n Spatial correlation function of the mean annual water runoff of the river of Ukraine S. Moskalenko1., L. Malytska2
1 – Taras Shevchenko National University of Kyiv 2 – Ukrainian hydrometeorological institute
Introduction Results of investigations.
The solution of the problems of spatial A series of observations of mean annual water runoff is considered representative for determining its arithmetic interpolation of hydro-meteorological characteristics mean if the value of the relative mean square error does not exceed 5% - for the zone of sufficient moisture and up to and optimization (rationalization) of a meteorological 10% - for the zone of insufficient moisture. or hydrological observation network is based on the Table 1 Relative mean square error of mean annual water runoff normals calculation
use of the spatial correlation function of an element ) ) )
) ) ))
) )
)
of the investigated hydro-meteorological regime. In
)
Buh )
addition, such functions are useful in the analysis of River Vylok Lystyane Lubny ( (
(hydrometric (
the spatial specificity of the water regime of rivers, Zapsillya Chernivtsi ( Desna Mozyr Dnister (
Sartana Donetsʹ (
Kalʹmius Prypʺyatʹ
gauging section) ( Chernihiv Siversʹkyy
stochastic regularities of synchrony and ( Zalishchyky Lysychansʹk Tysa Sula Dvorichchya ( ( Oleksandrivka ( Pivdennyy Psel
( asynchronous fluctuations of runoff of rivers in a Prut Salhyr certain area. Many scientists did such work , % 3,3 6,4 3,6 3,5 4,0 2,6 5,2 4,4 4,4 4,1 12,6 throughout the past, especially in the study of The spatial correlation matrix (Table 2) is composed of 55 correlation coefficients between the mean annual water cyclical fluctuations in water runoff. runoff, which is obtained from 11 series of observations on investigative rivers. The highest number of compatible years The purpose of this study is to calculate the of observations in the calculation of paired correlation coefficients was 133 years, the smallest - 51 years. spatial correlation function of the mean annual water Table 2 Spatial correlation matrix of time series of mean annual river water runoff of Ukraine
runoff for the territory of Ukraine, using the longest
)
) ) )
series of observations of annual water flow for
)
medium and large river basins. River (hydrometric gauging Vylok Lubny ( (
Prut
section) Desna Salhyr Salhyr Mozyr
Dnister Donetsʹ Donetsʹ ( Kalʹmius Kalʹmius
Prypʺyatʹ (Sartana) (Lystyane (Lystyane Chernihiv Siversʹkyy Siversʹkyy ( (Chernivtsi) Zalishchyky Tysa Sula (Lysychansʹk) ( (Dvorichchya)) Pivdennyy Buh Pivdennyy Psel (Zapsillya) Psel Method (Oleksandrivka) Tysa (Vylok) 1 0,70 0,57 0,43 0,39 0,24 0,31 0,41 0,31 0,27 0,06 Dnister (Zalishchyky) 0,70 1 0,71 0,55 0,50 0,18 0,27 0,35 0,25 0,23 0,27 The algorithm for calculating the spatial Prut (Chernivtsi) 0,57 0,71 1 0,33 0,42 0,17 0,31 0,32 0,23 0,28 0,03 correlation functions of an element of the Prypʺyatʹ (Mozyr) 0,43 0,55 0,33 1 0,44 0,47 0,30 0,38 0,12 0,09 0,18 Pivdennyy Buh (Oleksandrivka) hydrological regime involves determining the 0,39 0,50 0,42 0,44 1 0,39 0,65 0,68 0,55 0,49 0,05
following parameters Desna (Chernihiv) 0,24 0,18 0,07 0,47 0,39 1 0,78 0,73 0,43 0,29 0,17 • аrithmetic mean (normals) for all series of Sula (Lubny) 0,31 0,27 0,31 0,30 0,65 0,78 1 0,88 0,51 0,47 -0,05 observations: Psel (Zapsillya) 0,41 0,35 0,32 0,38 0,68 0,73 0,88 1 0,67 0,58 0,05 Siversʹkyy Donetsʹ (Lysychansʹk) 0,31 0,25 0,23 0,12 0,55 0,43 0,51 0,67 1 0,68 0,003 n j Kalʹmius (Sartana) 0,27 0,23 0,28 0,09 0,49 0,29 0,47 0,58 0,68 1 0,35 хj xj n j i1 Salhyr (Lystyane (Dvorichchya)) 0,06 0,27 0,03 0,18 0,05 0,17 -0,05 0,05 0,003 0,35 1 where: nj – amount of information that corresponds The spatial correlation function of the mean annual water runoff for the territory of Ukraine is the coefficients of to j hydrometric gauging section; paired correlation between the runoff of the rivers depending on the distances between the centers of gravity of the • standard deviation for all series of observations: river basins (km). The center of gravity in space is a conditional hypothetical point where the weighted relative position of the distributed mass is equal to zero. 2 n j For definition of river catchments used free ()x x n and open-source geographic information system j j j j i1 QGIS 3.12.0. and modules of Grass GIS:
“r.watershed” that generates a set of maps • pair correlation coefficients for the compatible indicating: 1) flow accumulation, drainage observation period: direction, the location of streams and watershed n kj basins, and 2) the LS and S factors of the ()()xik x k x ij x j Revised Universal Soil Loss Equation r i1 (RUSLE); also “r.water.outlet” which generates jk k jn kj a watershed basin from a drainage direction map and a set of coordinates representing the where: nkj – number of compatible years of outlet point of watershed (Figure 1). To create observations between j and k hydrometric gauging digital elevation model were used dataset of section; STRM released by NASA and distributed by the • distances between the centers of gravity of the USGS (http://srtm.csi.cgiar.org/). rivers basins. To determine the centers of gravity of the studied catchments were used a module “mean Input data coordinates”. This algorithm computes a point Figure 1 River basins centers of gravity, catchment areas of rivers and matrix of layer with the center of mass of geometries in distance (for example Pivdennyy Buh (Oleksandrivka) basin) Input data for constructing the spatial correlation catchments. function of the mean annual water runoff for the Table 3 Distance between river basins centers of gravity (L, km)
territory of Ukraine include: the mean annual river )
)
water discharge in the hydrometric gauging sections River (hydrometric gauging ) i) ky sʹk) Psel Psel Prut Buh Sula Sula Tysa ivka) hya)) Vylok
section) Desna (in brackets - the observation period and the rivers Salhyr Dnister ( Donetsʹ Donetsʹ (Lubny) (Mozyr) Zalishchy Kalʹmius Prypʺyatʹ Prypʺyatʹ (Sartana) (Lystyane (Lystyane (Dvorichc (Lysychan Siversʹkyy Siversʹkyy (Chernivts Pivdennyy ( (Chernihiv (Zapsillya) basins area) : (Oleksandr Tysa (Vylok) 0 119,4 88,6 433,2 419,5 855,2 719,9 811,3 1004 1040 862,9 Dnister (Zalishchyky) 119,4 0 122,9 312,7 394,1 775,8 661,5 760,6 962,5 1027 894,7 2 Prut (Chernivtsi) 88,6 122,9 0 386,1 331 776,2 634,4 724,2 916,2 952,8 788,3 • Tysa River –Vylok (1883-2015, F = 9140 km ); Prypʺyatʹ (Mozyr) 433,2 312,7 386,1 0 371,1 510,3 466,5 575,8 785,2 924,7 921,6 Pivdennyy Buh • Dnister River – Zalishchyky (1882-2015, F = 419,5 394,1 331 371,1 0 503,1 325,4 401,3 586,1 633,4 554,1 24600 km2); (Oleksandrivka) 2 Desna (Chernihiv) 855,2 775,8 776,2 510,3 503,1 0 204,1 231,4 367,9 601,1 810,1 • Prut River–Chernivtsi (1895-2015,F = 6890 km ); Sula (Lubny) 719,9 661,5 634,4 466,5 325,4 204,1 0 109,4 319,1 438,2 621,1 •Prypyat River–Mozyr(1882-2015,F=101000 km2); Psel (Zapsillya) 811,3 760,6 724,2 575,8 401,3 231,4 109,4 0 209,9 387,9 582,5 Siversʹkyy Donetsʹ •Pivdennyy Buh River – Oleksandrivka (1914- 1004 962,5 916,2 785,2 586,1 367,9 319,1 209,9 0 258,5 582,2 2 (Lysychansʹk) 2015 (with some omissions), F = 46200 km ); Kalʹmius (Sartana) 1040 1027 952,8 924,7 633,4 601,1 438,2 387,9 258,5 0 386,5 •Desna River–Chernihiv(1895-2015,F=81400 km2); Salhyr (Lystyane 862,9 894,7 788,3 921,6 554,1 810,1 621,1 582,5 582,2 386,5 0 2 (Dvorichchya)) •Sula River – Lubny (1936-2015, F = 14200 km ); •Psel River – Zapsillya(1927-2015, F = 21800 km2); •Siverskyy Donets River – Lysychansk (1892-2015 Conclusions (with some omissions), F = 52400 km2); •Kalmius River – Sartana (1928-2015 (with some It is established that the coefficients of pair correlation with increasing distance 2 omissions), F = 3700 km ); between the centers of river basins decreasing. A satisfactory correlation (at rQ •Salhyr River – Lystyane (Dvorichchya) (1952- = 0.60-0.70) between the mean annual runoff of rivers in general in Ukraine is 2 generally observed at a distance of 100-200 km. If we analyze the spatial 2012, F = 3540 km ). Figure 2 Spatial correlation function of mean annual runoff of rivers in Ukraine (r –correlation coefficients Q correlation function of individually flat territories, a satisfactory correlation is between river runoff, L (km) distances between the river observed at a distance of 180-300 km, for mountain territories - at a distance of basins centers of gravity) 20-80 km.