CIS and Remote Sensing in , Water Resources and Environment (Piocccdines of 1CGRHWE held at the Three Gorges Dam, China, September 2003). IAHS Publ. 289, 2004 1

Distributed hydrologie modelling for flood forecasting

BAXTER E. VIEUX School of Civil Engineering and Environmental Science, University of Oklahoma, 202 West Boyd Street, Norman, Oklahoma 73069, USA bvieux(5),ou.edu

Abstract As more accurate precipitation measurements and terrestrial characteristics are built into hydrologie models, the foundation for making hydrologie predictions is undergoing substantial change. The recent decade has seen rapid development of sophisticated computer programs capable of using the rich information content of remotely sensed geospatial data describing vegetative cover or ; distributed maps of precipitation derived from gauges, radar, and satellite; and digital terrain maps representing the drainage network. The goal of distributed hydrologie modelling is to take into account the heterogeneity of the watershed with the aim of making more accurate and reliable hydrologie predictions. An important area of application for distributed models is flood forecasting in urban and rural areas. Distributed modelling is a growing field of application worldwide, with varying degrees of empiricism and physical basis. Distributed modelling is currently applied from small catchments to large river basins ranging in size from 100 km" to over 100 000 km2.

Key words distributed hydrologie modelling; floods; forecasting; radar rainfall

INTRODUCTION

Mathematical modelling of watersheds began with Sherman's unit method published in 1932. Since then many types of hydrologie models have been developed. An ongoing debate within the hydrology community is how to construct a model that best represents the Earth's hydrological processes. A central theme in this debate is how best to use spatially explicit representations of heterogeneous characteristics of a watershed. Model development is striving to keep pace with the explosive growth of online geospatial data sources and remote sensing of the land surface. Because the full capabilities of a distributed model cannot be realized without spatially representative rainfall, radar and satellite technology as measurement of precipitation is advancing the state of hydrologie modelling. Geospatial data and spatially representative precipi­ tation measurements offer new possibilities for distributed modelling. This paper is organized as a review of major themes in hydrologie modelling with an emphasis on distributed approaches, particularly physics-based models and their applications. Recent advances in technology in remote sensing, data telemetry, and computing have led to increased interest in developing improved model representations. Much of the growth of distributed modelling is attributable to the availability of geospatial data and geographic information systems (GIS) for analysis and manipulation of digital terrain, soils, and landuse/cover into hydrologie parameters. The digital revolution re­ sponsible for the growth of geospatial data has spurred hydrologie model development 2 Baxter E. Vieux in the recent decade (Singh & Woolhiser, 2002). Availability of accurate precipitation measurement that is representative over a watershed can be a major limitation to accurate hydrologie forecasts. Concurrent development in raingauge networks, radar, and satellite technology for precipitation measurement has made distributed hydrologie modelling feasible. Hydrodynamic models employ a spatial discretization of the catchment and numerical integration of equations of momentum and mass conservation. Such models provide a basis for full use of distributed information relevant to the physical processes in the catchment. Ready access to worldwide geospatial data facilitates the development and initial parameterization of distributed models. The HYDRO-IK geospatial dataset provides digital elevation model (DEM) data and derivative products including streams and watersheds at 1-km resolution. Figure 1 shows a subset of DEM and stream channel data for the Asian Continent. The streams derived from the elevation data are superimposed over a hillshade relief map. Data such as this provides drainage network topology, slope, and subbasin arrangement for distributed modelling. Higher-resolution geospatial data can be used to refine distributed models, particularly in smaller subbasins. The HYDRO-IK data has been used to construct a forecast model for the Yantze River basin controlled by the Three Gorges Dam (Chen et al, 2003). One of the principal parameters derived from a DEM is flow direction for runoff routing through a network of grid cells or subbasins.

Hydrodynamic models

By better representation of the spatio-temporal characteristics governing the transformation of rainfall into runoff, distributed hydrologie modelling seeks to reduce

Fig. 1 HYDRO-IK geospatial data for Asia. Streams are derived from the elevation data, which is shown as a hillshade relief map. Data such as this provides drainage network topology, slope, and sub-basin arrangement for distributed modelling. Distributed hydrologie modelling for flood forecasting 3 prediction uncertainty. Approaches to flood forecasting range from simple empirical formulas to sophisticated models that utilize both conceptual and hydrodynamical mathematical relationships are described by Rodda & Rodda (1999). Distributed hydrologie modelling relies on geospatial data used to define topography, land-use/- cover, soils, and precipitation input. Distributed hydrologie modelling may be termed physics-based if it uses conservation of momentum, mass and energy to model the processes. Solution of flow analogies (e.g. kinematic, diffusive wave, or full dynamic) employs numerical methods with a discrete representation of the catchment as a finite difference grid or finite element mesh. Example models that can be classified as physics- or physically-based distributed models (PBD), include r.water.fea (Vieux & Gauer 1994; Vieux, 2001); a parallel version of r.water.fea called the distributed hydrologie model (DHM); Vflo™ distributed hydrologie model (Vieux & Vieux, 2002; Vieux et al, 2003); CASC2D (Julien & Saghafian, 1991; Ogden & Julien 1994); Système Hydrologique Européen (SHE) (Abbott etal, 1986a,b); the Distributed Hydrology Soil Vegetation Model (DHSVM) (Wigmosta etal, 1994); and the Large Scale Catchment Model (LASCAM) (Sivapalan et al, 2002). In the development of a distributed model of a watershed, issues related to para­ meter and input spatial resolution inevitably arise. Because a distributed model may rely on remotely sensed and geospatial data from various sources, each parameter may have a different resolution. The resolution that is necessary to capture the spatial varia­ bility is often not addressed in favour of using the finest resolution possible. However, from practical considerations, computer resources may be wasted if a coarser resolu­ tion would suffice, especially in real-time. The question of which resolution suffices for hydrologie purposes is answered in part by testing the quantity of information contained in a data set as a function of resolution (Vieux, 1993, 2001, 2004; Farajalla & Vieux, 1995). Slope derived from digital elevation data is resolution dependent, which can dramatically affect hydrologie modelling where landsurface slope is used in hydraulic equations of overland and channel flow. Grid based models that derive drainage direction and slope from digital elevation data show resolution-dependence as reported by Kojima & Takara (2003) for the 110-km2 Yada River basin in Japan. Similar to the resolution-dependent effects reported by Vieux (1993), they found that coarser resolution models, e.g. 250-m resolution, produce earlier and higher peaks than finer resolution (50-m) models. Precipitation input resolution can have significant effects on prediction accuracy of a distributed model. Shrestha et al. (2003) investigated the influence of forcing data resolution for various size basins. A distributed model was forced with different input resolution, and the sensitivity of predictions was tested for a range of basin sizes. The sensitivity of the model in relation to data resolution and basin size was found for the 132 350-km2 Huaihe, 29 844-km2 Wangjiaba, and 2093-km2 Suiping River basins in China. In their approach, a ratio between the input grid resolution and catchment size is formed, called the comparison index (CI). Marginal increases in performance were observed beyond a threshold, which indicates that input resolution has a more profound influence in smaller basins than in larger ones where some of the effects of input variability may be attenuated due to channel routing. The issue of subgrid parameterization of processes is beginning to be addressed in distributed modelling. Even though distributed models discretize the domain into 4 Baxter E. Vieux

subareas, the sub-grid parameterization becomes an important consideration. When models of large watersheds are constructed at coarse resolution, e.g. 100-km grid cells, runoff generation at this scale requires a stochastic distribution of parameters within the grid cell in order to achieve a reasonable representation of rainfall-runoff. Spatial averaging of rainfall intensities and soil properties in large grids tends to underestimate runoff. Probability density functions for distribution of rainfall and hydraulic conduc­ tivity helps overcome the lack of subgrid variability in coarse hydrologie model grids. Yu (2002) describes the subgrid parameterization in the Hydrologie Modelling System (HMS) applied to the 14 710-km2 Upper West Branch of the Susquehanna River basin in central Pennsylvania, USA. By including subgrid variability in hydraulic conduc­ tivity, streamflow predictions for this basin were improved. The large-scale catchment model (LASCAM) was developed for predicting the hydrologie impacts, both water quantity and quality, from human development, especially deforestation, in watersheds of Western Australia (Sivapalan et al, 2002). The model has a modular approach that relies on lumped subcatchment models, which may be refined where needed to improve predictions. LASCAM relies on an ordered collection of subcatchments that are selected based on computational considerations and availability of heterogeneous data related to soils, landuse, rainfall, and land management spatial extent and location. Such models represent the watershed with process-based submodels mixed with lumped conceptual type models. From a model perspective, a parameter should be representative of the surface or medium at the scale of the computational element used to solve the governing mathematical equations. This precept is often exaggerated as the modeller selects coarser grid cells, losing physical significance. In other words, runoff depth in a grid cell of 1 -km resolution can be taken as a generalization of the actual runoff process, and may or may not produce physically realistic model results. Depending on the areal extent of a river basin and the spatial variability inherent in each parameter, small variations may not be important while other variations may exercise a strong influence on model performance. Once the distributed model has been parameterized with initial parameter estimates at a chosen resolution, some adjustment is usually necessary to calibrate the model to agree more closely with observed quantities.

Distributed model calibration

Development of automated computer-based calibration methods has focused mainly on multi-criteria objective functions for CRR models (Boyle etal, 2001, 2003). Search algorithms for finding the optimal parameter set or sets are often plagued by local minima. Further, optimal parameter sets for one season or calibration period do not produce consistent results for other seasons or longer periods. Sorroshian & Dracup (1980), Duan etal. (1994, 2003) and Yapo etal. (1997) have sought various ap­ proaches to develop efficient multi-objective optimization procedures. The goal of the multi-objective complex evolution (MOCOM-UA) method is to automatically cali­ brate the model using streamflow records. Gupta etal. (2003) describe the multi- criteria optimization and uncertainty in the parameters, estimated by MOCOM-UA for the 1950-knr Leaf River Watershed near Collins, Mississippi, USA. Similar efforts to Distributed hydrologie modelling for flood forecasting 5 identify parameters for the CRR model called HYDROTEL are found in Turcotte et al. (2003) for the Chaudière River Basin located in Canada. Regardless of whether a model is distributed or lumped, multi-criteria optimization methods can be applied. Even so, distributed models may have more parameter values to adjust than lumped models. In either case special treatment may be demanded. Because hydrodynamic models are based on the physics governing the hydrologie processes, hydrologie forecasts extending beyond the range of calibration are made with more confidence than with CRR models (WMO, 1994). Calibration of a physics- based distributed hydrologie model can profit from a methodology that is specifically adapted to take advantage of the underlying conservation laws. The ordered physics- based parameter adjustment (OPPA) method described by Vieux & Moreda (2003) is adapted to the particular characteristics of physics-based models parameterized with geospatial data in raster format. Predictable parameter interaction and identifiable optimum values are hallmarks of the OPPA approach that can be used to produce physically realistic distributed parameter values. If the spatial pattern of a parameter is known, its magnitude may be adjusted while preserving the spatial variation. This calibration procedure can be performed manually by applying scalar multipliers or additive constants to parameter maps until the desired match between simulated and observed is obtained. Studies that have relied on the OPPA approach may be found in Vieux et al. (2004) for a model intercomparison experiment in the Blue and Illinois River basins; in Vieux & Bedient (2004) for an urban basin model for flood forecasting; in Vieux & Moreda (2003) for calibration of the Blue and Illinois River basin models; and Vieux et al. (2003) for operational deployment of a distributed flood forecasting system called Vflo™. Hydrologie models used to make real-time discharge forecasts benefit from adjust­ ments using measured streamflow. Adaptive calibration used to improve forecasting performance was reported by Brath & Rosso (1993). Adaptive schemes have been devised to take into consideration prior discharge information for online applications. Brath et al. (1999) found that adaptive adjustments using an ARIMA model resulted in improved forecasts on the Sieve River basin, located in central Italy. They found that the forecast efficiency increased when only a few observations were used to update the forecast model, but with decreasing improvements in accuracy as more past observa­ tions were included. Besides automated calibration done offline, real-time adjustment is often conduc­ ted by manual interaction with the model where lead times are sufficiently long enough to make effective use of upstream observations. This is the case with the US National Weather Service River Forecast System (NWSRFS). An operator makes adjustment to one or more of the 16 parameters of the SAC-SMA model to bring the forecast hydro- graph into agreement with observed streamflow (Smith et al., 2003). Estimation by the NWS of a priori parameters for the SAC-SMA model follows a scheme by Anderson (2002) where a watershed is selected for calibration that has the best data and fewest complicating factors. Then the calibrated factors are transferred to the hydrologically similar watersheds in the region. Initial values for some of the SAC-SMA parameters are derived from observed streamflow data (Anderson, 2002). Baseflow and the size of the upper zone tension water storage are identified in this way. A method for deriving eleven major parameters of the SAC-SMA model from soil texture information has 6 Baxter E. Vieux been proposed, and limited tests conducted for 18 watersheds in West Virginia, Ohio, Kentucky, Indiana, and North Carolina (Koren etal, 2003). To address the issues raised by various parameter-estimation methodologies, the MOPEX (Model Parameter Estimation Experiment) has been operating as a cooperative activity now involving many organizations internationally (MOPEX, 2004).

Distributed flood forecasting

Flood forecasting has long been dominated by lumped models that rely on unit hydrograph and conceptual model relationships. Flood forecasting is used to provide warnings to reduce property damage and loss of life before the hazard arrives at some downstream location. This necessarily means that hydrologie predictions are generated in real-time as the event evolves. Depending on the size of the watershed, terrain slope, and hydraulic characteristics, the travel time of runoff can vary from minutes to days. In the uplands, or in urbanized areas, the lead-time between measured or predicted rainfall and the peak discharge can be very short, leading to flash flood conditions. Whereas in downstream areas mainly affected by riverine flooding, the lead-time may be days. In downstream areas affected by larger rivers, the flood prediction depends mainly on routing of measured streamflow at upstream river locations. In the absence of upstream gauging stations, or where significant inflows are generated along major rivers, rainfall-runoff prediction can be as important as river routing. Because physics-based models use hydraulics to generate the hydrograph, channel hydraulics play an important role. Operational deployment of a physics-based distributed model configured for site-specific flood forecasts in an urban area is described by Vieux et al (2003), Vieux (2004), and Vieux & Bedient (2004). The distributed model intercomparison project (DMIP) compared simulations by a range of models. Results were submitted from participants for a number of watersheds including the 1200-km2 Blue River watershed. This basin is located in south central Oklahoma and drains into the Red River forming the border between Oklahoma and Texas. For more details on model calibration using the OPPA method, see Vieux (2001) and Vieux & Moreda (2003). The DMIP experiment is described in Smith et al. (2004) and Vieux et al. (2004), among other papers. Deployment of physics-based distributed models for operational flood forecasting is a relatively recent development (Bedient et al, 2003; Vieux et al, 2003; Vieux & Bedient, 2004). Operational flood forecasting in urban areas differ in terms of scale and purpose from those systems supporting national-level flood forecasting responsibilities of meteorological services such as the NWS. Urban areas often have specific locations that require customized flood forecasting systems where generalized warnings are not as meaningful. The 260-km2 Brays Bayou is a watershed located in Houston, Texas. Due to its urbanized character, flooding is produced when the basin receives either widespread intense rainfall or long duration rainfall of sufficient depth. Figure 2 shows the basin outline with rainfall totals superimposed for an event that occurred on 17 November 2003. Using radar input at 4 x 4 km resolution and a boundary condition upstream at Gessner Road (an interior point), the hydrograph produced by Nflo™ for this event is shown in Fig. 3. This example illustrates how a physics-based model configured at 120-m grid cell resolution can produce accurate Distributed hydrologie modelling for flood forecasting 7

• x File View

Wvg Depth = 4.31 in Main St.-Di'scharge

r, a e (cfs)

Fig. 3 produced by Vflo™ on 17 November 2003 using radar input at 4 x 4 km resolution and a boundary condition upstream at an interior point. The heavy dark line is simulated; the light grey line is observed discharge (35.4 cfs = 1 m3 s"1). 8 Baxter E. Vieux

forecasts, even with coarse resolution radar input (4x4 km). Further details on a customized flood warning system and operational features used in Houston, Texas, may be found in Bedient et al. (2003) and Vieux & Bedient (2004).

SUMMARY

Distributed hydrologie modelling is rapidly expanding to include many applications that have long been the domain of conceptual-lumped empirical models. Distributed flood forecasting in an urban drainage context is demonstrated, with several events reconstructed from archived radar rainfall. Real-time precipitation data opens the opportunity to apply distributed modelling in a flood forecasting context. Calibration of a physics-based distributed hydrologie model can profit from a methodology that is specifically adapted to take advantage of the underlying conservation laws. Because hydrodynamic models are based on the physics governing the hydrologie processes, hydrologie forecasts may be extended beyond the range of calibration with more con­ fidence than with lumped conceptual models. Initial parameterization of distributed models relies on geospatial data and remotely sensed data that characterize terrestrial characteristics of a watershed. Because a distributed hydrologie model relies on such geospatial data from various sources, each parameter often has a different resolution. Spatial resolution of the hydrologie model affects the accuracy and performance of the model. The advent of digital data has dramatically expanded the utility and feasibility of distributed hydrologie models as evidenced by the number and breadth of applica­ tions.

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