ERAD 2008 - THE FIFTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY
Analysis of the mean and the variability of the vertical profile of reflectivity over Belgium
Bernard Mohymont and Laurent Delobbe Royal Meteorological Institute of Belgium
Two types of algorithms for partitioning precipitation zones based on reflectivity radar data have been proposed in the literature. The first type of algorithms consists in identifying the bright band related to stratiform precipitation (Collier et al., 1980; Sanchez-Diezma et al., 2000; Gourley, 2003). The main drawback of such algorithms is that they are not able to be applied further than the distance where the lowest PPI starts to be affected by the bright band, where the observed VPRs do not capture the bright band peak. Sanchez-Diezma et al. (2000) found for their algorithm a detection limit of 70 km with a beam width of the order of 1°. The second type of algorithms searches for convective zones by mean of a background-exceedence criterion (Churchill and Houze Jr., 1984; Steiner et al., 1995). This criterion consists in detecting reflectivity peakedness on a horizontal reflectivity map as a signature of convective precipitation. In summary, the first type of algorithm searches for stratiform zones whereas the second type of algorithm searches for convective zones. We have chosen to implement an algorithm of the second type and in particular the Steiner algorithm (Steiner et al., 1995) for two reasons. It is easy to implement and it does not underestimate (if its parameters are well calibrated) the stratiform zones. We have adapted this algorithm for the Belgian climate. The original Steiner separation algorithm works on Cartesian-gridded reflectivity data at an altitude of 3 km with a mesh size of 2 km. The needed data are obtained from a volume file. The Steiner algorithm works in three steps. These steps are described in Steiner et al. (2005) as follows: 1) Intensity step: Any grid point in the radar reflectivity field presenting a reflectivity higher than or equal to 40 dBZ is labeled as a convective center. 2) Peakedness step: Any grid point not labeled as convective center in the first step but which exceeds the average intensity taken over the surrounding background by at least a certain reflectivity difference threshold is labeled as a convective center. The background intensity is calculated as the linear average of the nonzero values of reflectivity within a radius of 11 km around the grid point. 3) Surrounding area step: For each grid point labeled as convective by one of the two first criteria all surrounding grid points within an intensitydependent radius around that grid point are also labeled as convective points. Steiner developed his algorithm for the Tropics where the 0°C level is usually around 5 km altitude. So most of the
1. Introduction Various methods have been proposed in the literature to correct the errors arising from nonuniform vertical profiles of reflectivity (VPR). All these methods consist in estimating the shape of the VPR and to use it for extrapolating the radar reflectivities measured at high altitude towards ground level. These methods require an assumption on the spatial homogeneity of the VPR over appropriate subdomains during a considered time step. This assumption of spatial homogeneity must therefore ideally be verified in order to apply any correction. In this paper we will analyze the mean and the spatial and temporal variability of the VPR over Belgium for the years 2005 and 2006. The data are measured by the Wideumont radar in Belgium. It is a C-band Doppler radar that performs a 5elevation scan from 0.3° to 6.0° every 5 minutes and a 10elevation scan from 0.5° to 17.5° every 15 minutes. Some relevant parameters of the 10-elevation scan are given in Delobbe and Holleman (2006). The final objective of this study is to characterize the spatial and temporal variability of VPRs for different types of meteorological situations and to determine consistent spatial and temporal scales for VPR identification and correction. We will first describe an adaptation for Belgium of the Steiner algorithm aimed at separating convective from stratiform precipitation. Some results will be presented. We will also present the yearly mean VPR obtained from one Belgian radar. Two types of climatological VPR can be calculated: one for the stratiform and one for the convective zones. Then we will develop the theory related to variograms applied on VPRs. We will restrict our analysis to VPRs measured inside stratiform zones. Finally results concerning the spatial and temporal decorrelation distances between VPRs will be presented. 2. The Steiner algorithm adapted for Belgium As explained in the introduction, a VPR correction scheme consists in extrapolating the measurements taken aloft towards the level of the ground by using the shape of a VPR estimated beforehand. It appears that convective VPRs differ from stratiform VPRs. Convective VPRs show larger values of reflectivity and have a large height extension (up to 12 km). Stratiform VPRs usually show an enhanced layer of reflectivity (called the bright band) due to the melting of hydrometeors below the freezing level as well as a decrease of the reflectivity with altitude above the bright band. As a consequence a VPR correction scheme is less crucial for the convective zones than for the stratiform zones. One must therefore design an algorithm that is able to differentiate convective zones from stratiform zones.
ERAD 2008 - THE FIFTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY time the algorithm works below the bright band and is not affected by it. We had to modify the algorithm described above in order to apply it to the Belgian climate. In Belgium the altitude of the isotherm ºC varies between 0 and 5 km. It means that the Steiner algorithm in its initial form is affected by the bright band. It is necessary to avoid false detected convective zones when one of the PPIs intercepts the bright band. The principal modification made is that we work at two different altitudes (2.5 km and 5 km) and thus apply the Steiner algorithm twice. Close to the radar, the values of the highest PPI are used until the highest beam reaches the two selected altitudes. Far from the radar (when the altitude of the lowest beam is larger than one of the selected altitudes) the values of the lowest PPI are used. The separation between convective, stratiform and noprecipitation zones is done using the following criteria: 1) The final label for a grid point will be convective if it is labeled twice as convective at the two selected altitudes and if its reflectivity is larger than a certain threshold (25 dBZ) at the lower altitude (2.5 km). 2) The final label for a grid point will be 'no precipitation' if its reflectivity value is below the 7 dBZ threshold at the lower altitude. 3) The final label for a grid point will be stratiform otherwise (i. e. if it is neither a convective point and neither a no-precipitation point). Working at an additional higher altitude allows the algorithm to avoid false detected convective zones based only on the detection at the lower altitude. Moreover if a stratiform zone is detected at the lower level, the final label will be stratiform. A 25 dBZ reflectivity threshold was added to avoid the algorithm to detect a convective zone with too small values of reflectivity. One example of result of the modified Steiner algorithm is shown on Fig. 1. The corresponding Pseudo CAPPI map is given in Fig. 2. For this example the algorithm performs globally well. The convective and stratiform zones visible on the Pseudo-Cappi map are both well detected. However the algorithm is not perfect. Other examples (not shown) show that: 1. Clutter due to anomalous propagation is identified as stratiform precipitation. Further investigation is needed to solve this problem. 2. Some shallow convective zones are not seen by the algorithm. When the convection does not reach the altitude of 5 km, the algorithm diagnoses the zone of precipitation as stratiform (or as no precipitation) at the highest level and thus the final label is stratiform. 3. Some very weak levels of rainfall intensity are diagnosed as 'no precipitation' by the modified Steiner algorithm. Let us stress that a validation methodology of a separation algorithm is difficult to elaborate, the comparison being limited by the fact that we do not really know where are the ‘real’ convective and stratiform zones. Fig. 2. Pseudo CAPPI at 1500 m for the radar of Wideumont on 30/07/2002 at 15:15 UTC. 3. Climatological VPR A climatological VPR is supposed to be a mean VPR calculated over a long period of time (for instance 30 years). RMI archives volume scans of the radar of Wideumont since 2002. In this study we have calculated yearly and seasonnal mean VPRs for the years 2005 and 2006. These mean VPRs can then serve as input for a simple climatological VPR correction scheme. The followed methodology is based on the work of Franco et al. (2006). For each volume scan the Mean Apparent Vertical Profile of Reflectivity (MAVPR) is estimated in a annular sector close to the radar. The factors that must be taken into account in order to choose the best sector are discussed in Franco et al. (2006). For our study the internal and external radii of the sector have been fixed to the values of 10 km and 50 km respectively. The estimation of the MAVPR is done in three steps. The radar image is first separated into stratiform and Fig. 1. Output of the modified Steiner algorithm for Belgium on 30/07/2002 at 15:15 UTC. Red points correspond to convective zones, blue points correspond to stratiform zones and black points correspond to no precipitation zones.
ERAD 2008 - THE FIFTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY convective zones by means of the modified Steiner algorithm for Belgium. Then the apparent VPRs observed in the annular sector close to the radar are normalized by subtracting the profile by the reflectivity (in dBZ) at a reference height. In our study this reference height has been fixed to the value of 3 km. For a given profile, the value of reflectivity at the reference height is obtained by linear vertical interpolation of the dBZ values. Finally a vertical moving window of fixed size (200 m) is used to average the apparent VPRs (either convective or stratiform) in the chosen sector in order to obtain the estimated MAVPR. The averaging process is done separately for the convective and stratiform VPRs. The estimation procedure gives for each volume scan a convective and a stratiform MAVPR. Note that one or both MAVPRs can be undefined. Three types of averaging procedures can be used. We can average in Zvalues and then convert the result in dBZ. Another possibility is to average in dBZ values. We can also use the median which is more robust and gives the same value when one works in Z or dBZ values. We have chosen in this work to use the median to calculate the MAVPRs. The seasonal and yearly mean VPRs are obtained as an average (in dBZ) of all the individual MAVPRs. The calculation of those MAVPRs has been done using the 10-elevation volume scan of the radar of Wideumont.
Fig. 4. Yearly mean convective VPR for the year 2005. Fig. 4. shows the yearly mean convective VPR for the year 2005. We observe that the profile is more or less constant between 2 km and 4 km and shows a decrease of its reflectivity above 4 km. The difference in dBZ between the maximum reflectivity of this profile and the reflectivity at the altitude of 1 km is equal to 9.2 dBZ. For the year 2006 we obtain a value of 8.1 dBZ. It seems that on the basis of these mean convective profiles a VPR correction scheme would also be necessary for the convective zones.
Fig. 3. Yearly mean stratiform VPR for the year 2005. The red curve on Fig. 3 shows the yearly mean VPR obtained for 2005 when only the stratiform MAVPRs are averaged. The two black curves are a measure of the dispersion of all the individual MAVPRs (one standard deviation is used). We observe an average bright band in the lowest part of the profile and a linear decrease of the reflectivity above 4 km. The yearly mean stratiform VPR obtained for the year 2006 as well as all the seasonal mean stratiform VPRs present similar features. The difference in dBZ between the maximum reflectivity of the bright band and the reflectivity at the altitude of 1 km is equal to 3.7 dBZ for the yearly mean stratiform VPR of the year 2005. For the year 2006 we obtain a slightly larger difference (4.0 dBZ).
Fig. 5. Yearly mean stratiform VPR for the year 2006. Fig. 5. shows the yearly mean stratiform VPR obtained for the year 2006. Note that the seasonnal convective mean VPRs are badly defined for the winter season: for this season not enough convective pixels are present. We have analyzed the seasonal variability of the slope of the mean VPR (above 4km) for the stratiform case. Results of this analysis are contained in Table 1.
ERAD 2008 - THE FIFTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY Season\Year 2005 2006 Entire year -4.0 -4.6 Spring -3.1 -4.7 Summer -3.9 -4.1 Autumn -4.6 -4.7 Winter -5.3 -5.2 Table 1. Seasonal variations of the slope of the mean VPR above 4km for the stratiform case. All values are expressed in dBZ/km. We observe that except in spring the values of the slopes are similar for the two years analyzed. Moreover the strongest slopes are encountered in winter. 4. Variograms of VPRs In Mohymont and Delobbe (2008) a methodology to calculate variograms of VPRs was presented. We also proposed a definition for a distance between two VPRs. This methodology was used in the framework of a spatial analysis. Is is nevertheless straightforward to apply it for a temporal analysis as well: the spatial variable x must simply be replaced by the temporal variable t. The two following sections make use of this methodology to assess the variograms. 4.1 Temporal analysis of the VPR In order to assess the decorrelation time between VPRs we have calculated seasonal temporal variograms for the years 2005 and 2006. Those variograms are based on the series of stratiform MAVPRs calculated every 15 min from the 10elevation scan. An exponential model of variogram described in Mohymont and Delobbe (2008) has been fitted to each seasonnal experimental variogram. The three parameters of this model are the nugget variance, the magnitude of the sill and the decorrelation time. variogram obtained for given time t is a mean distance between all couples of MAVPRs separated by the time t. Table 2 gathers the values of the decorrelation times obtained for the eight seasons that we have analyzed.
Season\Year Spring Summer Autumn Winter
2005 47.9 46.8 47.9 26.1
2006 22.8 48.0 22.5 26.8
Table 2. Seasonal decorrelation times obtained for the eight seasons analyzed. All values are expressed in hours. W e observe that the decorrelation time between MAVPRs obtained by our methodology is comprised between one and two days. We also observe that the decorrelation times for spring 2005 and autumn 2005 are about two times as high as the corresponding values for spring and autumn 2006. Further investigation is needed and in particular other years are to be analyzed in order to assess if this observation is statistically significant. 4.2 Spatial analysis of the VPR In Mohymont and Delobbe (2008) some examples of spatial variograms of VPRs for a few cases were presented. The decorrelation distance for those cases was assessed. We present here a statistical study of the spatial decorrelation distance between VPRs based on the whole year 2006. From each volume file of the 10-elevation scan a spatial variogram is calculated. This spatial variogram is based on VPRs which are situated in the vicinity of the radar. More precisely only pixels that are situated at a distance smaller than 50 km from the radar are taken into account. Moreover a minimum threshold on the percentage of rainy pixels in the studied domain has been fixed (the chosen value is 40 %). The experimental variogram was calculated up to a distance of 50 km. The total number of analyzed cases is equal to 1558. Out of these 1558 cases, 652 cases presented a small relative error between the adjusted exponential model and the experimental variogram (smaller than 10%) as well as an estimated decorrelation distance smaller than 50 km. The mean decorrelation distance obtained for these 652 cases is equal to 26.4 km with a standard deviation equal to 11.2 km. Fig. 7 illustrates one of these cases. When looking at the dispersion of the decorrelation distance over the 652 cases it is found that the decorrelation distance varies between 6.3 km and 49.9 km. Such a large dispersion suggests that the decorrelation distance between VPRs varies strongly from one meteorological situation to another. Another consequence is that the mean decorrelation distance obtained is dependent of the chosen size of the domain for the study. Tests have shown that increasing the size of the domain increases the magnitude of the decorrelation distance. Due to the dispersion of this distance the average found is approximately equal to half the size of the chosen domain. 461 cases presented a relative error between the adjusted exponential model and the experimental variogram smaller than 10% but an estimated decorrelation distance larger than 50 km (sometimes much more larger). Fig. 8. shows one of these cases.
Fig. 6. Seasonal variogram of MAVPRs (summer 2006). The black curve represents the experimental variogram, the red dashed curve is the fitted exponential model and the two green curves show the confidence interval (one standard deviation) of the experimental variogram. Fig. 6 shows the seasonal variogram obtained for summer 2006. We observe that the variogram increases during the first hours and then reaches a sill. The value of the
ERAD 2008 - THE FIFTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY stratiform VPRs were encountered in winter. The temporal analysis of the VPR suggests that the decorrelation time between MAVPRs over a season is comprised between one and two days. The spatial analysis of the VPR reveals a large dispersion of the decorrelation distance according to the meteorological situations. About one third of the studied cases showed a decorrelation distance smaller than 50 km with a large dispersion of this distance. Another third of the cases showed a decorrelation distance larger than 50 km and for the last third of the cases the adjusted exponential model did not fit to the experimental variogram. These results show the difficulties of applying the variogram methodology to study the spatial variability of the VPR field. Acknowledgment Fig. 7. Spatial variogram of VPRs. The black dashed curve is the adjusted exponential model of variogram. The three black curves show the experimental variogram as well as a 95% confidence interval. The decorrelation distance for this case is equal to 24.0 km and the relative error equal to 3.5 %. For those cases the decorrelation distance given by the model is outside the studied domain and all that one can say is that this distance is greater than 50 km. As this value is extrapolated by the model its precision is not good enough to be taken into account in the statistics. This research is carried out with the financial support of the Belgian Federal Science Policy Office (project number MO/34/015). References Churchill, D. D. and R. A. Houze, 1984: Development and structure of winter monsoon cloud clusters on 10 December 1978. J. Atmos. Sci., 41, 933-960. Collier, C. G., S. Lovejoy, and G. L. Austin, 1980: Analysis of bright bands from 3-D radar data. Preprints, 19th Conf. on Radar Meteorology, Miami Beach, FL, Amer. Meteor. Soc., 44-47. Delobbe, L. and I. Holleman, 2006: Uncertainties in radar echo top heights used for hail detection. Meteorl. Appl., 13, 361-374. Franco, M., R. Sanchez-Diesma and D. Semperre-Torres, 2006: Improvements in weather radar rain rate estimates using a method for identifying the vertical profile of reflectivity from volume radar scans. Meteorologische Zeitschrift, Vol. 15, No 5, 521-536. Gourley, J. J., 2003: Automated detection of the bright band using WSR-88D data. Weather and Forecasting, 18, 585599. Fig. 8. Same as Fig. 7 but whith a decorrelation distance which is outside the studied domain. The decorrelation distance estimated for this case is equal to 243.4 km and the relative error equal to 9.6 %. Finally the remaining 445 cases presented a too large relative error (> 10%) between the adjusted exponential model and the experimental variogram to give acceptable results. 7. Conclusions We have presented a modified version of the Steiner algorithm for Belgium. While not perfect this algorithm seems visually to give good results. Yearly and seasonnal VPRs for the years 2005 and 2006 were presented. It was found that the strongest slopes of the mean seasonnal Steiner, M., R. A. J. Houze, and S. E. Yuter, 1995: Climatological characterization of three dimensional storm structure from operational radar and raingage data. J. Appl. Meteor., 34, 1978-2007. Mohymont and Delobbe, 2008: Is the variogram a good tool for assessing the spatial variability of vertical profiles of reflectivity? Proceedings of the International Symposium on Weather Radar and Hydrology (WRaH), Grenoble, France. Sanchez-Diezma, R., I. Zawadzki, and D. Sempere-Torres, 2000: Identification of the bright band through the analysis of volumetric radar data. Journal of Geophysical Research – D2, 105, 2225-2236.