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Radar Performance Monitoring Using the Angular Width of the Solar Image [Journal of Atmospheric and Oceanic Technology](Journal of Atmospheric and Oceanic Technology Via Acquire Media NewsEdge) ABSTRACT A method for the operational monitoring of the weather radar antenna mechanics and signal processing is presented. The method is based on the analysis of sun signals in the polar volume data produced during the operational scanning of weather radars. Depending on the hardware of the radar, the volume coverage pattern, the season, and the latitude of the radar, several tens of sun hits are found per day. The method is an extension of that for determining the weather radar antenna pointing and for monitoring the receiver stability and the differential reflectivity offset. In the method the width of the sun image in elevation and in azimuth is analyzed from the data, together with the center point position and the total power, analyzed in the earlier methods. This paper describes how the width values are obtained in the majority of cases without affecting the quality of the position and power values. Results from the daily analysis reveal signal processing features and failures that are difficult to find out otherwise in weather data. Moreover, they provide a tool for monitoring the stability of the antenna system, and hence the method has great potential for routine monitoring of radar signal processing and the antenna mechanics. Hence, it is recommended that the operational solar analysis be extended into the analysis of the width. (ProQuest: ... denotes formulae omitted.) 1. Introduction The method of using the sun signals detected from the sun at low antenna elevations during the operational scanning of a radar has been developed in a series of papers by Huuskonen and Holleman (2007) and Holleman et al. (2010a,b). Huuskonen and Holleman (2007) presented the use of signals detected from the sun at low antenna elevations for determining the weather radar antenna pointing, that is, the biases in elevation and azimuth. The method was extended by Holleman et al. (2010b) to the monitoring of the radar receiver chain stability and by Holleman et al. (2010a) to monitoring the receiver chain of the Zdr calibration. A summary of the prior work on using the solar observations is given, for example, by Huuskonen and Holleman (2007). Observations of the solar disk have also been used to determine the antenna beam shape. Puhakka et al. (2004) determined the half-power beamwidths using solar passages over a stationary antenna. Fitting data to a linear model produced larger beamwidths than using a logarithmic model, but both results were smaller than the factory values. Free et al. (2007) describe a system where the antenna scans either in azimuth or in elevation around the sun position for the determination of the beamwidths, and also give a formula to calculate the antenna beamwidth based on the observed width. In the present paper, we extend the sun-signal method to the use of the width of the sun hit distribution, for which Huuskonen and Holleman (2007) recommended that a fixed value is used in daily fits to increase the stability of the fitting. We study the widths both in the elevation and azimuth directions, especially their use in monitoring the antennamechanics and in detecting errors in the processing software. We also study the stability of the fitting and compare results with and without the widths as fitted parameters. 2. Method The automated detection of sun signatures in polar volume data from scanning weather radars is described in Huuskonen and Holleman (2007). Basically, a consistent reflectivity signal-that is, a signal from a continuous radio frequency source-at long ranges (.100 km) is searched along radials in the operational scan data. Data below 18 elevation are discarded to avoid severe refraction and to ensure that the long-range observations are above precipitation areas. Uncorrected reflectivity data are used for this analysis, as (time domain) Doppler clutter filters can attenuate the solar signal by several decibels. Depending on the hardware of the radar, the volume coverage pattern, the season, and the latitude of the radar, several tens of sun hits are found per day. As a radar signal processor usually corrects the received echoes for the range dependence and the atmospheric attenuation, the ''reflectivity'' signals from the sun increase with the range. The received solar spectral power at the antenna feed Pf (per MHz in dBm) can be calculated from the reflectivity signature as a function of the range Z(r) (dBZ) using ... (1) where Cr is the radar constant (dB) according to Probert- Jones (1962), a is the one-way gaseous attenuation (dBkm21), and Df is the receiver 3-dB bandwidth(MHz). The mean solar power Pf , averaged over range, is stored with its standard deviation, elevation, azimuth, date, and time stamp. These sun hits, when collected over a suitable period of time, show a symmetric distribution about the known positions of the sun, which has a slightly larger width in azimuth than in elevation, of which a good example is shown in Fig. 1. The distribution in linear power is well approximated by a Gaussian form, and hence the power Ps in decibels can be written as ... (2) where the coordinates x and y are defined as ... (3) ... (4) respectively, where f and u denote azimuth and elevation, ''read'' refers to the angle reading of the radar antenna, and ''sun'' refers to the calculated position of the sun for the time of observation. The observed azimuth differences are multiplied by cosusun to make them invariant to the elevation (e.g., Doviak and Zrnic 1993, p. 516). This term is especially important when analyzing widths observed at low latitudes where the sun reaches higher elevations. Note that we also assume that the biases and the widths are independent of the pointing angles, and that the microwave center of the sun is close to the center of the optical disk. Equation (2) is linear in the parameters ax to c, and thus the sun data can be easily fitted to this equation by the least squares method. Parameters ax and ay are related to the widths of the distributions of the x and y values, respectively; parameters bx and by to the elevation and azimuth biases, respectively; and parameter c to the peak solar power. The elevation width Du, the azimuth width Df, the elevation bias Bu, the azimuth bias Bf, and the power Po can be calculated from the linear parameters ... (5) ... (6) ... (7) respectively. The widths are obtained from Eq. (5) when the corresponding parameter ax,y is negative. The fitting is done as a two-stage process. After the first fit all points farther away than a given threshold from the best-fit line are removed, and the second fit is done to the remaining set. A threshold of 1 dB has been found to work well with our datasets. When data from different elevations are analyzed together, the solar elevation needs to be corrected for the effects of refraction. We use the new analytical formulas for the atmospheric refraction of radio waves, which are consistent with the commonly used k model or the 4/ 3 model (Holleman andHuuskonen 2013). As the solar signal traverses all of the atmosphere, the expected value of k is less than 4/ 3, which is valid close to the surface. Hence, we use k 5 5/ 4, which best fits the model calculations and radar observations according to Holleman and Huuskonen (2013). 3. Data Since 1997 the Royal Netherlands Meteorological Institute (KNMI) maintains an operational network of two identical C-band Doppler weather radars. Every 5 min the radars perform a 14-elevation volume scan between 0.38 and 258 elevations, and only the lowest elevation is scanned in long pulse. The pulse repetition frequency (PRF) increases from 250Hz (single PRF) at the lowest elevation to dual PRF with 900/1200Hz at the highest elevations. At the same time, the rotation velocity of the antenna increases from 158 to 368 s21. The FinnishMeteorological Institute (FMI) operates a network of eight C-band Doppler weather radars, of which the data from seven radars are used in this study. Every 15min the radars perform an 11-elevation volume scan between 0.38 and 458 elevations, where six elevations up to 98 are scanned in single PRF with 570Hz, and the others in dual PRF. Every 5min, 6 of these 11 elevations are repeated. A recent description of the FMI network is given by Saltikoffet al. (2010) and of the KNMI network by Beekhuis and Holleman (2008). For convenience some radar properties, important for the present study, are shown in Table 1. 4. Results and discussion a. Time series and sun images, KNMI Den Helder radar Figure 2 shows time series of elevation and azimuth widths of the sun image from the KNMI Den Helder radar. The azimuth width is around 1.88 until October and then the width drops to 1.48, whereas the elevation width is about 1.18, with a small drop coincident to the decrease in the azimuth width. A sun image, made of all sun hits collected over one month, is shown in Fig. 3 for periods of the wider and narrower azimuth widths. All power values have been scaled on a daily basis using the fitted power values to reduce the scatter produced by the sun flux changes occurring over the month. Comparison of the two scatterplots shows clearly that the distribution of the sun hits in azimuth is wider in January 2009 than in November 2009, in accordance with the results in Fig. 2. In the elevation direction, the image is a convolution of the antenna beam pattern with the sun disk. Hence the observed width, which is somewhat larger than the antenna beamwidth, is as expected. The widths in azimuth, on the other hand, are surprisingly large, and much larger than the width of the sun image shown in Fig. 1. The width in azimuth is affected, in addition to the sun and the antenna beam pattern, by the integration carried out in azimuth while the antenna is rotating. A typical integration window in azimuth is 18 wide, which produces azimuth widths only slightly larger than the corresponding elevation widths, as seen in Fig. 1. An azimuth width significantly larger than the elevation width thus indicates that the integration window must have been wider than the typical 18 window. A correction in the software of the signal processor was done in October 2009, after which the azimuth width dropped substantially. This case demonstrates the benefit of using the sun hit data. This processor artifact was not clearly visible in the precipitation data, because the precipitation objects are typically much larger than the azimuth width and hence the additional averaging is hidden. No operational analysis of the sun image width was done at the time, and likely the increased width would have been noticed sooner, if the width results had been available on a daily basis. b. Time series and sun images, FMI Anjalankoski radar Figure 4 shows the elevation and azimuth widths of the sun image from the FMI Anjalankoski radar during 2009. The vertical dotted lines indicate three important dates related to the replacement of the radar in September 2009. The first two lines indicate the date of stopping the operation of the old radar (which was similar to, for example, the Kuopio radar in Table 1) and the date of starting the operations of the new radar. The third line indicates the date when the signal processing was in the final configuration. The corresponding scatterplots are given in Fig. 5 for the old and new radars, and in Fig. 1 for the new radar in its final configuration. In the azimuth direction, three different cases are evident. The azimuth width of the sun image for the old system is about 1.48 and that for the new system is finally close to 1.08. There is a gap of about 30 days in between where no azimuth widths were obtained, only elevation widths. The corresponding scatterplots show clearly why no azimuth widths are available. The distribution is formed by two separate regions, which are symmetric in elevation, and in which the highest power values are on the left-hand edge, close to the nominal direction of the antenna. A polynomial fit to this dataset produces a positive second-order coefficient of the polynomial in Eq. (2) in the azimuth direction, and hence the square of the width became negative. A study of the signal processing revealed that this was caused by a bug in the 2D speckle filtering routine that copied the same data to adjacent azimuth bins. After the origin of the fault was located, and the 2D filtering disabled (and later the routine repaired), the distribution again resumed its symmetrical form, and both width values became available. This feature, just as the too-wide azimuth integration window at Den Helder, was not clearly visible in the precipitation data. After its discovery from the sun data, it could also be seen as doubled edges, or shadows, at one edge of the precipitation regions. The analysis of the width of the sun image was already in a preoperational phase when the error occurred, and hence the missing azimuth width was noticed readily. c. Failure of azimuth synchro system, FMI Kuopio radar Figure 6 shows the azimuth offset and the azimuth width of the sun image for a failure of the azimuth synchro system. On 26 March 2013 (first vertical line), the antenna azimuth offset suddenly jumped by several degrees, and simultaneously the azimuth width increased and remained abnormally high. On 5 April (second vertical line), the azimuth syncro belt, which was found to be loose, was tightened and the antenna pointing corrected. The antenna system did not, however, resume its normal operational status; the azimuth width and the day-to-day variation of azimuth offset values remained larger than normal.On 23April the synchro belt was changed, aswell as the synchro unit, whose bearings were found to be broken.After this the antenna systemresumed its normal status. This case demonstrates the value of sun monitoring, which indicated after the first corrective action that the system did not yet perform as expected. d. Image width statistics in elevation Figure 7 shows statistics of the elevation width of the sun image, based on one month of data. Radars with similar hardware and/or age are grouped together. The elevation widths of the five radars from the 1990s, all of Meteor 360 type, are about 10% larger than the antenna beamwidth, whereas the elevation widths of the four newer radars are closer to the beamwidth indicated by the horizontal lines in the figures. Also, the distribution of the widths, as measured by the difference of the first and third quartiles, is smaller for these radars. The elevation width is determined by the sun disk and the antenna beamwidth, and influenced by the stability of the antenna mechanics. The larger elevation widths of the older radars are attributed to their older antenna mechanics, especially the KNMI De Bilt radar (DBL; refer to Table 1 for the full name of each radar code) is showing a large elevation width and a huge scatter. If we assume that the increased width of the sun image is caused by random variations in the antenna pointing, then a relation between the mean width and variance can be derived. The mean is related to the variations of the deviations within a day, and the variance is related to the day-to-day variations. With normally distributed deviations (mean mu and variance s2u ), the distribution of the estimated variance s2u resembles a x2 distribution with Nhits degrees of freedom: ... (8) where s2u is the increase in the width of the sun image, which can be explained by random antenna pointing variations. The x2(k) distribution has mean k and variance 2k (see, e.g., Mood et al. 1974). Hence, the mean and variance of s2u can be expressed as ... (9) ... (10) So, the standard deviation can be expressed in terms of the mean: ... (11) Hence, there is a linear relation between the mean and the standard deviation, where the slope depends on the number of recorded sun hits per day. This is also what is observed in Fig. 7, where for the De Bilt radar a larger width value is accompanied by a wider distribution. e. Image width statistics in azimuth Figure 8 shows statistics of the azimuth width of the sun image, just as in Fig. 7 for elevation. For the azimuth widths, the span of width values is much larger than for the elevation widths. The azimuth width is, in addition to the factors affecting also the elevation width, affected by the signal processing. One KNMI Meteor 360 radar (DBL) has a much larger azimuth width and scatter than the other one (DHL) and the three FMIMeteor 360 radars (KOR, KUO, UTA), which in turn have wider widths than the newer FMI radars (VIM, VAN, ANJ, IKA). For the seven FMI radars, the azimuth widths repeat the pattern observed in elevation. The older radars show larger widths and wider width distributions that can be attributed to the antenna mechanics of these radars.Note that the formalism of section 4d also applies to azimuth. The difference between the old and new radars is also partly caused by themore flexible signal processing of the new radars in which narrower window functions can be applied in the processing. The azimuth width distribution of the DHL radar is comparable to those of the old FMI radars, but the width distribution of the DBL radar is clearly too wide. The statistics suggest that the increased width of the sun image is caused by problems with the antenna mechanics. In fact, the azimuth synchro of the De Bilt radar was repaired in June 2012 because it had problems with its bearings and after that its width statistics became much close to those of theDen Helder radar. Even though the problems concerned azimuth only, the elevation width increases as well because the errors of the elevation and azimuth widths are correlated because of their functional dependence in Eq. (2). f. Comparison of results with fixed and fitted image width values To analyze the stability of the full five-parameter fit, a dataset was reanalyzed so that the widths were fixed to the mean values obtained from the full fit.Asummary of the results is shown in Table 2, which gives the mean results of analysis over 2 months for the FMI Anjalankoski radar. The analysis was repeated for five radars in total, and the results shown in the table are representative. The results indicate that the antenna pointing results, and naturally the width results, are identical on average. The antenna pointing results have a very small standard deviation. A comparison against the solar flux values from the Dominion Radio Astrophysical Observatory (DRAO) shows that the flux results agree but that the scatter of power values fromthe full fit is larger than fromthe threeparameter fit. This indicates that the fluctuations seen in the fitted image widths are at least partly random and do not reflect true changes in the widths. On the other hand, the five-parameter model has more degrees of freedom and can adjust better to the dataset in the two-stage fitting process. Hence, fewer data are discarded after the first fit, although both fitting processes have the same data points with which to start. The overall quality of the fit is better as indicated by the cost function, which is x2 divided by the number of degrees of freedom: ... (12) where Nhits is the number of sun hits, Npar is the number of model parameters, Pm is the observed power, s2 m is its variance, andPs is the fitted power from Eq. (2).Theresults demonstrate that we can use the five-parameter model in the fitting.We obtain a better fit to the data at the expense of an increasing random error of the power (by 0.06 dB). 5. Conclusions The use of a full five-parameter fit in the solar analysis image brings many benefits. First of all, there is no need to find suitable width values for use in a three-parameter fit; second, there is no need to monitor whether the width values chosen remain valid. On the other hand, adding two more parameters increases the scatter of the analysis results. Moreover, there might be an increased risk for failures in the fitting, so that instead of receiving new information on widths, one would lose the offset and power results. Our experience with the KNMI and FMI radar data tells that the typical amounts of sun hits obtained with the radars are sufficient to determine all parameters on a daily basis. Failure of the five-parameter fit should be taken as a sign that there may be an error in the signal processing chain. A possible drawback of a five-parameter fit could be a lowering of the quality of the antenna offset values, which continue to be the main benefit of the solar monitoring. It is fortunate that the antenna offsets are statistically independent of the widths, and that the fitting of the widths does not increase the scatter of the antenna offset results. Hence, we will obtain additional information without decreasing the quality of the antenna offset results. The main application of the image width results is in the monitoring of the signal processing and the antenna mechanics. The elevation widths of the sun image are determined by the antenna beamwidth and the precision of the antenna mechanics only, but the azimuth width of the sun image is influenced in addition by the signal processing. The typical sizes of meteorological objects are (naturally) much larger than the azimuth beamwidths, and hence a study of weather targets will not reveal signal processing problems of the beamwidth size or smaller. In one of our two signal processing examples, a bug in the signal processing software copied the same data to adjacent azimuth bins. The result was that the analysis was not able to produce azimuth width values at all. The effect was also vaguely visible as doubled edges of precipitation areas, but locating the cause of the shadows might have been a tedious job without seeing the ''dual sun.'' The sun image pointed out that the effect was caused by signal processing. In the other example, the signal processor caused a significant broadening of the azimuth bin. Also, the case of the azimuth synchro system failure demonstrates that the monitoring of the width is valuable. Any increase from the base value is a symptom of problems in the antenna system. We have shown that time series of widths and width statistics provide important information on (malfunctioning of) the signal processing and on the health of the antenna mechanics. Based on this we recommend that the widths be included in all operational analysis of the sun hits. Acknowledgments. The numerical analysis and the figures have been prepared using the R software (R Development Core Team 2011). REFERENCES Beekhuis, H., and I. Holleman, 2008: From pulse to product: Highlights of the digital-IF upgrade of the Dutch national radar network. Proc. Fifth European Conf. of Radar Meteorology and Hydrology (ERAD), Helsinki, Finland, Finnish Meteorological Institute, 120. [Available online at http://www.knmi.nl/publications/fulltexts/ erad2008drup_0120.pdf.] Doviak, R. J., and D. S. 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Res., 15, 579-594. ASKO HUUSKONEN, MIKKO KURRI, AND HARRI HOHTI Finnish Meteorological Institute, Helsinki, Finland HANS BEEKHUIS AND HIDDE LEIJNSE Royal Netherlands Meteorological Institute (KNMI), De Bilt, Netherlands IWAN HOLLEMAN Institute for Molecules and Materials, Radboud University Nijmegen, Nijmegen, Netherlands (Manuscript received 18 November 2013, in final form 9 May 2014) Corresponding author address: Asko Huuskonen, Finnish Meteorological Institute, P.O. Box 503, Helsinki SF-00101, Finland. E-mail: [email protected] (c) 2014 American Meteorological Society |