1. Introduction
Ground-based weather radar is often affected by return signals that do not originate from precipitation. Return signals frequently originate from stationary objects, such as hills or buildings, or from moving objects such as birds and insects. At other times the radar beam is bent toward the ground because of atmospheric humidity and temperature gradients, resulting in increased returns from land or sea, a phenomenon known as anomalous propagation or anaprop. These spurious returns are collectively termed clutter; however, to differentiate their origin, the term ground clutter is reserved for returns from stationary objects that are present under normal propagation conditions. Clutter and anaprop (over land) are characterized by a Doppler velocity near zero and a narrow spectrum width (e.g., Doviak and Zrnić 1984); however, anaprop is distinguished from clutter by its transient temporal nature. Moreover, anaprop over sea has a nonzero Doppler velocity, since the waves and spray have measurable velocities.
Anaprop has been observed since the advent of radar, and the meteorological conditions that produce it have been well described in the literature (e.g., Doviak and Zrnić 1984; Meischner et al. 1997). It is easily recognized by operational forecasters due to its shallow vertical extent and transient temporal characteristics; however, these same properties make its automated detection difficult. Automated detection of anaprop is of fundamental importance in quantitative weather radar applications such as data assimilation for numerical weather prediction (NWP), as assimilation of anaprop may lead to large overestimates of precipitation totals and initiate spurious convection. Furthermore, small errors in quantitative precipitation estimation (QPE) have been shown to propagate nonlinearly in peak rate and runoff volume in hydrologic calculations (Faures et al. 1995), potentially having a dramatic impact on the efficacy of flood forecasts.
Several methods have been developed to mitigate anaprop, each of which has advantages and shortcomings (for a thorough review see Steiner and Smith 2002). The first is to site the radar at an appreciable height above the base level of the surrounding terrain as conditions conducive to anaprop usually occur close to the surface (Bech et al. 2007; Brooks et al. 1999); although this also limits the low-level coverage of the radar beam. Practicalities, however, do not always permit raised siting of the radar, so other methods have been developed. These methods can be classified into two broad categories: those which perform signal processing on the return radar beam at the radar site and those which analyze the data post-acquisition.
a. On-site processing
On-site processing is generally performed via filtering the Doppler spectrum in either the time or frequency domain (Keeler and Passarelli 1990). The near-zero Doppler velocity and narrow spectrum width of anaprop can be exploited to remove these signals; however, an unwanted side effect is that precipitation with a Doppler velocity near zero is also excluded. This is commonly observed in widespread stratiform rain, where data are often missing at the zero isodop. Additionally, the notch filtering of near-zero velocity echoes is ineffective for anaprop over sea as waves have true measurable velocities. Another disadvantage of this technique (and the reason that it is performed on site) is that it requires processing of the in-phase and quadrature-phase (I and Q) time series resulting in large datasets unable to be transmitted and archived given the current computing limitations at the Australian Bureau of Meteorology (hereinafter the bureau).
b. Postdata acquisition processing
Because of the aforementioned problems of archiving the raw I and Q signals, much effort has been placed on the postprocessing of archived data. Postprocessing techniques have relied mainly on analyzing quantities derived from the spatial and temporal information of the reflectivity field. Spatial information is usually conveyed in the form of gradients in the reflectivity field between adjacent range gates in either the horizontal or vertical dimensions (Alberoni et al. 2001; Kessinger et al. 2004; Steiner and Smith 2002). There are various mathematical descriptions of the gradient of the reflectivity field; however, common formulations are texture, the reflectivity fluctuations (SPIN; Steiner and Smith 2002), and the statistical features (mean, median, mode, and standard deviation) calculated within a local neighborhood of the range gate in question. These fields usually exhibit quite different probability distribution functions (PDFs) for echoes from precipitation, clutter, or anaprop. Parameters derived from the reflectivity gradient field have been used within differing probabilistic classification algorithms including fuzzy logic (Gourley et al. 2007; Hubbert et al. 2009; Kessinger et al. 2004), neural networks (Grecu and Krajewski 2000; Krajewski and Vignal 2001; Lakshmanan et al. 2007; Luke et al. 2008), and Bayesian (Moszkowicz et al. 1994; Rico-Ramirez and Cluckie 2008). Some of these have been developed using polarimetric variables; however, an advantage of each of these methods is that they can be applied to radar systems utilizing only reflectivity measurements at a single wavelength and polarization.
The Australian Bureau of Meteorology radar network consists of single-polarization C- and S-band radars, some of which have Doppler capability. Furthermore, the only moments that are routinely stored by the bureau are corrected reflectivity (the reflectivity after Doppler notch filtering and range correction have been applied) and Doppler velocity. Therefore, to extract as much useful information as possible from these moments and produce quality-controlled data useful for assimilation and QPE, texture-based methods combined with classification algorithm techniques need to be employed.
This paper is structured as follows. In section 2, we describe the operating characteristics of the radar used for data acquisition. In section 3, we present the development of a Bayesian classifier, known as a naïve Bayes classifier (NBC), which takes as input texture-based fields derived from corrected reflectivity. The NBC is a supervised learning classification algorithm, which requires training datasets where it is known a priori if the returns originate from precipitation or anaprop (Rico-Ramirez and Cluckie 2008). The algorithm developed is similar to that presented by Rico-Ramirez and Cluckie (2008); however, we demonstrate and quantify its efficacy with the use of single-polarization data using only corrected reflectivity. Furthermore, in section 4, the NBC is applied to two cases of convective storms embedded in anaprop signals: in the first, it is shown that the NBC is skillful at distinguishing precipitation from anaprop, while in the second example we demonstrate that the NBC is effective when applied to data from two nearby radars with differing wavelengths and beamwidths from the radar on which it was trained. Finally, we develop a strength of classification index (SOC), which is a measure of the relative magnitude by which the scaled probability of precipitation has exceeded that for anaprop. This index will prove useful from censoring data before being used for data assimilation of QPE/QPF (quantitative precipitation forecast. The conclusions are stated in section 5.
2. Data
The data were obtained with the Kurnell radar located south of Sydney at 34.01°S, 151.23°E at an altitude of 64 m MSL. The Kurnell radar is a C band (5-cm wavelength) with a 3-dB beamwidth of 1°. The data are collected in polar coordinate format, comprising 360 azimuthal beams each consisting of 596 range gates with a radial spacing of 250 m. The radar operating characteristics are summarized in Table 1. Analysis was performed on polar data rather than a transformation to Cartesian coordinates. One volume, consisting of scans at 11 tilt angles (spaced at 0.7°, 1.5°, 2.5°, 3.5°, 4.5°, 5.5°, 6.9°, 9.2°, 12.0°, 15.6°, and 20.0°) is completed in approximately 5 min. Standard UTC time will be used in this paper; however, for reference, local time (LT) is UTC + 10 h normally and UTC + 11 h during daylight saving. This radar was chosen for evaluation as it covers one of Australia's major population centers and anaprop is a common occurrence in this location, especially during the summer months when the prevailing subtropical high in the Tasman Sea produces strong temperature and humidity gradients off the Australian eastern coast.
Operating parameters for the Kurnell radar.
3. Bayes clutter classifier
a. Naïve Bayes classifier
b. Feature fields
In this section, we detail the feature fields used as input to the NBC. The feature fields can be described as texture-based fields that examine various gate-to-gate relationships in the retrieved radar fields. The use of feature fields obtained from reflectivity data is advantageous since they require minimal numerical computation. Moreover, they can be applied in a postprocessing capacity, negating any need to upgrade radar hardware or electronics. The three feature fields we will consider are texture of reflectivity, “SPIN,” and the vertical profile of reflectivity.
1) Texture of reflectivity
2) SPIN
3) Vertical profile of reflectivity
c. Construction of the conditional probabilities
The application of the NBC requires evaluating PDFs of the a priori conditional probabilities for each class using training datasets. Since we are attempting to distinguish anaprop from precipitation, we specify two classes 
(left) PPI obtained from the Kurnell radar at 1100 UTC 31 Jan 2011 (2200 LT). Some returns are of the order 35–45 dBZ, which is also typical of showers in this location. (right) RHI obtained at an azimuth of 100° from the north. Returns are prevalent between the 80- and 130-km range; however, they are only present in the lower two elevations, signifying their source is from anaprop. Only reflectivities above 10 dBZ are shown.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
Summary of time periods, number of radar volumes, and number of unique reflectivity samples used for the training dataset.
For the construction of the conditional PDFs for the precipitation class, four separate precipitation scenarios were chosen: shallow stratiform rain where cloud tops were below the freezing level and precipitation was generated by warm rain processes, a line of shallow convection with cloud tops below 5 km, deep isolated continental convection, and widespread stratiform rain with embedded convection. These will be referred to as Shallow, Sh conv, Convect, and Mixed, respectively. The reasons for these choices were twofold: 1) to capture a wide variety of meteorological cases and 2) to increase sampling statistics. Radar images (PPIs) representative of each of the scenarios are shown in Fig. 2. A visual comparison of anaprop with the shallow convection case (upper-right panel of Fig. 2) indicates that there is little information in the reflectivity field to distinguish them. Histograms of reflectivity (not shown) confirm this; in fact, there is little information in the reflectivity field (of a PPI) to distinguish each of the precipitation examples (except perhaps shallow stratiform rain) from anaprop. Therein lies the problem of automated detection of anaprop from the reflectivity field alone.
PPI radar reflectivity displays of the meteorological cases chosen for the training dataset. Clockwise from the top left depicts shallow stratiform (Sh strat), a shallow line of convection (Sh conv), deep intense lines of isolated convection (Convect), and widespread stratiform rain with embedded convection (Mixed). Only reflectivities above 10 dBZ are shown.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
More information can be gained from examining the feature fields, TDBZ and SPIN, which are shown for anaprop in Fig. 3. Immediately apparent is the lack of correspondence in structure of the feature fields compared with that of reflectivity (i.e., small/large values of reflectivity do not show up as small/large values of TDBZ or SPIN). TDBZ and SPIN are shown for the precipitation cases in Figs. 4 and 5, respectively. Again, the feature fields are relatively homogeneous through strong gradients in reflectivity; however, it is evident that both TDBZ and SPIN are 1) skewed to larger values and 2) noisier for anaprop than for the meteorological events. Furthermore, there is little distinction in the feature fields between each of the precipitation cases. These observations suggest that TDBZ and SPIN are efficient at distinguishing anaprop from precipitation and independent of the meteorology producing precipitation.
The texture (TDBZ) and SPIN fields for the anaprop case shown in Fig. 1. Only reflectivities above 10 dBZ have been included in the calculations.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
The texture feature field (TDBZ) for each of the precipitation cases as in Fig. 2. Only reflectivities above 10 dBZ have been included in the calculations.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
The SPIN feature field for each of the precipitation cases as in Fig. 2. Only reflectivities above 10 dBZ have been included in the calculations.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
For the purposes of constructing the conditional PDFs, time periods were chosen where the precipitation scenarios exemplified in Fig. 2 were applicable throughout. These periods were chosen subjectively by examining sequences of radar images and choosing a subset of contiguous retrievals such that the precipitation was similar (in the sense of areal extent and type) in each volume throughout the interval. Only samples from the lowest tilt of the volume scan were used to construct the PDFs. Combined, the precipitation samples consisted of 308 volumes comprising over 9 million separate reflectivity samples. Histograms of the feature fields were then constructed for each of the precipitation scenarios and for anaprop. They are shown in Fig. 6 and represent the conditional probabilities on the right-hand side of Eq. (2).
Probability distribution functions of the feature fields TDBZ, SPIN, and VPDBZ. PDFs are shown for each of the meteorological situations and for anaprop. These PDFs represent the likelihood function in the Bayes formula [Eq. (2)]. Note the logarithmic axes for TDBZ. Only reflectivities above 10 dBZ have been included in the calculations.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
d. Transformation of the conditional PDFs
To implement the conditional PDFs presented in the preceding section would require the use of a lookup table. For instance, the feature fields could be evaluated and a probability determined (via the lookup table) of that measurement occurring based on whether the classification was that of anaprop or precipitation. For operational purposes, however, this is unfeasible because of computational limitations. To facilitate the implementation of the classifier in an operational setting, it would be beneficial if the conditional probability distributions presented in Fig. 6 were parameterized by a mathematical distribution. This is achievable by applying a transformation to the data. One that is well established within the statistical literature is the Box–Cox transformation, which can map data to a nearly normal distribution via a power transform (Wilks 2011). This has the advantage that the conditional PDFs can be completely described by the mean μ and standard deviation σ, requiring minimal computation.
The log-likelihood functions for the TDBZ and SPIN feature fields were evaluated and the calculations for the TDBZ field of anaprop are shown in Fig. 7. The maximum of this parabolic function provides the optimal value of 
The log-likelihood as a function of λ [see Eq. (7)]. The value of λ, which maximizes the log-likelihood function, provides the best value to transform the data to an approximately normal distribution via Eq. (6). The dotted lines represent the 95% confidence interval for λ. This curve is the log-likelihood function evaluated for the TDBZ field of the anaprop case. Values for TDBZ and SPIN for each case are presented in Table 3.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
Calculated values of λ for the Box–Cox transformation described by Eq. (6) for anaprop and each of the precipitation cases. The last column shows the average value of λ for all precipitation cases combined.
Probability distribution functions of the feature fields TDBZ and SPIN after transformation according to the Box–Cox power law given by Eq. (6). Note that the distributions are now approximately normal.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
Mean μ and standard deviation σ of the feature fields for anaprop and precipitation. The values in the precipitation column are an average of each of the precipitation scenarios. They were obtained by applying the Box–Cox transformation to the feature fields of the training data and then computing μ and σ of the transformed distribution.
As in Fig. 8, including the best-fit normal curves determined from the mean and standard deviation of the Box–Cox transformed training datasets.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
e. Independence of the feature fields
The linear independence of the input feature fields is one of the key assumptions of the NBC. Despite this assumption, it has been proven to be effective even when the assumption of independence is violated (Friedman et al. 1997). However, it is worthwhile to examine the independence assumption between each of the feature fields. Pearson's correlation coefficients were calculated for each combination of the original and Box–Cox transformed feature fields. The results are summarized in Table 5. The VPDBZ field is either uncorrelated or very weakly correlated with TDBZ and SPIN; the same is true for the Box–Cox transformed counterparts BCTDBZ and BCSPIN. This may be expected as TDBZ and SPIN are measures of fluctuations of the reflectivity in a horizontal plane, while VPDBZ measures fluctuations in the vertical plane. However, the correlation coefficient for TDBZ and SPIN indicates a modest correlation (0.36) and a slightly greater correlation (0.48) after transformation. The correlation between TDBZ and SPIN is most likely due to each of them quantifying the fluctuation of the reflectivity field. The increased correlation between TDBZ and SPIN after transformation (for both anaprop and precipitation) is most likely due to the decreased range of the variables after transformation. For example, SPIN has values in the range [0, 100], whereas BCSPIN is in the range [2, 9]. Moreover, the Box–Cox transformation reduces larger values by a greater proportional amount than smaller values, thereby increasing the covariance of a feature field (Wilks 2011).
Pearson coefficient of correlation for anaprop conditions and the differing precipitation cases. All possible coefficients are shown for the original feature fields (TDBZ, SPIN, and VPDBZ) and the Box–Cox transformed values (BCTDBZ, BCSPIN, and VPDBZ).
4. Results and discussion
a. Varying input feature fields on the training dataset
It was stated in section 3 that the NBC implicitly assumes independence of the input feature fields; however, a modest degree of correlation between TDBZ and SPIN was also demonstrated. In this section, we examine how the NBC performs using differing combinations of the feature fields and determine if the correlation between TDBZ and SPIN affects the predictive power of the NBC. To illustrate this, we investigated all possible combinations of TDBZ, SPIN, and VPDBZ as input feature fields to the NBC (BCTDBZ, BCSPIN, VPDBZ, BCTDBZ–BCSPIN, TDBZ–VPDBZ, SPIN–VPDBZ, and TDBZ–SPIN–VPDBZ) and applied them to the case presented in Fig. 1 (which was representative of the training dataset for anaprop). A visual inspection was made to determine the least and most effective combinations, which are shown in Fig. 10. Returns classified as precipitation are colored blue while those from anaprop are colored orange. The use of BCTDBZ alone proved the least effective while the BCTDBZ–VPDBZ combination proved to the most effective classifier of anaprop. In general, VPDBZ had the greatest discriminatory power (combined with BCTDBZ or BCSPIN) for anaprop and was even quite effective if used as the sole feature field. The use of either BCTDBZ or BCSPIN alone was least effective since many range gates that were anaprop were misclassified as precipitation. Including all three feature fields resulted in little or no improvement over using either BCTDBZ or BCSPIN combined with VPDBZ.
The results of the NBC applied to the anaprop training dataset presented in Fig. 1. (left) The image was obtained using BCTDBZ only for classification, while (right) the image used BCTDBZ and VPDBZ.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
The possible NBC feature field combinations were evaluated using the precipitation cases from the training dataset. In all cases, the TDBZ–VPDBZ combination obtained similar results to the application of all three feature fields, while the SPIN–VPDBZ combination performed poorly. The addition of the SPIN feature field may not have enhanced the efficacy of the NBC because of the independence assumption of TDBZ and SPIN being violated. That the SPIN–VPDBZ combination performed worse than the TDBZ–VPDBZ combination may be due to the application of the kernel in Eqs. (3) and (4) being only evaluated in the radial direction. A kernel size of 20 was chosen, so as to allow a sufficient dynamic range in the evaluation of the SPIN (a kernel size of 20 will give a minimum discrete interval of 5% in the evaluation of SPIN). However, a kernel size of 20 equates to a radial range of 5 km, which may have the unintended consequence of smearing over precipitation and nonprecipitation pixels. The inclusion of azimuths in the evaluation of SPIN, which will enable the kernel size to be kept the same while decreasing the radial extent, is needed to evaluate the effectiveness of evaluating SPIN in one dimension only. Despite this, it appeared that using TDBZ and VPDBZ gave similar results to the application of all three feature fields and for this reason the BCTDBZ–VPDBZ combination will be used to present the NBC results herein.
The image, which was transmitted for public display by the bureau corresponding to the anaprop presented in Fig. 1, is shown in the left-hand side of Fig. 11. The NBC provides a substantial improvement over the current clutter mitigation system employed at the bureau. The current scheme uses basic thresholds of reflectivity and vertical height to censor data. However, in the image shown, the reflectivity and height thresholds were exceeded, allowing them to be included. The problem becomes more pronounced at greater distances from the radar because beam propagation causes the beam to be above the minimum height threshold once a certain range is reached.
Images transmitted for public display using the bureau's current clutter mitigation system. The images correspond to the anaprop data presented in Fig. 1 and the shallow stratiform case presented in Fig. 2. It can be seen that the current system is ineffective at removing anaprop, especially far from the radar, while it also removes many genuine precipitation pixels, especially close to the radar.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
b. Verification of the classifier
After conducting a visual evaluation of the best combination of feature fields to input to the NBC, the performance of the NBC was quantified. To achieve this we applied the NBC to each of the training datasets, which we assumed a priori consisted entirely of either anaprop or precipitation samples. The data were used to construct the conditional probability PDFs presented in Fig. 8 and therefore, if the NBC was perfect, would classify each pixel correctly. The total number of pixels classified as either anaprop or precipitation was calculated for each of the training datasets and the results are presented as a contingency table in Table 6. The numbers differ from those in Table 2 because all of the pixels in a volume were used to construct the contingency table, while only those from the lowest tilt were used to train the NBC. The raw values are presented above and the proportional values are presented below in the brackets. There are many different skill scores that can be derived from the contingency table; however, the dimensionality of the table is three and all the information contained in it can be summarized with three statistics (Wilks 2011). Three that are commonly used are the hit rate [
Contingency table constructed from the anaprop and precipitation training datasets. A minimum reflectivity threshold of 10 dBZ was applied. The raw values are presented first, and the proportional values are given after in parentheses.
c. Application to the training dataset precipitation cases
The results of applying the NBC to the precipitation cases, using the BCTDBZ–VPDBZ feature fields as discriminators, are shown in Fig. 12. For the shallow stratocumulus case (top left) the NBC has identified most (~70%) reflectivities larger than about 15 dBZ as precipitation. The formation of precipitation-sized droplets is indicated at radar reflectivities of about 5–10 dBZ for a C-band radar (Knight and Miller 1993), so the NBC has been particularly effective at identifying the shallow precipitation bands within these stratocumulus. We also note that the current method employed at the bureau to eliminate anaprop, which relies solely on examining the vertical profile of reflectivity, rejected these echoes in near entirety as anaprop (see the right-hand side of Fig. 11). This was because the precipitation was mainly confined below the height threshold designed to eliminate anaprop. The NBC represents a substantial improvement for the identification of shallow precipitation. Shallow cumulus convection is also well distinguished; however, some precipitation echoes, especially those at the edge of the radar volume, have been incorrectly classified as anaprop. This is due to the spread of the radar beam with distance and the use of VPDBZ as a classifier. In this case, cloud-top height was between 4 and 5 km and at large distances from the radar; two vertically aligned range gates were sufficiently large to overshoot cloud top, resulting in a VPDBZ value greater than zero, which is typical of anaprop (see Fig. 6). We note that the NBC using BCTDBZ only as the input feature field identified all of the returns as precipitation suggesting that, in the case of shallow precipitation, the use of BCTDBZ alone may perform better. The inclusion of BCSPIN degraded the performance of the NBC. However, since it is not known a priori what the source of returns is and the NBC cannot adapt its input feature fields accordingly, the use of the most effective combination over all precipitation types (BCTDBZ–VPDBZ) is preferable. The classification of the deeper precipitation, whether stratus or convective in nature (Convect and Mixed), has been mostly (88% and 94%, respectively) successful. Given that the current numerical weather prediction model used at the bureau—the Australian Community Climate and Earth-System Simulator (ACCESS; Puri et al. 2013)—has a grid spacing of 5 km, the raw radar reflectivity needs to be thinned (using superobservations); this level of accuracy is most likely suitable for data assimilation or QPE/QPF (Weng and Zhang 2012).
The results of the NBC applied to the precipitation cases from the training dataset. The original reflectivity images are shown in Fig. 2.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
d. Application to a case of rain embedded in anaprop
We now evaluate the NBC on a case other than the training dataset. Consider Fig. 13, which is a particularly interesting example as the image contains returns from both anaprop and precipitation. The returns in the northeast quadrant of the image are from anaprop, while those in the southeast are from convective storms. This becomes apparent when examining the PPI obtained at the second radar elevation (top right), where the returns originating from anaprop have disappeared as the radar beam is no longer internally reflected at the temperature and humidity inversion. This is further emphasized when the RHIs at 40° and 112° (reconstructed from the volume scan) are examined; the RHI at 40° only has returns in the lowest elevation, while the RHI at 112° indicates the presence of a well-developed convective storm containing reflectivities greater than 25 dBZ extending above 7 km. The simultaneous presence of both anaprop and precipitation in the same image provides a useful example with which to evaluate the efficacy of the NBC.
An example of anaprop and a convective storm obtained from the Kurnell radar on 22 Jan 2010. Anaprop is present in the northeast and a convective storm in the southeast. (top left) A PPI image obtained at the lowest elevation (0.7°); (top right) a PPI image obtained at the next highest elevation (1.5°). Note the absence of anaprop in the higher elevation. (bottom left) An RHI obtained at an azimuth of 40° through the anaprop; (bottom right) an RHI at 112°, showing the presence of a convective system extending to nearly 10-km height.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
Figure 14 shows the results of applying the NBC to this scene using BCTDBZ and VPDBZ as input feature fields. The PPI images (top row) show that the NBC is effective at distinguishing anaprop from precipitation; however, some precipitation pixels have been misclassified as anaprop. This is further illustrated by the RHI images (bottom row) again at 40° and 112°, which indicate that while the NBC has positively identified anaprop, some precipitation signals have been misclassified.
The results of the NBC applied to Fig. 13 using BCTDBZ and VPDBZ as input feature fields. The NBC has classified the anaprop correctly, completely eliminating the returns in the northeast; however, some pixels that are returns from precipitation have been incorrectly classified as clutter.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
e. The effect of the reflectivity threshold
For the preceding analysis, the minimum reflectivity threshold used (for the evaluation of the feature fields, their conditional PDFs, and for classification) was 10 dBZ, which, for a C-band radar, is near the value one would expect for the initiation of precipitation-sized droplets (Knight and Miller 1993). If values below this are included, then clear-air returns from insects and Bragg scattering from humidity gradients in the atmosphere become enhanced. The effect of setting a minimum reflectivity threshold at −30 dBZ (the smallest value returned by the radar) is shown in the left panel of Fig. 15. There is an increased number of returns close by the radar, especially over land, most likely due to the presence of insects and Bragg scattering. Conditions conducive to Bragg scattering would be expected since the same temperature and humidity gradient that produced anaprop over the sea would be prevalent, although to a lesser extent, over land. Despite the extra returns, when the reflectivity threshold is lowered the NBC did not classify most of the extra returns as precipitation. Since data below 10 dBZ were excluded during development of the NBC, it is interesting that most of the clear-air echoes have been classified as anaprop. Examination of a time sequence of images revealed that the echoes over land close to the radar (corresponding to those classified as precipitation) were due to Bragg scattering while those farther away (classified as anaprop) were caused by insects present after sunset. The NBC may therefore also prove useful in identifying insects and boundary layer humidity gradients; however, this will require further investigation. Nevertheless, for the purposes of data assimilation and QPE, setting a reflectivity threshold near 10 dBZ is advisable and will help mitigate this problem. However, the use of the Doppler wind field (e.g., Rennie et al. 2011) is advisable to identify insect echoes and such research is being undertaken concurrently at the bureau. Furthermore, software is being developed within the bureau that will enable selecting regions of interest and subjectively defining an a priori class to them to determine if and how PDFs of feature fields for insects (for instance) differ from those of anaprop.
(left) PPI image of mixed anaprop and precipitation using a minimum reflectivity threshold of −30 dBZ. Note the increase in returns over land close to the radar compared to Fig. 13. These returns were most likely due to Bragg scattering. (right) Results of the NBC using −30 dBZ as the minimum reflectivity threshold.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
f. Application to radars other than Kurnell
It is feasible that the texture and SPIN variables may be sensitive to radar operating characteristics such as wavelength, beamwidth, height above mean sea level (MSL), and range resolution. The Kurnell radar (64 m MSL) is ideally situated to test this hypothesis as two bureau radars are located to the north and south of it, each with differing operating characteristics. The Terrey Hills radar is an S-band (10 cm) 1° beamwidth radar located about 40 km to the north of the Kurnell radar at 195 m MSL, while the Wollongong radar is an S-band 2° beamwidth radar located about 55 km to the south at 449 m MSL. Together, the radars are a combination of 5- and 10-cm wavelengths and 1° and 2° beamwidth operating parameters.
Figure 16a is an example of shallow maritime convection and anaprop observed by each of the radars at approximately the same time. The same gross features are evident with many convective elements present over the ocean. The convection was very shallow and confined mostly below 4 km altitude. Consider the small convective element just east of the Kurnell radar, which is circled. It is clearly visible in all three radars; much anaprop is evident in the Kurnell and Wollongong radar images, however. Figure 16b shows the results of applying the NBC to the PPIs. It can be seen that the anaprop surrounding the convection in the Kurnell and Wollongong images has been correctly distinguished. It is encouraging that the NBC has managed to perform well when applied to radars with different operating characteristics and gives us confidence that the NBC can be directly applied to other radars around the country. It is unclear why more anaprop is present in the Kurnell and Wollongong radars compared to Terrey Hills. It may be due to the altitude of the radar; however, Terrey Hills is at an altitude midway between the other two indicating no obvious decrease in anaprop as a function of the height of the radar as may be expected. The radar beamwidth may be a contributing factor since Wollongong (with a 2° beamwidth) exhibits a greater amount of anaprop compared with the other two radars. In particular, tests of the NBC on radars at other locations around Australia reveal that the feature fields may be susceptible to beamwidth and range resolution. Another factor that may influence the NBC may be the climatic region for which it was tuned; that is, it may not perform so well in the tropical north of the country or in the temperate regions farther south. These points need further examination and will be the focus of future studies of the applicability of the NBC to the bureau's radars.
Shallow maritime cumulus convection observed with three different radars. (a) The reflectivity images; (b) the corresponding classification images obtained using the NBC. The three radars (Terrey Hills, Kurnell, and Wollongong) each have a differing wavelength and/or beamwidth. The NBC has performed well on data obtained with each radar despite having been trained with data obtained from the Kurnell radar.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
g. A strength of classification index
An example of the evaluation of the SOC applied to the precipitation training datasets is shown in Fig. 17. The color scale has been truncated at 0.5 as most values appear to be confined below this. To quantify the range of the SOC, PDFs of the training set data were constructed and are presented in Fig. 18. The SOC index is mainly confined to values below about 0.5. The PDFs of SOC exhibit a maximum at the first bin (0–0.05) showing that the majority of pixels identified as precipitation have only had a slightly higher a posteriori probability of precipitation than anaprop. However, the PDFs for each of the weather cases are relatively flat above an SOC of about 0.05. It is anticipated that the assimilation and QPE communities would be able to set a minimum value of the SOC, above which data pixels would be accepted. Increasing the SOC results in a decrease in the amount of information that can be assimilated; however, the flatness of the PDFs in Fig. 18 suggests that the information loss is approximately linear above an SOC threshold of about 0.05.
The strength of the classification index evaluated for each of the precipitation cases from the training dataset. A larger value indicates a larger confidence that a pixel is precipitation.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
SOC index PDFs evaluated for each of the precipitation training datasets. Theoretically, the SOC can have a maximum value of 1; however, the majority of values are confined below 0.5.
Citation: Journal of Atmospheric and Oceanic Technology 30, 9; 10.1175/JTECH-D-12-00082.1
5. Summary and conclusions
In this study, a naïve Bayes classifier was developed and tested. The NBC is an extension of Bayes's theorem, which classifies radar echoes into two classes, 
The NBC is a supervised learning technique, which requires a training dataset of examples in which the classification is known a priori. The training dataset consisted of five subclasses: one of anaprop and four distinct precipitation regimes consisting of shallow stratiform, shallow convection, deep convection, and deep stratiform precipitation with embedded convection. Probability distribution functions of the feature fields were evaluated for anaprop and each of the precipitation subclasses. The PDFs of the precipitation subclasses were found to be similar despite distinct meteorological forcing mechanisms. Moreover, the PDFs of the feature fields for anaprop were distinct from the PDFs of the precipitation subclasses, suggesting that they convey information that allows the categorization of precipitation and anaprop.
The feature field PDFs were found to be nonnormal, which, if used in their native form, would require the use of look-up tables to evaluate the conditional probability in Bayes's theorem. To parameterize the conditional PDFs they were transformed to approximately normal distributions via a Box–Cox transformation, which allowed them to be specified completely via the mean and standard deviation.
All (seven) possible combinations of the feature fields were investigated on the training datasets to evaluate the most effective combination, which was found to be TDBZ and VPDBZ. The use of all three feature fields did not, as a rule, add any benefit to the NBC and in some cases caused it to perform worse. This was attributed to TDBZ and SPIN not being linearly independent as they are both measures of the variability of the reflectivity field. When considered individually, VPDBZ was found to be the most effective feature field at distinguishing anaprop from precipitation.
The NBC was then applied to an independent case where precipitation and anaprop were present in the same region. The BCTDBZ–VPDBZ combination of feature fields proved most effective at classifying pixels correctly. Some pixels were incorrectly classified, but given the current data resolution required for purposes of data assimilation or QPE these errors were considered minimal. Some sensitivity to the reflectivity threshold was found, whereby returns from clear air appeared as the threshold was decreased. However, when the threshold was set at a reasonable level to distinguish most clear-air returns from the smallest precipitation-sized drops, (around 5 dBZ for a C-band radar) this problem was circumvented. The NBC, however, shows some promise in being able to distinguish Bragg echoes from insect echoes.
The NBC was extended via a strength of classification (SOC) index, which was constructed as a measure of the confidence with which a pixel was classified as precipitation. It was formulated as the difference of the scaled (to be in the range [0, 1]) a posteriori probabilities of weather and anaprop expressed as a proportion of the maximum possible difference. Formulated in this way, the SOC has a range [−1, 1]; however, since we are only interested in determining the confidence we have in identifying precipitation pixels, negative values (which correspond to anaprop) are discarded so the SOC is in the range [0, 1]. In practice, however, it was found that the SOC was confined to values below about 0.5. The PDF of SOC exhibited relatively constant values in the range [0.05, 0.5]. The SOC can be used to remove data below a specified threshold before processing in applications such as assimilation or QPE. Because of the relatively constant values of the PDF of SOC, increasing the SOC threshold in the range [0.05, 05] will result in an approximately linear decrease in the amount of accepted data.
The use of an NBC was found to be an effective method of distinguishing anaprop from precipitation. It should also be noted that it was effective using only a few derived feature fields and single-polarization data. This makes it useful for the bureau's radar network, which currently consists of single-polarized radars, a few of which have Doppler capability. At present, only corrected reflectivity and Doppler velocity are transmitted from the radar; however, plans exist to extend this to include spectrum width and uncorrected reflectivity. The inclusion of these variables and their associated feature fields should improve the capability of the NBC. At present, no dual-polarized radars exist in the bureau's operational network; however, the extension of the NBC to include polarimetric variables could be readily accomplished. The bureau now owns the CP2 dual-polarimetric research radar (previously owned by NCAR) so we plan to investigate the use of the NBC with polarimetric variables in the future.
Acknowledgments
We thank Drs. Alain Protat and Susan Rennie for informative discussions on many aspects of this work and also for providing feedback on an early version of the manuscript. The thoughtful and constructive comments of the three anonymous reviewers proved particularly helpful, especially with the development of the SOC index.
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Clear-air returns are returns measured when there are no meteorological targets (i.e., clouds/rain) present. They can be due to either 1) returns from birds or insects or 2) refractivity (humidity) gradients in the atmosphere, which is termed Bragg scattering.
