Discrete dynamic-stochastic model of long-term river runoff variations

Фролов, А. В.

doi:10.1134/s0097807811040051

Cited by 7 publications

(6 citation statements)

References 7 publications

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“…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.…”

Section: Methodsmentioning

confidence: 99%

“…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).…”

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confidence: 99%

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

Grigor’ev

Frolova

2018

Geogr. environ. sustain.

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Terrestrial water storage has a significant impact on the water balance of river basins. The analysis of its changes in the European part of Russia (EPR) using the GRACE (Gravity Recovery and Climate Experiment) data showed that its reduction was approximately 150 mm for 2002-2015 for the south of EPR, especially the Don basin, which is caused rather by a decline in the storages of surface and ground waters then to changes in soil waters. Quasilinear relation between the values of terrestrial water storages and a river runoff for the period of a summer low water level for a number of rivers has been revealed.

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Section: Methodsmentioning

confidence: 99%

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confidence: 99%

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

Grigor’ev

Frolova

2018

Geogr. environ. sustain.

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“…The variance, s 2 h , is determined by taking into account the variance of river runoff volume and e, which were estimated (only modern observation data can be used) as 0.026 and 0.007 (m/y) 2 (Golitsyn et al, 1998), correspondingly. Due to their practical independence (Frolov, 2011), s 2 h ¼ 0:033 ðm=yÞ 2 . Using these values, we obtain using (7)…”

Section: Adaptation Of Brownian Motion To Explain Csl Changes During mentioning

confidence: 99%

The interpretation of secular Caspian Sea level records during the Holocene

Kislov

2016

Quaternary International

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“…Equation (6) generalizes model by V. Klemé [7] for the case of modeling the long term fluctuations in precipitation and evaporation as mutually correlated Markov chains [8]. This equation can be considered as a discrete analog of the stochastic differentiated equa tion describing fluctuations in the water balance of the Caspian Sea [9], or as that of the Langevin equation which applied for describing the stochastic dynamics of many natural processes [10].…”

Section: A V Frolovmentioning

confidence: 99%

“…where = and the variance of runoff is (8) where is the evaporation dispersion; r e is the auto correlation coefficient of the evaporation; r pe is the coefficient of mutual correlation between evaporation and precipitation; the remaining designations are explained above. Figure 1 illustrates the dependence of dimensionless variance of Volga River runoff μ = from autocorrelation coefficient of evaporation r e and dimensionless variance of the evaporation ν = .…”

Section: A V Frolovmentioning

confidence: 99%

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

Фролов

2014

Dokl. Earth Sc.

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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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Discrete dynamic-stochastic model of long-term river runoff variations

Cited by 7 publications

References 7 publications

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

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

The interpretation of secular Caspian Sea level records during the Holocene

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

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