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ISSN 2617-2909 (print) ISSN 2617-2119 (online)
Journ.GeoI. Geograph.
Geology, 29(1), 166-175.
doi: 10.15421/112015
V. A. Ovcharuk, M. E. Daus, N. S. Kichuk, M. I. Myroshnychenko, Y. V. Daus Journ. Geol. Geograph. Geoecology, 29 (1), 166-175.
The analysis of time series of river water mineralization in the Dnipro basin with the use of theoretical laws of random variables distribution
Valeriia A. Ovcharuk1, Mariia E. Daus2, Natalia S. Kichuk1, Mariia I. Myroshnychenko1, Daus Yurii V.2
1 Odessa State Environmental University, Odesa, Ukraine, valeriya.ovcharuk@gmail.com
2 Odessa National Maritime University, Odesa, Ukraine
Received: 18.09.2019 Abstract. The analysis of current scientific work on the use of statistical methods in hydro-
Received in revised form: 25.09.2019 chemical research has shown that this approach is sufficiently substantial, both in Ukraine Accepted: 16°2.2020 and abroad. The purpose of this work is to determine the main statistical parameters and to
research the possibility of applying theoretical laws of distribution to the time series of water mineralization.This research presents the results of the application of standard statistical methods of hydrometeorological information processing for data on water mineralization at 28 gauges of the Dnipro basin (within Ukraine) for the period from 1990 to 2015. The dynamics of the obtained statistical parameters (long-term annual average, coefficients of variation, asymmetry and autocorrelation) within the Dnipro basin in Ukraine has been analyzed. The average annual values of mineralization vary substantially within the studied part of the Dnipro basin - in the northern part the maximum value of the annual average mineralization is 447 mg/l, as it moves to the south, the mineralization increases and in the sub-basin of the Middle Dnipro it reaches a maximum of 971 mg/l; the highest values are observed in the south (sub-basin of the Lower Dnipro), where they can reach extremely high values for particular small rivers (the Solon River - Novopavlivka village, 3356 mg / l). The long-term variability of mineralization in the rivers of the studied area is insignificant, and the autocorrelation coefficients of the mineralization series are quite high, in most cases they are significant and tend to decrease from the sub-basin of the Prypyat' river in the north to the sub-basin of the Lower Dnipro river in the south. Within the framework of the presented research, the possibility of using theoretical distribution curves known in hydrology to describe the series of river mineralization, using the example of the Dnipro basin, has also been analyzed. Using Pearson's fitting criterion, the Pearson type III distributions and the three-parameter distributions by S.M.Krytsky and M.F.Menkel have been verified on their correspondence with the empirical series of mineralization. As a result, it was found that in 85% of cases the Pearson type III distribution can be used, and the three-parameter by S.M.Krytsky and M.F.Menkel can be used in 60% of cases.
Keywords: mineralization, statistical parameters, distribution laws.
Аналiз часових ря пв мшеpалiзащт води pi40K у басейш Дншра з використанням теоре-тичних закошв розподшу випадкових величин
Овчарук В.А.1, Даус M. G.2, Ki4yK Н.С.1, Мирошниченко М.1.1, Даус Ю.В.2
Юдеський державний екологiчний утверситет, Одеса, Украта, valeriya.ovcharuk@gmail.com 2Одеський нацюнальний морський утверситет, Одеса, Украта
Анотащя. Анал1з сучасних наукових роб1т щодо використання статистичних метсдав у пдрсшм1чних дослщженнях показав, що такий тдхщ достатньо обгрунтований, як в Укрш'ш, так i за кордоном. Мета дано'1 роботи - визначити основш статистич-ш параметри та дослщити можливють застосування теоретичних закошв розподшу до часових рядiв мiнералiзащi. В пред-ставленому дослщженш наведеш результати застосування стандартних статистичних метсдав обробки пдрометеоролопчно'1 шформацп для даних спостережень за мiнералiзацieю води на 28 постах басейну Дншра (у межах Украши) за перюд з 1990 по 2015 роки. Проаналiзовано динамшу отриманих статистичних параметрiв (середшх багаторiчних значень, коефщенпв варiацii, асиметрп та автокореляцп) в межах басейну Дншра на територп Украши. Середш рiчнi значення мiнералiзацii сутте-во змшюються в межах дослщжувано'1 частини басейну Дншра - у твшчнш частиш максимальне значення середньобагато-рiчноi мiнералiзацii дорiвнюе 447 мг/л, iз просуванням на твдень мiнералiзацiя збшьшуеться, i вже у суббасейш Середнього Дншра ii максимум досягае 971 мг/л; найбiльшi значення спостер^аються на твдш (суббасейн Нижнього Дншра), де можуть досягати екстремально високих значень для окремих малих рiчок (р. Солона - с. Новопавлiвка, 3356 мг/л). Багаторiчна мшли-вють мiнералiзацii в рiчках дослщжувано! територп незначна, а коефщенти автокореляцп рядiв мiнералiзацii доволi висою, у
Journal of Qaology, Geography and Geoecology
Journal home page: geoIogy-dnu-dp.ua
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Introduction. Hydrochemical indicators of river water and, in particular, mineralization, are formed under the influence of natural and anthropogenic factors, due to the complex processes that occur during the daily, seasonal, annual and secular periods. The influence of each factor on the formation of mineralization cannot be taken into account unambiguously, so this process can be considered stochastic or probabilistic. In this case, taking into consideration that the samples of hydrochemical characteristics are random variables, there is a basis for the use of mathematical statistics in the study of the processes of formation of hydrochemical parameters of rivers.
This approach is used in Ukraine by scientists of the Ukrainian Hydrometeorological Research Institute (Kovalchuk et al., 2008; Osadchiy and Kovalchuk, 2013), in particular, to divide the magnitude of hydrochemical concentrations into natural and anthropogenic components based on theoretical distribution laws. In the foreign literature such an example can be found in the work of Chinese scientists (Yang and Jian-Ying, 2017), who investigated the possibility of using empirical distribution curves to analyze the concentration of chemicals in the water runoff of the river in different phases of water and for values of probability. The use of multidimensional statistical analysis by the scientists of different countries is also noteworthy, for example, for the geochemical assessment of groundwater quality in Cote d'lvoire (Guler et al., 2002), or the use of the principal component method for the study of the territory salinity in Spain (Morell et al., 1996). Among the recent works the studies by scientists from India on the hydrochemical composition of groundwater in different parts of the country (Reghunath et al., 2002; Umarani et al., 2019) using cluster and factor analysis are also worth noting.
The purpose of this work is to determine the main statistical parameters and to research the possibility of applying theoretical laws of distribution to the time series of water mineralization of rivers in the Dnieper basin (within Ukraine).
Output data. The research was carried out on the basis of data from the State Surface Water Survey, carried out by the State agencies for water resources management of the Civil Protection Department of the Ministry of
Emergency Situations of Ukraine. For determination of statistical regularities and distribution laws, the data of mineralization observations at 28 gauges of the Dnieper basin (Fig. 1) for the period from 1990 to 2015 has been selected (1990-2015, Shchorichni dani). The boundary of the study area of the Dnieper basin coincides with the state border between Ukraine and Belarus and Ukraine and Russia. Research methods. When performing hydrological calculations, one of the main tasks is to determine the probabilistic properties of a random variable on the basis of distribution laws. Each random distribution law is a mathematical function that fully describes a random variable from a probabilistic point of view. In practice, it is not necessary to consider the law of distribution as a mathematical expression, it is sufficient to indicate individual numerical characteristics that reflect its main features (1997, Rukovodstvo).
Specific statistical methods have been developed to estimate statistical parameters on a sample basis. The method of statistical moments is the most universal, it is not related to any theoretical law of distribution. In hydrological calculations methods of determining statistical parameters based on certain distribution laws are also used. These methods include the highest-likelihood method, the calculation formulas of which are derived from a three-parameter gamma distribution, and a graph-analytic method that uses theoretical distribution laws (most often Pearson III and log-normal).
The number of statistical parameters used in a theoretical distribution law should not be large. The world experience shows that in calculating runoff, the most optimal in terms of practical application are those theoretical laws of distribution, which require two or three statistical parameters for description -such as mathematical expectation, dispersion and the coefficient of variation dependent on it, distribution asymmetry characteristics.
In modern hydrometeorology, as a rule, the three most common methods of determining statistical parameters are used - method of moments, method of greatest plausibility and graph-analytical method. The calculations are performed on the basis of hydrological series (Hopchenko et al., 2014; Shkolnyi et al., 1999),
but in this research it is proposed to use time series of mineralization as the initial data. Results and their analysis. The authors have obtained statistical characteristics for the series of measured mineralization values for the long-term period from 1990 to 2015 with the help of the software "StokStat 1.2 - Statistics for hydrology" (http://www.geodigital. ru/soft_hydr), such as: the average value of the series of total mineralization and relative average squared deviation of arithmetical mean value o; coefficient of variation Cv; the Cs asymmetry coefficient of Cs/ C ratio, as well as the autocorrelation coefficient
v '
(Table 1).
The analysis of Table 1 shows that the length of the series of river water mineralization in the subbasin of the Prypyat' varies from 132 (the Ubort' -Perga village) to 185 values (the Styr - Lutsk). Average values of ions over a multi-year period range from 368 mg/l (the Stokhid - urban settlement Liubeshiv) to 442 mg/l (the Styr - Lutsk), accurate to the average value calculating from 1.08% to 1.60%; maximum deviations are noted in the gauge of the Ubort'-Perga village with the value = 339 mg/l at o = 3.17%, as well as at the gauge the Uzh - Korosten city, where
= 232 mg/l at o = 2.05%. In most gauges, the value of Cv is 0.14-0.19, and in the gauges of the Uzh -Korosten city and the Ubort'-Perga village it is 0.26 and 0.36 respectively. The Cs value varies from 0.57 to 1.15, the Cs/Cv ratio ranges from 4.0 to 4.4.
For the Desna subbasin, the length of the series ranges from 97 (the Seim - Mutin village) to 204 values (the Desna - Chernihiv). Average values of ion sums within for a multi-year period range from 300 mg/l (the Snov - Shchors village) to 447 mg/l (the Seim -Mutin village), with the accuracy of calculating of the average value of o from 1.06% to 2.11%. The C value makes 0.15-0.23. The value of C varies from
vs
0.37 to 0.30, the ratio varies from 2.4 to 1.6.
The diagrams in the Fig. 2 re] C sent a more evident characteristic of the distribution of statistical parameters of mineralization within the basins. Thus, in the Prypyat' basin (Fig. 2a), the average value of mineralization tends to decrease towards the west, where the upper river is, to the southeast, towards the Uzh basin. Naturally, the dynamics of the coefficients of variation have the opposite direction - the highest values are characteristics of the basins of the Ubort' and the Uzh. The number of samples varies slightly by
Symbols:
the boundary of the study area; — —
the Dnieper basin boundary; T - stream gauge
Fig. 1. Map-diagram of the observation gauge locations in the Dnipro basin (within Ukraine), mineralization
data of which has been used in the research
Table 1. Statistical characteristics of the general mineralization series of water bodies in the Dnipro river basin for the period 1990-2015.
№ of gauge on the map River-gauge Number of values n Period average value c. mg/1 Coefficient of variation C v Asymmetry coefficient C s C/C sv relative average squared -deviation of arithmetical mean value CT _ 100Nv Vn autocorrelation coefficient r(1)
Subbasin of the Prypyat' river
1 The Prypyat'-Ritchytsia village 169 405 0.19 0.71 3.7 1.48 0.36
2 The Turya - Kovel city 176 434 0.14 -0.57 -4.0 1.08 0.45
3 The Stokhid - urban settlement Liubeshiv 179 368 0.17 -0.06 -0.4 1.26 0.47
4 The Styr - Lutsk city 185 442 0.16 0.012 0.07 1.19 0.28
5 The Sluch - Novograd-Volynskyi city 140 407 0.15 -0.14 -0.9 1.28 0.51
6 The Sluch - Sarny 141 396 0.19 0.24 1.3 1.60 0.50
7 The Ubort'- Perga village 132 339 0.36 -0.04 -0.1 3.17 0.66
8 The Uzh - Korosten' city 166 232 0.26 1.15 4.4 2.05 0.19
Average 161 378 0.20 0.16 0.51 1.64 0.43
Subbasin of the Desna river
9 The Desna - Chernigiv city 204 372 0.15 -0.37 -2.4 1.06 0.38
10 The Desna -Litky village 189 374 0.16 -0.23 -1.5 1.15 0.33
11 The Golovesnia -Pokoshechi village 120 398 0.23 -0.05 -0.2 2.11 0.46
12 The Seim -Mutyn village 97 447 0.19 0.00 0 1.93 0.08
13 The Snov -Shchors village 110 300 0.19 0.30 1.6 1.76 0.19
Average 144 378 0.18 -0.07 -0.50 1.60 0.29
Subbasin of the Middle Dnipro
14 The Teteriv -Ivankiv village 92 373 0.18 1.21 7.1 1.85 0.26
15 The Irpin - Gostomel village (Mostyshche village) 171 476 0.13 -0.03 -0.2 0.99 0.21
16 The Ros' - Korsun'-Shevchenkivskyi city 92 531 0.13 -0.20 -1.5 1.35 0.24
17 The Tiasmyn -Velyka Yabkunivka village 105 699 0.20 0.14 0.7 1.91 0.29
18 The Trubizh - Pereryaslav-Khmelnytskyi city 179 610 0.12 -0.06 -0.5 0.90 0.09
19 The Sula - Lubny 177 807 0.19 0.72 3.8 1.43 0.31
20 The Udai - Pryluky city 87 831 0.18 -0.32 -1.8 1.91 0.01
21 The Psel - village Zapsillia 101 712 0.17 -0.03 -0.2 1.66 0.01
22 The Khorol - Myrgorod city 106 971 0.25 1.06 4.3 2.34 0.46
23 The Vorskla - Kobeliaky city 168 785 0.18 0.34 1.9 1.41 0.08
Average 128 680 0.17 0.28 1.36 1.58 0.20
Subbasin of the Lower Dnipro
24 The Vovcha - urban settlement Vasylkivka 170 3305.0 0.15 -0.31 -2.04 1.17 0.33
25 The Solona -Novopavlivka village 159 3356.0 0.18 -0.19 -1.06 1.43 0.33
26 The Mokra Moskovka -Zaporizhia city 172 1377.0 0.26 0.79 3.04 1.98 0.28
27 The Ingulets -Sadove village 103 357 0.11 5.00 45.45 1.08 0.06
28 The Ingulets -Kryvyi Rih city 171 1524.8 0.35 0.96 2.74 2.68 0.43
Average 155 1984 0.21 1.25 9.63 1.67 0.29
Average for sub-basins 145 772 0.19 0.36 2.26 1.61 0.29
Average for the Dnieper River 144 479 0.19 0.13 0.46 1.61 0.30
a)
b)
Fig. 2. Diagrams of statistical parameters of water mineralization in the Prypyat' (a) and the Desna (b) river basins.
the pool. In the Desna basin the situation is different
- mineralization does not change substantially across the territory, with some deviations in the Seim river basin; the number of samples decreases remarkably from the Desna to the Seim, and the coefficient of variation increases (Fig. 2b).
In the subbasin of the Middle Dnieper the length of mineralization series changes from 87 (the Udai -Pryluky city) to 179 values (the Trubizh - Pereyaslav-Khmelnytskyi). The average values of the total sum of ions for the investigated period increase from the west to the south east from 373 mg/l (the Teteriv -urban settlement Ivankiv) up to 971 mg/l (the Khorol
- Myrgorod), with the fluctuation of relative standard deviation o from 0.9 % to 2.34% (Table 1, Fig. 3a).
At the gauge of the Irpin - urban settlement Gostomel, the Trubizh - Pereyaslav-Khmelnytskyi city and the Ros - Korsun-Shevchenkivskyi city the values Cv equal 0.12-0.13; at the gauges of the Teteriv
- urban settlement Ivankiv, the Sula - Lubny city, the Udai - Pryluky city, the Psel - Zapsillia village and the Vorskla - Kobeliaky city, the values of Cv fluctuate between 0.17-0.19; the highest values of Cv are marked along the cross-sections of the Tiasmyn -Velyka Yablunivka village and the Khorol - Myrgorod city and make respectively 0.20 and 0.25 (Fig. 3a), so that there is a slight tendency to increase in the same direction as mineralization values. The values of asymmetry coefficients Cs vary at the most wide range
- from -0.03 (the Irpin - urban settlement Hostomel
a)
b)
Fig. 3. Diagrams of statistical parameters of water mineralization in the subbasins of Middle (a) and Lower Dnipro (b).
and the Psel -Zapsillia village) to 1.21 (the Teteriv -urban settlement Ivankiv), and the Cs/Cv ratio varies accordingly from -0.2 to 7.1.
Considering the subbasin of the Lower Dnipro, it can be noted that the length of the series of mineralization observations here ranges from 159 (the Solona - Novopavlivka village) to 172 values (the Mokra Moskovka - Zaporizhia city), and only at the Ingulets point - Sadove village it makes 103 values. The average values of the sum of ions vary from 3356 mg/l (the Solona - Novopavlivka village) to 357 mg/l (the Ingulets - Sadove village) over the perennial period, with the accuracy of the average value o 1.08% - 2.68% (Table. 1, Fig. 3b), i.e. there was a decrease in mineralization from the northeast to the southwest.
The C values for the series of mineralization
v
of the Lower Dnipro rivers vary from 0.11 - 0.35; the value of Cs ranges from -0.31 to 0.96, with the exception of the Ingulets - Sadove village, where the asymmetry coefficient is 5.00; the Cs/Cv ratio varies from -2.04 to 3.04, and for the Ingulets point - Sadove village reaches 45.45. Such a significant difference in all indicators for the Ingulets - Sadove village can be explained by the influence of the Dnipro waters, which flow down the river channel 75 km upstream (Khilchevskyi et al., 2012).
Table 1 also shows the average values of statistical characteristics for sub-basins and their averaged values for all basins. In this case, the average mineralization for a basin is equal to 772 mg/l, but this value will not be correct, because the small and
medium-sized rivers of the sub-basin of the Lower Dnipro have an average mineralization of 1984 mg/l, which is a feature of the small rivers of the Black Sea and Azov Sea region, but it does not correspond to the mineralization of the Dnipro itself in its lower flow. This situation can be explained by a small influence of the inflow of rivers of the Lower Dnipro on the runoff of the Dnipro River. Therefore, the average values of these rivers can be ignored in calculations, and the average mineralization of the Dnipro River can be calculated using its large tributaries in the upper and middle parts of the basin. Thus, the average mineralization for the Dnipro River (within Ukraine) can be accepted at the level of 479 mg/l , the average value of Cv is 0.19; the Cs / Cv ratio can be averaged as 0.5 and the autocorrelation coefficient is 0.30. The obtained values correspond well with the data on the mineralization of the main rivers of Ukraine presented in the paper (Khilchevskyi et al., 2018), where, according to the authors' calculations, the average mineralization of the Dnipro River is 488 mg/l, and the mineralization of the Black Sea and Azov region rivers is at the level of 2200 mg/l .
The analysis of the dynamics of variability and the autocorrelation coefficients throughout the Dnipro basin (within Ukraine) are also of interest. As well illustrated in the Fig.4, the variation of mineralization
The second stage of the research was checking of the series of general mineralization for compliance with the Pearson type III distributions and the three-parameter distributions by S.M. Krytsky and M.F. Menkel, the results of which are presented in the Table 2.
The analysis of the Table 2 shows that the series of mineralization during the study period at all the investigated gauge in the subbasin of the Prypyat' River, except for the gauge the Ubort' - Perga village, correspond to the the Pearson type III distributions and the three-parameter distributions by S.M.Krytsky and M.F.Menkel according to the fitting criterion x2(a,v) at a = 0.05 and v = 7. The series of mineralization of the Ubort' gauge - Perga village does not comply with any of the studied distribution laws. This can be explained by the fact that this series has the highest temporal variability and the highest autocorrelation coefficient, that is, the internal regulation of the series is not well described by the selected distribution laws.
In the subbasin of the Desna, the mineralization series at all the investigated gauges correspond to the Pearson type III distribution law and the three-parameter distribution by S.M.Krytsky and M.F.Menkel according to the fitting criterion x2(a,v) at a = 0.05 and v = 7, apart from the Golovesnia gauges - Pokoshychi village and the Snov - Shchors village, where the values x2 > X2(a,v), that is the series
Cv 0.4
0.7 r(1)
Fig. 4. Dynamics of variability and autocorrelation of river water mineralization series in the Dnipro basm.
within the considered territory is insignificant, the correlation coefficient of the trend line is not significant. On the other hand, the autocorrelation coefficients have a significant tendency to decrease from the subbasin of the Prypyat' to the Lower Dnipro.
of mineralization during the studied period do not correspond to the law of distribution by S.M.Krytsky and M.F.Menkel (Table 2).
In the subbasin of the Middle Dnipro, the series of mineralization during the studied period correspond
Table 2. Check of the series of general mineralization of water bodies in the Dnieper river basin for 1990-2015 for compliance with Pearson type III distribution law and three-parameter distributions by S.M.Krytsky and M.F. Menke
№ of gauge on the map River- stream gauge X2(a,v) Pearson type III distribution distribution by S.M.Krytsky and M.F.Menkel
x2 compliance x2 compliance
Subbasin of the Prypyat' river
1 The Prypyat'- Ritchytsia village 12.6 12.5 compliant 12.5 compliant
2 The Turya - Kovel city 12.6 7.8 compliant 7.9 compliant
3 The Stokhid - urban settlement Liubeshiv 12.6 9.8 compliant 10.4 compliant
4 The Styr - Lutsk city 12.6 7.5 compliant 10.1 compliant
5 The Sluch - Novograd-Volynskyi city 12.6 12.3 compliant 10.1 compliant
6 The Sluch - Sarny 12.6 8.1 compliant 9.6 compliant
7 The Ubort'- Perga village 12.6 17.7 not compliant 15.8 not compliant
8 The Uzh - Korosten' city 12.6 7.1 compliant 11.5 compliant
Subbasin of the Dnieper river
9 The Desna - Chernigiv city 12.6 7.1 compliant 7.4 compliant
10 The Desna -Litky village 12.6 7.4 compliant 11.1 compliant
11 The Golovesnia -Pokoshechi village 12.6 8.8 compliant 35.2 not compliant
12 The Seim -Mutyn village 12.6 8.7 compliant 12.4 compliant
13 The Snov -Shchors village 12.6 5.3 compliant 13.1 not compliant
Subbasin of the Middle Dnieper
14 The Teteriv -Ivankiv village 12.6 13.2 not compliant 16.9 not compliant
15 The Irpin - Gostomel village (Mostyshche village) 12.6 5.90 compliant 11.7 compliant
16 The Ros' - Korsun'-Shevchenkivskyi city 12.6 9.30 compliant 20.2 not compliant
17 The Tiasmyn -Velyka Yabkunivka village 12.6 7.48 compliant 15.5 not compliant
18 The Trubizh - Pereryaslav-Khmelnytskyi city 12.6 10.2 compliant 18.8 not compliant
19 The Sula - Lubny city 12.6 15.5 not compliant 14.4 not compliant
20 The Udai - Pryluky city 12.6 3.92 compliant 6.68 compliant
21 The Psel - village Zapsillia 12.6 2.86 compliant 12.96 not compliant
22 The Khorol - Myrgorod city 12.6 4.0 compliant 4.25 compliant
23 The Vorskla - Kobeliaky city 12.6 12.1 compliant 4.9 not compliant
Subbasin of the Lower Dnipro
24 The Vovcha - urban settlement Vasylkivka 12.6 9.7 compliant 5.9 compliant
25 The Solona -Novopavlivka village 12.6 3.45 compliant 3.96 compliant
26 The Mokra Moskovka -Zaporizhia city 12.6 7.65 compliant 12.3 compliant
27 The Ingulets -Sadove village 12.6 8.9 compliant 20.7 not compliant
28 The Ingulets - Kryvyi Rih city 12.6 15.37 not compliant 15.49 not compliant
to the Pearson III type distribution law at all gauges except the Teteriv gauges - urban settlements Ivankiv and the Sula - Lubny city, and the three-parameter distribution by S.M.Krytsky and M.F.Menkel in three cross sections (the Irpin - urban settlement Gostomel (Mostyshche village), the Udai - Pryluky city and the Khorol - Myrgorod city) according to the fitting
criterion x2(a,v) at a = 0.05 and v = 7 only within the cross section (Table 2).
To sum up: for the cross sections the Irpin -urban settlement Gostomel (Mostyshche village), the Udai - Pryluky city and the Khorol - Myrhorod city the series of mineralization correspond to both distribution laws, for other gauges it is possible to
use Pearson III type distribution law for calculations, which is determined by the condition x2 < X2(a,v), for the gauge of the Teteriv - urban settlement Ivankiv the series of mineralization do not correspond to any of the studied distribution laws (the Table 2).
In the subbasin of the Lower Dnipro, the series of mineralization at the three investigated gauges correspond to the Pearson type III distribution law and the three-parameter distribution by S.M.Krytsky and M.F.Minkel by the fitting criterion x2(a,v) at a = 0.05 and v = 7. At the gauge of the Ingulets River - Sadove village the series of mineralization correspond only to the Pearson III type distribution law, at the gauge of Ingulets - Kryvyi Rih the series do not correspond to any distribution law, which can be explained by significant anthropogenic loads and peak emissions of the mine waters of the Kryvyi Rih iron ore basin (the Table 2). Conclusions.
• As a result of a standard statistical processing (using the methods of moments and maximum likelihood), the statistical characteristics of the series of measured values of mineralization of water bodies of the Dnipro basin for the period from 1990 to 2015 have been determined.
• The average annual values of mineralization vary substantially within the studied part of the Dnipro basin within Ukraine. Thus, in the northern part (subbasins of the Prypyat' and the Desna) the average long-term mineralization fluctuates from 232 mg/l to 447 mg/l, and as it moves to the south, mineralization increases and in the subbasin of the Middle Dnipro it changes in the range from 373 mg/l to 971 mg/l; the highest values are observed in the south, in the subbasin of the Lower Dnipro, where they fluctuate from 357 mg/l (the Ingulets - Sadove village) to extremely high values of 3356 mg/l (the Solona - Novopavlivka village).
• The obtained data are consistent with the data (Khilchevskyi et al., 2018) on the spatial changes of the water mineralization of the rivers of Ukraine, in particular for the Dnipro basin, which indicates the statistical stability of the average long-term mineralization.
• The long-term variability of mineralization in the rivers of the studied territory is insignificant, the values of the coefficients of variation Cv vary in the Dnipro basin within Ukraine in the range from 0.11 to 0.3 and do not have a signified trend.
• The asymmetry of the mineralization series is sufficiently signified, and the corresponding coefficients vary over a wide range from -0.03 to 5.00.
• The autocorrelation in the mineralization series
is quite high and the coefficients r(1) are in most cases significant; in general within the basin there is a decrease of the autocorrelation coefficients from the north to the south.
• Within the framework of the presented research, the possibility of using theoretical distribution curves known in hydrology to describe river mineralization has been analyzed. In terms of the Dnieper basin, using the Pearson fitting criterion x2, the type III Pearson distributions and the three-parameter by S.M. Krytsky and M.F.Menkel have been checked for their correspondence with the empirical series of mineralization. As a result, it was found that in 85% of cases the Pearson type III distribution can be used, whereas the three-parameter by S.M.Krytsky and M.F.Menkel in 60% of cases.
• The obtained results make it possible to use theoretical curves to determine the mineralization values of different probability of exceedance, but for the final conclusions it is necessary to continue the study using more source of initial information.
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