Shoreline development index

Lakes in Saskatchewan with varying shoreline development indices (islands included): Peter Pond - 1.5, Churchill - 4.1, Ile a la Crosse - 8.2

The shoreline development index of a lake is the ratio of the length of the lake's shoreline to the circumference of a circle with the same area as the lake.^[1]^[2]^[3] It is given in equation form as ${\textstyle D_{L}={\frac {L}{2{\sqrt {\pi A}}}}}$ , where ${\textstyle D_{L}}$ is shoreline development, $L$ is the length of the lake's shoreline, and $A$ is the lake's area.^[2] The length and area should be measured in the units (e.g., m and m², or km and km²). The shoreline development index is $D_{L}=1$ for perfectly circular lakes.^[2] $D_{L}>1$ for lakes with complex shapes.^[2]

Patterns

Shoreline development correlates strongly with lake area, although this partly reflects the scale dependence of the index (see Limitations).^[4]^[5]^[6] To some extent, the shoreline development index reflects the mode of origin for lakes. For example, volcanic crater lakes often have shoreline development index values near 1, where are fluvial oxbow lakes often have very high shoreline development index values.^[7]

Application to lakes with islands

The index can also include the length of island shoreline, modifying the formula to ${\textstyle D_{L+L_{i}}={\frac {L+L_{i}}{2{\sqrt {\pi A}}}}}$ , where $L_{i}$ is the combined length of the lake's islands' shoreline.^[8]

Limitations

Lake shorelines are fractal.^[7] This means that measurements of shore length are longer when measured on high-resolution maps compared to low-resolution maps.^[9]^[10] Therefore, a lake's shoreline development index will be greater when calculated based on shorelines measured from high-resolution maps compared to low-resolution maps.^[10] Consequently, shoreline development index values cannot be compared for lakes with shorelines measured from maps with different scales.^[9]^[11]^[12] Additionally, the shoreline development index cannot be compared for lakes with different surface areas because large lakes automatically have higher values than smaller lakes, even if they have the same planform shape.^[10] Hence the shoreline development index can only be used to compare lakes with the same surface area that are also mapped at the same scale.^[10] Making comparisons like this can create suprious correlations between the shoreline development index and ecological variables.^[13]

References

^ Aronow, Saul (1982). "Shoreline development ratio". Beaches and Coastal Geology. Encyclopedia of Earth Sciences Series. Springer US. pp. 754–755. doi:10.1007/0-387-30843-1_417. ISBN 978-0-387-30843-2. Retrieved December 19, 2020.
^ ^a ^b ^c ^d Wetzel, Robert (2001). Limnology: Lake and River Ecosystems. Academic Press. ISBN 9780127447605.
^ Hutchinson, G.E. (1957). A treatise on limnology. Wiley. ISBN 0471425702.
^ Koshinsky, Gordon D. (1970). "The Morphometry of Shield Lakes in Saskatchewan". Limnology and Oceanography. 15 (5): 695–701. Bibcode:1970LimOc..15..695K. doi:10.4319/lo.1970.15.5.0695. ISSN 0024-3590. JSTOR 2834006.
^ Verpoorter, Charles; Kutser, Tiit; Seekell, David A.; Tranvik, Lars J. (2014). "A global inventory of lakes based on high-resolution satellite imagery". Geophysical Research Letters. 41 (18): 6396–6402. Bibcode:2014GeoRL..41.6396V. doi:10.1002/2014GL060641. hdl:20.500.12210/62355. ISSN 1944-8007.
^ Seekell, David A.; Cael, B. B.; Byström, Pär (2022-04-05). "Problems with the shoreline development index - a widely used metric of lake shape". Earth and Space Science Open Archive. doi:10.1002/essoar.10510804.3. Retrieved 2022-05-09.
^ ^a ^b Seekell, D.; Cael, B.; Lindmark (2021). "The Fractal Scaling Relationship for River Inlets to Lakes". Geophysical Research Letters. 48 (9): e2021GL093366. Bibcode:2021GeoRL..4893366S. doi:10.1029/2021GL093366. S2CID 235508504.
^ Rawson, D. S. (1960). "A Limnological Comparison of Twelve Large Lakes in Northern Saskatchewan". Limnology and Oceanography. 5 (2): 195–211. Bibcode:1960LimOc...5..195R. doi:10.4319/lo.1960.5.2.0195. ISSN 0024-3590. JSTOR 2832556. Retrieved December 19, 2020.
^ ^a ^b Kent, Clement; Wong, Jonathan (1982-06-01). "An Index of Littoral Zone Complexity and Its Measurement". Canadian Journal of Fisheries and Aquatic Sciences. 39 (6): 847–853. doi:10.1139/f82-115. ISSN 0706-652X.
^ ^a ^b ^c ^d Seekell, D.; Cael, B.B.; Byström, P. (2022-05-09). "Problems with the shoreline development index ‐ a widely used metric of lake shape Research Letter for consideration by Geophysical Research Letters". Geophysical Research Letters. doi:10.1029/2022GL098499. ISSN 0094-8276. S2CID 248718476.
^ Håkanson, L. (2004). Lakes: Form and Function. Caldwell, New Jersey: Blackburn Press. ISBN 1930665245.
^ Seekell, D.; Cael, B.; Norman, S.; Byström, P. (2021). "Patterns and variation of littoral habitat size among lakes". Geophysical Research Letters. 48 (20): e2021GL095046. Bibcode:2021GeoRL..4895046S. doi:10.1029/2021GL095046. ISSN 1944-8007. S2CID 244253181.
^ Seekell, D.; Cael, B. B. (2024-05-01). "Bias in the shoreline development index: Ecological implications illustrated with an analysis of littoral-pelagic habitat coupling". Limnologica. 106: 126173. doi:10.1016/j.limno.2024.126173. ISSN 0075-9511.

[1] Aronow, Saul (1982). "Shoreline development ratio". Beaches and Coastal Geology. Encyclopedia of Earth Sciences Series. Springer US. pp. 754–755. doi:10.1007/0-387-30843-1_417. ISBN 978-0-387-30843-2. Retrieved December 19, 2020.

[:0-2] Wetzel, Robert (2001). Limnology: Lake and River Ecosystems. Academic Press. ISBN 9780127447605.

[:5-3] Hutchinson, G.E. (1957). A treatise on limnology. Wiley. ISBN 0471425702.

[4] Koshinsky, Gordon D. (1970). "The Morphometry of Shield Lakes in Saskatchewan". Limnology and Oceanography. 15 (5): 695–701. Bibcode:1970LimOc..15..695K. doi:10.4319/lo.1970.15.5.0695. ISSN 0024-3590. JSTOR 2834006.

[5] Verpoorter, Charles; Kutser, Tiit; Seekell, David A.; Tranvik, Lars J. (2014). "A global inventory of lakes based on high-resolution satellite imagery". Geophysical Research Letters. 41 (18): 6396–6402. Bibcode:2014GeoRL..41.6396V. doi:10.1002/2014GL060641. hdl:20.500.12210/62355. ISSN 1944-8007.

[:6-6] Seekell, David A.; Cael, B. B.; Byström, Pär (2022-04-05). "Problems with the shoreline development index - a widely used metric of lake shape". Earth and Space Science Open Archive. doi:10.1002/essoar.10510804.3. Retrieved 2022-05-09.

[:1-7] Seekell, D.; Cael, B.; Lindmark (2021). "The Fractal Scaling Relationship for River Inlets to Lakes". Geophysical Research Letters. 48 (9): e2021GL093366. Bibcode:2021GeoRL..4893366S. doi:10.1029/2021GL093366. S2CID 235508504.

[8] Rawson, D. S. (1960). "A Limnological Comparison of Twelve Large Lakes in Northern Saskatchewan". Limnology and Oceanography. 5 (2): 195–211. Bibcode:1960LimOc...5..195R. doi:10.4319/lo.1960.5.2.0195. ISSN 0024-3590. JSTOR 2832556. Retrieved December 19, 2020.

[:2-9] Kent, Clement; Wong, Jonathan (1982-06-01). "An Index of Littoral Zone Complexity and Its Measurement". Canadian Journal of Fisheries and Aquatic Sciences. 39 (6): 847–853. doi:10.1139/f82-115. ISSN 0706-652X.

[:7-10] Seekell, D.; Cael, B.B.; Byström, P. (2022-05-09). "Problems with the shoreline development index ‐ a widely used metric of lake shape Research Letter for consideration by Geophysical Research Letters". Geophysical Research Letters. doi:10.1029/2022GL098499. ISSN 0094-8276. S2CID 248718476.

[:3-11] Håkanson, L. (2004). Lakes: Form and Function. Caldwell, New Jersey: Blackburn Press. ISBN 1930665245.

[:4-12] Seekell, D.; Cael, B.; Norman, S.; Byström, P. (2021). "Patterns and variation of littoral habitat size among lakes". Geophysical Research Letters. 48 (20): e2021GL095046. Bibcode:2021GeoRL..4895046S. doi:10.1029/2021GL095046. ISSN 1944-8007. S2CID 244253181.

[13] Seekell, D.; Cael, B. B. (2024-05-01). "Bias in the shoreline development index: Ecological implications illustrated with an analysis of littoral-pelagic habitat coupling". Limnologica. 106: 126173. doi:10.1016/j.limno.2024.126173. ISSN 0075-9511.

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