Relationships between tropical cyclones and heavy rainfall in the Carolina region of the USA

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. (2009) Published online in Wiley InterScience ( Relationships between tropical cyclones and heavy rainfall in the Carolina region of the USA Charles E. Konrad II a * and L. Baker Perry b a Department of Geography University of North Carolina at Chapel Hill Chapel Hill, NC , USA b Department of Geography and Planning Appalachian State University Boone, NC 28608, USA ABSTRACT: A strong association exists between exceptionally heavy rainfall and the movement of tropical cyclones (i.e. tropical depressions, tropical storms, and hurricanes) across the Carolina region of the USA. There is much variability, however, in the precipitation totals associated with each tropical cyclone. This variability is at least partially tied to various interactions between mid-latitude features and the moisture plume that is advected around the tropical cyclone. In the first part of this study, a 55-year precipitation events climatology is constructed that quantifies the influence of tropical cyclones on precipitation events with varying return intervals. In particular, it shows that the majority of the heaviest precipitation events in the eastern three-quarters of the region are associated with tropical cyclones. In the second part of this study, a synoptic climatology is developed that reveals the relationships between precipitation totals and various atmospheric variables. The variables include the speed of movement, size, and strength of the tropical system as well as the relative position and strength of various synoptic features surrounding the tropical system. These synoptic features include the location of fronts, regions of upper level divergence and areas of high water vapor contents in the atmosphere. A tree regression model is used to develop a classification that summarizes these multivariate relationships. Four classes of tropical cyclones are identified that effectively differentiate tropical cyclones that produce relatively light versus extraordinarily heavy rainfall. Copyright 2009 Royal Meteorological Society KEY WORDS tropical cyclone; heavy rainfall; Carolina; tree regression; synoptic climatology Received 26 August 2008; Revised 15 February 2009; Accepted 15 February Introduction Tropical cyclones (i.e. hurricanes, tropical storms, and tropical depressions) are frequently observed across the southeastern USA during the late summer and early fall. In fact, frequency maps plotted from the HUR- DAT dataset compiled by the National Hurricane Center (NHC) suggest that tropical cyclones occur more frequently along the coast of North Carolina than anywhere else in the western Atlantic Basin and Gulf of Mexico. Tropical cyclones contribute over 14% to the annual precipitation total along and inland of the North Carolina and South Carolina coasts, which is greater than anywhere else in the USA (Knight and Davis, 2008). Tropical cyclone frequencies vary markedly across the Carolina region with more than one per year observed on average along the coast, to less than one every three years on average across the southern Appalachians (Figure 1). Tropical cyclone activity has been especially prolific in recent years. Between 1990 and 2005, 31 tropical cyclones affected the Carolina region. Some of these systems (e.g. Hurricanes Hugo, Opal, Fran, Bonnie, Floyd, and Isabel) caused catastrophic damage and contributed * Correspondence to: Charles E. Konrad II, Department of Geography, University of North Carolina at Chapel Hill, Chapel Hill, NC , USA. konrad@unc.edu to North Carolina s dubious distinction of being associated with more billion-dollar disasters than any other state (Lott and Ross, 2005). There is a strong connection between tropical cyclones and heavy rainfall in the Carolinas, but much variability exists in the rainfall amounts associated with these systems. This is vividly illustrated in a comparison of the rainfall associated with Hurricanes Hugo and Floyd, both of which were large and tracked inland across the Carolinas. Hurricane Hugo produced relatively modest rainfall totals (i.e. broad swath of mm with isolated totals exceeding 150 mm) while Floyd produced extraordinary rainfall totals (i.e. broad swath exceeding 230 mm with isolated totals exceeding 500 mm) (Cline, 2002). The fast movement of Hurricane Hugo was tied to its lack of precipitation production (Cline, 2002). Hurricane Floyd, however, also moved rapidly, but its extreme precipitation production was tied, among other things, to its interaction with a strong upper tropospheric jet streak as it underwent extratropical transitioning (Atallah and Bosart, 2003). Climatological studies reveal several general factors that affect precipitation production in tropical cyclones. Cerveny and Newman (2000) showed a strong connection between the wind speed of a tropical cyclone (i.e. its strength) and precipitation totals, both in the core and in the spiral bands. The vast majority of their Copyright 2009 Royal Meteorological Society

2 C. E. KONRAD AND L. B. PERRY Figure 1. The mean annual number of tropical cyclones that pass within 200 km of a given location. The frequencies are calculated from position data found in the HURDAT dataset between 1950 and 2004, which is provided by the National Hurricane Center. sample, however, consisted of systems in a deep tropical environment and, therefore, not subject to extratropical influences. Konrad et al. (2002) investigated tropical cyclone rainfall totals with respect to the scale or size of the area of heavy rainfall. They found that the relationships vary according to the size of the precipitation region; in particular, precipitation over the broadest scales correlated most strongly with the size of the system, while local precipitation totals were most strongly related to the cyclone s speed of movement. Their sample was garnered from cyclones that made landfall in the eastern USA, thus, a portion of their events were subject to extratropical influences. Many of the tropical cyclones that affect the Carolinas move into an increasingly extratropical weather environment as evidenced by a re-curving track around the Bermuda High (i.e. a north to northeastward movement across the region). A study by Hart and Evans (2001) suggests that nearly half the tropical cyclones in the Atlantic undergo an extratropical transition whereby significant changes are observed in the nature and spatial pattern of precipitation. In particular, the precipitation and associated cloud shield become asymmetrical with a dry slot developing to the south and southwest of the system, and a shift observed in the area of heaviest rains to the left (i.e. west or northwest) of the track (Atallah et al., 2007). The changing precipitation pattern can be tied to the cyclone s acquisition of various extratropical circulation features including a deepening middle tropospheric trough-ridge couplet, a strengthening jet streak (i.e. outflow jet) and a frontogenesis pattern immediately downstream (Atallah et al., 2007). Several systems responsible for excessive rainfall in the Carolina region have undergone extra-tropical transitioning (ET) including Hurricanes Floyd (Atallah et al., 2003) and (Palmen, 1958). The ET process, however, often occurs gradually, thus, it is unclear to what extent these types of systems display classic ET characteristics in the Carolinas. Cline s (2002) examination of 14 tropical cyclones affecting North Carolina revealed that at least half were subject to extratropical influences that enhanced the precipitation. These included the presence of a front, which acts as focusing mechanism for the precipitation, and an ET wind and precipitation pattern, (i.e. upstream veering wind profile and precipitation maximum left of the track). Atallah et al. (2007), however, compared tropical cyclones with a predominantly left- and rightof-track precipitation maximum, and found that 13 out of 16 tropical cyclones in their sample were associated with a precipitation maximum to the right of the track south of 38 N latitude, which includes the Carolinas. It appears that many tropical cyclones crossing the region are beginning the ET process, but features associated with ET including the right-of-track precipitation maximum, are often not yet present. Moreover, there are other extratropical features, such as stalled frontal boundary or an upper tropospheric jet streak that may be present with or without ET that can focus the precipitation over a small region. In the Carolinas, heavy precipitation forecasting is especially challenging because there is much variability in the large-scale environments surrounding tropical cyclones. For example some systems are surrounded by a deep tropical environment with rain concentrated concentrically around the eye and spiral bands while other systems are moving into an extratropical environment. Since many systems are just starting to undergo ET, recently developed precipitation models incorporating the ET paradigm (e.g. Atallah et al., 2007) are not necessarily applicable. In the mountainous western portion of the Carolinas, precipitation forecasting is further challenged by the interaction of the tropical cyclone circulation with the terrain. In particular, strong orographic enhancement of precipitation often occurs on the windward southeastern slopes, while valleys to the northwest often lie within a rain shadow. The objective of this paper is to provide a detailed climatological perspective on tropical cyclones that move across the Carolinas and produce heavy rainfall. In the first section, a precipitation events climatology is developed that examines the contribution of tropical cyclones to heavy rain production across four subregions of the Carolinas. In the second section, various tropical cyclone attributes (i.e. strength, size, and speed of motion) are combined with variables associated with the large-scale synoptic environment (e.g. upper level divergence, precipitable water) and related to the highest precipitation totals observed over the regional scale. A tree regression model is developed that summarizes these relationships and provides insights on the forecasting of heavy rainfall around tropical cyclones.

3 TROPICAL CYCLONES AND RAINFALL IN CAROLINA, USA Figure 2. The Carolina study area with the four sub-regions identified: Mountains, Western Piedmont, Eastern Piedmont, and Coastal Plain. The triangles represent stations making the cooperative observer network of precipitation gauges. 2. Precipitation events climatology In this study, precipitation events were identified through estimates of areal precipitation across a region encompassing North and South Carolina as well as a small portion of North Georgia and a small portion of extreme eastern Tennessee (Figure 2). Owing to its irregular configuration, the immediate coastal region was not included because of an absence of rain gauges in the surrounding sounds and bays. In order to compare precipitation and tropical cyclone attributes, the study region was split into four equal-sized sub-regions (Figure 2). Each sub-region is oriented perpendicular to the northwest-to-southeast gradient in tropical cyclone frequencies identified in Figure 1. The mountain region (MT) encompasses the southern Appalachian Mountains with peaks and ridges between 1000 and 2000 m. This region also includes a small portion of the elevated and high dissected Piedmont of North Georgia. The western Piedmont (WP) and the eastern Piedmont (EP) regions consist of gently rolling terrain, interspersed with a few small mountains in the western section. The coastal plain (CP) is relatively flat, except for a portion of its western section where the Sandhills provide some slight relief. Daily precipitation totals from the Cooperative Observer Network were used and accessed from the Cooperative Summary of the Day CD ROMs (NCDC, 2004) for the period This network provides the best spatial coverage of gauges over the 55-year study period. Gauge-trained radar precipitation totals provide better estimates, however, this data is not available over much of the study period. Most of the 24-hour precipitation totals were recorded near 7 : 00 or 19 : 00 LST, although primary reporting stations (e.g. National Weather Service (NWS)) provided measurements near midnight. Unfortunately, no information was available on the recording times for a given station, thus it was not possible to establish a standard 24-hour time frame for estimating areal precipitation totals across a given network of stations. Two-day precipitation totals were estimated in order to encompass the typical period in which a tropical cyclone produces precipitation in a given area, and also to cover for the differences in measurement times. An overlapping time series of 2-day precipitation totals was estimated across each of the four sub-regions through the interpolation of network precipitation totals using Thiessen polygons. From the constructed precipitation time series, the heaviest 2-day precipitation events were identified and used to determine precipitation return intervals for each of the four sub-regions (Table I). The CP and MT regions display the greatest precipitation totals for the calculated return intervals. Most striking is the markedly greater precipitation total for the longest recurrence interval (23.1 cm or 9.08 ) in the CP. This extraordinary regional precipitation event is associated with Hurricane Floyd, and its recurrence interval is probably much greater than the reported 55 years, a length of time that is an artifact of the duration of the study period. Stream gauge analyses suggest that the recurrence interval for this event exceeded 500 years (Bales et al., 2000). The second heaviest precipitation event in the region was associated with a much lower precipitation total (14.6 cm or 5.74 ) and was relatively close to that heaviest event observed in the MT region. This suggests that had Floyd not occurred, the regional recurrence interval would be very similar to that in the mountains (13.9 cm or 5.48 ). These results indicate that precipitation totals associated with 55-year recurrence interval are sensitive to the occurrence or nonoccurrence of extreme events (i.e. those with much longer recurrence intervals). A similar pattern is noted for the return intervals associated with the highest point totals of precipitation: Hurricane Floyd was responsible for the 61.1 cm maximum and the second heaviest point total was more than 7 cm less. Given the high degree of spatial variability of precipitation in the point totals, the amounts garnered from the coarse network of stations in this study underestimate the true magnitude. In other words, it is very likely that heavier point totals of precipitation have occurred in areas where there are no rain gauges. Additionally, the high winds associated with tropical cyclones negatively bias the reported precipitation totals Table I. Precipitation totals (cm) for various return intervals by region: Mountains, Western Piedmont, Eastern Piedmont, Coastal Plain. The bolded and underlined numbers highlight the heaviest and lightest precipitation totals, respectively, for each return interval. Precipitation Regional mean total Maximum point total Rank (return interval) MT WP EP CP MT WP EP CP +55-year storm 5-year storm 2-year storm 1-year storm 6-month storm

4 C. E. KONRAD AND L. B. PERRY as the rain gauges do not catch all the wind-blown precipitation (e.g. refer Groisman and Legates, 1994). The next step in this study was to associate the precipitation events with tropical cyclones crossing the region. Information from the HURDAT dataset compiled by the NHC was used to identify and track tropical cyclones across the region. The dataset provides 6-hourly (i.e. 0000, 0600, 1200, 1800 UTC) positions (in tenths of a degree latitude and longitude) for all tropical cyclones (i.e. hurricanes, subtropical, and tropical storms) in the Atlantic basin. For the first 6 years of the study period (e.g ), only the 0000 and 1200 UTC positions were recorded by forecasters; therefore, the HURDAT dataset contains interpolations of the 600 and 1800 UTC positions. Other caveats regarding the precision of the position data are discussed in Jarvinen et al., (1984) and summarized in Konrad et al. (2002). Using both the HURDAT dataset and daily surface weather analyses, 75 precipitation events in the Carolinas were associated with tropical cyclones. Lastly, daily surface analyses were examined to identify and record the sixhour positions of eight tropical depressions crossing the region. Tropical depressions were added to the sample in order to determine if they contribute significantly to heavy rain climatology of the region. The addition of these events provided a study sample of 83 tropical cyclones. Figure 3 presents the tracks of tropical cyclones associated with precipitation events displaying regional recurrence intervals of one year or greater. These tracks are segregated into four groups on the basis of the subregion in which the heaviest mean rainfall was observed. Roughly 85% of the tropical cyclones display a northeastward component of motion as they cross the study region. Nearly 60% of the systems that make landfall do so along the Atlantic Coast while the remainder cross the Gulf Coast. There is, however, a marked east to west reversal in this pattern across the study region. Over 80% of cyclones in the CP make landfall on the Atlantic coast in contrast to the MT region where over 80% of the cyclones make landfall along the Gulf Coast. The region of heaviest precipitation aligns closely with the cyclone track; however, there are some interesting exceptions. In many of these cases, the moisture associated with the tropical cyclone was advected over a frontal boundary; thus, the precipitation was not directly connected with the tropical cyclone s core or spiral bands. This occurrence will be discussed in the next section. In contrast to the other regions, all the cyclones responsible for the heaviest rainfall in the MT region move overhead or west Figure 3. The tracks of tropical cyclones associated with mean areal precipitation totals that exceeded the one-year recurrence interval in each of the four sub-regions.

5 TROPICAL CYCLONES AND RAINFALL IN CAROLINA, USA of the area. This indicates a right-of-track precipitation maximum that can be tied to orographic enhancement of precipitation via southerly and southeasterly flow on the right side of the tropical cyclones. A majority of the heaviest precipitation events are associated with tropical cyclones (Table II). In fact, 90% of the precipitation events with recurrence intervals of 5 years and greater in the CP and EP regions are tied to tropical cyclones. This percentage, however, drops slightly in the WP (i.e. 70%), and dramatically in the MT (i.e. 40%), where tropical cyclone frequencies are much lower (e.g. Figure 1). A similar pattern is noted for the greatest point totals of precipitation, although tropical cyclones contribute slightly less in the eastern regions and much less in the west where other types of wet weather patterns can produce extraordinary point totals of rainfall. The two-day regional-scale precipitation totals associated with the tropical cyclone are ranked and used to provide a rough estimate of the recurrence interval using the following formulation: Recurrence Interval = (N + 1)/M where N = number of years in the precipitation time series, and M = magnitude or rank of the event. An important caveat here is that the confidence in these estimations decreases as the return interval increases; in other words, the confidence in the recurrence intervals of the most extreme events is the least. The regional-scale precipitation associated with the 83 tropical cyclones is distributed rather evenly in terms of its intensity or recurrence interval (Table III). In the eastern three regions, a given tropical event is nearly as likely to produce an extraordinary precipitation total (i.e. recurrence interval >5 years) as an ordinary precipitation total (recurrence interval of less than one year). The synoptic explanations for this variability will be explored in the next section. Maximum precipitation point totals show a slightly greater propensity for producing rainfall connected with a shorter recurrence interval (i.e. 2 years or less). This is especially the case in the MT region where orographic enhancement in non-tropical situations contributes more to extreme point totals of precipitation. More than half the tropical cyclones making landfall in the sample were hurricanes (Table IV). Slightly more Table II. Percentage of the heaviest precipitation events that are associated with a tropical system by sub-region: Mountains, Western Piedmont, Eastern Piedmont, Coastal Plain. Percentages exceeding 50% are bolded. Precipitation Regional mean total Maximum point total Rank (return interval) MT WP EP CP MT WP EP CP 1 11 (5 55 year) (2 5 year) (1 2 year) (1/2 1 year) Table III. The percentage of tropical systems that are associated with rainfall of different intensities by sub-region: Mountains, Western Piedmont, Eastern Piedmont, Coastal Plain. The bolded and underlined values highlight the highest and lowest percentages, respectively, for each return interval. Precipitation Regional mean motal Maximum point total Rank (return interval) MT WP EP CP MT WP EP CP (5 55 year) (2 5 year) (1 2 year) (1/2 1 year) Total Table IV. The number of tropical systems by intensity (hurricanes (H), tropical storms (TS) and tropical depression (TD)) at landfall versus the maximum regional mean precipitation in the Carolina study region. Precipitation Tropical system intensity Rank (return interval) H TS TD Total 1 11 (5 55 year) (2 5 year) (1 2 year) (1/2 1 year) >110 (<1/2) Total than 40 (70%) of these hurricanes were associated with median areal precipitation totals exhibiting a 5-year or greater (2-year or greater) recurrence interval across the Carolina region. This contrasts strongly with tropical storms, which account for only about 25 and 45% of the 2- and 5-year storms, respectively. Only one out of the eight tropical depressions was associated with extremely heavy areal precipitation totals. Three hurricanes were tied to ordinary precipitation totals (i.e. half-year storm or less). These results suggest a positive relationship between tropical cyclone strength and precipitation totals on the regional scale, however, there are some interesting exceptions. For example, the strongest tropical cyclone in the sample, Hurricane Hugo, moved through the centre of the study region but produced relatively modest precipitation totals (i.e. halfyear storm). These relationships are investigated in the next section. 3. Synoptic climatology In the second section of this paper, various characteristics of each tropical system and its surrounding synoptic

6 C. E. KONRAD AND L. B. PERRY environment are associated with the heaviest two-day totals over the regional scale. This analysis was restricted to 53 tropical cyclones whose centres moved across the study area. Note that this precludes 30 systems that moved along the immediate coastline, did not make landfall, or moved west of the study region. A routine was employed to identify the circular region (area = km) displaying the heaviest two-day rainfall totals associated with each tropical system. In order to locate the region of heaviest rainfall, areal mean precipitation totals were estimated within a circular ring moved systematically (i.e. pixel by pixel) across the km pixel precipitation grid. Details of this procedure are provided in Konrad (2001). Figure 4 provides an example for the precipitation field connected with Hurricane Floyd. Note that the diameter of the circular region (112 km or 1 latitude) is roughly equal to the width of each sub-region identified in the first part of this work. Also, while the centres of heaviest rainfall are situated within the study region, there are some events in which a portion of the heavy rain region extends beyond the study region borders. In these cases, the precipitation grid is simply extended by using cooperative precipitation data immediately outside the study area. Hourly precipitation data (HPD) were examined from closely situated stations in order to estimate the six-hour period of heaviest rainfall. The size, strength, and speed of movement of each tropical system were estimated for the six-hour map time immediately prior to landfall. Konrad (2001) found that these cyclone attributes displayed a significant relationship with precipitation totals across a range of spatial scales. The tropical cyclone size was defined by the area circumscribed by the outermost closed isobar (e.g. Konrad et al., 2002). Tropical cyclone sizes were calculated manually using all available six-hourly (e.g. 0000, 0600, 1200, 1800 UTC) NOAA Northern Hemispheric analyses. The distances from the centre of the system to the outermost closed isobar were measured in four cardinal directions and converted to kilometers. These distances were then used to estimate the area encompassed by the outermost closed isobar. The cyclone strength and speed-of-movement estimates were derived via measures obtained from the tropical cyclone position data in the HURDAT dataset described earlier. The tropical cyclone s strength can be tied to the minimum central surface pressure; however, the pressure data are not available for many systems prior to the 1970s. Therefore, the reported sustained wind maximum was used as a surrogate for the cyclone strength. The synoptic-scale aspects of the tropical system environment were accessed using gridded ( latitude/longitude mesh), twice-daily synoptic data extracted from the NCEP NCAR Reanalysis dataset (Kalnay et al., 1996). These data were spatially and temporally interpolated onto a coordinate system centred on the tropical system during the mid-point of the six-hour period of heaviest rainfall. Using the 0000 and 1200 UTC gridded synoptic fields, a temporal interpolation was undertaken Figure 4. Two-day precipitation totals associated with Hurricane Floyd. The large open circle circumscribes the area of heaviest rainfall. The track and six-hour positions of the hurricane centre are denoted by the dashed line and triangles, respectively. The small circle indicates the hurricane centre at the mid-point time of the six-hour period of heaviest rainfall within the large open circle. The arrowed line identifies the distance between the hurricane centre and the centre of the area of heaviest rainfall. to estimate field values for the mid-point of the six-hour period of heaviest rainfall. An inverse distance technique was used to carry out all spatial and temporal interpolations. Higher-resolution data (e.g. North American Reanalysis dataset) are available; however, they do not extend sufficiently far back to include tropical cyclones during the first half of the study period. Surface analyses were also examined to determine if fronts were present in the vicinity of heaviest rainfall and, if so, where they were located relative to the associated tropical system General connections between atmospheric parameters and precipitation totals Eleven synoptic-scale parameters (Table V) were estimated within the floating km 2 region centred over each tropical system (Figure 5). These variables were identified as potentially useful in assessing conditions leading to exceptionally heavy rainfall as well as determining the region of heaviest precipitation relative

7 TROPICAL CYCLONES AND RAINFALL IN CAROLINA, USA Table V. Atmospheric parameters investigated in this study and their correlation with regional-scale precipitation totals sorted by the strength. Statistically significant correlations at the 0.05 level and higher are italicized. Atmospheric Parameters Correlation 0.45 Tropical system size (area inside outermost 0.48 closed isobar) Area in which precipitable water > Area in which 200 hpa divergence >0 s 1 and PW >2.00 Areal mean 850 hpa moisture flux 0.41 Areal mean precipitable water 0.39 Tropical cyclone wind speed 0.31 Areal mean 700 hpa vertical velocity 0.25 Areal mean 200 hpa divergence 0.21 Tropical cyclone speed of movement 0.19 Presence of a front near precipitation event 0.10 Area in which 200 hpa divergence >0 s to the storm track. The areal mean calculations were made by computing an average across all the pixels within the floating square region. A total of 6 of the 11 parameters display statistically significant correlations with the regional-scale precipitation totals. Tropical cyclone size shows the strongest correlation with precipitation totals. This is followed closely by two related parameters: the area in which precipitable water exceeds 5.08 cm (2 ) and the area in which upper level divergence is present and precipitable water exceeds 5.08 cm. Note that there is statistically significant correlation between the precipitable water in a tropical cyclone and its size. The regional-scale precipitation totals also show significant correlations with the 850 hpa moisture flux and precipitable water as well as the strength of the tropical cyclone as estimated by the sustained wind speed immediately prior to landfall. The relationship of these parameters to heavy rainfall is illustrated through a brief examination of Hurricane Floyd. This cyclone was associated with the heaviest precipitation totals in the tropical cyclone sample as archived radar analyses reveal a broad region of heavy rainfall around its centre (Figure 4). However, drier air began wrapping around the south of the southern side before landfall as the heaviest rainfall was occurring in North Carolina. The cyclone displayed a relatively large size (i.e. fifteenth largest) and strength (i.e. eighth strongest) compared with other tropical cyclones (Table VI), and both these correlate with the occurrence of exceptionally heavy rainfall (e.g. Konrad, 2001). The cyclone, however, moved relatively quickly (i.e. twenty-eighth fastest) to the northeast, and the broad rain shield shifted quickly to the northeast as well. What was distinctive about the heavy precipitation was that it extended far downstream to the northeast underneath an exceptionally large region of 200 hpa divergence (Figure 5). This upper level feature can be tied to the entrance region of a departing jet streak as described by Atallah et al. (2007). Precipitable Figure 5. Regions of high precipitable water (solid line) and positive 200 hpa divergence (dashed line) on 16 September 1996 at 2Z, which is mid-point of the six-hour period of heaviest rainfall associated with Hurricane Floyd. The star indicates the centre of the region experiencing the heaviest rainfall. The speckled region identifies the area in which 200 hpa divergence is positive and precipitable water exceeds 2. The area within which mean field values are calculated is denoted by the large square. Means are calculated from values at 25 floating grid points (small triangles) centred over the tropical cyclone centre. water, which provides an integrated measure of the water vapor contents through the atmospheric column, was relatively high around the cyclone (i.e. fourteenth highest). Moreover, the highest precipitable water values near the cyclone centre were larger than those observed in any of the other tropical cyclones in the sample. Also, the region of overlap between the high precipitable water and 200 hpa divergence was also the greatest in the sample. This suggests a broad region with a large upward vertical moisture flux and heavy rainfall production (i.e. upper level divergence associated with middle tropospheric lifting of air containing copious amounts of water vapor). This upward moisture flux is also revealed by a broad area of strong ascending motions at 700 hpa northeast of the cyclone centre (not shown). The mean values of vertical velocity across the cyclone region are ranked as the seventh strongest A multivariate model for classifying tropical cyclones While a range of atmospheric variables, including precipitable water and tropical cyclone size, have been related to regional-scale precipitation totals, the interrelationships between these variables in controlling precipitation production in tropical cyclones is not clear. Traditional multiple regression approachesdo not necessarily identify or explicitly reveal (i.e. make transparent) these interrelationships, In particular, these approaches assume that homogeneity exists within the population of interest in terms of the nature of the relationships. In other words, an apriori assumption is made that the study sample

8 C. E. KONRAD AND L. B. PERRY Table VI. Ranks in the magnitude of the atmospheric parameters associated with Hurricane Floyd relative to the other 82 tropical systems in the sample. Atmospheric Parameters Rank Area in which DV2 >0 s 1 1 Area in which precipitable water (PW) 1 >5.08 cm Area in which DV2 >0 s 1 and PW >5.08 cm 1 Areal mean 200 hpa divergence 3 Areal mean moisture flux 3 Areal mean 700 hpa vertical velocity 7 Tropical cyclone wind speed 8 Areal mean precipitable water 14 Tropical system size (area inside outermost 15 closed isobar) Tropical cyclone speed of movement 28 is drawn from a homogeneous population in which the relationship between any two given variables is theoretically the same across the entire population. In practice, a sample of weather events (e.g. heavy rainfall) may be drawn from different populations of circulation that display unique relationship structures. More sophisticated approaches, such as neural network modelling, while effective at finding the strongest and most robust relationship across a diverse sample, do not make transparent the structure of these multivariate connections. In order to identify and account for the multivariate nature of these relationships, a tree regression modelling approach is employed in this study. Tree classification and regression (CaRT) approaches, popularized by Breiman et al. (1984), have been used in a number of atmospheric science studies (e.g. Peak and Elsberry, 1987; Elsner et al., 1996; Walmsley et al., 1999; Conner and Woodcock, 2000). A tree regression algorithm searches for the best relationship between the predictand (i.e. single dependent variable), and a specified number of predictor variables (PV). In this study, a tree regression is constructed to predict the regional-scale precipitation totals from eleven PVs (refer Table V) that summarize the large-scale atmospheric character of each tropical cyclone. The tree regression is carried out using the following algorithm as illustrated in Figure 6: First, a correlation analysis is performed to identify the PV 00 that explains the greatest amount of variation in the predictand. Second, the mean for PV 00 is calculated for the tropical cyclone sample (C 00 ) and designated as a splitting point that separates each observation (i.e. tropical cyclone event) into one of two classes (C 11 or C 12 ) or branches. If the observation falls below (above) the PV 00 mean, it is assigned to the C 11 (C 12 ) class. In other words, tropical cyclones that display relatively small or large values in PV 00 are assigned to a small class (C 11 )orlarge class (C 12 ), respectively. The procedure is then repeated independently for each of the two classes or branches: Specifically, the means for PV 11 and PV 12 (i.e. those Figure 6. Schematic diagram illustration of a three-level regression tree. Each level (L) consists of a group of classes C L1,C L2,C L3...C Ln, which are distinguished on the basis of the sample splits around the mean of PV L 1,1,PV L 1,2,PV L 1,3...PV L 1,n. explaining the most variance in the sub-sample) are used to split each class into two smaller classes, C 21, C 22 and C 23,C 24. The splitting or branching process may be continued to a user-defined terminal layer of tree, which is identified as the point immediately before the stability or robustness of the model is compromised (i.e. sample size of each class becomes unreasonably low). Regression trees offer several advantages over commonly used multivariate approaches, such as linear regression. Most significantly, no assumptions need to be made regarding the distribution of the sample; tree models can work with non-normal or highly skewed data (Breiman et al., 1984). Moreover, classification trees can readily incorporate a mix of variables, including continuous and nominal variables. Finally, details of the multivariate relationship are revealed through the displayed tree structure as well as the summary statistics of each class in the terminal layer of the classification tree. In order to improve the explanatory power and robustness of the tree regression model, an iterative bootstrapping approach is applied that involves training runs of the tree model that are validated by randomly derived samples. Specifically, the approach involves the following procedure: First, a large number of tree models (i.e. a forest) are generated from randomly selected sub-samples within the overall sample or population (i.e. all tropical cyclones in the study). Each tree is validated, that is, its performance is evaluated by determining how well it performs when it is applied to many randomly derived samples within the population. A coefficient of determination (r 2 ) is calculated for each validation model run, which quantifies the amount of variance explained by the model. A mean r 2 is computed to summarize the mean performance of the model across all the randomly determined sub-samples. Additionally an r 2 is calculated for the entire population to provide a second measure of overall performance. It should be noted that the random validation samples were drawn from a combination of independent events (i.e. events not used to build the given tree model) as well as events used to generate the tree model. By drawing randomly from the entire population, the validation samples contain the greatest mix of tropical cyclone events. This increases the variability of event

9 TROPICAL CYCLONES AND RAINFALL IN CAROLINA, USA mixes across samples and, hence, the testing of a wider variety tree regression models. The iterative tree modelling approach in this study was applied to a population of 53 tropical cyclones whose centres passed through the study area. Each tree model was constructed from a randomly chosen sample of 16 events (i.e. 30% of the population). Pilot work was carried out to identify the ideal sample size for maximizing the mean variance explained across the validation samples. Ten thousand tree models were generated and each was validated 100 times from randomly identified samples of 27 events (i.e. 50% of the population). Model performance approached an asymptote around 100 samples (i.e. validations using sample sizes exceeding 100 did not change the results significantly). In the last step of the procedure, a fully specified model was developed by taking the best performing model run and applying it to the entire population of events. Figure 7 summarizes the regression tree constructed to relate regional-scale precipitation totals in 53 tropical cyclones to 11 PVs (Table V). At the first level, the model split the sample into two classes of events according to the size of the tropical system with smaller (bigger) tropical cyclones associated with lighter (heavier) regional precipitation totals. At the second level, the class of relatively small tropical cyclones was further split according to the size of the area in which precipitable water was high and upper level divergence was present. Specifically, events displaying (not displaying) a region of high precipitable water with upper level divergence present were tied to heavier (lighter) precipitation totals. The class of events containing relatively large tropical cyclones was further split according to the presence or absence of a frontal boundary in the vicinity. The heavier (lighter) precipitation events were associated (not associated) with a front. This model explained nearly 73% of the variance in the training run (i.e. tree classification generated from the sub-sample of 16 events). The mean variance explained in the 100 validation runs was roughly 46%, and the application of the fully specified model to the entire population of 53 events explained slightly over 40% of the variance in the precipitation totals. The relatively modest sample sizes dictated that only two levels of the classification tree could be constructed, thus limiting the terminal layer of the model to four classes of tropical cyclones. Table VII summarizes the characteristics of the 4 tropical system classes utilizing statistics drawn from the entire population of 53 events. There is a notable spread in the mean regional-scale precipitation totals across the four tropical system classes (Figure 7). Most notably, 8 of the 10 lightest tropical cyclones in the study were assigned to Class I, while 8 out of 10 of the heaviest events were assigned to Class IV. Another characteristic to note is that class membership decreases progressively from Class I to Class IV; in fact, Class I contains twice as many events as Class IV. This skewed distribution of class membership developed by model closely approximates the skewed distribution observed in the precipitation totals of the sample (i.e. many relatively light events and few extraordinarily heavy events). Class I tropical cyclones are most distinguished by their small size and the absence of a region of overlap between high precipitable water and upper level divergence. In fact, the composite map (Figure 8) using data derived from the coarse-scale NCEP Reanalysis Data does not reveal any region of high precipitable Figure 7. Summary of the tree regression model that predicts two-day precipitation totals on the basis of the tropical system size, the area of overlap between high precipitable water and 200 hpa divergence (PW-Div200 Area), and the presence or absence of a front. Sample sizes for the training and fully specified models are provided in the boxes by the non-bolded and bolded values, respectively. The box and whisker plot at the bottom illustrates the 25 75th and 0 100th percentile ranges in the event precipitation totals constituting each class.

10 C. E. KONRAD AND L. B. PERRY Table VII. Summary statistics associated with the input variables in the tree model including the proportion of the variance described by the tree model (r 2 ) and the means by event class. Class means that are significantly higher or lower are italicized. Classes means that are the highest and the lowest for each variable are bolded and underlined, respectively. Variable r 2 Means by class Area of tropical system (km 2 ) Overlap 200 hpa div and high PW (km ) Front associated with system (%) Areal mean 850 hpa moisture flux Area of high precipitable water (km ) Wind speed 0.24 Hurricanes (%) Tropical storms (%) Tropical depressions (%) Areal mean precipitable water (cm) Areal mean 700 hpa vertical velocity (hpa/h) Areal mean 200 hpa divergence (s 1 ) Area of positive 200 hpa divergence (km ) System speed of movement (Km h 1 ) Month 0.21 Before Sept. 10 (%) After Sept. 10 (%) Distance from event to cyclone centre (km) Figure 8. Composites of 1000 mb heights (gray, dashed in meters), precipitable water exceeding 5.08 cm or 2 inches (blue, thick solid), and positive 200 hpa divergence (red, thin solid in sec 1 ) for each tropical system class. For comparison purposes, the isoline intervals for each map are the same. This figure is available in colour online at

11 TROPICAL CYCLONES AND RAINFALL IN CAROLINA, USA water (i.e. values exceeding 2 ). Relatedly, the 1000 hpa height composite (Figure 8) does not show a well defined cyclonic centre as the system size is too small to be resolved in the composite. The Class I systems display the lowest mean values of precipitable water, vertical velocity, and 850 hpa moisture flux across the km grid centred over the system centre. It is noteworthy that these variables display a significant positive relationship with the size of the system in the overall sample, thus, the modest values of the means may be tied to the small size of the Class I events. The Class I systems are not only smaller but also relatively weak; in fact none of the Class I systems were hurricanes immediately prior to landfall. About half these systems moved in the general vicinity of a frontal boundary, and nearly three-quarters of the Class I systems occurred before September 10, which is the mid-point of the tropical cyclone season. Class I tropical cyclones display the second greatest distance (compared to the other system classes) between the centre of circulation and the location of heaviest rainfall (Table VII). This is curious, given the fact that Class I systems display a relatively small and compact circulation. Examination of the synoptic maps connected with these systems reveals that the precipitation field is relatively broader in many events and is not as well organized. In some events, the precipitation observed along the downstream periphery is associated with a front. Also, the precipitation field in many of these events is skewed more to the right, or ocean side, quadrant of the system. Matyas (2007), who investigated the shape of the precipitation fields produced by tropical cyclones, found that weaker systems (e.g. tropical storms) display a more asymmetric precipitation distribution (i.e. more precipitation in the right, forward quadrant of the system). She related this to the presence of two factors: (1) Weaker cyclonic wind circulation, thus less advection of moisture towards the left or continental side of the cyclone. (2) The presence of directional wind shear (i.e. increasing synoptic-scale wind vector from left to right with height towards or across the tropical cyclone track. Class II tropical cyclones are distinguished from Class I systems by the presence of a region of overlap of high precipitable water and 200 hpa divergence. In fact, 14 out of 15 of these systems display some overlap in these two regions. Class II systems share several similarities with Class I systems: (1) They are only slightly greater in size (i.e. 822 vs. 555 km 2 ). (2) Slightly more than half of them occur in the vicinity of a front. (3) The majority of them are tropical storms (only 1 out of 14 of the Class II events was a hurricane immediately prior to landfall). (4) A high proportion of them (79%) occur in the first half of the hurricane season. Map composites (Figure 8), however, reveal that Class II events are better defined in the 1000 hpa height field, display stronger areas of 200 hpa divergence, and higher mean precipitable water values. Class III tropical cyclones are strongly distinguished from Class I and II systems in terms of size (more than four times larger) and the absence of a frontal boundary in the vicinity of the system. The regression tree distinguishes Class III systems from Class IV systems by the absence of a frontal boundary. Class III systems are distinguished from Class I and II systems in terms of their strength, as more than half of them were hurricanes immediately prior to landfall. Class III systems also display significantly higher mean values of precipitable water and 850 hpa moisture flux across the km region, which are significantly correlated with the tropical system size. Additionally, more than half the Class III events occurred after September 10. Compared to the other four classes, Class III events display the shortest distance between the region of heaviest rainfall and the cyclone centre. An examination of synoptic charts reveals that this short distance can be related to the absence of peripheral areas of heavy precipitation that are forced by isentropic lifting of maritime air over frontal boundaries. Several well known Class III tropical cyclones include Hurricanes David (1979, near Savannah, GA), Hugo (1989, in Charleston SC), and Isabel (2003, in the Outer Banks region of NC). It is noteworthy that each of these cyclones moved north to northwestward, unlike the vast majority of systems investigated in the sample. In fact, 8 out of the12 systems in the class displayed a west of north movement at the time of landfall. Unlike the other three classes, all the type III events made landfall along the Atlantic Coast. Class IV tropical cyclones are most distinguished from the other three classes by their large size and the presence of a front. They show the greatest degree of overlap of high precipitable water and upper level divergence (Figure 8). Furthermore, they display the greatest mean values of precipitable water, upper level divergence, 850 hpa moisture flux and 700 hpa vertical velocity. Class IV events also display the greatest mean distance between the region of heaviest rainfall and the upstream cyclone centre (i.e. nearly 70% greater than the mean for the three other classes). This long distance can be related the interaction of the tropical system with upstream midlatitude features. Specifically, each system is associated with an upstream frontal boundary, either to the northeast or northwest, that provides low-level convergence and the lifting of tropical moisture. Synoptic-scale lifting is also facilitated in the type IV systems by a broad area of 200 hpa divergence in the general vicinity of the front, which in some events is tied to the entrance region of an upper tropospheric jet streak. Details of this interaction are provided for Hurricanes Hazel (Palmen, 1958) and Floyd (Atallah and Bosart, 2003), which were both assigned to Class IV by the model. More than threequarters of the Class IV events occur after the mid-point of the tropical cyclone season. This is the portion of the hurricane season in which mid-latitude circulation features (e.g. fronts and upper tropospheric jet streaks) most frequently interact with tropical cyclones. Lastly, class IV systems display a mean speed of movement that is 40% faster than the other 3 classes. This relatively high speed can be tied to the fact that class IV systems have entered a region immediately downstream of an upper