The next problem is: how to construct the -set, that is, the set of climatic parameters (climates) prescribing a climate scenario?
Let us assume that the local climate is not changing (at least during the last two decades covered our observation interval from 1970 up to 1984 during 15 years). Thus, despite annual variation of crop yield as a consequence of weather variation, the local climate is fixed, and there is only one point (corresponding to this climate) in -space. Suppose we have the model of this climate, the ``statistical weather generator'', which is a stochastic parametric process. Its parameters are, in turn, characteristics of the mesoclimate at the given site. One realisation of this stochastic process (a trajectory) is considered as the weather at a given site and in a given year.
The simplest hypothesis is the following:
Let us take 15 (for each vegetation period) time-series ,
for the temperature, where is any point of time
within the vegetation period.
is the mean temperature in the course of a vegetation period for this site,
that is, a characteristic trait of the local climate. The average current
variance of the temperature is also calculated as
Using these values we calculate (by formula (5)) a statistical
consequence describing some standard daily temperature dynamics, which is
typical for the given site. As generalised characteristics for the local
climate we use the temporal averaging of the functions and
over the interval which is the vegetation
period, so that
are the ``vegetation'' temperature and variance. If the first value is the
mean temperature of the vegetation period, then the latter is a variance of a
seasonal temperature during a vegetation period.
In the same way, the mean precipitation for the vegetation period and its
variance are calculated. The ``weather generator'' is constructed in such a way
that the generated stochastic series do not differ statistically from the real
climatic time-series, that is, the statistical characteristics (means and
variances) of the generated series are equal to those of the local climate.
Thus, the next hypothesis may be formulated:
At the first stage we assume that as a result of climate change the mean temperature and its variance are changed. For instance, and for the Kursk region. The values of and make up the set of climatic parameters (climates), that is, the -set.
In accordance with different climate models (GCMs, paleoclimatic and extrapolation models), the increase of mean summer temperature in the Kursk region would be - C for the doubling of CO scenario. The methods of ``optimal filtration'' (in case if some marginal predictions are rejected) give us the interval equal to - C. Concerning the change of variance, there are only some qualitative estimations available. For instance, the estimations of variance by GCMs show that, in general, the variance of summer temperatures decreases [10]. It seems that this statement could be valid for the polar and tropic regions, but it is doubtful for such a temperate region as the Central Russia. On the other hand, statistical extrapolation of the observed data shows the increase of variance. We prefer the latter.
In our calculation we shall use an old empirical rule of statistics [11], which suggests that . Thereby, we obtain the following biased estimation: C. Assuming that the variance either does not change or rises, we obtain that the interval of possible values for is equal to - C.