Physical Processes and Circulation in Lakes and Reservoirs

Authored by: Sven Jørgensen , Jose Galizia Tundisi , Takako Matsumura Tundisi

Handbook of Inland Aquatic Ecosystem Management

Print publication date:  October  2012
Online publication date:  October  2012

Print ISBN: 9781439845257
eBook ISBN: 9781439845264
Adobe ISBN:

10.1201/b13038-5

 

Abstract

A lake or reservoir is a body of water located at a certain latitude, longitude, and altitude occupying depressions in a watershed or is a result of damming a river. Lakes and reservoirs are permanently interacting at the water–air interface by exchanging heat and gases (oxygen, nitrogen, carbon dioxide, and so on) with the atmosphere. They are also subject to forcing functions such as solar radiation, advection (inflows and outflows), and wind stress. The net input to the lake or reservoir varies seasonally, and it is dependent on the meteorological conditions in the watershed. The balance between the fluxes, the wind stress at the surface, and the inflows and outflows change continuously. In general, these hourly or daily variations are superimposed on the seasonal changes. Figure 3.1 Main processes of heat transfer and mechanical energy across a lake or a reservoir. (From Bloss, S. and Halemann, D.R.F., Effect of wind mixing on the thermocline formation in lakes and reservoirs, Report 249, MIT, Cambridge, MA, 147pp., 1979.)

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Physical Processes and Circulation in Lakes and Reservoirs

3.1  Introduction

A lake or reservoir is a body of water located at a certain latitude, longitude, and altitude occupying depressions in a watershed or is a result of damming a river. Lakes and reservoirs are permanently interacting at the water–air interface by exchanging heat and gases (oxygen, nitrogen, carbon dioxide, and so on) with the atmosphere. They are also subject to forcing functions such as solar radiation, advection (inflows and outflows), and wind stress. The net input to the lake or reservoir varies seasonally, and it is dependent on the meteorological conditions in the watershed. The balance between the fluxes, the wind stress at the surface, and the inflows and outflows change continuously. In general, these hourly or daily variations are superimposed on the seasonal changes.

Main processes of heat transfer and mechanical energy across a lake or a reservoir. (From Bloss, S. and Halemann, D.R.F., Effect of wind mixing on the thermocline formation in lakes and reservoirs, Report 249, MIT, Cambridge, MA, 147pp., 1979.)

Figure 3.1   Main processes of heat transfer and mechanical energy across a lake or a reservoir. (From Bloss, S. and Halemann, D.R.F., Effect of wind mixing on the thermocline formation in lakes and reservoirs, Report 249, MIT, Cambridge, MA, 147pp., 1979.)

3.2  Physical Processes

Figure 3.1 shows the main characteristics of the heat transfer and mechanical energy across a lake or a reservoir interface. Therefore, in lakes and reservoirs, mixing phenomena results from the external inputs of energy, such as solar radiation, and wind magnitude and direction and outflows and inflows. Complicated patterns of vertical structure are observed in these natural or artificial aquatic ecosystems. Mixing is a dynamic process that is the result of the wind stress or other disturbing forces (such as inflows and outflows) against the “potential energy gradient” (sic, Imberger and Patterson 1990, p. 34), which is a result of the radiation. For reservoirs, the situation is even more complicated due to outflows at different levels and the input of several tributaries that disturb the system.

Figure 3.2 shows the classical stratification pattern that occurs in lakes or reservoirs and the three layers that characterize the stratification system.

The depth of the first layer the epilimnion varies with latitude, longitude, or altitude. The depths of metalimnion and hypolimnion (see Figure 3.2) are dependent upon the volume and depth of the lake and the degree of stratification. Since the density of water varies with temperature (see Figure 3.1), the energy requirements to destratify a 1°C difference at 25°C is one order of magnitude higher than to destratify a 1°C difference at 5°C (Figure 3.3).

The energy available to warm the water of a lake or reservoir comes from solar radiation; therefore, it is expected that the seasonal behavior of this forcing function influences the degree of stratification and the stability of the water column. The thermal structure changes, therefore, with the seasonal behavior of the forcing functions that are decisive for the stratification and mixing processes. Lake D. Helvécio located in eastern Brazil in the Rio Doce valley can be used as an illustration of the complex behavior. This lake has very little wind influence. During the beginning of spring and summer, (August/March) the lake stratifies due to surface heating and practically no wind. Thermal structure shows a gradient from 30°C or 32°C at the surface to 22°C to 23°C at the bottom (hypolimnion) of the lake (maximum depth 30 metrics). When the air temperature and the solar radiation start to fall (from March, July, and to winter), the water temperature gradually changes until in the winter time (July), where there is only one continuous vertical structure of 23°C from surface to bottom (see Figure 3.4) (Tundisi and Saijo 1997).

Classical stratification figure in a lake.

Figure 3.2   Classical stratification figure in a lake.

Relationship of density of water with temperature. (From Bloss, S. and Halemann, D.R.F., Effect of wind mixing on the thermocline formation in lakes and reservoirs, Report 249, MIT, Cambridge, MA, 147pp., 1979.)

Figure 3.3   Relationship of density of water with temperature. (From Bloss, S. and Halemann, D.R.F., Effect of wind mixing on the thermocline formation in lakes and reservoirs, Report 249, MIT, Cambridge, MA, 147pp., 1979.)

Seasonal cycle of stratification and circulation in a monomictic tropical lake—D. Helvécio Lake of Eastern Brazil (Lat 19°46′43.89″ S, Long 42°36′16.39″O). (a) Oxygen saturation (%) and (b) temperature (°C). (From Tundisi, J.G. and Saijo, Y. (Eds.),

Figure 3.4   Seasonal cycle of stratification and circulation in a monomictic tropical lake—D. Helvécio Lake of Eastern Brazil (Lat 19°46′43.89″ S, Long 42°36′16.39″O). (a) Oxygen saturation (%) and (b) temperature (°C). (From Tundisi, J.G. and Saijo, Y. (Eds.), Limnological Studies at the Rio Doce Valley Lakes, Brazilian Academy of Sciences, University of São Paulo, São Paulo, Brazil, 5213pp., 1997.)

These thermal variations correspond to the period of 1 year and there is not much variability of stratification from year to year. Hypolimnetic temperature and thermocline depths are very similar from year to year. The surface layer or epilimnion responds to the surface fluxes and/or to the wind stress. Barbosa and Padisak (2002) and Imberger and Patterson (1990) called attention to the importance of the dynamic, diurnal reorganization of the surface layer in the upper strata of the epilimnion. This has an influence on the vertical distribution of density and on the distribution of nutrients, elements, substances, and phytoplankton.

Cycles of importance in the thermal structure of lakes and reservoirs are annual cycles, seasonal changes in temperature as a consequence of change is solar radiation, wind air temperature, and inflows or outflows. Diurnal cycles have a period of 24 h and correspond to heating and cooling periods, respectively, in daytime and nighttime. Other cycles that are typical for many lakes and reservoirs are the cycles related to the passage of cold fronts or warmer fronts as a result of the major weather systems. They are cycles with 5–10 day periods (synoptic cycles) (Tundisi et al. 2008).

When a lake or reservoir undergoes a cycle of stratification and circulation in the course of 1 year, it is called monomictic. When there are two circulations yearly, this is denoted as a dimictic system. Many circulations with permanent mixing are characteristics of what is named a polymictic system. A lake or reservoir permanently stratified is a meromictic ecosystem. Meromixis is due to salinity intrusions to deep water or the accumulation of organic matter at the bottom water below the thermocline in an ecosystem generally protected from wind. The knowledge concerning mixing and stratification in lakes and reservoirs is based on the vertical profile of temperature and its temporal and spatial variations. However, the distribution of the physical or chemical and biological variables follows the vertical temperature profile and the density profile (see Figure 3.5).

Therefore, a complex set of states follows the stratification and mixing processes in lakes under the influence of energy and wind. Figure 3.6 shows the complexity of mixing processes in lakes caused by energy flow variations and wind.

Figure 3.5   (See color insert.) Vertical structure of a stratified lake and its physical and chemical features (Original Degani and Tundisi 2011.).

Temperature and density are not uniform in the surface layer especially when surface heating is very strong and the wind stress is decreasing with time. Diurnal thermocline occurs close to the surface by a depth of a few centimeters or meters. This thermal microstructure is followed by a pleustonic and neustonic organization in the vertical axis.

Complex mixing processes in lakes. (From Imboden, D.M. and Wuest, A., Mixing mechanisms in lakes, in: Lerman, A., Imboden, D., and Gat, J. (Eds.),

Figure 3.6   Complex mixing processes in lakes. (From Imboden, D.M. and Wuest, A., Mixing mechanisms in lakes, in: Lerman, A., Imboden, D., and Gat, J. (Eds.), Physics and Chemistry of Lakes, Springer-Verlag, Berlin, Germany, pp. 83–138, 1995.)

Table 3.1   Characteristic Timescales of Mixing Processes in Lakes

Timescale

Process

Examples

Seconds and minutes

Surface waves

Turbulent overturns

Thorpe (1977) and Dillon (1982)

Stability oscillation in stratified water

Langmuir circulation

Leibovich (1983)

Hours

Wind setup

Spigel and Imberger (1980)

Internal waves

Diurnal mixed layer

Imberger (1985)

Lateral convection due to differential heating/cooling

Horsch and Stefan (1988)

Convective turbulence

Lombardo and Gregg (1989)

Turbidity currents

Lambert (1988)

Inertial modes

Days

Mixing due to storms

Imboden et al. (1988)

Basin modes (topographical waves)

Saylor et al. (1980)

Weeks and months

Annual stratification cycle

Basin-wide exchange due to horizontal density gradients

Wüest et al. (1988)

Internal-wave damping in regularly shaped basin

Mortimer (1974), Csanady (1974)

Thermal bar

Years

Meromixis

Sanderson et al. (1986), Steinhorn (1985)

Source: Imboden, D.M. and Wuest, A., Mixing mechanisms in lakes, in: Lerman, A., Imboden, D., and Gat, J. (Eds.), Physics and Chemistry of Lakes, Springer-Verlag, Berlin, Germany, pp. 83–138, 1995.

The mixing phenomena and stratification in lakes and reservoirs may cover a wide range of temporal and spatial scales as shown in Table 3.1.

For reservoirs, the patterns of mixing and circulation tend to be more complex (see Figure 3.7) due to the specific features of these artificial ecosystems, retention time, depth of the outflows, depth of the inflows, and currents near the mouth of tributaries.

Tundisi et al. (1990) showed for Barra Bonita reservoir (see Figure 3.8), São Paulo State, Brazil, how the daily needs of hydroelectricity govern the deep current flux in this reservoir due to variation in hydroelectricity production.

Patterns of circulation in reservoirs. (From Thornton, F.W. et al.,

Figure 3.7   Patterns of circulation in reservoirs. (From Thornton, F.W. et al., Reservoir Limnology: Ecological Perspectives, John Wiley & Sons, New York, 246pp., 1990.)

(See color insert.) Bara Bonita reservoir, S. Paulo State, Brazil.

Figure 3.8   (See color insert.) Bara Bonita reservoir, S. Paulo State, Brazil.

3.3  Potential Energy and the Turbulent Kinetic Energy

The potential energy of a lake or reservoir indicates the amount of work that is required to mix a stratified water column against the force of gravity:

PE = mgH = o z m gzA ( z ) ρ ( zt ) dz
  • m is the total mass of the lake and reservoir (kg)
  • g is the acceleration due to gravity (m · s2)
  • H is the height of the center of mass of the reservoir or lake 1 (m)
  • Zm is the maximum elevation (m)
  • z is the elevation above the lake or reservoir bottom (m)
  • A(z) is the horizontal area of the reservoir or lake at elevation Z (m2)
  • ρ(z, t) is the reservoir or lake density at elevation z and time t (kg/m3)
(See color insert.) Broa reservoir, S. Paulo State, Brazil.

Figure 3.9   (See color insert.) Broa reservoir, S. Paulo State, Brazil.

Potential energy is stored energy that a lake or reservoir has due to its configuration (morphometry, volume, mean depth, maximum depth, altitude, latitude, and longitude). This potential energy can be converted into kinetic energy. Turbulent kinetic energy (TKE) is the energy input from wind or inflows, which can produce partial or complete vertical mixing of lakes and reservoirs. TKE, for example, can change the thermocline and eventually result in complete vertical mixing. TKE from winds or inflows shows seasonal variations. For example, in natural lakes in Rio Doce (they are tropical lakes), TKE from the inflows dominates in summer, while TKE from wind is negligible all year round. At Lobo Broa reservoir (see Figure 3.9) in São Paulo State, TKE from inflows dominates during summer (December to March), and TKE from wind dominates during winter months (June to September; Tundisi and Matsumura Tundisi 1995).

3.4  Transport Process in Lake and Reservoir

Mixing and stratification patterns are followed by the transport of various substances and organisms between the different strata of water or at the interface of water and sediments. The transport processes are advection, molecular diffusion, turbulence, turbulent diffusion, convection, dispersion, or entrainment.

Advection—This is the transport due to the directional motion of a fluid. Inflows and outflows and wind shear at the air–water interface are examples of advective processes in lakes and reservoirs. The inflowing water intrudes horizontally into a stratified lake transporting substances and organisms and thereby changing the chemical composition of the stratified lake as shown by Tundisi and Saijo (1997) for Lake D. Helvecio, southeastern Brazil, and Rio Doce valley.

Molecular diffusion—This is a transport process determined by the concentration gradient. It follows Fick’s first law, rate = D*dc/dl, where D is the diffusion coefficient and dc/dl the gradient (c is concentration and l the distance). Molecular diffusion occurs, for example, from sediments to water, transferring elements or substances according to a concentration gradient at their interfaces.

Turbulence—This is the motion generated by a forcing function such as wind over the surface of a lake or reservoir, producing regions of eddies (or rotating areas of fluid). Turbulence flows can be irregular, diffusive, and spatially varying and dissipative (depends on a continuous source of energy to be permanent). Density stratification inhibits turbulence and mixing. In lakes and reservoirs, turbulence can be generated by wind, inflows, outflows, convection, and boundaries Thornton et al. (1990).

Turbulent diffusion—This is the transport of substances and elements through diffusion processes induced by turbulence. A large turbulence diffusion coefficient replaces the molecular diffusion coefficient. For details about this process see Imberger and Patterson (1990).

Convection—This is a vertical transport process induced by density instabilities. This is a buoyancy-induced flow occurring when a fluid becomes unstable due to density differences. This process can be measured by applying the Brünt Vaisalla Equation (Harris 1986).

Dispersion—The advection of fluid at different speeds and at different positions produces dispersion, which is common at the mouth of tributaries of lakes and reservoirs and at the riverine regions of reservoirs.

Entrainment—This process occurs at the boundary and interface between turbulent and nonturbulent regions of a lake or reservoir. The transport by advection advances into the unstirred layer and sharpens thereby the gradients (Ford et al. 1980, Lewis 1983).

3.5  Stratification and the Circulation of Lakes and Reservoirs and the Ecological Processes

The changes that a lake or a reservoir undergoes during daily, seasonal, or synoptic cycles have an impact on the water quality of these ecosystems and on the spatial and temporal organization of the biological communities from bacteria to fishes. The atmospheric heating and cooling processes impact the mixing (by adding or removing heat) and change water density. The wind force and wind shear transmit energy to the water body and produce surface waves, circulation currents, and turbulence. These transport mechanisms, both the vertical and the horizontal ones, have a strong interference with the biogeochemical cycles and with the dispersion of organisms. Circulation currents within a lake or reservoir are water movements controlled by external and friction forces or large-scale movement of water such as the Coriolis force generated by wind (TKE) or by other circulation processes (Bloss and Halemann 1979, p. 54; see the description of the Langmuir Cells; Matsumura Tundisi and Tundisi 2005).

These mixing processes can transport nutrients, concentrate suspended matter, and transport planktonic organisms such as bacteria and cladocera. Turbulent eddies can concentrate cyanobacteria blooms, and variations in the horizontal density of water can also concentrate organisms, toxic substances, and suspended matter.

The interaction between the dynamics of the mixing processes, the stratification pattern and the temporal and horizontal distribution of organisms, and the production and decomposition of organic matter govern the magnitude of the responses of the chemical and biological variables. Inflows can influence the lake or reservoir water quality by introducing suspended material with high oxygen demand, nutrients, and bacteria. The intrusion of eutrophic water from an upper lake or reservoir by a river can stimulate phytoplankton blooms. Excess bacteria in the intrusion water may harm the water quality in lakes and reservoirs used for recreation. Decrease of the euphotic zone by intrusion of inflowing water with high suspended matter concentration occurs in many lakes and reservoirs, particularly where deforestation of the watersheds is intensive. Interflows, underflows, or outflows have interference on water quality of lakes and reservoirs. Controlling these transport processes by monitoring is fundamental for the management of the lake and reservoir.

The knowledge of the circulation and transport process across the horizontal axis and the vertical boundaries of lakes or reservoirs are of fundamental importance for the management of phytoplankton blooms and of low oxygen concentration and for the success of recovery projects. Manipulation of retention time and controlling stratification and vertical density currents may be very useful methods to reduce phytoplankton blooms in reservoirs and lakes and thereby control the eutrophication. The knowledge of microstratification processes is useful to understand the complexity of the organization of the biological communities such as bacteria, phytoplankton, and fishes at very small spatial scales (a few centimeters). This may therefore provide new insights about the management of lakes and reservoirs at these scales.

From the ecological and management points of view, some processes are fundamental regarding the mixing patterns of lakes and reservoirs. Imberger and Patterson (1990) highlighted these processes as follows:

  1. Seasonal behavior—Comparative studies on the seasonal cycle of mixing and stratification in lakes and reservoirs at different latitudes is relevant for the better knowledge of the forcing functions that govern the stratification and mixing processes. Shallow lakes and reservoirs respond very fast to forcing function such as rainfall or wind. The knowledge of their seasonal behavior and their responses to these forcing functions could be very important in this context.
  2. Surface fluxes and horizontal transport processes in lakes and reservoirs—Lakes and reservoirs under the strong influence of inflows from upstream rivers exhibit horizontal gradients in chemical and biological variables as well as gradients in physical variables such as conductivity or water temperature. The advection process intrudes water with different properties or qualities, interfering with decomposition processes and the general rates of bacterial activity.
  3. Outflows and inflows—Outflows at different levels at the dam site in reservoirs or at the discharge gates of lakes can influence the water quality upstream and downstream. Monitoring of the water quality at the outflows is useful for management of downstream reservoirs or rivers. The water quality of the inflows changes of course quantitatively and qualitatively depending on the water quality of the lake or reservoir. The knowledge of the load introduced is of fundamental importance for the nutrient balance of the aquatic system, which is crucial for the environmental management.
  4. Mixing below the surface layer—The mixing efficiency generated below the surface layer by turbulent patches should be known in order to identify areas of nutrient input into the euphotic layer or areas of accumulation of organic matter in the reservoir or lake. Accumulation of organic matter by the inflow of more dense drainage water was identified in tropical lakes (Tundisi et al. 1984) and reservoirs (Tundisi and Matsumura Tundisi 1995).
  5. Upwelling—With the increase of surface wind stress, there is a longitudinal water movement with the isopycnals surfacing at the upwind and deepening at the downwind end. (Bloss and Harlemann 1979, Imberger and Patterson 1990). Vertical microstructures of different water temperatures, densities, and nutrient concentrations develop. Water enriched by these upwelling processes enhances primary production of phytoplankton. Upwelling occurring in lakes and reservoirs can promote the development of patches of phytoplankton as discussed by Tundisi et al. (2008) for Barra Bonita reservoir is São Paulo State, Brazil.

3.6  Classification of Lakes

Lakes have their origins by a wide variety of natural processes. A large number of lakes were formed between 15,000 and 6,000 years before present; therefore, they originated in the late Pleistocene. Hutchinson (1957) identified six major types of lakes originated from the following processes: glacial lakes, tectonic lakes, coastal, riverine, and volcanic and lakes with miscellaneous origins.

Figure 3.10 illustrates some of the important lake formation processes and Table 3.2 gives an overview of the six processes reviewed in the next sections. The table indicates the number of lakes and the lake areas formed by the six processes. As seen in the table, 85% of the lake areas are originated in glacial and tectonic processes.

3.7  Reservoirs

Man’s activity produced many reservoirs for thousands of years. These reservoirs of artificial origin have an important role in water storage for several purposes as listed in Chapter 2. Main differences between artificial lakes and natural lakes are also described in Chapter 2.

3.8  Lake Morphometry and Lake Forms

Lakes vary widely in morphometric features and shapes, depending on their origin and the mechanisms that gave origin to them. Lake forms can be circular, subcircular, elliptical, rectangular, triangular, and dendritic.

Mechanisms of lake formation and lake origin (

Figure 3.10   Mechanisms of lake formation and lake origin (Cole, 1983). (a) Various patterns of lakes and river floodplains, (b) formation of lakes in a horseshoe shape, (c) lakes formed by displacement of sediment by dams, (d) coastal lakes formed by dams, (e) volcanic lakes, (f) lakes formed by tectonic movement, and (g) lakes formed by sediment deposition: (1) profile of a deep lake and (2) profile of a shallow lake. (Modified from Welcome, R., River fisheries, FAO Fisheries Technical Papers 262, Rome, Italy, 1985; Horne, A.J. and Goldman, C.R., Limnology, 2nd edn, McGraw-Hill, New York, 1994; Wetzel, R.G., Limnology: Lake and River Ecosystems, Academic Press, San Diego, CA, 1006pp., 2001; Cole, G.A., Textbook of Limnology, 3rd edn., C.V. Mosby Company, St. Louis, MO, 402pp., 1983; Tundisi, J.G. and Matsumura-Tundisi, T., Limnologia, Oficina de Textos, São Paulo, Brazil, 632pp., 2008.)

Table 3.2   Overview of Lake Formation by the Six Reviewed Processes

Origin

Number of Lakesa

Total Lake Area (km2)

Percent Total Area

Glacial

3,875,000

1,247,000

50

Tectonic

249,000

893,000

35

Coastal

41,000

60,000

2

Riverine

531,000

218,000

9

Volcanic

1,000

3,000

<<1

Miscellaneous

567,000

88,000

4

Total

5,264,000

2,509,000

100

Source: Modified from Meybeck, M., Global distribution of lakes, in: Lerman, A. and Gat, J. (Eds.), Physics and Chemistry of Lakes, Springer Verlag, Berlin, Germany, pp. 1–32, 1995.

a Approximate value. Other total quoted is 8.4 × 106 lakes >0.01 km2.

Table 3.3   Morphometric Parameter of a Lake

Surface Area (km2)

A

Volume (m3 or km3)

V

Maximum length (m or km)

lm

Maximum width (m or km)

bm

Maximum depth (m)

Zm

Mean depth (m)

Z

Relative depth (%)

Zr

Length of shoreline (m)

S

Shoreline development

Ds

Volume development

Dv

The main morphometric characteristics of lakes are (see Table 3.3)

  • Maximum depth: Lake depths range from a few meters to 1.800 m. Lake Baikal in Siberia is the deepest lake known with 1.741 m. The second deepest lake is Lake Tanganyika with a maximum depth of 1.470 m.
  • Mean depth: This is the relationship between the volume (V) and the area (A) of a lake, which is V/A.
  • Length (l): This is the distance between the farthest points on the shore of a lake.
  • Area: A lake’s area is the extent of its surface in m2 or km2.
  • Volume: This is the volume of water contained in a lake, a pond, or a reservoir. It can be calculated by dividing the lake to a number of horizontal strata and estimating the volume of each stratum. A lake volume is measured in cubic meters (m3) or cubic kilometers (km3). The lake with the greatest volume is the Caspian Sea 79,319 km3 (Hutchinson 1957).
  • Shore length: It is used to describe a lake. Shoreline length is given in meters. Index of shoreline development is defined as the ratio of the shoreline to the length of a circumference of a circle of the same area as the lake. The shoreline gives the borderline between the lake and its environment and is therefore a measure of the lake’s openness.

Area—A lake’s area is the extent of its surface in m2 or km2.

Volume—The volume of water contained in a lake, a pond, or a reservoir. This is determined by measuring the area of each contour of the lake, finding the volume between the planes of successive contour, and summing the volume.

Maximum length—This is the shortest distance between the two most remote points on the lake shore.

Maximum width—This is the maximum distance between shores at right angles to the maximum length.

Maximum depth—This is read directly from the bathymetric map and represents the deepest point of the lake.

Mean depth—This is calculated by dividing volume/area. This is a very important morphometric feature of a lake or reservoir.

Relative depth—This is defined by the ratio of maximum depth (in meters) to the mean diameters of the lake: Z R = Z r = ( z m π / 20 A )

, where A is the area of the lake, in km2.

Length of shoreline—This is the length of the shore of the lake.

Shoreline development—This is the measure of the degree of irregularity of the shoreline. It is given by the formula D s = ( s / 2 A π )

. This ratio gives an index of the potential importance of littoral influences on a lake or a reservoir (Timms 1992).

Volume development—This index is used to characterize the form of the basin. The volume development compares the shape of the basin to an inverted cone with a height equal to Zm (maximum depth) and a base equal to the lake’s surface area.

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