1. Introduction

Flash flooding causes more deaths annually than any other weather phenomenon, killing over 1000 United States citizens over the 10-yr period 1983–92 (U.S. Army Corps of Engineers 1993). Flash flooding has significant economic impacts as well, causing an average of greater than $2 billion in annual losses over the same 10-yr period (U.S. Army Corps of Engineers 1993). In a study of 151 flash flood events over a 5-yr period, Maddox et al. (1979) found that a large majority (86%) occurred during the warm season months of April–September, with the peak (38 events, 25% of the total) occurring in July. Maddox et al. (1979) also found a distinct nocturnal nature to the events that occurred over the eastern two-thirds of the country.

These statistics highlight two disturbing forecast problems related to flash flood forecasting. First, the nocturnal nature of the majority of flash flood events makes it difficult for watches and warnings to reach a large portion of the intended audience (Maddox et al. 1979). For example, the devastating Johnstown, Pennsylvania, flash flood event of 19–20 July 1977 that killed more than 70 people was a late night event that began at approximately 2200 local time (NCDC 1977). Second, the warm season dominance of flash flood events, coupled with numerical models’ relatively poor precipitation forecasts during the warm season (Funk 1991), makes flash flood forecasting particularly challenging.

Although there are relatively few studies that examine a mesoscale numerical model’s ability to simulate flash flood events adequately, those that have been completed have shown some limited success. For example, although an 18-h simulation of the Johnstown, Pennsylvania, flood by Zhang and Fritsch (1986) using The Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR)Mesoscale Model generated a precipitation distribution similar to that observed, they included special observations in the model initialization that are not typically available from the regular observational network. Similarly, Zheng et al. (1995) found that they could not successfully simulate a flood-producing mesoscale convective system (MCS) in northwestern Oklahoma with standard observations alone. Only through a dynamic assimilation approach, that also included special field program observations, were they able to produce a good simulation of the MCS. Without special observations, the Zhang et al. (1989) simulation of an intense squall line produced precipitation fields that were “generally favorable” when compared to observations. Bresch (1991) used a mesoscale model (version 4 of the PSU–NCAR model; MM4) to simulate an MCS and found that the model was able to simulate the general area of heavy rainfall. However, Bresch speaks less favorably of the model’s ability to simulate the details of the event by stating that “some of the details of the rainfall pattern . . . including the heavy rainfall maximum were not simulated accurately.” Sénési et al. (1996) simulated a significant flash flood event that occurred in southeastern France using different versions of two numerical models and generally found that each simulation overestimated areas of light precipitation and underestimated areas of heavy precipitation, a well-known behavior among numerical simulations. They conclude that a simulation from a high-resolution (10-km grid spacing) model provides the most realistic chronology and spatial distribution of the rainfall, although it generated only a “relatively precise” rainfall maximum.

One important reason for the difficulties associated with quantitative precipitation forecasts (QPFs) is that in order for numerical models to produce a good QPF, they must predict accurately the development and evolution of convection. Kain and Fritsch (1992) and Stensrud and Fritsch (1994b) have shown that the simulations of convectively generated mesoscale patterns show considerable sensitivity to the formulation of the trigger function¹ within a convective parameterization scheme. Furthermore, Kain and Fritsch (1992) show that the simulation is sensitive not only to the specific trigger function formulation, but to the imposed values of functional parameters within a given formulation as well. Kuo et al. (1996) and Wang and Seaman (1997) observed model sensitivities to differences in the actual construction of the convective parameterization scheme. Kuo et al. (1996) found that the distribution and intensity of precipitation were“extremely sensitive” to the choice of the cumulus parameterization scheme. Thus, it is clear that the success of QPF is intimately related not only to the timing of the model convection, but also to the ability of the convective scheme to simulate the effects of deep, moist convection upon its surroundings. This is especially true for the warm season when a large fraction of the precipitation is associated with MCSs (Charba and Klein 1980; Fritsch et al. 1986).

The presence of steep topography often complicates the flash flood forecast problem by modulating weather systems and precipitation patterns. Hill (1993) discusses the dual role of orography in the western United States as it relates to flash flood forecasting. Given favorable flow patterns, the mountains may aid in producing heavy rainfall through orographic lift of potentially unstable air or they may assist in setting up long-lived, stationary low-level convergence zones that provide a source for new convection to develop. Akaeda et al. (1995) performed a numerical simulation of the flow around the island of Taiwan in the presence of surface heating and indeed found a persistent, quasi-stationary area of convergence in the foothills near the location of observed flash flood–producing convection. Katzfey (1995) used a hydrostatic mesoscale model to simulate three extreme precipitation events that occurred over the South Island of New Zealand and found that orography had a strong influence on the amount of precipitation. Two of the three cases were “quite successfully simulated” by the model, generally capturing the location and timing of the heavy precipitation. Further improvements were gained in the simulated precipitation when the orography was more realistic and the horizontal resolution increased.

In the absence of significant terrain features, details in the model initial conditions are sometimes necessary for the success of numerical simulations. Stensrud and Fritsch (1994a) used a mesoscale model to simulate MCSs developing in regions of weakly forced large-scale environments. They showed that by subjectively altering the mesoscale model’s initial conditions by creating artificial stations and soundings that include mesoscale details in high-gradient regions, a more accurate evolution of events is simulated than when the initial conditions are not altered to include mesoscale details. Specifically, the rainfall magnitudes and locations of heavy rainfall compare more favorably with observations when the mesoscale details are incorporated into the initial conditions. Zhang and Fritsch (1986) also discuss how the timing, location, and magnitude of mesoscale features within a mesoscale model simulation are subject to large errors when important mesoscale details are missing from the model’s initial conditions.

Although there have been some studies of flash floods in regions of strong terrain gradients, there have been few in regions of relatively flat terrain. By simulating six of these events, we hope to explore the ability of a mesoscale model to produce the conditions necessary in order to develop heavy, persistent rainfall: high rainfall rate and long duration.² In the present study, we investigate a mesoscale model’s ability to simulate six flash flood events that occurred across the central and eastern United States. Of particular interest are the model’s 1) placement and magnitude of heaviest rainfall compared to observations, 2) general distribution of rainfall, and 3) ability to generate heavy precipitation for long periods of time over a particular region. It is believed that these aspects of model performance are closely related to the formulation of the convective scheme, particularly to the imposed values of precipitation efficiency and the parameterization of convective downdrafts. The goals of this study are to explore model sensitivity to these two components as it relates to the simulation of heavy rainfall and to determine those aspects of convective schemes that deserve foremost attention as attempts to further enhance model QPF proceed. To do this, we develop three simple modifications to the chosen convective scheme, each designed to test model sensitivity to precipitation efficiency or convective downdraft strength. Model simulations using each of the convective scheme modifications (as well as the unmodified version) are performed for each of the six flash flood cases.

In section 2, the general framework and model physical parameterizations are outlined, including descriptions of three modifications to the convective scheme. Section 3 provides a brief overview of the six flash flood events under consideration. Section 4 contains a detailed case study illustration of one of the events that highlights the model’s sensitivity to details of the convective parameterization scheme, while section 5 provides an overview and simulation results for the remaining five cases. Section 6 discusses the impact that incorporating mesoscale details into the model initial conditions has on a model simulation. Finally, section 7 contains a summary and discussion.

2. Model description

The numerical model chosen for use in this study is the hydrostatic PSU–NCAR three-dimensional mesoscale model, MM4 (Anthes and Warner 1978; Anthes et al. 1987). Described below are the model framework and the parameterization schemes used in the simulations, including descriptions of the modifications that are made to the convective parameterization scheme.

3. Overview of six flash flood events

The six flash flood events under consideration represent a seasonally and geographically diverse dataset (Table 2). Each of the cases has 24-h accumulated precipitation reports of at least 127 mm (5 in.), whereas half of the cases have 24-h reports exceeding 229 mm (9 in.), which are representative of the heaviest rainfall totals found in flash flood events studied by Maddox et al. (1979). Descriptions of four of the six events can be found in the literature (Elsner et al. 1989, AUG86; Schwartz et al. 1990, JUL87; Doswell et al. 1996, SEP89; National Weather Service 1991, JUN90) and are not repeated in detail here. However, for completeness, a brief description follows of important synoptic and mesoscale features for the events, as well as a classification according to the Maddox et al. (1979) criteria.

Three of the events (SEP89, NOV92, NOV93) fit the“synoptic” event classification (Table 2). For these cases, a relatively intense synoptic-scale low pressure system is located several hundred kilometers north of the location of the flash flooding. A slow-moving surface front extends southwestward from the surface low. Low-level southerly winds advect relatively warm, moist air toward the frontal boundary and into the region fueling thunderstorm activity. Winds aloft typically have a large component parallel to the low-level frontal zone, such that the cloud layer mean winds are roughly parallel to the front and conducive for the development of train echoes (a series of convective storms that move over the same area).

The AUG86 case is classified as a “frontal” event, although Elsner et al. (1989) indicate that the event may not fit into the Maddox et al. (1979) classification. This event is consistent with the “frontal” classification in that the convection develops on the cool side of a slow-moving east–west-oriented surface front as warm, unstable low-level air flows over the frontal boundary. Winds aloft are weak and are generally oriented along the frontal zone.

The final two cases (JUL87, JUN90) are classified as“mesohigh” events. For both of these flash flood events, convective outflow from previous convection acts to focus thunderstorm development that leads to flash flood–producing rainfall. It is the interaction of the convectively induced cold pool with the influx of warm, moist low-level air that appears to be crucial in creating this type of flash flood event. Prediction of flash flooding is particularly challenging for events such as these in which low-level mesoscale features play such a vital role in the development and organization of thunderstorm activity (Stensrud and Fritsch 1994a,b).

4. Case study illustration: 7–8 September 1989

During the morning hours of 7 September, low-level southerly winds are advecting warm, moist air into parts of eastern Nebraska and southwestern Iowa just ahead of a surface front (Fig. 1). A convective outflow boundary from ongoing convection extends across eastern Nebraska and southern Iowa. A nearby sounding indicates the presence of a shallow moist layer capped by a 200-mb-deep layer of dry air, suggestive of strong convective downdraft potential (Fig. 2). A midtropospheric low pressure area is located across southern Canada, while Iowa is under a ridge axis characterized by moderate west-southwesterly flow (not shown).

Radar summaries (not shown) indicate that early morning convection across Iowa on 7 September gradually decreases in coverage and intensity and by midday the precipitation has mostly ended, leaving behind a weak surface mesohigh. As warm, moist low-level air moves northward, destabilization occurs across Iowa and Nebraska. At around 0200 UTC 8 September, severe convection develops across central Iowa and eastern Nebraska in the form of a squall line (Fig. 3) that moves slowly southeastward, resulting in flash flood–producing rainfall (Fig. 4).

The pattern of the 24-h precipitation totals from the simulation incorporating the unmodified version of the KF convective scheme (NOMOD; Fig. 5) is comparable to the observations, but the model amounts are much lower than observed and the model simulation fails to reproduce the two separate areas of heavy rainfall across Iowa. The model generates 77 mm in eastern Iowa with lesser amounts farther southwest. The maximum observed amount is nearly twice the simulated maximum. To understand why the NOMOD simulation is unable to reproduce accurately the heavy rainfall for this event, we consider the evolution of the model rainfall patterns and the associated convective outflow.

The 7-h (1900 UTC 7 September) lowest model level θ_e and wind field (Fig. 6a) show the southern edge of an outflow boundary extending from eastern Nebraska, across southern Iowa, and northward into Wisconsin. This boundary separates cool downdraft air from warmer air south and east of the outflow boundary. By this time, upward motion exceeding 16 μb s⁻¹ along the southward-moving boundary has helped to activate the convective trigger function and initiate new model precipitation across southern Iowa (Figs. 6a,b). Three hours later, strong upward motion along the leading edge of this convection’s cold pool (not shown) has, in turn, initiated further model convection into portions of northeastern Kansas and northern Missouri (Fig. 7). This rapid southward succession of outflow and new convection not only prohibits heavy rainfall from falling over a particular location for an extended period, but it also stabilizes eastern Nebraska and Iowa to the point that the evening convection that is reproduced over this region is much weaker than observed (cf. Fig. 3 and Figs. 8a,b). Our first attempt at examining model sensitivity is to maximize the precipitation efficiency within the KF scheme, thereby maximizing the convective precipitation and hopefully reducing the generation of convective downdrafts.

Precipitation totals from the MPE simulation show improvement over the NOMOD results (Fig. 9). The eastern Iowa maximum has increased to 93 mm and the area of >51 mm rainfall is larger than the NOMOD results and has an orientation much like that of the squall line. However, the rainfall maximum is still more than 51 mm (2 in.) less than the observed maximum and the MPE simulation fails to distinguish the two regions of heavy precipitation. By maximizing the PE within the limits of the KF scheme, convective downdraft potential is reduced, which limits (but does not eliminate) the movement of the convective region by repeated development along convective outflow boundaries. Indeed, even though MPE generates convection along previous outflow boundaries, the convection creates a less extensive and weaker cold pool than that generated by the NOMOD convection (not shown). The maximum value of rising motion along the leading edge of the outflow at 1900 UTC 7 September is 8.5 μb s⁻¹ (not shown), nearly 50% lower than found with the NOMOD simulation. This allows the model to develop a much stronger convective line across eastern Nebraska and central Iowa during the evening hours (cf. Figs. 10 and 8a). To explore the importance of convective downdrafts to the simulation, we next use the NDD version of the KF scheme.

Precipitation totals from the NDD simulation indicate that the elimination of subcloud convective downdrafts allows significant precipitation to accumulate across southeastern Nebraska, central Iowa, and southwestern Wisconsin (Fig. 11). In fact, the NDD precipitation maximum (170 mm) exceeds the observed maximum (150 mm). The large majority (>95%, in general) of the model precipitation is generated by the convective scheme rather than by grid-scale precipitation processes, highlighting the sensitivity of the precipitation field to the formulation of the convective parameterization scheme. In addition, the NDD simulation exaggerates the areal extent of the heavy precipitation (>51 mm) by about 500%, producing widespread heavy rainfall in a band that extends along the frontal boundary from Kansas to Wisconsin.

Heavy rainfall occurs in the NDD simulation because convective outflow is not allowed to reach the surface, stabilize the environment, and successively generate new convection progressively farther southward. For example, although the NDD 10-h precipitation field shows a broken line of cells extending from eastern Nebraska northeastward to Wisconsin (Fig. 12a), the low-level θ_e and wind patterns provide no indication of the presence of any significant outflow boundaries to stabilize the low levels (Figs. 12a,b). In fact, over the previous 3 h, the NDD simulation shows low-level θ_e values to have increased by nearly 8°C across southwestern Iowa as strong southerly winds continue to advect warm, moist air northward. The NDD 15-h precipitation field indicates a well-developed squall line across Nebraska and central Iowa (Fig. 13), similar to that observed. However, the intense NDD squall line moves slowly southeastward in comparison with observations and produces the large area of heavy rainfall shown in Fig. 11.

The elimination of subcloud downdrafts within the convective scheme results in precipitation totals that agree well with observations, but the areal extent of the heavy precipitation is overdone as a consequence. We believe it is much more useful to underpredict the total precipitation but produce a correct distribution of the rainfall. Forecasters can then adjust the total amounts upward while having high confidence in the locations of heavy rain. This leads to the third modification of the KF scheme in which the treatment of convective downdrafts is handled more realistically as described in section 2.

The 24-h total precipitation field from the DDD simulation represents a compromise between the MPE and NDD results (Fig. 14). The precipitation maxima are slightly larger for the DDD simulation than for MPE, but the amounts are significantly lower than the NDD totals. Most importantly, the DDD precipitation pattern appears to be superior as compared to the other simulations. The area of heavy rainfall (>51 mm) appears to better match observations than seen from the other simulations. In addition, the DDD placement of the two Iowa maxima is strikingly similar to the observations (Fig. 4), although the easternmost maximum is a little too far north.

As expected, the DDD simulation does produce convective downdrafts that trigger new convection. Low-level upward motions along the southern edge of the convective outflow are less than 8 μb s⁻¹ at 1900 UTC 7 September (not shown), again much smaller than those seen in the NOMOD simulation (Fig. 6b). The outflow, however, is not so dominant as to stabilize the low levels to the point that only weak convection develops along the cold front during the evening as in NOMOD. To the contrary, although pockets of cool, stable downdraft air are produced by the DDD storms, most of eastern Nebraska and southern Iowa maintain high-θ_e low-level air prior to the development of the evening squall line (Fig. 15).

5. Simulation results for the six cases

6. Incorporating mesoscale details into the initial conditions

Mesoscale features associated with convective outflow boundaries, drylines, and fronts are often poorly represented in the initial conditions of numerical models owing to the smoothing involved in objective analysis procedures, data rejection via quality control techniques, or simply because they are not well sampled. Stensrud and Fritsch (1994a,b) have shown that the absence of these features in initial conditions can have a detrimental impact upon numerical simulations. Three of the six cases in our investigation contain one or more poorly initialized convective outflow boundaries in the region of subsequent convective development. To assess how important the initialization of the outflow boundaries is to the success of the model simulations, especially regarding precipitation patterns and accumulations, we modify the initial conditions by adding convectively induced cold pools to the model initial conditions following the procedure of Stensrud and Fritsch (1994a) (Fig. 22). Only the thermodynamic fields are changed. The wind field then adjusts to the mass field through the course of the simulation (Stensrud and Fritsch 1994a).

Precipitation totals from the JUL87 DDD simulation that incorporates surface pressure perturbations associated with ongoing convection is presented in Fig. 23. This field shows a 37% increase in the western Wisconsin maximum versus the DDD simulation whose initial conditions were not modified (Fig. 17b). The magnitude of the rainfall maximum not only increases from 79 mm to 109 mm by including the details of the cold pool in the model initial conditions, but the location shifts west-southwestward to a position 50 km closer to Minneapolis, the location of the flash flooding. In addition, including the cold pool reduces the model precipitation in northern Minnesota to match observations better (Fig. 17a). Thus, for this case, the inclusion of surface mesoscale details in the initial conditions results in a significant improvement in the model precipitation fields, especially in the region of the flash flood–producing rainfall.

The JUL87 case provides the best example (from our limited set of cases) of improving precipitation fields by incorporating mesoscale details into the initial conditions. When a similar procedure was applied to the SEP89 and JUN90 simulations, there were no significant improvements, although the simulations were not adversely affected.

7. Summary and discussion

In this study of a mesoscale model’s ability to simulate six flash flood events, we created three modifications of the Kain–Fritsch convective parameterization scheme. The differences between the modifications are the values of the precipitation efficiency and the treatment of convective downdrafts. Model simulations using each of the modifications show improvement in total rainfall fields versus the simulations that use the unmodified convective scheme. Maximizing rainfall by forcing the PE to 0.9, in general, provides modest improvement in the simulated rainfall fields. Rainfall totals for MPE are slightly higher than NOMOD totals and the areal extent is increased somewhat.

Precipitation fields appear to be very sensitive to the way convective downdrafts are treated within the model, especially for cases such as those presented here in which convective precipitation far exceeds grid-scale precipitation. In particular, when convective downdrafts are prohibited below cloud base (NDD), magnitudes of model rainfall maxima are often near observed maxima. For example, the NDD simulation for the JUL87 case produces a western Wisconsin total precipitation maximum of 188 mm (7.4 in.), while the observed total is 254 mm (10.0 in.) at Minneapolis. Unfortunately, although the precipitation magnitudes are close to observations, the areal extent of heavy rainfall tends to be overdone for the NDD simulations since no low-level convective outflows are produced to help stabilize the environment and generate new convection in regions away from active convection.

When the convective scheme is modified to delay the onset of downdrafts (DDD), both the magnitude and areal extent of the heavy rainfall are reduced somewhat with respect to NDD. The fact that NDD produces the best rainfall maxima, while the other modified simulations generally produce better overall patterns of precipitation, suggests that an ensemble-type approach to precipitation forecasting may prove beneficial. Although the NOMOD, MPE, and/or NDD simulations outperform DDD for selected cases, our qualitative assessment is that the DDD simulation provides the best, overall rainfall fields for the six cases analyzed.

We have illustrated that the success of a mesoscale numerical model at simulating heavy rainfall is quite sensitive to the treatment of convective downdrafts (and to a lesser extent precipitation efficiency) within a convective parameterization scheme. It is emphasized that we are not proposing that the convective scheme modifications presented herein be implemented in operational mesoscale models, but rather suggesting that improvements in QPFs will be intimately linked to the development of improved parameterizations of convective downdrafts. The MPE and NDD modifications are really nothing more than an elementary attempt to explore the extent of model sensitivity to precipitation efficiency and convective downdraft strength, respectively, and represent no“serious” attempt at providing an operationally applicable convective scheme modification. Rather, these modifications provide information about the relative importance of two of the components whose realistic treatment is believed to be important for the successful simulation of heavy rainfall. The DDD modification, on the other hand, might represent one such “serious” attempt at improving QPF through improved convective parameterization, specifically by altering the timing of convective downdrafts. Moreover, it is important that any QPF improvements do not come at the expense of other aspects of model performance.

As previously mentioned, precipitation totals from the modified simulations indicate greater potential for flash flooding than the totals produced by the unmodified simulations. This suggests that the modifications have, in fact, provided useful information concerning those aspects of convective schemes (in particular, convective downdraft strength) that deserve special attention as improved convective parameterization schemes are pursued. Such improved parameterizations might prove particularly useful during events in which severe convective weather (e.g., large hail, tornadoes, and damaging winds) detracts forecasters from flash flood potential (e.g., Schwartz et al. 1990).

It is interesting that for the NOV93 flood event, all four simulations provide reasonable precipitation fields. Even the NOMOD simulation, which generally provides the lowest precipitation maximum, generates a 124-mm total precipitation maximum in southern Illinois. Soundings indicate that the atmosphere is characterized by a deep (∼400 hPa) layer of high relative humidity air in the lower and middle troposphere. This environment substantially reduces the differences between the NOMOD simulations and the simulations performed using modified versions of the KF convective parameterization scheme by 1) creating low cloud bases that contribute to high PE and 2) inhibiting the development of strong convective downdrafts, whose production often leads to poor precipitation fields within the NOMOD simulations. More simulations in moist environments (including landfalling hurricanes and tropical storms) are needed to further assess the NOMOD’s relative success in such environments.

Even though model solutions (i.e., precipitation forecasts) may provide little guidance concerning the potential for flash flood–producing rainfall, it is possible that the models provide signals that can alert forecasters to the flash flood potential. Doswell et al. (1996) provide a review of the ingredients involved in the production of flash flood–producing rainfall. Basically, heavy rainfall is associated with a high precipitation rate which, in turn, requires the rapid ascent of air containing substantial amounts of water vapor. In addition, movement of thunderstorms such that heavy rainfall can occur over the same area for long periods of time contributes to flash flooding.

As an example of identifying model signals, consider the JUN90 Shadyside, Ohio, case. It has been mentioned that each of the four simulations resulted in a rather poor precipitation field. However, the model output does suggest the assemblage of some of the basic ingredients often associated with flash flood–producing rainfall. The 1200 UTC 14 June surface analysis indicates southwesterly winds advecting moist air into Indiana and Ohio (Fig. 24a). The 9-h model output indicates that low-level dewpoint temperatures in the Shadyside region of eastern Ohio will rise by 5°C by 2100 UTC, increasing the potential instability (Fig. 24b). In addition, winds throughout cloud depth are expected to remain weak (generally less than 30 kts; not shown), suggesting the possibility of slow system movement. These model signals, combined with the presence of a nearby convective outflow boundary suggests the potential for heavy rainfall and flash flooding across the area, even though the model precipitation field might not. Also, familiarity with the hydrologic situation for this event might have proven useful. Rainfall during the month of May was in excess of 200% of normal in southeastern Ohio (National Weather Service 1991), which may have exacerbated rapid runoff. Although there had been no recorded history of flash flooding along the two creeks near Shadyside, the National Weather Service performance in Ohio on the day of the Shadyside flash flood was quite good (National Weather Service 1991).

Future studies will focus on refining the values of precipitation efficiency within the convective scheme and the treatment of downdrafts. Fankhauser (1988) suggests that the factors controlling thunderstorm precipitation efficiency are more complicated than the simple inverse dependence on the vertical shear of the horizontal wind. In fact, if anything, his results suggest a slightly positive correlation between precipitation efficiency and vertical wind shear. We anticipate using a three-dimensional numerical cloud model to investigate how to define precipitation efficiency and to provide guidance on how to further modify the KF scheme regarding the treatment of convective downdrafts. We believe that these simulations of convective updrafts (as opposed to the one-dimensional simulations within the KF scheme) will provide improved guidance on downdraft characteristics for a given environment.