Figure 2: Conceptual diagram of the crop model. Environmental (weather)
parameters: is the daily PAR, is a parameter of water
regime, is the CO concentration in the atmosphere,
is the daily temperature.
The basic state variables are the phytomasses of leaves, steams, roots and
generative organs (ears), correspondingly. All these
values are functions of time, , measured in days. The general equations
of the model are:
where the daily net production, Y, depends both on the state variables
and the weather parameters . Here is a daily amount of
the photosynthetically active radiation (PAR). The latter is presented in the
form of so-called solar hours. 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
and are the concentration of atmospheric CO and the
daily temperature.
The function Y is defined by standard dependencies taken from plant physiology and ecology (see, for instance, [8]). The coefficients , i=1,2,3,4 () 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.
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 , where k is an empirical coefficient and 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 -set, that is, the set of climatic parameters (climates) 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