A MODEL attempts to simulate the way in which a crop responds to its environment.
Model outputs are usually value-added parameters that are more closely linked
to crop yield than the inputs. For instance, crop soil moisture is more relevant
to crop growth than is rainfall, as rainfall might run off without entering the
soil, particularly on hilly terrain.
The outputs are empirically related to crop yield through standard
regression techniques. This procedure is known as "model
calibration". The result of the calibration is a mathematical
expression - known as "yield function" - that is used to
calculate yield estimates based on model outputs.
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.
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
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
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
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).
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
The computation of the water balance is illustrated by the following
example of Niamey during the 1996 season.
Cropping season: 1996-96
FAO Water Satisfaction Index for Bulrush Millet
Station: NIAMEY-AERO (Elevation: 227m)
Crop type: Millet (bulrush) - Cycle length: 9 dekads
Total water requirements: 359 - Normaal water requirements: 359
Planting dekad: 18 - Maximum soil water storage: 60 mm (WHC)
Effective/total rain: 100% - Pre-season Kcr: 0.15
|8||1||-999||1||91||0.15||14||-12||0|| || |
|9||2||-999||2||92||0.15||14||-11||0|| || |
|10||0||-999||1||89||0.15||13||-12||0|| || |
|11||2||-999||2||89||0.15||13||-10||0|| || |
|12||4||-999||4||89||0.15||13||-8||0|| || |
|13||8||2||2||94||0.15||14||-11||0|| || |
|14||12||1||1||93||0.15||14||-12||0|| || |
|15||16||75||75||89||0.15||13||62||60|| || |
|16||17||0||0||79||0.15||12||-11||48|| || |
|17||23||44||44||75||0.15||11||33||60|| || |
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".
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
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.