The processes that characterize crop growth have to be ordered in a rational way to simulate crop growth. This document describes these processes as they are implemented in WOFOST. Furthermore, this chapter provides some basic information on the development of WOFOST , its applications and its functionality. Chapter 4 discusses the calculation and conversion of meteorological data like: calculation of potential evapo(trans)piration, calculation of day length and solar elevation. Chapter 5 discusses how the crop growth processes are simulated like: daily assimilation, maintenance respiration, growth respiration, partitioning of assimilates, senescence and death. Chapter 6 discusses the soil water balance calculations that are used to calculate the soil moisture content.

3.1. Development of WOFOST

WOFOST originated in the framework of an interdisciplinary study on the potential world food production by the Centre for World Food Studies (CWFS) in cooperation with the Wageningen Agricultural University, Department of Theoretical Production Ecology (WAU-TPE) and the DLO-Centre for Agrobiological Research (currently Plant Research International), Wageningen, the Netherlands. After cessation of the CWFS in 1988, model development has been carried out at the DLO-Winand Staring Centre (currently Alterra) in cooperation with PRI and WAU-TPE.

WOFOST is a member of the family of crop growth models developed in Wageningen by the school of C.T. de Wit. Related models are the successive SUCROS models (Simple and Universal Crop Simulator) (Spitters et al., 1989; van Laar et al.., 1992), Arid Crop (van Keulen, 1975; van Keulen et al., 1981), Spring wheat (van Keulen & Seligman, 1987; Stol et al., 1993), MACROS (Penning de Vries et al., 1989) and ORYZA1 (Kropff et al., 1993). The first WOFOST model has been documented by Wolf et al.. (1986). All these models follow the hierarchical distinction between potential and limited production and share similar crop growth submodels, with light interception and CO2 assimilation as growth driving processes and crop phenological development as growth controlling process. However, the submodels describing the soil water balance and the crop nutrient uptake may vary much in approach and level of detail.

Development of WOFOST has been driven by its applications in several studies. Although most studies were not intended to develop the model as such, efforts were made to maintain parts of the developed software as options in subsequent model versions. WOFOST was originally developed to assess yield potential of various annual crops in tropical countries (van Keulen & Wolf, 1986; van Diepen et al., 1988; van Keulen & van Diepen, 1990). At first it was tried to keep the input requirements as low as possible by using average input values. However, it became clear that variability of environmental conditions determining crop growth, both in space and time, had to be taken into account. The use of long term mean monthly weather data, mean sowing dates, and averaged soil data as model input may lead to a false impression of the agro-ecologic potential of a region. This implies that original rather than averaged data must be used as model input and that, if needed, averaging can be done only after the simulation. In other words: calculate first and average later (De Wit & van Keulen, 1987; Nonhebel, 1994).

3.2. Applications of WOFOST

Over the last ten years, the successive WOFOST versions and their derivates have been used in many studies. WOFOST has been applied as a tool for the analysis of yield risk and inter-annual yield variability, of yield variability over soil types, or over a range of agrohydrological conditions, of differences between cultivars, of relative importance of growth determining factors, of sowing strategies, effects of climate change and critical periods for use of agricultural machinery. The model has also been used for predictive purposes, in quantitative land evaluation, such as regional assessments of crop yield potential in the form of maximum yield levels, estimation of maximum benefits from irrigation or from fertilizer use, detection of adverse growing conditions by simulation-monitoring the agricultural season, and regional yield forecasts. Some WOFOST workers have extended the growth model to forest and grass, and have replaced the soil water module by more detailed submodels.

Unfortunately, a complete overview of applications of WOFOST is not available, since there has never been a formal network or newsletter for exchange of experiences and (validated) data sets. This has severely hampered feedback to the model developers. Here, we mention the major application studies that influenced its development, and a few examples of other WOFOST applications and extensions.

The first major regional study on the basis of WOFOST (version 3.1) dealt with potential food production increases from fertilizer aid in three African countries, and was carried out by the CWFS at the request of the FAO. The study indicated that yield of food crops in Burkina Faso, Ghana and Kenya could be increased substantially with increased fertilizer use without requiring additional irrigation (CWFS, 1985).

Within the framework of the Monitoring Agro-ecological resources with Remote sensing and Simulation (MARS) project, WOFOST (version 4.1) has been proposed as a yield estimating tool in an early warning system for food security in Zambia. This system would consist of a GIS (Geographic Information System) and a crop model, and would be fed with data from meteorological satellites (Berkhout et al., 1988). For that purpose the WOFOST model has been calibrated and tested for maize (Huygen, 1990; Wolf et al.., 1989). WOFOST 4.1 was also applied to evaluate irrigation and water conservation strategies in support of rural development in small watersheds in the Peruvian Andes (Van der Zel, 1989).

An elaborated calibration and validation study for maize in Kenya was carried out by Rötter (1993) on the basis of WOFOST 4.4. Using data from experimental fields he found that the model predicted grain yields with an accuracy of 15 percent (Root Mean Square Error) which was considered satisfactory in the light of the quality of the available data. WOFOST was then applied to re-evaluate former field trials with varying planting dates and fertilizer treatments and to assess yield risks for specific sites, prior to interpolation to regions using GIS techniques.

The AGRISK project applied WOFOST for risk studies in Burkina Faso, in order to analyze farmer's strategies to cope with drought risks in relation to soil type, crop and cultivar, sowing date, runoff and location of crop fields (Mellaart, 1989). Bakker (1992), studied the scope for rainfall insurance as a part of ICRISAT's village level studies in India's semi-arid tropics.

In the NASREC program of ISRIC and UNEP supporting the establishment of National Soil Reference Collections and Databases for education, extension and research, in which 11 countries participate WOFOST has been adopted as the reference crop model. To facilitate the use of the model for detailed land/soil properties studies, ISRIC has developed a user-friendly shell for WOFOST (version 4.3), providing a link to the NASREC database applications (Pulles et al., 1991).

WOFOST (version 5.3) was used for the estimation of the regional production potential of the major field crops in the European Community, as a function of soil and climate conditions (De Koning and van Diepen, 1992; van Lanen et al., 1992). To that end, data sets a range of temperate crops (wheat, maize, oilseed rape, potato, sugar beet) were developed as well as a separate model version for grass. In this study the model was linked to a GIS to facilitate generation of model input data and to aggregate model output over regions. The data generated were used to determine input-output coefficients of cropping systems in the EC (De Koning et al., 1994). These coefficients were used in GOAL (General Optimum Allocation of Land use), an Interactive Multiple Goal Linear Programming Model developed by the Netherlands Scientific Council for Government Policy (1992) to explore feasible options for rural land use in the EU. One of the conclusions of the study was that in Europe at least 30 percent of the agricultural land could be taken out of production without endangering food security or compromising other major political objectives.

In other studies WOFOST has been used to asses the effect of climate change on crop growth (van Diepen et al.., 1987; Wolf and van Diepen, 1991; Wolf, 1993). The model is particularly suited to quantify the combined effect of changes in CO2, temperature, rainfall and solar radiation, on crop development, crop growth and crop water use, as all the relevant processes are simulated separately while taking due account of their interactions.

WOFOST version 6 was developed under the contract study "Models for yield forecasting" issued by the Joint Research Centre (JRC) of the European Commission at Ispra, Italy, in the framework of Action 3 of the Agriculture Project, also called MARS project (Monitoring Agriculture with Remote Sensing). The objective was to generate crop growth indicators to asses the quality of the current agricultural season over the whole of the EU as compared to the quality of historic seasons. These indicators are subsequently used for quantitative yield prediction per region and per country. To this end WOFOST has been incorporated in the Crop Growth Monitoring (Hooijer and van der Wal, 1994; van Diepen, 1992). The stand-alone version of WOFOST 6.0 has been maintained for learning, demonstration, test and validation purposes, and as a starting point for its application in other studies.

In addition to the mainstream WOFOST versions, several versions have been elaborated on the basis of WOFOST 4.1. A typical example is the SWACROP2 model formed by linking WOFOST to the SWATRE soil water and transpiration rate model (Huygen, 1992). Groot (1987) simulated the nitrogen dynamics in crop and soil. Poels and Bijker (1993) created the model TROPFOR to simulate growth and water use of tropical rainforest by adapting WOFOST 4.1. De Ruijter et al. (1993) reshaped WOFOST into a model simulating tulip growth.

3.3. Functionality

Crop growth is often described by an empirical model, consisting of a regression equation (e.g. a logistic function). Sometimes, environmental variables, such as radiation and rainfall, are incorporated in the regression. These models can generate accurate yield predictions, especially when the regression parameters are estimated on the basis of extensive sets of experimental data. These predictions however, are restricted to the environment on which the regression is based. Furthermore, these empirical/descriptive models give little insight into causes of the observed yield variation.

WOFOST 6.0 is a mechanistic model that explains crop growth on the basis of the underlying processes, such as photosynthesis, respiration and how these processes are influenced by environmental conditions. The predictive ability of mechanistic models does not always live up to its expectation. It should be realized that each parameter estimate and process formulation has its own inaccuracy and that these errors accumulate in the prediction of final yield


The meteorological parameters used by WOFOST are: maximum temperature, minimum temperature, global radiation, windspeed, vapor pressure, evapotranspiration and rainfall. The meteorological data are often measured on a daily basis. This is the reason why the time step, Dt (or delt), for simulation is set to one day. The Penman method is used to calculate the evapotranspiration. Concerning global radiation it should be mentioned that in the JRC version extra options to calculate this variable are introduced. In both the general and the JRC versions the global radiation is estimated using the Ångström formula when no actual data are available. The Ångström formula uses the sunshine duration as input. If this parameter is not available, in the JRC version the global radiation is estimated using either the equation proposed by Supit (1994) or the Hargreaves formula (1985). The method developed by Supit, uses cloud cover and maximum and minimum as input and its accuracy of the estimates comes close to the accuracy of the Ångström estimates. The Hargreaves formula uses maximum and minimum temperature only, and the accuracy of the estimates is less then either the Ångström formula or the method proposed by Supit.

The empirical coefficients of the Ångström formula have to be provided by the user in the general version. In the JRC version these coefficients are estimated from meteorological stations with known values (Supit, 1994; Supit & van Kappel, 1997) using the interpolation method developed by van der Goot (1997).

Actual rainfall data are used as input in both versions. In the general version however, it is also possible to use generated rainfall.

Crop growth

Crop growth depends on the daily net assimilation, which on its turn depends on the intercepted light. The intercepted light is determined by the level of incoming radiation and the leaf area of the crop. From the absorbed radiation and the photosynthetic characteristics of single leaves, the daily rate of potential gross photosynthesis can be calculated. Reduction of the transpiration due to water or oxygen stress results in a reduced production of assimilates. The assimilates are partitioned over the various plant organs.

Water balance

A crop growth simulation model also has to keep track of the soil moisture content to determine when and to what degree a crop is exposed to water stress. WOFOST uses a water balance, which compares for a given period of time, incoming water in the rooted zone with outgoing water and quantifies the difference between the two as a change in the stored soil moisture amount. WOFOST distinguishes three different situations. The first situation occurs when the soil moisture is at field capacity and the crop growth reaches its potential level. In the second situation, the influence of evapo(transpi)ration and percolation on the availability of soil moisture are considered. Production is diminished by the reduced availability of soil moisture. In the last situation not only evapo(transpi)ration and percolation are regarded but also influence of groundwater is taken into account. This last option is not included in the JRC version. Detailed information on this subject can be found in Chapter 6.

Influence of nutrients (nitrogen, phosphate and potassium) on the yield and the yield statistics are calculated on a yearly basis. The procedure which calculates the nutrient requirements is based on the work of Janssen et al (1990). The routine consist of four successive steps. First the potential supplies of nitrogen, phosphorus and potassium are calculated, applying relationships between chemical properties of the soil layer 0-20 cm and the maximum quantity of those nutrients that can be absorbed by maize. It is assumed that the yield is not limited by nutrients and growth factors. In the second step, the actual uptake of each nutrient is calculated as a function of the potential supply of that nutrient, taking into account the potential supply of the other two nutrients. The third step compromises the establishment of three yield ranges as depending on the actual uptakes of nitrogen, phosphorus and potassium, respectively. In step four these yield ranges are combined in pairs, and the yields estimated for pairs of nutrients are averaged to obtain an ultimate yield estimate. In the general WOFOST version, statistics and the nutrient limited production are included. In the JRC version these features are omitted.

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