Rajmund Skowron. Nicholas Copernicus University, Institute of Geography, Hydrology and Water Economy Department,

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1 Limnological Review 4 (2004) Description of lake basin in the light of selected morphometric indicators Rajmund Skowron Nicholas Copernicus University, Institute of Geography, Hydrology and Water Economy Department, Fredry 6/8, Toruń Abstract: Examinations of lakes are usually connected with a proper recognition of their surface area and vertical parameters, especially their maximum and average depths. The knowledge of lake water reserves (of their volume) is particularly important in determination of the natural environment influences as well as for the purposes of complementary studies. The author of the present paper has analysed 4 indices out of 16 best known in literature (2 of which have been discussed for the first time) and, basing on the calculations performed for 166 lakes, has shown their extreme. Key words: lake vasin, geometrical indices. Introduction The first examinations of lakes initiated on the Polish soil were mostly concerned with recognition and determination of their surface areas and maximum depths. Such mentions appeared as early as in XVIII th century in the works of Rączyński and Staszic (Pasławski, 1993). A real interest in depth measurements of lakes, however, started only in 2 nd half of XIX th. century. The examinations, focused on the area of Wielkopolska and Prussia, lead to drawing the first bathymetric plans of lakes (Seliego, 1903; Schütze, 1920; Schriften der physikalisch-..., 1903). With the development of measurement techniques and introduction of modern equipment, significance of the results obtained has grown and the number of parameters describing the horizontal and vertical of lake basins has increased (Fiłatowa, 1962; Okulanis, 1966). Lake basins have been most often compared to geometrical figures (Hutchinson, 1956) or solids (Bogosławski, Murawiejski, 1955). The character of the lie of the lake bottom was referred, via a system of isobaths, to the plans of more or less compact circles inscribed within the lake contour (Håkanson, 1977). However, only with the introduction of depth sounding of lakes and use of bathymetric plans (with the isobaths drawn) more detailed observations of the lake bottom and a deeper insight into the processes and mechanisms participating in the lake basin formation have become possible. These techniques have provided basis for determination and calculation of the main indices describing the dimensions and shape of lake basins. Among the numerous existing parameters and indices, those referring directly to the relations between horizontal and vertical dimensions of containers should be regarded as the most significant. The others are just their derivatives and characterise lake basins only in a supplementary way. As it follows from the studies devoted to the subject, both domestic and foreign, the following ones are the most frequently applied indices: surface area, maximum length and width, average and maximum depth, volume, as well as relative depth and depth index. There also exist many other indicators; their application, however, is limited

2 234 Rajmund Skowron due to their little usefulness and low representativeness. (Fiłatowa, 1962; Okulanis, 1966; Jańczak, 1985; Kilkus, 1985; Pietrucień, Skowron, 1987). One of the basic factors characterising the geometry of the lake basin is its depth, maximum and average. Maximum depth is a dimension describing the absolute overdeepening of the lake basin and it describes its character only in a limited way. As for average depth, it is the most representative parameter, most adequately rendering the relations between the vertical and horizontal dimensions of the lake, thus also being one of the most significant indicators, crucial for the natural resistance of containers to anthropopression. Ventz (after Kocięba, 1974) has shown that there exists a significant relation between the mean and the maximum depth of lakes. The character of this relation, in the form: d av. = ƒ(h max ) depends in the first place on the lake basin genesis. Jańczak and Sziwa (1984) when analysing the lakes in the Odra River basin have suggested that the significance of this relation is linked to lake size and that these correlate most strongly in lakes whose surface areas amount from 10 to 50 square hectares and most weakly in lakes exceeding 100 square hectares. Bajkiewicz-Grabowska (2002) has confirmed the existence of such a dependency for the lakes of North-Eastern Poland, suggesting at the same time that there occurs a differentiated surface drainage system for this area. Relations between these were taken into consideration by Håkanson (1977) when constructing a model shape of the lake basin. This method allows not only to monitor vertical distribution of lake volumes but also and most importantly to obtain information about the degree of development of the particular basin zones. Okulanis (1966) has included two types of data, morphometric and sub-aqua elements, in the set of basic features determining the character of lake basin geometry. In addition to lake volume and maximum and average depth the following factors are also of particular significance when determining of the lie of the lake bottom: relative depth, depth index, convexity index and the degree of convexity, mean bottom inclination, basin form index, volume trend index, and the depth of location of the isobaths covering half the lake surface and volume. Those parameters have been well documented in the works of Choiński (1995) using the example of Polish lakes. The author has discussed there, in a very clear way, the significance of the particular indices as well as determined their and differentiation for many lakes in Poland. The significance of the particular indices characterising the geometry of lake basins has been a subject of several studies dealing with the impact of the natural environment on degradation of lake water, on determination of lake water balance and on the character of lake water exchange, and often also of works characterising thermal and ice regimes (Mikulski, Okulanis, 1974; Lange, 1977; Kilkus, 1983; Skowron, 1991; Dmochowski et al., 1988; Borowiak, 2000; Bajkiewicz-Grabowska, 2002). In numerous studies on physical limnology the application of bathymetric indicators has been only indicative or even totally neglected, which has affected their value in a very unfavourable manner. The following indices characterising lake basin geometry are those most frequently described: mean inclination of the lake bottom and the lake basin index according to Murawiejski (Bogusławski, Murawiejski, 1955); volume trend index and depth index according to Fiłatowa (Fiłatowa, 1962); and basin permanence index according to Kerekes (Kerekes, 1977). That last parameter is applied as one of the indices providing information about lake susceptibility to degradation (Kudelska et al., 1984). In Table 1 there are 16 parameters characterising lake bathymetry. The first ten (1 10) describe basic lake basin features; the next four (11 14) characterise the shape and geometry of the lake hollow and have been presented in few papers only (Fiłatowa, 1962; Kerekes, 1977; Pietrucień, Skowron, 1987; Choiński, 1995; Choiński, Skowron, 1998, 1999; DoroŜyński, Skowron, 2002). The two remaining indices (15 16) have been discussed for the first time and that is why they require a more detailed discussion. Indicators describing lake basin geometry The analysis of indices has been based on the calculations of their for 166 selected lakes located on the Polish Lowland, studied with respect to water thermal characteristics. There are

3 Description of lake basin in the light of selected morphometric indicators 235 among them lakes characterised by very big surface areas of more than 3,000 hectares (Wigry, Jeziorak) as well as small lakes, whose area does not exceed 15 hectares (Kociołek, Jasne, Czarne, Średnie). The average depths are contained in a wide range from less than 2 m (Jamno, Gardno, Łebsko) to more than 22 m (Hańcza, Wukśniki, Babięty W.). The chosen lakes clearly constitute a differentiated set also with respect to the basic components of water balance, water exchange index, trophic level, exposure of water masses to wind action and the features identifying the character of their reception basin. Table 1. Parameters characterising the lake basin No. Parameter (Symbol) form Units 1 Volume (V) V in thousands of m 3 2 Maximum depth h maks. in m 3 Average depth a h. in m 4 Relative depth acc. to Halbfass H w = 5 Relative depth Acc. to Hutchinson H w = 50H maks. Hmaks. P Π P 6 Depth indexr W g = H. maks. 7 Volume index acc. to Hutchinson R v 3 H = H. maks. H 8 Contents index W z = V P 9 Mean bottom inclination tgα = 10 Convexity degree E = 11 Location of geometrical homothermal gravity centre 12 Index of the lie of the basin acc. to Murawiejski c = h P 3 100% H Hmaks H.. maks. S o H S 13 Basin permanence index acc. to Kerekes BPI = V L o l in degrees in % in m 14 Depth index acc. to Fiłatowa 15 Relative depth index c R = H maks. C = x 10-3 S úr. H S.. 16 Geometrical lake basin index k z = c H 1. r HG

4 Limnological Review 4 (2004) A study of the parameters characterising the lake hollow started with two factors, both already known from literature. However, due to their high usefulness and representativeness, they call for a more detailed presentation. They are: basin permanence index (Kerekes, 1977) and depth index (Fiłatowa, 1962). 1. Basin permanence index (BPI) is the quotient of the lake volume and its shoreline length (Kerekes, 1977). V BPI = (1), L where: V lake volume in m of m 3 ; L shoreline length in km. The index value decreases to 0 with the disappearance of the container. Lakes characterised by big volume and average depth manifest the highest degree of permanency. The value of this parameter, as given by Kerekes (1977) for very big lakes, amounts to: Bajkał > ; Ontario > 1.200; Winnipeg 168; for small postglacial lakes in North-Eastern Canada it is contained between For greater clarity the present author proposes to express the volume of the lakes in question in thousands of m 3 instead of millions of m 3. The obtained from this proportion for some chosen postglacial lakes in Poland are displayed in Table 2. Table 2. Extreme of basin permanence index for selected lakes (Acc. to the Catalogue of Polish Lakes), Peak (Acc. to Catalogue of Polish Lakes, Miedwie (I 60 44) Osetno (II 49 29) 234 Hańcza (II 9 20) Ostrowite (I 36 81) 259 Dargin Czarne (II 26 18) 266 Mamry Północne (II 16 2) Mogileńskie (III 22 43) 274 Śniardwy (II 37 7) Małe Partęczyny (II 49 42) 292 śarnowieckie (I 3 8) Średnie (II 26 17) 324 Wdzydze Płd. (I 28 47) Retno (II 49 66) 484 Wukśniki (II 23 49) StraŜym (II 49 61) 509 Powidzkie (III 34 4) GościąŜ (III 25 13) 601 Babięty Wielkie (II 36 5) Kociołek (II 26 16) 652 Lowest Working on Kerekes assumptions (Kerekes, 1977), basin permanence of the analysed lakes can be determined as amounting from > years (Miedwie, Hańcza and Dargin) to years (Osetno, Ostrowie, Czarne, Mogileńskie and Małe Partęczyny). Thus, the biggest containers of considerable depths (average > 10 m) are the most permanent lakes in Poland, whereas the smallest ones (< 100 ha) are the least permanent, being at the same time those most susceptible to degradation. 2. Depth index (c) according to Fiłatowa (1962) expresses the relation of the lake maximum depth to its mean width in the following form: c D W maks. = x 10-3 (2) av. where: D max. lake maximum depth; W av. lake mean width in m. The value of this index according to Bojanowicz (1970) may condition the occurrence of thermal stratification of water with a fully formed epi-, meta- and hypolimnion. As noted by Skowron (1990), for a number of lakes from the Gnieznian and Kujawskie Lake Districts the value of the index c > 15 x 10-3 meets the condition for a permanent hypolimnion to occur. The highest characterise lakes with a clearly indented basin but with short effective distances. The smallest, on the other hand, characterise big and very shallow containers, where there is a lack of thermal stratification during the summer (Tab. 3). The biggest of that index occur in lakes with a clearly indented basin, where they take on > (Kociołek, Hańcza, Trześniowskie), whereas the smallest refer to very shallow lakes without a well formed pelagic zone and they achieve < (Gardno, Łebsko, Jamno and Wielimie).

5 Description of lake basin in the light of selected morphometric indicators Relative depth index (C R ) expresses the relations between the horizontal and vertical components of the lake basin in this form: c D w av. = (3) R av. where: D av. mean lake depth in m; W av. mean lake width in m. Table 3. Extreme of depth index for selected lakes (Acc. to the Catalogue of Polish Lakes), Peak (Acc. to Catalogue of Polish Lakes, Lowest Kociołek (II 44 48) Gardno (I 5 2) Hańcza (II 9 20) Łebsko (I 2 1) Trześniowskie (III 28 38) Jamno (I 15 5) Popielewskie (III 22 20) Wielimie (I 45 53) UŜewo (II 18 17) Śniardwy (II 37 7) Głębokie (II 36 74) Jeziorak (II 32 41) Babięty W. (II 36 5) Zbąszyńskie (III 41 4) Głębokie (II 26 15) śarnowieckie (I 3 8) Wukśniki (II 23 49) Osetno (II 49 29) Retno (II 49 66) Wiecanowskie (II 22 36) The smallest of C R characterise shallow lakes (of < 2 m mean depth), with considerable surface areas ( > 2,000 ha) and amount to < 1.00 (e.g. Jamno, Gardno, Łebsko, Wielimie). The highest characterise very deep lakes (of > 15 m mean depth), with small surface areas (< 350 ha) and amount to > (Hańcza, Babięty W., Trześniowskie, UŜewo, Popielewskie, Szydłowskie). These index provide information about the contents of the lake basin and perfectly differentiate lakes with respect to the degree of development of their thermal stratification. Index below 5 refer to lakes characterised by decisive epithermal features, whereas those above 35 are typical for containers with a clear bradymixing (Tab. 4). Table 4. Extreme of relative depth index for selected lakes (Acc. to the Catalogue of Polish Lakes), Peak (Acc. to Catalogue of Polish Lakes, Hańcza (II 9 20) Gardno (I 5 2) 0.36 Kociołek (II 26 16) Łebsko (I 2 1) 0.37 Trześniowskie (III 28 38) Jamno (I 15 5) 0.63 UŜewo (II 18 17) Wielimie (I 45 53) 0.83 Babięty Wielkie (II 36 5) Śniardwy (II 37 7) 1.13 Głębokie (II 36 74) Jeziorak (II 32 41) 2.65 Szydłowskie (III 22 39) Zbąszyńskie (III 41 4) 3.37 Popielewskie (III 22 20) Dargin 3.53 Jasne (II 32 35) Mamry Płn. (II 16 2) 3.56 Wukśniki (II 23 49) Gopło (III 23 1) 4.19 Lowest 4. Geometrical basin index (k z ) determined on the basis of the formula below: k z = C 1 R D D av. where: C R relative depth index; G (4) D av. mean depth in m; D G the location depth of the geometrical gravity centre at a uniform water temperature (4 o C), describes geometrical features of the lake basin. It is the parameter by means of which it is possible to establish the differences between lakes in a very precise manner, indicative among others of containers resistance to natural degradation and

6 238 Rajmund Skowron of their mictic differentiation. This index value for the lakes under analysis is contained within the interval between 0.16 (Hańcza) and 3.21 (Gardno) (Tab. 5). Applicability of the analysed indices has been determined by calculating the degree of their mutual interdependency using regression analysis. The results of the analysis are displayed in Table Table 5. Extreme of geometrical lake basin index for selected lakes (Acc. to the Catalogue of Polish Lakes), Peak 2 in the form of a Person's correlation coefficient. Altogether 120 relations for 166 lakes have been subjected to examination, 19.2 % of which have manifested an occurrence of interdependency at a statistically significant level (correlation coefficient r > 0.60). Only 13.3 % collations were characterised by correlation coefficient r > 0.80, whereas only 5 % collations had r > (Acc. to Catalogue of Polish Lakes, Gardno (I 5 2) 3.21 Hańcza (II 9 20) 0.16 Jamno (I 15 5) 2.39 Babięty Wielkie (II 36 5) 0.17 Łebsko (I 2 1) 2.19 UŜewo (II 18 17) 0.18 Wielimie (I 45 53) 1.42 Trześniowskie (III 28 38) 0.18 Śniardwy (II 37 7) 1.16 Kociołek (II 26 16) 0.19 Jeziorak (II 32 41) 1.14 Głębokie (II 36 74) 0.19 Zbąszyńskie (III 41 4) 0.90 Popielewskie (III 22 20) 0.20 śarnowieckie (I 3 8) 0.74 Wukśniki (II 23 49) 0.20 Dargin 0.65 Szydłowskie (III 22 39) 0.20 Gopło (III 23 1) 0.64 Jasne (II 32 35) 0.21 Lowest The strongest correlations (r > 0.80) occurred between the relative depth index (acc. to Halbfass and Hutchinson) and empirical depth index (acc. to Fiłatowa); the relative depth index and lake basin geometrical index, as well as between the mean bottom inclination and indices 14, 15 and 16, and, finally, between the last two indices. Thus, indices 14, 15 and 16 form the most of statistically significant correlations (10 %) with the remaining 13 presented in this work. (Tab. 6). Table 6. Interdependecies between morphometric and bathymetric parameters as well as those describing the basic features of lake basins (numbering of parameters in accordance with Tabel) ,000 0,127 A A A A A A A A A A 0,633 A A A 2 1,000 0,840 A A 0,296 0,296 0,803 0,352 0,296 0,831 0,118 0,314 0,208 A A 3 1,000 A A A A 0,970 0,440 A 0,956 A 0,387 0,273 0,183 0, ,000 1,000 A A 0,136 0,674 A 0,143 A A 0,760 0,742 0, ,000 A A 0,136 0,674 A 0,143 A A 0,760 0,742 0, ,000 1,000 A A 1,000 A A A A A A 7 1,000 A A 1,000 A A A A A A 8 1,000 0,466 A 0,914 A 0,351 0,315 0,212 0, ,000 A 0,481 0,129 A 0,876 0,796 0, ,000 A A A A A A 11 1,000 0,174 0,368 0,322 0,231 0, ,000 A 0,128 0,105 0, ,000 A A A 14 1,000 0,899 0, ,000 0, ,000 Explanations: A Values of correlation coefficient (r) < 0,1 Conclusions With the development of limnology as a separate scientific discipline the prestige and importance of the particular morphometric and sub-aqua parameters have grown, too. Initially, they were used to characterise particular lakes. Later, by using them the differentiation of their for a bigger group of lakes was presented. The prestige and importance of the particular morhpometric and sub-aqua parameters were growing together with the development of supplementary research. At

7 Description of lake basin in the light of selected morphometric indicators 239 present they play the crucial role in all the elaborations on lake description, irrespectively of lake size, its role in the region and its geographical location. Lake basin geometry may be shown using numerical parameters and indices which approximately render its separate nature. in the spatial distribution of all of the above presented indices no clear regional distinctions have been observed, which indicates that the factors and processes participating in lake basins formation had region-wide or supraregional character; within the wide range of morphometric indices characterising the sub-aqua components of the lake basin the most representative are those relating directly to the vertical and horizontal dimensions of the lake; four indices presented and analysed in this paper (basin permanence index, empirical depth index, relative depth index and geometrical lake basin index) may turn out a good and objective reflection of lake environment transformations triggered by its disappearance; among the parameters analysed in the present paper the following ones should be regarded as the most representative indices: mean depth, relative depth acc. to Halbfass and Hutchinson, location of geometrical gravity centre, depth index C (acc. to Fiłatowa), relative depth index (C R ) and geometrical basin index (k Z ); new methods and measurement techniques (echo sounding and GPS) facilitate introduction of new indices, helpful in describing basin geometry and differences between the particular containers more adequately and more precisely, and they will also allow to monitor the transformations in lake basins more closely, both those caused by natural factors and by man. It must be also kept in mind that the majority of indices presented above refer to the whole lake basin without undermining its individual features such as: multi-basin structure, the number of extreme shallowings and overdeepenings and the degree of development of the littoral zone and extreme rooted vegetation. Therefore, their representativeness may turn out limited and in some extreme cases even totally non-significant. References Bajkiewicz-Grabowska E., 2002, Obieg materii w systemach rzeczno-jeziornych, Uniwersytet Warszawski, Wydz. Geografii i Studiów Regionalnych, Warszawa. Bogosławskij B. B., Murawiejski S. D., 1955, Očerki po ozerovedeniju, Izdatelstvo Moskowskogo Universiteta, Moskwa. Borowiak D., Borowiak M., 2001, Effects of morphometry and optical properties of water upon the thermal stratification of postglacial lakes of northern Poland, In: W. Marszelewski and R. Skowron eds., Limnological Review, vol. 1, Toruń, Borowiak D., 2000, ReŜimy wodne i funkcje hydrologiczne jezior NiŜu Polskiego, Badania Limnologiczne, 2, Gdańsk. Choiński A., 1995, Zarys limnologii fizycznej Polski, Wyd. UAM, Poznań. Choiński A., Skowron R., 1999, Jezioro Tobellus przykładem nowego typu genetycznego misy jeziornej, In: Acta Universitatis Nicolai Copernici, Geografia XXIX, z. 103, Toruń, Choiński A., Skowron R., 1998, Najgłębsze jeziora NiŜu Polskiego w świetle najnowszych pomiarów głębokościowych In: Czasopismo Geograficzne, LXIX, 3 4, Wrocław, DoroŜyński R., Skowron R., 2002, Changes of the basin of Lake Gopło caused by melioration work in the 18 th and 19 th centuries, In: Turczyński M., eds., Limnological Review, vol. 2/2002, Lublin, Dmochowski M., Szyjkowski A., Rösler A., 1988, Głębokość ednia jako wskaźnik dynamiki zbiorników wodnych, In: Wiadomości Instytutu Meteorologii i Gospodarki Wodnej, XI(XXXII), 3 4, Poznań, Fiłatowa T., N., 1962, Niekotoryje osobiennosti termiczieskowo reŝima małych ozier w pieriod, In: Trudy GGI, wyp. 85, Leningrad. Håkanson L., 1977, On lake form, lake volume and lake hypsographic survey, National Swedish Environment Protection Board, Limnological Survey, Geografiska Annaler, 59, A, 1 2, Upsala. Hutchinson G., E., 1957, A treatise on limnology, vol. 1, New York London. Jańczak J., 1985, Związki korelacyjne między parametrami i wskaźnikami morfometrycznymi jezior, In: Zesz. Nauk. UG, Geografia, 14, Gdańsk. Jańczak J., Sziwa R., 1984., Związki między głębokościami największymi a ednimi jezior, Przegl. Geofiz., XXIX, 1, Warszawa. Kerekes J., 1977, The index of lake basin permanence, In: Int. Revue ges. Hydrobiol., vol. 62. Kilkus K., 1985, Wlijanie morfometrii ozera na ich termiczeskije charakteristiki, In: Geografia, XXI, Wyd. Mokslas, Vilnius.

8 240 Rajmund Skowron Kudelska D., Cydzik D., Soszka H., 1984, Instrukcja systemu oceny jakości jezior, Instytut Kształtowania Środowiska, Warszawa, mscr. Okulanis E., 1966, Morfografia i batymertia Jezior Raduńskich, In: Zesz. Nauk. WSP w Gdańsku, 8, Gdańsk. Pasławski Z., 1993, Badania w dziedzinie limnologii fizycznej w Polsce, In: Przemiany stosunków wodnych w Polsce w wyniku procesów naturalnych i antropogenicznych, Kraków, Pietrucień C., Skowron R., 1987, Morfometria i batymetria jezior morenowych na południowym przedpolu lodowca Aavatsmarka, Acta Universitatis Nicolai Copernici, Geografia XX, 66, Toruń, Schriften der Physikalisch-Ökonomischen Gesellschaft zu Königsberg in Pr., Skowron R., 1991, Struktura termiczna wody w okresie letniej stagnacji na przykladzie wybranych jezior z Pojezierza Gnieźnieńskiego i Kujawskiego, In: Acta Universitatis Nicolai Copernici, Geografia XXII, Toruń, Streszczenie Początki badań jeziornych wiązały się przede wszystkim z określeniem ich powierzchni i maksymalnych głębokości. Dopiero później, gdy wzrosło znaczenie korzystania z zasobów wód jeziornych, rozpoczęto sondowania głębokościowe jezior, których efektem końcowym były plany batymetryczne. Pozwoliły one na określenie podstawowych parametrów morfometrycznych oraz wskaźników subakwalnych, wód których największe znaczenie posiada poza objętością oraz głębokością maksymalną i ednią, takŝe głębokość względna, wskaźnik głębokości, stopień wypukłości, ednie nachylenie dna (Okulanis, 1966), połoŝenie geometrycznego odka cięŝkości, wskaźnik kształtu misy jeziornej oraz pionowy rozkład objętości (tab. 1). Autor bazując na przykładzie 166 jezior obliczył wielkości czterech wskaźników (wskaźnik trwałości basenu jeziornego (BPI) wg Kerekesa (1977), empiryczny wskaźnik głębokości (C) wg Fiłatowej (1962), relatywny wskaźnik głębokości (C R ) oraz geometryczny wskaźnik misy jeziornej (k Z ), i przedstawia ich ekstremalne wartości (tab. 2 5). Dwa ostatnie wskaźniki zostają wprowadzone do literatury po raz pierwszy. W pracy określono równieŝ reprezentatywność oraz wzajemne relacje przy pomocy analizy regresji (tab. 6). Wskaźnik trwałości baseny jeziornego (BPI) określa stosunek objętości jeziora do długości linii brzegowej (Kerekes, 1977). Jego wartości w grupie badanych jezior zawarte są przeciętnie w granicach Wartość wskaźnika zmniejsza się wraz z zanikaniem zbiorników (tab. 2). Empiryczny wskaźnik głębokości (C) wyraŝa stosunek głębokości maksymalnej i szerokości edniej, osiągając wartości w przedziale (tab. 3). Wskaźnik jest dobrym identyfikatorem wystąpienia epi-, meta- i hypolimnionu w lecie (Bojanowicz, 1970; Skowron, 1990). Relatywny wskaźnik głębokości (c R ) jest ilorazem edniej głębokości i edniej szerokości jeziora. WyraŜa on relacje między poziomymi i pionowymi elementami misy jeziornej. NajwyŜsze wartości charakteryzują jeziora głębokie, o małych powierzchniach, osiągając wartości > 40,0 (Hańcza, Trześniowskie, Babięty W.), natomiast najniŝsze wartości odnoszą się do jezior bardzo płytkich, o duŝych powierzchniach (tab. 4), przyjmując wartości < 2,0 (Gardno, Łebsko, Jamno, Wielimie). Geometryczny wskaźnik misy jeziornej (k z ) obliczany jest ze wzoru: k z = c H 1. r HG gdzie: c R relatywny wskaźnik głębokości jeziora; H. głębokość ednia jeziora; H G głębokość połoŝenia geometrycznego odka cięŝkości w temperaturze 4 o C. Wartości wskaźnika wynoszą od > 2 dla jezior płytkich (Gardno, Jamno, Łebsko) do < 0,2 dla bardzo głębokich, głębokich duŝym nachyleniu dna (Hańcza, Babięty W., UŜewo). Wskaźnik ten moŝe być pomocnym przy określaniu naturalnej odporności na degradację zbiorników oraz miksji jeziora.