A distributed hydrologic model and threshold frequency-based method for flash flood forecasting at ungauged locations

Summary

A method to use a distributed hydrologic model in conjunction with threshold frequencies (DHM-TF) is proposed to improve the accuracy of flash flood forecasts at ungauged locations. The model produces high-resolution grids of peak flow forecast frequencies during rainfall events. Forecasters can compare these grids to locally derived threshold frequency (TF) grids to aid in warning decisions. TF grids may be derived from several sources of information such as known flood frequencies at selected river locations and local hydraulic engineering design standards. The proposed model characterizes flood severity at ungauged locations, and provides an inherent bias correction to reduce systematic errors in model predicted peaks. The distributed model basis for the approach offers advantages over current lumped model-based national weather service (NWS) flash flood guidance (FFG) procedures because it makes hydrologic calculations at spatial and temporal scales that are more commensurate with flash flooding. In this study, simulation results for 10 basins (eight nested) in Oklahoma and Arkansas, USA, were analyzed to (1) improve our understanding of distributed hydrologic model accuracy in small, interior basins, when forced by operational quality radar-based precipitation data, (2) validate that a distributed model can improve upon the lumped model-based NWS FFG, and (3) validate that the DHM-TF method can provide an inherent bias correction using available operational data archives to develop statistical parameters. We analyzed eight years of continuous hourly stream flow simulations and peak flows from 247 individual events. Both uncalibrated and calibrated distributed model results improved upon lumped model-based FFG at interior points. The DHM-TF method provided an average inherent bias correction for both uncalibrated and calibrated models in most basins examined. These positive results suggest that further development and testing of this technique should proceed.

Introduction

The National Oceanic and Atmospheric Administration National Weather Service Office of Hydrologic Development (NOAA/NWS/OHD) is investigating the use of distributed hydrologic models to improve the timeliness, resolution, and accuracy of hydrologic forecasts (Smith et al., 2004). Research and prototype operational applications are being used to evaluate the benefits of distributed hydrologic models with several applications in mind, including flash flood, river flood, and water resource forecasts. The focus here is on flash flood forecasting at ungauged locations.

Distributed hydrologic models provide a framework for forecasting flashy events that occur at higher spatial and temporal resolutions than the current, lumped, river forecast models used by NWS River Forecast Centers (RFCs). Given the accumulation of many years of radar-based, gridded rainfall products and the concurrent maturation of distributed modeling techniques, rigorous evaluation of distributed models for operational flash flood forecasting applications is now feasible.

Numerous researchers have investigated the use of distributed models for hydrologic forecasting applications. Smith et al. (2004) provide an extensive review of distributed hydrologic modeling research. Results of the Distributed Modeling Intercomparison Project (DMIP) (Smith et al., 2004, Reed et al., 2004) demonstrated that when driven by operational quality, radar-based precipitation estimates some distributed models are capable of producing reasonable simulations at interior points within a lumped parent basin. However, only one basin in DMIP was small enough to be a true flash flood basin according to the NWS definition. The NWS defines a flash flood as a flood that occurs within 6 h of the causative event (NWS Manual 10-950, 2002, http://www.nws.noaa.gov/directives/010/pd01009050a.pdf). This paper focuses on flash floods caused by heavy or excessive rainfall. Phenomena such as ice jams, dam failures, or levee failures may also cause flash floods. Davis (1998) suggests that rainfall induced flash floods occur in basins smaller than about 260 km².

Refsgaard and Knudsen (1996) also conducted an intercomparison study of a three models with various levels of structural complexity applied to three basins in Zimbabwe, Africa. They found that distributed and lumped models performed similarly with calibration, and the distributed models performed marginally better at basin outlets in cases without calibration. However, the basins modeled were larger than typical flash flood basins. Bell and Moore (1998) report tests of lumped and distributed-parameter models in three relatively small watersheds (142, 275, and 100 km²) in the United Kingdom. Using calibrated models, they did not find consistent gains from a distributed-parameter model in simulating basin outlet flows. More recently, Moore et al. (2006) describe a conceptual-physical area-wide model for ungauged basins with similarities to the model used here.

One concern in using high-resolution distributed models to forecast flash floods is whether the increasing model uncertainties at small scales will mask the expected benefits of high-resolution modeling. Using a Monte Carlo based approach, Carpenter and Georgakakos (2004) simulated increasing model uncertainty with decreasing basin sizes but did not have enough data to validate their results using observed streamflow data from interior points.

Due to data availability, some of the most detailed small basin modeling studies have been on experimental agricultural watersheds. Loague and Freeze (1985) compared three models of differing complexity on very small experimental basins (0.1 km², 7.2 km², and 0.13 km²) and reported poor results for all models. Using 24 validation events, Michaud and Sorooshian (1994) demonstrated value in using a distributed model compared to a lumped model for outlet simulations in the Walnut Gulch (150 km²) experimental watershed. Simulations at interior points showed relatively high peak prediction errors compared to outlet simulations. Senarath et al. (2000) analyzed distributed model simulations at the outlet of the 21.2 km² Goodwin Creek experimental watershed and at several interior points. Their analysis of results at interior points did not show a consistent trend of degraded results with decreasing basin size; however, the relative absolute peak errors reported for the smallest interior gauge (1.5 km²) were the largest. The Senarath et al. (2000) study is unique because data from a high-density rain gauge network (1.4 gauges/km²) were available.

A few recent studies have focused on the use of radar data for urban flash flood modeling. Smith et al. (2005) report on a detailed study of the hydrometeorology, hydrology, and hydraulics of flooding in a 9.1 km² basin in Baltimore, Maryland. Bedient et al. (2003) report on real time warning successes using radar forcings and a flash flood model in Houston, Texas. Vieux and Bedient (2004) report success using a distributed hydrologic model to reconstruct events (four calibration and one validation) for the same Houston area. Johnson, 2000, Yates et al., 2000 both retrospectively study the Buffalo Creek flash flood that occurred near Denver, Colorado in 1996.

In this study, we extend the current body of knowledge on the applicability and accuracy of high-resolution, distributed hydrologic models for flash flood applications by analyzing a relatively large number of events in several small basins. We rely solely on operationally available data inputs. As a practical matter, we emphasize comparisons between the proposed distributed model-based approach and NWS operational Flash Flood Guidance (FFG) procedures (Sweeney, 1992). In the previous studies mentioned above, only Johnson (2000) compared alternative approaches to the operational FFG-based approach and in this case for only one event. We also emphasize model evaluation at uncalibrated, gauged interior points to derive results that are indicative of expected performance at ungauged locations.

Aside from the difficulty of accurately modeling flow, another challenge in flash flood forecasting for ungauged locations is how to characterize the severity of forecasted flows. In other words, what flow level creates damaging or hazardous conditions? NWS FFG procedures use regionally derived empirical relationships to derive flood threshold flows at ungauged locations. Conceptually, these threshold flows are flows that exceed bankfull just enough to cause damage. In practice, it is difficult to develop consistent and accurate threshold flow estimates that satisfy this definition due to a lack of field measurements, geomorphologic heterogeneity, and the human risk factor component of the definition.

We propose using a distributed hydrologic model and threshold frequency-based (DHM-TF) method as an alternative to current FFG procedures for modeling ungauged locations. The proposed approach would produce high-resolution gridded forecasts of peak flow frequency in each model cell. The distributed model basis for the proposed approach addresses scale issues present in the current NWS FFG procedures (described in detail below). Expressing gridded results in terms of flood frequency provides historical context for assessing the severity of an event.

The statistical component of the approach can be implemented using a simple post-processor that converts gridded flow forecasts into gridded frequency forecasts. The method uses statistical characteristics derived from historical simulations to convert flow to frequency in each cell. The historical simulations are generated using the same model parameters and sources of forcing data used for the real-time forecasting. We suggest that a procedure in which peak flows are converted to frequencies using historical simulations from the same model and then compared to locally-specified, frequency-based warning thresholds can inherently correct for simulation model biases. We test this hypothesis in this paper.

We designed the simulation experiments described in this paper to understand the potential benefits and limitations of the proposed modeling approach and to guide further development. More specifically, modeling experiments address the four questions below.

• Is there a corresponding decrease in the simulation accuracy of distributed hydrologic models with decreases in basin size? If so, is there a scale at which the model is no longer useful?

• Compared to a completely uncalibrated model, what gains are expected in flood peak prediction at small interior gauges if a modest calibration effort is applied at the parent basin outlet? In our experiments, interior gauges are not used for calibration so results at these points are assumed to represent model prediction capability at ungauged locations.

• Can the proposed method improve prediction capability at ungauged locations compared with the NWS FFG approach? At what spatial scales can these gains be realized?

• Will the proposed frequency-based approach provide an inherent bias correction for the study basins when using the available multisensor precipitation archives? Are the data length, quality, and consistency adequate to provide this correction?