18165 Spatial Correlation Function of the Mean Annual Water Runoff of the River of Ukraine
18165 Spatial correlation function of the mean annual water runoff of the river of Ukraine
*S. O. Moskalenko (Taras Shevchenko National University of Kyiv, Ukraine), L. V. Malytska (Ukrainian hydrometeorological institute, Kyiv, Ukraine) SUMMARY
The purpose of the study is to calculate the spatial correlation function of the average annual water runoff for the territory of Ukraine according to the data on average annual water flow for medium and large river basins. The spatial correlation function is the coefficients of paired correlation between river water runoff depending on the distances between the centers of gravity of their river basins. Mathematical statistics, statistical analysis of the relationships between hydrological variables, and GIS technologies were used to construct the spatial correlation function. It is concluded that in the range of distances between the centers of gravity of river basins (from 88.6 to 1040 kilometers) there is a positive correlation between the runoff of the studied rivers (from -0.05 to 0.88). Correlation coefficients with increasing distance between river basin centers are killing. A satisfactory correlation (at = 0.60-0.70) between the average annual river water runoff for the plain territories of Ukraine has observed at a distance between the centers of the basins 180-300 km, for the mountain areas - at a distance of 20-80 km.
Geoinformatics 2020 11-14 May 2020, Kyiv, Ukraine
Introduction
The solution of the problems of spatial interpolation of hydro-meteorological characteristics and optimization (rationalization) of a meteorological or hydrological observation network is based on the use of the spatial correlation function of an element of the investigated hydro-meteorological regime. In addition, such functions are useful in the analysis of the spatial specificity of the water regime of rivers, stochastic regularities of synchrony and asynchronous fluctuations of runoff of rivers in a certain area. Many scientists did such work throughout the past, especially in the study of cyclical fluctuations in water runoff (Kalinin and Davydova, 1967; Kazakevich, 1989; Lukіanets and Sosedko, 1998, Lukіanets and Obodovskyi, Iu. 2015; Obodovsky et al., 2019). The purpose of this study is to calculate the spatial correlation function of the mean annual water runoff for the territory of Ukraine, using the longest series of observations of annual water flow for medium and large river basins.
Method
The algorithm for calculating the spatial correlation functions of an element of the hydrological regime involves determining the following parameters (Rozhdestvenskij, 1974; Lukianets, 2010; Khristoforov, 1994): аrithmetic mean (normals) for all series of observations
n j х j xnjj i1 , (1) where: nj – is the amount of information that corresponds to j hydrometric gauging section; standard deviation for all series of observations 2 nj j ()x jjxn j i1 , (2) pair correlation coefficients for the compatible observation period
nkj ()()xikxxx k ij j r i1 jk n kjkj , (3) where: nkj – number of compatible years of observations between j and k hydrometric gauging section; distances between the centers of gravity of the rivers basins.
Results of investigations
Input data for constructing the spatial correlation function of the mean annual water runoff for the territory of Ukraine include: the mean annual river water discharge in the hydrometric gauging sections (in brackets - the observation period and the rivers basins area) (Vishnevsky and Kosovets, 2003): Tysa River –Vylok (1883-2015, F = 9140 km2); Dnister River – Zalishchyky (1882-2015, F = 24600 km2); Prut River – Chernivtsi ((1895-2015, F = 6890 km2) Prypʺyatʹ River – Mozyr (1882-2015, F = 101000 km2); Pivdennyy Buh River – Oleksandrivka (1914-2015 (with some omissions), F = 46200 km2); Desna River – Chernihiv (1895-2015, F = 81400 km2); Sula River – Lubny (1936-2015, F = 14200 km2); Psel River – Zapsillya (1927-2015, F = 21800 km2); Siversʹkyy Donetsʹ River – Lysychansʹk (1892-2015 (with some omissions), F = 52400 km2); Kalʹmius River – Sartana (1928-2015 (with some omissions), F = 3700 km2); Salhyr River – (Lystyane (Dvorichchya)) (1952-2012, F = 3540 km2).
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A series of observations of mean annual water runoff is considered representative for determining its arithmetic mean if the value of the relative mean square error does not exceed 5% - for the zone of sufficient moisture and up to 10% - for the zone of insufficient moisture: 1 nVCn ( ) 100% , (4) where: CV - coefficient of variation, п - number of years of observations (Table 1).
Table 1 Relative mean square error of mean annual water runoff normals calculation
River (hydrometric gauging Desna Desna Salhyr Dnister Donetsʹ Donetsʹ (Mozyr) (Mozyr) Kalʹmius Kalʹmius (Sartana) Prypʺyatʹ Prypʺyatʹ (Lystyane (Lystyane section) Siversʹkyy (Chernihiv) (Chernihiv) Sula (Lubny) Tysa (Vylok) Tysa (Vylok) (Zalishchyky) (Lysychansʹk) (Lysychansʹk) (Dvorichchya)) Pivdennyy Buh Psel (Zapsillya) (Oleksandrivka) Prut (Chernivtsi) (Chernivtsi) Prut
n , % 3,3 6,4 3,6 3,5 4,0 2,6 5,2 4,4 4,4 4,1 12,6
The spatial correlation matrix (Table 2) is composed of 55 correlation coefficients between the mean annual water runoff, which is obtained from 11 series of observations on investigative rivers. The highest number of compatible years of observations in the calculation of paired correlation coefficients was 133 years, the smallest - 51 years.
Table 2 Spatial correlation matrix of time series of mean annual river water runoff of Ukraine
River (hydrometric gauging section) Dnister Sula (Lubny) Tysa (Vylok) Tysa (Vylok) (Zalishchyky) (Lysychansʹk) (Lysychansʹk) (Dvorichchya)) Pivdennyy Buh Psel (Zapsillya) (Oleksandrivka) Prut (Chernivtsi) (Chernivtsi) Prut Salhyr (Lystyane (Lystyane Salhyr Prypʺyatʹ (Mozyr) Desna (Chernihiv) Siversʹkyy Donetsʹ (Sartana) Kalʹmius 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 Prut (Chernivtsi) 0,57 0,71 1 0,33 0,42 0,17 0,31 0,32 0,23 0,28 0,03 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 0,39 0,50 0,42 0,44 1 0,39 0,65 0,68 0,55 0,49 0,05 (Oleksandrivka) Desna (Chernihiv) 0,24 0,18 0,07 0,47 0,39 1 0,78 0,73 0,43 0,29 0,17 Sula (Lubny) 0,31 0,27 0,31 0,30 0,65 0,78 1 0,88 0,51 0,47 -0,05 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 0,31 0,25 0,23 0,12 0,55 0,43 0,51 0,67 1 0,68 0,003 (Lysychansʹk) Kalʹmius (Sartana) 0,27 0,23 0,28 0,09 0,49 0,29 0,47 0,58 0,68 1 0,35 Salhyr (Lystyane 0,06 0,27 0,03 0,18 0,05 0,17 -0,05 0,05 0,003 0,35 1 (Dvorichchya))
The spatial correlation function of the mean annual water runoff for the territory of Ukraine is the coefficients of paired correlation between the runoff of the rivers rQ depending on the distances between the centers of gravity of the river basins L (km) (Rozhdestvenskij, 1974). The center of gravity in space is a conditional hypothetical point where the weighted relative position of the distributed mass is equal to zero (Doganovsky and Orlov, 2011). For definition of river catchments used free and open-source geographic information system QGIS 3.12.0. and modules of Grass GIS: “r.watershed” that generates a set of maps indicating: 1) flow accumulation, drainage direction, the location of streams and watershed basins, and 2) the LS and S factors of the Revised Universal Soil Loss Equation (RUSLE); also “r.water.outlet” which generates a watershed basin from a drainage direction map and a set of coordinates representing the outlet point of watershed (Figure 1). To create digital elevation model were used dataset of STRM released by NASA and distributed by the USGS (http://srtm.csi.cgiar.org/).
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To determine the centers of gravity of the studied catchments were used a module “mean coordinates”. This algorithm computes a point layer with the center of mass of geometries in catchments.
Figure 1 River basins centers of gravity, catchment areas of rivers and matrix of distance (for example Pivdennyy Buh (Oleksandrivka) basin)
The results of determining distances between catchment centers are given in Table 3.
Table 3 Distance between river basins centers of gravity (L, km)
River (hydrometric gauging section) Dnister Sula (Lubny) Tysa (Vylok) Tysa (Vylok) (Zalishchyky) (Lysychansʹk) (Lysychansʹk) (Dvorichchya)) Pivdennyy Buh Psel (Zapsillya) (Oleksandrivka) Prut (Chernivtsi) (Chernivtsi) Prut Salhyr (Lystyane (Lystyane Salhyr Prypʺyatʹ (Mozyr) Desna (Chernihiv) Siversʹkyy Donetsʹ (Sartana) Kalʹmius Tysa (Vylok) 0 119,4 88,6 433,2 419,5 855,2 719,9 811,3 1004 1040 862,9 Dnister 119,4 0 122,9 312,7 394,1 775,8 661,5 760,6 962,5 1027 894,7 (Zalishchyky) Prut (Chernivtsi) 88,6 122,9 0 386,1 331 776,2 634,4 724,2 916,2 952,8 788,3 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 419,5 394,1 331 371,1 0 503,1 325,4 401,3 586,1 633,4 554,1 (Oleksandrivka) Desna (Chernihiv) 855,2 775,8 776,2 510,3 503,1 0 204,1 231,4 367,9 601,1 810,1 Sula (Lubny) 719,9 661,5 634,4 466,5 325,4 204,1 0 109,4 319,1 438,2 621,1 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 1004 962,5 916,2 785,2 586,1 367,9 319,1 209,9 0 258,5 582,2 (Lysychansʹk) Kalʹmius (Sartana) 1040 1027 952,8 924,7 633,4 601,1 438,2 387,9 258,5 0 386,5 Salhyr (Lystyane 862,9 894,7 788,3 921,6 554,1 810,1 621,1 582,5 582,2 386,5 0 (Dvorichchya))
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Using the data of Tables 2 and 3, we obtained the spatial correlation function of the mean annual runoff of rivers for the territory of Ukraine (Figure 2).
Figure 2 Spatial correlation function of mean annual runoff of rivers in Ukraine (rQ –correlation coefficients between river runoff, L (km) distances between the river basins centers of gravity
As we can see, in the range of distances (from 88.6 to 1040 kilometers) a positive correlation between the runoff of the studied rivers (from -0.05 to 0.88) prevails.
Conclusions
It is established that the coefficients of pair correlation with increasing distance between the centers of river basins decreasing. A satisfactory correlation (at rQ = 0.60-0.70) between the mean annual runoff of rivers in general in Ukraine is generally observed at a distance of 100-200 km. If we analyze the spatial correlation function of individually flat territories, a satisfactory correlation is observed at a distance of 180-300 km, for mountain territories - at a distance of 20-80 km.
References
Vishnevsky, V. I., Kosovets, O. O. [2003]. Hydrological characteristics of rivers of Ukraine. Kyiv, 324 (in Ukrainian). Doganovsky, A.M., Orlov, V.G. [2011] Collection of tasks to determine the main characteristics of water bodies of land (workshop on hydrology). St. Petersburg, 315 (in Russian). Kalinin, G. P., Davydova, A. I. [1967] Study of cyclical fluctuations of river flow of the northern hemisphere / in the book: Long-term fluctuations of runoff and probabilistic methods for its calculation. Moscow: «Nauka», 34-44 (in Russian). Kazakevich, D.I. [1989] Fundamentals of the theory of random functions in problems of hydrometeorology. Leningrad, 228 (in Russian). Khristoforov, A.V. [1994] Theory of random processes in hydrology. Moscow, 4-94 (in Russian). Lukianets, O.I. [2010] Methodical instructions for the implementation of practical work in the discipline «Mathematical methods in hydrometeorology" for students of the Faculty of Geography. Kyiv, 38-46 (in Ukrainian). Lukіanets, O., Sosedko, M. [1998] Runoff assessment for next years in the Carpathian Mountains taking into account the multi-year runoff fluctuations. XIX. Conference of the Danube countries. Osijek (Croatia), 393-401 (in German). Lukianets, O., Obodovskyi, Iu. [2015] Spatial, Temporal and Forecast Evaluation of Rivers’ Streamflow of the Drainage Basin of the Upper Tisa under the Conditions of Climate Change. Scientific Journal of Environmental Research, Engineering and Management, Kaunas University of Technology, 71, 1, 36-46. Obodovsky, O., Lukіanets, O., Moskalenko, S., & Kornienko, V. [2019]. Generalization of the average annual water runoff of the rivers according to the hydrographic zoning of Ukraine. Visnyk of V. N. Karazin Kharkiv National University, Series "Geology. Geography. Ecology, (51), 158-170 (in Ukrainian). Rozhdestvenskij, A.V., Chebotaev, A.I. [1974] Statistical methods in hydrology. Leningrad, 316-355 (in Russian).
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