1. Introduction
Identifying regions within landfalling tropical cyclones (TCs) in which high rain rates occur and quantifying the evolution of these regions is critical for the improvement of hydrological models used to forecast flooding (e.g., Baeck and Smith 1998; Elsberry 2002; Ulbrich and Lee 2002; Medlin et al. 2007). When using radar reflectivity returns to identify these regions, researchers generally agree that 40-dBZ reflectivity values correspond to convective clouds, which produce high rain rates, while 30-dBZ values originate from stratiform clouds, which produce lower rain rates that are not a great concern for flooding. A clear consensus does not exist, however, regarding the classification of 35-dBZ reflectivity returns.
The contrasting growth patterns of the two main precipitation regimes occurring within TCs, convective and stratiform precipitation (Houze 1993), allow these regions to be identified by their spatial attributes when visualized using radar-derived data (Ulbrich and Atlas 2002). Because of their strong vertical velocity fields (Steiner et al. 1995), convective clouds cover small horizontal areas but produce high rain rates that can lead to flash flooding (Baeck and Smith 1998). Thus, these regions are extremely important to identify in regard to flood forecasting for landfalling TCs. When viewed using radar reflectivity returns, convective regions tend to be elliptical in shape (Churchill and Houze 1984; Rigo and Llasat 2004) and compact and to have high radial gradients of reflectivity (Marks 1985; Biggerstaff and Listemaa 2000) due to their strong vertical motions. Radar reflectivity values over a 34–41-dBZ range have been utilized to delineate convective precipitation within TCs by researchers, including Ryan et al. (1992) (34 dBZ), Barnes and Stossmeister (1986) (35 dBZ), Burpee and Black (1989) (38 dBZ), Jorgensen (1984) (40 dBZ), and Parrish et al. (1982) (41 dBZ).
In contrast, the slow ascent of air into stratiform clouds causes them to occupy a larger horizontal area (Yuter and Houze 1995; Biggerstaff and Listemaa 2000; Anagnostou 2004) and to produce low rainfall intensities. Stratiform regions appear as circular in shape when viewed using radar reflectivity returns because they encompass regions of heavier convective rainfall (Churchill and Houze 1984; Jorgensen 1984). Within landfalling TCs, stratiform regions can be circular yet have a long perimeter length relative to their area because of dry-air intrusions that erode the edges of the clouds (Gilbert and LaSeur 1957; Powell 1987).
Regardless of the reflectivity values detected by radar equipment, it is important to identify regions within the TC that produce rain rates high enough to cause flooding. Because both meteorological and hydrological factors must be present for flooding to occur (Vieux and Bedient 1998), it is not possible to identify one threshold rain rate above which flooding will always occur. However, high rain rates produced by convective clouds are more likely to cause flooding than are the lower rain rates produced by stratiform clouds. When stratifying stratiform and convective clouds according to rain rates, several researchers have utilized 10 mm h−1 as a threshold for convective rain rates (Burpee and Black 1989; Tokay et al. 1999; Ulbrich and Atlas 2002). It is important, therefore, to identify regions within TCs that produce rain rates of 10 mm h−1 or greater.
This study pursues two objectives. The first objective is to classify regions of 35-dBZ radar reflectivity returns within a landfalling hurricane as stratiform or convective based upon the spatial attributes of the regions. The second objective is to establish a range of rainfall rates for the reflectivity regions and to identify those capable of producing rain rates greater than 10 mm h−1 within this hurricane. These objectives are accomplished through analyses of radar reflectivity values, radar-estimated rainfall totals, and rainfall measured by rain gauges during the Florida landfall of Hurricane Charley (2004). Because of its ability to facilitate a spatial understanding of the relationships among environmental factors (Thornes 2005; Yuan 2005), a geographical information system (GIS) is employed to analyze the data obtained from radar sites and rain gauges. To pursue the first objective, the GIS groups together regions that contain the same reflectivity values and calculates the spatial attributes of these regions. Being that convective regions should have spatial attributes more similar to one another than to stratiform regions and vice versa, discriminant analysis (Tabachnick and Fidell 2001) is performed to classify the reflectivity regions according to their spatial attributes. If 35-dBZ regions are placed into the 30-dBZ (40-dBZ) group, this would indicate that 35-dBZ regions consist of predominantly stratiform (convective) clouds.
To accomplish the paper’s second objective, the GIS identifies the value of radar-estimated rainfall returned for the region of the atmosphere above each rain gauge. A range of rain rates is established for radar reflectivity values from 25 to 45 dBZ, and these values are evaluated against the 10 mm h−1 rain rate described by previous researchers as separating heavy rainfall from light rainfall. If several of the regions of 35-dBZ radar reflectivity values produce rainfall rates in excess of 10 mm h−1, then, regardless of their classification as convective or stratiform, these regions produce heavy rainfall and should be more closely examined in future work.
2. Pattern analysis of radar reflectivity returns
Section 2 details the spatial analysis of the radar reflectivity regions performed to fulfill the study’s first objective. The spatial attributes of regions enclosed by 30-, 35-, and 40-dBZ reflectivity values are calculated within a GIS and are statistically analyzed to determine whether 35-dBZ regions are more similar in size and shape to 30-dBZ regions or to 40-dBZ regions.
a. Data description and GIS analysis
Level-III composite radar reflectivity returns (Klazura and Imy 1993) are used to identify regions of precipitation contained within the circulation of Hurricane Charley. Level-II data provide a higher spatial resolution of data from multiple scan heights, but these data are missing or incomplete for one of the radar sites and thus cannot be utilized for this study. Given that data are interpolated to create the polygonal regions and that the shape metrics calculated for these regions do not require a precise placement of the polygon boundary, level-III data are sufficient for use in the current study.
Composite reflectivity data extend 460 km outward from each Weather Surveillance Radar-1988 Doppler (WSR-88D) site, allowing the entire hurricane to be within range of the radar prior to its landfall and limiting the need to create a mosaic of data from neighboring radar sites as would be necessitated by utilizing base reflectivity data. Charley is a good candidate for radar analysis, because its small size (Franklin et al. 2006) allows the entire storm to be within range of the WSR-88D site at Key West, Florida, 8 h in advance of landfall. Charley’s small size also limits the need to create a mosaic of data from neighboring radar sites. However, Charley is small in size because of a rapid intensification just prior to landfall, and thus the results obtained from this analysis may not be applicable to all other TCs.
Radar data are analyzed during a 22-h period that spans from 1200 UTC 13 August to 0900 UTC 14 August 2004. Data are acquired from the National Climatic Data Center (NCDC) archives for the following WSR-88D sites (Fig. 1): Key West (KBYX), Tampa (KTBW), Melbourne (KMLB), and Jacksonville (KJAX), Florida, and Charleston (KCLX), South Carolina. Prior to their importation into the GIS, the composite reflectivity data acquired for each WSR-88D site are georeferenced. The Java Next-Generation Weather Radar (NEXRAD) Tools collection of programs, authored by Ansari and Del Greco (2005), converts the radar data into a rectangular coordinate system by defining a latitude and longitude for each bin. The data are then imported into the proprietary software package ArcGIS 9.2 (Environmental Systems Research Institute 2006) as “shapefiles.”
Spatial analysis of the radar data within the GIS is performed with data that occur nearest to the top of each hour. An inverse-distance-weighting script groups together adjacent returns having the same reflectivity value to form polygons, with the outermost returns within the group forming the perimeter of the polygon (Fig. 2). Regions with areas that cover less than 50 km2 are eliminated from the analysis because of their small size. Within this paper, polygons are referenced according to the reflectivity value defining their perimeter (i.e., 35-dBZ polygons are bounded by 35-dBZ reflectivity values). Polygons composed of reflectivity values of less than 20 dBZ are excluded from the analysis. Polygons with reflectivity values in excess of 40 dBZ are too few and too small in size to be included in the analysis.
One limitation that occurs when utilizing composite reflectivity radar data is the detection of the bright band that forms in stratiform clouds. The bright band is caused by the change in the index of refraction and terminal fall speed of the precipitation. Because water has a higher index of refraction than does ice, melting snow produces high reflectivity values similar to those of large rain drops.
Reflectivity values in the bright band can be heightened by as much as 5–10 dB (Black et al. 1972; Austin 1987; Baeck and Smith 1998). As the hydrometeors get smaller and acquire a faster terminal fall speed, droplet concentrations are reduced as more droplets fall from the brightband region than enter the region. The bright band may also exist in a convective echo that is decaying (Black et al. 1972; Marks 1985; Geerts et al. 2000). To guard against the possibility that reflectivity data analyzed in this study include 35- and 40-dBZ reflectivity values from the bright band, level-III base reflectivity data are also acquired and are examined for WSR-88D receivers that detected a portion of the rainfall region of Charley at each hour. If the reflectivity values from the base scan are lower than those obtained from the composite data used to create each polygon, then that polygon is removed from analysis. Approximately 15% of the original 35- and 40-dBZ polygons are determined to be artifacts of the bright band and are eliminated from the analysis. The calculation of rain rates described in section 3 confirms that the remaining polygons are not representative of the bright band.
Calculations are performed to define the spatial attributes of each polygon remaining in the analysis, including area, perimeter length, perimeter roughness, and elongation (Table 1). To relate the spatial attributes of each polygon to those of the polygon that encompasses it (i.e., the parent polygon; Fig. 3), the attributes of each polygon (i.e., area, perimeter length, perimeter roughness, and elongation) are subtracted from those of its parent polygon. Small values resulting from these calculations indicate strong similarities between a polygon and its parent. These small values imply that if a parent polygon is stratiform (convective), the polygon inside of it is stratiform (convective) as well. The percentage of area that a given polygon occupies within its parent polygon is also calculated. Again, a polygon that is close in size to its parent is likely to have the same stratiform or convective classification as that of its parent. Last, the number of child polygons [abbreviated CP and defined as a polygon having a threshold reflectivity value 5 dBZ higher than its parent polygon (Fig. 3)] contained within a given parent polygon is noted. Thus, each polygon is associated with 10 attributes that describe its spatial properties and its similarities to the parent polygon that encompasses it (Table 1).
b. Statistical analysis
The statistical method employed to categorize 35-dBZ radar reflectivity values is multivariate linear discriminant analysis (DA). Through a linear combination of a set of predictor variables, the DA derives a function that maximizes the separation of two or more mutually exclusive groups (Wilks 1995). Smith et al. (2004) recently employed a multivariate linear DA when developing their damaging-downburst prediction and detection algorithm. They calculated a set of 26 predictors, including core aspect ratio and maximum reflectivity, using reflectivity and radial velocity data and were able to distinguish between cells that produced severe downdrafts and cells that did not produce a strong outflow.
Because 11 spatial attributes calculated for each polygon (Table 1) could serve as predictors in the model, a forward stepwise approach is utilized. The predictor that decreases the Wilks’s lambda statistic by the greatest amount (Tabachnick and Fidell 2001) is included in the model at each step. Lambda values close to 0 indicate that the group means differ; therefore, selecting variables that most lower this statistic assures that the variables that most differentiate among the groups are utilized to derive the discriminant functions. Mahalanobis distances between cases and each group centroid are calculated, and each case is placed into the group for which its distance to the centroid is smallest. A successful model classifies a high percentage of observations into their correct predetermined groups.
Three DAs are performed in this study. For the first DA, 178 cases enter the analysis with prior classification into one of six groups. Two criteria are utilized to group the cases, with the first being the polygon’s reflectivity value (30, 35, or 40 dBZ). The second criterion is necessary because researchers have demonstrated that stratiform and convective precipitation can occur in multiple regions within a TC (Maynard 1945; Senn and Hiser 1959; Jorgensen 1984). These studies concluded that all polygons located in the outer rainbands of TCs should be smaller in size and organized into shapes that are more elliptical than polygons located within the inner portion of a TC’s circulation (Powell 1990). This study considers polygons located within (outside of) 100 km of the circulation center to be interior-region (exterior region) polygons. Charley is small in size because of its rapid intensification just prior to landfall, and thus the use of 100 km to distinguish interior and outer regions of the storm may not work for all hurricanes. The classification of each case prior to its entrance into the DA is as follows: 1) exterior-region 30-dBZ polygons (30E); 2) exterior-region 35-dBZ polygons (35E); 3) exterior-region 40-dBZ polygons (40E); 4) interior-region 30-dBZ polygons (30I); 5) interior-region 35-dBZ polygons (35I); and 6) interior-region 40-dBZ polygons (40I).
The second and third DAs are performed to determine whether the 35-dBZ polygons are most similar to stratiform or convective regions by entering these cases into the analysis without prior classification. DA2 considers only the exterior-region polygons, and DA3 considers only the interior-region polygons. The predictors entering these DAs are the same as are utilized for the first DA; however, only the data from the 30- and 40-dBZ cases are used to build the model. After the values of the covariates are calculated using the data from the 30- and 40-dBZ polygons, the linear discriminant functions evolving from these cases are utilized to predict the classification of the 35-dBZ polygons.
c. Results
Five predictors combine to lower the Wilks’s lambda statistic to 0.043 in the first DA. Percent occupation (PO) is the most important predictor, demonstrating that 30-dBZ (40-dBZ) polygons occupied over 76% (under 19%) of their parent polygons (Table 2). Child polygons enter the analysis at the second step, distinguishing the 35E and 40E polygons from the others because they encompass five polygons on average. Area difference is included in the third step of DA1, helping to distinguish the 35-dBZ polygons having the highest difference in area from their parent polygons from the 30-dBZ polygons, which are the most similar in area to their parent polygons. The shapes of the polygons become important during the last two steps of the analysis because interior-region polygons are more circular with longer edge lengths while exterior-region polygons are nearly uniform in their elongation with relatively smooth edges.
Plotting each case against the first two discriminant functions derived from these predictors demonstrates that the first function separates the groups according to their reflectivity values, and the second function separates the groups according to their location (Fig. 4). Cases belonging to the stratiform groups (30E and 30I) are correctly classified over 90% of the time (Table 3). Almost 82% of 40I cases are correctly classified. The DA also classifies 35I cases well, with three cases each misclassified as 30I and 40I. The lowest classification success results from the analysis of the 35E and 40E polygons: only approximately 50% of these observations are correctly classified. The 35E and 40E centroids are located in close proximity to one another while individual cases are widely dispersed about their group centroids (Fig. 3).
Results from both DA2 and DA3 indicate that 35-dBZ polygons have spatial attributes more similar to 40-dBZ polygons than to 30-dBZ polygons. Approximately 83% (78%) of the 35-dBZ cases are classified as 40 dBZ in DA2 (DA3). Again, PO is the most important predictor in DA2 and DA3, where it lowers the Wilks’s lambda statistic to 0.171 and 0.082, respectively. Removal of the PO predictor from both analyses results in the perimeter length being the primary predictor. However, this only changes the 35-dBZ classifications by one case in DA3 and two cases in DA2. This finding demonstrates that multiple spatial attributes can be utilized to categorize 30-, 35-, and 40-dBZ regions.
d. Discussion
The results of the DAs suggest that the 35-dBZ reflectivity regions are more similar in shape to 40-dBZ regions than to 30-dBZ regions. An examination of the predictors entering the DAs show that the 30-dBZ stratiform polygons are very similar in size and shape to their parent 25-dBZ polygons, whereas the 35-dBZ polygons are very different in size and shape from their parent 30-dBZ polygons. On average, the 30-dBZ polygons make up over 76% of the area belonging to their parent 25-dBZ polygons (Table 2), whereas the 35-dBZ regions occupy much less space inside their parent 30-dBZ polygons. The length of the 30-dBZ polygons’ perimeters is only an average of 60 km less than their parent polygons, whereas the differences in perimeter lengths for all other polygons exceed 470 km. Also, the difference in elongation ratios for 30- and 25-dBZ polygons is less than 0.02, whereas it is greater than 0.1 for all other polygons. These findings illustrate how similar the 30-dBZ polygons are to the 25-dBZ polygons and how dissimilar they are to the 35-dBZ polygons. Based upon these results, the possibility that the majority of the 35-dBZ polygons examined in this study are composed mainly of stratiform precipitation is unlikely.
The inability of both DA1 and DA2 to distinguish between 35E and 40E polygons can be attributed to the sharp horizontal reflectivity gradient that exists between most of these polygons. The 35E and 40E polygons have compact yet elongated shapes, and these shape attributes are in agreement with those discussed by previous researchers as belonging to convective precipitation (Churchill and Houze 1984; Marks 1985; Biggerstaff and Listemaa 2000; Rigo and Llasat 2004). In their automated method for separating stratiform and convective radar echoes, Steiner et al. (1995) classify the regions adjacent to convective centers of 40 dBZ or higher as convective if a sharp horizontal reflectivity gradient is present. Thus, work by previous researchers supports the finding that these regions of 35-dBZ reflectivity values embedded within the outer region rainbands of Hurricane Charley could be convective in origin.
Most 35I polygons are classified by DA3 as convective. However, according to the DA1 results, 35I polygons occupy a middle ground between 30I and 40I polygons and three cases are each misclassified as belonging to the 30I and 40I groups. Therefore, it is possible that 35I reflectivity returns are representative of a third type of precipitation termed “transition” (Ulbrich and Atlas 2002) or “mixed” (Chen et al. 2003). This type of precipitation is generated by convective storms and is produced in the region between clearly convective clouds and clearly stratiform clouds. Although the rain does not fall directly below the convective cloud, droplets falling from transition regions do originate from convective clouds. Thus, these regions have the potential to produce higher rainfall accumulations than do regions composed solely of stratiform clouds.
Previous research has shown that identifying transition-type rainfall can aid the separation of convective from stratiform rainfall and that, given only the latter two choices, transition-type rainfall should be classified as convective. In their investigation of tropical rain-rate and drop size relationships, Yuter and Houze (1997) classified each observation as either stratiform or convective and did not consider transition regions as a separate group. When examining the characteristics of each group, they were unable to define two distinct populations. Upon re-examination of the data, Ulbrich and Atlas (2002) discovered that many of the stratiform observations occurring 3–10 km from convective clouds possessed rain rates exceeding 10 mm h−1. Ulbrich and Atlas (2002) identified these observations as being transition-type rain and stated that these observations should have been classified as convective rather than stratiform because of their high rain rates. The conclusions made by Ulbrich and Atlas (2002) support the findings of the current study that, based upon an examination of their horizontal spatial characteristics, 35-dBZ reflectivity regions may be composed of transition-type rainfall and that, given the choice between stratiform and convective, they should be classified as convective.
3. Rain-rate verification
The previous section found that 35I regions may be composed of transition-type rainfall within Hurricane Charley. This finding implies that the rainfall rates produced by the 35-dBZ regions are higher than those produced by stratiform clouds. This section details the use of rain gauge and radar-estimated precipitation data to approximate the rain rates produced by the reflectivity regions described in the previous section. Finding that some 35-dBZ regions produce rain rates near to or exceeding 10 mm h−1 would indicate that these specific regions should be considered convective rather than stratiform (Ulbrich and Atlas 2002).
a. Rainfall data and GIS analysis
To examine rainfall totals received on the ground during the passage of Hurricane Charley, rain gauge data are acquired from the Florida Automated Weather Network (FAWN). The FAWN consists of 34 meteorological observing stations located across Florida. The TE525 tipping bucket rain gauges collect data in 15-min intervals. Hurricane Charley produced rainfall at 20 of the FAWN sites (Fig. 1). Most of these sites are located to the left of Charley’s circulation center, and the distance from the storm track to each site varies from 5 to 140 km.
To compare rainfall measured by rain gauges with that estimated by radar, 1-h precipitation accumulation products (OHPs) (Klazura and Imy 1993; OFCM 2006) are acquired from the NCDC archive for the WSR-88D sites depicted in Fig. 1. The OHP utilizes data from all base reflectivity scans occurring within the past hour at a given WSR-88D site to estimate the amount of rainfall that occurred during the past hour. To create this product, a conversion factor relates the radar reflectivity factor scan Z and rain rate R. Both the Z and R values depend on the raindrop size and size distribution; R also depends on the fall velocity for a given drop diameter (Marshall and Palmer 1948). Several Z–R relationships can be employed (Austin 1987; Ulbrich and Lee 2002); however, S. Spratt (2007, personal communication) verified that the tropical Z–R relationship Z = 250R1.2 (Rosenfeld et al. 1993) was used to estimate rainfall accumulations for Hurricane Charley during the study period. The Java NEXRAD Tools (Ansari and Del Greco 2005) are used to georeference the OHP data, and they are imported into the GIS as shapefiles.
Within the GIS, the Intersect Point Tool authored by Beyer (2004) is implemented first to match the rain gauge locations with the radar reflectivity values detected in the atmosphere above the rain gauges. The Intersect Point Tool overlays each shapefile containing the radar-derived polygons described in section 2a with the rain gauge locations and determines which polygon occupies the atmosphere above the location of each rain gauge. The reflectivity value of this polygon is recorded in the attribute table of the rain gauge data. These data are utilized to develop a range of rainfall rates measured on the ground for each radar reflectivity value from 25 to 45 dBZ. Simple statistics including the minimum, maximum, mean, median, and mode of the rain rates are calculated for each dBZ interval. Data from the rain gauges receiving the most rainfall are plotted in a time series and are arranged according to their distance from the point of landfall so that rain rates can be related to the passage of the interior and outer regions of the storm.
Comparing the rain gauge data with the OHP is another method employed to quantify rain rates. First, the 15-min rain gauge data are summed to provide hourly accumulations ending at the top of each hour. Beyer’s (2004) Intersect Point Tool is then employed to compare the radar-estimated rainfall according to the OHP with the actual rainfall measured by the rain gauges. The Intersect Point Tool overlays the OHP generated nearest to the top of each hour with the rain gauge sites and determines the OHP total covering the region within which each rain gauge is located. The radar-estimated rainfall total is recorded into the rain gauge attribute table. Time series are also created using the OHP and rain gauge hourly totals for the seven sites receiving the highest rainfall totals. The time series make it possible to identify instances easily in which radar-derived rainfall values over- or underestimate those measured by the rain gauges.
b. Results
The most important finding when comparing gauge-measured rain rates with the reflectivity values of the regions producing the rainfall is that 32% of the 35-dBZ regions produce rain rates equal to or greater than 10 mm h−1. Most of the cases occur as the interior region of Charley passes over the rain gauges located closest to the storm track (Fig. 5), meaning that they are 35I polygons. Regardless of whether these regions are composed of convective or mixed-type precipitation as discussed in section 2, their rain rates exceed the 10 mm h−1 threshold for convective rain rates established by previous researchers (Burpee and Black 1989; Tokay et al. 1999; Ulbrich and Atlas 2002); thus, further investigations of these regions are needed.
Another key finding is that each reflectivity value has a large range of rain rates (Table 4). Some rain gauge observations lag the tropical Z–R rain rate by nearly 50%, while others are more than double the tropical Z–R rain rate. Twenty-five of the rain rates measured by gauges for 35-dBZ polygons exceed the tropical Z–R rain rate of 8.4 mm h−1 for 35-dBZ returns, and 12 of the 40-dBZ cases exceed the tropical Z–R rate of 21.6 mm h−1 for 40-dBZ returns. Several explanations for the large range of rain rates that the reflectivity regions exhibit are detailed in the discussion section.
Figure 5 is a time series comparing radar-derived and rain gauge rainfall rates and is used to identify the radar polygons that have rain rates higher than those from typical Z–R relationships. Figure 6 indicates where each gauge is located relative to the storm track. Three distinct rainfall and reflectivity peaks occur. The first peak coincides with the passage of an outer rainband located approximately 210 km from the circulation center of Hurricane Charley. This band forms over southern Florida around 1400 UTC when Charley’s center is still 170 km from land. Maximum reflectivity values within this band are 50 dBZ, with corresponding rain gauge measurements exceeding 13 mm in 15 min. The second peak in radar reflectivity and rainfall accumulation occurs approximately 3 h later and is caused by the principal rainband (Willoughby et al. 1984) of Charley located approximately 110 km from the circulation center. Radar reflectivity values again reach 50 dBZ, with rainfall accumulations as high as 20 mm in 15 min.
The third peak corresponds to the passage of the storm’s interior region, and rain rates and reflectivity values are somewhat lower overall relative to the two preceding peaks. Stations Apopka and Avalon (Fig. 6) experience rain rates as high as 44 mm h−1, corresponding to radar reflectivity values of 45 dBZ (Fig. 5). However, the majority of reflectivity returns occurring over the rain gauges as the interior region moves overhead are of 35-dBZ intensity. These regions correspond to rain rates of 24 and 32 mm h−1 in several cases. There are 25 cases in which the rain rates measured by rain gauges exceed the tropical Z–R rain rate for 35-dBZ polygons overall, and 23 of these cases occur within the interior region of Charley. Thus, it is within the interior region of the storm that 35-dBZ reflectivity values are producing rain rates that are higher than anticipated according to the tropical Z–R relationship.
The peaks in rain rate discussed above are also evident when examining the OHP and rain gauge hourly data (Fig. 5, right panels). However, it is now possible to discern differences in the accumulated rainfall totals. Rainfall totals estimated by the radar are greater than those measured by the rain gauges as the rainbands in the outer region of Charley pass overhead. This changes, however, with the passage of the interior region. In four instances, rain gauges measure 15 mm more rainfall within 1 h than is estimated by the radar. Once again, the majority of the reflectivity values combining to produce the high hourly rainfall totals relative to the radar-estimated totals are of 35-dBZ intensity.
c. Discussion
Many researchers agree that rain rates equal to or greater than 10 mm h−1 originate from convective clouds (Burpee and Black 1989; Tokay et al. 1999). Ulbrich and Atlas (2002) suggest that transition-type rain can possess rates that are greater than 10 mm h−1, and that they may also produce rain rates that are lower than this threshold. Also, Ulbrich and Atlas (2002) state that convective clouds can produce rainfall rates that are below the 10 mm h−1 threshold. In this study, all of the 40-dBZ convective regions exceed the 10 mm h−1 threshold. In addition, 21 of the 35-dBZ regions exceed this threshold. Therefore, whether the 35-dBZ regions are composed of convective or transition-type precipitation, they are capable of producing rain rates similar to those of 40-dBZ regions, and their contributions to flooding should be examined further.
The variability in the rain rates for the 35-dBZ regions that were sampled can be attributed to four factors: 1) the life cycle of a convective cell, 2) rain gauge undercatch, 3) radar beam filling and beam height, and 4) application of a single Z–R relationship to three differing precipitation types (convective, transition, and stratiform). The results of section 2 indicate that roughly 80% (20%) of the time, 35-dBZ regions have spatial attributes similar to 40-dBZ convective (30-dBZ stratiform) regions. In the decaying phase of a convective cell’s lifespan, vertical velocities weaken and precipitation rates decrease. The 20% of cases in which 35-dBZ regions had spatial attributes that were more similar to those of 30-dBZ regions and also had rain rates less than the 8.4 mm h−1 expected by the Z–R relationship may be due to the fact that these formerly convective regions were sampled during their dissipating phase.
Both rain gauges and radar have limitations that may account for a portion of the large variation in rain rates (Chumchean et al. 2003; Medlin et al. 2007). The mechanical limits of rain gauges can cause them to underestimate the actual precipitation by 20%–40%—in particular, when wind speeds are high (Miller 1958; Larson and Peck 1974; Wilson and Brandes 1979). This mechanical limitation may account for a portion of the underestimation of rain rates by the rain gauges during the passage of the outermost rainband, which contains reflectivity values in excess of 45 dBZ (Fig. 5). Adding a 40% correction to the gauge measurements at Lake Alfred and Avalon and a 20% correction to gauges at Apopka and Tavares would bring the rain gauge measurements into agreement with the radar-estimated values. However, adding this correction to the other gauge measurements would bring the totals above those estimated by the radar. In addition, radar-estimated rain rates could be higher than what actually occurred because of partial beam filling. The spreading and partial filling of the beam within regions having large horizontal reflectivity gradients can cause rainfall to be overestimated (Rosenfeld et al. 1993).
Furthermore, applying a correction to the gauge-measured rain rates to approximate a 20% undercatch as suggested by Larson and Peck (1974) and Wilson and Brandes (1979) would cause more than one-half of the rain rates for 35- and 40-dBZ radar reflectivity returns to equal or exceed those of the tropical Z–R relationship. With uncorrected rain gauge observations, 42% of 35-dBZ cases have rain rates that exceed the tropical Z–R relationship for 35-dBZ reflectivity values of 8.4 mm h−1. Adding a correction for 20% undercatch would yield 43 cases of rain rates in excess of the tropical Z–R relationship produced by 35-dBZ polygons. This result suggests that radar rainfall estimates may be lower than the actual rainfall that occurs in 50% or more of the 35-dBZ cases. Cases of radar underestimates of TC rainfall are not uncommon. Baeck and Smith (1998) and Medlin et al. (2007) found many instances of rainfall underestimations by radar during the landfalls of Hurricane Fran (1996) and Hurricane Danny (1997), respectively.
The fact that the beam height changes as it moves away from the radar station could also explain why regions that had 35-dBZ radar reflectivity values produced rainfall rates that were higher than expected. The lowest elevation angle for WSR-88D scanning is 0.5°, which corresponds to an altitude of approximately 1.6 km at a range of 100 km from the receiver and 4.2 km at a range of 200 km from the receiver. Barnes et al. (1983) found that convective cores in hurricane rainbands are often located at altitudes near 2 km. The base scan fails to sense the atmosphere below 2 km beginning approximately 125 km away from the station. The rain gauges at Ona, Lake Alfred, Apopka, and Avalon are all located within 107 km of the nearest radar site. However, beam height may be a factor that is causing 35-dBZ rain rates to be underestimated for gauges at Pierson, Tavares, and Umatilla because they are located 142–150 km away from the nearest radar site. Because beam attenuation is negligible for S-band radar, this explanation is not plausible for differences between reflectivity values measured and rain rates received at the ground. In addition, differing calibrations of the radar sites used for the analysis could also have contributed to the underestimation of rainfall totals by the OHP.
The application of a single Z–R relationship when a mixed type of precipitation is occurring (Rosenfeld et al. 1993) may also account for a portion of the variability in rain rates for the 35-dBZ polygons. Forty-two percent of the 35-dBZ regions analyzed had rain rates in excess of the tropical Z–R value for 35-dBZ reflectivity values. Convective, stratiform, and transition regions have different drop size distributions, which necessitate different Z–R relationships to estimate rainfall totals accurately for each region (Atlas et al. 1999; Tokay et al. 1999; Ulbrich and Atlas 2002). Atlas et al. (1999) specifically discuss the differences in the drop size distributions and Z–R relationships of convective zones and the trailing transition regions of mesoscale convective complexes.
The finding that most of the 35-dBZ regions meet or exceed the tropical Z–R relationship suggests that these regions are not representative of the bright band. Baeck and Smith (1998) discuss the detection of the bright band within the rainfall region of Hurricane Fran (1996) as it moved inland through North Carolina. They found that, when the bright band is not sampled, rain gauge estimates could be as high as a factor of 1.5 in excess of radar estimates. When the bright band is sampled, radar-estimated rain rates exceed those measured by rain gauges. The underestimation of hourly rainfall totals by the radar during the passage of the interior region of Hurricane Charley confirms that the 35-dBZ regions are not produced by the bright band.
4. Conclusions and future work
Improving rainfall forecasts for landfalling TCs necessitates quantifying the evolution of regions that produce high rain rates within these systems. Stratiform precipitation regions, identified by radar reflectivity values around 30 dBZ, are typically not a concern for heavy rainfall, but convective regions corresponding to reflectivity values of 40 dBZ or greater can produce high rain rates that may cause flash flooding. This research used a GIS to examine the spatial attributes of 35-dBZ regions to determine whether they were more similar to the 30-dBZ stratiform regions or to the 40-dBZ convective regions that occurred during the Florida landfall of Hurricane Charley (2004). Rain rates were calculated using radar estimates and rain gauge measurements to determine whether 35-dBZ regions are capable of producing rain rates in excess of 10 mm h−1, a threshold rate for convective rainfall that was identified by previous researchers.
Results indicate that regions of 35-dBZ reflectivity returns within the outer rainbands of Charley are spatially similar to the 40-dBZ polygons because of the high reflectivity gradients present within convective clouds. These regions are adjacent to 40-dBZ convective cores and could be considered to be convective themselves. The 35-dBZ returns within the interior region of Charley are more similar to 40-dBZ regions than to 30-dBZ regions but may best be ascribed to a transition-type region occurring between the convective and stratiform clouds. Despite the limitations of both rain gauges and radar, the 35-dBZ regions located within the interior region of Charley produced rain rates in excess of 10 mm h−1 in 32% of cases. Thus, the rain rates in these regions exceed both the radar-estimated rain rates and the 8.4 mm h−1 rain rate ascribed to 35-dBZ regions by the tropical Z–R relationship. Application of a 20% correction for rain gauge undercatch increases this statistic to over 50% of cases. Also, rain rates measured by rain gauges exceed those that were estimated by applying the tropical Z–R relationship to the 35-dBZ radar data. These findings support the identification of 35-dBZ interior regions as either convective or transition-type precipitation that is capable of producing rain rates equivalent to those of 40-dBZ regions. It is important to note that, because of Charley’s small size, the results of this study may be storm dependent.
Because most work detailing the spatial characteristics of transition regions has been done in association with tropical convective systems that were not TCs (e.g., Steiner et al. 1995; Biggerstaff and Listemaa 2000; Ulbrich and Atlas 2002), the extent to which transition regions may contribute to the storm total rainfall within TCs is not clearly defined in the current literature. The current study found that 35-dBZ regions can be associated with regions within a hurricane that produce rain rates in excess of 10 mm h−1; therefore, these regions should be examined more closely for incorporation into future rainfall analyses. The inclusion of data pertaining to the vertical structure of radar reflectivity returns could also facilitate classification of stratiform, transition, and convection regions within TCs (Barnes et al. 1983; Chen et al. 2003). Because of its relatively fast forward motion, rainfall produced by Hurricane Charley did not pose a large flood risk. However, future work will examine 35-dBZ regions within slow-moving TCs so that the data are available for a more lengthy study period and so that the potential to cause flooding can be further evaluated. The analysis of several landfalling TCs will facilitate comparisons among 30-, 35-, and 40-dBZ regions and will be an important undertaking to validate the findings within the current study.
Acknowledgments
The author thanks Dr. Peter Waylen for suggestions during data analysis and Dr. Julie Silva for reading an early draft of this manuscript. Comments from three anonymous reviewers helped to clarify the discussion of the results of this work.
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Hurricane Charley’s track over Florida during the study period, with radar sites and rain gauge locations.
Citation: Journal of Applied Meteorology and Climatology 48, 1; 10.1175/2008JAMC1910.1
Polygon regions created from interpolation of composite radar reflectivity data for Hurricane Charley at the hour of landfall.
Citation: Journal of Applied Meteorology and Climatology 48, 1; 10.1175/2008JAMC1910.1
Illustration of polygons termed “parent” and “child.” The reflectivity value of a parent polygon is 5 dBZ lower than the polygon that it encompasses. Child polygons are all polygons contained within a polygon that are 5 dBZ higher in reflectivity than the encompassing polygon.
Citation: Journal of Applied Meteorology and Climatology 48, 1; 10.1175/2008JAMC1910.1
Discriminant analysis cases plotted according to the first two discriminant functions and the group centroids.
Citation: Journal of Applied Meteorology and Climatology 48, 1; 10.1175/2008JAMC1910.1
Time series of rainfall and radar reflectivity values at seven rain gauge sites: (left) 15-min gauge-measured rainfall and the highest radar reflectivity value, and (right) corresponding comparison of 1-h rain gauge–measured and radar-estimated rainfall totals.
Citation: Journal of Applied Meteorology and Climatology 48, 1; 10.1175/2008JAMC1910.1
Rain gauge locations and polygon regions occurring within Hurricane Charley at 0100 UTC 14 Aug 2004.
Citation: Journal of Applied Meteorology and Climatology 48, 1; 10.1175/2008JAMC1910.1
Attributes for each radar reflectivity region and how they are obtained.
Predictors successfully entering the first stepwise discriminant analysis.
Classification results for the first discriminant analysis.
Radar reflectivity values and corresponding gauge-measured statistics for rain rates (mm h−1).
