AN ECOPHYSIOLOGICAL PROCESS MODEL FOR SEMI-ARID GRASSLANDS
Y. Nouvellon *,1 S. Rambal,2 A. Begue,1 J. P. Lhomme,3 M.S. Moran,4 J.Qi,4 A. Chehbouni,5 D. Loseen1
1CIRAD, Montpellier, France
2CEFE, CNRS, Montpellier, France
3ORSTOM/CICTUS, Hermosillo, Mexico
4USDA-ARS, Tucson, Arizona
5ORSTOM/IMADES, Hermosillo, Mexico
* Corresponding author: CIRAD-CA, Maison de la télédétection, 34093 MONTPELLIER, FRANCE;
e-mail : nouvello@cirad.teledetection.fr
1. INTRODUCTION
The ultimate objective of this study is to develop a model that describe water and carbon budget of semi-arid grasslands at the regional scale. At this scale, satellite remote sensing can provide valuable information to improve simulation results. One approach consists in assimilating radiometric data into the plant growth model by re-calibration of the plant growth model parameters (Bouman, 1991). This approach supposes the mediation of a radiative transfert model that uses the canopy structural parameters (LAI, percent cover, plant height,…) given by the plant-growth model to simulate temporal variations of surface reflectances.
In this paper, we describe in a first section an ecophysiological process model developed for this purpose. In a second section, we present its validation on a grassland site in San Pedro Basin.
2. MODEL DESCRIPTION
2.1. General model structure
The model aims at simulating, on a daily time step, the biomass dynamics of three main compartments : green shoots, dead shoots and living roots. The main processes simulated in a vegetation growth submodel are photosynthesis, allocation of photosynthetates to shoots and roots, translocation of carbohydrates from roots to shoots at the early regrowth, respiration and mortality. Many physiological processes such as photosynthesis and mortality are dependent of water availability in the root zone, which is calculated in a water budget submodel.
2.2. Model equations
2.2.1 Vegetation growth model
The biomass dynamics in the three main compartments is described by the three differential equations :
where Bag, Br, and Bad are green aerial biomass, root living biomass and standing dead aerial biomass respectively. Pg is the daily gross photosynthesis, aa and ar are the photosynthetates allocation coefficients to the shoot and root compartments respectively (aa + ar = 1), and Tra represents the translocation of biomass from the roots to the green aerial compartment. Rat and Rrt are the total daily respiration of aerial and root compartments, Sa and Sr represent the biomass losses of the living shoots and living roots due to senescence. L represents the litter production.
Photosynthesis sub-model
The daily carbon increment for the whole system comes from photosynthesis. The maximum gross daily canopy photosynthesis can be expressed as
where S is the daily incoming solar radiation, [epsilon]c is the climatic efficiency (=PAR/S), [epsilon]I the interception by green leaves efficiency (=PARi /PAR), and [epsilon]b the energy conversion efficiency (=g(CH2O) produced/PARi). f1 and f2 are empirical stress functions representing the effects of water and temperature stresses respectively. To calculate f2, we assume a linear relationship between daily photosynthesis and daily mean air temperature. Water stress reduces photosynthesis by reducing the CO2 diffusion from air to leaf tissues as an effect of stomatal closure. It is expressed as a function of leaf water potential as in Mougin et al. (1995) :
where rs and rsmin are actual and minimum canopy stomatal resistance to water vapor, rm and ra are mesophyll resistance and canopy layer boundary resistance to water vapor. 1.64 is the ratio of diffusivities of C02 and water vapor in the air at 20°C, and 1.39 is the ratio of the rate of transfer of CO2 and water vapor in the canopy boundary layer. rs is calculated as a function of leaf water potential [psi]l (see below).
The climatic efficiency [epsilon]c is approximately 0.45, and the interception efficiency [epsilon]I is calculated as a function of green LAI (LAIg) and total LAI (LAIt) :
where LAId is the dead biomass LAI, SLAg and SLAd are the specific leaf areas of the aerial green biomass and the standing dead biomass respectively.
The energy conversion efficiency [epsilon]b is dependent of many factors as the nutrient availability, the plant genotype, and physiological age of the plants. It is therefore site specific and varies during the growing season. The depressing effect of the aging on [epsilon]b is considered :
where [epsilon]bmax is the energy conversion efficiency for young mature tissues, and f3 is an empirical function representing the effect of the aging on [epsilon]b. The physiological leaf age and f3 where calculated as in the BLUEGRAMA model (Delting et al., 1979).
Allocation sub-model
Carbon pool resulting from photosynthesis is allocated into shoots and roots according to allocation coefficients, aa and ar respectively. The daily amount of (CH2O) which should be translocated from shoot to root Ta is calculated according to the model of Hanson et al. (1988). An excess amount of biomass in the shoots is determined as
where rx is the maximum root to shoot ratio. If Bax>0, biomass flows from the shoots to the roots. If not, there is no allocation. Ta is calculated so that the root to shoot ratio rx is maintained constant from one day to the next.
This function assures there is no more aerial phytomass than the present root biomass can support (HANSON et al., 1988). From Ta, allocations coefficients are calculated assuming than Ta should not overpass the gross photosynthesis Pg.
Root to shoot translocation submodel
Translocations of carbohydrates from roots to shoots, Tra can occur in the early season regrowth, or after if some process has removed a critical amount of green biomass. The model used to calculate Tra is the model proposed by Hanson et al. (1988). In order for this process to occur, three conditions must be met : (1) The average 10-day soil temperature must be greater than 12.5 °C, (2) The average 5-day soil water potential must be greater than -1.2 MPa, (3) Br > rx Bag .
If these conditions are met :
tr is the proportion of root biomass daily translocated to shoots.
Respiration sub-model
Total respiration Rt is the sum of total aerial respiration Rat and total root respiration Rrt. For C4 grasses photorespiration is negligible. Thus the total aerial respiration Rat can be expressed as the sum of aerial maintenance respiration and aerial growth respiration :
ma and mr are the maintenance respiration coefficients for aerial and root biomass, Yga and Ygr are the growth conversion efficiency for aerial and root biomass. The expressions (1- Yga) and (1- Ygr) are equivalent to the growth respiration coefficients for the aerial parts and roots, which represent the cost for producing new biomass.
Senescence sub-model
The amounts of green aerial biomass and root biomass which die each day, Sa and Sr are calculated as
where da and dr are the death rate for aerial parts and roots respectively. dr is assumed to be constant during the year, and da is calculated as a function of physiological leaf age and soil water potential following the BLUE GRAMA model of Delting et al. (1979).
Litter production sub-model
The model used to calculate litter production (La) is the model developed by Hanson et al. (1988), where the total transfer of standing dead to litter is made as a function of the daily wind run, the total daily precipitation and the livestock stocking rate.
2.2.2 water balance model
The water balance uses a simplified two layers canopy evapotranspiration model where soil profile is divided into three layers : a thin supifercial layer (0 to 4 cm) which is supposed to participate only to the soil evaporation process Es, and two deeper layers (4 to 15 cm and 15 to 60 cm) corresponding to the root zone, which participate both to evaporation and transpiration.
Estimation of actual evapotranspiration
The total evaporation from the sparce grass canopy is calculated as the sum of bare soil evaporation Es and of canopy evaporation EC. EC and Es are calculated empirically from the evapotranspiration of a continous canopy, and evaporation of a bare soil, tacking into account the relative surface which is covered by vegetation and bare soil. If fvg, fvd and fs are respectively the fractional cover of green vegetation, dead vegetation and bare soil (fvg + fvd + fs = 1), Ec and Es are calculated as
A is the available energy which is the sum of net radiation Rn and soil heat flux G, D is the vapor pressure deficit of the air at a reference height above the surface, [lambda] is the latent heat of vaporization, [rho] is air density, cp is the specific heat of air at constant pressure, [gamma] the psychrometric constant and s is the slope of the saturated vapor pressure curve at the temperature of the air Ta . rsc and rss are the surface resistances for a completely covering canopy and a bare soil respectively. rac and ras are the corresponding aerodynamic resistances. fvg and fvd are calculated as a function of LAIg and LAId
The evaporation Es is distributed between the different layers of the profile following an extinction coefficient which depends on the soil water content, thickness and depth of each layer:
Resistance models
The bulk stomatal resistance of the canopy rsc is calculated as a function of leaf water potential Yl as
where rsmin is the minimal stomatal resistance observed in optimal conditions, [psi]1/2 is the leaf water potential corresponding to a 50 % stomatal closure and n is an empirical parameter (Rambal and Cornet 1982).
The soil surface resistance rss is calculated as a function of the water content of the first soil layer by means of the empirical relationship (Camillo and Gurney 1986)
where w1 represents the volumetric soil moisture content of ground surface layer (dimensionless).
The aerodynamic resistances are calculated as
where zr is the reference height where wind speed U and air humidity are measured, k is the von Karman constant (0.41). d is the zero plane displacement and z0 is the roughness length calculated as a fraction of the mean height hc of the vegetation canopy: z0=0.1 hc and d=0.67 hc. For a bare soil: z0=0.01 m and d=0.
Soil water balance sub-model
The daily variation of the volumetric water content W1 of the first layer is
where P are the precipitations, D1 is the drainage from the first layer to the second layer and Es1 is the evaporation from the first layer. In the two other layers, the daily variation of the volumetric water content are
where i is the number of the soil layer, D(i-1) is the water drained from the previous layer, and Eci is the water extracted from the layer i due to transpiration (see below). Drainage from a layer i to the layer (i+1) occurs when wi>wfci wfci being the volumetric water content at field capacity.
Calculation of leaf water potential
The leaf water potential Yl is needed to calculate the canopy resistance and hence the canopy transpiration. It is obtained numerically by equaling Ec given by Eq.(21) in which rsc is replaced by its formulation in equation (25) to the sum of the water amounts extracted from the different soil layers and calculated following van den Honert’s equation
where rspi and [psi]si are the soil-plant resistance and the water potential in the ith soil layer. rspi are calculated as a function of root density in the ith layer, [psi]si are inferred from wi by a water retention curve of the type [psi]s=AwB, where A and B are functions of the textural composition. [psi]l of day n is calculated from [psi]si of day n-1, and is used to calculate rsc and Ec of day n.
3. SIMULATION RESULTS
The model has been validated with data acquired in 1990, 1991 and 1992
by the USDA-ARS Southwest Watershed Research Center in Kendall site. 
This site is located on the Walnut Gulch experimental watershed (31°43’N
110°W) within the San Pedro Basin in Southeastern Arizona. The annual
precipitation varies from 250 to 500 mm with approximately two thirds falling
during the ‘monsoon season’ (july-september). Elgin-Stronghold
complex soil association is found on this site, and the vegetation is dominated
by C4 grasses whose dominant species are black grama (Bouteloua eriopoda),
curly mesquite (Hilaria belangeri) hairy grama (Bouteloua hirsuta) and
three-awn (Aristida hamulosa). The parameters needed for the model have
been taken from the literature and data obtained on the site. However [epsilon]bmax
and the initial root biomass were unknown and have been optimized for one
year. The values obtained by optimization compared well with values given
in the literature for similar vegetation types and have been used for the
simulations of the other years, assuming little variations of these parameters
from one year to the following year.
During the period covered by the simulations (day 150 to 366), total
precipitations were 373, 283 and 284 mm for year 1990, 1991 and 1992 respectively.
Figure 1 represents precipitations repartition and seasonal aerial green
biomass dynamic for year 1992. This figure shows that drought effects are
well reproduced by simulations. Figure 2 shows that for the three years,
simulated aerial green biomass compared well with observed biomass. 
As shown in Figure 3, a good agreement was also obtained between observed
and simulated LAI, which is essential for the coupling of the plant growth
model with reflectivity models.
4. CONCLUSION
In this paper, a plant growth model for semi-arid grasslands is presented. This model is based on CO2 and water exchanges and requires a limited number of input data. Simulated biomass and LAI for the period 1990-1992 compares well with observations at the Kendall site in Southeastern Arizona. The ability to reproduce temporal variations of LAI is encouraging for the coupling with a radiative transfer model.
ACKNOWLEDGEMENTS
The authors wish to thank USDA-ARS for providing the data set. This research has been carried out in the framework of SALSA-Experiment, VEGETATION and EOS projects.
REFERENCES
Camillo, P.J. and Gurney, R.J., 1986. A resistance parameter for bare soil evaporation models. Soil Science, 141, 95-105.
Delting, J.K, Parton, W.J. and Hunt, H.W., 1979. A simulation model of Bouteloua gracilis biomass dynamics on the North American shortgrass prairie. Oecologia, 38, 167-191.
Hanson, J.D., Skiles, J.W. and Parton, W.J, 1988. A multi-species model for rangeland plant communities. Ecological Modelling, 44, 89-123.
Mougin, E., Lo Seen, D., Rambal S., Gaston, A., and Hiernaux, P., 1995. A regional Sahelian grassland model to be coupled with multispectral satellite data. I : Model description and validation. Remote Sens. Environ. 52, 181-193.
Rambal, S. and Cornet, A., 1982. Simulation de l'utilisation de l'eau et de la production végétale d'une phytocénose Sahélienne du Sénégal. Acta Oecologica Oecol. Plant . 3(17) 4: 381-397.
Bouman, B.A.M., 1991. The linking of crop growth models and multi-sensor sensing data, proceedings of the 5th International Colloquium - Phys. Measurements and Signatures in Remote Sensing. Courchevel France, 14-18 January 1991.
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