A method for probabilistic flash flood forecasting
Introduction
According to the U.S. Natural Hazard Statistics, flooding is the number one weather-related killer over a 30-year average (National Weather Service, 2014). In particular, flash flooding can be very dangerous due to its short timescales. Generally, flash floods are defined as flooding that occurs within six hours of a causative event (Hapuarachchi et al., 2011). They tend to occur in small headwater catchments, less than a few hundred square kilometers, due in part because these basins respond quickly to excessive rainfall amounts that fall in the short time periods characterized by flash flood-producing events (Kelsch, 2001). Unfortunately, these small basins can also be located in urban areas where the effects of flash flooding on society can be substantial.
In the simplest sense, as described by Doswell et al. (1996), “a flash flood event is the concatenation of a meteorological event with a particular hydrological situation.” Meteorologically, it is crucial to properly predict not only the occurrence of a rain event, but more importantly, the intensity and movement of the rainfall to accurately depict the conditions of a flash flood event. However, the meteorological component is only half of the problem. Hydrologically, it is necessary to understand the antecedent soil conditions, land and soil characteristics, topography, and basin size to know how the rainfall will impact the basin response (Davis, 2001).
Therefore, this study focused on both sides of the problem: inputting high-resolution quantitative precipitation forecasts (QPFs), that attempt to capture the dynamics of heavy rainfall (e.g. cell motion, development, intensity, duration) into a distributed hydrological model, that will take into account the necessary hydrological factors. It should be noted that the focus of this paper will be on the meteorological component and its application in a hydrological framework.
In regards to the meteorological component, several studies have examined the accuracy of high-resolution, convection-allowing numerical weather prediction (NWP) models. Simply considering resolution, Roberts (2005) showed that higher resolution NWP models (1- or 4-km) have more reliable forecasts of flood-producing rainfall (up to 7 h ahead) as compared to lower resolution (12- or 60-km) models. Schwartz et al. (2009) delved into the issue of convection-allowing versus convection-parameterizing models; the difference being that convection-allowing models can generate and resolve convection, while the parameterizing models represent convective processes that occur at sub-pixel resolution using a statistical approach. They found that higher resolution (2- and 4-km), convection-allowing models were more skillful at predicting amplitude and location of heavy rainfall as compared to the 12-km, convection-parameterizing model. Furthermore, Clark et al. (2009) compared a high-resolution, convection-allowing ensemble with a coarser, parameterized-convection model. They found the ensemble to produce more skillful precipitation forecasts, even with a small number of members, thus showing the promise of such ensembles.
Particular to the use of high-resolution QPFs comes the issue of displacement errors of finescale features (Ebert, 2008). These small errors can have significant effects on flash flood prediction since flash flooding is very location-dependent. The smallest offset of heavy rainfall can make the difference between an event and non-event because basins prone to flash flooding are commonly quite small (Vincendon et al., 2011). Probabilistic forecasting offers the potential to quantify this locational uncertainty, thus it is the focus of our study.
In regards to the hydrological component, the use of hydrological models for flood forecasting has been commonplace for many years (Singh, 1995). However, their use for flash flood forecasting is at a relative infancy (Reed et al., 2007). More and more operational hydrological models incorporate radar-derived estimates of rainfall as their main precipitation input. These estimates can have resolutions as high as 1-km with a 2-min update cycle, and once input into the model, provide a good depiction of the present state of the hydrologic cycle. However, the radar estimates are also subject to uncertainties (Zhang et al., 2015), but more importantly, only allow for hydrological modeling once the water is already hitting the ground. The time interval between heavy rainfall observations and flash flooding can be on the order of minutes, especially for small (sometimes, urban) basins. This short lead time makes it imperative to receive information prior to radar measurements of rainfall.
Increasing the lead time for these events is necessary in order to better protect life and property (Stensrud et al., 2009, Hapuarachchi et al., 2011, Vincendon et al., 2011). The best way to do this is by improving guidance to hydrological models via inputting quantitative precipitation forecasts, derived from numerical weather prediction models, into the models (Collier, 2007). Fritsch and Carbone (2004) discussed the need to focus on warm-season QPF improvement, with one of the main purposes being the application to hydrological forecasting. They argued that a major research area needs to be determining whether QPFs are valuable to hydrological prediction, especially since hydrological predictions “are among the principal societal payoffs resulting from warm-season QPF improvement…”. Our study assumes that QPFs on their own give an estimate of the relative location and intensity of future rainfall, however, giving them a hydrologic relevance is the only way they will be useful for flash flood forecasting.
In particular, the desire for ensembles of QPFs (no matter the resolution) as inputs for hydrological models is apparent in the field of flash flood forecasting (Cloke and Pappenberger, 2009). The methods thus far have been to: (1) input individual members of a QPF ensemble directly into a hydrological model to create an ensemble of hydrologic forecasts (Zappa et al., 2008, Verbunt et al., 2007), (2) perturb one deterministic QPF to create an ensemble for input into the hydrological model (Vincendon et al., 2011), or (3) perturb ensemble members and hydrologic model parameters. Our study is unique in that it creates a high-resolution deterministic representative of all ensemble members (via probability matching) for input into the hydrological model. This method cuts back the computational expense (compared to running multiple simulations), while still accounting for the optimal location defined by the ensemble mean, and the rainfall intensity represented by the entire QPF ensemble.
With such ensemble hydrologic outputs, probabilistic flash flood forecasting has been discussed in the above studies, and others (Krzysztofowicz, 2001, Drobinski et al., 2014). This study’s method is novel in that it creates a final probabilistic product not from considering the fraction of hydrologic output members that exceeds a certain discharge threshold, but rather from the multiplication of meteorological and hydrological probabilistic products. In brief, the ultimate goal of this study is to derive basin-specific probabilistic flash flood forecasts (PFFFs) using an ensemble of forecast members (QPFs), combined with simulated basin responses (derived from a distributed hydrological model), in order to identify basin scales and lead times for flash flood prediction. It is noted that the proposed method deals with locational uncertainties in QPFs alone. Future methods should also consider additional errors in timing, storm structure, and amplitude. The rest of this paper is outlined as follows: Section 2 describes the two precipitation datasets and the distributed hydrological model used in this study; Section 3 explains the error quantification procedure that was done to find the biases related to the QPFs; Section 4 details the methodology conducted to create the PFFFs, and is followed by Section 5 discussing the results from the case study; and finally, Section 6 summarizes the conclusions from the study.
Section snippets
Forecast rainfall
This study relies on the use of a NWP model that is capable of producing stormscale QPFs. These QPFs serve as the input precipitation field for the hydrological model. As part of the National Oceanic and Atmospheric Administration (NOAA) Hazardous Weather Testbed (HWT) Spring Experiment, the Center for Analysis and Prediction of Storms (CAPS) at the University of Oklahoma (OU) has developed a multi-model storm-scale ensemble forecast (SSEF) in real-time (Kong et al., 2011). Since the 2007
QPF error quantification
Before using the CAPS SSEF of QPFs within the hydrological framework, it is important to understand the error characteristics of the individual members in order to allow for better interpretation of the final results. Because location error is important for flash flood forecasting, using evaluation metrics that incorporate location errors is vital (Gilleland et al., 2009).
Additionally, with the use of high-resolution QPFs, the evaluation metrics must overcome the issue of displacement errors of
PFFF methodology
Now that we have some understanding of the errors associated with the ensemble of QPFs, they can be utilized within a hydrologic framework. As stated previously, location is the primary component for accurately forecasting flash flooding. The hydrologic characteristics (e.g. basin size, slope, soil type and saturation) and meteorological factors (e.g. rainfall intensity and duration) dictate the potential for flash flooding, but actually predicting the location of the rainfall dictates the
Results
Fig. 10 shows the PFFF for exceeding a five-year return period at 1400 and 1700 UTC during the June 14, 2010 Oklahoma City flash flood event. To properly interpret these maps, the reader should focus on the stream and river pixels. When the POE field is multiplied by the PQPF field, the overland grid cells take on the PQPF values entirely, due to being multiplied by approximately one. Hence, when looking at these overland areas, the high probabilities that existed in the PQPF map are clearly
Conclusions
This study offers a method for creating probabilistic flash flood forecasts (PFFFs) using an ensemble of high-resolution quantitative precipitation forecasts (QPFs). Firstly, the errors of the individual CAPS members were quantified in order to understand the biases associated with the ensemble before applying them to a hydrological framework. The SAL technique (Wernli et al., 2008) was chosen for this analysis because it builds on traditional metrics by providing information about the
Acknowledgments
The authors acknowledge the financial support of the National Science Foundation (NSF) Graduate Research Fellowship under Grant No. DGE-1102691. Partial funding was also provided by NOAA/Office of Oceanic and Atmospheric Research under the NOAA-University of Oklahoma Cooperative Agreement #NA11OAR4320072, U.S. Department of Commerce. Thank you to the University of Oklahoma (OU) and NOAA/National Severe Storms Laboratory (NOAA/NSSL) for providing the facilities, technical, and data support
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