Evaporation is the least studied component of the river basins water balances. Huge territories of large river watersheds are characterized by a variety of land scape and hydrometeorological conditions. The detailed account of the spatial temporal peculiarities of evaporation is complicated by the insufficient amount of field observations, which are necessary to obtain the respective long term series. However, inves tigation of the long term fluctuations in evaporation from river basins is of applied interest, especially with respect to possible assessment of climate change influ ence on river runoff [1,2].The present study is based on the idea about a river catchment as a hydrological system with one output process (river runoff) and two input ones (precipita tion and evaporation). The dynamic stochastic model of this hydrological system is based on the stochastic equation of the catchment water balance; the model enables us to obtain the dependences connecting the river runoff statistics and the respective characteristics of precipitation and evaporation over the river catch ment. The variance and autocorrelation coefficient of the long term fluctuations in evaporation are found in as a solution of the nonlinear equations system (which represent the dependences mentioned above).
BASIC EQUATIONS AND RELATIONSUnder the assumption that the components of the catchment water balance can be considered as station ary random processes, one of the characteristics of long term fluctuations in evaporation from the catch ment, namely, the mean value-is estimated as the difference between the mean values of precipitation and river runoff. For this estimation we use the sto chastic difference equation of the catchment water balance in the form:(1)where Δw t is the annual change in the total (surface and underground) water storage in the catchment; w t is the water storage in the watershed in the tth year; p t is the annual precipitation in the tth year; e t is the annual evaporation in the tth year; q t is the annual river runoff in the tth year (t = 1, 2, … is the year). Water balance equation (1), which is discrete relative to time t, is widely used to model river runoff from the watershed and runoff from non terminal lakes (for example, see [3,4]). It is also assumed that the water balance com ponents of (1) have finite statistical moments.After averaging the left and right parts of equation (1), and taken into account that under stationary condi tions 〈Δw t 〉 = 0, the mean evaporation 〈e t 〉 is found as the difference between the mathematical expectations of precipitation 〈p t 〉 and the river runoff 〈q t 〉:(2) hereinafter, triangular brackets mean the statistical averaging procedure. This method of estimating the average evaporation from the catchment has long been known and widely used by hydrologists (for example, see [5]). Now let us show how other stochastic characteris tics of evaporation (variance and autocorrelation coef ficient) can be derived using the stochastic equation of the catchment water balance.This bala...
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