## Abstract

A new fuzzy logic hydrometeor classification algorithm is proposed that takes into account data-based membership functions, measurement conditions, and three-dimensional temperature information provided by a high-resolution nonhydrostatic numerical weather prediction model [the Application of Research to Operations at Mesoscale model (AROME)]. The formulation of the algorithm is unique for X-, C-, and S-band radars and employs wavelength-adapted bivariate membership functions for (*Z _{H}*,

*Z*

_{DR}), (

*Z*,

_{H}*K*

_{DP}), and (

*Z*,

_{H}*ρ*

_{HV}) that were established by using real data collected by the French polarimetric radars and T-matrix simulations. The distortion of membership functions caused by deteriorating measurement conditions (e.g., precipitation-induced attenuation, signal-to-clutter ratio, signal-to-noise ratio, partial beam blocking, and distance) is documented empirically and subsequently parameterized in the algorithm. The result is an increase in the amount of overlapping between the membership functions of the different hydrometeor types. The relative difference between the probability function values of the first and second choice of the hydrometeor classification algorithm is analyzed as a measure of the quality of identification. Semiobjective scores are calculated using an expert-built validation dataset to assess the respective improvements brought by using “richer” temperature information and by using more realistic membership functions. These scores show a significant improvement in the detection of wet snow.

## 1. Introduction

The ability to perform hydrometeor classification (HC) in precipitating systems at high space–time resolution (5 min–1 km^{2}) is one of the main benefits brought by polarimetric radars. Polarimetric radar measurements of precipitation vary with hydrometeor properties such as shape, size, orientation, phase state, and fall orientation; see Straka et al. (2000).

Many approaches to HC have been proposed in the past. These approaches differ by the number and type of hydrometeors; the variables used in the classification algorithm; the nature of the supplementary information used; the radar wavelength; the formulation of the algorithm such as decision trees, Bayesian rule, or fuzzy logic with additive or multiplicative terms; whether the membership functions (MF) are obtained from real data or from simulations; and/or the subjective or objective validation method by using external data. Table 1 presents a bibliographical survey of some previous works on HC that outlines the above-mentioned variability in the approaches.

The literature review summarized in Table 1 leads to the following general remarks and questions:

As membership functions are intended to be applied to real data collected by operational scanning radars, it is important to derive them as much as possible directly from real radar data. For example, applying disdrometer-based MF to real radar data may not be appropriate because of differences in the spatial representativeness (e.g., specific differential phase

*K*_{DP}estimated over several gates) and because the unavoidable noise and bias on radar variables are not reflected in disdrometer-derived MF.The impact of adverse measurement conditions such as attenuation, signal-to-clutter ratio (SCR), signal-to-noise ratio (SNR), partial beam blocking (PBB), and distance on the MF (broadening) is rarely taken into account in the HC algorithm. The SCR represents the ratio between an actual and a basic reflectivity value for a given elevation. The basic reflectivity values are calculated using a case of clear air with clutter signal.

Validation often relies on a very limited number of cases, often involving a human expert.

Little is usually said about the quality, reliability, and spatial and temporal representativeness of the temperature information that is used in combination with radar variables to perform HC.

Temperature is an essential variable in HC for two reasons. First, some hydrometeor types can obviously not exist at certain temperatures (e.g., rain at −10°C or snow at +10°C). Second, variables collected with operational scanning radars cannot, alone, discriminate between some hydrometeor types (e.g., dry snow and light rain, whose radar signatures do not differ significantly given the inherent noise and biases on measured radar variables).

More complex information can also be used in HC: Schuur et al. (2012) combine a thermodynamic model (temperature, dewpoint, and pressure) from the Rapid Update Cycle model (RUC), which promotes a background precipitation classification type with a decision-tree approach. Kouketsu and Uyeda (2010) use temperature information along with relative humidity data. Note that the RUC has a horizontal grid spacing of 13 km and a vertical grid distance of 25 hPa between 1000 and 100 hPa. For more information see Benjamin (1989).

This paper introduces a new fuzzy logic HC scheme. The aim is to design an algorithm that is 1) simple, 2) realistic with respect to the inherent noise and biases associated with variables collected by operational scanning radars, and 3) more efficient in terms of discrimination among rain, wet snow, and solid precipitations. The new HC algorithm, with fewer parameters and without weights, is based on empirically derived MFs, takes into account actual measurement, and uses 3D temperature information provided by the French operational high-resolution nonhydrostatic numerical weather prediction (NWP) model [the Application of Research to Operations at Mesoscale model (AROME; Seity et al. 2011)]. Note that AROME has a horizontal latitude–longitude grid with 0.025° resolution (~2.5 km at 45°N), a vertical grid distance of 15 levels between 1000 and 100 hPa, and a temporal resolution of 1 h.

The paper is structured as follows: Section 2 provides an overview of the formulation of the fuzzy logic approach. Section 3 introduces and discusses the MFs and their dependency on actual measurement conditions. Section 4 presents a qualitative illustration, an objective evaluation of the performance and the analysis of the second choice of the algorithm, and the way temperature is included in the algorithm. Conclusions are summarized in section 5.

## 2. Formulation of the fuzzy logic approach

The fuzzy logic approach is a nonlinear method that is considered to be a good approach for hydrometeor classification (Bringi and Chandrasekar 2001; Zrnić et al. 2001). The input data vectors are reflectivity *Z _{H}*, differential reflectivity

*Z*

_{DR}, specific differential phase

*K*

_{DP}, copolar correlation coefficient

*ρ*

_{HV}, brightband (BB) location, and temperature. The output data are the dominant precipitation type for each pixel.

Polarimetric data used for classification in all wavelengths have been preanalyzed following these processing steps (Figueras i Ventura et al. 2012): 1) calibration of *Z*_{DR}, 2) detection of nonmeteorological echoes such as clear air, birds, insects, sea clutter, and ground clutter or precipitation type using a fuzzy logic scheme (see Gourley et al. 2007a), 3) identification of the bright band, 4) offset correction and filtering of the differential phase Φ_{DP}, 5) estimation of *K*_{DP} on the basis of 25 range gates and linear regression over the filtered Φ_{DP} curve, 6) correction of attenuation and differential attenuation using simple linear relationships [path-integrated attenuation correction (PIA) = *γ _{H}*Φ

_{DP}and PIA =

*γ*

_{DP}Φ

_{DP}]—the coefficients

*γ*

_{DP}and

*γ*at X band are

_{H}*γ*

_{DP}= 0.04 dB (°)

^{−1}and

*γ*= 0.28 dB (°)

_{H}^{−1}(Tabary et al. 2008). For C band,

*γ*

_{DP}= 0.03 dB (°)

^{−1}and

*γ*= 0.08 dB (°)

_{H}^{−1}(Gourley et al. 2007b). For S band,

*γ*

_{DP}= 0.004 dB (°)

^{−1}and

*γ*= 0.04 dB (°)

_{H}^{−1}(Bringi and Chandrasekar 2001).

The different hydrometeor types are rain, wet snow, dry snow, ice crystals, and hail. The rain type includes light, medium, and heavy rain and large drops. Wet snow type presents the precipitations that are in the BB. Dry snow and ice types present the solid precipitation above the BB where we differentiate them by the reflectivity and the temperature. Hail type presents the solid precipitation that has a large *Z _{H}* (>45 dB

*Z*). Adding more hydrometeor types at this stage would not be realistically compatible with the known discriminating power of the polarimetric variables collected operationally. Note that there are nonmeteorological categories such as clear air, birds, insects, sea clutter, and ground clutter that are classified before the execution of the HC algorithm and that the “simple polar” category includes all pixels that have an SNR of less than 15 dB.

The method can be summarized as follows: for each polar pixel (240 m × 0.5°), the actual measurement conditions (distance, SNR, SCR, and PBB) are taken into account to generate modified bivariate MFs for (*Z _{H}*,

*Z*

_{DR}), (

*Z*,

_{H}*K*

_{DP}), and (

*Z*,

_{H}*ρ*

_{HV}). The resulting MF values are calculated and added for each hydrometeor. The result is then multiplied by a

*Z*-dependent MF, a temperature-dependent MF, and a BB-dependent MF. The hydrometeor with the highest score is chosen as the dominant one. The value of the score is stored, as are the hydrometeor type (HT) that is ranked second and its score. Equation (1) summarizes the calculation of the probability:

_{H}where *i* stands for the HT and *F ^{i}* represents the MF.

In Eq. (1), the MFs of temperature and BB appear as multiplicative terms. They thus act as “sanity checks” in the algorithm. In the polarimetric processing chain, the BB characteristics (BB-top and BB-bottom heights), assumed to be uniform across the whole radar domain, are retrieved from the analysis of azimuthally averaged *ρ*_{HV} range profiles using the inverse method proposed by Tabary et al. (2006) by checking azimuthally averaged *ρ*_{HV} range profiles in different elevation angles to adjust the BB altitude given by the model AROME. If the BB cannot be estimated, the algorithm takes into account previous values of the BB to estimate the BB characteristics. Once the BB characteristics are retrieved, the BB MF is parameterized as follows for the various hydrometeor types:

If the height of the pixel is lower than the BB bottom minus a tolerance interval, then all hydrometeors but rain and hail are excluded. Here the tolerance interval depends on the width of the BB and is equal to 0.25 times the depth of the BB.

If the height of the pixel is higher than the BB top plus a tolerance interval, then rain and wet snow are excluded.

If the height of the pixel is higher than BB bottom minus a tolerance interval and is lower than the BB top plus a tolerance interval, then wet snow is the priority. Note that all of the rest of the hydrometeor types are tolerated.

Here a tolerance interval is added in the BB top and bottom to take into account the uncertainty on the detection of the BB; its value is equal to ¼ of the width of the BB. The reason for using bivariate MFs is the fact that the polarimetric parameters (Z_{DR}, *K*_{DP}, and even *ρ*_{HV}) vary significantly when *Z _{H}* is increasing.

The current HC algorithms used in the polarimetric chain are an adjusted version of Park et al. (2009) for X band, the one proposed by Marzano et al. (2006) for C band, and the one proposed by Park et al. (2009) for S band. The polarimetric chain represents the set of all processing and analyzing programs for polarimetric data; see Boumahmoud et al. (2010) for more details. In this paper, the current algorithms are compared with the new approach without a 3D temperature model (i.e., with new MFs and a new probability function) and with the new approach with a 3D temperature model. See Table 2 for more details about each HC approach.

## 3. Establishment of MF at X, C, and S band

### a. The membership function MF

A one-dimensional MF is a trapezoidal function of probability values (Zrnić et al. 2001) or a beta function (Liu and Chandrasekar 2000). The trapezoidal form is characterized by two principal parameters representing the two upper corners of the trapezoid, *X*_{2} and *X*_{3} in Table 3, and two other parameters representing the lower corners of the trapezoid for tolerance, *X*_{1} and *X*_{4} in Table 3. A bivariate MF is a domain of probability for each polarimetric variable paired with *Z _{H}*. MFs are segregated by HT and by wavelength (X, C, and S band). To establish MFs, different radars at X, C, and S band observing a variety of precipitation events have been used. Data from a single low elevation angle without significant PBB were used.

Using two half-Gaussian functions is more realistic, is more reliable, dispenses with the use of weights in the probability function, and has fewer parameters than a trapezoidal function. Each of the two half-Gaussian functions is characterized by three parameters: the position of the maximum, which is equal to 1, and the two half-widths *W*_{1} (left) and *W*_{2} (right), which depend on the standard deviations of this function. The mathematical expression for the two half-Gaussian functions is shown in Eq. (2):

where *W*_{1} is used in the left side and *W*_{2} is used in the right side. Inset a1 of Fig. 1a shows an example of the two half-Gaussian functions.

The steps to establish these functions are as follows:

Select data measured in so-called ideal conditions: low attenuation (Φ

_{DP}< 10°), high SCR (SCR > 10 dB), high SNR (SNR > 20 dB), low PBB (PBB < 10%), and short distances (*d*< 60 km).Subjectively identify areas of homogeneous and unambiguous hydrometeor types by looking only on the polarimetric variables,

*Z*and BB, and then select areas (a few pixels) in which we are “sure” to have one type at the same time. This part of the study is the most delicate and time consuming because it involves a human expert reviewing each PPI of each selected case. The calibration and validation datasets are constituted using this method. Note that the data used for the datasets have been collected from a large number of radar–episode couples. We tried to collect data from our polarimetric radars in the French metropolitan areas in stratiform and convective precipitation cases so as to have more than 20 full-day cases in different seasons; see Table 4._{H}Project the pairs of polarimetric parameters, (

*Z*–_{H}*Z*_{DR}), (*Z*–_{H}*K*_{DP}), and (*Z*–_{H}*ρ*_{HV}), in their corresponding planes.Model the bivariate MF by using two half-Gaussians per class of

*Z*with 5 dB_{H}*Z*as increment step. Note that Figs. 1–4 are examples to present the MF without hiding the others and that the sampling in these figures is randomly chosen for presentation (it is 2.5 dB*Z*of*Z*)._{H}

In the new approach, the (*Z _{H}*–

*ρ*

_{HV}) MF is 2D because empirically it was observed that the values of

*ρ*

_{HV}decrease when

*Z*increases (see Fig. 1). This behavior is a likely consequence of resonance effects in the presence of large drops. The presence of hail at high

_{H}*Z*cannot be excluded, but, because hail is a rare phenomenon in France, we do not think it biases our statistics. Note that the hail MFs presented here are preliminary. More data will have to be processed to establish robust hail MFs.

_{H}The bivariate MFs of (*Z _{H}*–

*Z*

_{DR}), (

*Z*–

_{H}*K*

_{DP}), and (

*Z*–

_{H}*ρ*

_{HV}) for X band and rain are shown in Fig. 1. Bivariate MFs for the five hydrometeor types in X, C, and S band are presented in Figs. 2–4, respectively. Note that in Figs. 1–4 a threshold of 0.1 is applied to the values of the two half-Gaussian functions (i.e., the areas where the value of the MF drops below 0.1 are not plotted). Figures 1–4 contain a lot of information. For example, at C band (Fig. 3),

*Z*in dry snow varies from 15 to 45 dB

_{H}*Z*,

*Z*

_{DR}varies from −1 to 1 dB,

*K*

_{DP}varies from 0° to 1° km

^{−1}, and

*ρ*

_{HV}varies from 0.93 to 1. At S (Fig. 4) and X bands (Fig. 2),

*Z*in dry snow varies from 15 to 45 dB

_{H}*Z*,

*Z*

_{DR}varies from −0.5 to 1.8 dB,

*K*

_{DP}varies from −0.5° to 1.5° km

^{−1}, and

*ρ*

_{HV}varies from 0.93 to 0.99. In general, the range of variation of

*Z*of each HT is the same at all three wavelengths and, as expected,

_{H}*K*

_{DP}values are smaller at S band than at C and X bands.

By looking to the MFs in these figures, we can specify some values of the polarimetric parameters for each hydrometeor type. For example, for C and S bands, between 10 and 45 dB*Z*, only *Z*_{DR} and *ρ*_{HV} can be discriminating; *K*_{DP} has no effect on the HC in this case (all of the hydrometeor types presented in this interval have the same variation of *K*_{DP}). In X band, however, *K*_{DP} can play a role in this interval because of the fact that *K*_{DP} values are larger at X band than at S and C bands. The same MFs are used for dry snow and ice, but the differences are in the interval of variations of *Z _{H}* (between 5 and 30 dB

*Z*for ice and between 15 and 45 dB

*Z*for dry snow) and in the temperature interval; see Table 3. We can also remark that, as expected,

*ρ*

_{HV}is better than

*Z*

_{DR}and

*K*

_{DP}for the classification of wet snow. For small values of

*Z*(<15 dB

_{H}*Z*), rain and ice are the only hydrometeor types that may exist, and the discrimination in this case is by using the temperature MF.

### b. T-matrix simulations

T-matrix simulation results are used to fill areas in the (*Z _{H}*–

*Z*

_{DR}), (

*Z*–

_{H}*K*

_{DP}), and (

*Z*–

_{H}*ρ*

_{HV}) rain domains where the number of points is not significantly high enough to be obtained empirically (typically high

*Z*). The black stars in Fig. 1 represent the T-matrix simulation results. These curves help to extrapolate the rain MFs when the number of observations is not large enough. In this case, the position of the maximum is derived from the T-matrix simulation and the corresponding widths are deduced by extrapolation of widths that have been calculated for the same plot.

_{H}The T-matrix method is a theoretical technique for computing electromagnetic scattering by single and distributed nonspheroid particles (Barber and Hill 1990; Mishchenko et al. 1996; Mishchenko and Travis 1998). Raindrops are considered to be oblate spheroids with a vertical axis of revolution and with an axis ratio that was represented by Brandes et al. (2002) as

The parameters *b* and *a* represent the vertical and horizontal axes of the raindrop, respectively. For raindrops, the equivolumetric diameter *D* is between 0.05 and 8 mm. Backscattering cross sections and forward and backward scattering coefficients are calculated at H and V polarizations. Calculations are performed at the exact wavelengths of the French radars. Raindrop spectra are modeled with a normalized gamma distribution as shown in Eq. (4) (Bringi and Chandrasekar 2001):

The shape parameter *μ* is assumed to be constant (and equal to 5; see Gourley et al. 2009), and the equivolumetric median drop diameter *D*_{0} (mm) and the normalized concentration *N _{w}* are varied. For more details on parameterization of the T-matrix algorithm see Ryzhkov and Zrnić (2005) and Gourley et al. (2009).

### c. Impact of measurement conditions on MF

By repeating the steps to establish the bivariate MF (section 3a) but not in ideal conditions, we find that the bivariate MFs are broadened (see red curve in the inset a1 in Fig. 1a) when Φ_{DP} = 19° and SNR = 12 dB (just a numerical example) in comparison with the blue curve in the inset (in ideal conditions). The impact of deteriorating measurement conditions is an increase in the amount of overlapping between the MFs of different hydrometeor types. By consequence, the difference between the highest (first choice) and second-highest (second choice) probability function values decreases.

Here we outline an empirical method to take into account the broadening rate: the widths of the two half-Gaussian functions are calculated initially in “ideal conditions.” Then, the widths are recalculated after changing one condition (i.e., taking pixels when Φ_{DP} > 10° while the other conditions remain ideal) and so on. The rates of variation denoted by *α*_{SNR}, , and *γ*_{SCR} represent the variation of the two half-widths *W*_{1} and *W*_{2} as a function of the variation of SNR, Φ_{DP}, and SCR, respectively, relative to the values of *W*_{1} and *W*_{2} in the ideal conditions. They are derived and assumed to be the same for all types of precipitation. The new two half-widths and are calculated according to Eq. (5):

Tables 5–7 summarize the empirical variation rate coefficients by *α*_{SNR}, , and *γ*_{SCR} of the bivariate MF at X, C, and S bands. Note that studies showed that PBB did not affect the MFs. Note also that in the case of perfect attenuation correction is expected to be 0.

### d. Inclusion of the temperature information

Polarimetric parameters alone cannot always be fully discriminating. By observing the MFs (see Figs. 2–4), it is clear that the amount of overlapping between some MFs appears to be larger than 80%. For this reason, it is absolutely necessary to include additional weather information in the HC algorithm.

The temperature MF is, with the *Z _{H}* MF, the most important one in the HC algorithm. It is used as a multiplicative term in Eq. (1). Temperature functions are the same for all radar wavelengths. Table 3 summarizes the values of the temperature domain of each hydrometeor type. The temperature domain should reflect 1) microphysical knowledge about the possible presence of hydrometeors in certain temperature conditions (Zrnić et al. 2001) but also and primarily 2) the known errors of the NWP model (e.g., known analysis/forecast errors) that is providing the temperature information.

In the operational dual-polarization processing chain of Météo France, temperature is estimated by using the BB detection algorithm. At the top of the BB, temperature is assumed to be 0°C, and the entire vertical profile is reconstructed using a standard −6.5°C km^{−1} lapse rate. This technique frequently leads to large errors in the temperature that is used in the HC algorithm and to subsequent errors in classifications.

In the new HC algorithm, short-range forecasts of temperature from the high-resolution French operational AROME model are interpolated onto the radar geometry. Temperature PPIs are then generated and fed into the HC algorithm.

## 4. Qualitative and quantitative evaluation

### a. Qualitative evaluation

Figure 5 shows an illustration of the *Z _{H}*,

*K*

_{DP},

*Z*

_{DR}, and

*ρ*

_{HV}polarimetric variables. Data have been collected by the X-band Mont-Maurel, C-band Toulouse, and S-band Nîmes radars, as detailed in the caption. The two thin black concentric circles in the panels represent the top and the bottom of the identified BB.

The signature of rain is visible inside the first circle for the three wavelengths: *Z _{H}* varies from 0 to 50 dB

*Z*,

*K*

_{DP}is between 0° and 0.5° km

^{−1},

*Z*

_{DR}is between −0.5 and 1 dB, and

*ρ*

_{HV}is close to 1. In the BB area—that is, between the two concentric circles—

*Z*varies considerably,

_{H}*Z*

_{DR}reaches high values in S band (3 dB),

*K*

_{DP}increases, and

*ρ*

_{HV}is lower than 0.94. In C band, a hail signature is also shown: large values of

*Z*(>50 dB

_{H}*Z*),

*K*

_{DP}(>2 dB), and

*Z*

_{DR}(4 dB).

Beyond the second circle, the range of variations is large for all polarimetric variables. Large values of *K*_{DP} (2° km^{−1}) appear on the north side of the S-band radar image (in the thick black oval), probably because of the presence of platelike crystals (Bechini et al. 2011). The temperature in the 3D model was near −15°C in that area, which is consistent with the Bechini et al. (2011) theory. Note that the new HC algorithm classified this area as ice (Fig. 6; S band).

The results of the HC algorithm are shown in Fig. 6: The top row represents the results of the current algorithm, the middle row represents the results of the new algorithm without a 3D temperature-scheme model, and the bottom row represents the results of the new algorithm with the same MF as the second row but with a 3D temperature-scheme model. All three algorithms provide the same results in the rain and dry-snow regions even though (apart from C band) the middle and bottom rows are more homogeneous.

The main difference among the three algorithms lies in the BB area. The hydrometeor field in the bottom row has a much more homogeneous detection of wet snow, which is a likely consequence of the improved temperature information and improved MF.

### b. Objective evaluation

Percentages of good classifications (i.e., the classification results match the type that was classified subjectively during the identification of areas—see the second step to establish the bivariate MF that is described in section 3a) for each HT are computed. Three cases are studied: the current algorithm, the new approach (i.e., new MF) without the 3D temperature model, and the new approach (i.e., new MF) with the 3D temperature model. Three scores are calculated, one each for rain, wet snow, and dry snow combined with ice.

The scores are presented for different radar–episode couples in Fig. 7. The common result is that for rain all three algorithms work well. The difficult area for HC is the melting layer and its surroundings. Here, the improvement brought by the new approach with 3D temperature model is obvious. The average percentage of good detection of wet snow is 77% for the new approach with 3D temperature, 52% with the new approach without 3D temperature, and 39% with the current approach. Note that the variation in the percentage of good detection of wet snow from one episode to another is due to the meteorological conditions, to being a stratiform case vs a convective case, and especially to a good detection of the BB as confirmed by a good score from an indicator such as the correlation coefficient or Nash coefficient between the reference profile and the analysis of azimuthally averaged *ρ*_{HV} range profiles. It should be recognized that those scores are semiobjective in the sense that the validation dataset was established subjectively by a human expert. Hydrometeor videosondes (Kouketsu and Uyeda 2010) or aircraft in situ measurements (Liu and Chandrasekar 2000) would certainly be more objective means to validate the algorithm, but such observations are rare and expensive.

The second choice of the algorithm is also considered (see Cremonini et al. 2004) to measure and quantify the discriminating power of the HC algorithm. Figure 8 shows a time series of the relative difference between the first and the second choice of the HC algorithm. Data were collected at an elevation of 1° with the Cherves radar (C band) on 14 November 2010. Figure 9 represents the number of pixels corresponding to each precipitation type in Fig. 8. As an example, at 0500 UTC there are 10 500 pixels that are classified as rain as first choice by the HC algorithm (see Fig. 9) and the average relative difference between the first (rain) and the second choice of the HC algorithm is 30% (see Fig. 8), meaning that on average the final value of the probability function [Eq. (1)] of the first choice (rain in that case) is 2 times the final value of the probability function of the second choice, whichever algorithm it may be. Considering now all pixels that were classified as wet snow as first choice by the HC algorithm, the average relative difference is 31.5%; that is, the ranking between the first and second choice is closer. As a rule of thumb, we suggest that the first choice of the HC algorithm be considered as reliable if the relative difference is larger than 25%. If that criterion is applied, then it appears that the identification of ice—for the dataset that is presented on Figs. 8 and 9—is often questionable. This can be explained by large overlapping in the MF between dry snow and ice. The same study was done for other days, and the conclusions are close, but in the stratiform case with measurement conditions that are close to ideal and for which the BB is clearly shown the difference may be large between the first and the second choice.

For each HT, the frequency of selection as second type was calculated; the results are presented in Table 8. The new HC algorithm (including new MF and usage of a 3D temperature model) was applied to the 1° elevation angle of the Cherves radar on 14 November 2010 to produce Table 8. Results are shown for 1000 and 1500 UTC and finally integrated over the full day. Table 8 reveals that, when rain was taken as a first choice, 99% of the second choices were wet snow and 1% were hail. When wet snow was taken as a first choice, 43% of the second choices were rain, 55% were dry snow, and 2% were hail. When ice was taken as a first choice, then all second choices were dry snow. By repeating this analysis using data gathered over a long period of time, we can be more precise in knowing the percentage of the second choice of the HT algorithm. This can then help us to conduct further research into the difference between each HT and which HT would have the highest probability to act as second choice in the HT algorithm. The probabilities can then be taken into account by using a Bayesian model that helps the fuzzy logic algorithm in the classification of hydrometeors.

## 5. Conclusions

A new HC algorithm was presented in this paper. The algorithm discriminates between a reasonable number of hydrometeor types (rain, wet snow, dry snow, ice, and hail) and uses offset-corrected and attenuation-corrected polarimetric radar variables as well as empirically established, wavelength-dependent MFs and outputs from a brightband identification algorithm that is included in the polarimetric processing chain. The algorithm also takes into account actual measurement conditions (PIA, SCR, SNR, and PBB) and incorporates temperature PPIs computed from forecasts provided by the French high-resolution nonhydrostatic AROME NWP model.

The algorithm adopts the same formulation at all three wavelengths (X, C, and S) and, unlike previous approaches, has no empirical weight. The temperature, *Z _{H}*, and brightband MF are introduced as multiplicative terms to act implicitly as so-called sanity checks in the algorithm. The specificity of each wavelength is introduced in the algorithm through the MFs, which have been established by a human expert selecting areas of homogeneous, unquestionable hydrometeor types on a large number of radar–episode couples. The broadening of the MF with measurement conditions is documented and is parameterized in the algorithm. The impact is an increase in the amount of overlapping in the MF and a tighter score between the first and second choice of algorithm. The relative difference between the scores of the first and second of the algorithms is proposed as a means to characterize the confidence level of the algorithm decision.

Semiobjective scores have been computed using the validation dataset built subjectively by the human expert. The improvement brought by the new MF and the 3D temperature information is particularly noticeable on the detection of wet snow. Indeed the percentage of correct wet snow identifications goes up from 39% to 52% when the new MFs are introduced and from 52% to 77% when the 3D temperature information is further considered. The outputs of the new HC algorithm will be further validated using data—in particular, in situ aircraft measurements—collected during the Hydrological Cycle in Mediterranean Experiment (HyMeX) field campaign (see http://www.hymex.org/ for more details).

The MF of hail will have to be established in a more robust way in the future, the difficulties being the scarcity of unquestionable and precise (date/location/size) hail observations and lack of unquestionable “no hail” observations. On the basis of previous studies, three classes of hail will be considered: small hail (diameter < 5 mm), medium hail (diameter between 5 and 20 mm), and large, damaging hail (diameter > 20 mm).

Last, because of Earth's curvature and the intrinsic geometrical limitation of radar observations, the hydrometeor-type PPIs will have to be combined with model data and in situ observations (temperature and visual observations) to provide in real time the best estimation of precipitation type reaching the surface, which is the information that is more relevant for road management authorities, airport authorities, hydrologists, and so on.

## Acknowledgments

The financial support for this study was provided by the European Union; the Provence–Alpes–Côte d'Azur Region; and the French Ministry of Ecology, Energy, Sustainable Development and Sea through the Risques Hydrométéorologiques en Territoires de Montagnes et Mediterranéens (RHYTMME) project.

## REFERENCES

*Light Scattering by Particles: Computational Methods.*World Scientific, 261 pp.

*35th Conf. on Radar Meteorology,*Pittsburgh, PA, Amer. Meteor. Soc., 7A.4. [Available online at https://ams.confex.com/ams/35Radar/webprogram/Paper191528.html.]

*Proc. Sixth European Conf. on Radar in Meteorology and Hydrology (ERAD2010): Advances in Radar Technology,*Sibiu, Romania, ERAD. [Available online at http://www.erad2010.org/pdf/oral/Tuesday/radpol2/3_ERAD2010_0272.pdf.]

*Polarimetric Doppler Weather Radar: Principles and Applications.*Cambridge University Press, 636 pp.

*Proc. Sixth European Conf. on Radar in Meteorology and Hydrology (ERAD2010): Advances in Radar Technology,*Sibiu, Romania, ERAD,

*32nd Conf. on Radar Meteorology,*Albuquerque, NM, Amer. Meteor. Soc., 9R.3. [Available online at https://ams.confex.com/ams/32Rad11Meso/webprogram/Paper95684.html.]

*Fourth European Conf. on Radar in Meteorology and Hydrology (ERAD 2006),*Barcelona, Spain, Servei Meteorològic de Catalunya, 17–20.

*Proc. Weather Radar and Hydrology Int. Symp.,*Grenoble, France.