ELSEVIER Catena 26 (1996) 137 160

C A T E N A

Testing the MEDALUS hillslope model

J.B. T h o r n e s a J .X. S h a o a E. D i a z a A. R o l d a n a M. M c M a h o n b,

J.C. H a w k e s "

a Department of Geography, King's College, Strand, London WC2R 2LS, UK b School of Geography, University of Leeds, Leeds, UK

Received 11 October 1994; accepted 13 September 1995

Abstract

In the Mediterranean environment formative erosional and runoff events are sporadic, intense and infrequent. They are difficult to study, their effects difficult to anticipate and the impact of vegetational and climatic change, whether natural or human-induced, difficult to predict. For these reasons, modelling has to augment the traditional approaches. In the Mediterranean Desertification and Land Use research programme, models have been developed to look at these problems at the hillslope (MEDALUS model) and large catchment scale (MEDRUSH model). Such models are only as good as their capacity to replicate, to an acceptable level, the magnitude, pattern in space and time and character of real world processes. These models can be tested by (a) examining their logical structure and performance against synthetic or control data (primary level) (b) evaluating their behaviour against published empirical spatial and temporal data (secondary level) and (3) by direct comparison with field test data (real world validation).

The MEDALUS catena model comprises atmospheric, plant growth, overland flow and erosion, and subsurface water redistribution components involving a number of important novel features especially for dryland environments. It produces vegetation biomass and storm event runoff and sediment yield for different positions over a hillslope at different times. It is here tested against plot data for events and vegetation, soil moisture, runoff, erosion and slope armouring for annual series over several years. The model is found to perform moderately well for runoff and very well for sediment yield for event-based simulations. The results for longer simulations, tested at the secondary level, perform well in comparison with responses cited in the literature.

1. Introduct ion

The objective of this paper is to provide a summary of an erosional model developed for field scale conditions in Mediterranean environments and to report on the compari- son of the model with field data and to explore its performance when subject to climatic

0341-8162/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved S S D I 0 3 4 1 - 8 1 6 2 ( 9 5 ) 0 0 0 3 7 - 2

138 J.B. Thornes et al. / Catena 26 (1996) 137-160

change scenarios. The MEDALUS programme (Brandt and Thornes, 1996) is an interdisciplinary programme designed to understand, model and provide techniques for mitigating desertification in Mediterranean regions. A major element of this problem is to understand the impact of both anthropogenic and climatic changes on hillslope runoff and sediment yield, especially as they affect water supplies, soil erosion and reservoir sedimentation. The programme is now in its second phase. Phase I dealt especially with the physical processes at the local scale. Phase II is now dealing with both physical and socio-economic processes at the regional scale.

A key feature of the programme is the development of a two new models, the MEDALUS model for predicting the impact of changes in inputs to hillslope catenas on the vegetation cover, discharge, sediment yield and topographic change resulting from erosion (Kirkby, 1993a) and the MEDRUSH model for the large (ca. 5000 km 2) catchment scale. The latter combines a simplified version of the MEDALUS model linked to the SHE routing algorithm and is described in Kirkby (1993b).

In Mediterranean environments there are two major difficulties which confront attempts to understand the processes and their outcomes. The first is that large areas are of continental facies deposited in dry environments which are poor for the preservation of fossil material and fossils well preserved in higher mountain regions are often unrepresentative of the areas most critical for erosion studies (Volk, 1967; Zuidam, 1975). The second is that formative events are few and far between and extreme in character, so that capturing their effects is both expensive and improbable (Lopez- Bermudez, 1973; Albaladejo et al., 1991). The modelling paradigm is not a substitute for detailed process investigations (indeed it depends fundamentally upon them) but it can help to overcome the limitations of time scales in understanding particularly the impact of global warming on Mediterranean hillslopes, the background to which is reviewed in Thornes (1994).

The model, which is described in more detail in the next section, involves three novel features adapted to semi-arid environments. The first is that it accommodates macro-scale roughness such as rills and gullies. The second is that it allows for selective patterning of the infiltration, especially taking into account an unequal distribution of topography, vegetation and soil characteristics such as organic matter content. The third is that it accommodates subsurface lateral redistribution of soil moisture from surface-saturated to surface-unsaturated areas assuming a columnar structure of the soil. In addition, the vegetative cover aspect of the model has paid particular attention to the development of bush cover, which is an essential component of Mediterranean semi-natural land use. As part of the MEDALUS programme the model is required to operate over varying time scales, ranging from storm-based simulations to simulations lasting several year or even decades. A core feature is that it is essentially event based, calculating the runoff and erosion during an event over very short time intervals. The model must be able to adequately simulate the primary responses to rainfall and it is this aspect to which we pay most attention here, although it is equally capable of simulating the effects of CO 2 concentrations and temperature changes. Fire and grazing have not yet been addressed by the model.

In a model as complex as this there are three stages in model testing and validation, with three levels of precision: (i) primary testing, in which individual parts of the model

J.B. Thornes et al. / Catena 26 (1996) 137 160 139

are tested at the development stage, for internal consistency and general acceptability in relation to the known processes, and often with strictly controlled artificially generated inputs; for example simple consistency checks such as the continuity of water, sediment and organic matter; (ii) s e c o n d a ~ leuel testing where controlled and artificial inputs are used on the completely assembled model and (iii) real world testing, where real data are used to validate the complete model performance. Moreover, since different components have different time scales over which significant change occurs, it is sometimes useful to test the model at different time resolutions. Here we test storm events at the real world level, and vegetation-erosion relationships and vegetation change at the secondary level against published data on these relationships, such as the relationship between vegetation cover and erosion (Francis and Thornes, 1990). As yet the potential for validation of the model against long term climate change at the real-world level is denied by the length of field data available. At the real world level we have chosen to evaluate the event simulation against data collected by E. Diaz and A. Roldan before the MEDALUS programme commenced (Albaladejo et al., 1994; Diaz et al., 1994). We expect to test it against the MEDALUS field sites (7 sites of the scale of hectares) as enough storm event data become available and to apply it in the MEDALUS target areas, which are

/ " / t / ~ ~'~ ~ .

VAV VAV VAV . . . . ~ ' ~ l ~

/

I I '1

Fig. 1. Overall structure of MEDALUS model, with the four components expressed as four faces of a tetrahedron.

140 J.B. Thornes et al, / Catena 26 (1996) 137 160

catchment scale research areas of 2000-5000 km 2, after validation. Primary and secondary level testing of the vegetation component of the model has been undertaken by the Sheffield plant ecology group of MEDALUS (Woodward, 1994) and is not discussed here.

2. Brief description of MEDALUS hillslope model

Hillslope processes, which may be physical, biological or chemical, are complex and dynamically interactive, and occur at different spatial and temporal scales. This com- plexity leads to the use of models, which we hope will be able to overcome the limitations of human observation in explaining these processes. They can be used to forecast the impact of external changes at the catchment scale or the hillslope scale, and so assist in resource management. The purpose of the MEDALUS hillslope model is to simulate processes on individual hillslopes at short (event based) or medium (tens of years) time scales. The model was developed and programmed by the MEDALUS teams at King's College London (Thornes, Baird and Shao), at Leeds University (Kirkby, Lockwood and McMahon) and at Sheffield University (Sheehy, Diamond and Wood- ward). The model is written in Turbo Pascal, runs on a PC under Windows.

The model has been constructed to predict hillslope vegetation (leaf area index, leaf, stem and root biomass), hydrology and erosion (runoff, sediment yield) and soil (texture, water movement) changes from known climate and landuse data. The model is physi- cally-based, and draws on knowledge of numerous individual processes, some of it developed in the first phase of MEDALUS from field observations at the seven field sites, which are described in Mairota and Thornes (1996). A full description of the model is contained in Kirkby (1993a). In order to cope with the complexity, the processes are split up into four sub models (see Figs. 1 and 2), which interact strongly and dynamically.

( l ) Soil component - - the soil profile can be set up in layers and structured vertically as a series of dynamically varying columns between which diffusion can occur. With surface saturation during a storm, the wetted area is allowed to infiltrate vertically into the column after which redistribution takes place by drainage and/or lateral diffusion. Soil moisture vertical movement over the depth of each dynamically width-varying column is modelled by the Richard's equation version of Darcy's Law which is solved by using Runge-Kutta 3rd order integration on central differences and a variable time step. Calculation of the hydraulic conductivity is based on the Van-Genuchten (1980) equations. This sub model also uses algorithms of other detailed processes related to infiltration and soil movement, e.g. splash, surface sealing and changes in infiltration rate due to the existence and quantity of soil organic matter. Organic matter mixing and decomposition is also calculated.

(2) Atmospheric interaction - - the Shuttleworth and Wallace (1985) model based on sparse crop covers and the Penman-Montieth approach for in-canopy air conditions, transpiration from the canopy and evaporation from the bare soil and vapour transport has been modified by J. Lockwood. For example in Mediterranean shrubs stomata are expected on one side of the leaf only. The resistance for water loss of the canopy as a

J.B. Thornes et al. / Catena 26 (1996) 137-160 141

Input parameters from field

Topographical roughness (cross sl.3pe

depth)

Slope gradient

Initial soil moisture over depth

,del output

~t yield

s in topgraphical

Saturated hydraulic conductivity

tyer composition ing)

Soil texture (clay; silt; sand) isture balance

Rainfall

Wind speed ration

Wet bulb temperature

Solar radiation

Air temperature

Vegetation type and % cover

Leaf Area Index

Plant height

Root depth

Site latitude (for daylength)

~tion

a / Litter production $

Field data read in by each model Movements of internally calculated parameters Final out~)uts

Fig. 2. Inter-relationships between different model components.

whole is computed from LAI, the stomatal resistance, and the cuticular resistance which is assumed to be constant. This version therefore accommodates the existence of bare, plant shaded and plant covered ground with different evapotranspirational rates. The sub model provides a moisture which is then used by the plant model after conversion to soil water potential.

(3) Surface hydrological and erosional component - - runoff is based on the model of Baird et al. (1992) using the concept of reticular flow, in which flow concentration is determined by topography and skin resistance by the Chezy roughness coefficient along

142 J.B. Thornes et al. / Catena 26 (1996) 137-160

the wetted perimeter of roughness elements and by vegetation cover. Erosion is modelled by a version of Kirkby's (1992) transport model modified by Shao to incorporate selective transport using the equation of Poesen and Savat (1981) which is based on resistance to detachment as a function of particle size. This is applied to a surface store of soil of known size distribution which can be selectively detached and transported by overland flow during storm events. Sediment yield due to overland flow runoff and the resulting armouring process due to erosion can be calculated at any point on the catena.

(4) Vegetation component - - this is a fully deterministic model, comprising 10 sub-models, including the six basic sub-models of Sheehy et al. (1979, 1980). It simulates the growth of vegetation, the production of litter above and below ground, and provides the height and leaf area index (LAI) for use in by the evapotranspiration model. The specific biomass provided by the model is for 1 m 2, i.e. what grows where there is vegetation. This means that if the cover is less than 100%, the average biomass is obtained by multiplying by the cover fraction. For example in Fig. 9 the cover is 40% and therefore the steady state peak biomass (which occurs in spring) is about 1.76 kg m -2. Shrubs in particular, often occur as bushes or clumps. In this model root spread may exceed crown spread so that water is gathered from a larger area. This is well known for senti-arid shrubs. Maximum rooting depth is assumed to be 1 m for shrubs and 30 cm for grass. The growth function is controlled essentially by available light energy, air temperature, CO 2 availability in the atmosphere and soil water stress. Nitrate availability is the only mineral constituent considered, and the overall model makes no attempt to consider soil chemical change. Allocation of plant materials is to roots, stem and leaves.

The geometric configuration comprises a slope catena divided into downslope segments, through which water and sediment is routed kinematically. Each segment is conceptualised as made up of a series of cross-slope vertical columns of variable depths to represent the cross slope roughness elements such as rills and gullies. These are obtained for the initial conditions from field observations, by estimating the standard deviation of surface elevations, but change as the erosion occurs. The spatial variations in roughness are distributed in a dowslope direction (i.e. from cell to cell), but provided as a fractally generated relief across the cells using the roughness properties.

The dynamic interactions are programmed by holding each element of the model in parallel and switching them on as required, for example when rain occurs. Moreover the model operates at a variable time step where the step length is determined by the inverse of the fastest process rate. For example when rain is occurring the time interval may be as little as 30 secs, when there is no rain it may be as long as a day.

Like all models, the MEDALUS model requires (a) specification of initial conditions e.g., initial soil moisture, initial surface topography roughness, catena profile and vegetation characteristics and (b) boundary conditions as environmental driving vari- ables, e.g. hourly rainfall, solar radiation and temperature. The lower boundary of the catena can be impeded or unimpeded. Some equations in the model have parameters whose values are decided by local conditions on the slope to be modelled, such as the Chezy coefficient, which is related to particle roughness and percentage of plant cover, and saturated hydraulic conductivity, which is associated with soil types and affected by

J.B. Thornes et a l . / Catena 26 (1996) 137-160

Table 1 Parameters required for runs of the MEDALUS model

143

Parameters Unit Sub-model From Method (for test runs)

Atmospheric Rainfall Wind speed Solar radiation Net radiation Air temperature Wet bulb temperature

Soil and surface Initial moisture Saturated moisture Saturated conductivity V-G equation Coeffs Soil texture Detach coefficient Chezy coefficient Slope gradient Area of plot Initial topography

Plant Plant type Plant cover Leaf area index Initial height lnitial root depth

mm/hour hourly data Soil, surface AWS measured m/sec hourly data Atmosphere AWS measured J /m 2 ground/day hourly data Plant AWS measured J / m 2 ground/day hourly data Plant AWS measured °C hourly data Plant, atmos AWS measured °C hourly data Plant, atmos AWS measured

% (volumetric) % (volumetric cm/day

ml/2/sec % m 2 mm

initial value Soil field measured fixed value Soil Lab. measured fixed value Soil Lab. measured fixed value Soil Liter. empirical initial value Surface field measured fixed value Surface estim estimated fixed value Surface liter, cited from fixed value Surface field measured fixed value Surface, soil field measured initial value Surface estim estimated

fixed value Plant, soil field observed % fixed value Plant, soil field observed m 2 leaf/m 2 ground initial value Plant field observed mm initial value Plant, soil field measured mm initial value Plant, soil field measured

others

the content o f soil organic matter. These initial and boundary condi t ions and equat ion

parameters are provided in the input files. In Table t the set of input data and parameters

required by the mode l are listed. In all cases the mode l can provide ei ther default values

or parameters for standard soil types.

M o r e details o f the interact ion be tween sub models and f low of informat ion within

the mode l are shown in Fig. 2. Each sub mode l either reads input data f rom provided

data files or accepts it f rom other sub models . Inside each sub mode l the corresponding

process is broken down to more detai led sub processes until they can be descr ibed by a

set of equat ions or an empir ica l relat ionship specif ied by a lookup table. For instance, in

the S O I L sub model two sub processes related to runoff are identified, i.e., infil tration

and soil water movement , f rom which the rainfall excess is calculated and transferred to

the S U R F A C E sub model , where the runof f and erosion are calculated. In the erosion

mode l the detachment process is es t imated f rom an empir ical relat ionship be tween

resis tance to de tachment and soil part icle d iameter (Poesen and Savat, 1981).

With parameters for equat ions based on empir ica l relat ionships, such a mode l has to

be cal ibrated before it can be used to make meaningfu l predictions. Dur ing model

calibration, values of parameters (in part icular those which cannot be measured directly

144 J.B. Thornes et al . / Catena 26 (1996) 137-160

in the field) are adjusted so that the discrepancy between model outputs (e.g., total runoff and total erosion during an event) and field observation during a specific rainfall event becomes acceptably small. When the model gives an acceptable goodness of fit between observed and field data for other storms, it is considered validated at the real-world level.

3. Single storm events

3.1. Site condit ions

The field data evaluated in this test were obtained from the CSIC experimental site in Abanilla (30 km north of Murcia, S.E. Spain) under the direction of Dr. J. Albaladejo. Fig. 3 shows the general location, Fig. 4 the plot layout and Fig. 5 a photograph of the site. This is one of the most degraded areas along the Spanish Mediterranean coast and has an annual rainfall averaging about 250 mm, mostly concentrated in autumn (especially October, when exceptionally heavy falls occur) and spring. This rainfall has

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/ ;-,' S P A I N x

t \

i / ~ /

= ~ - ~ '

~ _ _ Murcia o t,~

/ \_ / M U R C I A

10km L I

/ / /

,I i

• ~ " Location of plot

0 2km I I

Fig. 3. Location of field sites in the Province of Murcia, south-east Spain.

J.B. Thornes et a l . / Catena 26 (1996) 137-160 145

Plot no. ~--

Increase in organic matter (%)

Total residue added kg/m ~

@

Control

0.5

6.5

®

1.0

13.0

®

1.5

19.5

5m

2.0

26.0

Fig. 4. Plot layouts at the Abani[[a site.

a high interanuual variability and may be of high intensity. Summer evaporation rates are very high and there is a strong seasonal contrast in available soil moisture. The mean annual temperature is 19.2°C, the potential evapotranspiration reaches 900 mm yr i and the drought period can extend for 11-12 months. The climatic indices of Emberger (1932) and Thornthwaite (1948) are between semi-arid and arid. The soil in this area is a

Fig. 5. Photograph of Abanilla site.

146 J.B. Thornes et al. / Catena 26 (1996) 137-160

Xeric Torriorthent (Soil Survey Staff, 1975) developed from marls, with a clay loam texture. The natural vegetation is mainly slow-growing low shrubs with the proportion of plant cover less than 10%. The most abundant plants are Rosmarinus, Stipa, Helianthemum and Anthyllis. The very high rates of soil erosion rate reflect the lack of vegetal cover and the nature of the parent material. Thus the soil surface experiences periodic bouts of intense erosion. The magnitude and frequency pattern therefore in this region is one in which a small number of events do most of the work in any year and the overall rates of erosion are high (Romero-Diaz et al., 1988) and as such is typical of degraded lands in the Mediterranean region.

3.2. Experimental design and methods

A series of experimental plots was established on a hillside with an almost uniform 10% slope, consisting of five 75 m 2 rectangles (15 m long by 5 m wide). The experiment was originally set up as part of a project targeting on evaluation of methodologies for soil restoration. The technique used to improve soil quality was the addition of doses of urban (mainly kitchen) refuse (UR) in the first 30 cm top layer with a rotovator. The control plot was also tilled with rotovator. The amounts of UR added measured in kg m -2 were as follows: plot 0 (control) = 0; plot 1 = 6.5; plot 2 = 13.0; plot 3 = 19.5 and plot 4 = 26.0. The refuse used in this experiment was a solid fresh material (without composting or grinding treatment), after 10-15 day of natural matura- tion. Analytical characteristics of the UR as well as soil chemical changes in response to amendments can be found in Roldfin and Albaladejo (1993).

The UR was added in a simple application on October 1988 and runoff and sediment yields were monitored over 5 years compared to the control plot. The storm rainfall during events was measured with a standard rain-gauge. Runoff and sediment is concentrated along natural channels on the plots to a collecting device consisting of a first tank connected to a second with two 1 : 5 divisors so that only one twenty-fifth of the overflow from the first tanks enters the second (Albaladejo et al., 1991). The runoff volume is measured as depth in the tanks. Sampling of sediments from the tanks was carried out after thorough stirring. Five aliquots of one litre were taken from different depths and a further five when draining the tanks. Sediment concentration was taken to be the average of these. For saturated hydraulic conductivity soil samples were taken using a set of sample rings (50 mm diameter) for taking undisturbed soil samples and the laboratory measurement was carried out in a constant head permeameter.

3.3. Calibration

Most of the parameters in the model have been measured in the field but some have been obtained by calibration. This reflects the fact that some empirical parameters are defined for experimental condition which may not reflect the true situation in the field. Therefore the highest intensity rainfall event registered in five years was used for model calibration. This event was selected because it is desirable that the model performs adequately for large events, when most of the erosional work occurs and experiments had shown that the plots performed variably in calibration with events of different sizes.

J.B. Thornes et al. / Catena 26 (1996) 137-160 147

Table 2 Calibration data for MEDALUS hillslope model applied to the Abanilla (Murcia) plots. Event 06/09/91. Total rainfall 56 mm

Plot C D K Field data Model results (cm.dav i) - Q (1) S (g) Q (1) S (g)

0 45 1.3 25 4079 27261 1691.6 11879 l 33 0.9 25 2170 7371 1699 7215.2 2 2 0.2 84 157 237 125.1 658.4 3 3 0.25 141.6 110 289 95.4 737.8 4 I 0.25 357 32.5 59 0.3 0

This storm occurred in September 1991 with a total rainfall of 56 mm and a maximum intensity of 1~5 = 120 mm h 1. The values chosen for various parameters on plots 0 -4 are shown in Table 2.

The values of saturated hydraulic conductivity (Ksat) were chosen according to laboratory measurement of this parameter rather than field measurements of final infiltration rate. Several time-varying values for this parameter were available for each plot, so all of them were tested and those providing the greatest improvement in goodness of fit were selected.

The Chezy coefficient (C) and detachment coefficient (D) are closely related to such field conditions as plant cover, soil texture and topographic roughness. Usually their value are greater for bare soil, and smaller when there is more plant cover. A major differences between field experimental plots lay in percent of vegetal cover and organic matter content which yields different levels of soil. Values for C and D coefficients were chosen from literature and adapted to our plots after testing procedures.

3.4. Results

The data in Table 2 clearly shows that in the calibration exercise the model generally shows higher values of runoff and lower values of sediment yield for the field data compared with the model. These differences are less for the plots covered with more organic matter. Recall that plot 0 is the control plot (kept bare) and the progressively higher numbered plots have more surface organic matter and therefore the model calibration well maintains the order of runoff and sediment yield and its relation to organic matter cover. The calibration of sediment yield (r = 0.94) is more effective than the calibration for runoff (r = 0.64) and inspection of the calibration results suggest that this is due primarily to the under-estimation of runoff by the model. There is some doubt about the K-values here, though since these are lab-determined (rather than optimised parameters) we feel obliged to keep them, relying mainly on the C and D values for parameterisation.

Following calibration, the model was run on a series of storm events of varying magnitudes for each plot, the information on which is given in Table 3 for overland flow (Q, upper part of table), with the appropriate parameters given at the top of the table.

148 J.B. Thornes et al . / Catena 26 (1996) 137 160

Table 3 Comparison of model and field data for Abanilla plots

Event Plot ~

1 2 3 4 5

Runoff Q (1) 125 mm (05/09/89) field 514 434 431 206 64

model 11063 1924 68.9 0 0 52 mm (04/02/93) field 570 420 0 52.5 0

model 771.2 291.4 0 0 0 43 mm (04/06/89) field 512.5 408.8 17.6 26.3 20.6

model 1082.8 708 78.9 35.2 0 41.25 mm (13/06/92) field 414 167.5 25 20 12

model 284.8 96.9 0 0 0 25.75 mm (16/10/91) field 422 26.25 0 0 0

model 329.5 75.1 0 0 0 25 mm (28/05/90) field 416 22.5 16 17 7.5

model 461 276.4 0 0 0 20 mm (21/04/90) field 413 9 4.5 7 7

model 303.5 191.6 0 0 0 11 mm (08/06/93) field 412 78.75 0 0 (I

model 131.7 76.3 0 0 0

Sediment yield S (g) 125 mm (05/09/89) field 8526 3132 1566 522 348

model 3 3 9 0 1 . 7 5902.2 23.63 0 0 52 mm (04/02/93) field 1670 452 0 0 0

model 725.9 124.8 0 0 0 43 mm (04/06/89) field 16530 3393 60.03 61.38 57.42

model 4301 1201.6 273.2 135.1 0 41.25 mm (13/06/92) field 1967 420 0 0 0

model 144.8 38.8 0 0 0 25.75 mm (16/10/91) field 1211 57 0 0 0

model 150.8 10.7 0 0 0 25 mm (28/05/90) field 1751 34.8 33 24 44

mode[ 758 221.3 0 0 0 20 mm (21/04/90) field 2503 21.75 4.4 7.8 10.4

model 528 138.8 0 0 0 11 mm (08/06/93) field 7506.4 367.1 0 0 0

model 228.1 75.6 I/ 0 0

See Table 2 for C, D and K values for each plot.

A s imple regress ion of mode l and field results for o v e r l a n d f l o w indicates an

exp la ined var iance of only 17.7%, with very large residuals for the largest s torms.

Remova l o f plot 0 and 1 for the two largest s torms increases the explanat ion to 63% and

the regress ion coef f ic ien t is 1.09. This indicates that, if we assume the f ield data to be

accurate, for over land f low the mode l pe r fo rms tolerably well excep t for very large

s torms on bare or scarcely covered plot (plots 0 and 1, s torms o f 125 and 52 ram). I f all

the data are used, exc lud ing the 125 and 52 m m storms on the bare control plot, and the

mode l data logged then the expla ined var iance is about 64%. The results are shown in

J.B. Thornes et al . / Catena 26 (1996) 137-160 149

3 -

~ 2 (g

E

(a)

"m

0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-2 -111 m l I E •

f ' t ( t t

100 200 300 400 500 600

F ie ld r u n o f f d a t a ( ,~)

(b) 3 •

E • • • •

•

E o t)l Q ..J

-2 • •• • maN • •

-3- I I I I

-2 0 1 2 3 4

Log field sediment yield data (g/m s )

Fig. 6. Field versus log model values of (a) plot runoff (Q) and log field sediment yield versus tog model data (b), excluding the 125 and 52 mm storms on the bare control plot.

Fig. 6a. This indicates that there is a progressive departure of the model from the real world in runof f prediction for progressively larger events. This could be the case if the pre-exist ing soil moisture was incorrectly de termined or if the infil tration model is inadequate. The latter is based on the Darcian assumptions (i,e. no macropores) and

150 .LB. Thornes et al. / Catena 26 (1996) 137 160

generally, in dry soils, the use of almost any kind of relationship between soil moisture and conductivity at the " d r y " end of the curve runs into difficulty computationally. Both in the real world and in the model output the largest events occur when the soil is driest, so that the model is least able to cope. The other explanation is that the model inadequately accommodates the impact of intensity. Rainfall is provided on an hourly basis and this fails to resolve high intensity bursts common in large autumn rains. The model data were regressed against intensity as well as the raw data, but this did not provide a significantly better prediction of runoff for the 40 sets of data available.

Repeating the analysis of field and model data for sediment yield data results in an explained variance of 24.5% for all the data and 83% if the sediment yield for the 125 and 52 mm storms for plot 0 (the bare control plot) are excluded (i.e. with 38 observations). Significantly however the model yields about 0.225 of the field value suggesting a simple linear correction in one of the parameters, probably the Chezy parameter. Nonetheless the very high correlation indicates the model is performing well for sediment yield. The logged field and model data are shown in Fig. 6b.

3.5. Comments

The hillslope process is so complicated, involving so many sub processes, the details of each of which yet remain to be fully understood, that it is not surprising that the MEDALUS simulation model does not give predictions with the same accuracy that we usually expect from models describing much simpler processes in some exact sciences, such as those developed in computational fluid mechanics for flow and transport simulation. Nevertheless, with 64% explanation of overland flow and 83% for sediment yield after removal of two points, the model is performing quite well. The anomalous peak values on the bare plot may reflect errors in the data as well as the relations between the model and reality. Further tests are needed against the other MEDALUS field sites so that validation occurs over a wider range of conditions. The results encourage us to believe that this physically based model does reflect some critically important mechanisms of hillslope processes, and can be used to study the responses of these processes at the event time scale. In attempting to extend the model to longer time scales, the plant elements and slope surface evolution become more critical. What we do not have yet is data to evaluate these formally against long-term field experiments. Consequently they have to be evaluated against other types of empirical data and against our expectations from, say, spatial distributions. These are primary and secondary levels of testing. We believe that the application to longer slopes will provide higher explained variances because the delivery ratios are generally lower. However as slopes get much longer the MEDRUSH model could be more profitably used, and hence its greater suitability to large catchments.

4. Med iu m- and longer- term runs

In the following medium term runs of the model we have taken the weather data from the MEDALUS Entradas weather station in Portugal. This is in the Cobres catchment,

J.B. Thornes et al . / Catena 26 (1996) 137-160 151

modelled by Bathurst et al. (1993) using the SHE hydrological basin model. They obtained good replication of basin runoff and sediment yield using the SHE model. Here the rainfall data has been modified to concentrate more flow in the winter months, while maintaining the overall annual rainfall the same, at about 288 ram. This rainfall has then been allowed to repeat annually for a period of eight "wet" years and then the smallest storms have been progressively removed to provide a "dry" series for the remaining 7 years. Initially the slopes are assumed to have relatively low, uniform vegetation cover and biomass, characteristic of the early stages of abandonment. However the cover quickly adjust to the model rainfall conditions by adjusting growth rates. With such large numbers of runoff events the model simulation runs very slowly, the 15 years requiring about 60 hours of PC486 time. This sequence of events enables us to examine the behaviour of the model first with an evolving plant cover and then with a decreasing plant cover.

7O

~.6o 50

40 -6

3O

20

10

(b ) l :

7O

60

;E 50

> 30

20

10

i Surfac¢ Layer

I 50cm below surface

) 500 1000 1500 2000 2500

Julian Day

I,'" 1 I,'~ I I"11 r"~ I ~"" 1 ~"" I I,", . . . . . .

'T " ' '":1' [ ' T . 0

IOOem below surface ~ 60 i

80 E 7~

100

12o

140

lOOcm below surface

Surfa~ Layer !

- / i t

, ~ ~

0 500 106O 1500 2000 2500

Julian Day

160

180

21111

0

4O

6O

+ 100

T 12o@,

~ 14o ~

~ ,6o ~ 180

~ 200

3000

Fig. 7. Soil moisture for a 15 years run using Entradas modified data (a), [br the first 8 "wet" years (288 mm) and (b) for the following 7 "dr5," years under bare soil.

152 J.B. Thornes et al . / Catena 26 (1996) 137-160

Table 4 Entradas and Belmonte weather data for 1992 - - summary

Entradas

Dam Time

Belmonte

Data Time

Rainfall (mm)

Temperature (°C)

Monthly rainfall (mm)

Annual total 288.2 289.8 Daily maximum 28 15 Jan 31.6 Hourly maximum 24 3 pm 15 Jan 9.6

Annual average 15.97 13.3 Daily maximum 31.3 6 Aug 29.3 Hourly maximum 41.4 4 pm 4 Aug 39.6

January 63.2 1 February 9.6 36 March 31.4 17.2 April 49.2 25.2 May 4.6 22.4 June 6.2 87.4 July 0.8 2 August 3 3 September 11.8 21.6 October 40.6 59.6 November 28 1.8 December 39.8 12.6

22 Jun 3 am 26 Sep

1992 6 Aug 5 pm 25 Aug

Soil moisture over the 15 year run provides a useful evaluation of the model performance because the characteristics of soil moisture fluctuations in Mediterranean environments are well known. Fig. 7a shows the pattern of soil moisture over an eight year period using the modified Entradas data with bare soil, with the model starting in January, the data characteristics for which are given in Table 4. There is some slight transience at the beginning of the simulation (which starts with a 14% soil moisture but the model quickly settles down to produce a cycle of seasonal fluctuations of surface soil moisture characteristic of this area (Mooney et al., 1974). The strong damping with depth is apparent and there is a progressive lag in the build up of soil moisture at depth. In fact, soils of 5 0 - 1 0 0 cm thickness are relatively rare under bare conditions and so the 50 and 100 cm patterns are unrealistic because the plants are predominantly constrained to the upper 30 cm and are therefore not pulling water out of the deeper soil layers. Nonetheless the upper soil moisture well reflects the behaviour of this environment. In the succeeding drier period (Fig. 7b) minimum soil moisture progressively decreases and the impact of individual storms on surface soils is much less. By contrast the shrub covered parts of mid-slopes, shown in Fig. 8a, exhibit (a) much greater fluctuations in surface soil moistures due both to the greater capture of water in the storms (by shading and interception creating reduced evaporation) and (b) deeper troughs of dryness during the summer months, reflecting the impact of heavy transpiration losses during the drying periods. In the " d r y " years in the second part of the run (Fig. 8b), surface soils taken as a whole are much drier, with only large events producing strong spikes of soil moisture during storm events. Even then, the wetness of the system is significantly higher than

J.B. Thornes et al. / Catena 26 (1996) 137 160 1 5 3

(a)' i A 711

2 6O

~ 40

2O

10

0

8O

~ 70

613

~ ~o

20

10

0

I I "al'F ' al'I "al'l " l'r "Ial'I " 1'I '''' 40

, S u r ~ Layce 60 ]OOcm below surface

120 ~

• I~ 140

160

180

+ - - I _ _ +_ 50¢mbe lowsur~ , 200

0 500 1000 1500 2000 2500 3000

Julian Day

Surface Layer

IOOcm below surface

i 50cm below surface

0 500 1000 1500 2000

Julian Day

0

20

40

6O

120 ~

140

160

180 i

i 2011

2500 3000

Fig. 8. Soil moisture for a 15 years run using Entradas modified data (a), for the first 8 "wet" years and (b) the following 7 "dr5"" years under shrub.

under bare soil, suggesting a strong " i s l a n d " effect under shrubs. This is consistent with the observations of seasonal moisture changes in Mediterranean soils where the differ- ences are mainly in the near surface soil once a stable plant regime has been established (Thornes and Burke, 1993) and where deeper soils only occur underneath bushes, either because the bushes have created the hollows or because the bushes can only occupy hollows in the rock- so i l boundary (Mulligan, 1996).

Fig. 9a and b shows the development of plant cover with the modified Entradas data over the same 15 year period. The vegetation cover shows a strong transience in the first two years. This is partly because the initial root weight is assumed to be ephemeral and so woody roots take time to build up. The stable values are achieved from a low starting biomass of about 300 g m 2 after about 5 years show average total above ground biomass of approximately 2400 g m 2 and this changes very little thereafter. The dominant growth is in roots, about 60% by weight, which are able to take water from the surrounding bare areas, that is typical in dry Mediterranean environments (Kummerow,

1 5 4 J.B. Thornes et al . / Catena 26 (1996) 137-160

( a ) '5°° 4000

~-- 3500

3000 el

~ 2O0O e~

~ 1500

0

0

( b ) '5°° 4OO0

3s00

2500 ~L

~ 2000

1500 8

0

Fig. 9.

oo

I I ,oo 120 >'

160

I 180

I I I I i 200

0 500 1000 1500 2000 2500 3000

Julian Day

i 20

50

100

120

180

0 500 1000 1500 2000 2500 3000

Julian Day

Biomass for (a) first 8 "wet" years and (b) following 7 "dry" ),ears of modified Entradas data.

1981). The characteristic seasonal variation suggests a change of about 400 g in 2 in roots, 175 g m 2 in leaves and 100 g m -2 for stems. The nearly 30% turnover of leaves seems rather high given the relatively low recorded changes in percent bare area from season to season in bush matorral in almost identical climatic conditions in south-east Spain (Francis and Thornes, 1990) though they also show that litter production is of this order of magnitude.

As the dryness of the second period begins to bite, the effect is mainly felt in the root biomass, because this is more sensitive to available water, the surface biomass decreas- ing relatively little. This depends to some extent on the death-rate parameter of the species and the values here may be still somewhat too high for roots and too low for leaves and stems. Unfortunately there are very few data for the Old World Mediter- ranean species on which the root parameters or death rates can be either estimated or against which they can be validated.

Field observations reveal that plant cover on the slope can make a big difference in runoff and erosion processes. It affects several hillslope processes: reduction in raindrop

J.B. Thornes et al. / Catena 26 (1996) 137 160 155

(a ) '~ 8110

7110

5OO 8

400

30o

20o

lOO

o

(b ) ' ~ 900

80O

700

2eoo

30O

200

100

0

q • ..,,,~l,i...,,,l~, I ... ,,,r~l, [...,,,~1, i ... ,,,l~lT i...,,,l~l, i r' ' '~1' I ~' r '"~

I., J,l.l 5OO 1000

runoff/rainfall = 10.2% in the first 8 years

1500 2000

Julian Day

1,,',p T r,,', I

[ 2500

r,", I "'1"

,I runoff/rainfall = 28.7% in the last 7 years

k, L ,if, IIi 500 1000 1500

Julian Day

2OO0 2500

2o

6o

80 g

lOO .E llJ 1=° 140

160

180

200

3000

- 0

20

40

6o

80 E

100 ._~

120 ,-~

140

160

i 180

200 3000

Fig. I0, Mode l r u n o f f for (a) f irst 8 " w e t " yea r s and (b) f o l l o w i n g 7 " ' d r y " yea r s for m o d i f i e d En t radas data.

splash erosion, mechanical crust formation, interception of rainfall, the root system makes the soil more porous and increases infiltration (Brandt, 1989, 1990; Francis and Thornes, 1990; White, 1991). It has been recognised that analysis of surface runoff on upland areas requires identification of hydraulic roughness coefficients. Roughness coefficients are used in the calculation of flow velocity and the routing of runoff hydrographs. Understanding and properly modelling upland flow hydraulics is also essential in developing process-based erosion models. The present model uses different Chezy coefficients to represent the increase in hydraulic roughness due to the existence of plant cover, which is one of these effects. Fig. 10 shows the runoff simulations for the modified Entradas data. The evolution of the vegetation cover, coupled with the variation in surface conditions means that there is not a simple relationship between rainfall and runoff and that although the rainfall pattern is almost identical year after year, the runoff response is quite different. Again this matches what is known from field plot investigations in Mediterranean areas. For example, in a magnitude and frequency analysis of micro-catchment runoff against rainfall, Romero-Diaz et al. (1988) found

1 5 6 J.B. Thornes et al. / Catena 26 (1996) 137-160

4

(a)

A 3 40

60

8o ~ 8 year total erosion = 20.9 kg 100

12o ~"

140

I ,60 1oo

Julian Day

I

A 3

7 1 ~- 2 77

7 year total erosion = 15.9 kg

- -

0

4O

+ 60

480

+ 100 .~

+ 120 -~

+ 140

± 160

i 180

i i

2OO

Julian Day

Fig. 11. Simulated erosion for (a) first 8 "wet" years and (b) following 7 "dry" years for modified Entradas data.

that there was a poor correlation of both runoff and sediment yield with individual events. On the other hand when events were aggregated up to weekly or monthly levels, higher rainfalls were generally accompanied by higher runoff and erosion. In the second " d r y " period the proportion of runoff is much higher, reflecting in part the loss of the smaller storm events and in part the reduction in the vegetation biomass. At the moment these effects are difficult to separate

Fig. 11 shows the erosional yields for the two periods at a mid-slope position. In the first period, nearly all the yield is from the first few storms, reflectiong the low initial biomass in the model runs (about 300 g m 2). Again there is a problem of offsetting the reduction in cover in the second period from the lower rainfall, again indicating the complexity of response. The results is counter-intuitive, in so far as there is a slightly lower average sediment yield per year in the second period (2.271 kg) than in the first (2.614) despite the reduction in vegetation cover. In the first period nearly all the erosion occurred in the very first storms, with low biomass and there was a rapid reduction after

10

J.B. Thornes et al. / Catena 26 (1996) 137 160

Erosion against Biomass (leaf+stem+root)

157

I-- E

C,O

,~ 0.1-

• :- • ..m mmm •

• mm • • • ;m • m ~ m • m~m

• • • • •mlmm mmmim • • • m I •

• m_.. •

nmln • u • • • m u m • n •

0 0 1 , , = , . . . . , = • , •

1000 2000 3000 4000 SO00 6000

Biomass (g/m z)

Fig. 12. Event-based erosion plotted against biomass for modified Entradas series. Note that sediment transport from basal section is indicated in log scale to allow small erosion events to be shown.

the above-ground biomass increased. In the second period, the sediment yield first rose and then fell, reflecting first the reduction in vegetation cover and then the depletion of material. The result also partly reflects the emphasis on reduction in below ground biomass. With facultatively deciduous plants the effect of leaf loss might be expected to be greater. However, we cannot simply assume that drier conditions mean more erosion if the model is correct. Rather it will be controlled by the balance between reduced rainfall and reduced vegetation cover. On the dry side of the semi-arid peak erosion, reduced rainfall can imply reduced available runoff.

Regression analysis of the relationship between simulated sediment yield and total biomass and between runoff and biomass on a daily basis for the Entradas modified series gives only a weak correlation. Fig. 12 shows the plot of erosion against biomass for the simulated events, with erosion on a log scale indicating a wide scatter but with an exponential form and (as expected) a wide scatter at high biomass and low sediment yield.

In Fig. 13 we show the more conventional plot of plant cover against runoff and sediment yield this time for storm events of constant size and varying plant cover, using the Belmonte series (Table 4). Belmonte is in Castilla-La Mancha (Central Spain), the site of the European Union EFEDA project. Here the results of the simulation are almost identical in behaviour to those observed by Elwell and Stocking (1976) and Francis and Themes (1990) and is taken as further confirmation that the MEDALUS model is performing reasonably well at the event level. Finally in Fig. 14, also for the Belmonte series, simulated changes in particle size distribution of the surface layer of the mid-slope are shown indicating that armouring is effectively modelled and this in part can account for a drop in erosion yield, though may also lead to an increase in the runoff (Poesen et al., 1990). Although this is more difficult to validate at the real-world level,

158 J.B. Thornes et a l . / Catena 26 (1996) 137-160

o4

"E

100~ \ 80-

70-

60

50

40

30

20

t0

0

\ \,

~ ~'\

0,9 -~

0.8

-0,7 .a E -0,6 o

0.5 0.4 E

0.3 -0.2 e =

o.1 .E 0 ¢o

0 20 40 80 99 Plant Cover (% of total slope area)

Runoff ~ Erosion on slope ]

Fig. 13. Event-based runoff and erosion plotted against cover for Belmonte (Cuenca).

c_ E

1007 - -

°° t 80

70 4-

60

50 i / / * 40 ÷"

30 /

20 / / , / /

I0

0 0.001

At Node No. 13

/ z /

0.01 0.1 1 10 100 Particle Size (mm)

-~ 2Janyr l ~ 1 1 A p r y r 2 ~ 15Apryr4

7Julyyr6 * 23 Juneyr8

Fig. 14. Simulated development of armouring layer near toot of slope over an eight year period with no vegetation cover Belmonte (Cuenca, Spain) series.

the best option seems to be to test its capacity to produce spatial variation observed on real slopes. Work in this direction is now in hand.

5. Conclusions

Models such as the MEDALUS hillslope can be validated at three levels, by the logic of their operations, by comparison of the response of the model to synthetically generated input data when compared with empirical results reported in the literature and by comparison with real-world data either through time or across space. The ability to produce correct responses in space is as important as producing simple time based

,LB. Thornes et a l . / Catena 26 (1996) 137 160 159

results, such as basin-output hydrographs. In this paper all three validation criteria have

been used and the M E D A L U S model is shown to repl icate natural runof f and erosion

responses reasonably well. Further work is needed in the parameter isa t ion o f the plant

models for Medi ter ranean species The real world data analysis suggests that the model

still does not adequate ly a c c o m m o d a t e short term variat ions in intensity because there is

a systematic departure be tween real and s imulated erosion and runoff for the larger

events. The mode l h a s the capaci ty to compute higher f requency data but in large parts

of the Medi te r ranean ra inguages do not resolve the rainfall at less than an hour. As more

data at h igher f requency becomes avai lable f rom M E D A L U S sites further val idat ion of

the model will be undertaken.

Acknowledgements

The research for this paper was carried out as part of the M E D A L U S (Medi ter ranean

Deser t i f ica t ion and Land Use) col labora t ive research project. M E D A L U S is funded by

the European Union under its European P rog ramme on Cl imate and Natural Hazards

( E P O C H ) contract number E P O C - C T 9 0 - 0 0 1 4 - ( S M A ) and the support is grateful ly

acknowledged . W e also thank Dr. J. Alba lade jo for permiss ion to use the Abani l la data.

References

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