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Relative Depth (Zr) in % = 50 * Zmax * sqrt(π) * (sqrt(Ao))-1, where sqrt=square root
For most lakes, Zr < 2%. Deep lakes with small surface areas exhibit greater resistance to mixing and usually have Zr > 4%
Zmean = V ÷ Ao
Development of volume (Dv) = 3 Zmean÷ Zmax
For the majority of lakes, Dv will be greater than 1 (i.e., a conical depression). Dv is greatest in shallow lakes with flat bottoms (eg. Carolina Bay lakes). Among deep lakes, caldera lakes, graben lakes, and fjord lakes, Dv will be much greater than 1.5 (also in many rock basins). Most lakes in easily eroded rock have Dv in the range of 1 to 1.5. Extremely small values are found in only a few lakes with highly localized deep holes (ponors or sinks, sublacustrine kettle holes). Extensive action of shore processes is apt to reduce the ratio.
Shore Line Development (DL) = SL ÷ 2·sqrt(π·Ao)
Shore Line Development (DL) is important because it reflects the potential for development of littoral communities, which are usually of high biological productivity. Only a few lakes, such as Crater Lake in Oregon and a few kettle lakes approach the circular shape, i.e., DL = 1 (circular). DL ± 2 in many subcircular and elliptical lakes. DL is large for lakes of flooded river valleys.
The Index of Basin Permanence (IBP) is a morphometric index that reflects the littoral effect on basin volume.
Lakes within the Atlantic National Parks (IBP < 0.1) are dominated by rooted aquatic plants and indicate senescence (excessive shallowness, high water color and high TP). Lakes with IBP = 0.2 are more permanent.
Lake Baikal has a IBP of 10,000, for Lake Superior IBP = 4,000, for Lake Erie IBP = 450, and for Caspian Sea (largest inland water basin) IBP = 13,000.
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