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Large Basin
Runoff Model

Distributed Watershed

Other Watershed




Distributed Large Basin Runoff Model

Large Basin Runoff Model (LBRM)

+ download LBRM software

GLERL developed a large-scale operational model in the 1980s for estimating rainfall/runoff relationships on the 121 large watersheds surrounding the Laurentian Great Lakes. It is physically based to provide good representations of hydrologic processes and to ensure that results are tractable and explainable. It is a lumped-parameter model of basin outflow consisting of a cascade of moisture storages or “tanks” each modeled as a linear reservoir, where tank outflows are proportional to tank storage. The mass balance schematic is shown in Figure 1.

lbrm schematic

Figure 1: Large Basin Runoff Model Tank Cascade Schematic

Daily precipitation, temperature and insolation (the latter available from meteorological summaries as a function of location) may be used to determine snow pack accumulations, snow melt (degree-day computations) and net supply. The net supply is divided into surface runoff and infiltration to the upper soil zone, in relation to the upper soil zone moisture content and the fraction it represents of the upper soil zone capacity. Percolation to the lower soil zone and lower soil zone evapotranspiration are taken as outflows from a linear reservoir (flow is proportional to storage). Likewise, interflow from the lower soil zone to the surface evapotranspiration and deep percolation to the groundwater zone are linearly proportional to the lower soil zone moisture content. Groundwater flow and evapotranspiration from the groundwater zone are linearly proportional to the groundwater zone moisture content. Finally, basin outflow and evaporation from the surface storage depend on its content. Additionally, evaporation and evapotranspiration are dependent on potential evapotranspiration as determined by joint consideration of the available moisture and the heat balance over the watershed. Total heat available during the day is estimated from air temperature and split between potential and actual evapotranspiration. Actual evaporation is taken proportional to both the potential and to storage. Thus actual and potential evapotranspiration are complementary.

In solving the mass conservation equations for the LBRM for some time increment we generally take net supply and potential evapotranspiration as uniform over the increment. Storage values at the end of a time increment are computed from values at the beginning. In the analytical solution, results from one storage zone are used in other zones where their outputs appear as inputs. There are several different solutions depending upon the relative magnitudes of all coefficients in the LBRM mass conservation equations. Croley (2002) solved the equations, yielding storages at the end of a time increment as functions of the inputs, parameters, and beginning-of-time-increment storages (storages at the end of the previous time increment). Since the net supply and evaporation variables change from one time increment to another, then the appropriate analytical result as well as its solution varies with time. Mathematical continuity between solutions is preserved however. A more detailed explanation of the equations presented on this page can be found elsewhere (Croley and He 2005d; please click to download a pdf copy). This paper can also be found in the Products section of this website

The model is physically based and is calibrated by finding its nine parameter values by systematically searching the parameter space. We use gradient search techniques to minimize the root mean square error (RMSE) between modeled basin outflow and actual. The large basin runoff model is used and has been used for the daily time interval at GLERL for a variety of studies, including hydrological forecasting in GLERL’s Advanced Hydrologic Prediction System, which gives probabilistic outlooks of Great Lakes evaporation, runoff, and lake levels, among others. Uses also include past studies of climate change impacts on Great Lakes hydrology, and several analyses of management and regulation scenarios. Examples of these studies include:


Croley, T.E., II (2002), ‘Large Basin Runoff Model,’ In Mathematical Models of Large Watershed Hydrology (V. Singh, D. Frevert, and S. Meyer, Eds.), Water Resources Publications, Littleton, Colorado, 717-770.

Last updated: 2006-09-22 mbl