1 0.9 0,2 0,1 0,1 0,1

N-content leaves NCLMAXT N/C ratio leaves (maximum) kg N kg-1

C 0.089 0.085 0.1 0.05 0.09 0.065 0.05

FNCLMINT N/C ratio leaves (minimum) kg N kg-1

C 0.68 0,7 0,6 0.68 0.6 0.68 0.68

Crown area FB C Allocation to branches kg C kg-1 0.23 0.23 0.23 0.23 0.23 0.23 0.30

KCA Allometric constant linking C biomass in branches to crown

area m2 17 20 15.8 25 16 17 30

KCAEXP Allometric constant linking C biomass in branches to crown

area - 0.38 0,45 0.55 0.5 0.38 0.4 0.55

Leaf area LAIMAXT Maximum LAI m2 m-2 5,6 5.6 5.6 5.6 4 5.6 5.6

FLMAX C Maximum Allocation to

leaves m2 m-3 0.3 0.3 0.3 0.3 0,25 0.3 0.3

SLAT Specific Leaf Area m2 m-4 32 32 38 20 45 39 32

Growth rate KEXTT Light extinction coefficient m2 m-5 0.7 0.52 0.68 0.58 0.35 0.7 0.7

LUET Light use efficiency m2 m-6 0.00087 0.00087 0.00087 0.00087 0.00087 0.00087 0.00087

Self pruning TCCBT Life time of C in branches m2 m-7 2000 7300 2000 2000 1000 2000 2000

Remal Sylvie, MSc. Thesis, Appendices 28

APPENDIX 4 : Processes identified in conceptual evaluation of CAF2007, subsystems involved, ideal set of data needed and involved parameters involved in each one.

Test

Processes

Variables calculated in CAF2007

Inputs needed in the model Data of comparison

Parameters

involved 1. Flowering activation

Day of flowering activation

Daily rain amount (mm.d-1) Days of flowering

RAINHI

2. Flowering intensity

SINKP PAR shade LAI coffee

Number of flowers or fruits as an indicator of potential productivity

SINKPMAX, KSINKPPAR, KSINKPLAI

A- Coffee Phenology

3. Maturation Maturation day (harvesting day also (DVS=1)

Tmin and Tmax during reproductive stage and PARshade to calculate Tshade

Maturation days TTMATB, TTMATT, TDIFFMAX

B- Production of carbon

1. Carbon production under different type of shading

Potential C growth rate gSHsource (gC m-2 d-1)

LAT, LAI, CO2A, PARshade and Tshade (or PAR and LAITree and SA or CA), coffee current and potential transpiration rates to calculate tranF

Total coffee biomass increment in non limiting conditions at different radiation level

KEXT YG RUBISC (KEXTT)

1. Calculation of current soil evaporation and transpiration rate coffee and tree

Evap, Tran, relative soil water content

Climatic data: VP, WN, Global Radiation , Rain , Tmin, Tmax , PARshade LAI of coffee and tree, and soil variables: Water soil content, Runoff, Drainage

Measured evaporation and transpiration rates of tree and coffee, water content

ROOTD TRANCO FWCAD, FWCWP, FWCFC, FWCWET, WCST KRNINTC KRNINTCT

2. Runoff and drainage

Runoff and drainage

Soil water content, rain arriving to the soil, slope, LAI tot, Evaporation and transpiration rates

Measured run-off and drainage

SLOPE, KRUNOFF, ROOTD, FWCFC, WCST

C- Water dynamics

3. All the plot water dynamics

Transpiration rates of coffee and tree, runoff and drainage and soil water content, CA or SA

Climatic data, LAI Tree, LAI coffee, initial water content, slope

Measured run-off, drainage, coffee and tree transpiration rates

All previous parameters

1. N mineralisation

Mineral N soil content , mineralisation rate

all model inputs because depends of coffee phenology and growth, senescence…

Mineral N soil content, mineralisation rates

TCSOMF TCLITT TCSOMS NCW NCWT NCR NCRT

2. Coffee and tree N-uptake

Coffee and tree N-uptake

all model inputs because depends of coffee phenology and growth, senescence…

N absorption rates KNUPTT KNMINT KNUPT KNMIN

3. N-leaching N-leaching Nmin, soil water content, drainage Measured N-leaching

RNLEACH

4. N-emission N-emission Soil mineral N content, Soil current water content

Measured N-emission

KNEMIT, FWCAD FWCWP FWCFC FWCWET WCST ROOTD

D- N dynamics

5. N and C losses by run-off

N and C losses by run-off

Soil N and C content in litter Run-off

Measured amounts of C and N lost by surface runoff

RRUNBULK ROOTD

Remal Sylvie, MSc. Thesis, Appendices 29

APPENDIX 5: Table of parameters involved for model initialization a) In Turrialba, Costa Rica

Parameter Identifier Unit Default

data Turrialba/

EPMC Turrialba /

TMC Turrialba /

PSMC Turrialba /

EPAC Turrialba /

TAC Turrialba /

PSAC

Initial C biomass in branches CB0T kg C m-2 0,10 0,10 0,10 - 0,10 0,10 - Initial C biomass in leaves CL0T kg C m-2 0,05 0,05 0,05 - 0,05 0,05 - Initial C biomass in roots CR0T kg C m-2 0,20 0,20 0,20 - 0,20 0,20 -

Tree

Initial C biomass in stems CS0T kg C m-2 0,10 0,10 0,10 - 0,10 0,10 - Initial biomass leaves CL0 kg C m-2 0,05 0,05 0,05 0,05 0,05 0,05 0,05

Initial biomass storage organs CP0 kg C m-2 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Initial biomass roots CR0 kg C m-2 0,05 0,05 0,05 0,05 0,05 0,05 0,05

Coffee

Initial biomass stems plus branches CW0 kg C m-2 0,05 0,05 0,05 0,05 0,05 0,05 0,05 Time between start and full productivity DAYSPLNOP d 900 1095 1095 1095 1095 1095 1095

Time between pruning and full productivity DAYSPRNOP d 365 365 365 365 365 365 365 Coffee

production Initial development stage DVS0 - 0 0 0 0 0 0 0

Initial amount of litter CLITT0 kg C m-2 0.33 0,10 0,10 0,10 0,10 0,10 0,10 Initial concentration of C in organic matter CSOM0 kg C m-2 11 31,50 33,74 33,14 31,50 33,74 33,14 Initial fraction of the soil organic matter

which is unstable FCSOMF0 - 0,64 0,49 0,54 0,59 0,49 0,54 0,59

Initial C/N ratio in litter CNLITT0 kg C kg-1 N 17 1 1 1 1 1 1 Initial C/N ratio in unstable organic matter CNSOMF0 kg C kg-1 N 12 36 35 36 36 35 36

Initial values NMIN NMIN0 kg N m-2 0,001 0,001 0,001 0,001 0,001 0,001 0,001

Soil

Initial C/N ratio in stable organic matter CNSOMS0 kg C kg-1 N 11 36 35 36 36 35 36 Pruning coffee: first time DAYPRUNC0 d 1825 1110 1110 1110 1110 1110 1110 Pruning coffee: interval DAYPRUNCI d 1825 365 365 365 365 365 365

Pruning coffee: fraction removed FRPRUNC kg kg-1 0.95 0,22 0,26 0,26 0,22 0,26 0,27 Pruning trees: first time DAYPRUNT0 d 182 365 1095 - 365 1095 - Pruning trees: interval DAYPRUNTI d 365 182 365 - 182 365 -

Pruning trees: fraction removed FRPRUNT kg kg-1 0.5 0,40 0,10 - 0,60 0,10 - Thinning trees: first and second times DAYTHINT d [-1,1000] [2700,3075] [2586;2982] - [2700,3075] [2586;2982] -

Thinning trees: fraction removed FRTHINT # #-1 0.5 0.5 0,50 - 0.15 0,50 - Initial tree density TREEDENS0 # m-2 0.025 0,04 0,04 - 0,04 0,04 -

First day of fertilization DOYFERT(1 d 15 15 15 15 15 15 15 Second day of fertilization DOYFERT(2 d 136 136 136 136 136 136 136 Third day of fertilization DOYFERT(3 d 228 350 350 350 350 350 350

Management

Fertilization rate NFERT kg N ha-1 [100,100,100] [50,50,50] [50,50,50] [50,50,50] [100,100,100] [100,100,100] [100,100,100]

Latitude LAT ºN 9.92 9.53 9.53 9.53 9.53 9.53 9.53 Site

Slope SLOPE % 5,00 5,00 5,00 5,00 5,00 5,00 5,00

Remal Sylvie, MSc. Thesis, Appendices 30

b) In Masatepe, Nicaragua

Parameter Identifier Unit Default data Masatepe /

IGMC Masatepe /

PSMC Masatepe /

IGAC Masatepe /

PSAC

Initial C biomass in branches CB0T kg C m-2 0,10 0,004 - 0,004 - Initial C biomass in leaves CL0T kg C m-2 0,05 0,008 - 0,008 - Initial C biomass in roots CR0T kg C m-2 0,20 0,002 - 0,002 -

Tree

Initial C biomass in stems CS0T kg C m-2 0,10 0,003 - 0,003 - Initial biomass leaves CL0 kg C m-2 0,05 0,05 0,05 0,05 0,05

Initial biomass storage organs CP0 kg C m-2 0,00 0,00 0,00 0,00 0,00 Initial biomass roots CR0 kg C m-2 0,05 0,05 0,05 0,05 0,05

Coffee

Initial biomass stems plus branches CW0 kg C m-2 0,05 0,05 0,05 0,05 0,05 Time between start and full productivity DAYSPLNOP d 900 1095 1095 1095 1095

Time between pruning and full productivity DAYSPRNOP d 365 365 365 365 365 Coffee production Initial development stage DVS0 - 0 0 0 0 0

Initial amount of litter CLITT0 kg C m-2 0.33 0,10 0,10 0,10 0,10 Initial concentration of C in organic matter CSOM0 kg C m-2 11 21,88 24,44 30,41 32,07 Initial fraction of the soil organic matter

which is unstable FCSOMF0 - 0,64 0,71 0,65 0,75 0,67

Initial C/N ratio in litter CNLITT0 kg C kg-1 N 17 1,00 1,00 1,00 1,00 Initial C/N ratio in unstable organic matter CNSOMF0 kg C kg-1 N 12 7 9 7,5 15

Initial values NMIN NMIN0 kg N m-2 0,001 0,001 0,001 0,001 0,001

Soil

Initial C/N ratio in stable organic matter CNSOMS0 kg C kg-1 N 11 7 9 7,5 15 Pruning coffee: first time DAYPRUNC0 d 1825 1925 1925 1925 1925 Pruning coffee: interval DAYPRUNCI d 1825 365 365 365 365

Pruning coffee: fraction removed FRPRUNC kg kg-1 0.95 0,14 0,17 0,13 0,20 Pruning trees: first time DAYPRUNT0 d 182 1395 - 1395 - Pruning trees: interval DAYPRUNTI d 365 270 - 270 -

Pruning trees: fraction removed FRPRUNT kg kg-1 0.5 0,35 - 0,35 - Thinning trees: first and second times DAYTHINT d [-1,1000] [1945;2675] - [1945;2675] -

Thinning trees: fraction removed FRTHINT # #-1 0.5 0,5 - 0,5 - Initial tree density TREEDENS0 # m-2 0.025 0,07 - 0,07 -

First day of fertilization DOYFERT(1 d 15 180 180 180 180 Second day of fertilization DOYFERT(2 d 136 270 270 270 270 Third day of fertilization DOYFERT(3 d 228 300 300 300 300

Managment

Fertilization rate NFERT kg N ha-1 [100,100,100] [50,50,50] [50,50,50] [100,100,100] [100,100,100] Latitude LAT ºN 9.92 11,91 11,91 11,91 11,91

Site Slope SLOPE % 5,00 5,00 5,00 5,00 5,00

Remal Sylvie, MSc. Thesis, Appendices 31

APPENDIX 6: Coefficients of variation obtained for the model inputs and for each of the 7 chosen outputs

Table 1: coefficients of variation obtained for the initial state variables for each of the 7 chosen outputs. In orange, coefficient of variation with value > 0,1.

Initial state variables - Soil Initial state variables - Tree Initial state variables - Coffee CLITT0 CSOM0 FCSOMF0 CNLITT0 CNSOMF0 CNSOMS0 CBOT CLOT CROT CSOT CL0 CP0 CR0 CW0 YIELD 0,0064 0,1979 0,0969 0,0103 0,1099 0,0406 0,0129 0,0393 0,0510 0,0000 0,0229 0,0529 0,0581 0,0001 WOOD 0,0154 0,3468 0,1636 0,0301 0,2564 0,0694 0,0307 0,1087 0,0927 0,1309 0,0174 0,0000 0,0542 0,0000 NEMISSION 0,0222 0,4521 0,1502 0,0465 0,6762 0,1484 0,0045 0,0090 0,0176 0,0000 0,0163 0,0000 0,0486 0,0003 NLEACHING 0,0223 0,4610 0,1541 0,0469 0,6873 0,1505 0,0041 0,0074 0,0182 0,0000 0,0135 0,0000 0,0476 0,0003 CSEQUESTR 0,0094 0,2810 0,0659 0,0588 0,5082 0,1466 0,0140 0,0614 0,0452 0,0887 0,0321 0,0095 0,0765 0,0043 RUNOFF 0,0014 0,1315 0,2655 0,0360 0,2554 0,0694 0,0075 0,0498 0,0147 0,0000 0,1468 0,0000 0,0977 0,0014 DRAINAGE 0,0004 0,0046 0,0018 0,0008 0,0062 0,0022 0,0008 0,0048 0,0009 0,0000 0,0014 0,0000 0,0004 0,0000

MEAN 0,0111 0,2679 0,128279 0,03278 0,3570791 0,0895876 0,011 0,0401 0,03434 0,0314 0,0358 0,0089 0,0547 0,0009

Table 2.1: coefficients of variation obtained for the tree parameters for each of the 7 chosen outputs. In orange, coefficient of variation with value > 0,1. BETA FB FLMAX FS GAMMA KCA KCAEXP KEXTT KH KHEXP KNFIX KNMINT KNUPTT KRNINTCT LAIMAXT LUET NCLMAXT FNCLMINT NCRT

YIELD 0,011 0,136 0,021 0,034 0,092 0,201 0,269 0,135 0,000 0,000 0,043 0,210 0,227 0,001 0,113 0,058 0,050 0,005 0,056 WOOD 0,031 0,887 0,005 0,153 0,227 0,716 0,338 0,325 0,000 0,000 0,128 0,714 0,790 0,000 0,202 0,028 0,814 0,011 0,325 NEMISSION 0,008 0,114 0,006 0,022 0,070 0,141 0,114 0,059 0,000 0,000 0,490 0,130 0,143 0,001 0,059 0,016 0,036 0,002 0,043 NLEACHING 0,008 0,115 0,006 0,022 0,070 0,141 0,115 0,052 0,000 0,000 0,495 0,133 0,145 0,001 0,062 0,019 0,036 0,002 0,043 CSEQUESTR 0,025 0,528 0,004 0,114 0,189 0,478 0,253 0,204 0,000 0,000 0,198 0,439 0,489 0,001 0,125 0,016 0,388 0,008 0,292 RUNOFF 0,004 0,152 0,018 0,003 0,029 0,178 0,150 0,041 0,000 0,000 0,071 0,143 0,155 0,004 0,100 0,082 0,119 0,003 0,082 DRAINAGE 0,000 0,006 0,003 0,000 0,001 0,009 0,017 0,021 0,000 0,000 0,004 0,003 0,003 0,005 0,008 0,010 0,002 0,000 0,004 MEAN 0,012 0,277 0,009 0,050 0,097 0,266 0,179 0,119 0,000 0,000 0,204 0,253 0,279 0,002 0,096 0,033 0,206 0,004 0,121

Table 2.2: coefficients of variation obtained for the tree parameters for each of the 7 chosen outputs. In orange, coefficient of variation with value > 0,1. NCWT SHADEPROJ SLAT TCCBT TCCLMAXT FTCCLMINT TCCRT TRANCOT WOODDENS TDIFFMAX TOPTT TTOLT MEAN YIELD 0,018 0,144 0,141 0,004 0,025 0,000 0,010 0,001 0,000 0,029 0,075 0,015 0,068 WOOD 0,139 0,067 0,563 0,010 0,052 0,000 0,019 0,003 0,204 0,011 0,309 0,042 0,229 NEMISSION 0,013 0,055 0,093 0,004 0,002 0,000 0,005 0,001 0,000 0,007 0,059 0,010 0,055 NLEACHING 0,012 0,064 0,094 0,003 0,002 0,000 0,005 0,001 0,000 0,009 0,061 0,011 0,056 CSEQUESTR 0,127 0,107 0,362 0,009 0,045 0,000 0,012 0,003 0,000 0,016 0,226 0,034 0,151 RUNOFF 0,038 0,356 0,132 0,005 0,029 0,000 0,005 0,000 0,000 0,002 0,045 0,006 0,063 DRAINAGE 0,002 0,029 0,005 0,000 0,003 0,000 0,000 0,000 0,000 0,013 0,001 0,000 0,005 MEAN 0,050 0,118 0,199 0,005 0,023 0,000 0,008 0,001 0,029 0,012 0,111 0,017 0,090

Remal Sylvie, MSc. Thesis, Appendices 32

Table 3.1: coefficients of variation obtained for the coffee parameters for each of the 7 chosen outputs. In orange, coefficient of variation with value > 0,1.

KEXT CCONC DAYSPLNOP DAYSPRNOP KNMIN KNUPT KRNINTC NCLMAX FNCLMIN NCP NCR NCW RAINHI RUBISC SINKL SINKPMAX SINKR SINKW

YIELD 0,141 0,180 0,282 0,084 0,621 0,654 0,010 0,061 0,002 0,121 0,229 0,114 0,002 0,133 0,161 0,332 0,236 0,269 WOOD 0,032 0,000 0,003 0,001 0,207 0,211 0,009 0,004 0,001 0,003 0,040 0,022 0,000 0,137 0,017 0,003 0,047 0,052 NEMISSION 0,079 0,000 0,003 0,010 0,280 0,288 0,019 0,036 0,002 0,028 0,049 0,013 0,000 0,199 0,164 0,009 0,026 0,144 NLEACHING 0,081 0,000 0,004 0,010 0,279 0,287 0,016 0,035 0,002 0,031 0,049 0,013 0,000 0,198 0,158 0,009 0,025 0,143 CSEQUESTR 0,130 0,000 0,039 0,031 0,769 0,818 0,024 0,103 0,005 0,055 0,384 0,179 0,000 0,150 0,253 0,078 0,102 0,055 RUNOFF 0,036 0,000 0,012 0,022 0,416 0,428 0,052 0,084 0,008 0,020 0,215 0,106 0,000 0,116 0,421 0,028 0,222 0,165 DRAINAGE 0,000 0,000 0,000 0,000 0,005 0,006 0,050 0,001 0,000 0,001 0,002 0,000 0,000 0,002 0,003 0,000 0,002 0,000 MEAN 0,071 0,026 0,049 0,022 0,368 0,384 0,026 0,046 0,003 0,037 0,138 0,064 0,000 0,134 0,168 0,066 0,094 0,118

Table 3.2: coefficients of variation obtained for the coffee parameters for each of the 7 chosen outputs. In orange, coefficient of variation with value > 0,1.

SLAMAX FSLAMIN TCCLMAX FTCCLMIN TCCR TMATB TMATT TRANCO YG DVSSINKL KSINKLDVS KSINKPLAI KSINKPPAR KTCCLGCP MEAN YIELD 0,038 0,000 0,045 0,00015 0,045 0,223 0,103 0,005 0,175 0,00000 0,048 0,067 0,208 0,247 0,151 WOOD 0,008 0,000 0,011 0,00001 0,031 0,001 0,001 0,001 0,033 0,00000 0,004 0,001 0,002 0,015 0,028 NEMISSION 0,032 0,000 0,039 0,00008 0,032 0,004 0,002 0,003 0,104 0,00000 0,045 0,002 0,004 0,083 0,053 NLEACHING 0,031 0,000 0,039 0,00008 0,031 0,004 0,002 0,002 0,104 0,00000 0,045 0,001 0,004 0,084 0,053 CSEQUESTR 0,054 0,000 0,064 0,00015 0,042 0,045 0,021 0,004 0,194 0,00000 0,039 0,013 0,038 0,215 0,122 RUNOFF 0,148 0,000 0,159 0,00035 0,029 0,014 0,006 0,002 0,082 0,00000 0,118 0,005 0,012 0,173 0,097 DRAINAGE 0,001 0,000 0,003 0,00000 0,000 0,000 0,000 0,001 0,000 0,00000 0,003 0,000 0,000 0,002 0,003 MEAN 0,045 0,000 0,051 0,00012 0,030 0,042 0,019 0,003 0,099 0,00000 0,043 0,013 0,038 0,117 0,072

Table 4: coefficients of variation obtained for the soil parameters for each of the 7 chosen outputs. In orange, coefficient of variation with value > 0,1. FLITTSOMF FWCAD FWCWP FWCFC FWCWET FSOMFSOMS KNEMIT RNLEACH RRUNBULK KRUNOFF TCLITT TCSOMF TCSOMS WCST MEAN

YIELD 0,0200 0,0001 0,0796 0,7795 0,0000 0,0573 0,0271 0,0207 0,2520 0,0007 0,0027 0,1068 0,0292 0,0406 0,1012 WOOD 0,0283 0,0001 0,1516 0,7859 0,0000 0,0897 0,0331 0,0542 0,4509 0,0013 0,0006 0,2140 0,0730 0,0604 0,1388 NEMISSION 0,0606 0,0001 0,0451 0,2902 0,0000 0,1073 1,2356 0,1631 0,1135 0,0021 0,0002 0,3275 0,1797 0,1261 0,1894 NLEACHING 0,0613 0,0001 0,1283 0,4729 0,0000 0,1095 0,0728 0,0854 0,1261 0,0154 0,0012 0,3355 0,1833 0,0897 0,1201 CSEQUESTR 0,1200 0,0002 0,3147 14,5569 0,0000 0,0298 0,0922 0,0983 0,1454 0,0470 0,0017 0,1293 0,0554 0,1459 1,1033 RUNOFF 0,0482 0,0000 0,1561 0,7138 0,0000 0,0976 0,0622 0,0641 0,0893 0,3765 0,0041 0,2527 0,0687 0,0875 0,1443 DRAINAGE 0,0009 0,0003 0,0225 0,0126 0,0000 0,0017 0,0006 0,0019 0,0079 0,0216 0,0000 0,0040 0,0025 0,0048 0,0058 MEAN 0,0485 0,0001 0,1283 2,5160 0,0000 0,0704 0,2177 0,0697 0,1277 0,0664 0,0015 0,1957 0,0845 0,0793 0,2576

Remal Sylvie, MSc. Thesis, Appendices 33

APPENDIX 7 : Observed and simulated coffee annual yields in both modelling

situations

Figure 1: Observed and simulated coffee annual yields under full sun, in Turrialba DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

Figure 2: Observed and simulated coffee annual yields under Erythrina poepiggiana, in Turrialba DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

Remal Sylvie, MSc. Thesis, Appendices 34

Figure 3: Observed and simulated coffee annual yields under Terminalia amazonia, in Turrialba DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

Remal Sylvie, MSc. Thesis, Appendices 35

Figure 4: Observed and simulated coffee annual yields under full sun, in Masatepe DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

Figure 5: Observed and simulated coffee annual yields under Inga laurina, in Masatepe DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

Remal Sylvie, MSc. Thesis, Appendices 36

APPENDIX 8: Simulated vs. Observed coffee annual yields

Figure 1: Simulated vs. Observed coffee annual yields, under Erythrina poepiggiana, Turrialba DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

Figure 2: Simulated vs. Observed coffee annual yields, under Terminalia amazonia, Turrialba DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

Remal Sylvie, MSc. Thesis, Appendices 37

Figure 3: Simulated vs. Observed coffee annual yields, under full sun, Turrialba DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

Remal Sylvie, MSc. Thesis, Appendices 38

Figure 4: Simulated vs. Observed coffee annual yields, under Inga laurina, Masatepe DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional

Figure 5: Simulated vs. Observed coffee annual yields, under full sun, Masatepe DEF: model with default settings of inputs, MES: model with measured inputs, MC: Moderate conventional, IC: Intensive Conventional