Estimation of the statistical characteristics of long-term fluctuations in evaporation from large river catchments

Abstract

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...

Terrestrial Water Storage Change of European Russia and Its Impact on Water Balance

“…The parameter alin in the formula (3) determines how much the runoff value increases with an increase in TWSA by 1 mm. The higher alin, the lower the water-retaining capacity of a catchment area, the lower the runoff autocorrelation coefficient and the lower its inertia (Frolov 2014). Therefore, the variability of terrestrial water storages (σ TWS ) will be lower for the catchment areas with high alin values.…”

“…ERA-Interim covers the period from 1979 to 2017 with a resolution of about 0.75° in latitude and longitude. The data for 31 gauging stations were used to calculate the average monthly runoff ( Revealing a relation between TWS and the modulus of flow (Q) using the GRACE data in the form of a power dependence that has a physical basis (Dolgonosov 2008;Frolov 2011Frolov , 2014 is complicated by the fact that it is not the absolute amount of water in the basin that the available TWS values express, but its anomaly (TWSA), relative to the average value for any period taken as zero.…”

“…where a and c are coefficients, Q -modulus of flow ((m 3 /s)/ km 2 ).The power dependence for some assumptions about the similarity of a river network can be obtained from a kinematic wave equation for a slope runoff (Dolgonosov 2008), moreover, the exponent can be in the range from 1.5 to 3 depending on the preferred type of a runoff (1.5 for a turbulent and 3 for a laminar one). The value of the autocorrelation coefficient, the dispersion of a river runoff and the correlation coefficient between precipitation and a river runoff depend on the dependence R = f(TWS) (Frolov 2011;Frolov 2014).…”