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Distributed Large Basin Runoff Model
Distributed Large Basin Runoff Model
Model Overview | Materials Runoff | Solution | Testing | Next Steps | References
GLERL has expanded its lumped-parameter Large Basin Runoff Model structure (more information can be found in the Large Basin Runoff Model section of this website) by applying it to small cells of a watershed, and by adding surface and subsurface lateral flows to and from adjacent cell moisture storages. It is now a two dimensional, spatially-distributed accounting of moisture in several layers (zones) for every 1 km2 cell of a watershed. This version of the LBRM is known as the Distributed Large Basin Runoff Model (DLBRM)
Model Overview
We first modified the model to compute potential and actual evapotranspiration as if the two are independent; this is appropriate for small areas. We then modified it to allow lateral flows between all storage zones (tanks) in adjacent cells. This involved modifying model code to direct one cell’s storage’s lateral outflow into another cell’s storage zone as inflow. We allowed lateral flows between cells for all moisture storages: upper soil zones, lower soil zones, groundwater zones, and surface zones (Figure 1).
Figure 1: DLBRM Tank Cascade Schematic
We derived corrector equations (Croley and He 2005b) to express mass conservation for the DLBRM in terms of the LBRM mass conservation and changed the computer code correspondingly.
We have discretized 18 watersheds to date. The elevation map for the Kalamazoo River watershed and the Maumee River watershed are shown in Figure 2 and Figure 3 respectively. We started with elevations taken from a 1km digital elevation model (DEM) available from the United States Geological Survey. We soon adopted their 30m DEM to derive 1km elevations and slopes.
Figure 2: Kalamazoo Watershed Elevations (m).
Figure 3: Maumee Watershed Elevations (m)
Additionally, we compiled databases of all soil, land use, and derived parameters and all daily meteorology for each square kilometer of each watershed; see Figure 4 for examples. Each cell’s inflow hydrographs must be known before its outflow hydrograph can be modeled; therefore we arranged calculations by flow network to assure this. The flow network is implemented to minimize the number of pending hydrographs in computer storage and the time required for them to be in computer storage.
Figure 4: Examples of the Maumee Watershed databases.
We added flow routing for all upstream to downstream cell flows and used the same network for surface, upper soil, lower soil, and groundwater storages. A small example of flow routing derived from an elevation map is shown in Figure 5. We implemented routing network computations as a recursive routine to compute outflow that calls itself to compute inflows (which are upstream outflows) (Croley and He 2005a,b).
Figure 5: Watershed grid flows
In application, we use a gradient search technique to minimize RMSE between modeled and actual basin outflow by selecting the best spatial averages for each parameter; we allow the spatial variation of each parameter to vary as a selected watershed characteristic (Croley and He, 2005). To speed up calibrations, we preprocess all meteorology for all watershed cells and preload it into computer memory. We used the model to look at modeling alternatives, including alternative evapotranspiration calculations, spatial parameter patterns, and solar insolation estimates. We also explored scaling effects in using lumped parameter model calibrations to calculate initial distributed model parameter values (Croley and He 2005a; Croley et al. 2005).
Materials Runoff Model
Consider now the addition of some material or pollutant dissolved in, or carried by, the water flows in Figure 2, except that none is considered to be evaporated; see Figure 6. If these flows do not mix together, then the fraction of each of these flows runs off directly (without even entering the upper soil zone). Taking pollutant movement with evaporation as zero, we can derive a set of pollutant balance equations.
Figure 6: Distributed "Pollutant" Flows Model Schematic
Solution
Croley (2002) solved LBRM mass conservation equations simultaneously, deriving 30 analytical solutions, and Croley and He (2005b) derived corrector equations to the analytical solutions. However, consideration of an analytical solution of the DLBRM mass conservation equations and pollutant balance equations reveal even more multiple solutions; while tractable, a simpler approach is desired. The approach taken here is to use a numerical solution based on finite difference approximations of the LBRM mass conservation equations and pollutant balance equations. It is important to also consider initial and boundary conditions as a part of these solutions.
Testing
As a test of the numerical solution of the DLBRM mass conservation equations, we used them for t = 1.5 minutes to approximate the solution over about 17 years of daily values for the Maumee River watershed (Croley and He 2005b) and found them identical (in all variables) through three significant digits (all that were inspected) with the exact analytical solution.
For t = 15 minutes, the solution was nearly identical with only an occasional difference of one in the third significant digit. As the Maumee River watershed has a very “flashy” response to precipitation (very fast upper soil and surface storage zones) these comparisons are deemed significant and the time intervals should be more than adequate for the slower response of lower soil and groundwater zones (the Maumee application has no lower soil or groundwater zones).
A more detailed explanation of the equations presented on this page can be found in the Croley and He (2005) paper (please click to download a pdf copy). This paper can also be found in the Products section of this website
Next Steps
We are about to develop an hourly version of the model from the present daily version, for better tracking of the movement of water and materials within a watershed. We plan to change the model code structure to include diurnal hydrology concepts and to provide for the massive data handling necessary for hourly meteorology (precipitation and minimum and maximum air temperature over every square kilometer of a watershed’s surface). We are building hourly model data streams in cooperation with the National Severe Storms Laboratory (NSSL web site) to be operated in near real time; we are planning on preprocessing the data to aid in the repetitive simulations employed in calibration. (We will also incorporate these data streams into existing daily models as well as into the altered hourly model structure. We hope to demonstrate improved water accounting and accurate water level forecasting in GLERL’s Advanced Hydrologic Prediction System with the improved daily models.) These hourly data streams will directly couple high resolution, multiple sensor quantitative precipitation estimates to the hydrologic models. Many of these parameters are not available for most watershed, particularly large watershed. We will add sedimentation and selected non-point source pollutant transport to the hourly model, by using the Modified Universal Soil Loss Equation and relevant erosion and pollutant loadings. Hence, we will treat transport as sufficient to always carry the erosion loss and not consider deposition.
References
Croley, T. E., II, 2002. Large basin runoff model. In Mathematical Models
in Watershed Hydrology (V.Singh, D. Frevert, and S. Meyer, Eds.), Water
Resources Publications, Littleton, Colorado, 717-770.
Croley, T. E., II, and C. He, 2005a. Distributed-parameter large basin
runoff model. I: Model development. Journal of Hydrologic Engineering,
10(3):173-181.
Croley, T. E., II, and C. He, 2005b. Watershed Surface and Subsurface Spatial Intraflows. Journal of Hydrologic Engineering, (in press).
Croley, T. E., II, C. He, and D. H. Lee, 2005. Distributed-parameter large basin runoff model. II: Application. Journal of Hydrologic Engineering, 10(3):182-191.
Croley, T. E., II, and C. He, 2005. Great Lakes Spatially Distributed
Watershed Model of Water and Materials Runoff. Proceedings of the
International Conference on Poyang Lake Wetland Ecological Environment,
Jiangxi Normal University, Nanchang, Jiangxi, P.R. China, June 27, 2005,
12
pp.
Last updated: 2006-09-08 ks