Fourth Study Conference on BALTEX Scala Cinema Gudhjem

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Water Sub-Model of a Dynamic Agro-Ecosystem Model and an Empirical
Equation for Evapotranspiration
Jüri Kadaja
Estonian Research Institute of Agriculture, Teaduse 13, Saku, 75501, Estonia
Estonian Maritime Academy, Luise 1/3, Tallinn, 10142, Estonia, e-mail: kadaja@solo.ee
1. Introduction
An essential component of agro-ecosystems is water, having
cardinal importance in plants nutrient supply and in
production of new matter in photosynthesis process. Water
is permanent or contemporary limiting factor of plant
production in most of agro-ecosystems, both in conditions of
water deficit and excess.
Therefore, in modeling of agro-ecosystems we have to take
into consideration the water status of the system determined
by the water content of soil. It is a quantity immediately
measurable on the field. However, according to rapid
changes in soil spatial properties the variability of soil water
content is very high. It makes the producing of sufficient
number of soil moisture measurements impossible for
territorial applications. That is why a great number of agroecosystem
models use sub-models for soil water
calculations. Schemes on water balance equation are
prevailing. This paper describes the water sub-model and its
components used in potato production model POMOD.
2. The model POMOD and its applications
The potato model POMOD (Sepp, Tooming, 1991; Kadaja,
2001) is a dynamic model for describing the course of
production process and calculating the yield of potato crop.
The model integrates the major plant physiological
processes: photosynthesis, respiration and growth of plant
organs. The rate of photosynthesis is determined on the basis
of photosynthetically active radiation and limited by
temperature and soil water availability. From the running
environmental factors global solar radiation, air temperature
and precipitation are taken into account.
This model is composed for solving theoretical and practical
problems on the field (agro-ecosystem) and geographic
levels. It have been used for calculating and mapping of
radiation, agro-meteorological and agro-climatic resources
in yield units for potato cultivation in Estonia and in the
other Baltic republics (Sepp, Tooming, 1991; Kadaja, 1994).
Similar estimation of resources was carried out for Komi
territory situated near the polar circle (Sepp et al., 1989).
Using the longest available series of meteorological data for
Estonia and neighboring Russian areas the yield series were
calculated for almost a century period (Sepp, Tooming,
1991) allowing to analyze the impact of weather and its
factors to potato yield long before the variety itself came
into existence. The yield long time-series allowed to
construct their frequency distribution functions, which in
principle are the probabilistic climatic yield forecasts. On
the basis of the model POMOD, the probabilistic yield
forecast method of current year was elaborated (Sepp, 1988;
Zhukovski et al., 1989).
The estimate of the impact of potential climate changes on
the potato yield have been an output of the model. Neither
significant trends in mean computed yields nor in their
entropy was observed in Estonia during the 60-90 year
periods of previous century. The reactions of potato yield to
the possible climate scenarios for Baltic region were evident.
These scenarios (Keevallik, 1998), describing the global
warming, shift the optimum areas of potato cultivation to
north. Low and medium scenarios move it from
Byelorussia to South and North Estonia respectively, high
scenarios to Finland (Kadaja, Tooming, 1998).
3. Soil water content block of the model
In the model POMOD soil available water content is
calculated using the equation of soil water balance. The
water flows taken into the consideration are the
precipitation U, the evapotranspiration E and the sum of
runoff and infiltration through the soil V:
W = W0
+ U - E - V , (1)
where W is available water storage and W0 is its initial
value in the beginning of the calculating period.
Calculation of soil water balance can be initiated from the
spring soil moisture measurements, if these data are
available. Also, the initial value of soil moisture can be
regarded as equal to field capacity at the moment when
soil moisture condition becomes moderate (the best
suitable condition of soil for planting, observed visually in
meteorological stations).
Criterion for runoff and infiltration into deep layers was
derived, comparing the measured values of soil water
storage with its calculated curves using water balance
equation. It was concluded, that any precipitation
exceeding 20 mm per day turned out to be “excessive”.
Measured information is required for precipitation, e.g.
data from the meteorological network interpolated over
the territory. Evapotranspiration have to be calculated.
4. Equation for evapotranspiration
Selecting the method for calculation of evapotranspiration,
the dependence on the vegetation was expected.
Unfortunately, the more advanced evapotranspiration
formulae which take into account the vegetation would
increase the amount of model input information. E.g., the
widely used Penman-Monteith formula (Monteith, 1965)
would introduce need for running data of air water vapour
pressure and additional parameters for surface. Therefore
the use of an empirical equation was chosen. An equation
for computing potential evapotranspiration by global
radiation and leaf area index (LAI) was derived by Gojsa
and Bibik (1976) for maize. A quite similar simple
formula based on evaporation measurements in 1979 from
soil evaporimeters with and without plants was elaborated
by us for potato. In the case of good water supply the
evapotranspiration expresses as (Sepp,Tooming, 1991):
E = Q ( 0,
0872 + 0.
0406 L ) , (2)
where Q is the global radiation (MJ/m 2 ) and L the total
leaf area index of the canopy (m 2 /m 2 ). To get the resulting
evapotranspiration in mm (or kg/m 2 ) the numeric
coefficients of the formula are given in unit kg/MJ.
Additionally into this formula was included the soil water
storage to obtain adequate results in case of water deficit:
E = Q 0,
0872 + 0.
0406 L ) min( 1,
W / W ) . (3)
( opt,1