1. General Model Information



Main medium: aquatic
Main subject: biogeochemistry
Organization level: ecosystem
Type of model: ordinary differential equations
Main application:
Keywords: water quality, oxygene uptake, ice covered lake


Dr. David M. Livingstone
Überlandstrasse 133
CH-8600 Dübendorf
Phone: +41 1 823 5540
Fax : +41 1 823 5210
email: living@eawag.ch



A one-box exponential model with constant coefficients generally suffices to describe the winter oxygen uptake of a holomictic lake with no ice cover. A simple modification of the model - settling the gas transfer velocity to zero during periods of ice cover - allows the mean oxygen concentration in the lake to be predicted irrespective of whether the lake is frozen over or not.

Model purpose
Prediction of the winter oxygen uptake of a lake, including the effect of ice cover.

Source of the Abstract:
Joergensen S.E., B. Halling-Soerensen and S.N Nielsen (Edts.) 1996: Handbook of Environmental and Ecological Modelling. CRC Press Boca Raton et al. 672 pp.

II. Technical Information

II.1 Executables:

Operating System(s): MAC, EXCEL

II.2 Source-code:

Programming Language(s):

II.3 Manuals:

II.4 Data:

III. Mathematical Information

III.1 Mathematics

III.2 Quantities

III.2.1 Input

Cs = oxygen saturation concentration [M*L-3]
Co = homogeneous O2 contentration at time t=0(early winter) [M*L-3]
beta = O2 transfer velocity [L*T-1] sigma = mean lake depth [L]
J = net O2 consumption rate [M*L-3*T-1]
ta = time of freeze-up [T]
tb = time of break-up [T]

III.2.2 Output

C = Cs - J*sigma/beta=equilibrium O2 concentration [M*L-3]
Ca = C - (C - C0) exp[(-beta/2)ta] = O2 concentration at t = ta [M*L-3]
Cb = Ca-J(tb-ta)=O2 Concentration at t=tb[M*L-3]
Cm = C - (C - Cb)exp[(-beta/2) (tm-tb)] = O2 concentration at t = tm After timebreak [M*L-3]

IV. References

Livingstone, D.M., 1993. Lake oxygenation: Application of a one-box model with ice cover. Int. Rev. Ges. Hydrobiol., 78 (4) 465-480.

V. Further information in the World-Wide-Web

VI. Additional remarks

Last review of this document by: T. Gabele: 15 .10. 1998
Status of the document:
last modified by Tobias Gabele Wed Aug 21 21:44:42 CEST 2002

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