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Crop production model.

We use a specific crop production model [6][7], calibrated by data which have been collected by E. Denisenko in the course of two periods: 1978 and 1983. A model structure is shown in Fig. 2.

  figure107
Figure 2: Conceptual diagram of the crop model. Environmental (weather) parameters: tex2html_wrap_inline887 is the daily PAR, tex2html_wrap_inline889 is a parameter of water regime, tex2html_wrap_inline891 is the COtex2html_wrap_inline691 concentration in the atmosphere, tex2html_wrap_inline895 is the daily temperature.

The basic state variables are the phytomasses of leaves, steams, roots and generative organs (ears), tex2html_wrap_inline897 correspondingly. All these values are functions of time, tex2html_wrap_inline899, measured in days. The general equations of the model are:
 equation112
where the daily net production, Y, depends both on the state variables tex2html_wrap_inline903 and the weather parameters tex2html_wrap_inline905. Here tex2html_wrap_inline887 is a daily amount of the photosynthetically active radiation (PAR). The latter is presented in the form of so-called solar hours. tex2html_wrap_inline889 is the parameter determining the water regime of barley crops. In fact, this value depends on precipitation dynamics, in particular, on alteration and lengths of so-called ``dry'' and ``wet'' series, that is, series of days with no precipitation and days with significant precipitation without dry period between them. The parameters tex2html_wrap_inline891 and tex2html_wrap_inline895 are the concentration of atmospheric COtex2html_wrap_inline691 and the daily temperature.

The function Y is defined by standard dependencies taken from plant physiology and ecology (see, for instance, [8]). The coefficients tex2html_wrap_inline919, i=1,2,3,4 (tex2html_wrap_inline923) describe some allocation principle, that is, they show how the new phytomass is allocated among different organs of plant. In order to calculate them we postulate the following local variational principle which reflects the process of plant adaptation to variations of environment.

All the vegetation period is divided into two parts: before and after the appearance of generative organs.

Before:
the new phytomass is allocated among leaves, steam and roots in this way that to maximise the growth rate of total phytomass in the next time, under the condition that the state of environment does not change.
After:
the new phytomass is allocated among leaves, steams, roots and generative organs in this way that to maximise the growth rate of generative organs in the next time, under the condition that the state of environment does not change.

The comparison of the model results and observed data for 1983 is shown in Fig. 3.

  figure124
Figure 3: Comparison of the observed (markers) and model (lines) data of the Kursk region for the year 1983.

It is obvious that the crop yield tex2html_wrap_inline925, where k is an empirical coefficient and tex2html_wrap_inline929 is the end of the vegetation period. In this model the crop yield is a functional that depends on the trajectories of the daily temperature, precipitation and PAR during the vegetation period. It is obvious that the tex2html_wrap_inline931-set, that is, the set of climatic parameters (climates) tex2html_wrap_inline701 is a functional space, the elements of which are trajectories of the values mentioned above. In order to estimate the dependence of crop production on this type of trajectories for the future changed climate we have to know how to generate them. For this we have used a so-called


next up previous
Next: Statistical weather generator Up: Case-study: Barley crop production Previous: Case-study: Barley crop production

Werner von Bloh (Data & Computation)
Fri Jul 14 10:44:24 MEST 2000