Skip to main content
Log in

Scaling relationships between lake surface area and catchment area

  • Research Article
  • Published:
Aquatic Sciences Aims and scope Submit manuscript

Abstract

Scaling relationships, including power laws, provide quantitative predictions used in basic and applied sciences. We investigated scaling relationships between catchment area and lake surface area, the ratio of which has important implications for terrestrial-aquatic linkages. Synthesizing evidence from 9 datasets from three continents, we show that there is an approximately linear relationship between lake surface area and catchment area, and that reservoirs and other human-made lakes tend to have larger catchments than natural lakes. Using the example of DOC export from forested catchments, we illustrate how the relationships observed in this study can be used to provide first-order estimates of ecosystem processes coupling lakes and their catchments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Aitkenhead JA, McDowell WH (2000) Soil C: N as a predictor of annual riverine DOC flux at local and global scales. Global Biogeochem Cycles 14:127–138

    Article  CAS  Google Scholar 

  • Baker JP, Gherini SA, Christensen SW, Driscoll CT, Gallagher J, Munson RK, Newton RK, Reckhow KH, Shofield CL (1990) Adirondack lakes survey: an interpretive analysis of fish communities and water chemistry, 1984–87. Ray Brook, NY

    Google Scholar 

  • Bohk C, Rau R, Cohen JE (2015) Taylor’s power law in human mortality. Demogr Res 33:589–610

    Article  Google Scholar 

  • Canham CD, Pace ML, Papaik MJ, Primack AGB, Roy KM, Maranger RJ, Curran RP, Spada DM (2004) A spatially explicit watershed-scale analysis of dissolved organic carbon in Adirondack lakes. Ecol Appl 14:839–885

    Article  Google Scholar 

  • Doak DF, Bigger D, Harding EK, Marvier MA, O’Malley RE, Thomson D (1998) The statistical inevitability of stability-diversity relationships in community ecology. Am Nat 151:264–276

    Article  CAS  Google Scholar 

  • Downing JA (1979) Aggregation, transformation and the design of benthos sampling programs. Can J Fish Aquat Sci 36:1454–1463

    Google Scholar 

  • Downing JA, Prairie YT, Cole JJ, Duarte CM, Tranvik LJ, Striegl RG, McDowell WH, Kortelainen P, Caraco NF, Melack JM, Middelburg JJ (2006) The global abundance and size distribution of lakes, ponds, and impoundments. Limnol Oceanogr 51:2388–2397

    Article  Google Scholar 

  • Downing JA, Cole JJ, Middelburg JJ, Striegl RG, Duarte CM, Kortelainen P, Prairie YT, Laube KA (2008) Sediment organic carbon burial in agriculturally eutrophic impoundments over the last century. Global Biogeochem Cycles 22:1–10

    Article  Google Scholar 

  • Forsius M, Malin V, Makinen I, Kamari J, Kortelainen P, Verta M (1990) Finnish lake acidification survey: survey design and random selection of lakes. Envirometrics 1:73–88

    Article  Google Scholar 

  • Hallett LM, Hsu JS, Cleland EE, Collins SL, Dickson TL, Farrer EC, Gherardi LA, Gross KL, Hobbs RJ, Turnbull L, Suding KN (2014) Biotic mechanisms of community stability shift along a precipitation gradient. Ecology 95:1693–1700

    Article  Google Scholar 

  • Harrison JA, Maranger RJ, Alexander RB, Giblin AE, Jacinthe PA, Mayorga E, Seitzinger SP, Sobota DJ, Wollheim WM (2009) The regional and global significance of nitrogen removal in lakes and reservoirs. Biogeochemistry 93:143–157

    Article  CAS  Google Scholar 

  • Hayes NM, Vanni MJ (2018) Microcystin concentrations can be predicted with phytoplankton biomass and watershed morphology. Inland Waters 8:273–283

    Article  CAS  Google Scholar 

  • Hayes NM, Corman JR, Deemer BR, Strock KE, Razavi NR (2017) Key differences between lakes and reservoirs modify climate signals: A case for a new conceptual model. Limnology and Oceanography Letters 2:47–62

    Article  Google Scholar 

  • Kortelainen P (1993) Total organic carbon in Finnish lakes and its relationship to catchment characteristics. Can J Fish Aquat Sci 50:1477–1483

    Article  CAS  Google Scholar 

  • Kretser WA, Gallagher J, Nicholette J (1989) Adirondack lakes study 1984–87: an evaluation of fish communities and water chemistry. Ray Brook, NY

    Google Scholar 

  • Kuznetsova A, Brockhoff PB, Christensen RHB (2017) lmerTest package: tests in linear mixed effects models. J Stat Softw 82:1–26

    Article  Google Scholar 

  • Lagrue C, Poulin R, Cohen JE (2015) Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry. In: Proceedings of the National Academy of the United States of America 112.

  • R Core Team (2018) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

    Google Scholar 

  • Rasmussen JB, Godbout L, Schallenberg M (1989) The humic content of lake water and watershed and lake morphometry. Limnol Oceanogr 34:1336–1343

    Article  CAS  Google Scholar 

  • Reuman DC, Zhao L, Sheppard LW, Reid PC, Cohen JE (2017) Synchrony affects Taylor’s law in theory and data. Proc Natl Acad Sci 114:6788–6793

    CAS  PubMed  Google Scholar 

  • Robert A, Roy AG (1990) On the fractal interpretation of the mainstream length-drainage area relationship. Water Resour Res 26:839–842

    Article  Google Scholar 

  • Seekell DA, Pace ML (2011) Does the Pareto distribution adequately describe the size-distribution of lakes? Limnol Oceanogr 56:350–356

    Article  Google Scholar 

  • Shreve RL (1974) Variation of mainstream length with basin area in river networks. Water Resour Res 10:1167–1177

    Article  Google Scholar 

  • Sobek S, Tranvik LJ, Prairie YT, Kortelainen P, Cole JJ (2007) Patterns and regulation of dissolved organic carbon: An analysis of 7,500 widely distributed lakes. Limnol Oceanogr 52:1208–1219

    Article  CAS  Google Scholar 

  • Taylor LR (1961) Aggregation, variance and the mean. Nature 189:732–735

    Article  Google Scholar 

  • Taylor RAJ (2018) Spatial distribution, sampling efficiency and Taylor’s power law. Ecol Entomol 43:215–225

    Article  Google Scholar 

  • Thornton KW, Kennedy RH, Carroll JH, Walker WW, Gunkel RC, Ashby S (1980) Reservoir sedimentation and water quality-an heuristic model In: Stefan HG (ed) Proceedings of the symposium on surface water impoundments. American Society of Civil Engineering pp 654–661

  • Tippett MK, Cohen JE (2016) Tornado outbreak variability follows Taylor’s power law of fluctuation scaling and increases dramatically with severity. Nature Communications 7:1–7

    Article  Google Scholar 

  • U.S. Environmental Protection Agency (2016) National Aquatic Resource Surveys. https://www.epa.gov/national-aquatic-resource-surveys/data-national-aquatic-resource-surveys.

  • Xenopoulos MA, Lodge DM, Frentress J, Kreps TA, Bridgham SD, Grossman E, Jackson CJ (2013) Regional comparisons of watershed determinants of dissolved organic carbon in temperate lakes from the Upper Great Lakes region and selected regions globally. Limnol Oceanogr 48:2321–2334

    Article  Google Scholar 

  • Xiong C, Hoyer MV (2019) Influence of land use and rainfall variability on nutrient concentrations in Florida Lakes. Lake and Reservoir Management 35:25–37

    Article  CAS  Google Scholar 

  • Xu M, Schuster WSF, Cohen JE (2014) Robustness of Taylor’s law under spatial hierarchical groupings of forest tree samples. Popul Ecol 57:93–103

    Article  Google Scholar 

  • Zhao L, Sheppard LW, Reid PC, Walter JA, Reuman DC (2019) Proximate determinants of Taylor’s law slopes. J Anim Ecol 88:484–494

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by NSF Grants OAC-1839024 and OAC-1839011. JAW was also supported by a NatureNet Science Fellowship.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jonathan A. Walter.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Walter, J.A., Fleck, R., Pace, M.L. et al. Scaling relationships between lake surface area and catchment area. Aquat Sci 82, 47 (2020). https://doi.org/10.1007/s00027-020-00726-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00027-020-00726-y

Keywords

Navigation