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Article

Classification of Water Reservoirs in Terms of Ice Phenomena Using Advanced Statistical Methods—The Case of the Silesian Upland (Southern Poland)

1
Institute of Earth Sciences, Faculty of Natural Sciences, University of Silesia in Katowice, Będzińska 60, 41-200 Sosnowiec, Poland
2
Department of Systems and Computer Networks, Faculty of Computer Science and Telecommunications, Wrocław University of Science and Technology, Wyspiański Wybrzeże 27, 50-370 Wrocław, Poland
3
Institute of Social and Economic Geography and Spatial Management, Faculty of Natural Sciences, University of Silesia in Katowice, Będzińska 60, 41-200 Sosnowiec, Poland
*
Author to whom correspondence should be addressed.
Water 2023, 15(22), 3925; https://doi.org/10.3390/w15223925
Submission received: 3 October 2023 / Revised: 2 November 2023 / Accepted: 8 November 2023 / Published: 10 November 2023
(This article belongs to the Section Hydrology)

Abstract

:
Ice phenomena occurring in water bodies are an important indicator of natural changes (e.g., climate change) and the possibilities for economic use of water bodies (e.g., using the ice cover); hence, there is a need to adopt new advanced statistical methods for the purpose of their analysis and assessment. Material for this study was collected for three winter seasons in 39 water bodies in the Silesian Upland (southern Poland). Nine variables were used in the analysis, of which three pertained to the features of the water bodies studied (surface area, mean depth, the amount of water retained), and six pertained patterns to of ice phenomena (average near-surface water temperature during ice phenomena, average and maximum ice thickness, the number of days with ice phenomena, the number of days with ice cover, and average thickness of the snow accumulated on ice). The centroid class principal component analysis (CCPCA) method was found to be the most precise of the five methods used in the study for classifying water bodies in terms of their ice regimes. It enabled the most accurate division of the group of water bodies covered by the study in terms of their ice regimes in conjunction with their morphometric features and hydrological types. The presented method of classifying water bodies using advanced statistical methods is an original proposal, which was used for the first time in limnological research and in the analysis of ice phenomena.

1. Introduction

Observations of ice phenomena in rivers and lakes have been made for centuries. Initially, their primary motives were practical (related to transportation and lake fishing) as well as religious [1]. Nowadays, these phenomena also attract considerable interest from lake researchers worldwide [2,3,4,5,6,7,8]. The formation of lake ice is an inherent feature of lakes and other water bodies located in middle and high latitudes, and this phenomenon plays a key role in the functioning of limnic ecosystems in these regions [9]. Ice cover in lakes and other water bodies results in temporarily limiting, and in extreme cases, completely stopping gas and energy exchange between the atmosphere and limnic waters, which primarily affects thermal conditions, light conditions, and the amount of oxygen stored in the water and impacts the functioning of aquatic ecosystems and the maintenance of biodiversity in lakes [10,11,12,13].
Research into ice phenomena occurring in lakes and other water bodies situated in the temperate climate zone covers a broad range of issues. Among the most frequently discussed research problems is the possibility of using long-term ice phenology as an indicator of contemporary climate change [1,5,8,14,15,16,17,18,19,20,21,22,23,24,25,26,27].
A somewhat smaller number of studies touch upon the details related to ice phenomena in lakes and other water bodies during short periods (e.g., a single winter season). In these studies, the main focus has been on the correlation between the average daily air temperature and the rate at which the water body in question freezes or thaws, daily ice cover increments, the analysis of the types of ice that forms, ice cover thermal characteristics, movements and tectonics, impact on lake bed morphology, spatial variations in the thickness of ice cover, and the impact of broadly defined human pressure on ice phenomena [4,28,29,30,31,32,33,34,35,36,37,38].
Very little has been written on variation in the patterns of ice phenomena in regional terms, and there are few papers addressing the issue of classification of lakes in terms of variation in their ice regimes [3,39,40,41,42,43]. In the case of anthropogenic reservoirs, the identification of their ice regime is negligible and represents a research gap due, among other factors, to their short functioning in the environment. The anthropogenic reservoirs studied are the result of economic human activity (e.g., post mining, dams, dykes), or were created as an unintended effect of underground mining (reservoirs in subsidence troughs and sinkholes).
The purpose of the conducted research was to determine the regularity of the development of ice phenomena of anthropogenic water reservoirs and their classification in terms of ice regime using advanced statistical methods. The purpose of applying a number of statistical analyses was to identify variable structures that explain the relationships between the features of the studied water bodies and their ice regime (with a particular focus on average and maximum ice thickness). Filling an important research gap in the use of advanced tools of statistical analysis in the study of ice phenomena is of cognitive, methodological, and application importance [3,7,8,27,44]. Knowledge of the phenology of ice phenomena is useful not only for determining climate variability in the region over the past last years: the results of such studies can be successfully used to predict the course of limnic processes (e.g., the variability of mixing processes and thermal and oxygen conditions); this is a new aspect of limnological studies [37]. Identifying the regularities of the development of ice phenomena is important from a cognitive and utility point of view as it can contribute to increased safety in the use of water bodies, which is emphasised in multiple studies pertaining to lakes and anthropogenic water bodies [32,33].

2. Materials and Methods

2.1. Studied Lakes

This study covered 39 small water bodies (Figure 1 and Figure 2, Table 1). These water bodies are situated in the southern part of Poland, on the Silesian Upland. In this region, the natural environment has been considerably transformed as a result of centuries of industrial activity [45]. The area of the Silesian Upland is slightly less than 4000 km2, but the water bodies studied are situated in its central part and the largest distances between them do not exceed 50 km from east to west and 20 km from north to south. Although the water bodies studied are the (unintended or intended) result of human economic activity, they have been subject to the same processes as natural lakes since they formed. However, these processes are liable to be modified depending on the degree of human pressure to which each water body is subjected. The reservoirs studied operate under varying urban–industrial anthropogenic pressure and, to a lesser extent, agricultural conditions as well as in areas with natural conditions [46]. The course of ice phenomena may be locally modified for this reason. Examples of the impact of anthropogenic pressure on ice phenomena within water reservoirs are discharges of heated water (e.g., Pod Borem reservoir), or inflows of thermally polluted water (e.g., Dzierżno Duże reservoir).

2.2. Field Work

Material for statistical analysis was collected for three winter seasons (2010, 2011, and 2012). Field surveys were conducted frequently: every one to two days during water body freezing and thawing and every three to four days when ice cover was present. All measurements were taken in the same sectors of the reservoir from the beginning to the end of the season. Within small bodies of water, boreholes were drilled in the central part of them, and in the case of larger bodies of water, the boreholes were drilled away from the shore zone (depending on the size of the body of water, it was from a dozen to several dozen or several hundred metres from the shore). Measurements were made each time in a new borehole—as mentioned above—of the same sector of a given reservoir. To ensure maximum representativeness of the measurement results under the given conditions, a measuring device with a foot resting on the underside of the ice sheet approx. 20 cm from the edge of the borehole (ice thickness hook ruler) was used. This avoids the impact of above-normal ice buildup occurring as a result of poorer insulation from atmospheric conditions or ice buildup due to water flowing from the borehole. The minimum ice thickness (defined as the lowest ice thickness measured) was usually recorded on the first day of ice phenomena. Measurements were taken using a millimetre tape in a location where thin ice was freshly broken. A telescopic boom was also used to strike (break) thin ice and to bring thin ice floes closer to the shore in order to measure them. Measurements were taken from a pier (where one was present) or from a pontoon or small boat, which was used to break ice even where it was a few centimetres thick (also by pushing the bow onto the ice and applying pressure); in the littoral zone, thin ice was measured directly from the water using waders. Similar solutions were used at the stage of disappearing ice phenomena. During periods of full icing and ice cover safe for human movement, measurements were taken directly from the ice in several boreholes drilled, in one or more sectors of the reservoir depending on its surface area. The layout of ice thickness measurement sites was carried out for each reservoir, taking into account bathymetric and morphometric variation assessed from bathymetric plans.
During each observation and measurement series, measurements were conducted that pertained to ice thickness and structure, snow layer, slush, the water accumulated on the ice and water temperature at the depth of 0.5 m below the ice. The results of the measurements of the thickness of the layers (ice, snow, slush, and water) were presented with an accuracy of 0.5 cm, and measurements of water temperature in the system are presented in increments of 0.1 °C, the manufacturer-stated accuracy of the used YSI probe. Observations also pertained to the rate at which the water bodies froze and thawed, the extent of ice cover on the water bodies (shore ice, partial ice cover, incomplete ice cover, complete ice cover), and the presence and location of permanent freshwater polynyas (sites where no freezing took place). A freshwater polynya within bodies of water as an unfrozen section in the midst of a permanent and compact ice sheet is not a common phenomenon, but it still occurs. This phenomenon is likely associated with source water outflows occurring at the bottom of basins, especially post-mining reservoirs where exploitation has resulted in the activation of groundwater outflows from aquifers disturbed by exploitation.

2.3. Statistical Methods

Several statistical analysis methods were used in the study: redundancy analysis (RDA), principal component analysis (PCA), kernel principal component analysis (KPCA), linear discriminant analysis (LDA), gradient component analysis (GPCA), and centroid class principal component analysis (CCPCA). The effectiveness of the above models was compared, and the classification of the water bodies studied in terms of their ice regimes was conducted using the most accurate one.
As previously mentioned, the purpose of this study was to identify variable structures that explain the relationships between the parameters measured and the water bodies, with a special focus on average and maximum ice thickness. Nine variables were used in the analysis. Three of those pertained to the features of the water bodies studied (area, mean depth, and the amount of water retained). The next six variables pertained to the pattern of ice phenomena over the three seasons studied (average water temperature during ice phenomena, average ice thickness, maximum ice thickness, the number of days with ice phenomena, the number of days with ice cover, and the average thickness of the snow accumulated on the ice).
By building a set of features for each component identified, it was possible to construct a stronger predictive model based on a cluster. The use of various machine learning methods made it possible to estimate the number of components that best differentiate the estimated objects. All the algorithms used indicate that the studied space of features and objects is best explained by seven principal components. Various machine learning algorithms were used to optimally select the number of components and classify features and cases. Each classifier evaluated the quality of classification for the various principal components that emerged. The goal of this approach is to obtain the two best criteria, i.e., the number of components and the classifier that will best divide the space of features and cases. The main steps of the procedure are:
  • Determination of principal components using the CCPCA method; centroids are determined according to the cluster of traits and cases (traits are presented in columns and cases in rows);
  • Use of different classifiers separately for each of the selected components. The goal is to check whether each case and feature will be correctly classified, i.e., assigned to a component; in this way, a number of clusters and classifier is determined such that they most accurately reflect the distribution of the feature and cases;
  • Use of five-fold cross-validation to act against over-fitting to the data. This consists of dividing the collection randomly into five folds: four folds are used for teaching, and the last one is the fold used for testing. Then, the testing fold is attached to the teaching folds, and one of the teaching folds is the testing collection.
The advantage of the developed method is that the obtained results provide better discriminatory power in the prediction task than classical methods based, for instance, on redundancy analysis (RDA). Therefore, the final results were compared with the RDA method. Different feature selection methods were used in order to select the strongest model. Principal component analysis (PCA) is based on maximising the value of explained variance using the kernel of a linear transformation [47]. Another method that is a modification of PCA is KPCA (kernel principal component analysis). It assumes transformation functions other than linear ones [48]. Another method used is LDA (linear discriminant analysis), which defines boundaries using linear functions [49]. The last two models used were CCPCA (centroid class principal component analysis), which involves factor rotation according to class centroids [50,51,52], and GPCA (gradient component analysis), where a stochastic gradient is used to estimate the optimal rotation angle and search step [53].
The CCPCA method is more detailed than the classic PCA. It allows the grouping features of objects according to class. In other words, the classical principal component method rotates features according to a single centre of gravity for those features. The CCPCA method looks for classes (so-called clusters of features) for which centroids are determined and rotation follows these centroids. With this approach, a higher total variance is obtained. This, in turn, allows for a more accurate grouping of features and objects to be analysed.

3. Results

Field study results provided the basis for further calculations of parameters such as (Table 2, Table 3 and Table 4) average surface water temperature during ice phenomena (°C), maximum ice thickness (cm), average ice thickness (cm), average snow thickness (cm), the number of days with ice phenomena, and the number of days with ice cover. A database was created using these data (Table 1, Table 2, Table 3 and Table 4) in order to perform statistical analyses.
The results—calculated according to the algorithm described above, in terms of the percentage of total variance explained—varied from 75.32% to 83.33% (Table 5). The best percentage of total variance explained (83.33%) was obtained for the CCPCA method, and this model was used in further tests. A number of experiments using different machine learning methods were conducted (Table 6). The purpose of these experiments was to identify the number of principal components with the strongest effect for the predictive quality of the model.
The experiment demonstrated that in the case of CCPCA, even with only one component, a more accurate model was created than using redundancy analysis (RDA). The strongest CCPCA models were obtained for seven components. Using the CCPCA method, the centroids of the parameters (variables) were estimated and on this basis, the ranges with the strongest discrimination capability with respect to multivariate relationships were obtained. Eigenvalues and total explained variance values are shown in Table 7. Table 7 shows the seven strongest components with features associated with each other. Figure 3 shows the feature selection model. The proposed method divides the space of features (columns) and cases (rows) into clusters. So, components are certain clusters that associate features and the best corresponding row values.
An important criterion for selecting the extraction method was the percentage of explained variance. The methods differ in their approach to feature extraction. In the best method, CCPCA, rotation is performed based on centroids determined using the k-means method. The percentage of total explained variance is correlated with the prediction results obtained using the SVR support vector machine method. In principal component extraction methods, appropriate rotation (gaze) enables capturing better connections even in linear feature spaces.
The red-coloured sets (components 1–7) contain the features that are most strongly associated with each other. Similarities between them and between the associated water bodies are demonstrated.

4. Discussion

The CCPCA method selected as a result of the study allowed for the identification of seven principal components within the set of 39 water bodies studied (Figure 3). This method made it possible to classify water bodies located on the Silesian Upland with respect to their ice regimes more precisely than before [37]. The two largest subsets included nine water bodies each.
The first subset (C1) included the water bodies where the average ice thickness was greater than 14 cm and the maximum ice thickness was less than 25 cm. In this case, the number of days with ice cover was greater than 93 and the number of days with ice phenomena greater than 99. The near-surface water temperature, which was measured during ice phenomena at a depth of 0.5 m, was less than 1.9 °C, and there was at least 3.8 cm of snow cover on the forming ice. This subset included the following water bodies: the Akwen, Amendy, Gliniok, Grunfeld, Maroko, Rogoźnik Duży, Smrodlok, Szkopka, and Żabie Doły S. These are water bodies that formed in former mineral workings or in subsidence basins. They are characterised by very small areas (from 1.3 to 23.7 hectares, with an average of 5.4 hectares) and mean depths (from 1.2 to 4.6 m, with an average of 2 m), which translates into small amounts of water retained (from 21,400 to 272,900 m3, with an average of 89,000 m3). The majority of these are also endorheic (Table 1). The morphometric and hydrological characteristics of these water bodies translate into rapid freezing (usually in less than 24 h from the moment the air temperature drops below 0 °C), the potential for a thick layer of ice forming, the long presence of ice cover, and persistence of ice phenomena (except for the Rogoźnik Duży, these water bodies have no tributaries). Their ice regime can be described as natural.
An equally numerous group consists of water bodies where the average thickness of ice cover exceeded 15 cm and its maximum thickness was more than 28 cm (C2). In these water bodies, ice phenomena persisted for at least 96 days, and ice cover was present for a minimum of 86 days. In these water bodies, the water temperature at a depth of 0.5 m was about 2 °C. The water bodies included in this group were the Brantka, Kozłowa Góra, Kuźnica Warężyńska, Leśny, Moczury, Morawa, Nakło-Chechło, Pogoria III, and Skałka. These are water bodies with quite varied areas (from 5.9 to 543.8 hectares, with an average of 153.0 hectares) and amounts of water retained (from 110,300 m3 to 51.1 million m3). Much greater variation in the reservoirs of the C2 group in relation to the C1 group occurs in their average depths (from 1.6 to 9.4 m, with an average of 3.5 m). Nevertheless, the variation in the depth of water bodies is less in relation to the other morphometric features. These are reservoirs with varying surface areas, but low variation in average and maximum depths, which translate into freezing rates. They belong to different types in terms of their origins and hydrology (Table 1). This group of water bodies included almost all of the largest and most capacious water bodies selected for the study (except for the Dzierżno Duże). The morphogenetic features of these water bodies translated into a somewhat later emergence of ice phenomena and ice cover. In these water bodies, the ice cover disintegrated somewhat faster and ice phenomena also disappeared somewhat earlier, which was primarily due to their larger surface areas (no shading from solar radiation during spring) and the fact that most of these water bodies are classified as flow-through or having an outflow. Both these factors promote faster disappearance of the ice cover. However, no significant differences were noted in terms of average and maximum ice thicknesses. There were also no significant differences in average and maximum ice thicknesses between group one (C1) and group two (C2). These water bodies exhibit a natural ice regime.
Eight water bodies were included in the next subgroup (C3): the Brzeziny, Niezdara S, Ostrożnica, Przetok, Przy Leśnej, Rozlewisko Bytomki, Trupek, and Trzy Stawy Miechowice. In this group of water bodies, the ice regime was characterised by slightly longer persistence of ice phenomena and ice covers. In this case, the number of days with ice cover was 99, and the number of days with ice phenomena was 108. The average thickness of the ice cover in this case was less than 14 cm, and its maximum thickness was greater than 25 cm. A 4.5 cm thick snow layer formed on the ice. The average water temperature during ice phenomena was below 2 °C. This group was characterised by very small areas (from 0.1 to 4.1 hectares, with an average of 1.1 hectares) and mean depths (from 0.2 to 1.2 m, with an average of 0.9 m). Thus, the amounts of water retained ranged from 0.2 to 12.5 thousand m3, with an average of 9.4 thousand m3. In this group, variation in terms of origins and hydrological characteristics was present as well (Table 1). In this case, the very small areas, depths, and water volumes translated into the rapid freezing of water bodies, long ice cover presence, and long persistence of ice phenomena. These water bodies can also be classified as exhibiting a natural ice regime.
The next group includes three water bodies (C4): the Hubertus, Szczygłowice, and Żabie Doły N. The water bodies included in this group have areas ranging from 9.4 to 21.0 hectares, their mean depths range from 1.4 to 2.2 m, and their capacities range from 43,300 to 471,200 m3. These water bodies have varied origins and are hydrologically classified as having an outflow. The average thickness of ice forming on these water bodies was less than 14.0 cm and the maximum thickness was 26.0 cm. A 3.7 cm thick snow layer formed on the ice. The near-surface water temperature during the period when these water bodies were covered with ice was 2.0 °C. The number of days with ice phenomena was more than 98 and the number of days with ice cover was 88. The distinguishing feature of this group was the maximum ice thickness. The thickness of the ice cover of the water bodies in the group in question—understood as a characteristic feature of the ice regime—is the highest, considering all the C1–C7 groups included in the study. The persistence of ice phenomena and ice covers, ice thickness, and near-surface water temperature during the three study seasons attest to the natural ice regime of these water bodies.
Only the Balaton reservoir was included in the C5 group. This group was determined mainly on the basis of the morphometric and hydrogenetic features of this reservoir. It is a small, shallow flow-through reservoir. During the three study seasons, ice phenomena on the reservoir lasted from 98 to 111 days (with an average of 103 days), ice cover lasted from 85 to 103 days (with an average of 94 days), maximum ice thickness ranged from 18.5 to 32 cm (with an average of 24 cm), and average ice thickness ranged from 11.1 to 12 cm (with an average of (11.6 cm). The water temperature in the reservoir during the ice events averaged 2.2 °C. These features attest to its natural ice regime.
The analysis of the C6 component proves the group created by the CCPCA method, which is based on strong determinants (average water temperature during ice phenomena, average snow thickness, average ice thickness), but does not provide a group of any objects (reservoirs) in this group. Thus, this is a group of objects only potentially represented in the set of ice occurrence statistics considered.
Only the Farskie reservoir was included in the C7 group; it is a small, shallow, polymictic flow reservoir. A characteristic feature of the ice regime of this body of water is the shorter periods of ice phenomena and ice cover compared to other reservoirs. This is mainly due to the faster receding of the ice in spring, caused by the inflow of warmer river water.
The remaining eight water bodies included in the study do not form obvious larger clusters, and the results of feature selection demonstrate that their ice regime (in conjunction with their morphometric features) is different from the groups previously mentioned. Three of these water bodies had a disturbed ice regime. In the case of these water bodies, ice phenomena were virtually non-existent (Pod Borem) or only occurred for a short time during significant drops in air temperature (Sośnica, Somerek) [37]. The near-surface water temperature in these water bodies was much higher than in the others, averaging 9.5 °C, and ice thickness reached 0.5 cm (on average) and 1.1 cm (maximum). The disturbance of the thermal and ice regimes in these three cases was caused by discharges of heated water from dewatered coal mines. As a result, these water bodies were characterised by an ice regime that was significantly transformed by human activity [32]. Situated in the Brynica River valley, the Niezdara N water body also exhibited different characteristics in terms of its thermal and ice regimes, which were manifested by elevated near-surface water temperature (4.2 °C), smaller maximum (15.8 cm), and average (6.0 cm) ice thickness as well as a shorter duration of ice phenomena (73 days) and ice cover (49 days) but in this case, the main factor limiting these phenomena was its hydraulic contact with the warmer waters of the Brynica River.
The different pattern of ice phenomena in the Dzierżno Duże water body results primarily from its morphometric and hydrological features. The large surface area and volume of this water body translates into later dates on which ice phenomena start to occur and the ice cover forms, and the fact that it is a flow-through water body results in ice thickness being lower, ice cover receding faster and ice phenomena disappearing earlier [32,37]. The average near-surface water temperature in this water body was 2.9 °C, and the maximum thickness of the ice cover reached 23.3 cm, with an average of 13.3 cm. Ice phenomena in this water body persisted for an average of 66 days, and ice cover persisted for 53 days. A similar situation was obtained for a small water body located in Kamieniec; in this case, the flow of warmer river waters (2.7 °C) also limited the thickness of the ice cover forming. The ice cover forming on this water body reached a maximum thickness of 22.0 cm on average, with an average ice thickness of 11.6 cm. The small mean depth, area, and volume of this water body meant that ice phenomena and ice cover persisted for relatively long periods (98 and 87 days, respectively). In the case of the remaining four water bodies, near-surface water temperatures (2.3 °C) as well as maximum (26.3 cm) and average (13.0 cm) ice thicknesses did not differ significantly from those found in the other groups of natural water bodies, with the only differentiating element being the shorter duration of ice cover.
Results of the statistical analyses of ice phenomena in water bodies on the Silesian Upland are related to the results of studies of ice phenomena in lakes situated at different longitudes and latitudes [4,54] and exemplify the precise classification of lakes in terms of the occurrence of ice phenomena. The high level of detail in categorising lakes into groups C1–C7 as a result of using advanced statistical tools largely results from taking into account most, if not all, factors that affect the development of ice phenomena. Thus, our original method of statistical analysis is optimal due to the fact that it brings together, in a sense, the efforts of many researchers who considered ice phenomena as cryological processes and focused their attention exclusively on a specific, selected group of causal factors. The multitude of factors determining the presence of ice phenomena is highlighted in the limnological literature. Researchers dealing with lake icing processes have paid attention to the rate of freezing depending on air temperature and the impact of internal (morphometric) characteristics. In the case of the thawing of water bodies, it was pointed out that this process depends almost exclusively on external factors, the most important among which is air temperature resulting from the amount of solar radiation reaching the ice cover [2,4,18,40,54,55,56,57,58,59,60].
Case studies addressing lake freezing and thawing are plentiful, especially for those lakes located in temperate climate zones. One example of elaborate analysis of conditions for the occurrence of ice phenomena are the results cited by M.N. Futter [59], who analysed data from the multiannual period 1853–2001 for more than seventy lakes located in the southern part of the Canadian province of Ontario and found that morphometric characteristics influenced ice phenology. According to M.N. Futter [59], smaller and shallower lakes froze earlier than larger and deeper ones. Water bodies characterised by higher water transparency (cleaner lakes), which could accumulate more heat in the summer, froze later than eutrophic ones. In addition, in lakes located in the lower parts of catchments, ice cover receded faster than in those located higher, due to greater spring flows in lower parts of catchments and the lower absolute altitude of the lake basin. The role of water clarity which, in addition to lake depth, affects the rate of freezing, was stressed by J. Bernhardt et al. [60] based on research conducted in 38 water bodies located in Berlin and Brandenburg. According to these researchers, lakes that were deeper and retained more transparent waters froze later, as both parameters translated into their thermal capacity. S.G. Williams et al. [40] used data from 143 North American lakes to study the dependence of ice cover on climatic, geographic, and bathymetric variables. They found that the processes of lake ice cover formation, development, duration and disintegration are too complex for a single main independent variable to be identified. The authors showed that climatic factors, especially air temperature, are of primary importance for the lake ice regime, but the basins’ morphometric parameters are of significance as well [40]. Latitude and air temperature were closely related to ice phenology in the water bodies studied. Two additionally important factors are the average depth of the water body and its surface area. Particularly during the freezing phase, the average depth of the water body and the associated amount of heat accumulated in the water were important. The importance of morphometric factors in the formation of lake ice cover was also emphasised by G. Kirillin et al. [2]. The average depth of the lake, which may reflect the amount of heat accumulated in its waters, was found to be the most significant morphometric characteristic affecting the freezing rate. It can be assumed that for each additional metre of average depth, ice cover formation is delayed by one day [54].
The ability to group lakes by ice regime characteristics using advanced statistical analysis tools is an important step in effectively forecasting the occurrence of ice phenomena, particularly predicting ice cover thickness. These findings are highly important in order to reflect the reaction of lakes to contemporary climate changes. It can be assumed that the groups of lakes distinguished as a result of advanced statistical methods will demonstrate high levels of similarity, and the results of the study of one water body from a specific group will be representative of the others by analogy. One example is the Kozłowa Góra reservoir included in group C2, which was considered in earlier studies to be representative of contemporary climate change [27]. Therefore, the grouping in the current study can be considered to be the basis for similar treatment of the remaining reservoirs of this group. The applicability of the research results is reflected in the possibility of their use in identifying water bodies for safe use of their surfaces in winter, e.g., ice fishing, recreational ice skating, and iceboat sailing. Grouping water bodies using advanced statistical tools will enable applying the results of the study to the members of the identified groups, of which only several select water bodies were included in the ice thickness forecasting process. Thus, forecasting the ice thickness of individual bodies of water—usually tedious and requiring verification of empirical data in the field [61]—can be successfully replaced by an alternative method of assessing the ice regime of lakes, identified using the presented methodology. There is also a practical dimension to the use of statistical methods in ice regime studies: the acquired information allows for the elimination of water bodies that pose a risk of drowning from use. All water bodies distinguished by a lack of occurrence of ice phenomena or a thickness of the ice cover that does not ensure safe movement on the ice should be considered as such.
The results of the classification of water bodies in terms of the occurrence of ice phenomena carried out can be usefully leveraged in decision-making processes that are undertaken by virtually all bodies involved in the study, protection, and utilisation of inland water bodies, e.g., local authorities, educational institutions, planning, design and construction firms, scientific and research institutions, medical rescue and emergency services, fishing farms and angling associations, etc. The classification of a water body into a certain category as a result of the algorithm developed on the basis of advanced statistical tools, which are simplified into a computer program for daily use, provides a modern solution for the management of water bodies by inland water authorities.
Fish farms and angling associations will find it a lot easier to plan measures aimed at counteracting oxygen shortages during the winter, the scope and intensity of which measures (e.g., breaking the ice cover, drilling aeration holes, using straw for aeration purposes, or taking no action) will depend on the results of the proposed classification of water bodies (into groups C1–C7 in this case). Medical and other emergency services can use the results of this classification in planning the safe use of water bodies and reducing the risk of loss of health and life associated with planned or spontaneous use of the ice cover. Using the proposed classification algorithm, scientific and research institutions can significantly improve their assessments of the determinants and effects of climate change; after all, their modelling can rely on a set of archival data concerning ice phenomena as well as on hypothetical data instead of numbers derived from actual survey results and measurements obtained in real time. Planning, design, and construction firms can usefully leverage the results of the classification discussed above in the design and construction of installations that use the heat resources accumulated in lakes of different types, differentiated in accordance with their categorisation (into groups C1–C7 in this case). Educational institutions will be able to successfully adapt the results of the classification of water bodies in terms of the occurrence of ice phenomena for the purposes of their nature education activities, taking into account the peculiar features of individual classes of water bodies.

5. Conclusions

Of the five statistical methods used in this study, the centroid class principal component analysis (CCPCA) proved the most accurate. This method made it possible not only to identify the water bodies characterised by disturbed ice regimes (Pod Borem, Somerek, and Sośnica) within the group studied, but also to determine a more precise division of the remaining water bodies that exhibit natural ice regimes. In the case of water bodies where ice phenomena did not occur at all or occurred only episodically, mine water discharges were the decisive factor that disturbed their pattern. In the remaining cases, patterns of ice phenomena (except for daily air temperature, which was not included in the analysis due to the fact that data from only one station were available) were affected by several factors, including primarily differences in the morphometric characteristics of the water bodies studied. These differences primarily translated into the freezing rate, and thus indirectly into the length of ice cover and the persistence of ice phenomena. The second major factor affecting the pattern of ice phenomena was the hydrological type to which the water bodies belonged. In flow-through water bodies, ice cover thickness was smaller (e.g., Niezdara, Dzierżno, and Kamieniec), and the disintegration of ice covers and receding of ice phenomena occurred earlier, which translated into a shorter duration of ice phenomena (especially ice covers).
Conducted research based on an empirical data set and using a combination of five advanced tools of statistical analysis (RDA, PCA, KPCA, LDA, and CCPCA) allowed us to obtain innovative results and solutions of cognitive (e.g., developing a new way of identifying the main determinants of the ice regime of lakes), methodological (e.g., proposing the CCPCA method as the most accurate tool for statistical analysis of lake icing data) and application (e.g., the possibility of using a new way of grouping water bodies in terms of the development of ice phenomena, among other things, in assessing the safety of ice cover use).

Author Contributions

Conceptualization, M.R., M.T. and M.S.; Methodology, M.R., M.T. and M.S.; Software, M.T. and M.S.; Validation, M.R., M.T. and M.S.; Formal analysis, M.R., M.T. and M.S.; Investigation, M.R. and M.S.; Resources, M.R. and M.S.; Data curation, M.R. and M.S.; Writing—original draft, M.R., M.T. and M.S.; Writing—review & editing, M.R. and M.S.; Visualization, M.T. and M.S.; Supervision, M.R. and M.S.; Project administration, M.R. and M.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the University of Silesia in Katowice (Poland)—Institute of Earth Sciences (project no. WNP/INoZ/2020_ZB25) and the Institute of Social and Economic Geography and Spatial Management.

Data Availability Statement

Data are contained within the article.

Acknowledgments

We extend our thanks to all those who supported us in the implementation of the research, especially in transporting equipment between research sites and ensuring safety during observations and measurements of ice phenomena.

Conflicts of Interest

The authors declare no competing interests.

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Figure 1. Flowchart of the research performed and water body classification conducted using advanced statistical tools.
Figure 1. Flowchart of the research performed and water body classification conducted using advanced statistical tools.
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Figure 2. Location of the water bodies examined on the Silesian Upland: 1—surface waters, 2—major towns, 3—lakes studied (numbering as in Table 1).
Figure 2. Location of the water bodies examined on the Silesian Upland: 1—surface waters, 2—major towns, 3—lakes studied (numbering as in Table 1).
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Figure 3. Selection results of nine variable features for seven CCPCA principal components (C1–C7—CCPCA principal components, R2 = 0.788). Numbers indicate: 1—lakes studied (numbering as in Table 1), 2—correlated variables, 3—principal components (C1–C7—CCPCA principal components, R2 = 0.788).
Figure 3. Selection results of nine variable features for seven CCPCA principal components (C1–C7—CCPCA principal components, R2 = 0.788). Numbers indicate: 1—lakes studied (numbering as in Table 1), 2—correlated variables, 3—principal components (C1–C7—CCPCA principal components, R2 = 0.788).
Water 15 03925 g003
Table 1. Basic morphometric and hydrological characteristics of selected water bodies on the Silesian Upland [37] supplemented.
Table 1. Basic morphometric and hydrological characteristics of selected water bodies on the Silesian Upland [37] supplemented.
No.LakeOrigin (1)VolumeAverage DepthLake LengthLake WidthElongation IndexAbsolute Height of the Water TableLake AreaMixing Type (2)Hydrological Type (3)
[m3·103][m][km][km][m a.s.l.][ha]
1AkwenPe62.32.60.20.10.9241.02.4PB
2AmendyPe21.41.60.10.10.8287.71.3PB
3BalatonPe68.80.90.40.38.2262.07.4PO
4BrantkaN625.72.91.00.57.3270.021.3PO
5BrzezinyS9.61.10.20.10.8283.10.9PO
6Dzierżno DużePe66,000.011.25.71.552.4199.0587.2DP
7FarskieN149.51.20.60.310.3212.012.3PP
8GliniokN37.01.70.20.21.3288.22.2PO
9GrunfeldPe179.04.60.30.20.8290.03.9PB
10Hubertus IIPe249.41.40.90.213.0248.018.2PO
11KajakowyPg244.42.40.60.24.2258.810.0PP
12KamieniecG25.10.80.30.14.0233.13.2PP
13Kozłowa GóraZ13,050.03.03.41.8144.0278.6432.0PP
14Kuźnica WarężyńskaPe51,100.09.45.21.757.9264.0543.8DP
15LeśnyN1011.53.00.90.611.1240.033.4PO
16ŁąkaPg292.02.20.80.36.0258.513.1PP
17MarokoPg109.51.40.60.25.8264.98.1PB
18MoczuryN231.21.60.60.39.1244.514.5PO
19MorawaPe559.11.60.80.621.7250.134.7PO
20Nakło-ChechłoPe2100.02.62.10.830.8289.380.1PO
21Niezdara NPg0.40.20.20.01.0278.00.2PP
22Niezdara SPg0.20.20.00.00.5278.50.1PB
23OstrożnicaG21.50.50.50.28.2280.54.1PP
24Pod BoremS72.23.80.20.10.5282.01.9AP
25Pogoria IIIPe12,000.05.72.01.737.1261.5211.2DP
26PrzetokPe16.81.10.30.11.4260.01.5PO
27Rogoźnik DużyPe272.91.21.60.219.8291.923.7PP
28Rozlewisko BytomkiN14.31.20.20.11.0243.01.2PB
29SkałkaS110.31.90.30.33.1276.15.9PB
30SmrodlokN46.41.60.30.21.8284.52.9PB
31SomerekS131.13.10.30.21.4266.24.2AP
32Sośnica-MakoszowyS189.04.50.30.20.9224.04.2AP
33SzczygłowiceN471.22.20.60.59.5228.021.0PO
34SzkopkaPg21.81.60.30.10.9245.21.4PB
35TrupekPe8.11.20.10.10.6288.00.7PB
36Trzy Stawy M.G2.70.90.10.10.3285.20.3PP
37Przy LeśnejN2.00.70.10.10.4259.40.3PB
38Żabie Doły NPg140.41.50.60.36.3277.19.4PO
39Żabie Doły SN43.31.70.20.11.5278.02.6PB
Note: Explanations: (1) lake origin (G—dyke-type, N—subsidence bowl, Pg—polygenetic, Pe—former extraction pit, S—artificial bowl, Z—dammed-lake); (2) mixing type (A—anthropomictic, P—polymictic, D—dimictic lake); (3) hydrological type (B—non-drained, O—drained, P—flow-through).
Table 2. Basic characteristics of ice phenomena in selected water bodies on the Silesian Upland in winter season 2009/2010.
Table 2. Basic characteristics of ice phenomena in selected water bodies on the Silesian Upland in winter season 2009/2010.
No. of Water Bodies(See Table 1)Start and End Dates of Ice PhenomenaStart and End Dates of Ice CoverAverage Surface Water Temperature during Ice PhenomenaMaximum Ice Thickness
(Maximum Snow Ice Thickness)
Average Ice ThicknessAverage Snow ThicknessThe Number of days with Ice PhenomenaThe Number of Days with Ice Cover
(°C)(cm)(Number of Days)
113 December–24 March17 December–16 March1.227.0 (9.0)16.37.810193
213 December–22 March18 December–16 March1.922.5 (11.0)13.26.39994
313 December–24 March16 December–15 March2.122.5 (14.0)11.64.310194
413 December–24 March18 December–06 February1.926.0 (13.0)15.05.310196
513 December–24 March15 December–15 March0.623.0 (15.0)12.88.110195
605 January–13 March11 January–25 February2.422.0 (8.0)13.06.46753
713 December–16 March19 November–22 December2.527.0 (8.0)12.24.09373
814 December–24 March15 December–17 March1.725.5 (15.0)14.16.410197
915 December–24 March19 December–17 March1.425.0 (15.0)15.14.79993
1014 December–23 March18 December–15 March2.222.5 (9.0)14.34.59992
1116 December–22 March19 December–15 March2.026.0 (16.0)14.65.59690
1213 December–22 March15 December–13 March2.621.0 (11.0)12.55.69994
1314 December–23 March18 December–18 March1.529.0 (15.0)19.17.29993
1417 December–26 March2 January–19 March1.629.5 (12.0)19.24.69992
1514 December–23 March19 December–13 March1.828.5 (10.0)15.35.39993
1616 December–22 March25 January–9 February1.726.0 (10.0)14.75.69689
1713 December–24 March17 December–27 January1.128.0 (10.0)13.55.810194
1814 December–21 March18 December–27 January1.726.0 (10.0)11.76.49791
1914 December–23 March20 January–17 March2.028.0 (10.0) 14.44.59993
2013 December–24 March18 December–17 March2.326.0 (10.0)16.06.710194
2113 December–17 March14 December–22 December3.913.0 (7.0)4.41.48558
2213 December–24 March14 December–16 March2.022.0 (12.0)13.75.510297
2313 December–27 March17 December–16 March1.729.5 (15.0)18.47.910499
24(-)(-)12.6(-)(-)(-)00
2517 December–26 March2 January–16 March1.825.0 (10.0)16.94.69993
2613 December–23 March2 January–19 February1.026.0 (14.0)16.35.610097
2713 December–25 March17 December–16 March1.527.5 (10.0)15.77.310297
2813 December–23 March16 December–15 March1.419.0 (11.0)12.05.310096
2914 December–21 March16 December–14 March1.824.0 (8.0)13.45.89794
3013 December–25 March16 December–17 March1.626.0 (13.0)17.86.810296
3124 January–07 February(-)7.92.0 (-)1.10.5142
3223 January–01 February(-)9.01.0 (-)0.4(-)90
3313 December–22 March17 December–15 March1.623.0 (11.0)13.45.39993
3413 December–26 March15 December–17 March1.826.0 (12.0)16.84.1103100
3513 December–24 March13 December–17 March1.827.0 (14.0)16.86.7100100
3613 December–22 March14 December–13 March2.524.0 (13.0)12.65.49797
3713 December–21 March13 December–17 March1.026.0 (12.0)16.46.59696
3814 December–21 March16 December–17 March2.321.0 (11.0)12.65.99494
3913 December–21 March18 December–17 March1.923.0 (12.0)14.05.19494
Note: Explanation: (-)—lack of ice phenomena/lack of ice cover/lack of snow cover.
Table 3. Basic characteristics of ice phenomena in selected water bodies on the Silesian Upland in winter season 2010/2011.
Table 3. Basic characteristics of ice phenomena in selected water bodies on the Silesian Upland in winter season 2010/2011.
No. of Water Bodies
(See Table 1)
start and End Dates of Ice PhenomenaStart and End Dates of Ice CoverAverage Surface Water Temperature during Ice PhenomenaMaximum Ice Thickness
(Maximum Snow Ice Thickness)
Average Ice ThicknessAverage Snow ThicknessThe Number of Days with Ice PhenomenaThe Number of Days with Ice Cover
(°C)(cm)(Number of Days)
127 November – 20 March23 January–10 March1.122.0 (10.0)15.23.8113103
227 November–15 March1 December–9 March0.821.0 (11.0)14.33.8108102
326 November–17 March30 November–9 March1.618.5 (10.0)11.13.8111103
428 November–17 March4 December–9 March0.722.0 (9.0)15.24.8109104
526 November–20 March29 November–9 March1.420.0 (13.0)15.63.8114108
616 December–14 March21 December–9 March1.917.0 (4.0)8.40.98670
727 November–16 March28 December–9 March1.318.0 (12.0)9.73.510992
828 November–17 March30 November–9 March1.021.5 (13.0)15.54.5109106
92 December–18 March5 December–9 March1.219.0 (12.0)13.73.1106102
1028 November–16 March5 December–9 March1.321.5 (15.0)14.32.6108101
1128 November–16 March3 December–9 March1.122.5 (15.0)16.32.7108103
1227 November–14 March30 November–08 March1.416.0 (8.0)11.33.6107100
1326 November–19 March4 December–13 March0.825.0 (13.0)16.92.9113103
143 December–18 March17 December–9 March1.319.0 (5.0)12.91.910591
152 December– 16 March5 December–9 March1.121.0 (10.0)12.63.010499
1629 November–16 March2 December–9 March1.418.5 (12.0)12.83.2107100
1728 November–19 March1 December–9 March0.819.0 (13.0)14.63.6111104
1827 November–15 March4 December– 9 March0.821.5 (13.0)14.34.0108102
1927 November–16 March5 December–9 March1.221.5 (14.0)15.03.610999
2028 November–16 March3 December–9 March1.020.0 (12.0)15.42.8108100
2126 November–11 March2 December–5 March3.014.0 (2.0)5.32.08759
2226 November–19 March26 November–9 March0.821.5 (12.0)14.02.9113109
2326 November–20 March26 November–11 March0.526.0 (14.0)18.74.4114112
24(-)(-)12.9(-)(-)(-)00
255 December–19 March19 December–10 March 1.122.5 (2.0)14.71.610492
2626 November–18 March1 December–9 March1.020.0 (9.0)14.65.0112107
2729 November– 18 March30 November–9 March1.123.5 (10.0)17.64.1109105
2826 November–17 March29 November–08 March0.621.0 (10.0)16.23.5111106
2928 November–15 March2 December–9 March 1.021.0 (9.0)15.14.6107102
3027 November–19 March1 December–9 March0.822.0 (7.0)15.84.1112104
3129 December–31 December(-)7.70.5 (0.0)(-)(-)30
3230 November–25 February(-)5.21.0 (0.0)0.10.0130
3327 November–16 March5 December–9 March1.621.5 (10.0)12.43.110999
3426 November–20 March30 November–11 March 0.924.0 (11.0) 16.03.5114107
3526 November–19 March30 November–9 March 0.926.0 (12.0)17.94.7113107
3626 November–17 March4 December–9 March1.214.0 (11.0)9.03.7111106
3726 November–17 March27 November–9 March1.521.5 (16.0)16.92.5111109
3826 November–17 March1 December–9 March 0.722.0 (12.0)14.74.6111106
3927 November–16 March1 December–08 March 0.824.0 (14.0)15.53.8109104
Note: Explanation: (-)—lack of ice phenomena/lack of ice cover/lack of snow cover.
Table 4. Basic characteristics of ice phenomena in selected water bodies on the Silesian Upland in winter season 2011/2012.
Table 4. Basic characteristics of ice phenomena in selected water bodies on the Silesian Upland in winter season 2011/2012.
No. of Water Bodies
(See Table 1)
Start and End Dates of Ice PhenomenaStart and End Dates of Ice CoverAverage Surface Water Temperature during Ice PhenomenaMaximum Ice Thickness
(Maximum Snow Ice Thickness)
Average Ice ThicknessAverage Snow ThicknessThe Number of Days with Ice PhenomenaThe Number of Days with Ice Cover
(°C)(cm)(Number of Days)
111 November–23 March20 December–11 March3.130.5 (5.0)12.34.79271
212 November–03 March19 November–14 March2.836.0 (7.0)14.72.79682
312 November–22 March19 November–14 March2.932.0 (5.0)12.02.59885
415 November–21 March21 December–13 March3.135.0 (7.0)12.91.88470
513 November–23 March30 November–2 March2.631.0 (4.0)10.77.711382
627 January–13 March31 January–1 March 4.631.0 (5.0)18.60.44636
712 November–17 March29 January–28 February 3.634.0 (6.0)12.76.48759
813 November–24 March29 November–13 March3.731.5 (5.0)11.92.29784
920 November–24.March20 December–16.March3.836.0 (6.0)15.41.88872
1020 November–21 March17 January–13 March3.034.0 (5.0)15.01.78267
1120 November–22 March17 January–13 March 3.836.0 (6.0)15.12.38369
1212 November–17 March23 November–08 March4.229.0 (4.0)10.92.58868
1323 November–21 March21 December–14 March2.938.5 (6.0)16.41.47968
1420 December–26 March29 January–20 March 4.340.0 (5.0)18.35.07457
1512 November–22 March29 January–12 March 3.333.0 (5.0)13.23.99068
1620 November–22 March20 December–22 February 3.933.0 (4.0)13.41.68470
1712 November–22 March20 December–16 February2.736.0 (6.0)14.41.49267
1812 November–22 March21 December–28 February3.235.0 (5.0)14.04.29169
1920 November–21 March21 December–13 March 3.333.5 (4.0)14.61.58570
2013 November–21 March21 December–13 March 3.338.0 (7.0)15.21.29070
2113 November–25 February20 December–17 February 5.620.5 (3.0)8.32.44829
2212 November–29 March13 November–15 March 2.836.5 (6.)12.41.5119104
2312 November–23 March13 November–13 March 2.531.0 (5.0)10.82.8113103
24(-)(-)13.7(-)(-)(-)00
2520 December–26 March27 January–19 March 4.140.0 (6.0)18.03.37669
2612 November–22 March19 November–14 March 3.337.0 (7.0)12.92.610185
2713 November–24 March20 December–13 March 2.735.0 (6.0)14.04.39274
2812 November–21 March19 November–12 March 3.625.0 (5.0)8.32.211089
2915 November–21 March30 November–14 March 3.035.5 (6.0)14.35.08968
3012 November–22 March29 November–13 March 3.632.0 (5.0)11.62.59781
3102 February–19 February(-)8.22.6 (0.0)1.5(-)116
3231 January–19 February(-)8.03.0 (0.0)1.60.41610
3312 November–21 March21 December–9 March 3.531.5 (5.0)12.13.69168
3413 November–29 March19 November–15 March 2.931.0 (6.0)10.52.511386
3513 November–24 March19 November–13 March 3.730.0 (5.0)10.82.910284
3612 November–22 March14 November–14 March 2.428.0 (6.0)9.54.510998
3712 November–22 March13 November–12 March 2.132.0 (5.0)9.82.110998
3815 November–22 March30 November–14 March 2.237.0 (6.0)15.02.29072
3912 November–23 March29 November–14 March 3.036.0 (6.0)14.92.59684
Note: Explanation: (-)—lack of ice phenomena/lack of ice cover/lack of snow cover.
Table 5. Feature selection results for the five methods studied by percentage of total variance explained for the four principal components.
Table 5. Feature selection results for the five methods studied by percentage of total variance explained for the four principal components.
Method% of Variance Explained
PCA75.32%
KPCA79.63%
GPCA80.32%
CCPCA83.33%
LDA75.66%
Table 6. Classification quality results: the determination of principal components using different classifiers.
Table 6. Classification quality results: the determination of principal components using different classifiers.
ParameterNOCCPCA (Number of Principal Components)
1234567
RDA0.702
k-NN0.7110.7120.7170.7260.7270.7360.7430.749
SVM0.7260.7320.7390.7470.7480.7510.7600.762
MLP0.7320.7420.7430.7430.7480.7520.7570.765
CART0.7280.7330.7380.7420.7440.7480.7570.758
GNB0.7050.7120.7120.7200.7270.7330.7420.748
Table 7. Basic statistics for each of the seven principal components identified using the CCPCA method.
Table 7. Basic statistics for each of the seven principal components identified using the CCPCA method.
ComponentEigenvalue% of Total VarianceCumulative EigenvalueCumulative %
13.6728.433.6728.43
22.0921.325.7649.75
31.8114.117.5763.86
41.658.329.2272.18
51.425.4310.6477.61
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Rzetala, M.; Topolski, M.; Solarski, M. Classification of Water Reservoirs in Terms of Ice Phenomena Using Advanced Statistical Methods—The Case of the Silesian Upland (Southern Poland). Water 2023, 15, 3925. https://doi.org/10.3390/w15223925

AMA Style

Rzetala M, Topolski M, Solarski M. Classification of Water Reservoirs in Terms of Ice Phenomena Using Advanced Statistical Methods—The Case of the Silesian Upland (Southern Poland). Water. 2023; 15(22):3925. https://doi.org/10.3390/w15223925

Chicago/Turabian Style

Rzetala, Mariusz, Mariusz Topolski, and Maksymilian Solarski. 2023. "Classification of Water Reservoirs in Terms of Ice Phenomena Using Advanced Statistical Methods—The Case of the Silesian Upland (Southern Poland)" Water 15, no. 22: 3925. https://doi.org/10.3390/w15223925

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