Crops require solar energy to develop and grow. However, exposure to the sun also tends to increase the temperature of leaves, sometimes to such an extent that plants would die if they did not evaporate water to maintain their temperature at acceptable levels. In fact, the amount of solar energy that plants can accumulate is directly linked to amount of water that can be evaporated. The main aim of the crop model and water budget described here is to estimate the amount of water consumed which, in turn, is very closely related to crop yield.

Modelling approach
The modelling approach is based on a continuous monitoring of the cropping season, which determines a cumulative water balance for each period of 10 days ("dekad") from planting to maturity.

What do we mean by "cumulative"? The cycle of each crop is subdivided into successive 10-day (dekad) periods taken as time unit. For each dekad, rainfall, crop water requirements and crop stage are known. "Cumulative", then, means that the water balance is carried out from the beginning to the end of the crop cycle, the water available - i.e. soil moisture - at the beginning of each dekad being the amount available at the end of the previous one, plus rainfall, minus crop water consumption.

At the same time, the water stress that could affect the crop during its development is also calculated in a cumulative way. The approach takes into account both rainfall amounts and distribution and amounts: every ten days, the water available to crops (rainfall and stored soil moisture) is derived from weather data and crop water requirements.

This requires a preliminary investigation and collection of various agronomic parameters, i.e. cultivars, length of different growth stages, length of total growing period, crop coefficients allowing estimates of crop water requirements for each of the growth stages, soil water holding capacity, effective rainfall and soil runoff.

This model could be considered as a combination of the dynamic (water balance) and statistical (calibration of yield function) approaches. In fact, at harvest time, the sum of dekadal water stress suffered by the crop (the Water Satisfaction Index), crop water consumption - the most important parameter of "actual evapotranspiration" - and some other relevant variables are combined into a forecast yield by a regression equation.

The whole model is based on the Crop Specific Soil Water Balance (CSSWB) which is a very simple but physically sound soil water budgeting approach developed for operational use.

Rainfall and evapotranspiration
For crop forecasting, the impact of climate on crops is always transformed into a certain loss of water, i.e. "evaporation", which depends on the available water and on available energy. In case of cropped surfaces, this continuous loss in the form of vapour is called "evapotranspiration" since water loss is due to the combined evaporation from the soil and the transpiration through plant surfaces.

For crops, it is important to evaluate maximum water loss under certain climatic conditions and under unlimited water availability at the root system level, i.e. the "maximum evapotranspiration" (ETM). For practical purposes, the value of the "potential evapotranspiration" (PET) is then calculated. This is an adjustment to climatic conditions of the average ETM values of cropped surfaces in an optimum development state and without any physiological constraints.

For each of the growth phases, actual water availability is compared with the requirement (optimum). This point is illustrated in the graph below which shows the distribution over the cropping season for Niamey (Niger) of 1996 rainfall as compared to average rainfall and the average potential evapotranspiration (PET). A standard time interval of 10 days (dekad) has been adopted in all data processing and analysis. Water availability exceeds demand only during a limited period of the year.

Growing period and crop coefficient
Potential evapotranspiration is a climatic variable, i.e. it is the "water demand of the atmosphere", often referred to as water "requirement" of a conventional crop. Actual crops have different requirements, which are related to crop development - early stages require little water - and weather conditions (for example, dry and windy conditions increase water requirement).

In order to estimate real crop water requirements, PET values must be corrected. This correction brings us closer to the ETM values for the different crop development phases. In practice, PET values are transformed through the use of a crop coefficient (Kc). Values of Kc higher than 1.0 (i.e. ETM>PET) mean well developed crops, while values of Kc lower than 1.0 (i.e. ETM<PET) correspond to bare soils or a sparse crop.

As shown below crop water requirements grow slowly at the beginning of the crop cycle (early vegetative phases) but increase beyond PET at mid-cycle, to drop again when the crop matures.

The same information and analysis of rainfall and PET is used in assessing general crop feasibility under specific climatic conditions and to calculate the length of the crop growing period.

The graph below shows the average length of the growing and humid periods as calculated for Ouagadougou (Burkina Faso).

Water budget
The objective of the water balance model is to convert raw observations of the atmospheric environment into a set of parameters that are of direct importance to crop production. Those parameters include:

• the "Actual Evapotranspiration" (ETA), which is the amount of water actually used by the crop excluding runoff
• the amount of excess of water, which may damage crops through waterlogging
• a Water Satisfaction Index (WSI), which expresses which percentage of the crop's water requirements were actually met.

Basically, the water balance is the difference between the effective amounts of rainfall received by the crop and the amounts of water lost by the crop and soil due to evaporation, transpiration and deep infiltration. The amounts of water held by the soil and available to the crop is also taken into account.

In practice, the water balance is computed using a bookkeeping approach. The computation is done dekad-by-dekad (DEK), and starts before the planting in order to take into account previous rainfall amounts stored into the soil. From the planting dekad, the crop water requirements (WR) are calculated as the potential evapotranspiration (PET) times the crop coefficient (KCR) values. Thus, the available water amount (AvW) is the difference between the crop water requirements and the working rainfall (WRK). Those amounts do not consider water stored by the soil. The working rainfall amount reflects the effective water received by crop and is calculated through a ratio defined by the user on the basis of the type of soil, slope, etc. Normal rainfall (NOR) is used in case of missing values.

Surplus or deficit (S/D) result from the water budget between the soil water storage (SW), ranging between the field capacity and the permanent wilting point, depending on the root depth, and the soil water holding capacity (WHC). Finally, the water satisfaction Index summarizes, up to a specific growth stage or the end of its development, the degree to which cumulative crop water requirements have been met. The WSI represents, at any time of the growing period, the ratio between the actual and the potential evapotranspiration.

The computation of the water balance is illustrated by the following example of Niamey during the 1996 season.

The "agmet model" also includes crop specific constants as well as soil constants (water storage capacity) but takes no direct account of soil fertility, technology (mechanization, fertilizer use), varietal differences and farming practices. It is a characteristic of the FAO approach that these important parameters are brought in at the next step, the "yield function".

Yield function
The yield function is a statistically derived function relating the water balance parameters (which constitute the outputs of the "agmet model") and the other factors (farm inputs, trend) or NDVI with station yield.

The yield function is valid for a crop and a group of stations in an homogeneous cropping area. The input data correspond to different geographical units, from weather stations, to pixels (NDVI, CCD: 50 km2) to administrative units. It is an important step in the forecasting method to convert the data to comparable units (area averaging), usually administrative areas that are used by planners or decision makers in the field of food security.

Below is a very simple example of a yield function in an area where yields are mainly conditioned by limited water supply, as is the case -by definition- in most semi-arid areas of the world.

Regression lines similar to the one above have been used to prepare the yield maps shown in the following Outputs section.