JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY

A Spatial Analysis of Radar Reflectivity Regions within Hurricane Charley (2004)

CORENE J. MATYAS

Departmewnt of Geography, University of Florida, Gainesville, Florida

(Manuscript received 7 November 2007, in final form 12 June 2008)

ABSTRACT

Regions of 35-dBZ radar reflectivity returns are examined within a landfalling hurricane to determinewhether these regions are composed of stratiform, convective, or transition-type precipitation. After cal-culating spatial attributes of the reflectivity regions such as elongation and edge roughness within a GIS,discriminant analysis is performed to determine whether the 35-dBZ regions are more similar to 40-dBZregions of convective precipitation or to 30-dBZ regions of stratiform precipitation. Results show thatwithin the outer region rainbands of Hurricane Charley (2004) a sharp horizontal reflectivity gradient exists,indicating that 35-dBZ regions are similar in shape to adjacent convective regions of 40-dBZ reflectivityvalues. Within the interior region, the 35-dBZ regions are identified as transition regions similar to thosefound within mesoscale convective complexes rather than being strictly stratiform or convective in nature.The rain rates produced by the reflectivity regions are examined using rain gauge and radar estimates. In32% of cases, the 35-dBZ regions produced rain rates in excess of 10 mm h 1, exceeding both the radar-estimated rain rates and the 8.4mm hb1 rain rate ascribed to 35-dBZ regions by the tropical Z7R relationship.Thus, 35-dBZ regions surrounding the convective cores of additional landfalling TCs should be examined todetermine whether they also represent transition-type rainfall regions capable of producing convectiverainfall rates exceeding 10 imnn h-1.

1. Introduction

Identifying regions within landfalling tropical cy-clones (TCs) in which high rain rates occur and quan-tifying the evolution of these regions is critical for theimprovement of hydrological models used to forecastflooding (e.g., Baeck and Smith 1998; Elsberry 2002,Ulbrich and Lee 2002; Medlin et al. 2007). When usingradar reflectivity returns to identify these regions, re-searchers generally agree that 40-dBZ reflectivity val-ues correspond to convective clouds, which producehigh rain rates, while 30-dBZ values originate fromstratiform clouds, which produce lower rain rates thatare not a great concern for flooding. A clear consensusdoes not exist, however, regarding the classification of35-dBZ reflectivity returns.

The contrasting growth patterns of the two main pre-cipitation regimes occurring within TCs, convective andstratiform precipitation (Houze 1993), allow these re-gions to be identified by their spatial attributes when

Corresponding author address: Corene J. Matyas. 3141 Turling-ton Hall, University of Florida. Gainesville. FL 32611.E-mail: matyas@ufl.edu

visualized using radar-derived data (Ulbrich and Atlas2002). Because of their strong vertical velocity fields(Steiner et al. 1995), convective clouds cover small hori-zontal areas but produce high rain rates that can lead toflash flooding (Baeck and Smith 1998). Thus, these re-gions are extremely important to identify in regard toflood forecasting for landfalling TCs. When viewed us-ing radar reflectivity returns, convective regions tend tobe elliptical in shape (Churchill and Houze 1984; Rigoand Llasat 2004) and compact and to have high radialgradients of reflectivity (Marks 1985; Biggerstaff andListemaa 2000) due to their strong vertical motions.Radar reflectivity values over a 34-41-dBZ range havebeen utilized to delineate convective precipitationwithin 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 stratiformclouds causes them to occupy a larger horizontal area(Yuter and Houze 1995: Biggerstaff and Listemaa 2000;Anagnostou 2004) and to produce low rainfall intensi-ties. Stratiform regions appear as circular in shapewhen viewed using radar reflectivity returns becausethey encompass regions of heavier convective rainfall

DOI: 10.1 175/2008JAMCI91 0.1

© 2009 American Meteorological Society

130 VOLUME 48

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(Churchill and Houze 1984K Jorgensen 1984). Withinlandfalling TCs, stratiform regions can be circular yethave a long perimeter length relative to their area be-

cause of dry-air intrusions that erode the edges of theclouds (Gilbert and LaSeur 1957: Powell 1987).

Regardless of the reflectivity values detected by ra-dar equipment, it is important to identify regions withinthe TC that produce rain rates high enough to causeflooding. Because both meteorological and hydrologi-cal factors must be present for flooding to occur (Vieuxand Bedient 1998). it is not possible to identify onethreshold rain rate above which flooding will always

occur. However, high rain rates produced by convectiveclouds are more likely to cause flooding than are thelower rain rates produced by stratiform clouds. Whenstratifying stratiform and convective clouds accordingto rain rates, several researchers have utilized 10 mmh- 1 as a threshold for convective rain rates (Burpee andBlack 1989; Tokay et al. 1999; Ulbrich and Atlas 2002).It is important, therefore, to identify regions within TCsthat produce rain rates of 10 mm h 1 or greater.

This study pursues two objectives. The first objectiveis to classify regions of 35-dBZ radar reflectivity returnswithin a landfalling hurricane as stratiform or convec-tive based upon the spatial attributes of the regions.The second objective is to establish a range of rainfallrates for the reflectivity regions and to identify thosecapable of producing rain rates greater than 10 mm h- 1within this hurricane. These objectives are accom-plished through analyses of radar reflectivity values,radar-estimated rainfall totals, and rainfall measured byrain gauges during the Florida landfall of HurricaneCharley (2004). Because of its ability to facilitate a spa-tial understanding of the relationships among environ-mental factors (Thornes 2005; Yuan 2005), a geographi-cal information system (GIS) is employed to analyzethe data obtained from radar sites and rain gauges. Topursue the first objective, the GIS groups together re-gions that contain the same reflectivity values and cal-culates the spatial attributes of these regions. Beingthat convective regions should have spatial attributesmore similar to one another than to stratiform regionsand vice versa, discriminant analysis (Tabachnick andFidell 2001) is performed to classify the reflectivity re-gions according to their spatial attributes. If 35-dBZregions are placed into the 30-dBZ (40-dBZ) group,this would indicate that 35-dBZ regions consist of pre-dominantly stratiform (convective) clouds.

To accomplish the paper's second objective, the GISidentifies the value of radar-estimated rainfall returnedfor the region of the atmosphere above each rain gauge.A range of rain rates is established for radar reflectivityvalues from 25 to 45 dBZ, and these values are evalu-

ated against the 10 mm h-1 rain rate described by pre-vious researchers as separating heavy rainfall from lightrainfall. If several of the regions of 35-dBZ radar re-flectivity values produce rainfall rates in excess of 10mm h-1, then, regardless of their classification as con-vective or stratiform, these regions produce heavy rain-

fall and should be more closely examined in futurework.

2. Pattern analysis of radar reflectivity returns

Section 2 details the spatial analysis of the radar re-flectivity regions performed to fulfill the study's firstobjective. The spatial attributes of regions enclosed by30-, 35-, and 40-dBZ reflectivity values are calculatedwithin a GIS and are statistically analyzed to determinewhether 35-dBZ regions are more similar in size andshape to 30-dBZ regions or to 40-dBZ regions.

a. Data description and GIS analysis

Level-III composite radar reflectivity returns (Kla-zura and Imy 1993) are used to identify regions of pre-cipitation contained within the circulation of HurricaneCharley. Level-II data provide a higher spatial resolu-tion of data from multiple scan heights, but these dataare missing or incomplete for one of the radar sites andthus cannot be utilized for this study. Given that data

are interpolated to create the polygonal regions andthat the shape metrics calculated for these regions donot require a precise placement of the polygon bound-ary, level-III data are sufficient for use in the currentstudy.

Composite reflectivity data extend 460 km outwardfrom each Weather Surveillance Radar-1988 Doppler(WSR-88D) site, allowing the entire hurricane to bewithin range of the radar prior to its landfall and lim-

iting the need to create a mosaic of data from neigh-boring radar sites as would be necessitated by utilizingbase reflectivity data. Charley is a good candidate forradar analysis, because its small size (Franklin et al.2006) allows the entire storm to be within range of theWSR-88D site at Key West, Florida, 8 h in advance oflandfall. Charley's small size also limits the need tocreate a mosaic of data from neighboring radar sites.However, Charley is small in size because of a rapidintensification just prior to landfall, and thus the resultsobtained from this analysis may not be applicable to allother TCs.

Radar data are analyzed during a 22-h period thatspans from 1200 UTC 13 August to 0900 UTC 14 Au-gust 2004. Data are acquired from the National Cli-matic Data Center (NCDC) archives for the following

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r 09:00 UTC 14 Aug

JAX

X( Hýastmgs

"X Piersor/XOckalawahra /

X Umatilla 'Okah-mpka X Tavares '

X Brooksvile X Apopka

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D- ver-X Kenansvlle

Ký Bradenton X Ona X Seb X\Ft

)X Palmdale

SX Bellglad

X mrnalokee

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12:OUTC13Aug BX

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FIG. 1. Hurricane Charley's track over Florida during the studyperiod, with radar sites and rain gauge locations.

WSR-88D sites (Fig. 1): Key West (KBYX), Tampa(KTBW), Melbourne (KMLB), and Jacksonville(KJAX), Florida, and Charleston (KCLX), SouthCarolina. Prior to their importation into the GIS, thecomposite reflectivity data acquired for each WSR-88Dsite are georeferenced. The Java Next-GenerationWeather Radar (NEXRAD) Tools collection of pro-grams, authored by Ansari and Del Greco (2005). con-verts the radar data into a rectangular coordinate sys-tem by defining a latitude and longitude for each bin.The data are then imported into the proprietary soft-ware package ArcGIS 9.2 (Environmental Systems Re-search Institute 2006) as "shapefiles."

Spatial analysis of the radar data within the GIS isperformed with data that occur nearest to the top ofeach hour. An inverse-distance-weighting script groupstogether adjacent returns having the same reflectivityvalue to form polygons, with the outermost returnswithin 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 smallsize. Within this paper, polygons are referenced accord-

It , 0

Legend

Reflectivity Threshold25 dBZ30 dBZ

•35 dBZ': 40 dBZ 7

=45 dBZ A 0 75 15050 dBZ Km

FIG. 2. Polygon regions created from interpolation of compositeradar reflectivity data for Hurricane Charley at the hour of land-fall.

ing to the reflectivity value defining their perimeter(i.e., 35-dBZ polygons are bounded by 35-dBZ reflec-tivity values). Polygons composed of reflectivity valuesof less than 20 dBZ are excluded from the analysis.Polygons with reflectivity values in excess of 40 dBZare too few and too small in size to be included in theanalysis.

One limitation that occurs when utilizing compositereflectivity radar data is the detection of the brightband that forms in stratiform clouds. The bright band iscaused by the change in the index of refraction andterminal fall speed of the precipitation. Because waterhas a higher index of refraction than does ice, meltingsnow produces high reflectivity values similar to thoseof large rain drops.

Reflectivity values in the bright band can be height-ened by as much as 5-10 dB (Black et al. 1972; Austin1987; Baeck and Smith 1998). As the hydrometeors getsmaller and acquire a faster terminal fall speed, dropletconcentrations are reduced as more droplets fall fromthe brightband region than enter the region. The bright

Legendx Rain Gauges- Charley's TrackA Radar Sites

NA0 75 150

I IKm

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Attribute (abbreviation)

Identification No. (ID)IntensityTimeArea aPerimeter pCentroid distance

Roughness

ElongationParent polygon ID

POCPArea diffPerimeter diffRoughness diffElongation diff

TABLE 1. Attributes for each radar reflectivity region and how they are obtained.

How determined (units)

Assigned by GISReflectivity value serving as polygon perimeter (dBZ)Hour of study (tl = 12(00 UTC 13 Aug; t22 = 0900 UTC 14 Aug)Area occupied by polygon (kin2)Length of polygon perimeter (km)Spherical distance calculation using coordinates of geographic center of polygon and storm circulation

center (kin)(112/(0.282p) [formula reported by MacEachren (1985)], range 0-1: 0 = perimeter maximized and I

perimeter minimizedMinor axis length/major axis length; range 0-1: 0 straight line and t = circleID of polygon with the next lowest reflectivity threshold that encompasses current polygon; manual

inspectionPct of parent polygon's area occupied by current polygon (%)No. of polygons within a polygon having reflectivity threshold of 5 dBZ or greaterArea of current polygon subtracted from area of parent polygon (kmi2)Perimeter of current polygon subtracted from perimeter of parent polygon (kin)Roughness of current polygon subtracted from roughness of parent polygonElongation of current polygon subtracted from elongation of parent polygon

band may also exist in a convective echo that is decaying(Black etal. 1972; Marks 1985; Geerts et al. 2000). Toguard against the possibility that reflectivity data ana-lyzed in this study include 35- and 40-dBZ reflectivityvalues from the bright band, level-III base reflectivitydata are also acquired and are examined for WSR-88Dreceivers that detected a portion of the rainfall region ofCharley at each hour. If the reflectivity values from thebase scan are lower than those obtained from thecomposite data used to create each polygon, then thatpolygon is removed from analysis. Approximately 15%of the original 35- and 40-dBZ polygons are determinedto be artifacts of the bright band and are eliminatedfrom the analysis. The calculation of rain rates de-scribed in section 3 confirms that the remaining poly-gons are not representative of the bright band.

Calculations are performed to define the spatial at-tributes of each polygon remaining in the analysis, in-cluding area, perimeter length, perimeter roughness,and elongation (Table 1). To relate the spatial attri-butes of each polygon to those of the polygon that en-compasses it (i.e., the parent polygon; Fig. 3), the at-tributes of each polygon (i.e., area, perimeter length,perimeter roughness, and elongation) are subtractedfrom those of its parent polygon. Small values resultingfrom these calculations indicate strong similarities be-tween a polygon and its parent. These small values im-ply that if a parent polygon is stratiform (convective),the polygon inside of it is stratiform (convective) aswell. The percentage of area that a given polygon oc-cupies within its parent polygon is also calculated.Again, a polygon that is close in size to its parent islikely to have the same stratiform or convective classi-

fication as that of its parent. Last, the number of childpolygons [abbreviated CP and defined as a polygonhaving a threshold reflectivity value 5 dBZ higher thanits parent polygon (Fig. 3)] contained within a givenparent polygon is noted. Thus, each polygon is associ-ated with 10 attributes that describe its spatial proper-ties and its similarities to the parent polygon that en-compasses it (Table 1).

b. Statistical analysis

The statistical method employed to categorize 35-dBZ radar reflectivity values is multivariate linear dis-criminant analysis (DA). Through a linear combinationof a set of predictor variables, the DA derives a func-tion that maximizes the separation of two or more mu-tually exclusive groups (Wilks 1995). Smith et al. (2004)recently employed a multivariate linear DA when de-veloping their damaging-downburst prediction and de-tection algorithm. They calculated a set of 26 predic-tors, including core aspect ratio and maximum reflec-tivity, using reflectivity and radial velocity data andwere able to distinguish between cells that producedsevere downdrafts and cells that did not produce astrong outflow.

Because 11 spatial attributes calculated for eachpolygon (Table 1) could serve as predictors in themodel, a forward stepwise approach is utilized. Thepredictor that decreases the Wilks's lambda statistic bythe greatest amount (Tabachnick and Fidell 2001) isincluded in the model at each step. Lambda valuesclose to 0 indicate that the group means differ; there-fore, selecting variables that most lower this statisticassures that the variables that most differentiate among

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30 dBZ parent polygof interior regii

35 dBZ polyg

Child polygonsof 30 dBZ parentpolygon

Legend N

30 dBZ1 35 dBZ Ai::40 dBZ

0 50 100I IKKm

FIG. 3. Illustration of polygons termed "'parent" and -child."The reflectivity value of a parent polygon is 5 dBZ lower than thepolygon that it encompasses. Child polygons are all polygons con-tained within a polygon that are 5 dBZ higher in reflectivity thanthe encompassing polygon.

the groups are utilized to derive the discriminant func-tions. Mahalanobis distances between cases and eachgroup centroid are calculated, and each case is placedinto the group for which its distance to the centroid issmallest. A successful model classifies a high percent-age of observations into their correct predeterminedgroups.

Three DAs are performed in this study. For the firstDA, 178 cases enter the analysis with prior classifica-tion into one of six groups. Two criteria are utilized togroup the cases, with the first being the polygon's re-flectivity value (30, 35, or 40 dBZ). The second crite-rion is necessary because researchers have demon-strated that stratiform and convective precipitation canoccur in multiple regions within a TC (Maynard 1945;Senn and Hiser 1959; Jorgensen 1984). These studiesconcluded that all polygons located in the outer rain-bands of TCs should be smaller in size and organized

into shapes that are more elliptical than polygons lo-cated within the inner portion of a TC's circulation(Powell 1990). This study considers polygons locatedwithin (outside of) 100 km of the circulation center tobe interior-region (exterior region) polygons. Charley issmall in size because of its rapid intensification justprior to landfall, and thus the use of 100 km to distin-guish interior and outer regions of the storm may notwork for all hurricanes. The classification of each caseprior to its entrance into the DA is as follows: 1) exte-rior-region 30-dBZ polygons (30E); 2) exterior-region35-dBZ polygons (35E); 3) exterior-region 40-dBZpolygons (40E); 4) interior-region 30-dBZ polygons(301); 5) interior-region 35-dBZ polygons (351): and 6)interior-region 40-dBZ polygons (401).

The second and third DAs are performed to deter-mine whether the 35-dBZ polygons are most similar tostratiform or convective regions by entering these casesinto the analysis without prior classification. DA2 con-siders only the exterior-region polygons, and DA3 con-siders only the interior-region polygons. The predictorsentering these DAs are the same as are utilized for thefirst DA; however, only the data from the 30- and 40-dBZ cases are used to build the model. After the valuesof the covariates are calculated using the data from the30- and 40-dBZ polygons, the linear discriminant func-tions evolving from these cases are utilized to predictthe classification of the 35-dBZ polygons.

c. Results

Five predictors combine to lower the Wilks's lambdastatistic to 0.043 in the first DA. Percent occupation(PO) is the most important predictor, demonstratingthat 30-dBZ (40-dBZ) polygons occupied over 76%(under 19%) of their parent polygons (Table 2). Childpolygons enter the analysis at the second step, distin-guishing the 35E and 40E polygons from the othersbecause they encompass five polygons on average.Area difference is included in the third step of DAI,helping to distinguish the 35-dBZ polygons having thehighest difference in area from their parent polygonsfrom the 30-dBZ polygons, which are the most similarin area to their parent polygons. The shapes of thepolygons become important during the last two steps ofthe analysis because interior-region polygons are morecircular with longer edge lengths while exterior-regionpolygons are nearly uniform in their elongation withrelatively smooth edges.

Plotting each case against the first two discriminantfunctions derived from these predictors demonstratesthat the first function separates the groups according totheir reflectivity values, and the second function sepa-rates the groups according to their location (Fig. 4).

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TABLE 2. Predictors successfully entering the first stepwise discriminant analysis.

Analysis step

Variable enteredWilks's lambdaGroup l avgGroup 2 avgGroup 3 avgGroup 4 avgGroup 5 avgGroup 6 avg

Cases belonging to the stratiform groups (30E and 301)are correctly classified over 90% of the time (Table 3).Almost 82% of 401 cases are correctly classified. TheDA also classifies 351 cases well, with three cases eachmisclassified as 301 and 401. The lowest classificationsuccess results from the analysis of the 35E and 40Epolygons: only approximately 50% of these observa-tions are correctly classified. The 35E and 40E cen-troids are located in close proximity to one anotherwhile individual cases are widely dispersed about theirgroup centroids (Fig. 3).

Results from both DA2 and DA3 indicate that 35-dBZ polygons have spatial attributes more similar to40-dBZ polygons than to 30-dBZ polygons. Approxi-mately 83% (78%) of the 35-dBZ cases are classified as40 dBZ in DA2 (DA3). Again, PO is the most impor-tant predictor in DA2 and DA3, where it lowers theWilks's lambda statistic to 0.171 and 0.082, respectively.Removal of the PO predictor from both analyses resultsin the perimeter length being the primary predictor.However, this only changes the 35-dBZ classificationsby one case in DA3 and two cases in DA2. This finding

Legend

0 Group Centroids

6 40 dBZ inlerior

> 5 35 dBZ interior

4 30 dBZ interior

3 40dBZOuter

+ 2 35 dBZ outer

1 30 dBZouter

Function 1FiG. 4. Discriminant analysis cases plotted according to the first

two discriminant functions and the group centroids.

demonstrates that multiple spatial attributes can be uti-lized to categorize 30-, 35-, and 40-dBZ regions.

d. Discussion

The results of the DAs suggest that the 35-dBZ re-flectivity regions are more similar in shape to 40-dBZregions than to 30-dBZ regions. An examination of thepredictors entering the DAs show that the 30-dBZstratiform polygons are very similar in size and shape totheir parent 25-dBZ polygons, whereas the 35-dBZpolygons are very different in size and shape from theirparent 30-dBZ polygons. On average, the 30-dBZ poly-gons make up over 76% of the area belonging to theirparent 25-dBZ polygons (Table 2), whereas the 35-dBZregions occupy much less space inside their parent 30-dBZ polygons. The length of the 30-dBZ polygons' pe-rimeters is only an average of 60 km less than theirparent polygons, whereas the differences in perimeterlengths for all other polygons exceed 470 km. Also, thedifference in elongation ratios for 30- and 25-dBZ poly-gons is less than 0.02, whereas it is greater than 0.1 forall other polygons. These findings illustrate how similarthe 30-dBZ polygons are to the 25-dBZ polygons andhow dissimilar they are to the 35-dBZ polygons. Basedupon these results, the possibility that the majority ofthe 35-dBZ polygons examined in this study are com-posed mainly of stratiform precipitation is unlikely.

The inability of both DAI and DA2 to distinguishbetween 35E and 40E polygons can be attributed to thesharp horizontal reflectivity gradient that exists be-

"FABLE 3. Classification results for the first discriminant analysis.

Predicted group membership

Original group 1 2

1 22 02 2 29

3 1 114 1 05 0 06 0 0

3 4 5 6 Total

1623000)

100

2130

0100

164

2

40

318

23503922

2222

I

PO0.18577%12%23%87%45%18%

2

CP0.0992.14.94.91.01.)1.3

Area diff

0.0771586 km2

15 279 km2

4815 kn2

3855 knm-

15 847 km2

9524 km2

4

Elongation0.0610.440.420.400.680.610.51

5

Roughness0.0430.570.700.670.410.450.51

U-Q.1

3,

+ + 1

+ Qs, +S V-

v I I q I

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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY

tween most of these polygons. The 35E and 40E poly-gons have compact yet elongated shapes, and theseshape attributes are in agreement with those discussedby previous researchers as belonging to convective pre-cipitation (Churchill and Houze 1984; Marks 1985; Big-gerstaff and Listemaa 2000; Rigo and Llasat 2004). Intheir automated method for separating stratiform andconvective radar echoes, Steiner et al. (1995) classifythe regions adjacent to convective centers of 40 dBZ orhigher as convective if a sharp horizontal reflectivitygradient is present. Thus, work by previous researcherssupports the finding that these regions of 35-dBZ re-flectivity values embedded within the outer region rain-bands of Hurricane Charley could be convective in ori-gin.

Most 351 polygons are classified by DA3 as convec-tive. However, according to the DA1 results, 351 poly-gons occupy a middle ground between 301 and 401 poly-gons and three cases are each misclassified as belongingto the 301 and 401 groups. Therefore, it is possible that351 reflectivity returns are representative of a third typeof precipitation termed "transition" (Ulbrich and Atlas2002) or "mixed" (Chen et al. 2003). This type of pre-cipitation is generated by convective storms and is pro-duced in the region between clearly convective cloudsand clearly stratiform clouds. Although the rain doesnot fall directly below the convective cloud, dropletsfalling from transition regions do originate from con-vective clouds. Thus, these regions have the potential toproduce higher rainfall accumulations than do regionscomposed solely of stratiform clouds.

Previous research has shown that identifying transi-tion-type rainfall can aid the separation of convectivefrom stratiform rainfall and that, given only the lattertwo choices, transition-type rainfall should be classifiedas convective. In their investigation of tropical rain-rateand drop size relationships, Yuter and Houze (1997)classified each observation as either stratiform or con-vective and did not consider transition regions as aseparate group. When examining the characteristics ofeach group, they were unable to define two distinctpopulations. Upon re-examination of the data, Ulbrichand Atlas (2002) discovered that many of the stratiformobservations occurring 3-10 km from convective cloudspossessed rain rates exceeding 10 mm h- . Ulbrich andAtlas (2002) identified these observations as being tran-sition-type rain and stated that these observationsshould have been classified as convective rather thanstratiform because of their high rain rates. The conclu-sions made by Ulbrich and Atlas (2002) support thefindings of the current study that, based upon an ex-amination of their horizontal spatial characteristics, 35-dBZ reflectivity regions may be composed of transi-

tion-type rainfall and that, given the choice betweenstratiform and convective, they should be classified asconvective.

3. Rain-rate verification

The previous section found that 351 regions may becomposed of transition-type rainfall within HurricaneCharley. This finding implies that the rainfall rates pro-duced by the 35-dBZ regions are higher than those pro-duced by stratiform clouds. This section details the useof rain gauge and radar-estimated precipitation data toapproximate the rain rates produced by the reflectivityregions described in the previous section. Finding thatsome 35-dBZ regions produce rain rates near to or ex-ceeding 10 mm h-1 would indicate that these specificregions should be considered convective rather thanstratiform (Ulbrich and Atlas 2002).

a. Rainfall data and GIS analysis

To examine rainfall totals received on the groundduring the passage of Hurricane Charley, rain gaugedata are acquired from the Florida AutomatedWeather Network (FAWN). The FAWN consists of 34meteorological observing stations located acrossFlorida. The TE525 tipping bucket rain gauges collectdata in 15-min intervals. Hurricane Charley producedrainfall at 20 of the FAWN sites (Fig. 1). Most of thesesites are located to the left of Charley's circulation cen-ter, and the distance from the storm track to each sitevaries from 5 to 140 kin.

To compare rainfall measured by rain gauges withthat estimated by radar, 1-h precipitation accumulationproducts (OHPs) (Klazura and Imy 1993; OFCM 2006)are acquired from the NCDC archive for the WSR-88Dsites depicted in Fig. 1. The OHP utilizes data from allbase reflectivity scans occurring within the past hour ata given WSR-88D site to estimate the amount of rain-fall that occurred during the past hour. To create thisproduct, a conversion factor relates the radar reflectiv-ity factor scan Z and rain rate R. Both the Z and Rvalues depend on the raindrop size and size distribu-tion; R also depends on the fall velocity for a given dropdiameter (Marshall and Palmer 1948). Several Z-R re-lationships can be employed (Austin 1987; Ulbrich andLee 2002); however, S. Spratt (2007, personal commu-nication) verified that the tropical Z-R relationshipZ = 250R1

L2 (Rosenfeld et al. 1993) was used to estimate

rainfall accumulations for Hurricane Charley duringthe study period. The Java NEXRAD Tools (Ansariand Del Greco 2005) are used to georeference the OHPdata, and they are imported into the GIS as shapefiles.

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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 de-

tected 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 re-

corded 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 an-

other 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 com-

pare 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 re-

gion of Charley passes over the rain gauges located

closest to the storm track (Fig. 5). meaning that they are

351 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 mmh-1 threshold for convective rain rates established by

previous researchers (Burpee and Black 1989: Tokay et

al. 1999; Ulbrich and Atlas 2002); thus, further investi-

gations 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- '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 andrain 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 2 10 km from the circulation cen-

ter of Hurricane Charley. This band forms over south-

ern 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 accumu-

lation occurs approximately 3 h later and is caused by

the principal rainband (Willoughby et al. 1984) of Char-

ley 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-t, corre-

sponding 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 cor-respond to rain rates of 24 and 32 mm h-1 in several

cases. There are 25 cases in which the rain rates mea-

sured by rain gauges exceed the tropical Z-R rain ratefor 35-dBZ polygons overall, and 23 of these cases oc-

cur within the interior region of Charley. Thus, it is

within the interior region of the storm that 35-dBZ re-

flectivity values are producing rain rates that are higher

than anticipated according to the tropical Z-R relation-

ship.The peaks in rain rate discussed above are also evi-

dent when examining the OHP and rain gauge hourly

data (Fig. 5, right panels). However, it is now possible

137MATYAS

JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY

20 50

" 16. 15-min 45i(=E 1 2 -j > Y V *, , G a u g e C4 0

""-" . .Peak dBZ 35~ 8- ,-~ 30-Ona a

. 4 25Nco

0 •0-, .20-20 50

S16- Lake Alfred (D

-12 V40 '

" 8 304- 4 25 C

0 205

20 - 50

"16 " Avalon 45C212• 40F

S8-* ~30~4- , , ,30

4 4 2 5 wN0. 20"-

20 50

" 16 Apopka 45 X0

12 0l 4008" 30 -s4 2500 -- --- 20

-40E230

'ii 20

'• 10

ox'

40

S2S30

S20

10

0

40

E 30

M~ 20

S10

0

Ona - --- hr GaugeS'. Radar OHP

Avalon

40 Apopka

_E30

c20

0 1o -

Tavares

Sv 7.

V V V

Pierson

71819202122230 1 2 3 4Time (UTC)

5

504540 (D

35 <.30 z

25 C20504540035 :53025N205045 (D40 M

35S.

30a-25C20

40ES30

.f 20

10

0

Tavares

40 UmatillaE 302 20

10

0

40 Pierson

Cu3I_.C_

20 /"

10.

017 18 19 20 21 22 23 0 1 2 3 4 5

Time (UTC)

FIG. 5. Time series of rainfall and radar reflectivity values at seven rain gauge sites: (left) 15-mingauge-measured rainfall and the highest radar reflectivity value, and (right) corresponding comparisonof 1-h rain gauge-measured and radar-estimated rainfall totals.

20

~1612

"E8;4

020

'16

12"4E 8

,- 4

020

"1612

"E 8cc 4

0

138VOLUME 48

2\1"'

TABLE 4. Radar reflectivity values and corresponding gauge-measured statistics for rain rates (mm h- ').

Reflectivity value

45 dBZ40 dBZ35 dBZ30 dBZ25 dBZ

No. of Min Max Mean Median Mode

ohs rain rate rain rate rain rate rain rate rain rate

2246697631

20.410.44.83.00.8

73.246.827.2

8.03.6

37.621.2

9.23.21.2

31.618.08.0

2.80.8

214. 016.08.02.00.8

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 re-

gion. 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 com-

bining 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

0 Sebring * Ft. Pierce

* Palmdale

rI a Bel.glade2

*ImmalokeeN

0 50 100

Km

FiG. 6. Rain gauge locations and polygon regions occurringwithin Hurricane Charley at 0100 UTC 14 Aug 2004.

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 ' 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 contribu-tions to flooding should be examined further.

The variability in the rain rates for the 35-dBZ re-

gions that were sampled can be attributed to four fac-

tors: 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 dif-

fering 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 convec-

tive cell's lifespan, vertical velocities weaken and pre-

cipitation 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 dissipat-

ing 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 me-

chanical limits of rain gauges can cause them to under-

estimate the actual precipitation by 20%-40%-in par-

ticular, when wind speeds are high (Miller 1958; Larson

and Peck 1974; Wilson and Brandes 1979). This me-

chanical 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

Tropical Z Rrain rate

56.421.6

8.43.21.2

139MATYASJANUIARY 2009

IýN

JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY

a 40% correction to the gauge measurements at LakeAlfred and Avalon and a 20% correction to gauges atApopka and Tavares would bring the rain gauge mea-surements into agreement with the radar-estimated val-ues. However, adding this correction to the other gaugemeasurements would bring the totals above those esti-mated by the radar. In addition, radar-estimated rainrates could be higher than what actually occurred be-cause of partial beam filling. The spreading and partialfilling of the beam within regions having large horizon-tal reflectivity gradients can cause rainfall to be over-estimated (Rosenfeld et al. 1993).

Furthermore, applying a correction to the gauge-measured rain rates to approximate a 20% undercatchas suggested by Larson and Peck (1974) and Wilson andBrandes (1979) would cause more than one-half of therain rates for 35- and 40-dBZ radar reflectivity returnsto equal or exceed those of the tropical Z-R relation-ship. With uncorrected rain gauge observations, 42% of35-dBZ cases have rain rates that exceed the tropicalZ-R relationship for 35-dBZ reflectivity values of 8.4mm h-t. Adding a correction for 20% undercatchwould yield 43 cases of rain rates in excess of the tropi-cal Z-R relationship produced by 35-dBZ polygons.This result suggests that radar rainfall estimates may belower than the actual rainfall that occurs in 50% ormore of the 35-dBZ cases. Cases of radar underesti-mates of TC rainfall are not uncommon. Baeck andSmith (1998) and Medlin et al. (2007) found many in-stances of rainfall underestimations by radar during thelandfalls of Hurricane Fran (1996) and HurricaneDanny (1997), respectively.

The fact that the beam height changes as it movesaway from the radar station could also explain whyregions that had 35-dBZ radar reflectivity values pro-duced rainfall rates that were higher than expected.The lowest elevation angle for WSR-88D scanning is0.5', which corresponds to an altitude of approximately1.6 km at a range of 100 km from the receiver and 4.2km at a range of 200 km from the receiver. Barnes et al.(1983) found that convective cores in hurricane rain-bands are often located at altitudes near 2 km. The basescan fails to sense the atmosphere below 2 km begin-ning approximately 125 km away from the station. Therain gauges at Ona, Lake Alfred, Apopka, and Avalonare all located within 107 km of the nearest radar site.However, beam height may be a factor that is causing35-dBZ rain rates to be underestimated for gauges atPierson, Tavares, and Umatilla because they are lo-cated 142-150 km away from the nearest radar site.Because beam attenuation is negligible for S-bandradar, this explanation is not plausible for differencesbetween reflectivity values measured and rain rates re-

ceived at the ground. In addition, differing calibrationsof the radar sites used for the analysis could also havecontributed to the underestimation of rainfall totals bythe OHP.

The application of a single Z-R relationship when amixed type of precipitation is occurring (Rosenfeld etal. 1993) may also account for a portion of the variabil-ity in rain rates for the 35-dBZ polygons. Forty-twopercent of the 35-dBZ regions analyzed had rain ratesin excess of the tropical Z-R value for 35-dBZ reflec-tivity values. Convective, stratiform, and transition re-gions have different drop size distributions, which ne-cessitate different Z-R relationships to estimate rainfalltotals 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 dropsize distributions and Z-R relationships of convectivezones and the trailing transition regions of mesoscaleconvective complexes.

The finding that most of the 35-dBZ regions meet orexceed the tropical Z-R relationship suggests that theseregions are not representative of the bright band.Baeck and Smith (1998) discuss the detection of thebright 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 1.5in excess of radar estimates. When the bright band issampled, radar-estimated rain rates exceed those mea-sured by rain gauges. The underestimation of hourlyrainfall totals by the radar during the passage of theinterior region of Hurricane Charley confirms that the35-dBZ regions are not produced by the bright band.

4. Conclusions and future work

Improving rainfall forecasts for landfalling TCs ne-cessitates quantifying the evolution of regions that pro-duce high rain rates within these systems. Stratiformprecipitation regions, identified by radar reflectivityvalues around 30 dBZ, are typically not a concern forheavy rainfall, but convective regions corresponding toreflectivity values of 40 dBZ or greater can producehigh rain rates that may cause flash flooding. This re-search used a GIS to examine the spatial attributes of35-dBZ regions to determine whether they were moresimilar to the 30-dBZ stratiform regions or to the 40-dBZ convective regions that occurred during theFlorida landfall of Hurricane Charley (2004). Rainrates were calculated using radar estimates and raingauge measurements to determine whether 35-dBZ re-gions are capable of producing rain rates in excess of 10mm h 1, a threshold rate for convective rainfall that wasidentified by previous researchers.

140 VOLu-mE 48

JANUARY 2009

Results indicate that regions of 35-dBZ reflectivity

returns within the outer rainbands of Charley are spa-

tially similar to the 40-dBZ polygons because of the

high reflectivity gradients present within convectiveclouds. These regions are adjacent to 40-dBZ convec-

tive cores and could be considered to be convective

themselves. The 35-dBZ returns within the interior re-

gion 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 convec-

tive 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-' rain rate as-

cribed to 35-dBZ regions by the tropical Z-R relation-

ship. Application of a 20% correction for rain gaugeundercatch increases this statistic to over 50% of cases.

Also, rain rates measured by rain gauges exceed thosethat were estimated by applying the tropical Z-R rela-

tionship to the 35-dBZ radar data. These findings sup-

port the identification of 35-dBZ interior regions aseither 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 bestorm dependent.

Because most work detailing the spatial characteris-

tics 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 withinTCs is not clearly defined in the current literature. The

current study found that 35-dBZ regions can be asso-ciated with regions within a hurricane that produce rain

rates in excess of 10 mm h-i' therefore, these regions

should be examined more closely for incorporation intofuture rainfall analyses. The inclusion of data pertain-

ing to the vertical structure of radar reflectivity returns

could also facilitate classification of stratiform, transi-

tion, and convection regions within TCs (Barnes et al.1983; Chen et al. 2003). Because of its relatively fast

forward motion, rainfall produced by Hurricane Char-

ley 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 floodingcan be further evaluated. The analysis of several land-

falling TCs will facilitate comparisons among 30-, 35-,and 40-dBZ regions and will be an important undertak-ing to validate the findings within the current study.

Acknowledgments. The author thanks Dr. PeterWaylen 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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TITLE: A Spatial Analysis of Radar Reflectivity Regions withinHurricane Charley (2004)

SOURCE: J Appl Meteorol Climatol 48 no1 Ja 2009

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