As described above, two types of test pattern were observed in collected data: (1) contaminated reflectivity, but normal radial velocity and spectrum width; (2) both radial velocity and spectrum width contaminated, as per reflectivity. When a test pattern occurs, reflectivity data will be contaminated and spread extensively over the radar coverage area. And for the first type of pattern, good reflectivity data might be obtained inside the corresponding radial velocity coverage range, while contaminated reflectivity data occur over the rest of the area. For the other type, both reflectivity and radial velocity are contaminated and spread over their coverage areas, and contaminated velocity will be observed as RF value. Test pattern has another obvious feature, which is that reflectivity is almost the same azimuthally, but increases with radial distance. Based on our understanding of the possible causes of test pattern, the contaminated signal of test pattern should be constant. Thus, to reflect the feature of the test pattern signal, removing the distance correction from the reflectivity first, then, the subsequent reflectivity (i.e., after removing the distance correction), which in this case reflects the test pattern signal, has small fluctuations in specific area range. Therefore, five feature parameters that can identify test pattern are proposed: effective reflectivity data percentage (RZ, subscript Z indicate reflectivity data); velocity RF data percentage (R RF, subscript RF indicates range fold); missing velocity data percentage (R M, subscript M indicates missing velocity data); averaged along-azimuth reflectivity fluctuation (RN_ r, Z, see section 3.4.1 for subscript meaning); averaged along-beam reflectivity fluctuation (RN_ a, Z, see section 3.4.2 for subscript meaning). It should be noted that identification of test pattern is for each PPI, so these feature parameters are calculated to reflect the characteristic of the entire PPI. When a PPI has been flagged as test pattern, each echo pixel in that PPI will be classified only if quality control for each echo pixel in it is still needed.
When the test pattern appears, compared to all other kinds of echoes (precipitation, clear air, and other non-meteorological echoes), it fills the entire radar coverage. Its reflectivity field has the most data pixels covered in a PPI. The effective reflectivity data percentage (RZ) is thus proposed to compute the coverage of total obtained data pixels in the total detection range. This feature parameter represents the reflectivity characteristic of the test pattern, and can be expressed as
where Zi, j is the reflectivity at gate (i, j) [units in dBZ; i and j represent the pixel's azimuth and radius, respectively (radar coordinates)]; MZ counts the total number of effective observations in a PPI; N a and N r indicate total numbers of azimuths and gates along each beam, and N a, Z and N r, Z are N a and N r for reflectivity, respectively; and I v indicates invalid-value at gate (i, j).
Being almost fully covered with effective data is one obvious feature of a test pattern PPI. In order to avoid classifying heavy precipitation cases as test pattern based on this feature, heavy stratiform precipitation and typhoon precipitation cases were chosen as precipitation echo samples in this study: namely, torrential rain events in Henan, Anhui and Hunan in 2010; typhoon rain in Haitang and Longwang in 2005; and typhoon rain in Saomei in 2006. However, no misclassifications caused by this parameter occurred during testing of these precipitation cases. Statistical results (Fig. 2a) show that the ratio of PPIs of heavy rain with RZ larger than 65% to total precipitation PPIs is 56/1800, and for RZ exceeding
60% the result is 154/1800. However, the RZ of test pattern PPIs larger than 65% to total test pattern PPIs is 114/114, and for RZ exceeding 60% the result is 117/144. As one of the parameters for recognizing a test pattern, RZ performs well, and therefore will not cause any problems for other kinds of echoes.
Comparison plots of Z and ZD in a random radial from (a) test pattern case and (b) precipitation echo case.
As mentioned above, the echo power returned from test pattern does not change much in certain fields. In order to describe this feature, a value ZD with a constant gap from the echo power is computed from observed data as
where Zi, j means the same as in Eq. (1); Di, j (units: km) represents the distance between the radar center and the pixel at position (i, j).
The variance of Z and ZD with distance plotted shows the radial at azimuth 56 (true north as azimuth 0, clockwise) for the test pattern case observed by the radar at Shenzhen at 0912 UTC 7 April 2010 (Fig. 3a), and the radial at azimuth 264 (true north as azimuth 0, clockwise) for the precipitation case observed by the radar at Zhengzhou at 0141 UTC 8 June 2010 (Fig. 3b), respectively. It is also shown in Fig. 2 that reflectivity of the test pattern increases with distance, but reflectivity of precipitation echoes changes little. ZD has no obvious changes with distance after removing the constant related to distance from Z, showing the true echo signal of the test pattern; while in contrast, the ZD of precipitation echoes changes a lot with distance.
The reflectivity Z of the test pattern changes little with azimuth; neither does ZD, the reflectivity after correction (Fig. 3a). This means the fluctuations of the echo signal of the test pattern in a specified field is small for a given pixel.
Therefore, Z f, the reflectivity fluctuation in a specific field is calculated as
Here, subscript f indicates fluctuation of ZD. As shown in Fig. 4, each pixel of the test pattern has a small Z f in the
specified field (11×11 in this study). Comparing the Z f value between the test pattern case and the precipitation case from the data in Fig. 3, it is obvious in Fig. 4 that the Z f of the test pattern is smaller than 1, while the precipitation echo is the opposite. Because of this feature of test pattern, these two parameters are proposed as candidates for identifying test pattern.
Comparison plot of mean variation from corrected reflectivity Z f of the same case in Fig. 2.
Scatter diagram of the five feature parameters from all samples: test pattern PPI (green dots); precipitation echo PPI (yellow dots); clear air echo PPI (blue dots); and other non-meteorological echo PPI (red dots). (a) RZ (%); (b) R RF (%); (c) R M (%); (d) RN_ r, Z (%); (e) RN_ a, Z (%).
Probability distribution [P (%)] of five feature parameters collected from the test pattern (long/short dashed line), precipitation echo (solid line), clear air echo (dot-dashed line) and other non-meteorological echo samples (dashed line): (a) RZ (%); (b) R RF (%); (c) R M (%); (d) RN_ r, Z (%); (e) RN_ a, Z (%).
Five test pattern identified membership functions plots: (a) RZ (%); (b) R RF (%); (c) R M (%); (d) RN_ r, Z (%); (e) RN_ a, Z (%).42mm
The first three parameters mentioned above are computed directly using the whole PPI data. Two more are computed as follows, first in a radial (or a range circle), and then in the entire PPI. The reason for doing this are: (1) test pattern identification is aimed at each PPI, and therefore the calculated parameters must represent the feature of the entire PPI; and (2) a test pattern does not always show as a full circle all of the time, but as a semicircle, as fan-shaped etc. Thus, it would be very useful to identify these typical test pattern using the radial (or range circle) parameter to present the feature of the entire PPI. When PPIs that have been identified as test pattern need to be processed, especially for those that have heavy precipitation information inlayed, it would be helpful to determine whether a radial is contaminated or not by calculating the radial parameter. Then, combined with other parameters, even whether or not a pixel is contaminated can be determined.
3.4.1. Averaged along-azimuth reflectivityfluctuation(RNr, Z)
From the above analysis, the average fluctuation of Z f in the field from corrected reflectivity (ZD) has been computed, and Z f is small for test pattern. In order to decide whether the PPI is a test pattern, the operation should be performed on the total PPI. First, the gate with small Z f (smaller than 1) is counted along-azimuth, presented by MZ_ f in Eq. (6); and M v in Eq. (6) counts the valid Z f along-azimuth; then, comes the percentage R a of small Z f in a circle (the total pixel number is 360 because of organizing radar data within interval of 1°); for lower tilts in SA/B radar, 460 (460 gates in a radial mean 460 range circles) R a values obtained. To represent the feature of the whole PPI, R a values are counted as percentages in range circle as long the value is larger than 60%, while RN_ r, Z presents the feature of the whole PPI. Mathematically, R a and RN_ r, Z are defined as
The subscript of RN_ r, Z indicates that the last step of calculating RN_ r, Z is along-bean. Because the corrected reflectivity (ZD) of the test pattern changes little with azimuth, as mentioned above, the RN_ r, Z of the test pattern is large for precipitation and other kinds of echoes. RN_ r, Z becomes small, and even reaches 0 at some gates.
3.4.2. Averaged along-beam reflectivity fluctuation (RNa, z)
Likewise, M v in Eq. (8) counts the valid Z f along-beam, then data pixels with small Z f(<1) can be counted along a radial to percentage small Z f along-beam, which is presented by R r (for lower tilts in SA/B radar, the total along-beam number is 460 because of 460 gates in a radial). Three hundred and sixty R r values are obtained because organizational radar data have azimuth intervals of 1°. R r with values larger than 50% are counted, which leads to the RNa, Z that can present the feature of the whole PPI. R r and RNa, Z are defined as
MZf is the same as in Eq. (6). The subscript of RNa, Z indicates that the last step of calculating RN_ a, Z is along-azimuth. Also, RN_ a, Z for the test pattern is much larger than other kinds of echoes.
In the above formulas, R a and R r are the percentages of small averaged reflectivity fluctuation (Z f) along-azimuth and along-beam, respectively; these then lead to the percentage of the whole PPI. For those flagged as test pattern, R r (R a) is used to determine whether or not a beam (azimuth) is contaminated; together with other parameters, such as R a(R r), Z f and R M, an echo pixel can be determined as to whether or not it is contaminated by a test pattern. The steps for checking and removing test pattern contamination in pixels will be detailed in section 5.2.
Five feature parameters were statistically analyzed for the PPIs, which included 144 test pattern PPIs, 1800 precipitation PPIs, 565 clear air PPIs, 723 other kinds of clutter PPIs (Fig. 2). As shown in Fig. 2, the five feature parameters of the test pattern have larger values compared to all other kinds of echoes, but the test pattern could not be recognized by only one of the parameters. Therefore, the purpose of the study is to recognize test pattern PPIs as much as possible without misjudging all other kinds of echo (precipitation echo, clear air echo, electromagnetic interference and ground clutter echo) PPIs.