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e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 373–382

avai lab le at www.sc iencedi rec t .com

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practical approach for assessing the sensitivity of thearbon Budget Model of the Canadian Forest Sector

CBM-CFS3)

homas Whitea,∗, Nancy Luckaib, Guy R. Larocquec, Werner A. Kurza, Carolyn Smytha

Natural Resources Canada, Canadian Forest Service, Pacific Forestry Centre, 506 West Burnside Road, Victoria, BC, V8Z 1M5 CanadaFaculty of Forestry and the Forest Environment, Lakehead University, Thunder Bay, ON, P7B 5E1 CanadaNatural Resources Canada, Canadian Forest Service, Laurentian Forestry Centre,055 du P.E.P.S., Stn. Ste. Foy, Quebec, QC, G1V 4C7 Canada

r t i c l e i n f o

rticle history:

ublished on line 26 August 2008

eywords:

ncertainty analysis

oreal forest

orest carbon cycle

ead organic matter

a b s t r a c t

We present a case study approach to assessing the sensitivity of the dead organic matter sub-

module of the operational-scale version of the Carbon Budget Model of the Canadian Forest

Sector (CBM-CFS3) to variation in model parameters controlling inputs to and throughput in

this module. Parameters examined included those controlling biomass growth and turnover,

dead organic matter decay and model initialization. Our approach is based on the use of sen-

sitivity and uncertainty analysis software packages that are freely available on the Internet

and accessible to model users. We simulated four different landscapes, three with different

species but the same rotation length and one using the same species with two different rota-

tion lengths, to evaluate interactions between modelled scenarios and assumptions about

parameter variability. We assessed the impacts of parameter variation on stocks and fluxes.

The model was sensitive to variation in parameters controlling the foliage and fine root

pathways, but the sensitivity differed depending on whether a softwood or hardwood land-

scape was being simulated. Our findings indicate that inferences drawn from sensitivity

and uncertainty analysis of forest carbon models are specific to the landscapes and time

horizons being modelled.

Crow

Increasingly, the importance of uncertainty estimates to

. Introduction

he potential role of forests and forest management in mit-gating the build-up of atmospheric carbon (C) is recognizedn the scientific literature (e.g., Ceulemans et al., 1999; Agrennd Hyvonen, 2003; Masera et al., 2003; Lal, 2005; Nabuurst al., 2007) and through domestic and international policy

easures. Quantifying the losses and gains of C in forest

cosystems in support of reporting requirements (e.g., Kyotorotocol) is, however, a complex undertaking. Carbon account-

∗ Corresponding author.E-mail address: thwhite@nrcan.gc.ca (T. White).

304-3800/$ – see front matter. Crown Copyright © 2008 Published by Eoi:10.1016/j.ecolmodel.2008.07.012

n Copyright © 2008 Published by Elsevier B.V. All rights reserved.

ing must consider C stocks in several above- and below-groundpools, including vegetation, dead organic matter (DOM) andsoils, and stock changes in these pools caused by multipleand interacting processes including biomass growth, litterfall,turnover, and natural and anthropogenic disturbances such asfire or harvesting.

model interpretation is recognized by C model developers, pol-icy makers and buyers of C credits (Smith and Heath, 2001;Peltoniemi et al., 2006) and required under various report-

lsevier B.V. All rights reserved.

374 e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 373–382

Fig. 1 – Basic framework of CBM-CFS3 illustrating the pathways of carbon from foliage, stem, other, and root biomasshum

od co

through the litter (medium, fast and very fast DOM) and soilindicate pools that are separated into softwood and hardwo

ing and trading schemes (e.g., Intergovernmental Panel onClimate Change (IPCC) 2006 Guidelines for National Green-house Gas Inventories and California’s Climate Registry ForestProject Protocol). Despite this, the inclusion of uncertaintyestimates in the predictions of process-based models of for-est ecosystems is not common practice (Smith and Heath,2001; Verbeeck et al., 2006). The particular difficulties involvedin generating uncertainty estimates for forest C cycle mod-els (Peltoniemi et al., 2006) include (1) imperfect knowledgeof the systems being modelled, (2) lack of coverage and com-pleteness of data used to drive the models, (3) the large scaleand range of variability of natural systems and (4) computa-tional limits (Parysow et al., 2000; Linkov and Burmistrov, 2003;Garbey et al., 2006). The latter, in particular, confounds analready complex problem, requiring model users and develop-ers to seek computationally efficient methods. For this reason,we present a case study based on the use of the GEM-SA(Centre for Terrestrial Carbon Dynamics (CTCD)1; O’Hagan,2006) and SimLab (Saltelli et al., 2004) software packages toinvestigate the sensitivity of the Carbon Budget Model ofthe Canadian Forest Sector (CBM-CFS3) to variation in modelparameters controlling biomass growth and turnover, DOMdecay and the historical disturbance regime.

The Canadian Forest Service is developing the NationalForest Carbon Monitoring, Accounting and Reporting System(NFCMARS) to support Canada’s commitments for reportingon sources and sinks of greenhouse gases in Canada’s forestand to assist with development of forest policy by enablingforward-looking analyses (Kurz and Apps, 2006; Kurz et al.,2008). The operational-scale version of CBM-CFS3 allows forest

managers to assess the impacts of alternative forest manage-ment strategies on the C budget of their landscapes. Details onNFCMARS and CBM-CFS3 are available elsewhere (Kurz and

1 http://www.tonyohagan.co.uk/academic/GEM/index.html(accessed 6 September 2007).

ified organic matter (slow DOM) pools. Shaded boxesmponents.

Apps, 2006; Kurz et al., 2002; Kurz and Apps, 1999; Kurz etal., 1992). However, neither the NFCMARS nor the operational-scale CBM-CFS3 has readily available options to understandand evaluate uncertainties in these systems.

CBM-CFS3 simulates the dynamics of several C pools inforest ecosystems (Fig. 1) utilizing a mixture of default anduser-defined inputs. Although primarily designed to assessC dynamics at the operational-scale, it can be applied atthe stand level. It has been used to assess C stocks andchanges on national (Kurz and Apps, 1999) and regional(Banfield et al., 2002) scales, to assess past C stock changesand to evaluate the impact of management options onfuture changes (Kurz et al., 1998). Although specific sub-routines to provide uncertainty estimates can be developedand incorporated in the model, the computation timeusing conventional analysis techniques (e.g., Monte Carlo)would be prohibitive. Thus, alternative approaches must beconsidered.

The objectives of our study were to (1) identify moretractable method or methods of sensitivity analyses that canbe applied by users of the operational-scale CBM-CFS3 and (2)determine if sensitivity analyses can identify areas where fur-ther improvements in the representation of DOM dynamics inCBM-CFS3 can be made.

2. Materials and methods

In the CBM-CFS3 modelling framework, a default set of param-eters is provided, but these can be changed by users dependingon their circumstances. Our case study focused on the impor-tant parameters governing stock changes in the biomass andDOM pools of CBM-CFS3. We examined the sensitivity ofmodel outputs for total DOM stocks and stock changes to vari-

ation in these input parameters. In CBM-CFS3, DOM includesall dead organic compounds in the ecosystem and can berequested as a single output value (“DOM”). More specifically,DOM is the sum of “Deadwood” (C in fast above-ground (AG),

e c o l o g i c a l m o d e l l i n g 2 1

Fig. 2 – Yield curves for black spruce, jack pine andtrembling aspen that were used to simulate carbonaccounting in forests located in northwestern Ontario. Thevertical lines delineate the range in the assumed historicd

fh(fffi

sj(dasyuf(tasp(rdw(ttrFeplbDdb

porate change over time to variation in the input parameters.We chose to evaluate model sensitivity using the Pearson cor-

isturbance return interval (between 65 and 85 years).

ast below-ground (BG), medium DOM, softwood (SW) andardwood (HW) stem snag, SW and HW branch snag), “Litter”

C in very fast AG and slow AG pools), and “Soil C” (C in veryast BG and slow BG pools). Each pool receives C originatingrom vegetative biomass (stems, branches, foliage, coarse andne roots).

We selected three common, commercially importantpecies: Sb, black spruce (Picea mariana (Mill.) B.S.P.); Pj,ack pine (Pinus banksiana Lamb.) and At, trembling aspenPopulus tremuloides Michx.) that would allow us to observeifferences associated with stand age, growth rate, biomassllocation and turnover rates. In CBM-CFS3, the silvics ofpecies are described through model inputs such as empiricalield tables, allometric equations, and biomass turnover val-es. Yield tables define the merchantable volume production

or each species while species-specific allometric equationsBoudewyn et al., 2007) convert merchantable volume produc-ion into above-ground biomass by component. Productivitynd biomass allocation differed substantially among the threepecies (Figs. 2 and 3). Turnover parameters specify the pro-ortion of a biomass pool that turns over annually. Hardwoods

At) and softwoods (Sb and Pj) have specific foliage turnoverates (see Table 1). DOM turnover rates, representing decay,efine the rate of annual transfers from one C pool to the next,ith a certain proportion being released to the atmosphere

Table 1). Base decay rates (BDR) are modified by tempera-ure following a Q10 relationship. Proportions to air determinehe amount of C lost through heterotrophic respiration. Theemainder is transferred to one of the slow DOM pools (seeig. 1). For example, if the decay from the Fast BG pool isqual to 100 g (calculated as the amount of C in the Fast BGool multiplied by the Fast BG BDR), 83 g (or 83%) would be

ost through respiration (transferred to air) and 17 g would

e moved to the Slow BG pool. Ultimately all non-respiredOM C reaches the BG Slow pool (Fig. 1). Information aboutisturbance-related transfers is provided through a distur-ance matrix (Kurz et al., 1992), which defines a one-time

9 ( 2 0 0 8 ) 373–382 375

transfer from biomass to wood products, gasses, and DOMpools that is applied at the time of disturbance. Following astand-replacing disturbance, the age of a stand is reset to 0and the stand begins to grow again following the same growthcurve. All three species scenarios were run using a rotationage of 138 years. Sb was also run using a 200-year rotation.In all scenarios, stands were single-species, even-aged with auniform age-class distribution (based on 20-year age-classes)across the landscape. All scenarios had the same total forestarea.

Twenty model parameters related to DOM were selectedand a range of variation was specified based on literature rel-evant to boreal and temperate forests and expert judgement(Table 1). If the default value for a parameter in CBM-CFS3 wasoutside the range reported in other publications, the range wasexpanded to include the CBM-CFS3 default value. A uniformdistribution was assumed for each parameter for the range ofvariation identified. The “stand-replacing disturbance inter-val” parameter specifies the historic disturbance regime andis only used in a sub-routine in the CBM-CFS3 framework,called “makelist”, that initializes the soil and DOM pools usinga spin-up procedure that takes into consideration past distur-bances, site productivity, the most recent disturbance, and thecurrent age of the stand (Kurz and Apps, 1999). The remain-ing parameters (e.g., base decay rates, biomass turnover rates,transfers to air) are common to the “makelist” spin-up routineand the CBM-CFS3, regardless of species. Species are identi-fied as either hardwoods (HW) or softwoods (SW) and someparameters (such as biomass allocation and litterfall rates) areadjusted accordingly.

GEM-SA was developed by researchers at the Centre for Ter-restrial Carbon Dynamics and has been used to quantify theuncertainties associated with the terrestrial carbon balancein England and Wales (Kennedy et al., 2006). GEM-SA includesa statistical emulator, based on the application of Bayesianstatistics, designed to simplify the task of performing sensi-tivity and uncertainty analyses of complex computer models(CTCD2, O’Hagan, 2006). A Maximin Latin Hypercube or MLH(Morris and Mitchell, 1995) design was used to generate 250sets of 20 input points covering the full range of variation spec-ified in Table 1. Each set was run through CBM-CFS3 once, foreach species/age scenario (total of 1000 runs). For each sce-nario, the total DOM stock values at scenario initialization (i.e.,after the “makelist” spin-up sub-routine was run and prior toimposition of the full scenario) were used to train the emu-lator. The emulator was then run to provide results for thesensitivity analysis. GEM-SA calculated the contributions ofthe parameters as main effects to the overall variation.

Although GEM-SA could have been used at other pointsin the scenario, each time-point required re-training and re-running of the emulator. We, therefore, used the SimLabsoftware package (Saltelli et al., 2004) to assess the sensitiv-ity of CBM outputs from the initial 250 runs. SimLab offersvisualization tools as well as statistical metrics that can incor-

relation coefficient function in SimLab, which allowed us to

2 Ibid.

376 e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 373–382

her b

Fig. 3 – C content in merchantable biomass, coarse roots, ot

rank parameters by importance for each time step in the sim-ulation.

3. Results

Variation in the input parameters accounted for about 97%of the explained variance in total DOM at the completion ofthe “makelist” spin-up phase in the 138-year rotation scenar-ios for black spruce (Sb138), and trembling aspen (At138) and200-year rotation scenario for black spruce (Sb200) (Table 2).The remainder (e.g., for Sb138, 3%) represents unexplainedvariance, some of which may be due to interactions. Resultstherefore indicated that joint effects between parameterswere negligible. This is not unexpected as the parametersselected for the sensitivity analysis are independent in CBM;that is, no parameter value is determined or modified by the

value of another parameter in the model. Additionally, no cor-relations were included in the input design.

The five parameters with the greatest influence on initialconditions were relatively consistent across all four scenar-

iomass (tops, stumps and branches), fine roots and foliage.

ios (Table 2). In all scenarios, total DOM at the beginning ofthe simulation was most sensitive to variation in the slowbelow-ground base decay rate (S BG BDR), generally followedby the very fast BG proportion to air (VF BG PA). Other impor-tant parameters included the fine root turnover (FRT), slowabove-ground (AG) BDR and very fast AG PA, with their relativerankings differing somewhat between scenarios. The historicstand-replacing disturbance interval was important in boththe spruce and aspen scenarios but was not a factor in thejack pine scenario.

The sensitivity of the total DOM stock change, as opposedto stocks, to variation in input parameters was evaluatedusing SimLab. The slow above- and below-ground base decayrates, very fast above-ground proportion to air, historical dis-turbance interval, stem annual turnover, and mean annualtemperature emerged as important parameters for most sce-narios at time steps 10 and 250 years (Table 3). Whereas the

Slow AG BDR was ranked in second or third place at boththe beginning and end of the simulations, the slow BG BDRgreatly influenced the stock change at the end of the simula-tion, but was unimportant at the beginning. The VF BG PA also

e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 373–382 377

Table 1 – Variation in the parameters of interest for an uncertainty analysis using the CBM-CFS3 model in northwesternOntario, Canada

Parameters Default Minimum Maximum Reference/comments

Branch turnover rate 0.04 0.012 0.04 Adapted from Peltoniemi et al. (2006)Coarse root turnover rate 0.02 0.007 0.023 Peltoniemi et al. (2006)Fast above-ground base decay rate 0.1435 0.1 0.29 Adapted from Liski et al. (2005)Fast above-ground proportion of C respired 0.83 0.7 0.9 Liski et al. (2005) and Smyth (submitted)Fast below-ground base decay rate 0.1435 0.1 0.29 Adapted from Liski et al. (2005)Fast below-ground proportion of C respired 0.83 0.7 0.9 Liski et al. (2005) and C. Smyth, personal

communicationFine root turnover 0.641 0.6 0.92 Adapted from Peltoniemi et al. (2006)Foliage turnover rate for hardwoodsa 0.95 0.8455 0.999Foliage turnover rate for softwoodsa 0.1 0.1 0.2 Adapted from Peltoniemi et al. (2006)Mean annual temperature −0.435 −3.555 2.684 Mean ± 2S.D. for ecological unitMedium base decay rate 0.0374 0.01 0.08 Adapted from Yatskov et al. (2003) and

Bond-Lamberty et al. (2003)Medium proportion of C respired 0.83 0.7 0.9 Liski et al. (2005)Slow above-ground base decay rate 0.015 0.002 0.02 Liski et al. (2005)Slow below-ground base decay rate 0.0033 0.0008 0.004 Adapted from Liski et al. (2005)Stand-replacing disturbance interval 75 65 85 Used only in the spin-up sub-routineStem annual turnover 0.005 0.003 0.007 Peltoniemi et al. (2006), Hennon and

McClellan (2003)Stem snag turnover 0.032 0.032 0.14 Based on 1/2 life or rates reported in

Vanderwel et al. (2006), Wilson andMcComb (2005), Russell et al. (2006),Garber et al. (2005)

Very fast above-ground base decay rate 0.355 0.284 0.426 ±20%Very fast above-ground proportion of C respired 0.815 0.742 0.888 Smyth (submitted)Very fast below-ground base decay rate 0.5 0.4 0.6 ±20%Very fast below-ground proportion of C respired 0.83 0.55 0.85

Unit for turnover rates and decay rate is yr−1.a None of the scenarios included both softwoods and hardwoods.

Table 2 – Sensitivity of initial DOM stocks to parameter variation

Parameter Variance (%)

Sb138 Pj138 At138 Sb200

Branch turnover rate 0.24 0.23 0.4 0.3Coarse root turnover 0.05 0.07 0.03 0.08Fast above-ground base decay rate 0.01 0.01 0.25 0.01Fast above-ground proportion to air 0.32 0.3 0.67 0.36Fast below-ground base decay rate 0.01 0.02 0.02 0.02Fast below-ground proportion to air 0.13 0.09 0.22 0.12Fine root turnover 2.92a 3.53 1.26 3.16Foliage turnover rate (softwoods or hardwoods) 0.68 0.26 0.08 0.94Mean annual temperature 0.87 0.7 0.86 1.08Medium base decay rate 0.14 0.15 0.09 0.18Medium proportion to air 0.75 0.72 0.56 0.75Slow above-ground base decay rate 3.20 2.51 5.27 3.58Slow below-ground base decay rate 75.16 77.01 68.04 73.29Stand-replacing disturbance interval 2.49 0.55 1.88 2.09Stem annual turnover 0.11 0.14 0.02 0.19Stem snag turnover 0.03 0.03 0.05 0.03Very fast above-ground base decay rate 0.00 0 0.06 0.01Very fast above-ground proportion to air 2.24 1.57 1.97 2.8Very fast below-ground base decay rate 0.00 0.01 0.08 0.01Very fast below-ground proportion to air 7.40 9.06 7.95 7.79

Total 96.75 96.95 89.75 96.78

a Values in bold within each scenario identify the parameters that had the greatest influence on initial conditions.

378 e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 373–382

Table 3 – Parameter importance by scenario and ascending rank, at time steps 10 and 250 years for DOM stock changes

Parameter Sb138 Pj138 At138 Sb200

10 250 10 250 10 250 10 250

Branch turnover rate 12 20 12 16 9 14 12 20Coarse root turnover 20 18 19 18 14 12 18 17Fast above-ground base decay rate 8 9 9 9 6 7 9 10Fast above-ground proportion to air 14 12 18 12 20 16 15 13Fast below-ground base decay rate 18 19 16 20 17 15 19 19Fast below-ground proportion to air 10 13 13 14 11 11 11 12Fine root turnover 16 15 17 15 19 20 17 15Foliage turnover rate (softwoods or hardwoods) 6 7 10 11 18 17 5 7Mean annual temperature 5 8 5 7 5 5 6 8Medium base decay rate 7 11 3 8 15 19 7 9Medium proportion to air 15 16 15 19 12 13 14 16Slow above-ground base decay rate 3 2 2 2 2 2 2 2Slow below-ground base decay rate 17 1 8 1 13 1 13 1Stand-replacing disturbance interval 1 4 6 4 4 6 3 5Stem annual turnover 4 6 4 6 7 8 4 6Stem snag turnover 13 14 11 13 10 10 16 14Very fast above-ground base decay rate 9 10 7 10 8 9 10 11Very fast above-ground proportion to air 2 3 1 3 3 4 1 3Very fast below-ground base decay rate 19 17 20 17 16 18 20 18

94

Very fast below-ground proportion to air 11 5SimLab coefficient of determination on ranks 0.84 0.

increased in importance between time steps 10 and 250 yearsfor all three softwood scenarios. The stem annual turnover,historic disturbance interval and mean annual temperaturewere more important at the beginning of the simulationthan towards the end. Aspen was more sensitive to varia-tion in the VF BG PA than were the softwoods. Conversely,the softwood scenarios were more sensitive to variation inthe foliage turnover rate. The coefficients of model determi-nation for the sensitivity measures in SimLab ranged from0.59 to 0.94, indicating that most of the variation was wellexplained.

The model prediction for stock changes using the defaultparameters (without the integration of sensitivity analysis)was within the range predicted by the sensitivity analysis,but below the 10th percentile in all cases (Fig. 4)3. The defaultparameter values were within the ranges used for sensitivityanalysis, albeit at the margins in some cases. In every scenario,the median fell below the middle of the range of outcomes,indicating that the distribution of stocks and stock changeswas positively skewed, a finding also reported by Peltoniemiet al. (2006) in their study.

The very fast, fast, medium and slow pools adjusted atdifferent rates as the landscape transitioned from a distur-bance regime with a 75-year interval (in the spin-up phase)to a disturbance regime with a 138- or 200-year returninterval (Fig. 5). The sensitivity analysis scenarios intro-duced noise into the rate at which pools change but didnot alter the sequence in which the pools stabilized. Bythe end of the simulations, all except the slow pools hadstabilized.

3 Only shows results for one scenario, but all are similar.

14 5 1 3 8 40.70 0.93 0.59 0.79 0.90 0.94

4. Discussion

The base decay rates for the above- and below-ground slowpools and the transfer to air for the above- and below-groundvery fast pools were the most influential parameters affect-ing DOM stocks and DOM stock changes in all four scenarios.These results were consistent with other studies. The impor-tance of decomposition on soil C was also noted by Heath andSmith (2000), Komarov et al. (2003) and Garten and Hanson(2006). Much of the uncertainty in the process-based forest fluxmodel studied by Verbeeck et al. (2006) was attributed to soilrespiration. Peltoniemi et al. (2006) and Nalder and Wein (2006)also reported on model sensitivities to soil model parametersand fine root turnover rates.

The relatively strong influence of these parameters on DOMcycling highlights the importance of the rapid cycling of mate-rial in the foliage and fine root pathways in CBM-CFS3. Foliageand fine root litters turnover rapidly and are transferred intothe VF AG and BG DOM litter pools, which decompose rapidly,as shown by the BDR of 0.35 and 0.5 yr−1 (Table 2, Fig. 1).Decayed material from these pools is either respired to theatmosphere or transferred to the AG or BG Slow pools. Even-tually all non-respired DOM winds up in the Slow BG pool,which decays very slowly (BDR of 0.0033 yr−1). The base decayrate of the BG Slow pool is the final “valve” that controls thequantity of C maintained in the system.

This cascading transfer of C explains why the effect of vari-ation in the slow BG pool BDR increases in importance overtime (Table 3). In all of the scenarios, the landscape is tran-sitioning from a landscape with a 75-year return interval (no

stands ever allowed to grow past 75 years) to a 138-year (or200-year) return interval. The rate at which this adjustmenttakes place is not constant (Fig. 4). In all scenarios, stocksare increasing, at a declining rate. The transition from one

e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 373–382 379

Fig. 4 – DOM stock change over 250 years for sensitivity analysis scenarios and base scenario using default parameters. Them narip

srtsVt(roosreBct

itt

edian and range are shown for the sensitivity analysis sceercentile of the sensitivity analysis scenarios.

teady-state to another begins with a rapid decrease in theate of accumulation, followed by a long and steady transi-ion, reflecting that the individual pools that make up DOMtabilize at different rates. For instance, the AG VF and BGF pools adjust rapidly, stabilizing early in the run, whereas

he slow pools are still adjusting at the end of the simulationFig. 5). The medium pool pathway (Med BDR, Stem turnoverate) is also more important at the beginning than at the endf the simulations. These different rates of change influenceur assessment of model sensitivity at different times in theimulation. Parameters that govern the change in pools thatespond rapidly and that make up a large share of total DOMmerge as important at the beginning of the run. As the SlowG pool increases in importance as a share of total DOM stockhange, so does the importance of variability in parametershat determine the size of this pool.

One inference from these results is that the potential fornteraction between model parameters and the dynamic ofhe landscape being simulated should be a key considera-ion for sensitivity and uncertainty analyses of stock and flow

os. The default scenario was typically below the 10th

ecosystem models. As illustrated here, the change in carbonstocks in a landscape transitioning between two disturbanceregimes can be non-linear, with the effect that conclusionsabout model sensitivity to parameter variation differ depend-ing on where in the transition model sensitivity is assessed.The current set of scenarios assumed a constant disturbanceregime, in order to observe a controlled transition between twolong-term equilibria (the historical and modelled conditions).In reality, some landscapes may be in a perpetual state ofadjustment due to varying disturbance regimes. Further workis needed to determine the impacts on parameter sensitivityof including a variable disturbance regime, particularly in theinitialization phase of the model.

Assumptions about the historic disturbance return intervalwere important in some of the scenarios under considera-tion. This parameter is a determinant of the size of the soil

and DOM pools at time zero (Table 2) and, as a result, alsoinfluenced stock changes during a simulation (Table 3). Thegrowth dynamics of a landscape determined how strongly thevariation in this parameter influenced initial conditions and

380 e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 373–382

base

Fig. 5 – Landscape-level DOM stocks per hectare for

the yield curves also determined the rate and magnitude ofchange in the soil pools between the spin-up phase and theend of the model simulations. The yield curves in Fig. 2 showthe limits of variation assumed for the return interval for threespecies. The magnitude of the effect of uncertainty in thereturn interval on initial conditions depends on the differencein the growth increment over the assumed range of the dis-turbance return interval. Black spruce and trembling aspenvolumes increased by 43 and 40 m3 between ages 65 and 85,respectively, while jack pine volume increased by 22 m3. As aresult, DOM stocks in black spruce and trembling aspen standswere proportionally larger at the beginning of a simulation ifthe return interval was set to 85 rather than 65 when comparedagainst jack pine stocks. In landscapes with longer distur-bance return intervals, where stands are able to reach a mature

state before being disturbed, the effect of uncertainty in thehistoric return interval is much less pronounced (Trofymowet al., in press). In the current CBM infrastructure, the distur-bance return interval is set by default at the ecozone level,

scenarios over 250 years using default parameters.

which is a relatively large scale. The results presented heresuggest that users of the operational-scale CBM-CFS3 shouldadjust this parameter to better reflect their local conditions,particularly for application in landscapes with a short returninterval and stands still in a growth phase. They also suggestit might be beneficial to modify the model to allow the returninterval to be specified by forest type.

These results also demonstrate that it is important toconsider the species composition of landscapes when evalu-ating model sensitivity to parameter variation. Differences ingrowth rates and biomass allocation affected the magnitude ofstock change between the initial conditions and the final timestep of the model simulation, when there was a change in thedisturbance regime. The magnitude of this change for eachscenario (Fig. 4) can be explained by examining the change in

biomass for each species between the historical maximum ageof 65–85 for the “makelist” phase and the maximum age in thesimulation (138 or 200), as shown in Fig. 2. For jack pine, there isless of an increase in biomass production by pool between age

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5–85 and age 138 than for the other species; the cumulativetock change over any given simulation (Fig. 4) is correspond-ngly smaller for jack pine than for the other species.

We also noted species differences in sensitivity to the VFG PA and foliage turnover rate parameters. Aspen was moreensitive to variation in the VF BG PA than the two softwoodpecies because fine root biomass is up to twofold greaternder aspen than under black spruce or jack pine (Fig. 3). Jackine and black spruce were more sensitive to variation in theoliage turnover rate despite a lower overall turnover becausehe range of variation assumed for softwood species repre-ented a doubling of the volume of turnover, from 10% to 20%,hereas for aspen it represented a much smaller proportional

hange, from 85% to 99%. In this case, a large uncertainty in amall turnover rate proved to be more important than a smallncertainty in a large turnover rate.

. Conclusion

he iterative approach and tools demonstrated here are con-eptually simple and could be integrated as part of futureodelling analyses using CBM-CFS3. In this first iteration, we

ave identified which model parameters strongly influenceotal DOM stocks and stock changes and which have relativelyittle influence. The latter can be fixed at the present defaultalues and may not need to be considered in future sen-itivity analyses. We have identified possible improvementso the CBM-CFS3 framework and have also identified con-traints to uncertainty or sensitivity of CBM-CFS3 that usersf the model should consider. In particular, we caution thatonclusions about model uncertainty may be specific to theandscapes under consideration. The age-class structure, his-oric return interval, species composition, and growth andield assumed for a landscape – information often providedy model users as data – interact with parameters, such thatonclusions drawn about the importance of the uncertaintyn a specific model parameter could differ based on the appli-ation of the model. Additional work is needed to improveur understanding of how uncertainty in data and parameters

nteract.

cknowledgements

he authors gratefully acknowledge the modelling assistancef A. Innerd, M.Sc.F., and the helpful comments of two anony-ous reviewers. Growth curves were developed by Dr. M.

enner (Forest Analysis Limited) and provided by the Ontarioinistry of Natural Resources. Drs. N. Luckai and G.R. Larocque

eceived financial support from the Ontario Forestry Futures –nhanced Forest Productivity Science program.

e f e r e n c e s

gren, G.I., Hyvonen, R., 2003. Changes in carbon stores inSwedish forest soils due to increased biomass harvest andincreased temperatures analysed with a semi-empiricalmodel. Forest Ecol. Manage. 174, 25–37.

9 ( 2 0 0 8 ) 373–382 381

Banfield, E.B., Bhatti, J.S., Jiang, H., Apps, M.J., 2002. Variability inregional scale estimates of carbon stocks in boreal forestecosystems: results from West-Central Alberta. Forest Ecol.Manage. 169, 15–27.

Bond-Lamberty, B., Wang, C., Gower, S.T., 2003. Annual carbonflux from woody debris for a boreal black spruce firechronosequence. J. Geophys. Res. 108 (D3), 8220.

Boudewyn, P., Song, X., Magnussen, S., Gillis, M.D., 2007.Model-based, volume-to-biomass conversion for forested andvegetated land in Canada. Natural Resources Canada,Canadian Forest Service, Pacific Forestry Centre, Victoria, B.C.,Information Report BC-X-411.

Ceulemans, R., Janssens, I.A., Jach, M.E., 1999. Effects of CO2

enrichment on trees and forests: lessons to be learned in viewof future ecosystem studies. Ann. Bot. 84, 577–590.

Garber, S.M., Brown, J.P., Wilson, D.S., Maguire, D.A., Heath, L.S.,2005. Snag longevity under alternative silvicultural regimes inmixed-species forests of central Maine. Can. J. Forest Res. 35(4), 787–796.

Garbey, C., Garbey, M., Muller, S., 2006. Using modeling toimprove models. Ecol. Model. 197, 303–319.

Garten Jr., C.T., Hanson, P.J., 2006. Measured forest soil C stocksand estimated turnover times along an elevation gradient.Geoderma 136, 342–352.

Heath, L.S., Smith, J.E., 2000. An assessment of uncertainty inforest carbon budget projections. Environ. Sci. Policy 3, 73–82.

Hennon, P.E., McClellan, M.H., 2003. Tree mortality and foreststructure in the temperate rain forests of southeast Alaska.Can. J. Forest Res. 33 (9), 1621–1634.

Kennedy, M.C., O’Hagan, A., Anderson, C.W., Lomas, M.,Woodward, F.I., Heinemeyer, A., Gosling, J.P., 2006. Quantifyinguncertainty in the biospheric carbon flux for England andWales. Research Report no. 564/06, Department of Probabilityand Statistics, University of Sheffield.

Komarov, A., Chertov, O., Zudin, S., Nadporozhskaya, M.,Mikhailov, A., Bykhovets, S., Zudina, E., Zoubkova, E., 2003.EFIMOD 2—a model of growth and cycling of elements inboreal forest ecosystems. Ecol. Model. 170, 373–392.

Kurz, W.A., Apps, M.J., 1999. A 70-year retrospective analysis ofcarbon fluxes in the Canadian forest sector. Ecol. Appl. 9 (2),526–547.

Kurz, W.A., Apps, M.J., 2006. Developing Canada’s National ForestCarbon Monitoring, Accounting and Reporting System tomeet the reporting requirements of the Kyoto Protocol.Mitigation Adapt. Strategies Global Change 11, 33–43.

Kurz, W.A., Apps, M.J., Webb, T.M., McNamee, P.J., 1992. Thecarbon budget of the Canadian forest sector: Phase I. ForestryCanada, Northwest Region, Northern Forestry Centre,Edmonton, Alberta. Information Report NOR-X-326.

Kurz, W.A., Beukema, S.J., Apps, M.J., 1998. Carbon budgetimplications of the transition from natural to manageddisturbance regimes in forest landscapes. Mitigation Adapt.Strategies Global Change 2, 405–421.

Kurz, W.A., Apps, M.J., Banfield, E., Stinson, G., 2002. Forestcarbon accounting at the operational scale. Forestry Chronicle78, 672–679.

Kurz, W.A., Stinson, G., Rampley, G.J., Dymond, C.C., Neilson, E.T.,2008. Risk of natural disturbances makes future contributionof Canada’s forests to the global carbon cycle highlyuncertain. Proc. Natl. Acad. Sci. 105 (5),1551–1555.

Lal, R., 2005. Forest soils and carbon sequestration. Forest Ecol.Manage. 220, 242–258.

Linkov, I., Burmistrov, D., 2003. Model uncertainty and choicesmade by modelers: lessons learned from the InternationalAtomic Energy Agency model intercomparisons. Risk Anal. 23,1297–1308.

i n g

382 e c o l o g i c a l m o d e l l

Liski, J., Palosuo, T., Peltoniemi, M., Sievänen, R., 2005. Carbonand decomposition model Yasso for forest soils. Ecol. Model.189, 168–182.

Masera, O.R., Garza-Caligaris, J.F., Kanninen, M., Karjalainen, T.,Liski, J., Nabuurs, G.J., Pussinen, A., de Jong, B.H.J., Mohren,G.M.J., 2003. Modeling carbon sequestration in afforestation,agroforestry and forest management projects: the CO2FIX V.2approach. Ecol. Model. 164, 177–199.

Morris, M.D., Mitchell, T.J., 1995. Exploratory designs forcomputational experiments. J. Stat. Plan. Inference 43,381–402.

Nabuurs, G.J., Masera, O., Andrasko, K., Benitez-Ponce, P., Boer, R.,Dutschke, M., Elsiddig, E., Ford-Robertson, J., Frumhoff, P.,Karjalainen, T., Krankina, O., Kurz, W., Matsumoto, M.,Oyhantcabal, W., Ravindranath, N.H., Sanz Sanchez, M.J.,Zhang, X., 2007. Forestry. In: Metz, B., Davidson, O.R., Bosch,P.R., Dave, R., Meyer, L.A. (Eds.), Climate Change 2007:Mitigation. Contribution of Working group III to the FourthAssessment Report of the Intergovernmental Panel onClimate Change, Cambridge University Press, Cambridge,United Kingdom and New York, NY, USA.

Nalder, I.A., Wein, R.W., 2006. A model for the investigation oflong-term carbon dynamics in boreal forests of westernCanada. I. Model development and validation. Ecol. Model.192, 37–66.

O’Hagan, A., 2006. Bayesian analysis of computer code outputs: atutorial. Reliability Eng. Syst. Saf. 91, 1290–1300.

Parysow, P., Gertner, G., Westervelt, J., 2000. Efficientapproximation for building error budgets for process models.Ecol. Model. 135, 111–125.

Peltoniemi, M., Palosuo, T., Monni, S., Mäkipää, R., 2006. Factorsaffecting the uncertainty of sinks and stocks of carbon in

2 1 9 ( 2 0 0 8 ) 373–382

Finnish forests soils and vegetation. Forest Ecol. Manage. 232,75–85.

Russell, R.E., Saab, V.A., Dudley, J.G., Rotella, J.J., 2006. Snaglongevity in relation to wildfire and postfire salvage logging.Forest Ecol. Manage. 232, 179–187.

Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M., 2004.Sensitivity Analysis in Practice. A Guide to AssessingScientific Models. John Wiley and Sons Publishers.

Smith, J.E., Heath, L.S., 2001. Identifying influences on modeluncertainty: an application using a forest carbon budgetmodel. Environ. Manage. 27, 253–267.

Smyth, C.E., Trofymow, J.A., Kurz, W.A., the CIDET Working Group.Decreasing uncertainty in CBM-CFS3 estimates of forest soil Csources and sinks through use of long-term data from theCanadian Intersite Decomposition Experiment, submitted.

Trofymow, J.A., Stinson, G., Kurz, W.A. Derivation of a spatiallyexplicit 86-year retrospective landscape-level forest carbonbudget for the Oyster River area of Vancouver island, BC.Forest Ecol. Manage., in press.

Vanderwel, M.C., Caspersen, J.P., Woods, M., 2006. Snag dynamicsin partially harvested and unmanaged northern hardwoodforests. Can. J. Forest Res. 36, 2769–2779.

Verbeeck, H., Samson, R., Verdonck, F., Lemeur, R., 2006.Parameter sensitivity and uncertainty of the forest carbonflux model FORUG: a Monte Carlo analysis. Tree Physiol. 26,807–817.

Wilson, B.F., McComb, B.C., 2005. Dynamics of dead wood over 20

years in a New England oak forest. Can. J. Forest Res. 35,682–692.

Yatskov, M., Harmon, M.E., Krankina, O.N., 2003. Achronosequence of wood decomposition in the boreal forestsof Russia. Can. J. Forest Res. 33, 1211–1226.