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# Real-Time Flash Flood Forecasting

## Summary and Keywords

Flash floods are one of the world’s deadliest and costliest weather-related natural hazards. In the United States alone, they account for an average of approximately 80 fatalities per year. Damages to crops and infrastructure are particularly costly. In 2015 alone, flash floods accounted for over \$2 billion of losses; this was nearly half the total cost of damage caused by all weather hazards. Flash floods can be either pluvial or fluvial, but their occurrence is primarily driven by intense rainfall. Predicting the specific locations and times of flash floods requires a multidisciplinary approach because the severity of the impact depends on meteorological factors, surface hydrologic preconditions and controls, spatial patterns of sensitive infrastructure, and the dynamics describing how society is using or occupying the infrastructure.

Real-time flash flood forecasting systems rely on the observations and/or forecasts of rainfall, preexisting soil moisture and river-stage states, and geomorphological characteristics of the land surface and subsurface. The design of the forecast systems varies across the world in terms of their forcing, methodology, forecast horizon, and temporal and spatial scales. Their diversity can be attributed at least partially to the availability of observing systems and numerical weather prediction models that provide information at relevant scales regarding the location, timing, and severity of impending flash floods. In the United States, the National Weather Service (NWS) has relied upon the flash flood guidance (FFG) approach for decades. This is an inverse method in which a hydrologic model is run under differing rainfall scenarios until flooding conditions are reached. Forecasters then monitor observations and forecasts of rainfall and issue warnings to the public and local emergency management communities when the rainfall amounts approach or exceed FFG thresholds. This technique has been expanded to other countries throughout the world. Another approach, used in Europe, relies on model forecasts of heavy rainfall, where anomalous conditions are identified through comparison of the forecast cumulative rainfall (in space and time) with a 20-year archive of prior forecasts. Finally, explicit forecasts of flash flooding are generated in real time across the United States based on estimates of rainfall from a national network of weather radar systems.

# Introduction

Compared to other weather-related natural hazards, flash floods pose the most difficult challenges in terms of their monitoring and forecasting. The rapidity of both their onset and subsequent recession make them difficult to even observe. The key to forecasting flash floods begins with rainfall. The challenge with extreme rainfall is that people experience rainfall on a relatively frequent basis; in fact, society depends on it. Water is used for drinking, agriculture, transportation, recreation in rivers, oceans, and lakes, and other vital functions; rainfall is as familiar to humans as the air for breathing. While this may appear to be a casual observation, it presents a clear distinction from other weather hazards like tornadoes, hail, high wind, ice storms, and hurricanes. Humans recognize these latter events as being rare and unusual, potentially impactful on their daily routines, and are thus more inclined to respond and take precautionary measures (Terti, Ruin, Anquetin, & Gourley, 2015). It becomes a tremendous challenge for a weather forecaster (a) to identify the synoptic or mesoscale environments that may lead to anomalous rainfall; (b) to identify flash flood–producing storms from individual radar images; (c) to forecast the specific locations, times, magnitudes, and impacts of flash floods accurately given the observation of heavy rainfall; and (d) to communicate this information to the public in a way that will lead to precautionary measures.

It is useful, once again, to make comparisons to other weather-related hazards. The environment or “ingredients” associated with tornadoes, hail storms, high winds, and heavy rainfall are well known (Doswell, Brooks, & Maddox, 1996). Maddox, Chappell, and Hoxit (1979) identified the environmental characteristics associated with heavy convective rainfall and flash flooding. They found four different types of flash floods, with each having the following characteristics in common: high surface dew points, deep moisture throughout the troposphere, weak-to-moderate wind shear, and either a shortwave trough or a mesoscale boundary to initiate, concentrate, and sustain upward motion. Most events in their study data set occurred during the warm season months, and they noted that many of the flash floods were nocturnal. The ingredients favorable for deep, moist convection and heavy rainfall become more difficult to identify as the scale of the event decreases in size and the forecast horizon increases. Thus, forecasters can generally more easily recognize the synoptic and mesoscale environments favorable to severe weather events; localizing this information to the storm scale is much more challenging.

The advent of the weather surveillance radar network has yielded many observational clues related to the potential presence of tornadoes, damaging hail, and high winds. Tornadoes are associated with parent circulations in supercell thunderstorms that are detectable using Doppler velocity products. Tornadic debris signatures also can be identified using the correlation coefficient product available from dual-polarization radars. Dual-polarization radar fields and Doppler velocities are also useful in the identification of damaging winds and large hailstones. All these signatures are identifiable using radar products—which the forecaster is properly trained to recognize—available at a single moment in time. On the other hand, anomalously high rainfall intensities observed from weather radar at a particular instance in time are a necessary but insufficient condition for the development of flash flood impacts. Successful forecasters must consider these rates and their cumulative impact when integrated in time and space. C. F. Chappell, in Doswell et al. (1996), stated this point succinctly as follows: “the heaviest precipitation occurs where the rainfall rate is the highest for the longest time” (p. 561).

Given that the forecaster has diagnosed anomalous rainfall intensities properly over a specific duration, the challenge turns to the forecast of concomitant flash flooding. The mere presence of a tornado, hail, or high winds is enough to warrant an alert to the public and infrastructure in the path of the storm. In contrast, heavy rainfall alone is insufficient to trigger a flash flood. Flash floods represent a multidisciplinary hazard that is forced by the natural hazard of anomalous rainfall with spatial patterns and intensities that are modified by hydrologic initial conditions and surface controls. This results in complex and nonlinear spatial patterns and causes the timing of flash flood impacts to be offset by the causative atmospheric forcing. Flash flood impacts have controls that are very localized (e.g., clogged storm drains) and results in a highly discontinuous pattern of damages and other impacts. Moreover, there is often a lag, such that the flash flood impacts follow the heavy rainfall; this lag depends on several factors, including basin scale, slope, antecedent conditions, and degree of urbanization.

Finally, there are challenges in communicating the flash flooding hazard. The National Weather Service (NWS) in the United States operates 122 local forecast offices distributed across the country. Forecasters in these offices are responsible for issuing warnings of weather-related hazards, including flash floods. In the case of a tornado, the forecaster issues its warnings based on the environmental conditions, particularly on the radar-based signatures that it is monitoring in real time. These warnings then are disseminated to the public through media (i.e., television, radio, Twitter), through Wireless Emergency Alerts directly to subscribers’ cell phones, and to local emergency managers who may choose to sound tornado sirens in their local communities. In general, the public responds promptly to these warnings by moving to an interior room in their residence, taking shelter in a fortified safe room, or going below ground. The public response to flash flood warnings is considerably reduced compared to tornado warnings, despite their similarities in fatality rates in the United States. There are many reasons for this, involving societal behavior that go beyond the scope of the present discussion. However, a starting point for actionable warnings is real-time flash flood forecasting systems. If these systems can be reliable, timely, and specific regarding anticipated impacts from flash floods, rather than merely monitoring the occurrence of heavy rainfall, then there is great potential to better inform the public and local authorities to ultimately save lives and minimize damage to property and infrastructure.

# History of FFG

Some form of flash flood guidance (FFG) has served as the primary tool for flash flood monitoring and prediction in the US NWS and the weather services of several other countries. FFG was originally developed and introduced by Georgakakos (1986), and it is defined as the amount of rainfall required over a specific time (typically 1, 3, 6, 12, or 24 hours) and area to produce bank full conditions on small streams. A shared characteristic of all versions of FFG is the computation of rainfall thresholds at different accumulation periods that are designed to be associated with bank full conditions indicative of fluvial flooding in small streams.

The method operates by running a hydrologic model with initial states of soil moisture and river stages. Rainfall scenarios are introduced to the model until bank full thresholds have been reached. Then these rainfall accumulations at multiple durations are recorded and transmitted to forecasters. One can interpret the computation of FFG values as doing inverse hydrology. Instead of taking observed or forecast precipitation and forcing the model in real time to forecast flash floods, the method uses rainfall scenarios conditioned on the soil and river states to arrive at rainfall rate thresholds.

The major benefits of this approach are computational efficiency and forecaster ease of interpretability. The FFG system was designed in an era when running a distributed hydrologic model at continental scale in real time based on rainfall estimates from radar or forecasts by a numerical weather prediction model was infeasible. The inverse method relies on running a model, but not in a real-time forecast setting. Also, each of the 122 NWS local forecast offices, or Weather Forecast Offices (WFOs), across the United States employs meteorologists. Some, but not all, also have personnel with hydrologic backgrounds on staff. FFG is a rainfall threshold that was designed to account inherently for complex nonlinear hydrologic processes. In theory, meteorologists would only need to concern themselves with the short-term forecast and monitoring of rainfall rates that exceed FFG; the rest of the complicated hydrologic factors were designed to be included in the derivation of FFG.

The FFG method has evolved over time in response to increases in computational power, improvements in precipitation forcings from remote-sensing systems and numerical weather prediction models, increased resolution in geospatial data sets describing Earth’s geomorphology, and remote sensing of the land surface state, including vegetation characteristics, soil moisture, streamflow, and areal extent of flood inundation. The hydrologic model structures, however, are largely conceptually based and have not changed as rapidly as the model precipitation forcings or observations of the land surface states and parameters.

## The Early Days

Mogil, Monro, and Groper (1978) discussed the state of flash flood watches, warnings, and forecasts just a few years after the NWS began to focus closely on flash flood events. From the 1940s to the 1970s, the average annual number of deaths due to flash flooding tripled, while the monetary damages due to flash flooding increased more than sixfold (Mogil et al., 1978). The increase in flooding events over that period was experienced across the entire United States, but the authors placed much of the blame for increasing fatalities, injuries, and monetary damages on rising population density in areas prone to flash flooding. The NWS flash flood warning program was not deployed nationally until 1971, but as the authors note, severe thunderstorms and tornadoes had national warning programs for years or decades before that. In the first decade after the advent of the NWS flash flood warning program, the National Meteorological Center’s Quantitative Precipitation Branch issued national precipitation forecasts. In the late 1970s, those precipitation forecasts were produced only on the synoptic scale and did not include localized convective rainfall. Maddox (1980) stated that mesoscale convective complexes (MCCs) are largely responsible for flash flooding events in the United States east of the Rocky Mountains. Based on the descriptions of Maddox (1980) and Mogil et al. (1978), therefore, it seems likely that the precipitation forecasts of the late 1970s were of limited utility in forecasting flash floods, since they mostly excluded the convective precipitation that drives flash flood events.

At the time that Mogil, Monro, and Groper were writing, NWS River Forecast Centers (RFCs) already produced an early FFG product—original FFG—based on drainage basin configuration and past rainfall. RFCs also helped the local NWS offices to produce localized forecast and warning procedures based on the needs of individual communities. However, in all FFG products, accurate estimates of rainfall are required to determine when or if issuance of a flash flood warning is necessary. Weather surveillance radar (WSR-57s and WSR-74s) had been deployed at some NWS offices and could be used to estimate precipitation amounts.

One method described by Mogil et al. (1978) is manually digitized radar (MDR), in which a relationship between radar reflectivity factor and rainfall rate (also called a Z-R relationship) is used to determine a storm’s total rainfall. However, the authors note that this method sometimes did not identify flash flooding until after the event had begun. A newer method at that time was Radar Digitizer and Processor (RADAP), which also used a Z-R relationship to determine convective rainfall amounts. Although deployed at only five radar sites by 1978, it was already believed to be of great utility, at least for some parts of the country. Other methods of reducing fatalities due to flash floods were discussed, including locally run flash flood alarm systems. However, the authors noted that the critical element in local programs was still the FFG product being generated at the RFCs.

Sweeney (1992) elucidated some problems with the original FFG (OFFG) system. Vast inconsistencies in the spatial resolution of OFFG led to abrupt changes in FFG values on the boundaries between RFCs. In some cases, these RFC boundaries divide WFO county warning areas; thus, WFOs or even individual counties could be covered by very different FFG values and very different methods of FFG generation. In addition, each RFC handled the effects of frozen precipitation and topography differently. Some of the components that underlie FFG also were generated at different spatial scales. Sweeney (1992) related that threshold runoff (ThreshR), one of these components, was computed at dozens of different streams in one RFC, but at only four locations in another RFC. In still other RFCs, the method used to generate ThreshR values had never been clearly defined.

During the 1970s and 1980s, the NWS developed the NWS River Forecast System (NWSRFS) (RFC Development Management Team, 2003). This system was initially used only to produce forecasts for larger-scale fluvial floods, but it provided national consistency between the RFCs for those products. By the 1980s, the use of NWSRFS to produce FFG was being explored as well, due to the local and regional differences between the FFG being produced at each RFC. This work eventually resulted in the modern FFG system that is described in Sweeney (1992).

## Modern FFG System

Sweeney and Baumgardner (1999) described the procedure behind modernized FFG or lumped FFG (LFFG). This version of FFG was still being produced at multiple RFCs as late as 2012. There were two main impetuses behind the development of LFFG: the deployment of the Advanced Weather Interactive Processing System (AWIPS) and the more accurate and higher-resolution precipitation estimates available from the new WSR-88D network. An additional benefit was the increased consistency in FFG generation method at each RFC (Sweeney, 1992). This modernization project also put FFG generation into the same framework as the RFC river-stage forecast system that had been developed during the 1980s. For the first time, national standards were available to guide RFCs in the process of generating FFG products.

LFFG results in only a single FFG value for each large (300–5,000 km2) lumped basin, so improvements in the spatial resolution of FFG were often insignificant. However, LFFG values could be plotted on the Hydrologic Research Analysis Project (HRAP) grid, which has grid cells roughly 4 km on a side (Sweeney, 1992). Therefore, plots of precipitation-to-LFFG ratio could exhibit variability from grid cell to grid cell due to the relatively higher resolution of the radar precipitation estimates. Although some WFOs use AWIPS to monitor individual HRAP grid cells for FFG exceedances, other WFOs average FFG values over a county or other area (RFC Development Management Team, 2003). The rainfall used with lumped FFG is derived from WSR-88D precipitation estimates. Then specific grid cells (or counties) where the radar precipitation estimate exceeds the LFFG value can be monitored for additional action on the part of the local forecaster, if necessary.

Although Sweeney and Baumgardner (1999) described some improvement in spatial resolution over the previous versions of FFG in some areas, even the smallest LFFG basins are still much larger than the resolution of the radar-derived precipitation estimates. Furthermore, despite their large size, the lumped basins used in this process are usually not equipped with stream gauges, although the gauged headwaters of some larger basins are sometimes coterminous with the lumped model basins. Because precipitation estimates were available at fine spatial and temporal scales but LFFG was available only at scales much larger than that at which flash flooding occurs, problems with the LFFG system spurred more changes only a decade later.

In 2003, the RFC Development Management Team issued a report regarding the state of FFG at that time, as well as several recommendations regarding the future direction of the program. The most significant advance described in the report is the delineation of small, truly flash flood–scale basins. In the 1980s and the 1990s, Areal Mean Basin Estimated Rainfall (AMBER) was a project at the NWS’s Pittsburgh WFO. The AMBER project was designed to identify small flashy (or flash flood–prone) basins in the Pittsburgh office’s area of responsibility. Eventually, this same methodology was used across the conterminous United States (CONUS) in the National Basin Delineation Project (NBDP), which used geographic information system (GIS) technology to produce flash flood–scale basin data sets for each NWS WFO (Arthur, Cox, Kuhnert, Slayter, & Howard, 2005). These basins then are used as part of the Flash Flood Monitoring and Prediction (FFMP) system, which is part of the larger AWIPS software package.

The spatial scale of these small flash flood basins is much more like the scale of precipitation estimates from the WSR-88Ds. The average basin area traced by the NBDP is around 10 km2 (RFC Development Management Team, 2003) and the minimum size is 5 km2 (Davis, 2007). Despite the improvement in basin resolution, this still results in a mismatch of spatial scale between the FFMP basins and Next-Generation Radar (NEXRAD) precipitation estimates on the one hand and the lumped FFG basins used at the RFCs (300–5,000 km2) on the other. The RFC Development Management Team (2003) noted this limitation, but due to computational requirements and scientific limitations, this issue was still partially unresolved as of 2012.

## Modifications to FFG

The RFC Development Management Team (2003) focused on suggesting small changes to the FFG system rather than major modifications or a complete overhaul. Although many of the individual problems cited in its report are minor, the issues when considered in the aggregate may contribute to a decrease in the utility of FFG. Within some RFC areas, some HRAP grid cells always have missing data; this problem is also noted on the boundaries between RFCs. The authors also noted the opposite problem, where grid cells along RFC boundaries have overlapping (and different) values of FFG. Of course, when these overlapping values are different, there will be sharp gradients in FFG along an RFC boundary, with no corresponding physical reasoning. Although many of these simple concerns could be resolved with new national guidance to the RFCs on standards for producing FFG products, these issues originally described in 2003 remain present over a decade later. In general, these problems are due to software and hardware limitations, hydrologic model parameter differences between RFCs, or differences between RFCs in the type of hydrologic model used to generate FFG.

In 2003, the RFC Development Management Team also recognized the lack of a verification program for FFG. One cited reason for this was a lack of observational data, particularly information about the precise times and locations of flash flood impacts. Another was due to an inability to know what type of quantitative precipitation estimate (QPE) algorithm was in use at each RFC for each FFG generation point. FFG is also sometimes misapplied in urban areas where natural drainage networks have been heavily altered by anthropogenic influence. Due to the definitions used in the development of FFG products, FFG is not directly applicable to urban areas without substantial modification.

Some RFCs made significant changes to the FFG product during and immediately after the RFC Development Management Team recommendations were released. The Colorado Basin River Forecast Center (CBRFC) covers the states of Arizona and Utah, as well as parts of New Mexico, Colorado, Wyoming, Idaho, Nevada, and California. In the CBRFC’s area, flash flooding is not necessarily always associated with bank full conditions on small streams; for example, in many recreational areas, the threat to human lives begins at flow rates well below those associated with bank full conditions (Smith, 2003). In addition, in the western United States, there is evidence that soil moisture is a less important component of determining when and where a flash flood might occur than it is in the eastern United States (RFC Development Management Team, 2003).

In 2003 and 2004, CBRFC undertook a project to develop a new style of FFG for the WFOs within its area of responsibility (Smith, 2003). The resulting product was the Flash Flood Potential Index (FFPI), which uses physiographic information to determine if flash flooding is likely in each FFMP basin. Some of the factors contributing to this tool, as listed in Smith (2003), are soil characteristics, vegetation cover (including forest density), slope, land use and urbanization, and seasonal effects like wildfire. Although many of the factors making up the FFPI for a basin may be static over many years, land use changes, wildfire locations (or burn scars), and other factors act to modify hydrologic responses over seasonal or annual timescales.

Each data set used in the method from Smith (2003) is plotted on grids of consistent resolution, and most of these are weighted equally relative to one another, although topographical slope is treated as more important than the other variables in the resultant FFPI. The FFPI output then is averaged onto the flash flood basins used in the FFMP system. Smith (2003) indicated that during early testing of the product, the Salt Lake City WFO was pleased with the additional information that the FFPI product provided to the forecasters during the flash flood monitoring and warning process. These forecasters still utilized FFMP to determine the amounts of radar-indicated precipitation that had fallen in various flash flood basins. Then the FFPI product allowed forecasters to determine whether basins experiencing that rainfall had high or low susceptibility to flash flooding events. The FFPI method developed at CBRFC was eventually deployed in 2008 at the California Nevada RFC (CNRFC), which also covers small portions of southern Oregon and Idaho, and it continues to serve as the primary FFG method for WFOs in the western United States.

East of the Rocky Mountains, soil moisture (used in OFFG and LFFG) is an important factor in determining the likelihood of a flash flood. Between 2005 and 2006, the Arkansas Red-Basin River Forecast Center (ABRFC), which covers the entire state of Oklahoma and portions of all adjoining states, developed and deployed a new method of producing FFG known as gridded FFG (GFFG) (Schmidt, Anderson, & Paul, 2007). GFFG is a misnomer, though; the modern FFG referred to in Sweeney and Baumgardner (1999) is also produced on a grid. However, ABRFC’s GFFG product does vary spatially from grid cell to grid cell, whereas the modern FFG product has a constant value for each FFG basin.

The method of Schmidt et al. (2007) imitates LFFG but allows an increase in the spatial resolution of the product. Because GFFG allows adjacent grid cells in the same basin to have different values, the effective spatial resolution of GFFG is the same as the resolution of the HRAP grid (4 km on a side). This resolution (each grid cell having an area of 16 km2) is much closer to the resolution of the FFMP basins, unlike the basins used in LFFG. This mitigates but does not eliminate the issue of scale mismatch between LFFG basins and FFMP basins noted earlier in this article. Gourley, Erlingis, Hong, and Wells (2012) found that the distribution of GFFG values over the ABRFC domain from 2006 to 2008 was roughly comparable with the distribution of LFFG values over the same area and period. Schmidt et al. (2007) also noted that in a visual comparison of ABRFC GFFG with the products issued by neighboring offices, although the spatially variable characteristics of the ABRFC product result in a different appearance, the actual values match up well with the LFFG product being produced by adjacent RFCs. In 2007 and 2008, the GFFG method was extended to other RFCs, including the Lower Mississippi RFC (LMRFC), the Southeast RFC (SERFC), and the West Gulf RFC (WGRFC). By the end of 2008, GFFG was in use across the entire southeastern and south-central United States.

A fourth type of FFG is generated at the Middle Atlantic River Forecast Center (MARFC) into the early 21st century. It uses the continuous–Antecedent Precipitation Index (API) model on the HRAP grid for the soil moisture component of FFG. This is supplemented with radar-derived QPE. The net result is an FFG product (called DFFG hereafter in this article) with similar spatial variability to the GFFG method derived at ABRFC.

The history of the NWS flash flood warning program involved only minor alterations for its first 20 years of existence. With the advent of the modernized FFG program at the beginning of the 1990s, RFC methodologies were mostly standardized across the United States. However, several problems of varying severity continued to be noted by forecasters and others throughout the next 10 years. Beginning in the late 20th century, hydrologists at some RFCs developed completely new FFG products. This patchwork of different methods of FFG generation (LFFG, FFPI, GFFG, and DFFG) represented the state of flash flood operations in the NWS in the early 2010s. The LFFG method has been expanded to other countries in the world by the Hydrologic Research Center, including Central America, Haiti, Dominican Republic, and other nations in the Middle East. The rainfall forcings are adapted to the availability of data in the individual countries and may include satellite-based rainfall from the HydroEstimator algorithm from National Oceanic and Atmospheric Administration (NOAA) or precipitation forecasts from operational models running in the specific countries.

# Current State of FFG

## Lumped FFG Methodology

Sweeney and Baumgardner (1999) described the methodology used to generate LFFG values. Two variables were of critical importance in this process: ThreshR and soil moisture. (Some RFCs include the effect of snowmelt in their FFG derivation as well.) Normally, a rainfall-runoff model is used to determine the amount of runoff generated by a given amount of rainfall for a particular soil moisture condition. However, in producing LFFG, the model is run in reverse—the LFFG values transmitted to WFOs are the amounts of rainfall required to cause bank full (or flooding) conditions on small streams in a particular soil moisture condition. In this process, the unknown variable is the rainfall—the ThreshR and soil moisture conditions are known.

According to Sweeney and Baumgardner (1999), the soil moisture conditions across each RFC domain are already used (outside the FFG system) to produce river-stage forecasts. This same information then is used to drive the rainfall-runoff model underlying the LFFG system. These soil moisture conditions are generated considering soil properties and recent rainfall events, which means that they change over relatively short timescales; typically, the NWS updates these soil moisture conditions four times per day. ThreshR values, on the other hand, are assumed to be constant for a given drainage basin because in LFFG, ThreshR is a function of geography only. The RFC Development Management Team (2003) defined ThreshR as “the ratio of a basin’s flood flow to its unit hydrograph peak” (p. 5). Usually, the flood flow for a basin is the flow associated with a two-year return period (Gourley et al., 2012). The unit hydrograph allows the determination of runoff volume, which is defined as the runoff volume that results from a unit of rain occurring evenly over a given drainage basin (Sweeney & Baumgardner, 1999). Of course, this method of calculating ThreshR values is most useful at gauged points on basin outlets. Unfortunately, most basins susceptible to flash flooding are ungauged. As Sweeney and Baumgardner (1999) pointed out, determining the flood flow on an ungauged basin requires fieldwork. Even then, an estimate of ThreshR obtained from a survey is valid only at the point where the survey took place. But because RFCs must produce FFG over large areas, ThreshR values are usually contoured between gauged points to produce areal averages (Gourley et al., 2012). Additional information on the available ThreshR calculation methods can be found in Carpenter, Sperfslage, Georgakakos, Sweeney, and Fread (1999).

Because the modernized FFG system described in Sweeney and Baumgardner (1999) simply uses the same soil moisture data that the RFCs need to produce river-stage forecasts, the LFFG generation process is independent of the exact rainfall-runoff model being used. In other words, LFFG works with any sort of soil moisture information and does not require a specific rainfall-runoff model. However, the RFC Development Management Team (2003) attributed some of the LFFG incongruities along RFC boundaries to differences in the characteristics of the rainfall-runoff models used to generate LFFG. Although the exact issuance schedule varies between RFCs, it is possible to transmit updated LFFG to the WFOs every six hours; if precipitation data is available on schedule at the RFCs, the soil moisture information used for RFC river-stage forecasts is updated every six hours (Sweeney & Baumgardner, 1999). This allows the LFFG products to reflect changes in soil moisture states that may take place over a few hours.

The largest single limitation of the rainfall-runoff component of LFFG is the lumped character of the basins. Model parameters are constant for each of the basins of 300–5,000 km2 over which the various rainfall-runoff models run (RFC Development Management Team, 2003). However, flash flooding events are often observed on basins of much smaller size. The lumped-parameter method does not allow variability in soil moisture conditions within each lumped basin, so areas of a basin with recent heavy rainfall may have similar LFFG values to areas of the same basin without recent rainfall, depending on the exact method used to determine basin ThreshR values. In addition, the rainfall-runoff models used by the RFCs are usually calibrated using six-hourly observed streamflow values. However, flash flood events take place on timescales of less than six hours (RFC Development Management Team, 2003).

Originally, ThreshR values for ungauged basins were derived using various methods at each RFC (Sweeney & Baumgardner, 1999). At one extreme, some RFCs assigned the same ThreshR value to an entire state. Sometimes counties were defined as basins and one ThreshR value was assigned to each county. Finally, some RFCs divided their forecast domains into basins, each with areas on the order of 1,000 km2, and then calculated ThreshR values at the headwaters of each of these basins. Then these basin ThreshR values were averaged on a county-by-county basis. When Sweeney and Baumgardner (1999) outlined the NWS’s modern FFG system, they suggested that ThreshR values be updated using GIS techniques. Using digital elevation models (DEMs), new basins between 5 and 2,000 km2 were drawn. The traits of these basins were used to develop new ThreshR values that were then gridded to the HRAP grid (Reed, Johnson, & Sweeney, 2002).

Where applicable, the modernized FFG system includes the ability to account for snowmelt (Sweeney & Baumgardner 1999). The authors noted that the addition of snowmelt effects in LFFG resulted in a much broader range of potential FFG values. In those cases where snowmelt effects are included in LFFG generation, the Snow-17 model is used in the production of LFFG (Gourley et al., 2012).

The original FFG method has been expanded to other regions throughout the world and has been improved. Georgakakos (2006) provided uncertainty estimates with FFG by presenting an analytic solution comparing SAC-SMA surface runoff to FFG rainfall thresholds. Ntelekos, Krajewski, and Georgakakos (2006) and Villarini, Krajewski, Ntelekos, Georgakakos, and Smith (2010) pointed out the deterministic nature of the FFG system and proposed a probabilistic approach that considered FFG uncertainty, with the latter study providing a framework to model uncertainties in the rainfall forcing, model parameters, and initial states. Reed, Schaake, and Zhang (2007) proposed a “threshold frequency” method for computing threshold discharge values associated with flooding in ungauged basins. The method works by using an archive of precipitation forcings over a given basin. The model simulates discharge using the precipitation over the period of record and the peak discharges are stored. A flood frequency analysis is then performed at each grid point, not unlike conventional analyses that are conducted with observed discharge data. Then, a flooding threshold based on an assumed relation between flood frequency and bank full conditions is used during the forecast period. In agreement with Carpenter et al. (1999), which derived the ThreshR values for the NWS, Reed, Schaake, and Zhang (2007) assumed that a recurrence interval of two years was associated with bank full conditions and flooding. If the hydrologic model, which can be lumped or fully distributed, can rank the events properly, then the threshold frequency method provides flooding thresholds that inherently correct for model bias and apply to ungauged grid cells. The method requires a sample of precipitation that represents the long-term climatology, assumes climatic stationarity, and is based upon an assumed relation between flood frequency and bank full conditions.

The threshold frequency method was originally evaluated on 10 basins in the southern United States using 8 years of observed gauge-adjusted radar data. The method showed an improvement over FFG using both the calibrated and uncalibrated model. Other studies, such as Norbiato, Borga, Degli Esposti, Gaume, and Anquetin (2008), applied the threshold frequency concept using a semidistributed probability distributed moisture (PDM) model described in Moore (1985) to 16 basins in Italy and France. They focused on the transferability of model parameters and soil states from parent basins to interior points and showed some skill with the method. This study and Norbiato et al. (2009) also highlighted some sensitivity of the results to the selection of the threshold frequency. A recurrence interval of 2 years had an assumed association to bank full conditions. However, the sample size was limited for this threshold in their study and was susceptible to sampling problems, so they dropped the threshold frequency to 0.5 year. The threshold frequency concept was later applied across the continental United States at the National Severe Storms Laboratory using distributed hydrologic models and was tested in real time using NWS forecasters. The final report of the experiment (available at http://blog.nssl.noaa.gov/flash/wp-content/uploads/sites/7/2014/06/hwt-hydro_final_report_2014.pdf) noted that there were many locations in the United States with poor sample sizes caused by poor NEXRAD coverage, infrequent precipitation, or both, which limited the skill of the threshold frequency approach. Other threshold-based methods were considered later.

## Flash Flood Potential Index

Like all RFCs, the RFCs that cover the western United States, the Northwest River Forecast Center (NWRFC), CNRFC, and CBRFC, are responsible for producing FFG. However, these RFCs cover areas where geography is often more important to predicting flash flooding than soil moisture. Recognizing these facts, the CBRFC/Western Region Flash Flood Analysis project was launched to delineate the characteristics of FFMP basins that fall under the purview of the western region’s RFCs (RFC Development Management Team, 2003). The eventual result of this project was the FFPI method of FFG generation now used in NWRFC, CNRFC, and CBRFC.

Smith (2003) described this method in detail. The CBRFC obtained several GIS data sets believed to influence the flash flood potential of a given basin. Because these data sets often were of differing resolutions, each had to be resampled to a consistent resolution. Each grid cell was assigned a flash flood potential index on a scale of 1–10 for each layer of data. Then, each grid of flash flood potential index values was averaged to create the final FFPI product. Initially, only the slope parameter was weighted above the other data layers.

The data used in Smith (2003) included slope, land use, forest cover, and soil type. These data sets were resampled to a consistent resolution of 400 meters; this means that the smallest drainages in the resulting product encompass areas of roughly 60 km2. Although this represents a significant resolution improvement over lumped FFG basins, it is still coarser than the underlying FFMP basins or HRAP grid cells. Slope data are derived from a US Geological Service (USGS) DEM, soil types from the State Soil Geographic (STATSGO) data from the Natural Resources Conservation Service (NRCS) data set, land use information from the Landsat satellite program, and forest density data from satellite imagery.

The initial gridded FFPI product was interpolated to FFMP basins over the CBRFC area of responsibility. Initially, FFPI was used by the Salt Lake City WFO alongside traditional LFFG. In this initial use, forecasters could see areas within the FFMP program where rainfall exceeded LFFG. Then they could look at that same area on an FFPI map and determine whether that basin was truly susceptible to flash flooding (Smith, 2003). After this initial project met with some success, the tool was deployed across the CBRFC area. The FFPI product does allow changes in basin susceptibility with time; for example, over the 2006–2010 period, several changes in CBRFC’s FFG grids were executed. Some of these changes were due to specific WFO requests to alter the FFPI of specific basins, while other changes are due to wildfires; after such events, FFPI can be modified to reflect changes in soil permeability and forest cover. Still other variations in the FFPI grid are due to seasonal changes in vegetation and snow cover (RFC Development Management Team, 2003). The CBRFC FFG being sent operationally to WFOs within their area of responsibility consists of a 2.54-mm-per-hour rainfall rate nudged by FFPI, such that high FFPI (greater susceptibility to flash flooding) is associated with lower values of FFG. In the fall of 2008, the CNRFC switched from LFFG to the FFPI system. The NWRFC also uses a static FFPI map.

## GFFG Methodology

GFFG was developed at the ABRFC in 2005 and 2006 as an attempt to correct the mismatch in scale between large LFFG basins and small FFMP basins, since in the ABRFC area, there are an average of 200 FFMP basins contained within each LFFG basin (Schmidt et al., 2007). Therefore, GFFG attempts to take full advantage of the resolution improvements in QPE resulting from the WSR-88D network and those in geomorphology arising from space-borne sensors and the FFMP basin delineation project. GFFG attempts to mimic the methodology of LFFG in many ways. In fact, Gourley et al. (2012) had the ABRFC run LFFG in hindcast mode from 2006 to 2008, after LFFG had already been deprecated for that area. They then compared LFFG values to GFFG values and found extremely close agreement between both for the 1-hour, 3-hour, and 6-hour products. It is thus reasonable to assume that in operational use, the main advantages of GFFG are increased spatial resolution and spatial variability rather than accuracy or forecast skill, since the actual values from each type of guidance should be very similar.

GFFG is run on the HRAP grid, just like LFFG. However, GFFG uses a distributed hydrologic model to monitor the soil moisture component of FFG, unlike the older lumped hydrologic model used in LFFG (Schmidt et al., 2007). Like the FFPI method discussed earlier, GFFG requires land cover, soil type, and slope; and like LFFG, the GFFG method requires a soil moisture model, a rainfall-runoff model, and the determination of ThreshR values. Land use and soil type are combined to yield an NRCS curve number, CN. Higher curve numbers are associated with larger runoff generation potential, and therefore with a greater flash flood potential. These curve numbers are then adjusted to account for recent soil moisture conditions (Schmidt et al., 2007). In GFFG, this is accomplished by calculating a saturation ratio for each grid cell from the NWS Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM). This distributed model runs in continuous mode and the upper zone tension and free water contents (UZTWC and UZFWC) model parameters are stored (Gourley et al., 2012). The two model parameters are summed, and the ratio of this sum to the maximum possible values of the two parameters (Koren, Smith, Wang, & Zhang, 2000) is the saturation ratio at each grid cell (Schmidt et al., 2007).

Using the saturation ratio, the CN is adjusted to better reflect the impact that soil moisture has upon runoff generation. Two equations—called “wet” and “dry”—are used to set the upper and lower bounds of the adjusted curve numbers, respectively. The wet equation represents 100% saturation in the HL-RDHM model and is given in Equation (1):

$Display mathematics$
(1)

where ARCIII is the soil moisture–adjusted curve number due to totally saturated conditions and CN is the original curve number given by the land use and soil type of the model cell. Similarly, the dry version (representing 0% saturation in HL-RDHM) is given in Equation (2):

$Display mathematics$
(2)

where ARCI is the soil moisture adjusted curve number due to completely unsaturated conditions and CN is the original curve number (Schmidt et al., 2007). The adjusted curve number lies somewhere between ARCI and ARCIII and is determined using linear interpolation and the HL-RDHM saturation ratio. For example, for an ARCI of 40, an ARCIII of 80, and a saturation ratio of 50%, the final adjusted CN is 60. This final adjusted CN is used in Equation (3):

$Display mathematics$
(3)

where CN is now the curve number adjusted for soil moisture and S is maximum rainfall retention (Gourley et al., 2012).

The final remaining variable in the GFFG system is ThreshR. Schimdt et al. (2007) noted that the traditional NWS definition of ThreshR as used in the LFFG system worked for parts of the ABRFC domain, but not all areas of it. The GFFG method does not use the two-year return period flow that underlies the LFFG system. Instead, a five-year return period, 3-hour design rainfall event is assumed to be the precipitation associated with the runoff that yields the flood stage flow at the pixel (Schmidt et al., 2007). The unit hydrograph peak is found using the NRCS curve number method (Gourley et al., 2012) and requires basin slope, rainfall duration, soil moisture conditions, basin area, rainfall duration, and other characteristics (Schmidt et al., 2007). Then, as in the LFFG method, ThreshR is the ratio of flow at flood stage to the unit hydrograph peak. The resultant GFFG ThreshR acts like LFFG ThreshR, but Schmidt et al. (2007) noted that the GFFG ThreshR is lower in high elevations and higher in low elevations. In other words, the newer ThreshR values make logical sense, considering the topographical differences between locations; the newer values also display greater spatial variability than the legacy ThreshR values.

The final calculation of GFFG is given in Equation (4) and requires S from Equation (3) and the ThreshR values at each grid cell:

$Display mathematics$
(4)

where Q is the ThreshR value, S is the soil moisture–adjusted curve number, and P is the precipitation required to generate bank full conditions at the grid point; in other words, it is the value of gridded FFG at the grid point (Schmidt et al., 2007).

Although the spatial scale of GFFG (roughly 16 km2 per grid cell) is much closer to the scale of FFMP basins than the large basins that make up the older LFFG system, Gourley et al. (2012) found no improvement in the forecast skill of GFFG compared to LFFG over the same domain and period. However, they did find that in some cases, the finer spatial resolution of the GFFG product was able to resolve small-scale details that would not be visible to a forecaster relying on LFFG. Because the GFFG system mimics the values produced by the LFFG system and thus does not require much retraining of the forecasters using the tool, the GFFG system could be deployed in areas beyond the ABRFC domain (Schmidt et al., 2007). In 2007, GFFG became operational at the LMRFC and the WGRFC. In early 2008, it was also deployed at the SERFC. Therefore, as of 2010, GFFG was the operational flavor of FFG running across the entire southeastern and south-central United States. By 2014, the GFFG system was running in various forms across most of the eastern two-thirds of the United States.

## Distributed FFG Methodology

One CONUS RFC uses an FFG generation method that does not fall into any of the aforementioned categories. The Middle Atlantic RFC (MARFC), which covers parts of Pennsylvania, New York, Maryland, New Jersey, Virginia, and West Virginia, uses the continuous–antecedent precipitation index (API) model as the rainfall-runoff component of FFG generation. The MARFC FFG product uses antecedent precipitation estimates derived from the WSR-88D network covering their forecast domain to force the API model in scenario mode. Unlike the rainfall-runoff models used in LFFG, the continuous-API model operates on the HRAP grid with distributed parameters, and thus does not use the basin lumped parameters of the older LFFG system. As a result, this system contains spatial variability roughly similar to that observed in regions running GFFG.

## Skill of FFG

Gourley et al. (2012) evaluated FFG over the ABRFC forecast region from September 1, 2006 to August 22, 2008. Over this period, GFFG was the tool being operationally generated at the RFC, but for this study, RFC forecasters produced reforecasts of the legacy LFFG product for the same period and spatial domain. GFFG values were found to be very similar to LFFG for the 1-hour product, 8% higher than LFFG values for the 3-hour product, and 6% higher than LFFG for the 6-hour product.

The authors then compared the times and locations of known flash flood impacts (from the NWS Storm Data publication) with gridded QPE-to-FFG ratio data to calculate contingency table statistics (Table 1). In this study, the QPE came from the Stage IV product, which is a gridded, hourly, multisensor product generated at RFCs. Stage IV begins with estimates of precipitation from weather radar, into which are merged any point observations of rainfall from rain gauges. Then NWS forecasters engage in manual quality control of this merged product before release. Initially, Gourley et al. (2012) treated situations in which Stage IV exceeded FFG as forecast flash floods. Using this criterion, they found that Stage IV–to-FFG ratios detected between 41 and 66% of flash floods, depending on which of 1-, 3-, or 6-hour GFFG or LFFG was used. However, the false alarm rate of the tool was between 84% and 97%, and the CSI (CSI) ranged from 0.03 to 0.13. In addition, GFFG was not shown to be more skillful than LFFG. Then the authors considered other QPE-to-FFG thresholds, ranging from situations in which QPE was just 50% of FFG to situations in which QPE was 300% of FFG. In this expanded search window, the maximum CSI of 0.14 occurred when QPE reached 125% of the 1-hour LFFG. In addition, this secondary search indicated that GFFG was less skillful than LFFG at most QPE-to-FFG thresholds and FFG accumulation windows.

Table 1. Example of Contingency Table and Simple Metrics for Assessment of FFG Forecasts

Did QPE exceed FFG?

Was the event recorded in Storm Data?

Section 1.01 Classification

Yes

Yes

Hit

No

Yes

Miss

Yes

No

False alarm

No

No

Correct negative

Probability of detection

False Alarm Rate

CSI

Hits / (Hits + Misses)

False alarms / (Hits + False alarms)

Hits / (Hits + Misses + False alarms)

0.0 to 1.0, where 1.0 is desirable

1.0 to 0.0, where 0.0 is desirable

0.0 to 1.0, where 1.0 is desirable

Clark, Gourley, Flamig, Hong, and Clark (2014) assessed the CSI of FFG nationally from October 1, 2006, to August 31, 2010 (Fig. 1).

Click to view larger

Figure 1. CSI for the FFG method applied in each RFC region.

CONUS-wide, they found that the CSI of FFG ranged from 0.01 to 0.07, depending on the accumulation window of the FFG tool and the QPE-to-FFG ratio used for verification. The authors broke down statistics by RFC, which showed that, when only QPE-to-FFG ratios of 1.0 were considered, the CSI of FFG ranged from 0.00 along the West Coast to 0.19 in the MARFC domain. When any QPE-to-FFG ratio between 0.5 and 3.0 was considered, the CSIs again ranged from 0.00 in the West to 0.19 in the MARFC region. Clark et al. (2014) found comparable CSI, POD, and FAR numbers to Gourley et al. (2012) over the ABRFC. Both studies found that the low CSI of FFG products is driven by high false alarm rates.

Higher skill values were generally encountered in RFCs using DFFG or LFFG, and lower values were generally concentrated in regions using FFPI. However, the authors noted that they assessed operational FFG, and because RFCs operationally produce only one form of FFG at a time, a true side-by-side comparison of different FFG production methods over the same region and period is not possible. Although FFPI exhibited low CSIs, it is likely that forecasting flash floods in the western United States is more difficult due to underreporting of impacts in lightly populated areas, difficulties with Stage IV precipitation estimates in regions with poor weather radar coverage, and problems with the method itself.

# Continental-Scale Flash Flood Forecasting

Technological advances in computing and remote sensing of the Earth have spawned a new generation of flash flood forecasting systems that are used operationally across continental scales. These are quite diverse in terms of their forcings being model-based, from precipitation observations, or both; the scales of application; and the variables and thresholds that are used to forecast flash floods. The greatest advantage of a particular forecast system operating at continental scale is its consistency, which greatly facilitates forecaster training and usability, ultimately reaching a larger pool of users.

## Rainfall-Based Indices (EPIC, ERIC, Swiss, ARIs)

The European Flood Awareness System (EFAS) (Thielen, Bartholmes, Ramos, & de Roo, 2009) provides forecasts of fluvial flooding across Europe. It utilizes medium-range forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the German Weather Service (DWD), as well as the Consortium for Small-scale Modeling—Limited-Area Ensemble Prediction System (COSMO-LEPS). The precipitation forcings are provided to the spatially distributed LISFLOOD hydrological model (van der Knijff, Younis, & de Roo, 2010), which yields forecasts of river discharge with lead times up to 15 days. These forecast streamflow values are compared to prior discharge forecasts from the numerical weather prediction (NWP) and hydrologic model (referred to as reforecasts) over a 20-year period to compute return periods at each pixel. EFAS flood forecasts have a spatial grid cell resolution of 5 km and variable temporal resolution depending on the NWP model forcing and thus is designed for medium- and large-scale basins across Europe.

The European Precipitation Index based on simulated Climatology (EPIC) methodology was developed to complement the EFAS forecasts by providing information at the flash flood scale (Alfieri & Thielen, 2015). The EPIC forecasts are based on 20 members of QPFs from COSMO-LEPS provided at 7-km grid cell resolution, updated twice per day (00 and 12 UTC), with forecasts going out to 132 hours at 3-hour time steps. EPIC runs once per day for each pixel of the river network at 1-km grid cell resolution. It is designed to provide forecasts on basin scales from approximately 50–5000 km2. Similarly to EFAS flood forecasts, EPIC compares the ensemble QPFs to a regularly updated 20-year model climatology to provide forecasts of the return period of the event and the probability of exceeding reference return period thresholds. EPIC is computed according to the following:

$Display mathematics$
(5)

where UPdi is the accumulated precipitation over periods of 6, 12, and 24 hours, considering all upstream grid cells; and the denominator represents the mean of the maximum annual discharge computed at each cell. If the EPIC value is 0, then there is no rainfall forecast for that grid cell, whereas if the value reaches 1, then the forecast precipitation is the same as the mean of the annual maxima at that grid cell. A gamma distribution is then fit to the ensemble of EPIC forecasts. Then the EPIC ensemble can be converted to a return period using the 20-year model climatology by using a Gumbel extreme value distribution applied to the annual maxima of EPIC values. An alert threshold corresponding to a 5-year return period is assumed and is consistent with the alerting used in the larger-scale EFAS forecasts.

The EPIC approach is based on quantitative precipitation forecasts alone and thus does not consider hydrologic processes such as initial soil states, slopes, depth of the soil layers, runoff generation processes, land use, etc. It does include the precipitation from grid cells upstream and thus incorporates some knowledge about basin boundaries and scales. Furthermore, the EPIC method yields ensembles, and a great deal of the spread between the individual members is attributable to the uncertainty of the model weather forecasts, rather than the neglect of detailed hydrologic processes. Alfieri et al. (2015) showed that with modest filtering, the frequency of the model-forecast rainfall amounts is well correlated with hydrologic model–based discharge return periods using the same precipitation forcings. The greatest advantages of the EPIC approach are its simplicity, ability to provide lead time on the order of days, and consistency with the NWP climatology. Even if the model-based forecasts are historically biased, then the comparison of forecasts to the climatological values inherently removes this bias. The accuracy of the EPIC flash flood forecasts is conditioned on the skill of the QPF members in representing the magnitude, location, and timing of extreme rainfall amounts.

The EPIC approach has been extended to runoff forecasts. The extreme runoff index (ERI) compares streamflow forecasts from the ECMWF land surface model to a 20-year reanalysis (Alfieri, Pappenberger, & Wetterhall, 2014). The formulation to compute ERI is analogous to the EPIC approach and applies to flooding in large, ungauged basins. Because the horizontal grid cell spacing is approximately 32 km and the model is run daily, the ERI applies to catchments larger than 1,000 km2. Raynaud, Thielen, Salamon, Burek, Anquetin, and Alfieri (2015) proposed the European Runoff Index based on Climatology (ERIC), which is also quite similar to the EPIC. It differs from the ERI in that it uses proxy variables to essentially downscale and weight the EPIC values so that they apply at flash flood scale. This method capitalizes on the EPIC approach by including soil moisture states available from a coarser resolution (5 x 5 km2) LISFLOOD hydrologic model within the EFAS. The runoff coefficient is shown to be correlated to EFAS initial soil moisture conditions. It weights the forecast precipitation from COSMO-LEPS in the upstream cells by the simulated runoff coefficient from EFAS, which responds to impermeable soils, shallow profiles, and high slopes. The ERIC method is computed on a 6-hour time step on a 1 x 1–km2 grid and provides flash flood forecasts on basins with catchments up to 5,000 km2.

Flash flood forecasting systems have been developed within the continent of Europe and apply to regional or country-scale domains. In the south of Switzerland, intensity-duration-frequency (IDF) curves have been developed using rain gauge–based archives and also based on the COSMO-LEPS reforecast data set. The observation-based IDFs are compared to real-time observations of rainfall from rain gauges and radar, while the COSMO-LEPS-based IDF analysis is compared to COSMO-LEPS forecasts. This system is capable of providing real-time estimates of the return period of rainfall from observations, as well as for forecast rainfall. The Swiss system has been developed further into a process-based hydrological forecasting chain named RGM-PRO. It relies on information on the spatial distribution of dominant runoff processes based on Scherrer and Naef (2003) and Antonetti, Buss, Scherrer, Margreth, and Zappa (2016). The module is grid-based (500-m grid spacing), and the time step is 1 hour. It is driven by a nowcasting product that combines radar and rain-gauge rainfall data (CombiPrecip; Sideris, Gabella, Erdin, & Germann, 2014) and meteorological data from the deterministic COSMO-1, with 33 hours of lead time and probabilistic COSMO-E (21 members, with 113 hours of lead time), whereas soil moisture data are assimilated from simulations with PREVAH for the whole Switzerland (Viviroli, Zappa, Gurtz, & Weingartner, 2009). The forecast product is streamflow.

In Catalonia, a flash flood early warning system (FF-EWS) has been designed on radar-based estimates and forecasts of rainfall (Corral, Velasco, Forcadell, & Sempere-Torres, 2009; Alfieri, Velasco, & Thielen, 2011; Versini, Berenguer, Corral, & Sempere-Torres, 2014). The system begins with radar QPE on a 1 x 1–km2 grid produced every 5–10 min. The radar rainfall fields are extrapolated forward in time up to 3 hours to provide added lead time. The rainfall amounts are aggregated in time, and also in space based on the upstream precipitation, as in EPIC, and then compared to available IDFs. There is an assumption that the computed return periods of rainfall are linked to those with streamflow. In other words, flash floods at the high return periods become rainfall-driven so that the soil moisture states and other geomorphologic characteristics that dictate dominant runoff processes can be neglected.

## Forward Simulation of Hydrologic Conditions

Javelle, Demargne, Defrance, Pansu, and Arnaud (2014) described a flash flood alerting system run by Météo-France for the French Mediterranean region. The Adaptation d’Information Géographique pour l’Alerte en Crue (AIGA) warning system uses precipitation forcing from radar QPEs that have been corrected by rain-gauge data. Correction factors are computed on an hourly basis and are applied downscale to the 5-min radar-based rainfall rate products generated by the operational French radar product called PANTHERE. Quality indexes are computed for individual radar-centric grid points and become the basis for merging the QPEs from neighboring radars onto a common Cartesian grid covering France (Tabary, 2007). These QPEs are provided to a simple distributed hydrologic model run on a limited 1-km2 domain grid every 15 min.

The distributed hydrologic model employs partitioning of the rainfall to effective rainfall and that which is lost to evapotranspiration. Then, the effective rainfall enters conceptually based soil and routing reservoirs. Javelle, Fouchier, Arnoud, and Lavabre (2010) described the process for calibrating the hydrologic model parameters. Next, the peak discharge forecasts are compared to reference peak flow quantiles that are computed offline based on a regionalized stochastic rainfall generator that yields the rainfall and flood frequency analyses. Note that the same hydrologic model is used in the generation of the offline flood frequency analysis, and so there is an inherent bias correction when comparing flood peak forecasts to historic distributions to estimate flood average recurrence intervals (ARIs, also commonly referred to as return periods). Flash flood alerts are determined based on the resulting ARIs in the following categories: 2–10 years (yellow), 10–50 years (orange), and more than 50 years (red). Javelle et al. (2014) evaluated the AIGA-based peak discharges with estimates obtained from the field. In general, the unit peak discharges (peak discharge normalized by the drainage area) agree reasonably well with the field estimates, despite some noted limitations due to bias in the QPEs and the hydrologic model. While the method runs on a limited domain in the south of France, where flash flooding near the Mediterranean is more problematic, there are plans to expand the methodology to the entire country of France. Another planned improvement to AIGA is to utilize forecast rainfall scenarios, providing the potential to increase the lead time for impending flash floods.

Vincendon, Ducrocq, Nuissier, and Vié (2011) focused on the uncertainties associated with QPFs as forcings to a coupled land surface–hydrologic model. While the computational demands limit its application to small basins and for offline simulation, they introduced a perturbation method to QPF fields that was based on their prior error characteristics (structure, amplitude, and location). The object-based approach perturbs each of the precipitation objects and then inputs them to the coupled land surface-hydrologic modeling system to yield an ensemble discharge forecasts comprised by as many as 50 members. The utilization of ensemble QPFs for direct forward simulation in land surface and/or hydrologic models across continental or even global scales will continue to evolve provided ever-increasing computational capabilities.

Flash flood prediction systems have been designed for individual basins in arid and semiarid regions. Rozalis, Morin, Yair, and Price (2010) presented a flash flood modeling system applied to a 27-km2 watershed in a Mediterranean basin in Israel. It was forced with radar-based rainfall estimates with updates every 5 min and a daily bias adjustment from rain gauges. The mass balance component of the system was based on CN (i.e., the same approach used to generate GFFG in the United States). Once surface runoff is generated using the CN method, it is routed downstream to the basin outlet and to the next subbasin using the kinematic wave solution to the Saint Venant equations. A study of 20 rainfall events indicated that the model could simulate peak discharges with reasonable accuracy, especially for the largest events. Some weaknesses were noted in the model’s simulation of soil drying, which affected the ability to simulate the low and moderate peaks. Despite the model’s simplicity, it was shown to forecast the category of flash flooding correctly as falling into low, medium, or high classes.

The KINEROS2 (K2) model has been developed in and applied to watersheds in the semiarid West of the United States. It uses forcing from radar-based rainfall estimates and provides the value of modeling channel transmission losses, which is an important factor in arid and semiarid watersheds with ephemeral channels. Soil infiltration can occur directly from above via rainfall excess and from upstream ponded water. The vertical movement of water through the soil is computed following the solution methods to Richard’s equation, described in Smith, Smettem, Broadbridge, and Woolhiser (2002). Surface water is routed into the overland pixels and channels simultaneously with infiltration, to create a more realistic treatment of advancing flow fronts on highly permeable soil and to simulate channel transmission losses in ephemeral channels. K2 uses the Parlange three-parameter model for infiltration (Parlange, Lisle, Braddock, & Smith, 1982), which includes realistic infiltration curves that fall within the limits specified in Green and Ampt (1911) and Smith and Parlange (1978).

The K2 model has been implemented as a demonstration tool in the US NWS on select high-risk basins in the western United States. Schaffner et al. (2017) described several case studies of the model application on Fish Creek Canyon in the Anza-Borrego Desert State Park. The creek was ungauged, so they obtained high-water marks from field surveys and other ancillary sources of data. The model calibration procedure required the development of a rating curve using idealized channel geometry and assumed flow velocities to relate discharge to river stage. Then, flood categories (i.e., minor, moderate, and major) flooding must be estimated using prior events. Overall, the model was found to categorize the flooding correctly as falling into the minor, moderate, or major category, similar to the Israeli system, and was skillful at forecasting the duration of the flooding. The same calibration procedures were implemented on Short Creek Basin, located upstream of Colorado City, Arizona, and the model yielded similar outcomes in terms of forecasting the proper flood category.

In the United States, two real-time, continental-scale hydrologic modeling applications have evolved for use in the NWS: the National Water Model and the Flooded Locations and Simulated Hydrographs (FLASH) system. The National Water Model is based upon the Weather Research and Forecasting (WRF) Hydro framework, and models land surface states using the Noah-Multiparameterization (NOAH-MP) land surface model (Gochis, Yu, & Yates, 2015). Once there is ponded water on the surface, it is routed downstream using a diffusive wave solution to the Saint Venant equations and continues downstream in the channels using Muskingum-Cunge channel routing. The National Water Model runs under different configurations to provide short-, medium-, and long-term forecasts of hydrologic conditions at 2.67 million river reaches across the United States. The short- and medium-term forecasts are forced by deterministic QPFs from the High Resolution Rapid Refresh (HRRR) and Global Forecast System (GFS) models, respectively.

Short-term forecasts of streamflow and streamflow anomaly are provided out to 15 hours and are updated hourly with a data latency of almost 2 hours. Medium-term forecasts are generated once per day and go out 10 days in the future. Finally, long-range forecasts from the Climate Forecast System (CFS) model are cycled every 6 hours to produce a 16-member forecast of streamflow and land surface variables out to 30 days. All forecasts utilize a nudging scheme to adjust forecast streamflow values to those that have been observed at USGS stream gauging sites. The National Water Model advances the state of operational hydrologic modeling in the United States by providing forecasts at ungauged sites, thus providing new potential for forecasting droughts and floods by RFCs and beyond.

The FLASH system encompasses a suite of rainfall and hydrologic products that have been designed to provide NWS forecasters with information regarding impending flash floods (Gourley et al., 2017). This system is driven by rainfall estimates from the MultiRadar MultiSensor (MRMS) system (Zhang et al., 2016). MRMS provides a suite of radar products across the United States in real time on a grid with horizontal spacing of 1 km2. The radar-only QPE products are used in FLASH and have an update frequency of 2 min. Figure 2a shows the MRMS QPE for a significant flash flooding event that occurred in Richwood, West Virginia, on June 23, 2016. Three-hourly rainfall accumulations have values of 75–100 mm. There are three basic categories of products contained within FLASH: (a) rainfall ARIs, (b) comparison of rainfall to FFG values, and (c) direct simulations of discharge from the Ensemble Framework For Flash Flood Forecasting (EF5) system. The rainfall-based products in the first two categories are produced at the same frequency and on the same grid as the MRMS rainfall estimates (i.e., every 2 min on a 1-km2 grid) across the CONUS.

Click to view larger

Figure 2. Examples of FLASH products from a flash flood that occurred on June 23, 2016, in Richwood, West Virginia. All the following products are valid at 1700 UTC: (a) Three-hourly, radar-only rainfall accumulation from the MRMS algorithm; (b) maximum ARI of rainfall; (c) maximum MRMS rainfall-to-FFG ratio; and (d) maximum unit streamflow from the CREST model core.

Rainfall ARIs are computed by comparing the MRMS QPEs accumulated over 30 min and 1, 3, 6, 12, and 24 hours to rainfall frequency maps for the corresponding accumulation period at each grid point. The rainfall frequencies are based on long-term rain-gauge accumulations as part of the NOAA Atlas 14 project (Perica et al., 2013). The rainfall ARIs are computed in real time and provide a measure of rainfall anomalies. Very little research has been conducted on the relation of the rainfall ARIs to flash flood impacts in the United States. A major consideration of the product is that the ARIs are computed by comparing radar-based rainfall estimates to a rain gauge–based climatology. These are two different sources of data, with the radar estimates more capable of capturing the spatiotemporal variability of rainfall while also being more subject to bias. Further, the rainfall frequency analysis varies in quality from state to state, and all the frequencies assume climatic stationarity. Figure 2b shows an example of a max ARI product. At each grid point, the maximum recurrence interval from all the accumulation periods is determined, and these values are used to create the composite plot. In this case of a significant flash flood, rainfall ARIs reach values as high as 200 years.

The QPE-to-FFG ratio product merely ingests the FFG products that are generated by the NWS RFCs and compares them to MRMS-based QPEs for accumulation periods of 1, 3, and 6 hours. Similar to the max ARI product, there is also a max QPE-to-FFG product that considers the maximum exceedance from all three accumulation periods. Forecasters are quite accustomed to this product, given its long legacy in the NWS, and the FLASH QPE-to-FFG product has the added advantage of being computed from MRMS QPEs that are updated every 2 min. In general, forecasters consider issuing flash flood warnings when rainfall exceeds the FFG thresholds (i.e., the QPE-to-FFG ratio exceeds 1.0). Figure 2c shows a large area with ratios greater than 1.0 and isolated rainfall maxima that have exceeded FFG by a factor of 3. Note that FFG was designed to indicate bank full conditions, not necessarily to rank the magnitude of flash flooding.

The most novel products in FLASH come from EF5, a modular framework that supports multiple inputs (for precipitation and potential evapotranspiration estimation), parameter optimization schemes, data assimilation, snowmelt, channel routing, and three water balance schemes. EF5 runs in real time across the entire globe using forcings from global data sets of precipitation estimates and forecasts (http://floods.global) and regionally at higher resolutions using local data sets for parameter estimates and forcings (Clark et al., 2017). The simplest rainfall-runoff concept is the hydrophobic module, which permits no infiltration and diverts all the effective rainfall into direct overland runoff and channel discharge. This module is effective for modeling runoff over burn scars and identifying precipitation biases and anthropogenic impacts that are not considered in the more sophisticated water balance components. It also provides an upper bound in ensemble hydrologic forecasting. The second water balance component is the Sacramento Soil Moisture Accounting (SAC-SMA) model (Burnash, Ferral, & McGuire, 1973) with a priori parameters based on observable features of the land surface. This water balance concept has been used in the NWS for decades and provides a separate forecast of discharge that can be used to generate an ensemble.

The third mass balance concept supported in EF5 is the Coupled Runoff and Excess Storage (CREST) model, described in Wang et al. (2011). Figure 3 shows the basic structure of the CREST model.

Click to view larger

Figure 3. Hydrologic model structure of the CREST model, which shows rainfall-runoff model cores supported in EF5.

All the parameters that are related to mass balance are estimated a priori and are based on DEMs, land cover classes, and soil characteristics. Once water enters a defined channel cell, EF5 routes the water downstream using the kinematic wave solution. The routing parameters are known at locations with stream gauges and then are regionalized to all channel cells using a data-driven approach, as described in Vergara et al. (2016).

EF5 produces forecasts of streamflow and degree of soil saturation. A useful derived product is the forecast streamflow normalized by each grid cell’s drainage area, or unit streamflow. One challenge is the identification of anomalous conditions associated with flooding or bank full conditions at ungauged locations. In the continental implementation in the United States, the emphasis is on flash flood forecasting so that useful information can be provided to forecasters on the location, timing, and magnitude of flash flooding. EF5-based products are generated on the same grid as the MRMS rainfall products (1-km2 horizontal grid cell spacing) every 10 min, with only 6–8 min of latency. This frequency is sufficiently high to communicate impending rainfall-driven flash flooding hazards to forecasters.

A series of experiments were conducted during 3–4-week periods during the summers of 2013–2016 that involved NWS forecasters. One outcome from the Hydrometeorology Testbed—Hydro experiment (HMT-Hydro) was the change from using frequency-based flood thresholds (based on a decadal NEXRAD archive input to a hydrologic model reforecast) to using unit streamflow values. NWS forecasters evaluated FLASH products in real time and subjectively determined thresholds for the CREST unit streamflow values that were associated with minor and catastrophic flooding. Objective data from NWS local storm reports were introduced to corroborate the unit streamflow thresholds. Figure 4 shows a histogram of unit streamflow values from the CREST mass balance scheme that are associated with NWS local storm reports of flooding.

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Figure 4. Histogram of CREST model unit streamflow values for events that had local storm reports of flash flooding from the NWS.

Raw unit streamflows from 1–3 m3/s/km2 are associated with reported flash flooding, which agrees well with the subjective analysis provided by NWS forecasters in Martinaitis et al. (2017). These thresholds, in addition to the threshold for catastrophic flash flooding (i.e., unit streamflow > 10 m3/s/km2), are used in training materials for operational NWS users (http://training.weather.gov/wdtd/courses/ffawoc/index.php).

Figure 2d shows the unit streamflow forecast for the flash flooding case in Richwood, West Virginia, discussed previously. There is a large swath of unit streamflow values exceeding the threshold for minor flooding, and many pixels have exceeded the catastrophic flash flooding threshold of 10 m3/s/km2. The flash flood took the lives of 23 people across the state and left the town of Richwood in ruins. A significant advance in flash flood forecasting has been accomplished through improved detection of flash flooding using continental-scale hydrologic models forced with radar-based QPEs from MRMS. The FLASH system adds the capability to segregate between minor and much more impactful events.

## Machine Learning Approaches

Machine learning is a subset of the broader field of artificial intelligence, in which algorithms learn and evolve over time by iterating through vast amounts of data thousands, millions, or hundreds of millions of times. The value in these approaches as applied to weather forecasting lies in their ability to identify patterns that might elude traditional methods like model output statistics, training/experience, empirical indexes, or rules of thumb (Kohavi & Provost, 1998). Supervised machine learning is a specific type of learning in which a label, or dependent attribute, is provided to the algorithm such that the algorithm is told what to predict.

Clark (2016) used random forests, a type of machine learning algorithm, to predict flash flooding impacts from GFS NWP forecasts. In this supervised learning exercise, flash flood events from the NWS Storm Data publication were associated in space and time with vectors of GFS forecasts of atmospheric and land surface conditions to identify conditions associated with flash flood impacts (as well those not associated with them). Nearly 19,000 flash flood reports covering the CONUS (and over 11 million location-time pairs in which no flash flooding was reported) were fed to the random forest algorithm for the period extending from October 2006 to the end of 2015. These reports and nonreports were divided systematically into training and testing data sets; the random forest learns from the training data, and its ability to forecast flash floods is tested on the independent testing data. Clark (2016) found that a random forest model trained on Storm Data reports of flash floods and corresponding GFS forecasts was better at discriminating between flash floods and nonevents than any of the traditionally used rules of thumb he tested, including precipitable water, K-index, soil moisture, and precipitation rates. The random forest method can optimize the incorporation of multiple pieces of information into a final assessment of the flash flood threat.

Random forests also can be used to assess flash floods probabilistically. A random forest is an ensemble of weakly correlated classifiers, each of which is a classification tree (Breiman, 2001). The proportion of classifiers (or trees) in the forest voting for a given outcome (or forecast) can be treated as a measure of the entire ensemble’s confidence in that outcome. For example, if, in a 100-tree forest, 99 trees yield a forecast of a flash flood, the classifier is more confident in that outcome than if only 51 of the 100 trees yielded that forecast. Clark (2016) used this property of the classifier to generate calibrated probabilistic forecasts of flash floods, based on methodologies originally used to apply random forests to air turbulence prediction (Williams, 2014); this method yielded reliable probabilistic estimates of flash flood impacts.

The structure of random forests also allows the assessment of the relative importance of the various components of the vectors of forecast data associated with each grid cell in space and time (Tan, Steinbach, & Kumar, 2005). Clark (2016) found that the K-index, typically used to assess the probability of widespread thunderstorm activity and related to instability through a layer in the middle troposphere (George, 1960), was among the variables most important to the success of the random forest predictions. Although the K-index has been used to forecast thunderstorms for decades, it typically has not been explicitly associated with flash flood forecasting. Other variables, including precipitable water, specific humidity at 700 and 850 hPa, precipitation and convective precipitation rate, precipitable water anomaly, and lifted index, were shown to be important to successful predictions. These quantities are among, or are related to, the ingredients necessary to get the persistently high rainfall rates that are usually required for the development of flash flood impacts (Doswell et al., 1996).

In two case studies, Clark (2016) showed that random forests applied to the GFS can identify large-scale, synoptically driven flash flood outbreaks up to seven days in advance. In a test comparing the US system to flash flood reports over the European continent, the system showed performance like that achieved throughout the United States. Because global NWP is available in data-sparse regions, this method or others like it may enable reliable probabilistic forecasts of flash floods even in areas that lack weather radar, dense in situ rainfall measurements, and high-resolution, distributed hydrologic models.

# Conclusion

Flash floods pose significant challenges to forecast systems due to their small, spatiotemporal scale of impact; their multidisciplinary nature, which cuts across meteorology, hydrology, and social science; and the fact that the observational databases describing them are limited. All of this comes at the expense of flash flooding being a worldwide phenomenon that is generally considered the deadliest weather-related natural hazard. The design and implementation of systems to forecast flash floods are an essential first step to begin mitigating their impacts. The spatial scales of basins that respond to heavy rainfall within a few hours is small (generally less than 1,000 km2). These small spatiotemporal scales of flash flooding impacts pose challenges to the forecasting systems that must provide information with low data latency in the correct locations to provide enough lead time for mitigating actions. Ensemble approaches are preferred to address these uncertainties, but their computational demands are high. This has led to real-time forecasting chains that rely solely on forecast precipitation ensembles alone, or they incorporate variables from a larger-scale land-surface or hydrologic model that are related to the initial soil moisture states or the expected responses of the basin. Nevertheless, as computation resources are ever-increasing, more and more models are being run operationally on a continental scale or even a global scale and provide useful information at the flash flood scale.

Future systems will incorporate ensemble forcings from convection-resolving numerical weather prediction models that assimilate data from satellite and radar observations at subhourly timescales. These ensemble QPFs will expand the forecast horizon out to several hours and will drive hydrologic models that also run on a subhourly scale. Most flash floods occur in ungauged basins, so model parameters and flooding thresholds will need to be quantified by observed streamflow and regionalized to ungauged points using geomorphologic properties, soil surveys, and land cover characteristics. Remote-sensing observations will continue to expand and inform spatially distributed forcings, parameter values, and model states to improve flash flood forecasts. Finally, flash flood forecasts largely describe the precipitation-driven natural hazard, and yet a majority of impacts involve significant contributions from social behavior. Terti et al. (2017) pointed out the dynamic nature of flash flood impacts; more than 90% of fatalities in the United States are a result of victims who were outside of their permanent residences or workplaces. Future research will cast flash flood forecasts into impact-based scenarios using dynamic vulnerability concepts.

# Acknowledgments

Funding for this work was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement #NA11OAR4320072, US Department of Commerce. The authors appreciate the inputs provided by Manuel Antonetti, Massimiliano Zappa, Marco Borga, and Lorenzo Alfieri.

Alfieri, L., Berenguer, M., Knechtl, V., Liechti, K., Sempere-Torres, D., & Zappa, M. (2015). Flash flood forecasting based on rainfall thresholds. In Q. Duan, F. Pappenberger, J. Thielen, A. Wood, H. Cloke, & J. Schaake (Eds.), Handbook of hydrometeorological ensemble forecasting (pp. 1–38). Berlin, Heidelberg: Springer.Find this resource:

Wood, E. F., Roundy, J. K., Troy, T. J., van Beek, L. P. H., Bierkens, M. F. P., Blyth, E., . . ., Whitehead, P. (2011). Hyperresolution global land surface modeling: Meeting a grand challenge for monitoring Earth’s terrestrial water. Water Resource Research, 47, W05301.Find this resource:

## References

Alfieri, L., Burek, P., Dutra, E., Krzeminski, B., Muraro, D., Thielen, J., & Pappenberger, F. (2013). GloFAS—global ensemble streamflow forecasting and flood early warning. Hydrology and Earth System Sciences, 17, 1161–1175.Find this resource:

Alfieri, L., Pappenberger, F., & Wetterhall, F. (2014). The extreme runoff index for flood early warning in Europe. Natural Hazards Earth System Sciences, 14(6), 1505–1515Find this resource:

Alfieri, L., & Thielen, J. (2015). A European precipitation index for extreme rainstorm and flash flood early warning. Meteorological Applications, 22(1), 3–13.Find this resource:

Alfieri, L., Velasco, D., & Thielen, J. (2011). Flash flood detection through a multi-stage probabilistic warning system for heavy precipitation events. Advances in Geosciences, 29, 69–75.Find this resource:

Antonetti, M., Buss, R., Scherrer, S., Margreth, M., & Zappa, M. (2016). Mapping dominant runoff processes: An evaluation of different approaches using similarity measures and synthetic runoff simulations. Hydrology and Earth System Sciences, 20, 2929–2945.Find this resource:

Arthur, A., Cox, G., Kuhnert, N., Slayter, D., & Howard, K. (2005). The National Basin Delineation Project. Bulletin of the American Meteorological Society, 86, 1443–1452.Find this resource:

Ashley, S., & Ashley, W. (2008). Flood fatalities in the United States. Journal of Applied Meteorology and Climatology, 47, 806–818.Find this resource:

Breiman, L. (2001). Random forests. Machine Learning, 45, 5–31.Find this resource:

Burnash, R. J. C., Ferral, R. L., & McGuire, R. A. (1973). A general streamflow simulation system—Conceptual modeling for digital computers. Technical report to the Joint Federal and State River Forecast Center, US National Weather Service and California Department of Water Resources, Sacramento, CA.Find this resource:

Carpenter, T., Sperfslage, J., Georgakakos, K., Sweeney, T., & Fread, D. (1999). National ThreshR estimation utilizing GIS in support of operational flash flood warning systems. Journal of Hydrology, 224, 21–44.Find this resource:

Clark, R. A. (2016). Machine learning predictions of flash floods (Doctoral Dissertation). School of Meteorology, University of Oklahoma, Norman, OK.Find this resource:

Clark, R. A., Flamig, Z. L., Vergara, H., Hong, Y., Gourley, J. J., Mandl, D. J., . . ., Patterson, M. (2017). Hydrological modeling and capacity building in the Republic of Namibia. Bulletin of the American Meteorological Society, 98, 1697–1715.Find this resource:

Clark, R. A., Gourley, J. J., Flamig, Z. L., Hong, Y., & Clark, E. (2014). CONUS-wide evaluation of National Weather Service flash flood guidance products. Weather and Forecasting, 29, 377–392.Find this resource:

Corral, C., Velasco, D., Forcadell, D., & Sempere-Torres, D. (2009). Advances in radar-based flood warning systems. The EHIMI system and the experience in the Besòs flash-flood pilot basin. In P. Samuels, S. Huntington, W. Allsop, & J. Harrop (Eds.), Flood risk management: Research and practice (pp. 1295–1303). London: Taylor & Francis.Find this resource:

Davis, R. (2007). Detecting the entire spectrum of stream flooding with the Flash Flood Monitoring and Prediction (FFMP) program. Preprints, 21st Conference on Hydrology, San Antonio. American Meteorological Society, 6B.1. Available online at https://ams.confex.com/ams/pdfpapers/28589.pdf.Find this resource:

Doswell, C., Brooks, H., & Maddox, R. (1996). Flash flood forecasting: An ingredients-based methodology. Weather and Forecasting, 11, 560–581.Find this resource:

Georgakakos, K. P. (1986). A generalized stochastic hydrometeorological model for flood and flash-flood forecasting. 1. Formulation. Water Resource Research, 22, 2083–2095.Find this resource:

Georgakakos, K. P. (2006). Analytical results for operational flash flood guidance. Journal of Hydrology, 317, 81–103.Find this resource:

George, J. (1960). Weather forecasting for aeronautics. New York: Academic Press.Find this resource:

Gochis, D. J., Yu, W., & Yates, D. N. (2015). The WRF-Hydro model technical description and user’s guide, version 3.0. NCAR techical documentation. Available online at www.ral.ucar.edu/projects/wrf_hydro/.Find this resource:

Gourley, J. J., Erlingis, J., Hong, Y., & Wells, E. (2012). Evaluation of the tools used for monitoring and forecasting flash floods in the United States. Weather and Forecasting, 27, 158–173.Find this resource:

Gourley, J. J., Flamig, Z., Vergara, H., Kirstetter, P. Clark, R. III, Argyle, E., . . ., Howard, K. (2017). The Flooded Locations And Simulated Hydrographs (FLASH) project: Improving the tools for flash flood monitoring and prediction across the United States. Bulletin of the American Meteorological Society, 98, 361–372.Find this resource:

Gourley, J. J., Hong, Y., Flamig, Z. L., Arthur, A., Clark, R. A., . . ., W. F. Krajewski (2013). A unified flash flood database across the United States. Bulletin of the American Meteorological Society, 94, 799–805.Find this resource:

Green, W. H., & Ampt, G. (1911). Studies of soil physics, part I—the flow of air and water through soils. Journal of Agricultural Science, 4, 1–24.Find this resource:

Javelle, P., Demargne, J., Defrance, D., Pansu, P., & Arnaud, P. (2014). Evaluating flash-flood warnings at ungauged locations using post-event surveys: A case study with the AIGA warning system. Hydrological Sciences Journal, 59(7), 1390–1402.Find this resource:

Javelle, P., Fouchier, C., Arnoud, P., & Lavabre, J. (2010). Flash flood warning at ungauged locations using radar rainfall and antecedent soil moisture estimations. Journal of Hydrology, 394, 267–274.Find this resource:

Kohavi, R., & Provost, F. (1998). Glossary of terms: Special issue on applications of machine learning and the knowledge discovery process. Machine Learning, 30, 271–274.Find this resource:

Koren, V., Smith, M., Wang, D., & Zhang, Z. (2000). Use of soil property data in the derivation of conceptual rainfall-runoff model parameters. Preprints, 15th Conference on Hydrology, Long Beach, CA. American Meteorological Society, 103–106.Find this resource:

Maddox, R. (1980). Mesoscale convective complexes. Bulletin of the American Meteorological Society, 61, 1374–1387.Find this resource:

Maddox, R. A., Chappell, C. F., & Hoxit, L. R. (1979). Synoptic and meso-α‎ scale aspects of flash flood events. Bulletin of the American Meteorological Society, 60, 115–123.Find this resource:

Martinaitis, S. M., Gourley, J. J., Flamig, Z. L., Argyle, E. M., Clark, R. A., Arthur, A., . . ., Albright, B. (2017). The HMT Multi-Radar Multi-Sensor Hydro Experiment. Bulletin of the American Meteorological Society, 98, 347–359.Find this resource:

Mogil, H., Monro, J., & Groper, H. (1978). NWS’s flash flood warning and disaster preparedness programs. Bulletin of the American Meteorological Society, 59, 690–699.Find this resource:

Moore, R. (1985). The probability-distributed principle and runoff production at point and basin scales. Hydrological Science Journal, 30, 273–297.Find this resource:

Norbiato, D., Borga, M., Degli Esposti, S., Gaume, E., & Anquetin, S. (2008). Flash flood warning based on rainfall thresholds and soil moisture conditions: An assessment for gauged and ungauged basins. Journal of Hydrology, 362(3), 274–290.Find this resource:

Norbiato, D., Borga, M., & Dinale, R. (2009). Flash flood warning in ungauged basins by use of the flash flood guidance and model-based runoff thresholds. Meteorological Applications, 16, 65–75.Find this resource:

Ntelekos, A. A., Krajewski, W. F., & Georgakakos, K. P. (2006). On the uncertainties of flash flood guidance: towards probabilistic forecasting of flash floods. Journal of Hydrometeorology, 7, 896–915.Find this resource:

Parlange, J.-Y., Lisle, I., Braddock, R. D., & Smith, R. E. (1982). The three-parameter infiltration equation. Soil Science, 133(6), 337–341.Find this resource:

Perica, S., Martin, D., Pavlovic, S., Roy, I., St. Laurent, M., Trypaluk, C., . . ., Bonnin, G. (2013). Precipitation-frequency atlas of the United States, Vol. 9, Version 2.0. US Department of Commerce, National Oceanic and Atmospheric Association (NOAA), and National Weather Service (NWS). Available online at http://www.nws.noaa.gov/oh/hdsc/PF_documents/Atlas14_Volume9.pdf.Find this resource:

Raynaud, D., Thielen, J., Salamon, P., Burek, P., Anquetin, S., & Alfieri, L. (2015). A dynamic runoff co-efficient to improve flash flood early warning in Europe: Evaluation on the 2013 central European floods in Germany. Meteorological Applications, 22(3), 410–418.Find this resource:

Reed, S., Johnson, D., & Sweeney, T. (2002). Application and national geographic information system database to support two-year flood and ThreshR estimates. Journal of Hydrology Engineering, 7, 209–219.Find this resource:

Reed, S., Schaake, J., & Zhang, Z. (2007). A distributed hydrologic model and threshold frequency-based method for flash flood forecasting at ungauged locations. Journal of Hydrology, 337, 402–420.Find this resource:

RFC Development Management Team. (2003). Flash Flood Guidance Improvement Team—Final report. River Forecast Center Development Management Team Report to the Operations Subcommittee of the NWS Corporate Board. Available online at http://www.nws.noaa.gov/oh/rfcdev/docs/ffgitreport.pdf.Find this resource:

Rozalis, S., Morin, E., Yair, Y., & Price, C. (2010). Flash flood prediction using an uncalibrated hydrological model and radar rainfall data in a Mediterranean watershed under changing hydrological conditions. Journal of Hydrology, 394, 245–255.Find this resource:

Schaffner, M., Tardy, A., Dandrea, J., Unkrich, C., Goodrich, D., & Laber, J. (2017). Operational success with distributed modeling to inform flash flood warning operations at weather forecast office, San Diego. Technical Attachment No. 17–02, National Weather Service (NWS), Western Region. Available online at http://www.weather.gov/media/wrh/online_publications/TAs/TA1702.pdf.

Scherrer, S., & Naef, F. (2003). A decision scheme to indicate dominant hydrological flow processes on temperate grassland. Hydrological Processes, 7, 391–401.Find this resource:

Schmidt, J., Anderson, A., & Paul, J. (2007). Spatially-variable, physically-derived, flash flood guidance. Preprints, 21st Conference on Hydrology, San Antonio, American Meteorological Society, 6B.2. Available online at https://ams.confex.com/ams/pdfpapers/120022.pdf.Find this resource:

Sideris, I. V., Gabella, M., Erdin, R., & Germann, U. (2014). Real-time radar–rain-gauge merging using spatio-temporal co-kriging with external drift in the alpine terrain of Switzerland. Quarterly Journal of the Royal Meteorological Society, 140, 1097–1111.Find this resource:

Smith, G. (2003). Flash flood potential: Determining the hydrologic response of FFMP basins to heavy rain by analyzing their physiographic characteristics. Report to the NWS Colorado Basin River Forecast Center. Available online at http://www.cbrfc.noaa.gov/papers/ffp_wpap.pdf.Find this resource:

Smith, R. E., & Parlange, J.-Y. (1978). A parameter-efficient hydrologic infiltration model. Water Resource Research, 14(3), 533–538.Find this resource:

Smith, R. E., Smettem, K. R. J., Broadbridge, P., & Woolhiser, D. A. (2002). Absorption and infiltration relations and the infiltrability-depth approximation. In Infiltration Theory for Hydrologic Applications. Water Resources Monograph Series (Vol. 15, pp. 63–96). Washington, DC: American Geophysical Union.Find this resource:

Sweeney, T. (1992). Modernized areal flash flood guidance. NOAA Technical Report NWS HYDRO 44, NOAA/NWS/Hydrologic Research Laboratory, Silver Spring, MD.Find this resource:

Sweeney, T., & Baumgardner, T. (1999). Modernized flash flood guidance. Report to NWS Hydrology Laboratory. Available online at http://www.nws.noaa.gov/oh/hrl/ffg/modflash.htm.Find this resource:

Tabary, P. (2007). The new French operational radar rainfall product. Part I: methodology. Weather and Forecasting, 22(3), 393–408.Find this resource:

Tan, P.-N., Steinbach, M., & Kumar, V. (2005). Introduction to data mining. Boston: Addison-Wesley.Find this resource:

Terti, G., Ruin, I., Anquetin, S., & Gourley, J. (2017). A situation-based analysis of flash flood fatalities in the United States. Bulletin of the American Meteorological Society, 98, 333–345.Find this resource:

Terti, G., Ruin, I., Anquetin, S., & Gourley, J. J. (2015). Dynamic vulnerability factors for impact-based flash flood prediction. Natural Hazards, 79, 1481–1497.Find this resource:

Thielen, J., Bartholmes, J., Ramos, M. H., & de Roo, A. P. J. (2009). The European flood alert system—part 1: Concept and development. Hydrology and Earth System Sciences, 13, 125–140.Find this resource:

van der Knijff, J. M., Younis, J., & de Roo, A. (2010). A GIS-based distributed model for river basin scale water balance and flood simulation. International Journal of Geographical Information Science, 24, 189–212.Find this resource:

Vergara, H., Kirstetter, P. E., Gourley, J. J., Flamig, Z. F., Hong, Y., Arthur, A., & Kolar, R. L. (2016). Estimating a-priori kinematic wave model parameters based on regionalization for flash flood forecasting in the conterminous United States. Journal of Hydrology, 541, 421–433.Find this resource:

Versini, P., Berenguer, M., Corral, C., & Sempere-Torres, D. (2014). An operational flood warning system for poorly gauged basins: Demonstration in the Guadalhorce basin (Spain). Natural Hazards, 71, 1355–1378.Find this resource:

Villarini, G., Krajewski, W. F., Ntelekos, A. A., Georgakakos, K. P., & Smith, J. A. (2010). Towards probabilistic forecasting of flash floods: The combined effects of uncertainty in radar-rainfall and flash flood guidance. Journal of Hydrology, 394, 275–284.Find this resource:

Vincendon, B., Ducrocq, V., Nuissier, O., & Vié, B. (2011). Perturbation of convection-permitting NWP forecasts for flash-flood ensemble forecasting. Natural Hazards and Earth Systems, 11, 1529–1544.Find this resource:

Viviroli, D., Zappa, M., Gurtz, J., & Weingartner, R. (2009). An introduction to the hydrological modelling system PREVAH and its pre- and post-processing-tools. Environmental Modelling Software, 24(10), 1209–1222.Find this resource:

Wang, J., Hong, Y., Li, L., Gourley, J. J., Khan, S. I., Yilmaz, K. K., . . ., Okello, L. (2011). The coupled routing and excess storage (CREST) distributed hydrological model. Hydrological Sciences Journal, 56, 84–98.Find this resource:

Williams, J. (2014). Using random forests to diagnose aircraft turbulence. Machine Learning, 95, 51–70.Find this resource:

Zhang, J., Howard, K., Langston, C., Kaney, B., Qi, Y., Tang, L., . . ., Kitzmiller, D. (2016). Multi-Radar Multi-Sensor (MRMS) quantitative precipitation estimation: Initial operating capabilities. Bulletin of the American Meteorological Society, 97, 621–638.Find this resource: