Skip to main content
SpringerLink
Log in

New Approaches to the Modelling of Lake Basin Morphometry

  • Published:
Environmental Modeling & Assessment Aims and scope Submit manuscript

Abstract

In lake modelling, a general and useful method of describing variations in area and volume with depth is of fundamental importance to describe processes and properties that change vertically within a given lake. In this work, two mathematical approaches to describe the shape of a lake basin are introduced and tested against empirical data. The two methods require only three easily available input parameters: maximum depth, surface area and volume. The first method is based on a traditional morphometric parameter, the volume development (V d), and the second method on the new hypsographic development parameter (H d). Both methods give area and volume at any depth of a lake and can furthermore be used to estimate lake bottom slopes. Comparisons with empirical area–depth and volume–depth distribution curves from 105 lakes that cover a wide range of lake morphometric characteristics have revealed that the two methods give very satisfactory results. The V d-model yields r 2-values of 0.924 and 0.907 for area and volume description with lake depth, respectively. The corresponding r 2-values for the H d-model are 0.988 and 0.996, respectively. Using the H d-model, an approach has also been developed to test when and by how much it is necessary to correct the empirical volume of a lake given the number of measured strata and basin shape.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Anderson, C. (1997). Limnologisk undersökning av Lötsjön, april–augusti 1996. Scripta Limnologica Upsaliensia 1997, B:4, 47 (in Swedish).

    Google Scholar 

  2. Andersson, P., Borg, H., Holmgren, K., & Håkanson, L. (1987). Typsjöar och tillrinningsområden i projektet kalkning-kvicksilver vid naturvårdsverkets PU-Lab, SNV Rapport 3396 (p. 80) (in Swedish).

  3. Bengtsson, Å., Viklund, T., Häggblom, M., Andersson, T., & Håkanson, L. (1987). Typsjöar och tillrinningsområden i Västernorrlands län, SNV Rapport 3402 (p. 81) (in Swedish).

  4. Blais, J. M., & Kalff, J. (1995). The influence of lake morphometry on sediment focusing. Limnology and Oceanography, 40, 582–588.

    CAS  Google Scholar 

  5. Blom, G., van Duin, E. H. S., & Lijklema, L. (1994). Sediment resuspension and light conditions in some shallow Dutch lakes. Water Science and Technology, 30, 243–252.

    Google Scholar 

  6. Bodbacka Fältman, L. (1991). Sedimentary structures and sediment accumulation in the lakes lilla Ullfjärden and stora Ullfjärden, studied by the X-ray radiographic technique, UNGI Rapport 83. Uppsala University, Institute of Earth Sciences, Physical Geography (p. 113).

  7. Charlton, M. N. (1980). Hypolimnion oxygen consumption in lakes: Discussion of productivity and morphometry effects. Canadian Journal of Fisheries and Aquatic Sciences, 37, 1531–1539.

    Google Scholar 

  8. Cole, J. J., & Pace, M. L. (1998). Hydrological variability of small northern Michigan lakes measured by the addition of tracers. Ecosystems, 1, 310–320.

    Article  Google Scholar 

  9. Cornett, R. J. (1989). Predicting changes in hypolimnetic oxygen concentrations with phosphorus retention, temperature, and morphometry. Limnology and Oceanography, 34, 1359–1366.

    CAS  Google Scholar 

  10. Cornett, R. J., & Rigler, F. H. (1987). Vertical transport of oxygen into the hypolimnion of lakes. Canadian Journal of Fisheries and Aquatic Sciences, 44, 852–858.

    Google Scholar 

  11. Crapper, P. F., Fleming, P. M., & Kalma, J. D. (1996). Prediction of lake levels using water balance models. Environmental Software, 11, 251–258.

    Article  Google Scholar 

  12. Duarte, C. M., & Kalff, J. (1986). Littoral slope as a predictor of the maximum biomass of submerged macrophyte communities. Limnology and Oceanography, 31, 1072–1080.

    Google Scholar 

  13. Elert, M., Meili, M., Östlund, M., & Johansson, J-Å. (1998). Kvicksilver i Rolfstaån - Delångersån, undersökningar och modelleringar av ackumulation och transport, SNV Rapport 4868 (p. 68) (in Swedish).

  14. Fee, E. J. (1979). A relation between lake morphometry and primary productivity and its use in interpreting whole-lake eutrophication experiments. Limnology and Oceanography, 24, 401–416.

    CAS  Google Scholar 

  15. Fee, E. J., Hecky, R. E., Kasian, S. E. M., & Cruikshank, D. R. (1996). Effects of lake size, water clarity, and climatic variability, on mixing depths in Canadian Shield lakes. Limnology and Oceanography, 41, 912–920.

    CAS  Google Scholar 

  16. Gibson, C. E., & Guillot, J. (1997). Sedimentation in a large lake: The importance of fluctuations in water level. Freshwater Biology, 37, 597–604.

    Article  Google Scholar 

  17. Goodchild, M. F., Steyaert, L. T., Parks, B. O., Johnston, C., Maidment, D., Crane, M., et al. (1996). GIS and environmental modeling: Progress and research issues. Fort Collins, CO: GIS World Books.

    Google Scholar 

  18. Grahn, P., Thorssell, S., Nilsson, Å., & Håkanson, L. (1987). Typsjöar och tillrinningsområden i Örebro län, SNV Rapport 3384 (p. 83) (in Swedish).

  19. Ha, S. R., Bae, G. J., Park, D. H., & Cho, J. H. (2003). Improvement of pre- and post-processing environments of the dynamic two-dimensional reservoir model CE-QUAL-W2 based on GIS. Water Science and Technology, 48, 79–88.

    CAS  Google Scholar 

  20. Håkanson, L. (1977). On lake form, lake volume and lake hypsographic survey. Geografiska Annaler A, 59, 1–29.

    Article  Google Scholar 

  21. Håkanson, L. (1977). The influence of wind, fetch, and water depth on the distribution of sediments in Lake Vänern, Sweden. Canadian Journal of Earth Sciences, 14, 397–412.

    Google Scholar 

  22. Håkanson, L. (1981). A manual of lake morphometry. Berlin, Heidelberg, New York: Springer-Verlag.

    Google Scholar 

  23. Håkanson, L. (1981). Determination of characteristic values for physical and chemical lake sediment parameters. Water Resources Research, 17, 1625–1640.

    Google Scholar 

  24. Håkanson, L. (1981). On lake bottom dynamics – the energy–topography factor. Canadian Journal of Earth Sciences, 18, 899–909.

    Google Scholar 

  25. Håkanson, L. (1982). Lake bottom dynamics and morphometry – the dynamic ratio. Water Resources Research, 18, 1444–1450.

    Google Scholar 

  26. Håkanson, L. (1994). How many lakes are there in Sweden? Geografiska Annaler A, 76, 203–205.

    Article  Google Scholar 

  27. Håkanson, L. (1997). Testing different sub-models for the partition coefficient and the retention rate for radiocesium in lake ecosystem modelling. Ecological Modelling, 101, 229–250.

    Article  Google Scholar 

  28. Håkanson, L. (1999). Water pollution – methods and criteria to rank, model and remediate chemical threats to aquatic ecosystems. Leiden: Backhuys Publishers.

    Google Scholar 

  29. Håkanson, L. (2000). The role of characteristic coefficients of variation in uncertainty and sensitivity analyses, with examples related to the structuring of lake eutrophication models. Ecological Modelling, 131, 1–20.

    Article  Google Scholar 

  30. Håkanson, L. (2005). The importance of lake morphometry for the structure and function of lakes. International Review of Hydrobiology, 90, 433–461.

    Article  Google Scholar 

  31. Håkanson, L., Parparov, A., & Hambright, K. D. (2000). Modelling the impact of water level fluctuations on water quality (suspended particulate matter) in Lake Kinneret, Israel. Ecological Modelling, 128, 101–125.

    Article  Google Scholar 

  32. Håkanson, L., & Peters, R. H. (1995). Predictive limnology – methods for predictive modelling. Amsterdam: SPB Academic Publishing.

    Google Scholar 

  33. Hamilton, D. P., & Mitchell, S. F. (1996). An empirical model for sediment resuspension in shallow lakes. Hydrobiologia, 317, 209–220.

    Article  Google Scholar 

  34. Hamilton, D. P., & Mitchell, S. F. (1997). Wave-induced shear stresses, plant nutrients and chlorophyll in seven shallow lakes. Freshwater Biology, 38, 159–168.

    Article  Google Scholar 

  35. Hanna, M. (1990). Evaluation of models predicting mixing depth. Canadian Journal of Fisheries and Aquatic Sciences, 47, 940–947.

    Google Scholar 

  36. Hellström, T. (1991). The effect of resuspension on algal production in a shallow lake. Hydrobiologia, 213, 183–190.

    Article  Google Scholar 

  37. Henriksson, L., & Nyman, H. G. (1992). Mjörn - En limnologisk studie 1990. Länsstyrelsen Älvsborgs Län, 1992(4), 107 pp. (in Swedish).

    Google Scholar 

  38. Henrikson, L., Nyman, H. G., & Oscarson, H. G. (1987). Lyngern - 1984 och för hundra år sedan, Länsstyrelsen Älvsborgs län 1987:1 & länsstyrelsen Hallands län 1987:1, 133 pp. (in Swedish).

  39. Henson, E. B. (1993). Estimating the areal extent of the littoral zone in lakes. Verhandlungen Internationale Vereinigung Limnologie, 25, 414–418.

    Google Scholar 

  40. Hilton, J., Lishman, J. P., & Allen, P. V. (1986). The dominant processes of sediment distribution and focusing in a small, eutrophic, monomictic lake. Limnology and Oceanography, 31, 125–133.

    Google Scholar 

  41. Horne, A. J., & Goldman, C. R. (1994) Limnology. Singapore: McGraw-Hill.

    Google Scholar 

  42. Imboden, D. M. (1973). Limnologische transport- und Nährstoffmodelle. Schweizerische Zeitschrift fur Hydrologie, 35, 29–68 (in German).

    Article  Google Scholar 

  43. James, W. F., & Barko, J. W. (1993). Sediment resuspension, redeposition, and focusing in a small dimictic reservoir. Canadian Journal of Fisheries and Aquatic Sciences, 50, 1023–1028.

    Google Scholar 

  44. James, R. T., Martin, J., Wool, T., & Wang, P. F. (1997). A sediment resuspension and water quality model of Lake Okeechobee. Journal of the American Water Resources Association, 33, 661–680.

    Article  CAS  Google Scholar 

  45. Jansson, M. (1977). Vattenbalans och kemiska budgetberäkningar för Stugsjön 1971–1975. In Experiment med gödsling av sjöar i Kuokkelområdet, Kuokkelprojektets rapport Nr. 5 (pp. 3–42). Uppsala: Uppsala universitet, Limnologiska institutionen (in Swedish).

  46. Jansson, M. (1978). Abiotiska förhållanden i Gunillajaure 1977. In Sjögödslingsexperiment i Kuokkelområdet, Kuokkelprojektets rapport Nr. 6 (pp. 5–24). Uppsala: Uppsala universitet, Limnologiska institutionen (in Swedish).

  47. Johansson, H., Lindström, M., & Håkanson, L. (2001). On the modelling of the particulate and dissolved fractions of substances in aquatic ecosystems – sedimentological and ecological interactions. Ecological Modelling, 137, 225–240.

    Article  CAS  Google Scholar 

  48. Johnson, T. C. (1980). Sediment redistribution by waves in lakes, reservoirs and embayments. In H. G. Stefan (Ed.), Proceedings of the symposium on surface water impoundments, June 2–5, 1980, Minneapolis, Minnesota (pp. 1307–1317). USA: American Society of Civil Engineers.

  49. Kalchew, R., Botev, I., Hristozova, M., Naidenow, W., Raikova-Petrova, G., Stoyneva, M., et al. (2004). Ecological relations and temporal changes in the pelagial of the high mountain lakes in the Rila Mountains (Bulgaria). Journal of Limnology, 63, 90–100.

    Google Scholar 

  50. Konitzer, K. (1999). Redistribution of Chernobyl 137Cs in lake sediment, Licentiate thesis, Uppsala University, Uppsala, Sweden.

  51. Kuo, J. T., & Wu, J. H. (1991). A nutrient model for a lake with time-variable volumes. Water Science and Technology, 24, 133–139.

    CAS  Google Scholar 

  52. Lind, O. T., Chrzanowski, T. H., & Dávalos-Lind, L. (1997). Clay turbidity and the relative production of bacterioplankton and phytoplankton. Hydrobiologia, 353, 1–18.

    Article  CAS  Google Scholar 

  53. Lind, O. T., Dávalos-Lind, L. O., Chrzanowski, T. H., & Limón, J. G. (1994). Inorganic turbidity and the failure of fishery models. Internationale Revue der Gesamten Hydrobiologie, 79, 7–16.

    Article  Google Scholar 

  54. Lindström, M., Håkanson, L., Abrahamsson, O., & Johansson, H. (1999). An empirical model for prediction of lake water suspended particulate matter. Ecological Modelling, 121, 185–198.

    Article  Google Scholar 

  55. Meybeck, M. (1995). Global distribution of lakes. In A. Lerman, D. M. Imboden & J. R. Gat (Eds.), Physics and chemistry of lakes (pp. 1–32). Heidelberg, New York: Springer Verlag.

    Google Scholar 

  56. Molot, L. A., Dillon, P. J., Clark, B. J., & Neary, B. P. (1992). Predicting end-of-summer oxygen profiles in stratified lakes. Canadian Journal of Fisheries and Aquatic Sciences, 49, 2363–2372.

    Article  CAS  Google Scholar 

  57. Naoum, S., Tsanis, I. K., & Fullarton, M. (2005). A GIS pre-processor for pollutant transport modelling. Environmental Modelling & Software, 20, 55–68.

    Article  Google Scholar 

  58. Neumann, J. (1959). Maximum depth and average depth of lakes. Journal of the Fisheries Research Board of Canada, 16, 923–927.

    Google Scholar 

  59. Nõges, P., Tuvikene, L., Nõges, T., & Kisand, A. (1999). Primary production, sedimentation and resuspension in large shallow Lake Võrtsjärv. Aquatic Sciences, 61, 168–182.

    Article  Google Scholar 

  60. Parparov, A., & Hambright, K. D. (1996) A proposed framework for the management of water quality in arid-region lakes. Internationale Revue der Gesamten Hydrobiologie, 81, 435–454.

    Article  Google Scholar 

  61. Patalas, K. (1984). Mid-summer mixing depths of lakes of different latitudes. Verhandlungen Internationale Vereinigung Limnologie, 22, 97–102.

    Google Scholar 

  62. Rasmussen, J. B. (1988). Littoral zoobenthic biomass in lakes, and its relationship to physical, chemical, and trophic factors. Canadian Journal of Fisheries and Aquatic Sciences, 45, 1436–1447.

    Article  CAS  Google Scholar 

  63. Rasmussen, J. B., Godbout, L., & Schallenberg, M. (1989). The humic content of lake water and its relationship to watershed and lake morphometry. Limnology and Oceanography, 34, 1336–1343.

    Article  CAS  Google Scholar 

  64. Rawson, D. S. (1952). Mean depth and the fish production of large lakes. Ecology, 33, 513–521.

    Article  Google Scholar 

  65. Rawson, D. S. (1955). Morphometry as a dominant factor in the productivity of large lakes. Verhandlungen Internationale Vereinigung Limnologie, 12, 164–175.

    Google Scholar 

  66. Rempel, R. S., & Colby, C. J. (1991). A statistically valid model of the morphoedaphic index. Canadian Journal of Fisheries and Aquatic Sciences, 48, 1937–1943.

    Google Scholar 

  67. Rhode, A. (1972). Termiska studier i sjöar i Kassjöåns representativa område, 3-betygsuppsats i hydrologi, naturgeografiska institutionen, avdelningen för hydrologi. Uppsala: Uppsala universitet (in Swedish).

  68. Rowan, D. J., Kalff, J., & Rasmussen, J. B. (1992). Estimating the mud deposition boundary depth in lakes from wave theory. Canadian Journal of Fisheries and Aquatic Sciences, 49, 2490–2497.

    Google Scholar 

  69. Schallenberg, M., James, M., Hawes, I., & Howard-Williams, C. (1999). External forcing by wind and turbid inflows on a deep glacial lake and implications for primary production. New Zealand Journal of Marine Freshwater Research, 33, 311–331.

    Article  Google Scholar 

  70. Walker, W. W. (1979). Use of hypolimnetic oxygen depletion rate as a trophic state index for lakes. Water Resources Research, 15, 1463–1470.

    Article  CAS  Google Scholar 

  71. Wetzel, R. G. (1983). Limnology. Philadelphia: Saunders College Publishing.

    Google Scholar 

  72. Weyhenmeyer, G. A. (1996). The significance of lake resuspension in lakes. PhD thesis, Uppsala University, Uppsala, Sweden.

Download references

Acknowledgements

We would like to express our gratitude to Gunnar Persson at the Swedish University of Agricultural Sciences for giving us access to several unpublished lake hypsographic curves from a database maintained by the Department of Environmental Assessment.

Author information

Authors and Affiliations

  1. Department of Earth Sciences, Uppsala University, Villavägen 16, SE-752 36, Uppsala, Sweden

    Håkan Johansson, A. Angelica Brolin & Lars Håkanson

Authors
  1. Håkan Johansson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Angelica Brolin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lars Håkanson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Angelica Brolin.

Appendix A

Appendix A

Table 7 Limits in V d and relative depth within which the Simpson approximation (equation (5)) or the linear approximation (equation (6)) is recommended for calculations of the volume below the relative depth in question
Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Johansson, H., Brolin, A.A. & Håkanson, L. New Approaches to the Modelling of Lake Basin Morphometry. Environ Model Assess 12, 213–228 (2007). https://doi.org/10.1007/s10666-006-9069-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10666-006-9069-z

Keywords

Search

Navigation