2001 JAOT Zrnić

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892 VOLUME 18J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y

2001 American Meteorological Society

Testing a Procedure for Automatic Classification of Hydrometeor Types

DUSAN S. ZRNIC

NOAA/National Severe Storms Laboratory, Norman, Oklahoma

ALEXANDER RYZHKOV

Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma

JERRY STRAKA

School of Meteorology, University of Oklahoma, Norman, Oklahoma

YIDI LIU

Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma

J. VIVEKANANDAN

National Center for Atmospheri c Research, Boulder, Colorado

(Manuscript received 18 April 2000, in final form 7 September 2000)

ABSTRACT

Examples of automatic interpretation of polarimetric measurements made with an algorithm that classifiesprecipitation, from an Oklahoma squall line and a Florida airmass storm are presented. Developed in this paperare sensitivity tests of this algorithm to various polarimetric variables. The tests are done subjectively bycomparing the fields of hydrometeors obtained using the full set of available polarimetric variables with adiminished set whereby some variables have been left out. An objective way to test the sensitivity of the algorithmto variables and rank their utility is also devised. The test involves definition of a measure, which is the numberof data points classified into a category using subsets of available variables. Ratios of various measures (similarto probabilities) define the percentage of occurrence of a class. By comparing these percentages for cases in

which some variables are excluded to those whereby all are included, a relative merit can be assigned to thevariables. Results of this objective sensitivity study reveal the following: the reflectivity factor and differentialreflectivity combined have the strongest discriminating power. Inclusion of the temperature profile helps eliminatea substantial number of spurious errors. Although the absence of temperature information degrades the scheme,it appears that the resultant fields are generally coherent and not far off from the fields obtained by addingtemperature to the suite of polarimetric variables.

1. Introduction

Knowing what precipitation type is reaching theground is a fundamental prerequisite for accurate de-termination of amount. Thus, for quantitative precipi-tation estimation (QPE), first a correct classification

needs to be made so that appropriate semiempirical re-lations can be chosen to estimate the corresponding ratesand/or accumulations. Because of sensitivity to hydro-meteor concentration, shape, orientation, dielectric con-stant, and size, polarimetric variables have emerged as

Corresponding authors address: Dusan S. Zrnic, NOAA/NationalSevere Storms Laboratory, 1313 Halley Cr., Norman, OK 73069.E-mail: [email protected]

leading discriminators of precipitation type (Zrnic andRyzhkov 1999).

Very early in the development of differential polar-ization measurements, it became apparent that thesecould be used to determine the presence of hail andpossibly gauge its size (Seliga and Bringi 1978). Later,

Hall et al. (1980) proposed a table of relations betweenthe reflectivity factor and differential reflectivity to clas-sify hydrometeors; noteworthy are the descriptive (non-quantitative) entries in the table that, it turns out, arevery suitable for building fuzzy classification rules.A more detailed table can be found in Doviak and Zrnic(1993); it served as a starting point for some decision-tree type classification schemes (e.g., Lopez and Au-bagnac 1997; Carey and Rutledge 1996), which wereused to discriminate among rain, graupel, and hail. A

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JUNE 2001 893Z R N I C E T A L .

similar decision type rule has been advanced and appliedto data collected with a 5-cm wavelength radar by Holleret al. (1994).

Building on the table in Doviak and Zrnic (1993),Straka and Zrnic (1993) developed a scheme based onfuzzy logic principles in which boundaries betweenclasses were allowed to overlap, but the weighting(membership) functions were of a pulse type (i.e., valuesof 0 and 1). Subsequently, Straka (1996) used a varietyof overlapping weighting functions with smooth tran-sitions in one and two dimensions; this scheme becamethe basis of several subsequent attempts for classifica-tion of hydrometeors (Zrnic and Ryzhkov 1999; Vivek-anandan et al. 1999). A further step in the developmentis reported by Liu and Chandrasekhar (2000) who useda feedback scheme to adjust the weights of the fuzzyclassifier; they also give a comprehensive set of valuesfor the one-dimensional membership functions.

Meanwhile Straka et al. (2000) have presented anextensive set of relations in the form of tables and two-

dimensional graphs that delineate regions, in the spaceofZh (the reflectivity factor for the horizontally polarizedwave) and any polarimetric variable, where specific hy-drometeor signatures reside. These graphs (or variantsthereof) have been used by the authors to build mem-bership functions for fuzzy classification schemes(Straka 1996; Ryzhkov and Zrnic 1999), one of whichhas been implemented on the NCARs S-Pol radar (Vi-vekanandan et al. 1999).

The purpose of this paper is to present details of thealgorithm not found elsewhere and a methodology forsensitivity analysis to the various polarimetric variablesused for classification. Verification, let alone simplecomparisons of classification algorithms, is a daunting

task because in situ observations are too few and oftennot coincidental with the radar measurements. More-over, the radar sampling volumes are several orders ofmagnitude larger than the typical particle probes whoseimages contain uncertainties as well. Because there areother simpler means to develop and evaluate the algo-rithm, no comparison with in situ probes is attemptedherein. Rather, we rely on spatial continuity, heightabove ground, and comparison with conceptual modelsto qualify the algorithms performance. An importantthrust of our paper is a procedure we developed to com-pare the merits of the polarimetric variables for clas-sifying various hydrometeors. This procedure and self-consistency checks based on intuition, precipitationphysics, and conceptual models can be carried out be-fore in situ comparisons are attempted.

In section 2 of the paper we briefly describe the al-gorithm. Then follows a description of data that are usedby the algorithm. In section 3 we present the perfor-mance of the algorithm on the data from the Cimarron(Zahrai and Zrnic 1993) and the S-Pol polarimetric ra-dars (Lutz et al. 1997). Ramification for operational ra-dars are then mentioned, and relative merits of various

polarimetric variables to isolate hydrometeor types arediscussed.

2. Algorithm

The classification algorithm described herein belongsto the fuzzy logic family. Much has been writtenabout this method (Mendel 1995), and several articleswith applications to meteorological problems have ap-peared (Straka 1996; Cornman et al. 1998; Vivekan-andan et al. 1999; Liu and Chandrasekar 2000). None-theless, none of the jargon used in that discipline isneeded to understand its principles. In the followingdescription, we utilize the key nomenclature, define two-dimensional membership functions, and rely on analogywith probability density functions for reasons that willbe apparent shortly.

In its essence a classifier assigns (maps) an observedpoint X in the multiparameter space to a class j (whichrefers to the bulk hydrometeor type such as rain, hail,graupel, snow, etc.). In this paper, the point X has forcoordinates the following six variables:

1) the reflectivity factor for horizontally polarizedwaves Zh ,

2) the differential reflectivity ZDR ,3) the specific differential phase KDP ,4) the cross-correlation coefficient between the hori-

zontally and vertically polarized (copolar) waveshv (0),

5) the linear depolarization ratio LDR , and6) the environmental temperature T.

The crux of a hydrometeor classification scheme isto partition this six-dimensional space of observed var-

iables into subsets such that each can be associated witha specific hydrometeor type (j). The classical statisticaldecision theory solves, in principle, this type of a prob-lem as follows. It starts with the probability densitiesPj(X) for each class. Then, the integral

P (X) dX (1) jVj

over a subset (here six-dimensional volume Vj ), cor-responding to the likely class j, gives the probability ofcorrect classification, whereas the integral over the com-plement of Vj is the probability of misclassification ofthe specific class j. The choice of the volume Vj amounts

to identification of a boundary delineating the class;misclassification occurs because of the ambiguity at andin the vicinity of the boundaries between classes. Byconsidering consequences of either decision (the pointdoes or does not belong to a class), one can partitionthe space of the polarimetric variables (universe in thenomenclature of set theory) to optimize the outcome.Normally an accepted false alarm rate for misclassifi-cation would be adopted, and by trial and error, theboundary would be changed as long as the probability

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of correct classification increases while the probabilityof misclassification is kept at or below the desired level.This is analogous to the dilemma facing weather fore-casters who are about to issue warnings. Over warningincreases the probability of detection at the expense ofmore false alarms. A proper balance between these twodecisions is often a subjective call.

In most cases of practical significance, and certainlyfor hydrometeor classification, the probabilities of clas-ses are not available, and it is unlikely that these wouldbecome known in the near future. Therefore, simplifi-cations are sought such that reasonable classification canbe made.

An obvious solution is to decouple the variables, con-sider each individually, and then make a final judgmenton the basis of weighted averages. This is the simplestform of a fuzzy classifier (Mendel 1995). One-di-mensional weighting functions Wj(Yi ), somewhat sim-ilar to probabilities, are defined in a way that mimicsones expectation (Straka and Zrnic 1993; Vivekanan-dan et al. 1999; Liu and Chandrasekhar 2000). Here, Yistands for any one of the polarimetric variables. Anintuitive yet good practice is to restrict the maxima ofWj s to be 1 and locate these at values for which thevariable almost always corresponds to the jth class. Fur-ther from these maxima, the weighting function shoulddecrease to reach zero in regions where the variable isunlikely to be associated with the jth class. To distin-guish between reliable and less reliable variables, Yi,one can multiply the Wj(Yi ) with a multiplicative factorA i less or equal to one. In this manner, relative changesof confidence in various variables can be easily ac-counted for. Thus, the classification based on thisscheme involves sums

M

A W(Y) i j ii1

S , (2)j MA i

i1

where M is the number of variables, and the naturalassignment is the one that maximizes Sj.

But, there is more to come. Because the numericalvalues of Sj allow quantitative assignment of the con-fidence in the classified bulk hydrometeors (in the res-olution volume), if the weights represent the truthwell, then the values (in %) of Sj can be interpreted asthe confidence in outcome of the classification proce-

dure. That is, the higher the max (Sj) is, and the largerthe difference between the max (Sj ) and the next to max(Sj), the more likely it is that the classification is correct.

A short discussion concerning maximization of thesum (2), as opposed to some other combination of theweights, is in order. For example, Liu and Chandrasekar(2000) maximize the product of weights and report con-siderable skill of their classifier. Simple considerationssuggest that with the sum, the probability of correctclassification should be larger. That is, if due to noise,

one of the weights (for a specific class) is zero, the reststill can contribute significantly to bring the datum intothe correct category. On the other hand, the percent offalse (absurd) classifications should be smaller in theproduct maximization scheme. That is, if one variableis considerably out of range for a given class, its verysmall weight will suppress that class. Another difference

between the two procedures concerns the way that con-fidence in the variables is expressed. In the maximi-zation of sums, the multiplicative factors Ai primarilydetermine the confidence, whereas the width of theweighting functions has a secondary role. In the max-imization of products, the width of the weighting func-tions determines the confidence in the variables; in-crease of the width lowers the confidence in the variable.Because comparisons between the two procedures haveyet to be made, further research and tests are requiredto evolve an optimum scheme.

Because of high dimensionality and unknown shapeof the partition boundaries, a reasonable approach is todeal with projections to smaller dimensions. At the mo-ment, this is a sound practical approach as much hasbeen learned about how values of individual variablesrelate to hydrometeor types (Herzegh and Jameson1992; Doviak and Zrnic 1993; Holler et al. 1994; Strakaet al. 2000). Although simple, the use of one-dimen-sional weighting functions gives a less tight partitionthan what is possible by capitalizing on the dependen-cies (correlations) between the variables. If two polar-imetric variables (corresponding to a specific class ofhydrometeor types) are related, their scattergram has atrend as opposed to a centrally symmetric shape foruncorrelated variables; see, for example, the Zh, ZDRscattergrams (Leitao and Watson 1984), the Zh, KDP scat-tergrams (Balakrishnan and Zrnic 1990a; Ryzhkov etal. 1997), and the Zh , hv scattergrams (Balakrishnanand Zrnic 1990b). Thus, a more precise classificationwould be achieved if the class is delineated with aboundary that follows a fixed percentage contour in thescattergram of the two variables for a specific hydro-meteor type. Straka et al. (2000) suggest how to partitionpairs of variables (two-dimensional subspaces) into re-gions of dominant hydrometeor types. According to sev-eral investigators, discrimination in two-dimensional(2D) regions produced very promising results (Straka1996; Carey and Rutledge 1998; Lopez and Aubagnac1997; Zrnic and Ryzhkov 1999; Vivekanandan et al.1999; Liu and Chandrasekar 2000).

Simulations (Scarchilli et al. 1996) and observationsallow definitions of regions in the subspace of three ormore variables (triplet Z, ZDR , KDP in the cited reference)whereby hydrometeors of one type prevail. Nonetheless,direct partition (i.e., creation of boundaries) in largerthan two-dimensional subspaces is quite complex and,to our knowledge, has not yet been attempted. Moreover,two-dimensional partitioning is readily visualized, andtherefore, the connection between changes in the bound-aries and the corresponding effects on classification be-

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FIG. 1. Two-dimensional weighting function for moderate rain,WMR(Zh , ZDR), over the space Zh, ZDR.

TABLE 1. Increment of polarimetric variables over which the weighting function changes from 1 to 0.

Increment of polarimetric variables Hydrometeors to which weighting applies

Zh 5 dB AllZDR 0.3 dB Light, moderate, heavy rain, large drop rain, graupel/small

hail, and wet snowZDR 0.1 dB Rain/hail mixtureZDR 0.25 dB HailZDR 0.2 dB Dry snow, ice crystals

KDP 0.23 0.023Zh 6.6 10

4 Z2h( km1 for Zh in dBZ)

Light, moderate, heavy rain, large drop rain, and rain/hailmixture

KDP 0.2 km1 Hail, wet snow

KDP 0.1 km1 Graupel/small hail, horizontally, and vertically oriented ice

crystalsKDP 0.05 km

1 Dry snowhv 0.02 Light, moderate, heavy rain, large drop rain, rain/hail mix-

ture, graupel/small hail, hail, dry snow, horizontally, andvertically oriented ice crystals

hv 0.05 Wet snowLDR 2 dB All

comes apparent. This is important for the evolution ofthe algorithm, which requires numerous iterations, andthis visual-cognitive feedback can lead to a rapid con-vergence toward satisfactory performance.Accordingly,we have defined 2D weighting functions Wj(Zh, Yi)where Zh is the reflectivity factor for horizontally po-larized waves, and Yi is one of the other five variables.

Boundaries of hydrometeor classes presented byStraka et al. (2000) are used to define the values of theweighting functions. In regions identifying a specifichydrometeor type, the corresponding weighting functionis set to 1; from the boundaries and outward, the valuesdecrease linearly with distance. To construct the 2Dweighting functions, the analogy with probability den-sities is very helpful. For example, the 2D weightingfunction can be expressed as a product of a one-di-mensional weighting function (analogous to a prioryprobability) with a conditional weighting function (anal-ogous to marginal probability density function),

W(Z , Z ) W(Z )W(Z | Z ).j h DR j h j DR h (3)

As an example, the shape of the weighting functionfor the class moderate rain (Straka et al. 2000) isplotted in Fig. 1. Here, WMR (Zh ) 1 for Zh between 35

and 45 dBz; from these boundaries, the weighting func-tion decreases linearly (with the slope of 0.2 dB1) sothat if Zh is displaced by 5 dB from the boundary, itreaches 0. The conditional weighting functions are alsotrapezoidal except the coordinates defining each trape-

zoid (Fig. 1) depend on the value of Zh; the decreaseof WMR (ZDR | Zh) from 1 to 0 occurs over the intervalof 0.3 dB in ZDR .

In a similar way, all other 2D weighting functions aredefined on, altogether, five pairs of variables. All the apriory and conditional Ws are trapezoids whose topvertices are prescribed by the diagrams in Straka et al.

(2000) in a similar manner, as explained in the previousparagraph. The weighting functions overlap and inter-sect at the value of. Some minor deviations from thesediagrams have evolved in the course of this work.

The increments in the polarimetric variables overwhich various weighting functions change from 1 to 0(or vice versa) are listed in Table 1. These were obtainedin a subjective manner from experience, examination ofscattergrams, and consideration of statistical errors inestimates of the polarimetric variables.

Tests of the algorithm demonstrated that the zero de-gree isotherm of the environmental temperature was of-ten above the one inferred by the location of the meltinglayer (which is lowered by the downdraft). This canproduce inconsistent weighting functions. To avoid suchcontradictions, we modify the environmental tempera-ture profile so that its zero degree height coincides withthe minimum ofhv . That is, in cases where the verticalcross section of hv shows a well-defined melting zone(Zrnic et al. 1993), a vertical profile through the meltingzone is constructed, and the location of its minimum isfound. In this way, the heights of the melting layerbottom obtained from the temperature and polarimetricmeasurements are forced to coincide. But through con-vective cores, the melting zone is lifted in the updraftand lowered in the downdraft and, thus, offset from theimposed zero T height. Nonetheless, the polarimetric

variables have such strong signatures in the convectivecell that their weighting functions overwhelm the tem-peratures, and hence, the offset does not affect the out-come of classification. We emphasis that it is not nec-essary to have an actual temperature profile. A standard

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TABLE 2. The transition points for the weighting trapezoidalfunctions of temperature.

T1 (C) T2 (C) T3 (C) T4 (C)Hydrometeors to which

weighting applies

5 0 NA NA Light, moderate, heavy rain10 0 NA NA Large drop rain60 50 1 1 D ry s now, hor iz onta lly, a nd

vertically oriented ice crys-tals

3 0 7 10 Wet snow156040

03515

200

15

402040

Rain/hail mixtureGraupel/small hailHail

TABLE 3. Values of thresholds and types of suppressedhydrometeors.

Vari-ables Thresholds Suppressed hydrometeors

ZDR 0 dB Light, moderate, heavy rain,and rain with large drops

T 20C or 10C Wet snow

T 15C Rain/hail mixtureT 15C Light, moderate, heavy rain,

and rain with large drops

TABLE 4. Multipliers (Ai) of the weighting functions.

AZh AZDR AKDP Ahv ALDR AT

Cimarron dataS-Pol data

11

11

0.80.8

0.30.5

NA0.5

0.40.4

FIG. 2. Sketch of a trapezoidal weighting function for temperature.The points T1, T2, T3, and T4 serve to define the numerical values inTable 2.

atmosphere profile suffices if it is modified to have thezero isotherm at a heigh determined by the radar.

The weighting functions of temperature are rooted inphysical principles and are also trapezoidal, except theones for rain are open ended at temperatures larger than0C. We have tabulated the transition points of theweighting trapezoidal functions in Table 2, whereas Fig.

2 relates the tabulated values to the typical trapezoidalweights.

Currently, there are 11 hydrometeor classes that buildon the synthesis in Straka et al. (2000). The hydrometeorclasses are

1) light rain (LR 5 mm h1),2) moderate rain (MR: 5 to 30 mm h1),3) heavy rain (HR 30 mm h1 ),4) rain dominated by large drops (LD),5) rain/hail mixture (R/H),6) graupel and/or small hail (GSH),7) hail (HA),8) dry snow (DS),

9) wet snow (WS),10) horizontally oriented ice crystals (ICH), and11) vertically oriented ice crystals (ICV).

Throughout this paper (in the figures and the text), theclasses are numbered as in the above list. There is alsoa nonhydrometeor class that absorbs biological scatter-ers, ground clutter, and other strong point scatterers aswell as noise. This class is excluded from the displays.

The real-time version of this algorithm implementedon the S-Pol radar (Vivekanandan et al. 1999) differsin some categories. Drizzle, cloud drops, supercooled

droplets, irregular ice crystals, and insects are additionalclasses of scatterers, but there is no distinction betweenhorizontally and vertically oriented ice crystals, nor isthere a category for rain with large drops. Vertical ori-entation of crystals is caused by strong electric fieldsand their presence might be a precursor to the onset oflightning. The extra hydrometeor categories for the S-Pol radar may be possible because it measures LDR ,which is not available on the Cimarron radar.

In addition to the described weighting functions, thereare thresholds on differential reflectivity and tempera-ture such that the confidence (sum Sj) in a hydrometeorclass j is set to zero if the thresholds are satisfied. Table3 lists the thresholds and the affected hydrometeors. Itis self evident that these thresholds prevent absurd clas-sification.

Finally, the multipliers A i representing the importanceattached to the various polarimetric variables are listedin Table 4. Experience combined with trial and errorlead us to adopt these values. Reasons related to hard-ware on the Cimarron radar cause bias in the hv suchthat the values are lower and noisier than expected, andtherefore, A

is set to 0.3 as opposed to 0.5 for the S-

Pol radar.It is of utmost importance to present valid data to this

or any other automated algorithm. To that end, we utilizea median filter on Zh, a running average to smooth theZDR , hv , and LDR , and a least-squares fit (Ryzhkov andZrnic 1996) to obtain specific differential phase. Fur-thermore, we discard KDP in and adjacent to regionswhere its values are below 0.5 km1. Reflectivityfactor and differential reflectivity are corrected for at-tenuation following the procedure suggested by Bringiet al. (1990).

3. Sensitivity tests

Objective comparison of polarimetric schemes forclassification could be done, in principle, if a large setof comprehensive in situ observations were available.

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FIG. 3. Vertical cross sections of the fields of (a) reflectivity factor (color contours are in dBZ as indicated on the color bar), (b) differentialreflectivity (contours are in dB as indicated on the color bar), (c) cross-correlation coefficient (contours are indicated on the color bar), and(d) specific differential phase (contours km1 are indicated on the color bar). Data were obtained on 6 Jun 1996, at 2316 UTC with theCimarron polarimetric radar at the azimuth of 148.2; range from Cimarron radar is in kilometers, and the grid cell is 10 5 km.

Currently, there are no platforms to provide such ob-servations over large volumes and at rates compatiblewith radar scanning times; nonetheless, for the purposeof this paper, such comparisons are premature. For pre-liminary comparisons and crude adjustments of theweighting (membership) functions, there is a much sim-pler procedure that we have adopted. It consists of visualidentification of the obvious gross errors and determi-nation of the responsible variables. Then, the boundariesand/or membership functions built on these variablesare changed until the gross errors are reduced or dis-appear. This requires care so that the ripple effect onthe previously correct classification is minimized,whereas the reduction in erroneous classes is maxi-mized.

The reflectivity factor and environmental soundingare available to all those with access to ubiquitous non-polarimetric radars. Hence, it is pertinent to determinehow these two variables fair in comparison with the fullset of polarimetric variables. In addition, it is useful toknow which polarimetric variable in combination withthe reflectivity factor has the most discriminatory power.

To illustrate the effects of temperature, we present re-sults of classification whereby use only of the pair Zh,T is contrasted with application of the other variables.Similarly, we consider the other pairs individually andin suitable combinations.

We have chosen a dataset obtained with the Cimarronpolarimetric radar from a hail storm and a dataset ob-tained with the S-Pol radar from an airmass storm inFlorida to demonstrate the effects variables have on theclassification outcome. Besides presenting images of

classified hydrometeor fields, we also make a somewhatsubjective but nonetheless quantitative ranking of thevariables according to their relative importance.

a. Hail storm observed with the Cimarron radar

1) VISUAL ANALYSIS OF CLASSIFIED FIELDS

The polarimetric variables available on the Cimarronradar are reflectivity factor Zh, differential reflectivityZDR , specific differential phase KDP , and cross-correla-tion coefficient hv . Vertical cross sections of the fieldsof these variables through a convective storm revealsome well-defined hydrometeor signatures as well asartifacts (Fig. 3). For example, the high reflectivity corealoft (Fig. 3a) likely contains hail. The positive ZDR nearground indicates rain, and the column of positive ZDRat 80 km (Fig. 3b) contains large drops in relatively lowconcentration. Positive ZDR above the storm top is dueto mismatch of antenna sidelobes for vertical and hor-izontal polarizations; these data are excluded from theforthcoming presentations. The KDP shows concentration

of rain between 70 and 80 km, and there is a columnof KDP that overlaps the ZDR column (Fig. 3d).The censored values aloft correspond to KDP 0.5

km1, which are likely due to artifacts (Ryzhkov andZrnic 1998). The field of correlation is least reliable,and there is no indication of the melting layer in thisstorm (Fig. 3c). An abrupt increase of ZDR in the lowerpart of precipitation in this case hints at the onset ofmelting of graupel and snow. Because the strong verticalgradient of ZDR at its highest point above ground (at the

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FIG. 4. Vertical cross section of classified hydrometeors for thedata from Fig. 3. The letters below the color bar correspond to thehydrometeor categories as follows: LR light rain, MR moderaterain, HR heavy rain, LD rain with large drops, R/H rain/hailmixture, GSH graupel small hail, HA hail, DS dry snow,WS wet snow, IH horizontally oriented ice crystals, and IV vertically oriented ice crystals. Classification was made using allavailable polarimetric variables (Zh , ZDR, KDP, hv) and the environ-mental temperature T.

FIG. 5. Vertical cross sections of classified hydrometeors for the data from Fig. 3 except only a pair of variables is used for each field asfollows, (a) the pair Zh , ZDR; (b) the pair Zh, KDP; (c) the pair Zh, hv; and (d) the pair Zh, T.

range of 40 km) almost coincides with the 0C isothermof the sounding, no adjustment was made to the envi-

ronmental temperature.The algorithm was applied to the fields of polarimetric

variables (Fig. 3), and it created the hydrometeor classesrepresented in Fig. 4. We consider this field to be thestandard against which fields obtained with less than thefull set of variables can be gauged. Although we do nothave independent verification about the quality of thefield in Fig. 4, we submit that the comparison can revealsome useful information. Things like relative merit ofpolarimetric variables and the average confidence (Men-del 1995) in various classes of hydrometeors can bequantified.

Figures 5ad contain the fields of hydrometeors, eachof which was obtained from a single pair of variables

(one variable in any of the pairs is always Zh); com-parison with Fig. 4 reveals the relative significance ofthe selected pair. This significance will be quantifiedafter a brief qualitative description of salient features

attributed to the various pairs.The primary variables responsible for locating the

onset of rain are the Zh and ZDR , as can be seen in Fig.

5a. Further, the heavy rain and rain with large drops at50 km as well as aloft at 80 km are also identified fromthe Zh, ZDR pair. The light rain in the anvil is erroneousand is a consequence of inability to distinguish between

light rain and dry snow in the two-dimensional subspaceZh, ZDR . The areas of light rain and dry snow overlapin a large region of the Zh, ZDR subspace (see Figs. 2aand 2b in Straka et al. 2000). With further research, it

might be possible to decrease the overlapping area.The pair Zh, KDP identifies some horizontally oriented

ice crystals, but at the top of the cloud it misclassifies

crystals into light rain. Otherwise, graupel and rain/hailmixture are the two dominant categories. Both extendinto the region where their presence (in this case) isphysically forbidden; for rain/hail that is throughout a

large upper part of storm, and for graupel it is the north-

west part near ground. These errors are a consequence

of inadequate information in the Zh, KDP pair. Sporadic

data void regions (black patches within the field) are

where the KDP is excessively negative.

The pair Zh, T (Fig. 5d) produces a smooth field in

which the vertical stratification of hydrometeors is con-

trolled by the temperature profile. Note how the phase

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FIG. 6. Same as in Fig. 4 except a specific pair has not been applied to the classification scheme, but other pairs each of which includesZh have been applied. (a) The pair Zh, ZDR has not been used. (b) The pair Zh, KDP, has not been used. (c) The pair Zh, hv has not beenused. (d) The pair Zh , T has not been used.

transition at zero temperature is at the constant heightof about 4 km; it is followed in height with graupel/small hail, and dry snow is at the top. This generalpattern is modulated in the horizontal direction by theinfluence of the reflectivity factor. Although pleasing tothe eye and somewhat physically satisfying, the clas-sification misses important details seen in Fig. 4.

The pair Zh, hv produces the least reliable classifi-cation due to extensive overlap of discrimination regions(Straka et al. 2000). The classes close to the ground arecredible mainly due to the influence of Zh . Data-voidregions are where the values of the correlation coeffi-cient are below 0.3.

Figures 5ad indicate that none of the pairs by them-selves can create wet snow in the melting layer; itspresence is revealed only if the algorithm is applied toall the polarimetric variables (Fig. 4). The pairs Zh , ZDR ,and Zh, T produce fields that closely match what isexpected as function of height in storm cells. Otherworks (Wakimoto and Bringi 1988) and our experiencesuggest that the boundary between frozen and liquidprecipitation at low levels is faithfully delineated using

the Zh, ZDR pair.For further comparison and analysis, it is worthwhileto examine classified fields obtained from the sets ofthe polarimetric variables in which one polarimetric var-iable is absent (Fig. 6). Absence of ZDR (Fig. 6a) pro-duces a field in which the strong influence of KDP andTis seen, whereas the absence ofKDP (Fig. 6b) replicatesfairly well the field in Fig. 4; neither one of these fieldscontain wet snow in the melting layer. Only if Zh, ZDR ,and KDP are simultaneously present do the weights add

up to produce wet snow in the melting layer (Figs. 6cand d).

Absence of hv (Fig. 6c) has a minor effect on theclassification outcome; however, it increases the thick-ness of the wet snow region. The value of temperaturein eliminating physically impossible classes is seen inFig. 6d. These are the sporadic areas of wet snow atheights above 7 km, spots of rain/hail mixture at similarheights, patches of light rain at the edges of storm, someice crystals close to the ground, and wet snow in theupper part of the storm.

Comparison of Figs. 6ad clearly shows that ZDR isthe most important polarimetric variable. In its absence,the classified fields clash with those expected from con-ceptual models and physical considerations.

2) RELATIVE IMPORTANCE OF THE VARIABLES

Next, we will quantify the discussion concerning rel-ative contribution of variables to hydrometeor classesin Figs. 46. This we do, as in the previous section, byexamining classification with single pairs versus the rest

of variables. The reader is referred to appendix A forexplanation of the measure that we assign to the fieldof classified hydrometeors. Briefly, the measure is anumber of data points that are classified to the samecategory of hydrometeors. With appropriate normali-zation of measures, we obtain various percentages (akinprobabilities) of classification, which are entered in ta-bles. Thus, from the tables one can objectively establishrelative merits of variables used in the classificationscheme. Two tables (5 and 6) are presented and dis-

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TABLE 5. Percent of correctly classified hydrometeors (P A)/(A) using the pair alone; Oklahoma storm.

With

Hydrometeor categories

LR MR HR LD R/H GSH HA DS WS ICH ICV Tot 70%* 30%*

ZDRKDPhv

T

96627098

774094

100

812683

100

100000

69959026

9165

083

9524

078

817

064

01

150

9000

098

00

70512568

6245

4675

* 70% and 30% indicate the number of classes for which these conditions hold.

cussed in detail herein; several others are in appen-dix B.

We will often make reference to appendix A (Fig. A1and Table A1) in the following text. Thus, (A), (P),and (R) stand for the number of data in a class obtainedfrom all the available variables, a single pair of vari-ables, and the rest of the variables (i.e., excluding thepolarimetric variable that was part of the pair), respec-tively, as explained in appendix A. The notation in TableA1 clarifies the meaning of various measures presentedhere and in appendix B. The total number of classifieddata points (i.e., resolution volumes) for this storm was14050.

We start with Table 5 to illustrate values obtained forthe Oklahoma hailstorm data. The entries are percent-ages with respect to the case in which all the variablesare used for classification (see also Table A1). Thus, thelarge value indicates that a particular pair contributessignificantly to the classified category, whereas verysmall value indicates irrelevance of the variable. If acolumn contains one large value and other very smallvalues, then the variable corresponding to the large val-ue is almost exclusively responsible for the classificationto the corresponding category. In the twelfth columnare the percentages for the whole data field (i.e., for allthe classes combined).

A glance at the Table 5 reveals that Zh, ZDR pair isthe most significant of the pairs. In column 14 listed isthe number of hydrometeor classes for which the percentof correct classification is larger than 70. (For Gaussiandistributions, this is almost equal to the probability with-in one standard deviation.) If we rank the variables ac-cording to the number of hydrometeor classes for whichthe pair produces 70% of agreement with that pro-duced by the complete set, the order would be ZDR , T,hv , KDP (6 categories 70% for ZDR , 5 for T, 4 for hv ,and 2 for KDP ). But if the rank is according to the number

of categories for which the percent is

30%, the rankingwould be slightly altered to ZDR , T, KDP , hv ; in thisranking the variable with the smallest number of cate-gories is ranked highest because it fails to classify thesmallest number of categories. (The other variables failto classify more categories.) Ranking according to thepercentage for all classes (column 12) is ZDR , T, KDP ,hv .

It is significant that Zh , T pair is ranked second, al-though the multiplier for its weighting function is 0.4

(Table 4); only the multiplier Ahv has a smaller weight

of 0.3. This strong influence of temperature is partlydue to its independence of the radar variables (whichinherently are somewhat related). Furthermore, the tem-perature information influences a large number of dataabove the melting layer and in weak reflectivity regionswhere the classification is often ambiguous. These fac-tors and the strong effect of Zh (in the horizontal di-rection) are likely the cause for such a high importanceof the Zh, T pair.

Even though the Zh, KDP pair has a 0.8 weight mul-tiplier, for classification it is of secondary importance,similar to the Zh, hv pair. This is because for the majorityof hydrometeors, the boundaries in the Zh, KDP spaceoverwhelmingly overlap. Further in this case, there isa large region of KDP close to 0, which is ambiguous.But the specific differential phase offers advantages forrainfall measurement (Zrnic and Ryzhkov 1996), whichare not included in our ranking.

Further examination of the table reveals features indata that are a direct consequence of the classificationscheme, like the large drop category is detected exclu-sively with the Zh, ZDR pair. Dry snow, wet snow, andvertically oriented ice crystals are not at all classifiedby this pair. Vertically oriented ice crystals are exclu-sively detected with the Zh , KDP pair, but in this partic-ular case, KDP misses large drops and horizontally ori-ented crystals.

Another aspect of the scheme and the variables in-fluence can be gleaned by normalizing with respect tothe number of points obtained if a particular pair (P) orlack thereof (i.e., the rest R of the pairs) is used in theclassification. For that reason, we present Table 6. Thevalues in Table 6 correspond to the categories that arewrongly classified (analogous to false alarm) by the useof the pair. That is for each category, the measures arenormalized to the total number of points classified into

that category. For example, 71% of the data are erro-neously classified as light rain out of all data classifiedas LR from the Zh, ZDR pair; these are mostly in theanvil (Fig. 5a). The missing entries indicate that therewere no such categories identified by the pair [i.e., thecorresponding (P) is 0]. This lack of identification isa deficiency routed in the fact that the particular hy-drometeor signature in the polarimetric pair is week ornonexistent. From Table 6, it becomes immediately ap-parent what pairs misclassify which categories. So in

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TABLE 6. Percent of wrongly classified data (per category) P P A/(P) using a pair of variables out of all those classified usingthe same pair; Oklahoma storm.

With


LR MR HR LD R/H GSH HA DS WS ICH ICV Tot 70% 30%

ZDRKDP

hvT

71597523

243

7240

49325466

6

2566526

143328

318

6

134344

9398

84100

33

30417132

2230

6204

TABLE 7. Relative rank of the variables; Oklahoma storm.

Summaries from Tables 5, 6,and B1 to B5

Rank in order fromleft to right

5B1B2B3B46B5

(P A)/(A)(R A)/(A)(R P A)/(A)(P A R P A)/(A)(R A R P A)/(A)(P P A)/(P)(R R A)/(R)

ZDR, T, KDP, hvT, ZDR, KDP, hv

ZDR, T, KDP, hvT, Z , K , hv* *DR DP

ZDR, T, KDP, hvZDR, T, KDP, hvT, ZDR, KDP, hv

* ZDR and KDP are ranked the same.

addition to the Zh, ZDR pair, significant misclassificationof LR is caused by the Zh , KDP pair and also by the Zh,hv pair. Substantial mis-classifiers of other categoriesare Zh, KDP for R/H, WS, and ICH; and Zh, hv for LR,MR, R/H, and WS. Use of combined variables elimi-nates these misclassifications. Nonetheless, we have noindependent confirmation that the combined use of allthe variables produces a correct field of hydrometeors.Hence as stated earlier, the values in this and other tablesare only meant for relative comparisons. As far as the

number of categories that can be identified (that is, min-imum of missing entries), the ranking would be KDP ,ZDR , T, hv . The total percentages imply the followingranking: ZDR , T, KDP , hv . Other aspects of merits ofdifferent polarimetric variables can be seen in TablesB1 to B6 in appendix B. This is where the ranking ofvariables is justified and explained. The summary of therankings according to the columns labeled total (Table7) indicates that the Zh, ZDR pair (note that Zh is alwaysused) is overall most effective in the classificationscheme. The strong importance of temperature, in spiteof its relatively low weight (0.4 in Table 4), suggeststhat ambiguities in polarimetric signatures and statisticaluncertainty might be significant spoilers. It remains to

be seen if the addition of spatial filters and quantitativeuse of weighting functions can reduce the importanceof temperature. (This is pertinent for cases where T isnot available.) As expected, because of the 0.3 multi-plier, the hv contributes least to our current classificationscheme.

b. Ordinary storm observed with the S-Pol radar

During August and September 1998, the S-Pol radarwas located near Melbourne, Florida, to support the Tex-

as-Florida Under flying experiment (TEFLUN). Be-cause the S-Pol radar measures LDR and produces betterquality hv than the Cimarron, this set allows an aug-mented analysis and a more extensive comparison ofthe utility of the various variables. Also, comparison oftwo different storm types adds value to the analysis.

1) VISUAL ANALYSIS OF CLASSIFIED FIELDS

The fields of the polarimetric variables (Fig. 7) in-

dicate the storm is well developed with peak reflectiv-ities of about 55 dBZ below the melting layer. The tran-sition from ice to rain is seen in the ZDR as an abruptincrease between 3.5 and 4 km; it is also apparent inthe LDR field as a sharp decrease to less than 26 dB.The bright band in the hv is well defined and discernablein few places even within the storm core. The height ofthe minimum of the bright band was used to shift downby 1.1 km the temperature profile of the environmentalsounding (0C isotherm from 4.7 to 3.6 km). Both ZDR ,and KDP have visible columns that coincide, and KDPindicates heavy rain (100 mm h1 ) between 20 and23 km from the radar. Note the LDR cap (Jameson et al.1996; Hubbert et al. 1998) at a range of 20 km that

coincides with the top of the ZDR column. It indicatesfreezing of the supercooled drops lifted by the updraft.Adjacent to it (at farther range) is a vertical band of LDRminima that suggest the presence of graupel.

Classification from the whole suite of variables andfrom single pairs produces the results in Fig. 8. Graupel/small hail is located in the frozen region of the threedistinct cells (Fig. 8a). Dry snow fills most of the restof the cloud above the melting layer, and at the top ofthe cloud, some horizontally and even vertically ori-ented ice crystal are indicated. The sporadic presenceof vertically oriented crystals suggests that these arelikely artifacts. Although the horizontally oriented crys-tals are expected at cloud tops, the detection hereincould be fortuitous; this is because the crystals alsoappear at the bottom of the anvil in the region of weakreflectivity where they do not belong. Heavy rain andR/H mixture are interleaved below the main core, andthere is a small patch of hail in the core just above themelting zone. Noteworthy is the presence of snow inthe bright band, and a sliver below it is rain composedof large drops.

Examination of the ZDR field (Fig. 7b) indicates its

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FIG. 7. Vertical cross section of the fields of (a) reflectivity factor, (b) differential reflectivity, (c) correlation coefficient, (d) specificdifferential phase, (e) temperature, and (f) linear depolarization ratio. Range from the radar is in kilometers, and the grid cell size is 10 5 km. Data were obtained on 14 Aug 1998, in Florida with the S-Pol radar.

strong influence on the moderate, heavy, and large droprain (Fig. 8b). The wet snow is correctly located, andits chief identifier is the hv (Fig. 8f). Hydrometeorswithin the major cell (1727 km from the radar) arealmost equally well identified with the ZDR , Zh pair aswith the KDP , Zh pair (Fig. 8c), except the field obtainedfrom the latter one is noisier and has a larger area ofheavy rain. The phase of precipitation in the two weak

cells is correctly separated with the ZDR , Zh pair but isnot separable with the KDP , Zh pair. Note that the ZDR ,Zh pair fails to discriminate between light rain and drysnow in a large region above the freezing level; neitherdoes it detect vertically or horizontally oriented ice crys-tals. Clearly KDP , Zh identifies the horizontally and ver-tically oriented ice crystals. Note the area of verticalcrystals just above the cell at 40 km (Fig. 8c). Althoughin the composite classification (Fig. 8a) this area is ab-sent, it might have been wrongly eliminated; similar

signatures above growing storms have been previouslynoted and attributed to aligned crystals (Zrnic and Ryzh-kov 1999; Caylor and Chandrasekar 1996).

Identification based on the T, Zh pair is too smooth,generally credible, but lacks details of wet snow or rain/hail mixture. We stress again that in this particular case,the minimum of hv was used to place the zero degreeisotherm at a correct altitude. If the LDR , Zh pair is the

only discriminant, the field of hydrometeors showsstructure, but with the exception of some light and mod-erate rain below the melting layer and some snow above,the types are mostly wrong. The field produced by thehv , Zh is surprisingly smooth (Fig. 8f). The strength ofthis pair is in identifying the wet snow and moderateto heavy rain below the melting layer. As expected, itis not possible to discriminate between rain and iceforms above the melting layer.

By examining the effects of omission of variables

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FIG. 8. Vertical cross sections of classified hydrometeors for the data in Fig. 7. (a) All available variables were used to classify this field.(b) Only the pair Zh, ZDR was used. (c) Only the pair Zh , KDP was used. (d) Only the pair Zh, T was used. (e) Only the pair Zh, LDR was used.(f) Only the pair Zh , hv was used.

from the classification process, one can obtain anotherfeel for the relative merits among the variables (Fig. 9).Absence of ZDR caused misclassification in the rain re-gion where some LR and MR are assigned to GSH. Thiswould degrade rainfall measurement. Also in the regionof frozen hydrometeors, there are substantial sporadicareas of horizontally and vertically oriented ice crystals

(although the area above the two-week cells at 40 kmcould contain vertically oriented crystals). For most ofthe hydrometeor categories, the absence of KDP has littleor no effect (Fig. 9c), except in the core of the strongestcell; there, below the melting layer, GSH occupies largerarea, the one touching the ground looks suspicious. Oth-erwise the fields are smoother and, thus, more appealingthan in Fig. 9a! Perhaps KDP should be used only inregions where its signatures are strong (moderate orlarger rain, rain/hail mixture, etc.). It is very satisfying

that the absence of T does not change the basic patternsof the classified fields (Fig. 9d). As expected, the fieldlooks noisier; sporadic dry snow appears below themelting layer, and speckles of light rain are seen in theregion of snow. The absence of either LDR or hv has asimilar effect. Minor differences are in the depth ofregions with oriented crystals at the top (larger in the

absence of LDR ) and in the area of rain/hail mixture(slightly larger in the absence of hv ).The presented images indicate the significance of Zh,

ZDR in convective cores, the importance of hv for wetsnow, and the temperature for resolving ambiguitiesabove and below the melting zone. It is significant thatthe absence of temperature information leaves generallyconsistent fields. Nonetheless, LDR or T are needed todiscriminate between dry snow and light rain, as canbe seen in Fig. 10. Absence of LDR and T (Fig. 10a)

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FIG. 9. Same as in Fig. 8 except a specific pair has not been applied to the classification scheme, but other pairs each of which includesZh have been applied. (a) All available variables were used to classify this field. (b) The pair Zh, ZDR has not been used. (c) The pair Zh ,KDP, has not been used. (d) The pair Zh , T has not been used. (e) The pair Zh , LDR has not been used. (f) The pair Zh, hv has not been used.

produces a light rain throughout most of the upper partof the storm where the ice phase should dominate. In-clusion of LDR at the expense of hv and T (Fig. 10b)restores the snow region above the melting layer. Thisfinding is significant for applications to winter stormsin which the spatial distribution of temperature is notavailable, and hence, LDR might be the most importantdiscriminator between rain and snow.

In the absence of temperature, hydrometeor classes

appear noisier but, nonetheless, have coherent structureand are at the expected location. This attests to thestrength of the polarimetric variables. Thus, we believethat in similar cases, additional processing with spatialfilters would reduce the incoherent speckles.

2) RELATIVE IMPORTANCE OF THE VARIABLES

Some 14 812 data values were classified (between 10and 50 km from the radar), and the smallest number

in a class was 20 for hail; the next smallest was 220for wet snow. Because of insufficient sample size, wewill refrain from quantitative interpretation of data clas-sified as hail.

The percentage of hydrometeors classified using apair of variables that agree with those obtained from thefull set is tabulated in Table 8. The ranking accordingto column 13 would be first ZDR and T, second hv , andthird L

DR

and KDP

, but according to column 14, the rank-ing would be ZDR and T, KDP , hv , LDR . For all classescombined, the temperature leads and is followed by ZDR ,KDP , LDR , and hv . The 25% lead of T over ZDR is some-what unexpected considering that in the Oklahomastorm, temperature was a close second (Table 5). Butin the Florida event, a large portion of frozen precipi-tation has weak reflectivity whereby classification is of-ten ambiguous (Fig. 9d is an example where the T isexcluded), unlike the Oklahoma storm, which has highly

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FIG. 10. Same as in Fig. 8 except two variables have not beenapplied to the classification scheme. (a) The missing variables are

LDR and T. (b) The missing variables are hv and T.

TABLE 8. Percent of correctly classified hydrometeors (P A)/(A) using the pair alone; Florida storm.

With



ZDRKDP

LDRhv

T

9459699699

9654749998

8174259999

850

5200

942176

10

946420

074

83000

94

181929

085

010

098

0

249

085

8

084

000

5038332575

72257

45764

reflecting upper part (see how few obviously wrongclasses are in the frozen part in Fig. 6d). Perhaps thereason is that the 0C isotherm is set to the correctheight, which is constant for the Florida storm.

The equivalents to false alarms, that is, percentagesof data wrongly classified by the pair, are in Table 9.

From this table and according to the totals, the order ofvariables is T, ZDR , KDP , LDR , and hv . It is noteworthythat the three less useful variables KDP , LDR , and hveach has a large false classification for a specific hy-drometeor type. Here, KDP misclassifies 100% of hail,LDR mis-classifies 97% of the large drops, and hv mis-classifies 85% of the large drop rain.

Relative merits of other variables are discussed andtabulated in appendix C, and the rank of variables ac-cording to the metrics in these tables is listed in Table10. Comparison of the rows of this table with the cor-responding rows of Table 7 brings out the followingcurious fact. The first variable in Table 7 it always sec-

ond in Table 10 and vice versa. Moreover, according toall the criteria in Table 10, the hv is ranked consistentlylast. Because of immense practical implications of asimultaneous scheme proposed for the WSR-88D (Dov-iak et al. 2000), we further focus on the relative meritsof LDR versus hv .

Current plans are to simultaneously transmit and re-

ceive the Hand Vpolarizations, and this precludes mea-surement of LDR (unless it is done on alternate scans).At least in this Florida storm, LDR does not seem to addsignificantly more to the classification, as can be seenby the fact that omission of either LDR or hv (with theuse of temperature) has almost the same effect (95%and 96% agreement in column 12 of Table C1). Thiswe have verified in an alternate manner by comparingthe percentage of agreement for classification, whichomits LDR with the one that omits hv (93% of classifieddata agree). A more important question (to which wehave no answer) asks, Can the addition of LDR be theonly way to detect a significant precipitation type (likeicing conditions)?

We do have, however, an objective way to determinethe potential utility ofLDR in special meteorological con-ditions such as transition between rain and snow in thehorizontal direction. Because surface temperature mea-surements are sparse, the horizontal T field might notbe available, in which case, the polarimetric variablesmust stand on their own. Figure 10 suggests that in theabsence of temperature, LDR should be a much betterdiscriminator of dry snow than hv . This assertion isquantified in Table 11, where the percent of correctlyclassified hydrometeors is presented for the case withoutT and LDR , as well as for the case without T and hv . IfLDR is lacking, only 36% of dry snow is correctlyidentified. In the absence of

hv

(but presence of LDR

)88% of the dry snow is still correctly classified. Al-though these results are for vertical cross sections, theyapply equally well to horizontal fields of the classifi-cation variables.

4. Discussion

Both the specifics of our classification scheme andthe particular dataset to which it is applied bear on thededuced merits of the variables. Presently, we have notyet evolved the boundaries to the point of diminishedreturn, nor do we have optimum weighting functions.

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TABLE 9. Percent of wrongly classified data (per category) (P P A)/(P) using a pair of variables out of all those classifiedusing the same pair; Florida storm.

With



ZDRKDP

LDR

hv

T

8079498525

5141863

9

655196345

3397

32735060

16395413

0100

76

498

6

6357

35212029

93

4960647514

14111

53314

TABLE 10. Relative rank of the variables; Florida storm.

Summaries from Tables8, 9, 10 and C1 to C5

Rank in order fromleft to right

8C1C2C3C49C5

(P A)/(A)(R A)/(A)(R P A)/(A)(P A R P A)/(A)(R A R P A)/(A)(P P A)/(P)(R R A)/(R)

T, ZDR, KDP, LDR, hvZDR, T, KDP, LDR, hvT, ZDR, KDP, LDR, hv

ZDR, T, KDP, L , * *DR hvT, ZDR, KDP, LDR, hvT, ZDR, KDP, LDR, hv

ZDR, T, KDP, LDR, hv

* LDR and hv are, for this row, ranked the same.

Therefore, we cannot isolate the two effects. Nonethe-less, comparison of the relative performance of classi-fication for the two storms can, in some instances, pointout to what extent data affect the classifier.

Although the two storms are convective, they havedistinct characteristics that might induce substantiallydifferent responses of the classifier. Note that the per-centages of identified hydrometeor categories out of thetotal for the two storms differ by a factor of 2 in five

categories (Table 12); these are R/H, HA, DS, ICH, andICV. The contrast in hail is good and expected consid-ering that the Oklahoma storm was a cell in a squallline, and the Florida storm was an airmass storm. Thisis also the reason that the Florida storm has substantiallymore dry snow; the deficit of the Oklahoma storm indry snow is made up by an increase in graupel-smallhail.

It is gratifying that all four rain categories are com-parable (Table 12), this implies consistency in detectingrain. Similar conclusions apply to the wet snow. As faras the rain and wet snow are concerned, the algorithmis not sensitive to the type of convective storm or theradar.

The algorithms relative performance on theOklahoma and Florida data is similar. Comparison ofentries in Tables 5, 6, B16 with corresponding Tables8, 9, C16 indicates that on the average, the differencebetween likewise entries in the tables exceeds 30% inonly 15% of the total number of entries. Thus, in thesecases, the relative merits of the polarimetric variablesare invariant to differences in the type of storm andenvironment, the extra LDR available on the S-Pol radar,and the quality ofhv data.

Comparison of Tables 7 and 10 reveals that for all

rows except the seventh the leading two variables (eitherZDR or T) are opposite. It is significant that the LDR andhv rank similarly behind the rest of the variables, andthe LDR is ahead of hv . For several reasons, the polar-imetric scheme contemplated for upgrades of the WSR-88D is one with simultaneous transmission and recep-tion of H and V waves (Doviak et al. 2000). In thatmode the LDR is not available, but if needed, it couldbe obtained in alternate volume scans that transmit H

and receive H and V. Our analysis supports the notionthat LDR might not be essential for precipitation iden-tification in convective storms. But where temperatureis not available, such as when it changes through zeroon the ground, like in winter storms, LDR might offeradvantages not found in the other variables. This wasdeduced by excluding the temperature and comparingclassifications in the presence and absence of LDR andhv .

A very important aspect for future examination isranking classification according to the value associatedwith the knowledge of a specific hydrometeor type. Suchranking might not even be unique; rather, it would bea function of the utility in a given situation. The value

of detecting hail in convective storms is much higherthan detecting snow aloft. But in a snow storm, theprincipal utility would be to detect the freezing zoneand accurately measure the amounts. Pragmatic reasonssuggest that in a short run, tuning the algorithm for astorm type might result in a faster evolution towardbetter performance.

We realize that our analysis incorporates partly a cir-cular argument. That is, we have given weights (whichdepend on the confidence in the variables, Table 4) tothe variables, and the results of the analysis are generallyconsistent with these weights. Yet, specifics differ. Forexample, the Zh, ZDR , which both have a weight of one,come in as a strong first in most comparisons. But T,

which has a weight of 0.4, is a very close second (behindZDR ). Two reasons could explain its importance: one, Thas information independent of the polarimetric vari-ables, and two, it is paired with Z, which has very strongdiscriminatory power.

5. Conclusions

Polarimetric measurements from an Oklahoma squallline and a Florida airmass storm were automatically

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TABLE 11. Percent of hydrometeors correctly classified without T and either LDR or hv; Florida storm.

With-out


LR MR HR LD R/H GSH HA DS WS ICH ICV Tot 70%

LDRhv

7572

8685

9289

5171

7991

9597

7883

3688

9579

9745

8686

6385

911

TABLE 12. Percent of hydrometeors classified in various categories for the Oklahoma (OK) data and the Florida (FL) data.

LR MR HR LD RH GSH HA DS WS ICH ICV

OKFL

8.710.5

6.85.7

4.33.4

1.92.2

9.92.9

27.319.1

19.10.1

12.548.1

1.11.5

0.74.8

7.71.6

interpreted. The automatic interpretation is in the formof an algorithm that classifies hydrometeors. The prin-ciples behind the algorithm are so simple that a prereq-uisite for understanding is high school algebra. Becausethe equations are linear sums, it would seem that thereshould be no difficulty in analyzing and improving itsperformance. Yet this is far from the truth. It is themultidimensionality that obfuscates the progress here.The partitioning boundaries are many, and they overlap;furthermore, there are numerous combinations of valuesof the variables that can cause maxima in the confidencefactors. Therefore, the analysis is involved and the evo-

lution tedious. It will just take much time to develop afine version of the algorithm. At this early stage ofalgorithm development, in situ verification seems pre-mature; thus, we have opted to access its attributes byexamining self consistency of data, spatial continuity,and compliance with conceptual models.

Our first goal was to test sensitivity of the algorithmto the various polarimetric variables. This was donesubjectively by comparing the fields of hydrometeorsobtained using the full set of available polarimetric var-iables with a diminished set whereby some variableshave been left out. Comparisons reveal the following.The reflectivity factor and differential reflectivity com-bined have the strongest discriminating power. Inclusion

of the temperature profile helps eliminate a substantialnumber of spurious errors. Although the absence of tem-perature information degrades the scheme, it appearsthat the resultant fields are generally coherent and notfar off from the fields obtained by adding T to the suiteof polarimetric variables.

An objective way to test the sensitivity of the algo-rithm to variables and rank their utility was devised. Itinvolves definition of a measure (appendix A), whichturns out to be a number of data points classified intoa category in the presence or absence of variables. Ra-tios of various measures (similar to probabilities) definethe percentage of occurrence of a class. By comparingthese percentages for cases in which some variables are

excluded to those where all are included, a relative meritcan be assigned to the variables.

Acknowledgments. Partial funding for this researchwas provided by the National Science FoundationGrants ATM-9120009, ATM-9311911, EAR-9512145,and ATM-9617318, the National Severe Storms Labo-ratory, the Cooperative Institute for Mesoscale Meteo-rological Studies, the Graduate College of the Univer-sity of Oklahoma (Dr. E. C. Smith), and the FederalAviation Administration. Mike Schmidt and RichardWahkinney have maintained and calibrated the Cimar-ron radar, Joan OBannon drafted Figs. 2 and A1, where-as Chris Curtis produced Fig. 1, respectively. Finally aperceptive reviewer pointed out an inconsistency with

the weighting functions for temperature and promptedus to correct it.

APPENDIX A

Metrics for Quantitative Comparisons

Definitions of metrics for quantitative comparisons ofthe effects of various polarimetric variables on the out-come of the classification scheme are presented herein.

To aid the reader, we start with a conceptual diagram(Fig. A1) of the field of an identified class of hydro-meteors. One can think of it as a horizontal or verticalcross section in which only one class of hydrometeors

is shown. The set A corresponds to the data points (herefrom radar resolution volumes), which have been clas-sified as one hydrometeor type (e.g., hail) using all (A)the available variables; this set is a standard for com-parisons, and the corresponding classification will becalled correct. The set P corresponds to the samehydrometeor class (hail) except that the data have beenclassified using a single pair (P), and the set R corre-sponds to the same class (hail), but the data have beenclassified using the rest (R) of the variables (all exceptthe pair that was used to generate P). For the sake ofsimplicity in the sequel, the sets P, R, and A refer toany single hydrometeor type or to all the classified hy-drometeors. Contrast this to the cumbersome PLD (Zh ,

ZDR ), which could otherwise signify the set of largedrops classified using the pair Zh, ZDR . From the context

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FIG. A1. Sketch of fields of any one classified hydrometeor type.A (all) is obtained using all the available variables. P (pair) is obtainedusing one pair of variables of which the first variable is always Zh.R (rest) is obtained using all the variables except the second variableof the pair P.

TABLE A1. Metrics used for relative comparisons between variables.*

(P A)/(A) % of correctly classified hydrometeors using the pair alone(R A)/(A) % of correctly classified hydrometeors using the set without one variable(R P A)/(A) % of correctly classified hydrometeors for which use of a pair and absence

of a variable produces the same class

(P

A

R

P

A)/(A) % of c orre ctly cl as sifie d h ydrom ete ors tha t w ould be m is cla ss ifie d in theabsence of a variable(R A R P A)/(A) % of c orre ctly cl as sifie d h ydrom ete ors tha t w ould be m is se d in th e a bse nc e

of the remaining variables(P P A)/(P) % of wrongly classified hydrometeors using a pair of the variables out of

all those classified using the same pair(R R A)/(R) % of wrongly classified hydrometeors using the rest of the variables out of

all those classified using the rest of the variables(A R A P A R P A)/(A) % of hydrometeors that can be correctly classified only if all the variables

are used

* The intersection operation takes precedent over algebraic operations.

and in the tables, it should be clear to which hydro-meteor classes the shorthand notation refers.

Next, we prove that the partitions (i.e., subsets) inFig. A1 are the only ones possible. That is, for theclassification procedure based on Eqs. (2) and (3), agree-ment of the pair with the rest implies that the use of allthe variables will also agree. In other words, the seven

subsets including the null category in Fig. A1 are theonly ones possible.

Without loss of generality, assume that the pair is Zh,ZDR , and the classified category by the pair and by therest is the same, say snow(s). Thus, the weighting func-tion for the pair satisfies

W (Z , Z ) W(Z , Z ), j s.s h DR j h DR (A1)

Similarly, the sum of weights for the rest of variablessatisfies

A W (Z , Y) A W(Z , Y), (A2) i s h i i j h iY Yi i

j s, and the summation is over all the variables Yiexcept ZDR . Normalization by the Ai is omitted from(A2) as it has no bearing on the proof.

Now, multiply both sides of (A1) with AZDR and addthe right side of (A1) to the right side of (A2) and theleft side of (A1) to the left side of (A2). This operationdoes not change the inequality, neither does normali-zation by A i, which is actually used when all thevariables are present. This completes the proof.

The readers might recognize that the sets P, R, Abelong to a Borel field (e.g., Papoulis 1965) and so dothe various intersections and unions of these sets. Next,we discuss assignment of a measure to these sets, fromwhich some quantitative comparison of performancewill ensue. Briefly, a measure on a Borel field is an

assignment of a number (E) for every element E thatbelong to the field such that (E) 0. For our purpose,the measure will be the number of data points in aclassified category of hydrometers. (Each data point cor-responds to a single resolution volume.) That is, wecount the number of classified data points (in a specifichydrometeor category) for which use of all variables,

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TABLE B3. Percent of correctly classified hydrometeors (P A R P A)/(A) that would be misclassified in the absence ofthe variable.


LR MR HR LD R/H GSH HA DS WS ICH ICV Total

ZDRKDPhv

T

512

34

3819

258

6715

214

100000

43326

0

520

21

18202

300

40

0180

9000

098

00

1414

319

TABLE B2. Percent of correctly classified hydrometeors (R P A)/(A) for which the pair and its absence (i.e., the rest ofvariables) produce the same class.



ZDRKDPhv

T

91616865

39219242

144

8286

0000

60626426

8562

063

7822

076

517

024

0070

0000

0000

56372249

3022

6876

TABLE B1. Percent of correctly classified hydrometeors (R A)/(A) using one less variable; the variable not used is indicated tothe left of the table.

With-out



ZDR

KDPhv

T

95

999866

62

819842

33

859886

0

100100

71

96

677499

94

959679

82

989698

61

98100

34

36

189286

0

100100

39

100

0100

94

80

859577

5

811

7

2

201

use of the single pair, and use of the remaining variables(without the single pair) agree or disagree. Then, a suit-able combination and normalization of these measurescan reveal the relative importance of the variables. Thusin our notation, we define metrics as ratios of measures(completely analogous to probabilities); for example,

(P A)/(A),indicates the % of points (correctly classified) in a class(obtained with a specific pair), which agrees with thepoints obtained if all the variables are used. On the graph(Fig. A1b), this is the stapled (45) area divided withthe sum of the two stapled areas (depicted with 45and 45 lines), and the value thus computed is anal-ogous to a probability of detection. A quantity similarto a false alarm ratio is

(P P A)/(P);

it indicates the % of points in a class (obtained using aspecific pair), which does not contribute to the finalclassification (that uses all the variables). Its graphicaldepiction (Fig. A1b) is the ratio of the stapled (vertical)area to the sum of the stapled areas (vertical and 45).Seven meaningful metrics of this type are described inTable A1. A quick look at this table, at Fig. A1, andsimilar figures can help physical understanding and vi-sualization of comparisons between the relative values

of variables in the classification scheme. For example,the points for which use of a pair, use of the rest of thevariables, and use of all the variables agree are depictedin Fig. A1c (45 staples); on the same figure is the area(45 staples) corresponding to points (categories) thatcan be obtained only if all the variables are used.

APPENDIX B

Relative Comparison of Variables UtilityOklahoma Storm

Tables with various metrics for relative comparisonof the variables utility in the classification scheme arelisted herein. In tables with measures on P and subsetsof P, the second member of the relevant pair is listedin the vertical column defining the rows. (The first mem-ber of the pair is always the reflectivity factor Zh.) Thus,the variable is either part of the pair used exclusivelyfor classification, or it is the one that is excluded fromthe classification; from the table titles and appropriatelabel of the defining column, it should be clear whichone it is. The indicated class categories are as listed inthe text and the figures. The meaning of various mea-sures presented in the forthcoming tables is explainedin appendix A.

Similar to Table 4, Table B1 presents percentages of

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TABLE B4. Percent of correctly classified hydrometeors (R A R P A)/(A) that would be missed in the absence of theremaining variables.



ZDRKDP

hvT

43830

2

2360

60

197417

0

0100100

71

3659

74

8339617

5769622

5681

10011

36188586

0100100

39

1000

10094

24487327

TABLE B5. Percent of wrongly classified data (R R A)/(R) using the rest of the variables out of all those classified using therest of the variables.

With-out



ZDRKDPhv

T

1930

60

1118

18

394637

0

100403

34203

25836

2401

838

120

20

5792

17

081

18

07

2015

524

12

78

108

TABLE B6. Percent of hydrometeors (A P A R A P A R)/(A) that can be correctly classified only if all thevariables are used.

With



ZDRKDPhv

T

0000

0000

0000

000

29

0001

1240

0340

3620

26

6482

014

9100

61

0206

6225

classified precipitation, except it is for the case wherebya variable has been excluded. Large percentages indicatethat the variable is relatively insignificant; that is, with-out it classification is still successful; small numbersindicate the opposite. Ranking of the variables accord-ing to the number of classes for which the percent is70% is ZDR , T, KDP , hv ; smaller numbers in column13 mean increased importance of the excluded variablebecause less classes are correctly identified by the restof the variables. Ranking of the variables according tothe number of classes for which the percent is 30%is ZDR , KDP , T, hv , and according to the percentage inthe total (column 13), the ranking would be T, ZDR , KDP ,hv .

To determine how one pair and the rest of the vari-ables contribute to the various categories, we present inTable B2 the percentages of correctly classified data for

which the pair and the absence of the variables producesthe same class (see Table A1 for definition). The tablecan loosely be interpreted as the information carried bythe pair that is also present in the rest of the pairs. Thismeans that the pair is worth as much as the rest; hence,large numbers imply higher ranking of the pair. Thusin this data, a good portion of light rain, graupel/smallhail, and hail would be classified the same with or with-out the Zh, ZDR pair; that is for these categories, this pairis as good as the rest of the pairs. The information about

heavy rain (86% of data in Table B2) and hail (76%)carried by the pair Zh , T is also very high. The Zh, hvpair is almost sufficient for LR, MR, and HR classifi-cation. This occasional redundancy of a pair is partlycaused by the common presence of Zh in all pairs.

Small percentages in B2 indicate that the main con-tributor is either the variable or the rest but not both.According to the total, the variables (understood to bealways paired with Zh ) would rank as ZDR , T, KDP , hv .

Counting the data points in sets described by rows 4and 5 of Table A1 produces Tables B3 and B4 (forclarity, see also Fig. A1). Thus, in B3 is the percentageof data that is missed in the absence of a variable. InB4 is the percentage of data that is missed in the absenceof the rest of the variables. According to Table B3, HRand LD are primarily classified by the Zh, ZDR pair, thesignificant contributor to MR is the pair Zh , T, and ver-

tically oriented ice crystals are due to Zh, KDP . In theoverall hydrometeor categories, the percent of contri-bution by any single pair is 19% or less, and accordingto the totals, the ranking is T, ZDR , and KDP second, andhv last.

Table B4 is almost, but not quite complementary toB3, and from column 12, the rank of variables is ZDR ,T, KDP , hv .

Table B5 presents somewhat complementary infor-mation to Table 6. It indicates the percent of mis-clas-

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TABLE C3. Percent of correctly classified hydrometeors (P A R P A)/(A) that would be mis-classified in the absence ofthe variable.



ZDRKDP

LDRhv

T

32063

19

382314

3422

439

660

2500

494

2000

64202

83000

17

7010

10

030

180

026

051

0

084

000

145338

TABLE C2. Percent of correctly classified hydrometeors (R P A)/(A) for which the pair and its absence (i.e., the rest ofvariables) produce the same category.



ZDRKDP

LDRhv

T

6358639280

5853719894

4752209591

190

2700

441756

10

886118

073

0000

78

111928

076

070

810

223

034

8

00000

3533302167

10146

67866

TABLE C1. Percent of correctly classified hydrometeors (R A)/(A) using one less variable; the variable not used is indicated tothe left of the table.

Without



ZDRKDP

LDRhv

T

67100

9397

81

61989799

96

66789697

91

33997599

75

518280

100

89

91959798

98

16100

8383

83

649896

100

88

62888882

100

9572

10048

97

970

100100

85

70949596

90

3101110

11

1100

0

sified data for cases whereby a specific variable is ex-cluded from the scheme. Small percentages indicate theexcluded variable is not very relevant for a classifiedcategory (i.e., the lack of it does not cause significantmis-classification). Large values signify substantial mis-classification due to the missing variable. Hence, thiscriteria would rank the variables as T, ZDR , KDP , hv .

Note again the ZDR and Tlead because the first is neededto identify LD and the second to identify WS. The miss-ing entries are where (R) 0; hence, the omittedvariables prevent classification in the corresponding cat-egory.

Finally, Table B6 presents the percentage of correctlyidentified hydrometeors for which all the variables areneeded. These percentages are relative with respect tothe pair and its absence. The mis-classified data is be-cause the pair assigns it one class; the rest assigns itanother class, but use of all the variables assigns it aclass different from either of these two. That is the com-bined use of the pair, and the rest overrides either one.For example, consider dry snow (DS) and the pair Zh ,ZDR ; if this pair and the rest were used separately, then36% of dry snow would be missed. Note the high per-cent of wet snow obtained by combining Zh , KDP , andthe rest which could not be obtained by either one. As

expected the, categories where percentages are rela-tively high are those for which there is significant over-lap in the boundaries (i.e., DS, WS, ICH).

APPENDIX C

Relative Comparison of Variables UtilityFlorida Storm

In Table C1 are the percentages of classified hydro-meteors that agree if one variable is excluded from theset with those obtained from all the variables. Largepercentages go with relatively unimportant variables.Thus, the leading variable according to the number ofcategories that can be classified (column 13) would beZDR ; the rest are of about equal importance. This sameranking ensues if the total % of the field is a benchmark(column 12).

The information carried by a pair of variables that isalso present in the rest of the variables is summarizedin Table C2. Here, the large percentages imply that thepair has relatively high importance. A surprisinglystrong influence ofTis seen in both the total percentage(column 12) and the number of categories (column 13).This is perhaps due to the generally weaker polarimetric

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TABLE C4. Percent of correctly classified hydrometeors (R A R P A)/(A) that would be missed in the absence of theremaining variables.



ZDRKDP

LDR

hv

T

44130

40

24626

12

192675

11

1499489975

665249889

334799826

5100

8383

6

537968

10013

628188

2100

9349

1001489

970

100100

85

3560647523

TABLE C5. Percent of wrongly classified data (R R A)/(R) using the rest of the variables out of all those classified using therest of the variables.

Without


LR MR HR LD R/H GSH HA DS WS ICH ICV Total 70% 30%

ZDRKDP

LDRhv

T

9251

30

34101

485

2200

824

3060

4588

139

23900

15

022

006

16013

175

193116

911

90

17

9154

025

30651

10

20000

710101111

TABLE C6. Percent of hydrometeors (A P A R A P A R)/(A) that can be correctly classified only if all thevariables are used.

With



ZDRKDP

LDRhv

T

20100

10000

00000

1101

25

014

00

11

32220

110

1717

0

291302

389

1201

51013

316

00

15

162202

signatures in the Florida storm compared to theOklahoma one.

The strength of a pair for classification can be gaugedby the percent of data that would be missed in the ab-sence of it (Table C3). The dominant pair for hail de-tection is Zh, ZDR ; in its absence, 83% of the hail wouldnot be detected. (The importance of this miss is dimin-ished by the fact that sample size for hail is very small.)The order of importance according to the total per-centage is ZDR , T, KDP , and the last spot is shared byLDR and hv .

The importance of T is seen in Table C4 whereby thepercent of correctly classified data in the absence of avariable is indicated. Small percentages mean that therest of the variables contribute relatively little to the

class. Accordingly, we rank in order of importance T,ZDR , KDP , LDR , and hv .Percentages of wrongly classified hydrometeors due

to the absence of one variable are in Table C5. Fromthe total percent of misclassified data (Table C5), wenote that the absence of ZDR has the largest effect onthe total: 30% of the misses (column 12). This is fol-lowed by T, then LDR , KDP , and hv .

The last Table, C6, indicates the percent of classifiedhydrometeors for which combination of the pair and the

rest is needed to accomplish classification. The resultsare similar to the ones in Table B6. There are few dif-ferences such as in wet snow for (Zh, KDP ) and hori-zontally oriented crystals (Zh, ZDR ), which have a muchlower percentage for the Florida storm.

REFERENCES

Balakrishnan, N., and D. S. Zrnic, 1990a: Estimation of rain and hailrates in mixed phase precipitation. J. Atmos. Sci., 47, 565583.

, and , 1990b: Use of polarization to characterize precipi-tation and discriminate large hail. J. Atmos. Sci., 47, 15251540.

Bringi, V. N., V. Chandrasekar, N. Balakrishnan, and D. S. Zrnic,1990: An examination of propagation effects in rainfall on radarmeasurements at microwave frequencies. J. Atmos. OceanicTechnol., 7, 829840.

Carey, L. D., and S. A. Rutledge, 1996: A multiparameter radar casestudy of the microphysical an kinematic evolution of a lightningproducing storm. Meteor. Atmos. Phys., 59, 3366.

Caylor, I. J., and V. Chandrasekar, 1996: Time-varying ice crystalorientation in thunderstorms observed with multiparameterradar.

IEEE Trans. Geosci. Remote Sens., 34, 847858.Cornman, L. B., R. B. Goodtich, C. S. Morse, and W. L. Ecklund,

1998: A Fuzzy logic method for improved moment estimationfrom Doppler spectra. J. Atmos. Oceanic Technol., 15, 12871305.

Doviak, R. J., and D. S. Zrnic, 1993: Doppler Radar and WeatherObservations. Academic Pre

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