Next Generation Large Basin Runoff Models

Thomas E. Croley II

Collaborators
Chansheng He, Western Michigan University (WMU web site)
David Watkins, Michigan Technological University (MTU web site)

Executive Summary

The Great Lakes Environmental Research Laboratory and Western Michigan University are developing an integrated, spatially distributed, physically-based water quality model to evaluate both agricultural non-point source loadings from soil erosion, animal manure, and pesticides, and point source loadings at the watershed level.

Project Rationale

Estimating point and non-point source pollution and Combined Sewage Overflows (CSOs) is critical to planning and enforcement agencies in protection of surface water and groundwater quality. Currently there are no integrated spatially distributed physically based watershed-scale hydrological/water quality models available to evaluate movement of materials (sediments, animal and human wastes, agricultural chemicals, nutrients, etc.) in both surface and subsurface waters in the Great Lakes watersheds.

Potential Watershed Pollution Sources

Non-point Sources: animal wastes, soil erosion, pesticides
Point Sources: combined sewer outflows (CSOs)

During the past four decades, a number of simulation models have been developed to aid in the understanding and management of surface runoff, sediment, nutrient leaching, and pollutant transport processes. GLERL has reviewed the available water quality models and is taking a different approach augmenting an existing physically based integrated surface/subsurface hydrology model.

Existing Distributed Agricultural Runoff Models

ANSWERS (Areal Non-point Source Watershed Environment Simulation)
CREAMS (Chemicals, Runoff and Erosion from Agricultural Management Systems)
GLEAMS (Groundwater Loading Effects of Agricultural Management Systems)
AGNPS (Agricultural Non-point Source Pollution Model)
EPIC (Erosion Productivity Impact Calculator)
SWAT (Soil and Water Assessment Tool)
HSPF (Hydrologic Simulation Program)

These models all use the SCS Curve Number method which is considered to have limitations.

DLBRM: Current GLERL Hydrologic Modeling Focus

Two-Dimensional spatially-distributed model (DLBRM)
The DLBRM model addresses the smaller time and space scales of concern to the ecological forecaster (daily or shorter fluctuations over areas from 1-1000 km²). Such time and space scales are particularly relevant for assessing runoff impacts on lake environments.

GLERL has expanded its distributed-parameter Large Basin Runoff Model structure (described below) by adding surface and subsurface lateral flows to and from adjacent cell moisture storage in a watershed. GLERL has acquired and reduced databases for the Maumee and Sandusky watersheds and tested the model on the Kalamazoo, Maumee, and Sandusky watersheds, developing its capability to simulate outflows into Lake Erie and to model the effects of land use and climate change.

Additional GLERL Hydrological Models

Advanced Hydrologic Prediction System (AHPS) Used daily to make extended probabilistic forecasts of many hydrological variables, including Great Lakes evaporation, runoff, and lake levels by GLERL and at also several US and Canadian agencies concerned with operational decision making.

Large Basin Runoff Model (LBRM) Large basin runoff model developed in the 1980s for estimating rainfall/runoff relationships on the 121 large watersheds surrounding the Laurentian Great Lakes. The LBRM model serves the needs of the long-range forecaster in water resource supply considerations. Currently it is used at the daily time interval at GLERL for a variety of studies, including hydrological forecasting in GLERL’s Advanced Hydrologic Prediction System

2006 DLBRM Modeling Plans

Continue to use hourly data in calibrations to daily and hourly flows
Extend hourly calibrations from the Maumee to other watersheds.
Survey available information on movement of chemicals and sediment in watersheds where we have calibrations.
Survey the Grand River watershed (flowing into Lake Michigan) and, resources permitting, the Maumee River watershed to determine point and non-point sources of pollutants and erosion, for use in making Grand River and Maumee predictions.
Expand the DLBRM to include movement of other materials besides a conservative pollutant: sediment, chemicals, and microbes.
Add erosion and sedimentation mechanics to the DLBRM including modeling additions, calibration, and revised universal soil loss equation, version 2 (RUSLE2) parameter acquisitions for the Maumee River, Grand River, and Saginaw Bay watersheds.
Identify flow regulation points, combined sewer outflows, and other point sources of material within the watersheds and incorporate into the model.
Incorporate the real-world information on some of these materials, collected last year for the Saginaw Bay watersheds, to calibrate and use the DLBRM to simulate known cases of chemical and sediment movement.
Simulate movement of specific materials into Saginaw Bay, Lake Michigan, and Lake Erie.
Map DLBRM-water quality outputs over the watershed and build animations for analysis and display of results.
Use the model on selected Lake Erie watersheds in a hindcast mode to estimate the contribution of each cell in the watershed to the total outflow into Lake Erie on selected dates for various flow times. This will be used in connection with the forecasting of "Resource Sheds" associated with each point in Lake Erie as a function of time.

2005 DLBRM Accomplishments

Modified the lumped-parameter Large Basin Runoff Model (LBRM) into a two-dimensional, spatially-distributed model (DLBRM)
Applied DLBRM to every 1 square kilometer cell of a watershed, and modified it to allow routing flows between adjacent cells' surface zones, upper soil zones, lower soil zones, and groundwater zones.
Modified the LBRM continuity equations for these additional flows and added corresponding corrector terms to the original solution equations
Replaced the analytical solution with a numerical one, demonstrating convergence.
Applied the DLBRM to several new Great Lakes watersheds; discretized and compiled databases of watershed characteristics and meteorology for 18 watersheds and calibrated the daily model to nine.
Began expanding the DLBRM by adding material transport capabilities to it (conservative pollutant)
Compared model predictions on the Maumee with an experimental field study of the movement of SF6.

2004 LBRM Accomplishments

Lumped-Parameter Model. GLERL developed their Large Basin Runoff Model (LBRM) as a serial and parallel cascade of linear reservoirs (outflows proportional to storage) representing moisture storage within a watershed: surface, upper soil zone, lower soil zone, and groundwater zone; see Figure 1 (ignoring flows shown in red color).

Computes potential evapotranspiration from a heat balance, indexed by daily air temperature, and takes actual evapotranspiration as proportional to both the potential and storage.
Uses variable-area in-filtration (infiltration proportional to unsaturated fraction of upper soil zone) and degree-day snowmelt.
Uses daily precipitation and minimum and maximum air temperature and is calibrated in a systematic parameter search to minimize the root mean square error (RMSE) between modeled and observed daily watershed outflows.

GLERL applied it extensively to the 121 riverine watersheds draining into the Laurentian Great Lakes for use in both simulation and forecasting.

tank cascade schematic

Figure 1. LBRM Tank Cascade Schematic with Lateral Flow Additions.

Distributed Surface Flow. Previously, GLERL adapted the LBRM from its lumped-parameter definition for an entire watershed to a two dimensional representation of the flow cells comprising the watershed and applied it to the Kalamazoo watershed. This involved changes to the model structure to apply it to the micro scale as well as organization of water-shed cells and an implementation of spatial flow routing. GLERL modified the LBRM continuity equations to allow upstream surface inflow when the model is applied to a single cell within a watershed and found the modifications in terms of corrector equations to be applied to the original solution. They considered flows between adjacent cells’ surface storages while keeping the upper soil zone, lower soil zone, and groundwater zones in each cell independent. Thus each cell’s upper soil zone, lower soil zone, and groundwater zone connected only to that cell’s surface zone and not to any other cell, but the surface zones connected between adjacent cells. Application of the spatially distributed LBRM to the Kalamazoo River watershed yielded outflow errors comparable to the original lumped model, but flows in the soil zones and groundwater zone were judged unrealistic since storage there flowed only into the surface zone in each cell and not between cells.

Distributed Subsurface Flows. As accurate accounting of soil water storage and spatial variation produces better runoff estimates, GLERL further modified the model to allow subsurface routing between cells of flows of the upper soil zone, the lower soil zone, and the groundwater zone. This allows surface and subsurface flows to interact both with each other and with adjacent-cell surface and subsurface storages. It involves additional flows out of the various subsurface storages in a watershed cell and additional flows (from upstream watershed cells’ subsurface storages) into the storages. Figure 1 depicts these additional lateral flows in red. The continuity equations were modified in terms of corrector equations ap-plied to the original solution and were derived directly. GLERL then organized LBRM application to constituent watershed cells into a flow network by again identifying the flow network and automatically arranging the cell computations accordingly. Finally, GLERL applied the model to investigate alternatives and to demonstrate surface-subsurface interactions in a distributed spatial context.

Each cell in a watershed has flows from its surface and subsurface components into its surface channel system, and it has flows from an upstream cell into its surface channel systems and subsurface flow system (except for the most-upstream cells). Here the surface and subsurface flow networks are taken as identical and so computation ordering, developed previously for routing of surface flows, is applied again to the same network for routing of all subsurface flows. At each cell it:

Sums all tributary inflows from each zone to determine the total input hydrographs into each of the storage zones of the current cell.
Routes by solving the mass continuity equations for every time interval in the hydrographs.
Assembles an outflow hydrograph from each storage for the current cell.

Figure 2. Selected Kalamazoo Watershed Descriptors

GLERL used a lumped-parameter calibration procedure in a distributed-parameter setting to optimize the spatial-average values of all parameters while imposing a spatial structure onto each parameter over the cells of the watershed. While parameters describing the degree-day snowmelt and heat available for evapotranspiration were taken as spatially constant, and while evapotranspiration from the groundwater and surface zones were taken as zero, the spatial structures of other parameters were assigned as follows. The linear reservoir coefficients for percolation, upper soil zone lateral outflow, and upper soil zone evapotranspiration were taken proportional to the spatial variation observed in upper soil zone permeability (see Figure 2). The linear reservoir coefficients for interflow, deep percolation, lower soil zone lateral outflow, lower soil zone evapotranspiration, groundwater, and groundwater zone lateral outflow were taken proportional to the spatial variation ob-served in lower soil zone permeability (see Figure 2). The surface zone outflow linear reservoir coefficient was taken proportional to the spatial variation in the square root of the observed surface slope divided by the observed Manning’s roughness factor (as suggested by Manning’s flow formula) and the upper soil zone capacity was taken proportional to the spatial variation observed in capacity.

Kalamazoo Re-Application. The Kalamazoo River watershed is agriculturally dominated with a drainage area of 5,612 km² in southwestern Michigan. The model was calibrated to the 1948-1964 data set of daily meteorology and watershed outflow; the first two years were used only for initialization of the model and the last 15 years were used to compare model and actual outflows. GLERL found slightly better calibrations by using meteorology spatially interpolated for every point in the watershed by inverse squared distance from each station (see Figure 3) for comparison of alternate interpolations). spatial interpolation schemes

Figure 3. Alternate Spatial Interpolations: a) Thiessen, b) inverse distance, c) inversed distance squared.

Several model variations were considered:

The supply entering USZ storage is affected by relative storage content (variable-area infiltration)
Both the supply and the upstream USZ flow entering storage are affected by relative storage
Neither the supply nor the upstream USZ flow entering storage are affected by relative storage (unconstrained storage).

As expected, the model with both the supply and the upstream USZ flow entering storage affected by relative storage proved superior (lowest calibrated RMSE). The correlation between model and observed watershed outflows was 0.88; the RMSE was 0.19 mm/d (compare with a mean flow of 0.78 mm/d); the ratio of model to actual mean flow was 1.00; and the ratio of model to actual flow standard deviation was 0.87. The original lumped parameter model Kalamazoo calibration gave RMSE = 0.18 mm/d and the previous best distributed model (only surface flows across cell boundaries and no subsurface lateral flows) gave 0.22 mm/d. Additionally, we experimented with several alternatives to the set of observations used for the spatial variation of model parameters depicted in Figure 2. These included spatially constant values for both the USZ capacity and evaporation parameters; the spatial variations of Figure 2 proved superior, although there are several alternatives left to investigate.

Kalamazoo water balance

Figure 4. Kalamazoo Water Balance (1949-1964)

Immediately apparent in a model water balance for the Kalamazoo is the absence of storage in the lower soil zone; (see Figure 4). The watershed soil zone moisture storages are apparent only as a two-layer system: upper soil and groundwater zones. Groundwater flow forms the majority of the outflow; there is a small groundwater flow out of the watershed, which is not part of the streamflow. Figure 5 compares observed watershed outflow with the model for January 1950—June 1951, showing good agreement. The base flow seems well represented but several peak flows are under-estimated. Figure 6 shows the Kalamazoo watershed spatial response for recession AB in Figure 5 (June 2—5, 1950). The ranges shown in Figure 6 do not correspond to maximums but were chosen for best illustration of watershed response.

kalamazoo hydrograph
For example, the maximum Kalamazoo model outflow between 1948-1964 is about 2,000 cm/d over the last cell’s 1-km2 surface area (231 m³s^-1) but only the range of 0—100 cm/d (0—11.6 m³s^-1) is shown to emphasize the lower flows [flows above 100 cm/d (11.6 m³s^-1) are shown at the same brilliance as 100 cm/d (11.6 m³s^-1)]. Figure 6 shows the watershed supply; the supply is near 5 cm/d on the first day and quickly goes to zero by day 3. Figure 6 also shows a flow out of each of the active storages: surface runoff flows out of the upper soil zone into the surface zone, groundwater flows from the groundwater flow zone to the surface, and outflow flows from the surface zone. Thus these flows represent the moisture storages within the watershed. The first two flows are within-the-cell flows while the last crosses cell boundaries and is accumulated down the flow network, reaching much larger values than within-the-cell flows. The general behavior of the watershed is depicted in this example. The supply on the first day results in a very flashy response in the upper soil zone, as seen by the immediate response in surface runoff. The groundwater zone is little affected and the groundwater flow is seen to be very nearly constant throughout the period. The surface response lies in between; the outflow network is more dense at the beginning than at the end as water flows through the network throughout the period. This strong groundwater component is characteristic of the Kalamazoo outflow.

Kalamazoo watershed precipitation

Figure 6. Distributed Large Basin Runoff Model Output for the Kalamazoo Watershed.

Maumee Application. The Maumee River is the largest tributary to Lake Erie, with a drainage area of 17,541 km2, draining portions of northern Ohio, eastern Indiana and southeast Michigan. Figure 7 shows maps of Maumee watershed descriptors necessary for defining the spatial model parameter variations. Note in the map for USZ capacity in Figure 7 that the northern-most part of the watershed is distinctly different from the rest of the watershed. The demarcation between the two parts follows the Michigan-Ohio state boundary and is related to differences in definitions used in soil maps in the two states. These differences were not resolved further here and the data sets were used as they appear in Figure 7. The model was again calibrated to a 1948-1964 data set of daily meteorology and watershed outflow in the same manner as used with the Kalamazoo calibration. GLERL found slightly better calibrations by using meteorology for every point in the watershed the same as the nearest station (Thiessen; see Figure 3). Again, the model with both the supply and the upstream USZ flow entering storage affected by relative storage was adopted. The correlation between model and observed watershed outflows was 0.91; the RMSE was 0.56 mm/d (compare with a mean flow of 0.79 mm/d); the ratio of model to actual mean flow was 1.08; and the ratio of model to actual flow standard deviation was 0.84. The lumped parameter model Maumee calibration gave 0.88 correlation and 0.63 mm/d RMSE. Thus, for the Maumee, the distributed model provides better statistics than the lumped model; the Maumee watershed is large enough to allow the distributed model to capture significant spatial variations.

Immediately apparent in a water balance, constructed from a model simulation of the Maumee watershed, is the absence of storage below the upper soil zone; see Figure 8. The watershed soil zone moisture storage is apparent only as a one-layer system consisting of the upper soil zone.

Maumee watershed descriptors

Figure 7. Selected Maumee Watershed Descriptors

Maumee water balance

Figure 8. Maumee Water Balance (1949 - 1964).

Surface response is indicated by the outflow plots and shows maximum response at the beginning with a well-defined recession apparent over the remaining days in the sequence. The absence of groundwater response is consistent with the hydrology of the Maumee. The Maumee application has only one lateral (upstream-down-stream) component: surface outflow; there are no flows between cells of upper soil zone, lower soil zone, or groundwater zone moisture. Therefore, only the surface exhibits a hierarchy of drainage (as shown in Figure 10); the other zones show no such hierarchy.

Figure 9 compares observed outflow with the model for January 1950-June 1951, showing generally good agreement. The model under-estimates most of the peak flows but over-estimates as many of the small peak flows as it under-estimates. Figure 10 shows the Maumee watershed spatial response for recession AB in Figure 9 (April 30—May 2, 1950). Since Thiessen weighting was used to reduce meteorological station data over the Maumee watershed, the Thiessen-polygonal pattern is evident in several of the plots in Figure 10. One can also discern patterns related to the soil parameter structures shown in Figure 7, including the northern demarcation between Ohio and Michigan. Since soil moisture storage occurs only in the upper soil zone, upper soil zone attributes are mostly shown. Most of the supply occurs on the first day of the sequence in Figure 10 and both infiltration and surface runoff mirror its spatial distribution (both on that day and on later days with spotty supplies). Evaporation appears maximum on the last day of the sequence.

Maumee watershed model output

Figure 10. Distributed Large Basin Runoff Model Output for the Maumee Watershed.

Summary. GLERL’s LBRM continuity equations were modified to allow upstream inflows when the model is applied to a single cell within a watershed. The LBRM is now applied, in both spatial dimensions, to a system of cells comprising a watershed. The inflows to each cell can now consist of outflows from upstream surface storages, upper soil zones, lower soil zones, and groundwater zones. The outflows from a cell consist of similar flows from the cell’s own moisture storage zones. The modifications to the LBRM were devised in terms of both the original continuity equations (with no upstream/down-stream flows) with new parameters (so we can use the same computer code) and new corrector equations to be applied to the original equation solution. LBRM applications to constituent watershed cells are organized in a flow network by identifying the network flow cascade and then automatically arranging the cell computations accordingly.

Calibration consists of finding the spatial means of 15 model parameters that best minimize the root mean square error between observed and modeled daily watershed outflows, while fixing spatial variation of each parameter to match that of selected observable water-shed characteristics. GLERL used upper and lower soil zone permeabilities, the upper soil zone available water capacity, and the square root of surface slope divided by Manning’s roughness coefficient. Application was made to the Kalamazoo River watershed in Michigan and to the Maumee River watershed in Ohio. The former is recognized as having a strong base flow component while the latter is not. The model calibrations yielded behavior consistent with these observations. The Kalamazoo was found to have a groundwater storage that dominates the surface flow, allowing delayed hydrograph response to rainfall, while the Maumee was found to lack any significant groundwater storage; its response to rainfall is governed rather by the very large (spatially) surface network.

Products

Software

Large Basin Runoff Model Software
http://www.glerl.noaa.gov/wr/lbrmexamples.html

Data Products

GLERL Advanced Hydrologic Prediction System Products: Links to plots for monthly values of inflow, outflow, total supply and mean lake level for each of the Great Lakes and Lake St. Clair. For each lake there is also a page (accessed by clicking on the lake name) with many other hydrology and meteorology variables. (AHPS web page)

Publications

CROLEY, T. E. II, and C. He. 2006. Watershed surface and subsurface spatial intraflows model. Journal of Hydraulic Engineering 11(1):12-20.

Croley, T. E., II, 2005. Using Climate Predictions in Great Lakes Hydrologic Forecasts. In Climatic Variations, Climate Change, and Water Resources Management (J. Garbrecht and T. Piechota, Eds.), ASCE, Arlington, Virginia, pp. 166-187.

Croley, T. E., II, and C. He, 2005. Distributed-parameter large basin
runoff model I: model development. Journal of Hydrologic Engineering,
10(3):173-181.

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.
http://www.glerl.noaa.gov/pubs/fulltext/2005/20050017.pdf

He, C., and T. E. Croley II, 2005. Estimating Nonpoint Source Pollution
Loadings in the Great Lakes Watersheds. Proceedings of the International
Conference on Poyang Lake Wetland Ecological Environment, Jiangxi Normal
University, Nanchang, Jiangxi, P.R. China, June 27, 2005, 12 pp. Compact Disc.
http://www.glerl.noaa.gov/pubs/fulltext/2005/20050016.pdf

He, C. and T. E. Croley II, 2005. Integration of GIS and visualization for distributed water-shed modeling of the Great Lakes basin. Proceedings of The International Geographical Union Commission for Water Sustainability International Conference on Environmental Change and Rational Water Use, Buenos Aires, Argentina, August 29-September 1, 2005, (in review).

He, C., and T. E. Croley II, 2004. Development of a 2-d large basin
operational hydrologic model. Proceedings of the Workshop on Modeling and
Control for Participatory Planning and Managing Water Systems, September
29-October 1, 2004, Venice, Italy, International Federation for Automatic
Control, 12 pp. Compact Disc.

Croley, T. E., II, 2004. Spatially Distributed Model of Interacting Surface and Groundwater Storages. Proceedings, World Water and Environmental Resources Congress 2004, June 27—July 1, 2004, Salt Lake City, Utah, Environmental Water Resources Institute, American Society of Civil Engineers, Washington DC, 10 pp., Compact Disc.

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 R. A. Assel, 2002. Great Lakes evaporation model sensitivities and errors. Proceedings, Second Federal Interagency Hydrologic Modeling Conference, Subcommittee on Hydrology of the Interagency Advisory Committee on Water Data, Las Vegas, 28 July-1 August, 12 pp., Compact Disc.

Croley, T. E., II, and C. He, 2002. Great Lakes large basin runoff model. Proceedings, Second Federal Interagency Hydrologic Modeling Conference, Subcommittee on Hydrology of the Interagency Advisory Committee on Water Data, Las Vegas, 28 July-1 August, 12 pp., Compact Disc.

He, C., and T. E. Croley II, 2002. A development framework for two-dimensional large basin operational hydrologic models. Proceedings, Second Federal Interagency Hydrologic Modeling Conference, Subcommittee on Hydrology of the Interagency Advisory Committee on Water Data, Las Vegas, 28 July-1 August, 12 pp., Compact Disc.

2003 Milestone Report

Milestone: Apply GLERL's Large Basin Runoff Model in a distributed-parameter fashion for the Kalamazoo River Basin and calibrate and adjust the model to account for difference in soil characteristics.

Last updated: 2006-06-01 mbl