1. Introduction

As with other convective weather hazards, inland flash flooding poses a significant forecasting and warning challenge that is made worse by its severe consequences on life, property, and agriculture. Reduction of this impact has come from advances in the understanding of the precipitation extremes that contribute to such flooding. Extreme rainfall is most often identified and studied in terms of 24-h rainfall accumulations (Bradley and Smith 1994; Konrad 2001; Schumacher and Johnson 2005, 2006; Silva and Berbery 2006; Smith et al. 1994), owing in part to a broader availability of data, especially from cooperative rain gauge networks (Hammer and Steurer 2003). For instance, Bradley and Smith (1994) used daily accumulation data from gauges to define extreme events and then further classified the events according to the strength of the larger-scale dynamical forcing.

Further advances have been made from studies relating extreme precipitation events to the type of precipitating weather systems responsible for the event. Recently, Schumacher and Johnson (2005) linked mesoscale convective systems (MCSs) and mesoscale convective complexes (MCCs) to daily extremes in the United States. Using hourly gauge data to examine the events more closely, and radar data for classification purposes, they found that about 65% of all the events were the result of MCSs, whereas 25% were driven by synoptic-scale processes. Other modes of cumulus convection—namely, supercell thunderstorms—have also been shown to generate extreme amounts of rainfall (Bauer-Messmer et al. 1997; Smith et al. 2001). Bauer-Messmer et al. (1997) concluded that rainfall at time scales <1 h are critical to flash-flood response.

Beyond operational forecasting and warning issues is the potential impact of anthropogenic global warming on precipitation extremes. Trends in observational data as well as climate model simulations have been used to project future increases in both the frequency and intensity of daily extremes (e.g., Chen et al. 2005; Emori and Brown 2005; Groisman et al. 2005; Hennessy et al. 1997; Karl and Knight 1998; Wilby and Wigley 2002). Whether or not these projections also apply to extremes at shorter time scales is an open question and, indeed, Trenberth (1998, 1999) and Trenberth et al. (2003) have recommended a closer examination of extreme precipitation at an hourly temporal scale in both observations and climate models. We follow this recommendation herein with our focus on subdiurnal extreme precipitation, as guided by the following, overarching questions: Do the convective cloud systems that produce extreme subdiurnal precipitation have unique characteristics, and are these events predictable?

Our motivation stems from the limited research to date on short time-scale rainfall extremes. Important contributions have been made by Winkler et al. (1988), who considered hourly rainfall in the conterminous United States by using the National Climatic Data Center’s (NCDC) hourly precipitation dataset (HPD), gridded into cells with a horizontal dimension of 75 km × 75 km. Hourly precipitation was binned into four categories, the largest of which was for rainfall of ≥1.00 in. h⁻¹ (25.4 mm h⁻¹). Although regional variation existed, extreme hourly precipitation was found to occur later in the day, with this being more pronounced in the summer season. Similarly, Brooks and Stensrud (2000) examined the frequency of heavy rainfall using the HPD. They found a peak during June–August in hourly precipitation ≥1.00 in. for much of the United States.

A concern expressed by Brooks and Stensrud (2000) is that the HPD is not adequate to resolve the spatial distribution of subdiurnal extreme precipitation events due to the coarse distribution of the gauge network (e.g., Bauer-Messmer et al. 1997; Smith et al. 1994). On the other hand, the national network of Weather Surveillance Radar-1988 Doppler (WSR-88D) radars provides derived rainfall products for a nearly continuous spatial domain, although these products are not without their own biases, for example (Fulton et al. 1998). A synthesis of these two precipitation datasets is available in a product produced by the National Centers for Environmental Prediction (NCEP) known as stage II and stage IV rainfall analysis (Fulton et al. 1998). These data are available hourly as a mosaic covering the conterminous United States in a 4 km × 4 km grid. The present study makes use of the HPD as well as the stage II/IV data to identify and characterize precipitating systems that produce subdiurnal extreme precipitation.

This research is the first component of the multistage project mentioned earlier, with the ultimate goal of assessing the predictability of subdiurnal extreme-precipitation-producing systems. To meet this goal, a methodology to quantify the characteristics of these systems needs to be established. Accordingly, a sample set of subdiurnal extreme precipitation events are identified using the HPD and subsequently characterized from stage II or stage IV precipitation data.

A description of HPD analysis procedures, including our definition of an extreme, is presented in section 2. In section 3, we couple the results of the HPD analysis to an analysis of stage II/IV data and characterize the precipitating systems associated with subdiurnal precipitation extremes. Two case studies are presented in section 4 to further illustrate such characteristics, and concluding remarks and future work are given in the last section.

2. Rain gauge analysis

Rain gauge stations that were continuously operating during the period 1956–2005 are considered for this study. We focus on the midwestern region of the United States, and 48 gauges are chosen to sample a broad area across this region (Fig. 1). The reason for the focus on the midwestern region is because of the lack of significant terrain in the area and the lack of tropical influences on the precipitation regime. This area is also well sampled by the stage II/IV precipitation product, and the region contains many agricultural areas that are affected by extreme precipitation events. These data required some initial preprocessing. First, data values are rounded to the nearest tenth of an inch, in response to an instrumentation change in most gauges in the 1960s that resulted in a subsequent decrease in recording precision from hundredths to tenths of inches. Second, erroneously large data values (>4 in.) with no data in the hour preceding or following the large value are removed (see Brooks and Stensrud 2000).

Each 50-yr time series is fit to the generalized Pareto distribution (GPD), and exceedances over a high threshold are chosen by standard threshold selection techniques (e.g., Coles 2001). The GPD is used in favor of the generalized extreme value (GEV) distributions because the GEV uses a block maxima approach to fit the observations instead of the peak-over-threshold approach used by the GPD. The block maxima approach limits the number of observations used, whereas the peak-over-threshold approach is preferred in this study because it uses any observation that exceeds the threshold. To investigate precipitation at other subdiurnal time frames, the observations in an HPD time series are grouped into consecutive 3-h periods [0000–0300 local standard time (LST), 0400–0600 LST, and so on], 6-h periods (0000–0600 LST, 0700–1200 LST, and so on), and 12-h periods (0000–1200 LST, and so on), and 10-yr return levels are calculated for each of these groupings of observations (Table 1). A moving-window approach was considered to construct the observation periods but was dismissed. However, the issue of underestimation based on window selection as well as other aspects of defining extreme events from the HPD will be more carefully explored in future work, based on reliable estimates of the tail index (e.g., Qi 2008), a key parameter in predicting extreme events. Using these return levels, an extreme precipitation event is defined as a 6-h period that surpasses the respective 10-yr return level at a gauge. The choice of a 6-h period follows the upper-temporal boundary for events that commonly produce flash flooding (NOAA 2006).

Over the 48 gauges, the return levels for 6-h events range from 54 to 94 mm. In general, the return levels are lower in the states that are farther north (Michigan, Minnesota, Wisconsin) as well as in Ohio, which is the easternmost state. During the 50-yr period of study, there are a total of 336 events that surpass the return level for 6-h events. Furthermore, 78% of the 6-h extreme events contain a period that also qualifies as a 3-h event, and 71.8% of the events that meet the criteria for both 3- and 6-h events are part of a 12-h event.

If each 6-h extreme event is analyzed by hour (the highest one hour of precipitation, the highest two consecutive hours of precipitation, and so on), as in Fig. 2, it is seen that on average the hour with the highest precipitation accounts for nearly half of the total rainfall. Likewise, the 2-h period of highest precipitation accounts for 71% of the total accumulated rainfall during the 6-h event.

3. Stage II/IV precipitation analysis

In this section, we consider only those extreme precipitation events that additionally have corresponding stage II/IV precipitation data, which are available beginning May 1996 (January 2002 for stage IV). Of the 336 total gauge events, 36 meet this additional criterion. As indicated in Table 2, each event occurs on a different date, hence they are treated here as independent samples.

The stage II/IV data are analyzed at the hour of peak precipitation at the gauge, as well as for several hours preceding and following the peak hour, using the Baldwin object identification algorithm (BOIA; Baldwin et al. 2005). This algorithm forms precipitation “objects” from pixels with values over a user-defined threshold (Figs. 3a,b). For the purpose of this study, the threshold is 6 mm hr⁻¹, which is considered the lower bounds for convective rainfall (Johnson and Hamilton 1988). Objects are constrained by a user-defined search radius, defined here as one pixel, which has physical dimensions of 4 km × 4 km. Hence, areas of pixels with no more than a single-pixel gap are grouped into objects (Figs. 3b,c). A 1-pixel search radius is used with the BOIA to identify objects to study only the area of intense rainfall that was directly affecting the gauge. A larger search radius may include areas of precipitation in the object that are being influenced by different processes. The BOIA then diagnoses attributes of these objects, such as size (area); precipitation mean, maximum, and variance; and centroid location.

The characteristics of precipitating systems associated with the gauge extremes are revealed by the attributes of the objects affecting the gauge location at the time of peak event precipitation (Table 2). For example, the size of these objects varies between 34 480 and 96 km², with a mean of 8054 km². As a point of reference, an MCC has an interior cloud shield (satellite IR brightness temperature ≤−52°C) with an area ≥50 000 km², which corresponds to its convective region (Maddox 1980). Hence, morphologically, the associated precipitating systems range from MCCs and large MCSs to much smaller, relatively isolated, and slow-moving convective storms (see section 4). These smaller systems, and thus smaller objects, may pose challenges for predictability, whereas larger systems present a potential for more widespread flooding.

The size of the object and hence precipitating system would appear to relate to the object’s precipitation characteristics. In comparing the size of an object at the time of peak precipitation at the gauge to the maximum object precipitation (Fig. 4), there is a moderately positive trend in the data (R² value of 0.3), suggesting that larger objects have a higher amount of maximum precipitation. Object size also correlates positively to precipitation variance, because maximum precipitation relates nearly linearly to variance (Table 2). It should be noted that discrepancies between the gauge maximum precipitation and the corresponding object’s maximum precipitation value are partly because of spatial offsets between the gauge location and the location of the object maximum and also because of quality control procedures performed during the processing of stage II and stage IV data, effectively dampening these object maxima.

4. Case studies

In this section, we highlight two of the events in our database that illustrate the range of association between a gauge extreme and its corresponding precipitation object.

5. Conclusions

The goal of this work was to establish a methodology to identify and characterize extreme subdiurnal precipitation events, which ultimately will be used toward the assessment of the predictability of subdiurnal extreme-precipitation-producing systems. Such systems are capable of generating inland flash floods, which pose a significant hazard to life, property, and agriculture. HPD data were examined to define thresholds for extreme events at selected locations. An extreme precipitation event is one in which precipitation exceeded the 10-yr return level over a 6-h period. Our analysis revealed that the majority of precipitation in these subdiurnal extremes fell over one or two hours. We suggest here the possibility that many of the extreme events defined by daily accumulations are also influenced heavily by precipitation over a few hours.

Those events that had corresponding stage II/IV data were examined further using the BOIA, with object attributes compiled at the hour of peak gauge precipitation. The use of the BOIA is a unique approach for the quantitative and objective characterization of precipitating systems, and it showed that the size (area) and maximum precipitation of the systems varied strongly across the events. In particular, some events featured relatively small, isolated, convective storms that likely would not have been considered in other classification schemes. The analyses of the sample events for which stage II/IV precipitation data are available provide basic characteristics for these events—information which is currently unknown.

This study has built on the work of Brooks and Stensrud (2000), Schumacher and Johnson (2006), Smith et al. (2001), Winkler et al. (1988), and others, and serves as an important next step in characterizing subdiurnal extreme precipitation events. It is important to emphasize that the current study did not attempt to identify extreme precipitating systems per se but rather sought to characterize those systems that produced extreme precipitation at specific point locations. Hence, one branch of our future research will be devoted to the identification of extreme systems, through the use of the BOIA. We will also attempt to relate these events to the larger-scale forcing, and to explore their predictability, by way of high-resolution model simulations.