1. Introduction
Urban hydrologic engineering relies on the estimation of design storms for specific durations and return periods. These design storms are based on historical precipitation records for the region of interest. Intensity–duration–frequency (IDF) curves are developed for precipitation and applied to the design of drainage system elements such as sewers, culverts, or control elements such as detention basins (Chow et al. 1988; Kothyari and Grade 1992; Madsen et al. 2009; Simonovic and Peck 2009). Under the IDF curve approach, typically a single curve interpolated from rain gauges in the area is applied to a catchment (Hershfield 1963). The extreme events are assumed to be independent in time, and the design estimates for each location are computed separately without a spatial dependence structure. However, the spatial variability of rainfall, especially for smaller catchments and shorter durations, is often identified as the primary source of error in investigations of rainfall–runoff processes and hydrological modeling (O’Loughlin et al. 1996; Syed et al. 2003). This issue is particularly important for a dense urban area like New York City (NYC), which operates on combined sewer systems, that is, the rainwater and street runoff along with the sanitary and industrial wastewater are collected in the same sewer and conveyed to treatment plants (NYCDEP 2013).
Much of the storm water flows over impervious surfaces into catch basins in the streets and to sewers. Storm water can pose significant challenges to cities in the form of flooding and combined sewer overflows. The combined sewer overflows and storm discharges vary spatially because of the spatial variations in rainfall and can hence influence the quality of the water bodies to support recreational uses in waterways and nearby beaches. Scenarios that properly address the associated spatial patterns of rainfall can help improve the operation of these systems and the assessment of system performance, especially as drainage network modifications are considered. Rainfall observations used to develop such scenarios are currently limited spatially by the relatively sparse distribution of rain gauges. With advances in weather radar technologies, a very high-resolution spatial dataset for precipitation is available for most of the United States. A big difference between rain gauges and radar is the punctual-to-areal information, that is, radars are providing gridded spatially distributed rainfall products. These spatial fields can provide a basis for properly understanding the clustering and distributional properties of rainfall intensity, timing, and areal extent. These data can be used for developing stochastic scenarios to evaluate the critical links in an urban hydrologic network and consequently improving the design parameters and operations of these systems, including the component drainage elements and storm water control elements. They can also be used to perform assessments on system vulnerability to local and widespread flooding.
In this paper, we explore the spatial variability of two significant attributes of extreme rainfall events over the greater New York (GNY) area (Fig. 1): the simultaneous areal extent, that is, the grids that have rainfall exceeding a threshold at the same time, and their average intensity by applying the partitioning around medoids (PAM) clustering algorithm (Kaufman and Rousseeuw 1990) on radar rainfall data. Since these extreme events impact specific regions and the physical processes associated with them vary considerably by location and timing, we focus on understanding the spatial manifestation of these event attributes for specified durations and connecting them to synoptic-scale atmospheric precursors (e.g., circulation patterns and their characteristics). While the spatial structure of extreme rainfall has been explored over large areas (e.g., Tetzlaff and Uhlenbrook 2005; Jones and Carvalho 2012; Bernard et al. 2013; Stevenson and Schumacher 2014), research on the spatial structure of extreme events at rainfall time scales that are critical for urban drainage network evaluation has been limited (Berne et al. 2004; Smith et al. 2012; Wright et al. 2014; Zhang et al. 2014). Furthermore, no literature was found that looked at the areas covered by extreme rainfall and their joint dependence with the intensities and time of occurrence for a specific duration at these scales.
Study area: GNY and the five boroughs of NYC.
Citation: Journal of Hydrometeorology 18, 3; 10.1175/JHM-D-16-0193.1
For extreme rainfall of a specified duration, we have considered the partial duration series with events that exceed the 90th percentile of all rainfall at a given grid. We have considered 1- and 24-h accumulations to represent the short- and long-duration rainfall events and seasons of December–February (DJF) and June–August (JJA) to represent winter and summer events, and we used the Next Generation Weather Radar (NEXRAD) hourly weather radar data to identify the extreme rainfall partial duration series. The total area associated with simultaneous exceedance of the 90th percentile is then recorded. For each rainfall duration of 1 and 24 h, and for winter and summer seasons, we are interested in exploring whether there are significant spatially organized clusters in the intensity and areal extent (number of grids exceeding a threshold at the same time). We employ the PAM classifying algorithm to assess the congruence in spatial characteristics and to validate them with reported extreme events in the region using the NOAA Storm Events Database (NOAA/NCEI 2016). The causal factors, that is, the storm mechanisms associated with the clusters for different seasons, are explored in brief in this paper using compositing analysis on ERA-Interim data.
The rest of the paper is organized as follows. The NEXRAD data used in the study and the extreme event identification process are described in section 2. The clustering analysis details and results along with the analysis on atmospheric teleconnections are presented in section 3. In section 4, we present the summary and conclusions.
2. Description and processing of radar rainfall data
The NEXRAD system comprises 160 Weather Surveillance Radar-1988 Doppler (WSR-88D) sites installed throughout the United States and at selected overseas locations (Heiss et al. 1990). Maximum coverage radius of single radar is 250 nautical miles (~460 km). The WSR-88D continuously collects reflectivity, radial velocity, and spectrum-width base data. These three meteorological quantities are used to generate hydrometeorological products, which are subsequently mapped onto the polar stereographic projection called Hydrologic Rainfall Analysis Project (HRAP; Fulton et al. 1998). An integral part of the precipitation determination algorithms is the ability to dynamically apply the appropriate reflectivity factor Z and rainfall rate R relationship [suggested by Marshall and Palmer (1948); Joss and Waldvogel (1970); Woodley et al. (1975)] with respect to the type of precipitation (e.g., convective or stratiform). While single radar records may suffer from a blockage at certain locations (Vivekanandan et al. 1999; Lang et al. 2009) as well as range limitations, multisensor (gauge, radar, and satellite) products minimize these errors (Miller et al. 2010). Multisensor precipitation estimator (MPE) algorithms provide a real-time suite of gridded radar products at different spatial scales and stages (Hudlow 1988; Vasiloff et al. 2007; Kitzmiller et al. 2013). We refer the readers to Nelson et al. (2010) for more details on weather radars.
In this study, the National Centers for Environmental Prediction (NCEP) stage IV radar product [archived in Gridded Binary (GRIB) format; see WMO (2003)] is employed to produce extreme rainfall fields over the GNY region. Stage IV radar data are a mosaic of the regional multisensor precipitation from all 12 National Weather Service (NWS) River Forecast Centers (RFCs), together with calibration and adjustment for different biases using automatic rain gauge measurement and quality-control processes (Lin and Mitchell 2005). However, stage IV data have a bias for big snowfall events, especially in the east since the RFC stations in the eastern United States do not derive the liquid equivalent precipitation for snow (http://data.eol.ucar.edu). Owing to this factor, the stage IV data in the northeastern United States are exclusively rainfall data. The data comprise 1121 × 881 pixels covering the entire continental United States with the spatial resolution of 4 km × 4 km and a temporal resolution of 1 h. The 1- and 24-h rainfall radar data are provided by NCEP and are available from the Earth Observing Laboratory (EOL) from 2002 to present with a UTC time stamp. While higher-resolution products are also available for urban areas (e.g., NEXRAD Q2 and Q3 are available at 1 km × 1 km resolution), they are only archived from 2010. In this study, we used 14 years of stage IV data from 2002 to 2015 to give us as much temporal coverage as possible. The 24-h data (1200–1200 UTC) are accumulated from the 6-hourly data (Fulton et al. 1998). The probability distribution of rainfall obtained from the radar data conforms well to the probability distribution of the rainfall data obtained from the corresponding rain gauge at John F. Kennedy International Airport, NYC (COOP ID 305803). Zhou (2008) compared radar estimates with rain gauge records in the NYC and Long Island area and showed that at the annual scale, there is little difference between the radar-derived estimates and gauge observations. Allen and DeGaetano (2005) conducted an analysis over the northeastern United States and showed that for extreme precipitation, the areal reduction factors (ARFs) at large spatial scales are similar while independent differences exist between radar ARFs and rain gauge ARFs.
The stage IV data we obtained were further processed as follows to compute the total areal extent and average intensity of the extreme rainfall events.
The 1-h (accumulated over short duration) and 24-h (accumulated over long duration) rainfall events were identified for the GNY area, which includes 2612 radar grids from the above dataset.
The 90th percentile R90 of the rainfall was determined at each grid box for each of the 1- and 24-h durations.
We then look through all 122 688 h (5112 days) in the 14-yr record and process the 1 (24)-h rainfall data to identify the rainfall in a grid box that exceeds the estimated R90 for that grid box in that hour (day). This process identifies multiple grids across GNY for each hour (day) that meets the criteria of extreme rainfall events. This resulted in a total of 13 258 extreme event hours for the 1-h duration and 1177 extreme event days for the 24-h duration. Among the 13 258 extreme event hours for the 1-h duration, we identify 1401 extreme event hours for the winter season (DJF) and 6316 extreme event hours for the summer season (JJA). Similarly, among the 1177 event days for the 24-h duration, we identify 170 extreme event days for DJF and 487 extreme event days for JJA. Figure 2 schematically indicates an extreme event’s field development applying an arbitrary threshold.
For each rainfall duration of 1 and 24 h, the total area Ai, for the ith event that exceeds the R90, and the corresponding average intensity Ii was recorded. The clustering in the distribution of Ai and Ii for the winter extreme events (DJF) and summer extreme events (JJA) are then investigated using the PAM approach. We chose winter (DJF) to represent the rainfall associated with extratropical cyclones and nor’easters and summer (JJA) to represent rainfall associated with convective storms and hurricanes. Both these seasons are considered important for hazard management in NYC (http://www.nyc.gov/html/oem/html/hazards/storms.shtml).
Schematic procedure of generating extreme rainfall field from radar rainfall data.
Citation: Journal of Hydrometeorology 18, 3; 10.1175/JHM-D-16-0193.1
3. Classification of extreme rainfall events’ areal extent and intensity
a. PAM clustering analysis
Attribute vector preparation and clustering approach; for each event, corresponding area, and average intensity are developed as input variables of clustering analysis.
Citation: Journal of Hydrometeorology 18, 3; 10.1175/JHM-D-16-0193.1
b. Clustering results
Mean silhouette coefficient from the clustering analysis; K = 2 is the optimum.
Citation: Journal of Hydrometeorology 18, 3; 10.1175/JHM-D-16-0193.1
Silhouette values and hypotheses test results from the PAM clustering analysis (K = 2) for different rainfall durations.
1) Results for 1-h events
The outputs of average intensity and areal extent for the 1-h events are presented in Fig. 5, with the scatterplots showing the joint distribution and the box plots showing the marginal distributions. In each of the winter (DJF) and summer (JJA) seasons, cluster 1 (in red) corresponds to events with low average intensity and small areal extent and cluster 2 (in blue) corresponds to events with high average intensity and large areal extent. From Fig. 5, we observe that for the short duration (1 h), the summer events have higher average rainfall intensities than the winter events. From Fig. 5a, we can observe that the median average intensity of the 1277 winter events in cluster 1 is 7.5 mm h−1. The median areal extent of these events is 20 grids (~320 km2). The median average intensity of the 124 winter events in cluster 2 is 9.5 mm h−1. The median areal extent of these events is 500 grids (~8000 km2). Similarly, from Fig. 5b, we can observe that the median average intensity of the 4922 summer events in cluster 1 is 8.5 mm h−1 and the median areal extent is 15 grids (~240 km2). The median average intensity of the 1324 summer events in cluster 2 is 15 mm h−1 and the median areal extent is 150 grids (~2400 km2).
Results of clustering analysis for the 1-h extreme rainfall data for (a) DJF and (b) JJA. Red and blue colors represent clusters 1 and 2, respectively.
Citation: Journal of Hydrometeorology 18, 3; 10.1175/JHM-D-16-0193.1
Figure 6 presents the spatial distribution (georeferencing) of the probability of assigning cluster 2 for the five boroughs in NYC for the 1-h events. As described earlier, we compute the probability of assigning cluster 2 as the number of events of grid j that are in cluster 2 divided by Nj, the number of events of grid j. Blue color in the map indicates that the probability of assigning cluster 2 to the grid is close to 1 in that season. This implies that most of the events of the grid are grouped in cluster 2 (high intensity and large areal extent), an indication that this grid has a higher likelihood of experiencing extreme rainfall events with high intensity and large areal extent in that season. On the other hand, a red color indicates that the probability of assigning cluster 2 is close to 0, implying that most of the events of the grids are grouped in cluster 1, indicating a lower likelihood of experiencing high-intensity, large-areal-extent extreme events. We can see a clear west-to-east gradient in the spatial distribution of cluster 2 for the 1-h winter extreme events (Fig. 6a), indicating that the grids west of NYC are associated with low intensity and small areal extent, while the grids east of NYC are associated with high intensity and large areal extent for short-duration winter events. Figure 6c, which shows the box plots of the spatial distribution of the probability of cluster 2, provides a closer look at the five NYC boroughs (also see Fig. 1) for the winter events. We see that the borough of Queens (fourth box from the left) has increased likelihood of high-intensity and large-areal-extent short-duration extreme events during winter, compared to the other boroughs. We also observe that, while Manhattan, Bronx, Brooklyn, and Queens have a probability greater than 0.5, the borough of Staten Island has a lower probability for cluster 2 (median is around 0.42), indicating a higher likelihood of events associated with low intensity and small areal extent.
Spatial distribution of the probability of cluster 2 for the 1-h extreme events over NYC in (a) DJF and (b) JJA. The box plots of the probabilities for the five NYC boroughs are also presented for (c) DJF and (d) JJA.
Citation: Journal of Hydrometeorology 18, 3; 10.1175/JHM-D-16-0193.1
The summer 1-h extreme events (Fig. 6b) are more homogenous, and much of the NYC area experiences high-intensity and large-areal-extent events. Figure 6d (box plots of the spatial distribution of the probability of cluster 2 in the five NYC boroughs for the summer) indicates that all the boroughs have a higher probability of cluster 2. It is important to realize that the median areal extent in cluster 2 during winter is larger than the median areal extent in cluster 2 during summer. On the other hand, the average intensity in cluster 2 during winter is much lower than the average intensity in cluster 2 during summer (Fig. 5). This indicates that the winter 1-h extreme events seen in cluster 2 are associated with higher areal extent (a manifestation of synoptic-scale organized storms) compared to the events seen in cluster 2 during summer (a manifestation of more localized convective storms). However, the summer events have greater intensity.
2) Results for 24-h events
The outputs of average intensity and areal extent for the 24-h events are presented in Figs. 7a and 7b. A perusal of the clusters in winter and summer seasons indicates that the average intensities of the events in cluster 2 are similar across seasons with a median average intensity of 1.5 mm h−1. The median average intensity of the winter events in cluster 1 (1.2 mm h−1) is lower than the median average intensity of the summer events in cluster 1 (1.4 mm h−1). The areal extent of the winter events in cluster 2 (median is around 2000 grids, ~32 000 km2) are larger than the areal extent of summer events in cluster 2 (median is around 1200 grids, ~19 200 km2), while the areal extents of the events in cluster 1 for winter and summer are comparable.
Results of clustering analysis for the 24-h extreme rainfall data for (a) DJF and (b) JJA. Red and blue colors represent clusters 1 and 2, respectively.
Citation: Journal of Hydrometeorology 18, 3; 10.1175/JHM-D-16-0193.1
Figure 8 presents the spatial distribution (georeferencing) and the corresponding box plots of the probability of assigning cluster 2 for the five boroughs in NYC for the 24-h events. We can again notice that for the winter season, the five boroughs exhibit a higher likelihood of having 24-h extreme events with high intensity and large areal extent. Individual differences between boroughs exist, with Queens and the Bronx having the highest probabilities and Staten Island and Brooklyn having lower probabilities. On the other hand, for the summer 24-h extreme events, we find that the probability of falling in cluster 2 is around 0.5 for all the boroughs, making them indistinguishable from random chance. In other words, the 24-h extreme events in these boroughs during summer are mixed between high intensity, large areal extent (possible tropical storm and hurricane induced events) and low intensity, small areal extent (possible localized convective storms).
Spatial distribution of the probability of cluster 2 for the 24-h extreme events over NYC in (a) DJF and (b) JJA. The box plots of the probabilities for the five NYC boroughs are also presented for (c) DJF and (d) JJA.
Citation: Journal of Hydrometeorology 18, 3; 10.1175/JHM-D-16-0193.1
c. Atmospheric teleconnections
In this section, we investigate the meteorological context and the conditions that lead to large areal extent (cluster 2) 24-h extreme events for the GNY area for both winter and summer seasons. Large-areal-extent events may be associated with organized transport of moisture to the region. Hence, we examine the synoptic-scale weather anomalies associated with the events under cluster 2. To do this, we generate composites, using ERA-Interim data (Dee et al. 2011). The composites show the sea level pressure (SLP) and 2-m temperature anomalies. The anomalies are with respect to daily means for 1979–2012, which have been smoothed with a 5-day running mean. SLP provides insights into the circulation patterns and storm strength, while 2-m temperature can help show the importance of advection and/or fronts. Figure 9a shows the composite for the winter season (DJF) based on the 24 events that were classified into cluster 2 under winter. The composite SLP field shows a deep, closed-low circulation typical of extratropical cyclones that generate winter precipitation in the region. The 2-m temperature anomaly shows a dipole of warm and cold anomalies, suggestive of the warm and cold advection generated by the storms. The SLP contours and temperature anomalies are not collocated in the manner observed in individual storms. We interpret this to be a bias introduced by the compositing analysis, partially related to the SLP being full fields and the 2-m temperature being anomalies. The important result in this figure is the identification of the stormlike synoptic pattern expected during winter. The upper-level circulation moving eastward is reinforced by the surface low and from cold air moving from the south. Moisture is picked up from the ocean surface and the system moves along the coast of the mid-Atlantic and causes precipitation due to horizontal convergence (Miller and Frederick 1969).
Composites for cluster 2 events of 24-h extreme rainfall events for (a) DJF and (b) JJA. Contours show the SLP (contour intervals: 2.5 hPa, boldface contours are labeled). Shading shows the 2-m temperature anomaly.
Citation: Journal of Hydrometeorology 18, 3; 10.1175/JHM-D-16-0193.1
We further verified these results using the NOAA Storm Events Database, which contains continental-scale records of the occurrence of storms (from 1950 to present) and other significant weather phenomena having sufficient intensity to cause loss of life, injuries, significant property damage, and disruption to commerce (NOAA/NCEI 2016). From the 24 events in winter classified under cluster 2, we found 14 unique episodes and 28 recorded storm events in the GNY area. An episode is defined as an entire storm system that contains many different types of events. An event is defined as an individual type of storm event, such as thunderstorm, flood, tornado, wind hurricane, etc. An investigation into the episode narratives revealed that many of these episodes were associated with low pressure systems that developed along the Gulf Coast states or in the Tennessee Valley and moved toward the Northeast, causing intense rain or winter weather; a few episodes were associated with slow-moving frontal systems that moved from the Ohio Valley and northeastern Missouri into the GNY region.
For the JJA cases, the heavy precipitation events are most likely caused by frontal storms (Lombardo and Colle 2010), and there is a chance that tropical storms or hurricanes also generated some of the extreme events. To identify the tropical storm events, we adapt a storm association method of Booth et al. (2015), using HURDAT2 (Landsea and Franklin 2013), to identify tropical storm tracks that pass within 1000 km of NYC during the dates of the 36 events in the JJA cluster 2 for 24-h precipitation. We find that four events are either hurricanes or post-tropical storms. Figure 7b shows the composite for the 36 events from JJA, including the four storms with tropical origins (also reported here: http://www.weather.gov/okx/HistoricFlooding_081314). The SLP contours show a weak closed low, typical of summertime frontal storms in the Northeast (Lombardo and Colle 2010). The 2-m temperature anomaly shows a gradient that is oriented in the southwest-to-northeast direction, indicative of a cold front, suggesting that these are indeed summertime frontal storms. The gradient in the temperature anomaly field hugs the coastline, and therefore one could assume that the composites are simply capturing a land–sea temperature difference. However, during summer the temperatures of the land and ocean in the climatology are nearly equal, with the land being slightly warmer. Therefore, the anomaly pattern is more likely related to the synoptic structure of summertime frontal storm events. For the summer events, we identified 13 unique episodes and 37 recorded storm events from the NOAA Storm Events Database. Hurricane Irene and Tropical Storm Andrea stand out in these episodes as the major ones; the rest of the episodes are associated with localized thunderstorms that developed along the stationary warm fronts in the region. Taken together, the composites for winter and summer show that, for cluster 2 of the 24-h extreme rainfall events, our analysis of the radar precipitation extremes can be identified with the archetypal storms at the synoptic scale (e.g., Kunkel et al. 2012).
4. Summary and conclusions
Urban hydrologic systems exist at the interface between natural processes and human impacts. An improved representation of the critical forcing of these systems by meteorological and climatic processes is an essential aspect of predicting the functioning of such systems, especially as drainage network modifications are considered. Moreover, knowledge on extreme events’ areal scaling helps in developing improved risk and performance analysis techniques for urban water systems. In this regard we embarked on classifying rainfall extremes based on high-resolution radar rainfall data, exploring the spatial variability at the urban scale, and relating these classifications to synoptic circulation patterns. We first develop spatial fields of extreme rainfall events and compute the average intensity and areal extent of the events for short-duration (1 h) and long-duration (24 h) during winter (DJF) and summer (JJA) seasons. We developed a simple and effective probabilistic classification approach (PAM-based event classification and spatial attribution using probability of occurrence) for these extreme rainfall events and attempted to understand areal coverage by extreme rainfall and its joint dependence with the intensities and time of occurrence. We also investigated the relationships of the classified 24-h events with synoptic circulation patterns and validated them with the storm event database. Following are the main findings:
For the 1-h duration, the summer extreme events have higher average rainfall intensities than the winter extreme events.
The areal extent of the high-intensity 1-h extreme rainfall events during winter is larger than the areal extent of the high-intensity 1-h extreme events during summer.
In NYC, during winter, the borough of Queens has the highest likelihood of experiencing large-areal-extent, high-intensity 1-h extreme events while the borough of Staten Island predominantly experiences low-intensity, small-areal-extent 1-h extreme events.
For the 24-h duration, the summer extreme events and the winter extreme events have similar intensities.
The areal extent of the 24-h extreme rainfall events during winter is larger than the areal extent of the 24-h extreme rainfall events during summer.
In NYC, during summer, all the boroughs have equal probability of experiencing high-intensity, large-areal-extent extreme events and low-intensity, small-areal-extent 24-h extreme events.
Investigation into the relationships of the 24-h high-intensity classified events reveals that the winter events are associated with deep and organized circulation patterns that lead to more areal extent and the summer events are a manifestation of localized frontal systems, hence leading to smaller areal extents.
Acknowledgments
This research was supported by NOAA CREST Cooperative Agreement NA11SEC4810004; the Professional Staff Congress–City University of New York (PSC-CUNY) Award 68670-00 46; the University Transportation Research Center (UTRC) Region 2 award 49198-25 27; the Ralph E. Powe Junior Faculty Award 2015/16 for the second author; and the NOAA Cooperative Institute for Climate and Satellites at the University of Maryland (CICS-MD) Award 76514-05 01. The statements contained within the manuscript are not the opinions of the funding agency or the U.S. government but reflect the authors’ opinions. We thank William Rossow and Michael Grossberg from City College of New York for providing valuable feedback during the inception of this work.
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