A method is described for estimating regional evaporation and plant primary production. The method employs a relatively simple model to simulate evaporation and biomass production based on ambient environmental conditions. The model containd submodels for the vegetation growth and soil water balance processes. Data obtained from NOAA AVHRR imagery are used to calibrate model simulations. Spatially distributed data and model simulations are organized within a raster GIS. The procedure is demonstrated using data from the Walnut Gulch Experimental Warershed, a semiarid rangeland located in southeastern Arizona.

Satellite remote sensing can be an effective method for assessing surface evaporation and vegetation resources of a geographical region (Jackson 1985, Moran and Jackson 1991, Moran et al. 1992, Kustas et al. 1994). While satellites can easily survey large areas of the earth's surface, a drawback to their use in operational monitoring programs is the relative infrequency of their observations as a result of their overpass frequency or the occurrence of cloud cover. Satellite observations represent discrete time events which may indicate little about how the biosystem got to its observed state or what its condition will be in the future. In contrast, mathematical models of the vegetation-soil-atmosphere system can produce essentially continuous descriptions of vegetation growth and evapotranspiration (Maas et al. 1992, 1993). They can also be used to project the future condition of the biosystem. Unfortunately, deterministic simulation models utilize a set of parameters and inputs that is specific to the location being simulated. The resulting model simulation is appropriate only for an area within which the values of parameters and inputs do not significantly change. This precludes the explicit application of simulation models to a geographical region in which there is significant spatial variation in environmental conditions.

Previous studies (Maas 1988a, 1988b, 1991a, 1991b, Maas et al. 1992, 1993, Moran et al. 1995) have demonstrated that remotely sensed information can be incorporated into model simulations of agricultural and natural biosystems. These efforts have involved the extraction of remotely sensed data for a point in the landscape for which the model was applied. In this presentation, we describe the use of a geographic information system (GIS) to expand the application of a simulation model over a geographical region to make use of the inherent spatial quality of remotely sensed image data. This procedure is demonstrated using data acquired during 1990 at the Walnut Gulch Experimental Watershed, a semiarid rangeland located in southeastern Arizona.

• To demonstrate the incorporation of remotely sensed information in model simulations.
• To demonstrate the organization of data and execution of the simulation model in a GIS.

Field Study

Field data were collected in 1990 from sites within the Walnut Gulch Experimental Watershed located in southeastern Arizona (see Figure 1). Micrometeorological observations, including air temperature and solar radiation, were collected at eight sites within the watershed. Aboveground biomass, percent canopy cover, and soil moisture were measured periodically at these locations during the study. Data collection procedures are summarized by Kustas et al. (1991a). An essentially uninterrupted sequence of 27 days of data (July 28 through August 15) was available for use in this modeling effort.

Figure One

The Model

The model used in this study is similar to earlier versions described by Maas et al. (1992, 1993) and Moran et al. (1995). It consists of two submodels-- a soil water balance submodel and a vegetation growth submodel. These submodels produce daily simulations of surface evaporation, soil moisture, leaf canopy density, and aboveground biomass production.

The formulation of the soil water balance submodel is based on the following assumptions:

1. For vegetated surfaces in semiarid environments, the contribution of soil evaporation to evapotranspiration (ET) is negligibly small compared to the contribution from plant transpiration, except immediately after a rainfall.
2. When soil water is abundant, ET approaches potential ET (PET) for the vegetation canopy.
3. Except in areas of steep slope, surface runoff of rainfall occurs following saturation of the surface soil layer.

Based on these assumptions, ET is determined on most days by the degree to which the evaporation from the vegetation canopy approaches PET and the degree to which the vegetation canopy covers the surface. On days immediately following a rainfall, a contribution from soil evaporation to ET may also occur.

Studies involving agricultural crops indicate that the ratio of vegetation canopy evaporation to PET can be expressed as a function of the available soil water in the plant root zone. Available soil water is defined as the amount of water between the wilting point of the vegetation and the maximum drained capacity of the soil, normalized by the maximum drained capacity. Thus, available soil water (ASW) is a number between zero and one. Studies also indicate that, when soil water is abundant, the ratio of vegetation canopy evaporation to PET increased with increasing leaf area index (LAI). LAI is a measure of vegetation canopy density, determined as the ratio of total plant leaf area to plant ground surface area. When soil water is not limiting, vegetation canopy evaporation approaches PET at an LAI of around 3 (roughly complete vegetation canopy cover).

Using these relationships, the soil water balance submodel calculates vegetation canopy evaporation (TRAN) as follows:

where FSW and FGC are the ratios determined by ASW and LAI, respectively. On the day following a rainfall, soil evaporation (SOIL) is calculated as follows:

The value of SOIL cannot exceed the amount of rain that fell on the previous day. The value of ASW on any day during the simulation is given by the balance:

in which ASW' is the soil water on the previous day and RAIN is rainfall. The value of RUNOFF is determined as the positive difference between the term ASW'+RAIN-TRAN-SOIL and the maximum drained capacity of the soil. Admittedly, this is a simple model, but it suffices for the demonstration contained in this presentation.

The formulation of the vegetation growth submodel is similar to that used in earlier agricultural crop growth models (Maas 1992, 1993a, Maas et al., 1993, Moran et al. 1995). Daily biomass growth (DELBM) is determined as follows:

where APAR is the photosynthetically active solar radiation absorbed by the vegetation canopy, EC the "conversion efficiency" between APAR and new biomass, and FTEMP a nondimensional function of ambient temperature. APAR is determined as a function of LAI. Newly formed aboveground biomass is partitioned between leaves and stems, and existing leaf area senesces at a rate determined by its age. The presence of the factor FSW in Equation 4 results in a decrease in new biomass production with decreasing soil water.

Model Calibration

Remotely-sensed information is not required by the model to simulate surface evaporation and biomass production. Remotely sensed data allow the model simulation to be operationally adjusted during the simulation period to insure that modeled and observed conditions are in agreement. Such adjustment is often neccessary because it is recognized that the models are only mathematical approximations of the real system. Maas (1988a) showed that the most effective method of adjusting simulation models was through reinitialization and/or reparameterization. In these procedures, which are collectively termed "within-season calibration," the values of certain model initial conditions and/or parameters are manipulated until the model simulation of a quantity fits a corresponding set of observations. An iterative numerical procedure is built into the model to manipulate the initial conditions and/or parameters so that they converge on values that result in a fit of the simulation to the observations. The mathematics of this numerical procedure has been described in detail by Maas (1992, 1993b). Maas (1991a, 1991b) showed that within-season calibration using remotely sensed data could significantly improve the accuracy of agricultural crop growth simulation models.

Two quantities in the soil water balance submodel are affected by the calibration procedure - the maximum drained capacity of the soil, and the initial amount of soil water at the start of the simulation. Calibration of these quantities occurs through comparison of modeled ET to obervations of ET. In the vegetation growth submodel, two other quantities take part in the calibration procedure - the initial value of LAI at the start of the simulation, and a parameter that determines the lifespan of leaves following their formation in the canopy. For these quantities, calibration occurs by comparing simulated LAI to observations of LAI obtained during the simulation period. This calibration procedure is shown diagrammatically in Figure 2. In the complete model, calibration is first performed for the vegetation growth submodel, using default values for the soil water related quantities. The resulting LAI simulation is then used in a calibration of the soil water balance submodel. The resulting soil water conditions are used in a second calibration of the vegetation growth submodel. This sequence continues until changes in the vegetation and soil water simulations from subsequent calibrations become negligibly small. Usually two to three passes through the calibration sequence are required for this convergence.

Figure Two

Remotely Sensed Information

NOAA-11 AVHRR images were obtained for two dates during the 1990 field study, July 28 (Day 209) and August 4 (Day 216). As the study period occurred during the relatively rainy Arizona "monsoon" season, these were the only days for which the watershed region was cloud-free. Atmospheric correction and processing of the satellite images is described by Kustas et al. (1994). The images in band 1 (red waveband), band 2 (near-infrared waveband), and bands 4 and 5 (thermal infrared wavebands) were resampled to create 1.1-km pixels, and portions of the images containing the watershed were extracted an coregistered. Pixels falling outside of the watershed boundary were masked. A split window approach (Doraiswamy and Perry 1991) was used to determine the surface temperature for each pixel from data in the thermal infrared bands. Data in the red and near-infrared bands were used to compute the normalized difference vegetation index (NDVI) for each pixel according to the formula:

in which NIR and RED are the surface reflectances in the near-infrared and red wavebands.

Data Organization (GIS)

The surface temperature and NDVI data obtained from the NOAA AVHRR imagery is in a spatially distributed form. A GIS was employed to produce spatially distributed simulations for comparison with the remotely sensed information. Thus, the remotely sensed data could then be used in calibrating the model simulations.

For this application, we chose to use a raster GIS to organize the spatial arrays of the environmental conditions (daily air temperature, solar irradiance, PET, and rainfall) needed to produce a model simulation. The scale of these arrays matched that of the remotely sensed data. If one then accepts the assumption that environmental conditions do not vary significantly over the area of a grid cell, executing the model for each grid cell in the array produces the desired spatially distributed simulation. The assumption of homogeneity within the grid cell can almost always be satistified by using relatively small array elements. In practice, the user must decide on an array element size that optimizes the balance between known spatial variability and desired simulation accuracy. Since the Walnut Gulch watershed has a naturally vegetated, gently rolling landscape, the use of 1.1-km array elements should be acceptable for this demonstration.

Observations of weather data required for determining daily air temperature, solar radiation, and PET were obtained from the eight micrometeorologocal stations located within the watershed. Daily PET at each station was calculated using the method described and validated by Van Bavel (1966). Values of daily air temperature, solar radiation, and PET were extrapolated from the eight micrometeorological station sites to the center of each grid cell using a distance-weighted procedure:

where Vx is the data value computed for the grid element, Vi the observed data value at station i, Di the distance between the center of the grid element and station i, and SUM (...) indicates a summation of the values in the parentheses over the eight stations. This resulted in the generation of a spatial array (essentially, an "image") of daily temperature, solar radiation, and PET for each of the 27 days in the study. Because these three factors are continuous over the lanscape, and the Walnut Gulch watershed is relatively small (27 km long and 11 km wide), the values of each factor showed little spatial variation on any given day.

Rainfall was observed at 112 sites in and around the watershed. Equation 6 was used to compute spatial arrays of daily rainfall, except that only observation sites within 5 km of the center of a grid element were used in the extrapolation. This resulted in the generation of a daily rainfall array (or "image") for each of the 27 days in the study that preserved the discontinuous quality of that factor.

The generation of these arrays provided the environmental data needed to execute the model and produce a simulation of ET and LAI for each grid element. The remotely sensed surface temperature and NDVI images for Day 209 and Day 216 were used to produce spatial arrays of observed ET and LAI for calibrating the model simulations for each array element. ET was estimated from surface temperature using the following relationship (Kustas et al. 1991b):

in which RNET is net radiation, G the heat flux into the ground, TSURF the remotely sensed surface temperature, and TAIR the air temperature. The constants A and B have the values 1 and 0.2, respectively, and the units of RNET and G are mm/day (evaporated water). RNET and G were evaluated from data observed at the eight micrometeorological stations. Since the values of RNET, G, and TAIR exhibited little spatial variation over the watershed, an average value of each was used in Equation 7 in computing ET for each array element on Day 209 and Day 216. LAI was computed from NDVI for each array element using the following relationship:

This relationship was developed from ground-based reflectance and ground cover observations made at sites within the watershed. The resulting ET and LAI "images" for Day 209 and Day 216 are shown in Figure 3.

Figure Three

A number of raster GISs are available for applications like that of this study. A feature of the GIS used in this study (EASI/PACE by PCI, Inc., Ontario, Canada) was its incorporation of a programming language that allowed us to combine data management, image display, and model execution in a single program. The user has a wide variety of image- and data-related procedures within the system that can be incorporated into a program, along with standard I/O, looping, and branching features and the ability to call, execute, and return from external programs (like the model used in this study). The program activities carried out for this demonstration were relatively simple - for each array element, extract the environmental data needed to run the model, extract the remotely sensed ET and LAI data, execute and calibrate the model, and build spatial arrays of the desired model results (ET, LAI, soil water, and biomass). Following completion of the program, the daily "images" of ET, LAI, soil water, and biomass could be viewed in sequence (like a movie) to visualize the changes in the watershed over time.

The model appeared to produce results consistent with what was observed on the ground. ET measured on 10 days at the Kendall micrometeorological site (station #5) averaged 2.49 mm/day (std. dev. 1.06 mm/day). Modeled ET for the array element containing this site over the same period averaged 2.50 mm/day (std. dev. 0.75 mm/day). The complete ET simulation for this array element is shown in Figure 4. Simulated LAI and biomass growth for this array element are shown in Figure 5. The biomass simulation is in reasonable agreement with the magnitude of biomass observations obtained around the Kendall micrometeorological site (the simulation does not include dead biomass already in the vegetation canopy at the start of the simulation). Daughtry and Perry (1991) reported an LAI of 0.6 from measurements around the Kendall site during the period from Day 207 to Day 217. This is in reasonable agreement with an average simulated LAI of 0.57 (std. dev. 0.04) over that period for the array element containing that site.

Figure Four

Total ET and biomass production "images" produced by the model for the 27-day period of this study are shown in Figure 6. Total water loss through evaporation from the entire watershed is estimated at 7.56 gigaliters (613,000 acre-ft) over the duration of the study. This may be compared with the amount of water input to the watershed through rainfall, estimated to be 18.32 gigaliters (1,485,000 acre-ft). It is estimated that a total of 32.75 gigagrams (29,700 U.S. tons) of new aboveground biomass was produced within the watershed during the study period. Assuming a carbon content of 38 percent of the biomass carbohydrates (Charles-Edwards 1982), this would imply that 12.45 gigagrams (11,290 U.S. tons) of atmospheric carbon would have been fixed by vegetation within the watershed during the 27 days of this study.

Figure Five

Figure Six

This relatively simple model was able to produce reasonable simulations of ET and biomass production over the 27-day period of this study. ET and LAI estimated from NOAA AVHRR observations were effective in calibrating the soil water and vegetation growth components of the model. The raster GIS was effective in organizing spatially distributed data and model executions. Use of the programming language within the GIS results in great flexibility in coordinating data input, model execution, and output of results. This strategy could provide a means of developing useful analytical tools for resource managers.

The authors wish to thank the participants of the MONSOON 90 Experiment for making this data set available for our use. In particular, we thank William P. Kustas (USDA-ARS, Beltsville, MD), David Goodrich (USDA-ARS, Tucson, AZ), James H.
Blanford (Univ. of Arizona, Tucson, AZ), William D. Nichols (USGS, Carson City, NV), Mark A. Weltz (USDA-ARS,
Tucson, AZ), M. Susan Moran (USDA-ARS, Tucson, AZ), Thomas R. Clarke (USDA-ARS, Phoenix, AZ), C.S.T. Daughtry
(USDA-ARS, Beltsville, MD), and Eileen M. Perry (Battelle Pacific Northwest Laboratories) for guidance and the use of data.

Mention of trade names within this document does not imply endorsement by the U.S. Department of Agriculture.

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Stephan J. Maas
Plant Physiologist, USDA-ARS Shafter Research Station
17053 Shafter Avenue
Shafter, California, USA 93263
Telephone: (805) 746-8002
FAX: (805) 746-1619
Email: smaas@academic.csubak.edu