1. Introduction
Flash flooding in urban drainage basins is an increasingly important hazard in terms of loss of life and property damage (i.e., Carpenter et al. 1999; Smith et al. 2002; Ogden et al. 2000). In this paper we examine the linkage between organized thunderstorm systems and flash floods in urban drainage basins through analyses of cloud-to-ground (CG) lightning observations and discharge data from the Baltimore, Maryland, metropolitan region.
The questions that motivate this study arise from the alteration of the physical environment through urbanization. The altered flood hydrology of urban catchments, which is tied to expansion of the drainage network through the storm drain system and increasing impervious area, is characterized by increased sensitivity to short-duration rainfall rates (Smith et al. 2002, 2005a, b). The altered hydrologic response associated with urbanization leads to the hypothesis that warm-season thunderstorm systems should become an increasingly important component of the climatology of flash flooding.
Alteration of the physical environment due to urbanization also affects the climatology of precipitation in urban environments (Landsberg 1956; Manley 1958; Changnon et al. 1971; Diem and Mote 2005; Shepherd and Burian 2003; Moelders and Olson 2004). Observational and numerical modeling studies suggest that the urban heat island (UHI), frictional effects associated with building canopy, and urban aerosols can affect the initiation and evolution of thunderstorm systems (Shepherd and Burian 2003; Bornstein and Lin 2000; Rozoff et al. 2003; Bentley and Stallins 2005; Orville et al. 2001; Baik et al. 2001; Lowry 1998; Peterson 2003; Li et al. 2004; Hafner and Kidder 1999; Van den Heever and Cotton 2004). Summer convective precipitation anomalies over urban environments have been examined over several cities in the United States and worldwide [see Shepherd (2005) for a recent discussion and summary]. Although there have been numerous studies of precipitation anomalies in urban environments, there have been few studies that examine thunderstorm and flash flood climatologies for urban regions [see Underwood and Schultz (2004) and Holle and Bennett (1997) for studies dealing with aspects of the issue].
We use a point process framework (Karr 1991; Diggle 1983; Guttorp 1995; Smith and Karr 1985) for analyses of CG lightning strikes and the occurrences of flash floods. Analyses of lightning strikes as a space–time point process focus on the mean intensity function, from which we examine the seasonal, diurnal, and spatial variation in mean lightning frequency. Cloud-to-ground lightning data from 1991 to 2004 from the National Lightning Detection Network (NLDN) are used to study the spatial and temporal frequency of thunderstorm systems. Discharge data during the period 2000–04 from 11 U.S. Geological Survey (USGS) stream gauging stations are used to analyze flash flood occurrences over the Baltimore metropolitan region.
The structure of the paper is as follows. In section 2 the study area and data are introduced. The point process modeling framework used for statistical analysis of lightning and flash flood occurrences is presented in section 3. Results follow in section 4 and conclusions are summarized in section 5.
2. Data and study region
The NLDN (Cummins et al. 1998; Orville et al. 2002) consists of 106 CG lightning sensors operated and maintained by Vaisala, Inc., in Tucson, Arizona. The network records the date, time, latitude, and longitude (decimal degrees, three decimal points accuracy), polarity (kA), and multiplicity (number of strokes per flash) of CG lightning strikes over the conterminous United States. Upon detection, only CG lightning strikes that have an effective peak current magnitude greater than 5 kA are recorded. The network has been extensively used for climatological analyses of lightning and thunderstorms over the United States (Carey and Rutledge 2003; Orville and Huffines 2001; Orville and Silver 1997). The NLDN has an overall detection efficiency of about 80%–90% and a location accuracy of approximately 1 km (Cummins et al. 1998; Idone et al. 1998a, b). Error characteristics of the NLDN sensors vary with geographic location, peak current magnitude, season of the year, and density of the detectors (for additional details, see discussion in the references listed above). For this study, a record of 14 yr (1991–2004) of lightning data from the NLDN were used.
The Baltimore Ecosystem Study (BES) is a Long-Term Ecological Research (LTER) project that focuses on the impacts of urbanization on riparian ecosystem form and function (see Groffman et al. 2003). A major observational component of the BES has been the development of a dense network of stream gauging stations in small urban watersheds by the USGS. We use discharge observations for 11 of these stations (see Table 1). The time resolution of discharge observations ranges from 1 to 15 min. The discharge data used in this study cover the 5 year period from 2000 to 2003 or 2004, with the exception of the Moores Run station at Radecke Avenue (hereafter abbreviated as “Moores Run”) and its tributary, for both of which the observing period is 1998–2003.
We concentrate our study on a region centered over the Baltimore metropolitan area (Fig. 1). The urban environment of Baltimore and Washington D.C., the mountainous terrain of the Blue Ridge and Valley and Ridge province to the west, and the ocean–land boundary to the east make this region a complex setting for examining warm-season thunderstorm systems.
For analyses of the diurnal cycle of thunderstorms and investigation of urbanization effects on thunderstorm rainfall, we focus on three subareas. These areas are depicted in Fig. 1 with the three intermediate size squares of the same latitude marked as “Piedmont,” “Urban,” and “Ocean.” The urban area covers the Baltimore and Washington D.C., metropolitan areas. The Piedmont and ocean regions are of comparable size and are located, respectively, to the west of the Baltimore–Washington region and over the open ocean east of Baltimore. The 11 USGS stream gauge stations used for flash flood analyses (Table 1) are contained within the box covering Baltimore.
3. Methodology
We represent CG lightning strikes over the study region as a space–time point process. Because thunderstorms are fundamentally linked to the diurnal cycle of heating of the land surface, the basic time element of the space–time model of lightning strikes is one day. Each CG lightning strike is associated with a point in space and a time, that is, the spatial location at the ground surface of the CG strike and the time of the CG strike. For a given day, let N denote the number of lightning strikes. For N > 0, denote the time of the kth strike (k ≤ N) by Tk and the location by Yk. Then {Tk, Yk} is a space–time point process defined on [0, 1] × D, where the unit interval represents time during the day and the domain of study is the two-dimensional region D. We choose the beginning and ending time of the day, that is, times 0 and 1, to be 1200 UTC.
The CG lightning sample consists of observations from every day of the year and from multiple years. Let Nij denote the number of CG strikes in the study region on day j of year i. Days vary from 1 to 365 with 1 January being the first day of the year and 31 December being the last one. Leap years are neglected by omitting 29 February (with no impact on subsequent analyses due to the low lightning frequency in February). The number of years in the sample is denoted by n. For Nij > 0, that is, on days with lightning, Tijk ∈ [0, 1] denotes the time of the kth CG strike on day j of year i, and Yijk ∈ D denotes the location in the domain D of the kth CG strike on day j of year i. The first day extends from 1200 UTC 1 January to 1200 UTC 2 January.
The mean intensity function does not completely specify the distribution of the space–time point process. We also examine aspects of the lightning distribution that are not directly linked to the mean intensity function. To examine the initiation of thunderstorms, we analyze the distribution of the location of the first CG strike Yij1 on a given day. We are particularly interested in the initiation of thunderstorms on major outbreaks of thunderstorms, so analyses will be conditioned on total CG strikes for the day. We examine the evolution of CG strikes in the following section through two examples involving major flash flood episodes. To characterize the evolution of CG strikes over the course of a day, it is necessary to completely specify the distribution through the “conditional intensity function” (Karr 1991). Heuristically, the conditional intensity function specifies the rate of occurrence of lightning strikes at a point in time t and a point in space x, conditioned on the history of CG lightning strikes up until time t. Analyses in the following section point to useful directions to pursue in specifying explicit models for the conditional intensity function.
We will also examine the occurrence of flash floods in a drainage basin in a point process framework. Let Zij denote the maximum daily discharge, as a unit discharge (m3 s−1 km−2), at a stream gauging station on day j of year i. Denote the time of the peak discharge on day j of year i by Uij, with time again ranging from 0 to 1, with the beginning and ending times equal to 1200 UTC. The peak discharge on each day will not necessarily be a “flood.” We introduce a discharge threshold (m3 s−1 km−2) to define a flood.
4. Results
Statistical analyses of lightning and flash flood occurrences in the Baltimore metropolitan region are presented in this section. We begin with the space–time point process representation of CG lightning strikes. These results are followed by analyses of the occurrence of flash floods and an examination of the joint occurrence of major thunderstorm systems and regional flash flooding.
a. Lightning climatology
The annually averaged rate of occurrence of lightning ĥ(y) (Fig. 2) over the study area varies from 1.5 to 4.6 strikes km−2 yr−1. The values are lowest in the Valley and Ridge physiographic province, which lies west and north of the Blue Ridge. An elongated region of maximum lightning strikes extends from the southern portion of the Blue Ridge, in our study region, to the Baltimore–Washington metropolitan region. The sharp gradients that parallel the strike of the lower portion of the Blue Ridge, with lower flash densities to the west in the Valley and Ridge and higher flash densities to the east over the Piedmont province point to the role of the “first ridge” for the climatology of thunderstorms in the region. As will be shown below, the Blue Ridge is a region with a high frequency of thunderstorm initiation.
Lightning frequency varies in complex fashion around the Baltimore–Washington metropolitan regions (Fig. 2), with areas of larger flash densities south and east of the cities. The impacts of urbanization on the thunderstorm climatology of the region are linked to the impacts of sea-breeze circulations associated with the Atlantic Ocean, Chesapeake Bay, and the Potomac estuary.
If the time window is restricted to the summer season (the months of June, July, and August), the estimated rate of occurrence of lightning ĥ(y) (Fig. 3) shows similar patterns to the annual analyses, but with markedly larger rates (4.3−15.1 strikes km−2 yr−1). These values of lightning frequency are rates. A value of 15.1 strikes km−2 yr−1, for example, is the value that would result at the spatial location of maximum frequency if the mean summer rate of occurrence persisted for the entire year. Since the summer season consists of 3 months, the summer climatology (strikes km−2 summer−1 in this case) could be obtained by dividing the values of Fig. 3 by a factor of 4. If the values of Fig. 3 are divided by 4 they are close to the annual values of Fig. 2, implying that lightning is concentrated in the summer months (see also Fig. 4).
Amplification of CG flash rates southeast of Baltimore and Washington D.C. is a more pronounced feature in the summer analyses. Lightning strikes increase to about 13.5 strikes km−2 yr−1 to the southeast of the cities and the amplification extends for distances of 50–60 km. Future studies will examine whether this amplification of CG strikes is tied to urbanization impacts on thunderstorm evolution.
The seasonal occurrence of thunderstorms is tightly concentrated during the warm season (Fig. 4), as reflected in estimates of the seasonally varying intensity function
The diurnal cycle of warm-season lightning occurrences over the Baltimore–Washington domain (Fig. 1), as represented by the spatially averaged rate of occurrence mj(t), has a sharp peak of 38 strikes km−2 yr−1 between 2100 and 2200 UTC. For the analyses in Fig. 5, the diurnal flash rate mj(t) is averaged over the warm season (June–August). Cloud-to-ground flash rates are close to 0 from 0900 to 1500 UTC, which is a principal rationale for beginning the day of our lightning model at 1200 UTC.
The diurnal cycle of the Piedmont domain is generally similar to that of the Baltimore–Washington domain, except that the peak diurnal flash rate is approximately 1 h earlier and slightly smaller. The timing difference reflects the preferential initiation of thunderstorms along the Blue Ridge and their eastward progression over the course of the day, as discussed in more detail below. The diurnal cycle of thunderstorms is strikingly different for the eastern region over the Atlantic Ocean, with its 0300 UTC peak at a flash rate that is almost 5 times smaller than the Baltimore–Washington maximum [see Toracinta et al. (2002) and Nesbitt et al. (2000) for analyses and discussion of mechanisms associated with land–ocean contrasts in lightning frequency].
Of particular interest in examining flash floods are major thunderstorm systems. We examine below the linkage between these storms, as reflected in total regional lightning counts, and the occurrence of flash floods. The 10 largest thunderstorms for the broader study area and for the area covering just the city of Baltimore are listed in Tables 2 and 3, respectively. The largest storm for the larger study region occurred on 16 August 2003 and produced a flash density of 0.6 strikes km−2 over the 56 066 km2 study region. For the Baltimore area, the largest storm occurred on 7 July 2004 and produced a mean flash density of 1.31 strikes km−2 over the 1973 km2 region. This result is enlightening in understanding the magnitude of this particular thunderstorm. In a matter of few hours, approximately 40% of the mean annual lightning activity of the area was observed. The storm produced record flooding over the Baltimore metropolitan region (Smith et al. 2005a, 2007). Only two of the events from the larger area are also included in the list of events impacting the city of Baltimore (16 June 1994 and 25 May 2004).
Under the i.i.d. assumption made for the space–time point process model in section 2, it is presumed that there are no time trends in lightning from year to year. In this connection, it is notable that 7 of the 10 largest events for the broader study region occurred during the last 5 yr. Updates to the NLDN (Cummins et al. 1998) could possibly lead to reduced detection prior to 1995. Even so, in the list of the 10 largest events here there is only one between 1995 and 1999. Even with the different set of events from the smaller Baltimore study region the conclusions are the same. The frequency of major thunderstorm events has been higher during the 2000–04 period than for the preceding time period.
For the major storm events (Table 3) in the Baltimore region (Fig. 1), the distribution of initiation locations {Yij1} was examined (Fig. 6). We computed the probability that a grid of resolution 0.02° by 0.02° was the initiation location by taking the first 100 CG strikes for each of the 10 days and computing the frequency by grid. All of the 10 largest storms for the Baltimore region initiated far from the city and propagated over it. The initiation locations cluster along and adjacent to the Blue Ridge. This conclusion is not sensitive to the number of storms. There is a strong link between the Blue Ridge and initiation of thunderstorm systems that pass over the Baltimore region.
b. Life cycle of warm-season thunderstorm systems
The life cycle of thunderstorm systems that produce flash floods in the Baltimore metropolitan region exhibit systematic elements in their initiation and evolution. These include initiation of thunderstorms along the Blue Ridge (as described above), eastward propagation of thunderstorm systems over the Piedmont, and interaction of thunderstorm systems with the urban environment and sea-breeze circulation systems. These properties are illustrated by storms on 7 July 2004 (Fig. 7) and 13 June 2003 (Fig. 8). These storms produced the floods of record in, respectively, Dead Run (Table 1; see also Smith et al. 2005a, 2006) and Moores Run (see analyses below and Table 1; see also Smith et al. 2005b). The 7 July 2004 storm ranks first in CG flash density over the Baltimore metropolitan region, and the 13 June 2003 storm is not in the list of the 20 largest lightning producing storms over Baltimore.
The life cycle of thunderstorm systems is reflected in quantities derived from the mean intensity function, like the spatial rate of occurrence function h(y) (Figs. 2 and 3) and the diurnal frequency mj(t) (Fig. 5). The mean intensity function does not, however, capture the complete distribution of CG lightning strikes. In particular, those elements that are associated with propagation and interaction of thunderstorm systems are not represented. To completely specify the space–time point process of CG strikes requires specification of the conditional intensity function (Karr 1991). Future studies will explore the climatology of thunderstorms through analyses based on explicit models of the conditional intensity function.
c. Joint occurrence of lightning and flash floods
The relationship between thunderstorm climatology and flash flood climatology is examined through discharge observations from 11 USGS stream gauging stations in the Baltimore metropolitan region and the point process framework introduced in section 2. To examine the occurrence of flash floods, we select the discharge threshold z0 such that there are 10 events per year on average at each stream gauging station. The BES network comprises gauging stations that span a broad spectrum of urban development. The threshold, z0 (Table 1) ranges from 1.76 m3 s−1 km−2 for Moores Run to 0.09 m3 s−1 km−2 for Baisman Run (the value of 2.30 m3 s−1 km−2 is for a tributary of the 9.1 km2 Moores Run watershed, which drains less than 5% of the basin). Moores Run is located in northeastern Baltimore City and is characterized by residential development constructed prior to implementation of storm water management regulations. It has one of the highest frequencies of occurrence of 1 m3 s−1 km−2 flood peaks in the conterminous United States (Smith et al. 2005b). Baisman Run is the forest reference watershed for the BES. Flood response for this basin reflects hydrologic response of the region prior to urban development.
The seasonal cycle of flood response in Moores Run (Fig. 9) mimics the seasonal cycle of lightning occurrence with a sharp maximum during June and July. The frequency of events ranges from a maximum of 25 events yr−1 during June and July to frequencies that are more than an order of magnitude smaller in November–February.
The diurnal cycle of flash floods in Moores Run (Fig. 10) exhibits a sharp maximum frequency between 2100 and 2200 UTC. The maximum frequency is more than a factor of 3 larger than the minimum frequency. The maximum frequency of flash floods corresponds with the maximum frequency of lightning, reinforcing the link between flash flood occurrence and thunderstorm occurrence.
To examine the joint occurrence of major thunderstorm systems and regional flash flooding, counts of CG lightning strikes were compared with counts of flash flood events, based on observations from 11 USGS stream gauging stations (Table 1). The joint occurrence is examined through comparisons of the number of stream gauging stations with floods on a given day and the number of CG strikes for the Baltimore region (see Fig. 11 in which results for the year 2000 are illustrated). The observations show a strong correspondence between lightning counts and flash floods during the summer months (June–August).
The correspondence between intensity of thunderstorms and flash flooding is illustrated through a scatterplot (Fig. 12) of the total number of lightning strikes in a day over Baltimore (expressed in strikes km−2 yr−1) versus the number of stations with peak discharge exceeding the flood threshold for the same day during the summer months of 2000–03. This analysis includes all the summer days during the 4-yr period. As the number of lightning strikes increases there is a corresponding increase in regional flash flooding, especially as CG strike frequency increases beyond 0.05 strikes km−2 or about 100 strikes over the area covering Baltimore for a certain day. There are a total of 56 days during the 4 yr (total of 368 summer days) with one or more stream gauging stations reporting floods. Of those 56 days, 50 were days for which lightning was observed over the area. This translates to a 90% conditional probability that lightning occurs given that a flash flood has occurred.
5. Summary and conclusions
The climatology of thunderstorms and flash floods in the Baltimore metropolitan region has been examined through analyses of CG lightning observations and discharge observations from USGS stream gauging stations. A point process modeling framework serves as the foundation for theses analyses. A space–time point process representation of CG lightning strikes is introduced for the study of the climatology of thunderstorms. Principal conclusions of the study are the following:
The spatial frequency of CG lightning strikes for thunderstorms that affect the Baltimore metropolitan region is characterized by pronounced spatial heterogeneity. Elements of the spatial heterogeneity of thunderstorms include a maximum frequency over the Blue Ridge, a minimum frequency to the west of the Blue Ridge in the Valley and Ridge province, large variation in lightning frequency around the Baltimore and Washington metropolitan areas, and decreased thunderstorm frequencies to the east over the open ocean. These analyses indicate that the climatology of thunderstorms, and consequently the climatology of flash floods, is strongly dependent on orographic precipitation mechanisms along the Blue Ridge. The climatology of thunderstorms may also include significant effects associated with urbanization (UHI, frictional effects associated with urban canopy, and urban aerosols) and sea-breeze circulation systems.
The climatology of thunderstorms in the Baltimore metropolitan region exhibits pronounced seasonal and diurnal cycles. These cycles are reflected in the climatology of flash floods in Baltimore.
There are systematic elements to the life cycle of thunderstorm systems that produce flash floods in the Baltimore metropolitan region. These include initiation of thunderstorms along the Blue Ridge, eastward propagation of thunderstorm systems over the Piedmont, and interaction of thunderstorm systems with the urban environment and sea-breeze circulation systems.
Most of the large thunderstorm events impacting the study region occurred between 2000 and 2004 in a dataset that extends back to 1994. The interannual variation of lightning climatology warrants additional study.
There is a strong link between the occurrence of regional flash flooding and major thunderstorm outbreaks (see also item 2 above). Urbanization in Baltimore, and along the major urban corridors of the eastern United States, has made warm-season thunderstorm systems the principal agent of flash flooding in urban drainage basins.
Acknowledgments
The research was supported by the National Science Foundation (NSF Grants EAR-0208269, EAR-0409501, and ITR-0427325). This support is gratefully acknowledged.
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Study area (large white box) and subareas of focus (smaller white boxes).
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Regional contour map of mean annual lightning flash density in strikes km−2 yr−1 over the study area. Data are from 1991 to 2004.
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Regional contour map of mean summer (June–August) lightning flash density in strikes km−2 yr−1 over the study area. Data are from 1991 to 2004.
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Seasonal cycle of lightning flash density over the study region in strikes km−2 yr−1. Original data have been smoothed with a Gaussian filter (σ = 10 days). Data are from 1991 to 2004.
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Diurnal cycles of summer (June–August) lightning flash density in strikes km−2 yr−1 for three subregions of Fig. 1. The black, dark gray, and light gray lines are respectively for the boxes covering the Piedmont, the Baltimore–Washington metropolitan, and the ocean sites of the same latitude (see Fig. 1). Data are from 1991 to 2004.
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Raster map of the initiation locations, expressed in probability (%), of the first 100 CG lightning strikes of the 10 largest lightning-producing thunderstorm events over Baltimore City (see Table 3). Each thunderstorm day starts at 1600 UTC. Raster resolution is 0.02° by 0.02°. Data are from 1991 to 2004.
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Hourly CG lightning strikes (white x marks) for the 7 Jul 2004 event. Gray-shaded areas with black outline denote the urban regions of Baltimore and Washington D.C. See also Fig. 1.
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Same as in Fig. 7 but for 13–14 Jun 2003.
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Seasonal cycle of flash floods for USGS gauging station “Moores Run at Radecke Avenue in Baltimore City, MD.” Original data have been smoothed with a Gaussian filter (σ = l month).
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Diurnal cycle of flash floods for USGS gauging station “Moores Run at Radecke Avenue in Baltimore City, MD.” Original data have been smoothed with a Gaussian filter (σ = 2 h).
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Daily CG lightning strikes (solid black line) over the area covering Baltimore City and of daily number of USGS gauging stations exceeding the flood threshold, z0 (vertical gray bars ending with solid circles) for the year 2000. Data from 11 stations were used (see Table 1).
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
Scatterplot of regional flooding (expressed in number of stations for which z ≥ z0) vs total number of lightning strikes over Baltimore City (in strikes km−2) for days with lightning activity. Only the summer months are included (June–August). Data are from 2000 to 2003.
Citation: Journal of Hydrometeorology 8, 1; 10.1175/JHM558.1
USGS/BES stations used in this study along with the available data and the flood level, zo (cms km−2), for each station.
Ten largest lightning events over the study region. Data are from 1991 to 2004.
Ten largest lightning events over Baltimore City. Data are from 1991 to 2004.
