FLake: a Fresh-water Lake Model for LM

Last updated: September 2006

FLake is a fresh-water lake model intended for use in numerical weather prediction (NWP), climate modelling , and other numerical prediction systems for environmental applications. The model is capable of predicting the vertical temperature structure and mixing conditions in lakes of various depth on time scales from a few hours to a year.

Note that these pages document FLake mainly with respect to LM model. FLake model has its own dedicated web site, where you can find more related and recent material (like publications, applications, source code etc)


FLake is a bulk model. It is based on a two-layer parametric representation of the evolving temperature profile and on the integral budgets of heat and of kinetic energy for the layers in question. The structure of the stratified layer between the upper mixed layer and the basin bottom, the lake thermocline, is described using the concept of self-similarity (assumed shape) of the temperature-depth curve. The same concept is used to describe the temperature structure of the thermally active upper layer of bottom sediments and of the ice and snow cover. The result is a computationally efficient bulk model that incorporates much of the essential physics.

FLake incorporates

  1. a flexible parameterization of the temperature profile in the thermocline,
  2. an advanced formulation to compute the mixed-layer depth, including the equation of convective entrainment and a relaxation-type equation for the depth of a wind-mixed layer, both mixing regimes are treated with due regard for the volumetric character of solar radiation heating,
  3. a module to describe the vertical temperature structure of the thermally active layer of bottom sediments and the interaction of the water column with bottom sediments, and
  4. an advanced snow-ice module.

Empirical constants and parameters of FLake are estimated, using independent empirical and numerical data. They should not be re-evaluated when the model is applied to a particular lake. In this way, FLake does not require re-tuning, a procedure that may improve an agreement of model results with a limited amount of data but should generally be avoided.

In order to compute fluxes of momentum and of sensible and latent heat at the lake surface, a parameterization scheme is developed that accounts for specific features of the surface air layer over lakes. The scheme incorporates:

  1. a fetch-dependent formulation for the aerodynamic roughness of the water surface,
  2. advanced formulations for the roughness lengths for potential temperature and specific humidity in terms of the roughness Reynolds number, and
  3. free-convection heat and mass transfer laws to compute fluxes of scalars in conditions of vanishing mean wind.


FLake in LM

FLake is implemented into the limited-area NWP system LM (Steppeler et al. 2003) used operationally at the German Weather Service (DWD). In order to be incorporated into LM (or into any other NWP system), FLake requires a number of two-dimensional external-parameter fields. These are, first of all, lake fractions (area fraction of a given LM grid box covered by lake water that must be compatible with the land-sea mask used) and lake depths.

A two-dimensional lake-fraction field for the LM1 domain (that was operationally used at DWD prior to the implementation of LME) is developed on the basis of a Global Land Cover Characterization (GLCC) data set with 30 arc sec resolution, that is ca. 1 km at the equator. A data set containing mean depths of a number of European lakes and of a few lakes from other regions of the world is developed at DWD. On the basis of that data set, the lake-depth external-parameter field is developed for the DWD LM1 domain. Since no tile approach is used in LM (i.e. each LM grid-box is characterised by a single land-cover type), only the grid-boxes with the lake fraction greater than 0.5 are treated as lakes.

Each lake is characterised by its mean depth. Other external parameters, e.g. optical characteristics of the lake water, are assigned their reference values offered by FLake. Using the above external-parameter fields, an extended version of LM that incorporates FLake is tested through parallel experiments including the LM data assimilation cycle. Results are monitored. In the present configuration, the heat flux through the water-sediment interface is set to zero and a layer of snow over the lake ice is not considered. The effect of snow above the ice is accounted for parametrically through changes in the surface albedo with respect to solar radiation (cf. Mironov and Ritter 2004). External parameter fields for the LME domain are being developed.

Testing FLake in LM (LME)