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Wilfred von Dauster

June 2002 FSL Forum F2D By Lynn E. Johnson and Brian E. Skahill


Urbanization of land has long been recognized to result in more rapid removal of storm water with corresponding increases in the volume and peak runoff rates. For example, a general English rule of thumb established in the mid-1800s was that about half of the total rainfall would appear as runoff from urban surfaces. Approaches to characterizing flood runoff response in urban watersheds began with macroscopic empirical formulas that considered the entire drainage basin as a single unit, assumed rainfall was uniformly distributed over the drainage area, and estimated flow at only the most downstream point.

Todayıs urban flood runoff procedures have evolved into microscopic formulas that account for the spatial and temporal distribution of rainfall, land characteristics, and flood runoff responses at any location within a watershed. Technologies such as the geographic information system (GIS), remote sensing, and numerical analysis have fostered advances in urban watershed modeling. GIS supports development of spatial databases at refined scales for land surface characteristics and flow conveyances, and is also a spatial data and model integrator and user-friendly interface for enhanced modeling support. In earlier research, we illustrated how GIS tools could be applied to a variety of hydrologic modeling procedures. Remote sensing, using meteorological radars, provides rainfall intensity estimates at time intervals of a few minutes and space scales on the order of square kilometers. Numerical analysis techniques allow us to simulate incident rainfall, infiltration, flood runoff and channel routing at these small time and space intervals.

The F2D (Flood, Two Dimensional) model was developed to help operational forecasters provide early warning on flood threats in urbanized areas. GIS serves as a data and model integrator for F2D where land surface and rainfall base datasets are translated through modeling and visualization to derive coverages on flood flows and depths.

Model Design

F2D is an event-based kinematic, infiltration-excess distributed rainfall-runoff model developed to acknowledge and account for the spatial variability of parameters relevant to storm surface runoff production and surface flow in urbanizing watersheds. The model operates on a square grid of specified spatial resolution.

The principal model components include spatially varied interception, accounting of input rainfall to lakes and reservoirs and routing into reservoirs, spatially varied infiltration, kinematic-wave overland and channel flow routing, and channel losses. Several of the model components may be "switched" on or off. The main model outputs include a volume summary, discharge hydrographs for interior locations, the main basin outlet, and raster maps of variables such as cumulative infiltration and water depth throughout the basin. The model was expressly designed to support the Monte Carlo simulation (repeating the experiment many times) with the intent of estimating the range of possible system responses.

GIS Data and Model Integration

GIS provides the environment for the development of spatial database and integration of models. Primary GIS functions for F2D were obtained from the 1993 Geographic Resources Analysis Support System (GRASS). The main model inputs include grid and tabular datasets describing the watershed boundary, flow direction based on the D-8 method, slope, overland flow distance to the main basin outlet, the stream network topology and channel geometry, forest type and density, soil textural classification, land use and land cover, lakes and reservoirs and associated surface areas, spatially varied roughness values, initial moisture content, and impervious areas. These data are compiled in compatible grid and vector formats.

Modeling procedures for drainage system delineation, soil moisture and infiltration, and overland and channel flow hydraulics are integrated into a unified code for simulating flood runoff.

F2D relies on the topographic representations derived from a digital elevation model. Terrain preprocessing generates coverages for slope, aspect, basin outline, and channel network to a user-selectable level of detail. This network is then used as input to hydraulic routing algorithms that move flood waters over the land surface and through downstream channels.

Radar-rainfall remote sensing imagery is the predominant dynamic input to the F2D modeling system. Rain intensity field updates are provided at nominal 6-minute inter-vals during storm operations. The spherical-coordinate radar-rainfall verification research has shown that the radar-rainfall Z-R data uncertainty can be reduced significantly through real-time bias correction based on rain gauges. We found that reductions of 60% to 30% are possible, whereas others found that 63% to 25% reductions are possible with bias correction (generally overestimates). F2D provides visualization of rainfall fields and flood runoff flows. Figure 1 shows F2D rainfall and computational products, including cumulative infiltration, water depth, and runoff hydrographs. Animations of rainfall and flood flows are intended to be prototypes for forecaster evaluations.

F2D - Fig. 1

Figure 1. F2D showing radar - rainfall, cumulative infiltration, and flow level, and an outlet hydrograph for the Buffalo Creek, Colorado, flash flood of
12 July 1997.

Application and Results

In addition to Buffalo Creek, F2D was applied to simulate storm surface runoff from the Ralston Creek and Goldsmith Gulch basins, two watersheds located within the Denver region with drainage areas of approximately 225 km2 and 15 km2, respectively. The upper portions of the Ralston basin drain into Ralston reservoir, which effectively eliminates that area from lower basin runoff response. The lower portion of the basin is urbanizing (estimated 20% impervious), with the primary soil type, silt loam. The Goldsmith Gulch watershed is predominately an urban basin (estimated 40% impervious) with loam soil.

Eight events from 1995 – 1997 were selected for F2D application on the Ralston Creek basin; six events were selected for the study application on the Goldsmith Gulch basin. Figures 2 and 3 show observed runoff hydrographs overplotted with 95% uncertainty bounds which were obtained from the F2D model for the two basins.

F2D - Fig. 2a

F2D - Fig. 2b

Figure 2. Observed runoff hodographs showing 95% uncertainty bounds obtained from F2D for (a) 1 June 1991 and (b) 26 May 1996 storms on the Ralston Creek basin.

F2D - Fig. 3a

F2D - Fig. 3b

Figure 3. Same as Figure 2 except for (a) 28 July 1997 and (b) 12 July 1996 storms on the Goldsmith Gulch basin.

A complex distributed, physically based model like F2D must be calibrated in order to verify that predictions are realistic. A variation of the Generalized Likely Uncertainty Estimation (GLUE) procedure was applied as a method to calibrate the model and estimate uncertainty.

Although based on a limited number of Monte Carlo simulations and events, the model results are considered good. Efficiency scores were obtained from the model for the calibration and validation events on the Ralston Creek and Goldsmith Gulch basins, respectively. While using rain gauge adjusted radar-rainfall estimates and operating at a coarse spatial scale, the model was very accurate in simulating time to peak and reasonably accurate in simulating runoff volume and peak discharge. Also, the 95% uncertainty bounds obtained from the model envelop almost all observed responses at the main basin outlets for the events considered, suggesting an acceptable model structure.

A model sensitivity analysis was performed to examine the relative contribution of the model parameters, initial conditions, and rainfall to the modelıs overall predictive uncertainty. The 28 July 1997 event on the Goldsmith Gulch basin was chosen for the sensitivity analysis. As an example, the model sensitivity analysis indicates that one can be 90% confident that the peak flow (in this case, on 28 July) will be less than 135% of a model prediction due to the runoff processes. This level of predictive uncertainty associated with the runoff process is in contrast to that of the radar-rainfall, which is on the order of 160% – 200%.


The F2D infiltration-excess distributed rainfall-runoff model developed at FSL acknowledges and accounts for the spatial variability and uncertainty of radar-rainfall fields and various parameters relevant to storm surface runoff production and surface flow. The model routes excess rainfall over the land surface and through an organized stream network using the kinematic wave approximation of the equations describing one-dimensional unsteady free-surface flow as overland or open channel flow. F2D was expressly designed to include Monte Carlo simulation for a single storm event, with the intent of supporting model calibration and uncertainty estimation. The model structure addresses some of the issues that have been raised regarding the calibration of an advanced distributed surface runoff model. F2D can be used to investigate and evaluate uncertainty in rainfall-runoff modeling. Using rain gauge adjusted radar rainfall estimates, the model was applied to route storm surface runoff from two urbanized watersheds located within the Denver Urban Drainage and Flood Control District (UDFCD). Even though the model was based on a limited number of Monte Carlo simulations and considered events, the results were still quite positive.


Special acknowledgments go to Michael Dixon with NCAR's Research Applications Program for providing the processed radar data; Kevin Stewart with the UDFCD for providing the rain gauge and streamflow data; and Scott O'Donnell with FSL for many helpful discussions.

Note: A complete list of references and more information on this and related topics are available at the main FSL Website www.fsl.noaa.gov, by clicking on "Publications" and "Research Articles."

(Dr. Lynn Johnson is a Hydrologist/Research Scientist in the FSL Modernization Division. He is also affilated with the Cooperative Institute for Research in the Atmosphere (CIRA), Colorado State University at Fort Collins, and the Department of Civil Engineering, University of Colorado at Denver. He can be reached at ljohnson@fsl.noaa.gov or Lynn.Johnson@cudenver.edu).

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