Rain cell size distribution inferred from rain gauge and radar data in the UK

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1 RADIO SCIENCE, VOL. 44,, doi: /2008rs003984, 2009 Rain cell size distribution inferred from rain gauge and radar data in the UK Sahena Begum 1 and Ifiok E. Otung 1 Received 1 August 2008; revised 8 January 2009; accepted 18 February 2009; published 11 April [1] Knowledge of rain cell size distribution is relevant for the modeling and design of Earth-space communication systems. Long-term rain rate time series were processed to determine the spatial structure of rain cells by applying the synthetic storm technique assuming some known value of storm translation speed. Using a 3 1/2 year record of rain rate at Sparsholt, UK, the size distributions of rain fields were determined using rain cell translation speeds derived from analysis of radar plan position indicator scans. The results were compared with distributions of rain cell sizes determined directly from 66 radar reflectivity scans performed in seven rain events and found to give cell sizes in the region of 10 km for rain cells of threshold 20 mm/h. Citation: Begum, S., and I. E. Otung (2009), Rain cell size distribution inferred from rain gauge and radar data in the UK, Radio Sci., 44,, doi: /2008rs Introduction [2] Reflectivity fields of precipitation from high resolution scanning radar show structures of various sizes often embedded in each other. Although precipitation intensities are highly variable in space and time they manifest some organization as higher intensity cores are clustered in features of various scales of cells measuring a few square kilometres most of the time. If a cell is sufficiently long-lived, it is possible to track their movement through successive scans separated in time. [3] Scanning Doppler radar being coherent can measure the phase of the returning signal, thus enabling the determination of the radial velocity component of the targets. Wind movement is in general three-dimensional and varies over time and space. Complete characterization of the wind movement requires simultaneous measurements using multiple Doppler radars. However, making some simplifying assumptions about the structure of the observed wind field, a single Doppler radar measurement will suffice to extract the wind field [Sauvageot, 1992]. [4] In this paper, rain cell translation speed is obtained by tracking cells through correlation analysis of consecutive PPI (plan position indicator) radar scans in section 3. The translation speed so obtained is compared with the wind speed derived from corresponding Doppler radar measurements and with scaled ground measured wind 1 Faculty of Advanced Technology, University of Glamorgan, Pontypridd, UK. Copyright 2009 by the American Geophysical Union /09/2008RS speed (section 4). In section 5, rain cell diameters are determined by applying this cell translation speed to transform rain rate time series into a spatial series. PPI radar scans of these rain events are analyzed to directly determine their cell sizes. A comparison of the rain cell size distributions resulting from the two methods is also presented. 2. Data Sets [5] Reflectivity, dbz (mm 6 mm 3 ) and Doppler radial velocity (m/s) available in 300 range gates, each of 300 m length at 0.25 s interval from CAMRa (Chilbolton Advanced Meteorological Radar) situated at Chilbolton UK ( N, W) were used for 7 events on 26 September, 8 October and 12 May in 2001, 1 July, 22 September and 31 October in 2003 and on 23 March in The reflectivity data is calibrated and noise free. The unambiguous velocity measured by Chilbolton radar is ±15 m/s and velocity measured beyond these ranges is unfolded. Rain gauge data by a drop counting rain gauge recorded at Sparsholt, 7.8 km from Chilbolton were used for the whole year of 2000, 2003, 2005 and January 2004 to May Wind measurements at Brize Norton, 63 km from the radar location, were also used for the corresponding periods of radar observation. 3. Rain Cell Translation Velocity [6] Radar can provide information on the horizontal structure of storm (rain) cell from PPI measurements of the radar reflectivity factor through constant elevation slices. 1of7

Figure 1. Identified rain cell on PPI on 23 March 2004. (a) Cell in the previous scan. (b) Correlated cell in the next scan.

2 Figure 1. Identified rain cell on PPI on 23 March (a) Cell in the previous scan. (b) Correlated cell in the next scan. Different definitions of rain cell are found in the scientific literature with different meanings [Capsoni et al., 1987]. In the work of Crane [1979], rain cell refers to a volume in which convective phenomena take place. In other approach, a rain cell is considered to be an entity constituted by an area inside of which the rain rate (or the radar reflectivity) is equal to or higher than a specified threshold value. This definition implies that the cell is continuous and that along the contour that bounds it, the rain rate is at the threshold value. The area where rain rate falls below threshold is ignored [Sauvageot et al., 1999]. [7] A rain cell defined by the latter approach can be identified in consecutive PPI scans separated by a fixed time interval. To track the movement of the rain cell a correlation technique is employed, which partitions the reflectivity fields of each scan into blocks and determines by trial and error the displacement of the previous scan that maximizes its correlation with the next scan. Dividing this displacement by the interscan interval yields the cell translation velocity. Cross-correlation techniques treat the data as a two-dimensional field from which the movement of features may be inferred [Dixon and Wiener, 1993]. [8] A correct match of each cell to its corresponding appearance in a subsequent scan is complicated by the physical changes that rain cells exhibit between radar scans. For example a rain cell might decay, grow, merge or split between observations. Moreover, a rain cell might move independently in directions that differ from that of the whole radar image. The movement of a rain cell can be either a propagation, whereby a portion of the cell movement arises from growth on new echoes, or a translation, which is the motion of the cell centroid not resulting from propagation [Battan, 1973]. [9] To identify a rain cell within the precipitation areas, a threshold reflectivity value of 35 dbz was used [Dixon and Wiener, 1993]. When tracking a previous rain cell (at time t 1 ) based on a current scan (at time t 2 ), difficulties arise as new cells can appear and existing cells can split, merge or disappear. There are five possible scenarios [Hinterberger and Bauer, 1998]: (1) A cell at t 2 has no predecessor at t 1, which means a new cell came into existence. (2) A cell at t 1 has no successor at t 2, which means an existing cell disappeared. (3) A cell at t 1 has exactly one successor at t 2. This is cell translation. (4) A 2of7

3 Figure 2. Doppler velocity from event on 23 March 2004 at range 58 km. cell at t 1 has more than one successor at t 2 (i.e., the cell split into several parts). (5) A cell at t 2 has more than one predecessor at t 1 (i.e., several cells merged into one). [10] The above correlation analysis was performed only to find cell translation, ignoring cell growth and cell decay. A frame is taken centered at peak intensity around an identified cell in the previous image (at time t 1 ). The size of this frame is guided by two considerations: A frame that is too small in size will contain too few data points for the correlation coefficients to be stable, whereas a frame that is too large will only give a general mean flow on a broad spatial scale. In our study, a 5 km 5 km frame size, partitioned into blocks, was considered a good compromise in reliably tracking a cell. Each block was assigned a value of zero if its reflectivity fell below threshold and a value of 1 otherwise. The search for maximum correlation (i.e., approximate match) between a frame from the previous scan and a neighborhood in the current scan extends from zero displacement up to an excursion limit set by a maximum translation speed of 30 m/s. [11] As an example, Figure 1 shows two successive scans of a rain event on 23 March 2004 featuring isolated and intense rain cells (maximum reflectivity 51 dbz). The time difference between the successive scans is from 2 min 15 s to 3 min. The block at the center of a frame in the LHS scan (at time say t 1 ) is marked, and has coordinates say (x 1,y 1 ). At a later time t 2 corresponding to the RHS scan, the location of this block will be at point (x 2,y 2 ) within the RHS scan which gives the highest correlation between the frames centered at (x 1,y 1 ) and (x 2,y 2 ). The translation speed v and direction of motion q (counterclockwise from east) are then obtained as q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi. v ¼ ðx 2 x 1 Þ 2 þðy 2 y 1 Þ 2 ðt 2 t 1 Þ; ð1þ q ¼ tan 1 ½ðy 2 y 1 Þ=ðx 2 x 1 ÞŠ Translation speeds and directions were similarly computed for all other events. 4. Wind Field From Doppler Analysis [12] Browning and Wexler [1968] showed that if a wind field varies almost linearly then the velocity components of a wind field can be approximated by a Taylor series expansion limited to first derivatives. In this way, the velocity field inside an observed domain is described by the sum of the value at the center and the gradient terms. 3of7

4 Figure 3. Comparison of wind speed, Doppler wind speed, and cell translation speed. As the radar senses only radial velocity, the tangential component can be determined by analyzing measured radial velocity values at various points along a circle (corresponding to different azimuth b and range r values within a scan). Under these assumptions, the radial velocity V r (b) can be seen as a periodic function with base period 2p that can be written in the form of a Fourier series expansion [Sauvageot, 1992]: V r ðbþ ¼a 0 þ X1 n¼1 ða n cos nb þ b n sin nbþ The first three coefficients are given by, a 0 ¼ 1 2 r cos2 a du dx þ dv þ w sin a dy a 1 ¼ v 0 cos a b 1 ¼ u 0 cos a ð2þ ð3þ ð4þ ð5þ where u 0 and v 0 are the horizontal components of velocity and a is the elevation angle. [13] However, if there is no scatterer at a particular point on the circle or the scatterer motion at this point is perpendicular to the radar beam, then the radial velocity will be zero. Such points were filled by cubic interpolation. The data were smoothed (Figure 2) using an ideal lowpass filter of cutoff 50 cycles/deg and an FFT was applied to obtain the coefficients that yielded the horizontal wind speed as V H ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 o þ v2 o ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a 2 1 þ b2 1 cos a ð6þ Figure 3 shows comparisons of the radar Doppler-derived wind speed, the correlation-based storm translation speed, and the ground measured wind speed at Brize Norton for corresponding events or observation intervals (numbered Table 1. Statistics of Rain Cells From Rain Gauge and Radar Data Rain Rate Threshold Number of Cells From Rain Gauge Number of Cells From Radar 5 mm/h mm/h mm/h mm/h of7

5 Figure 4. Cumulative distribution of rain cell sizes from rain gauge data. from 1 to 14 along the x axis). Rain cells are expected to move with the wind speed at 700 mb pressure level at 2 to 3 km above ground [Yau and Rogers, 1984]. The wind speed measured at ground level was increased by a factor of 1.5 to account for the variation of wind speed with height above ground [Tozer and Grace, 2001]. It can be seen that the computed translation speed of rain cells shows broad agreement with elevated wind speed. The differences could be due to the fact that although rain cell movement is driven by winds, the rain cell pattern observed on the ground at a given region may reflect the speed and direction of the generating precipitation at a higher altitude [Marshall, 1953]. There is, however, a considerable difference between cell translation speed and Doppler derived wind speed. It is worth noting that the Doppler method described above gives a reliable measure of only the radial velocity component of a large rain volume, and the steps employed to derive horizontal translation speed from this radial measurement assumes a linear flow field which is not the case in localized convective events. 5. Rain Cell Size Distributions [14] Rain gauges provide a record of the amount of rainfall over time, or rain rate time series, at different locations. Since rain is a moving entity, this time series can be converted into a spatial series by employing some known value of rain translation speed. This is the so-called synthetic storm technique [Matricciani and Bonati, 1997]. Rain rate measurements at 10 s integration time were converted into 1-min rain rate time series before determining the event durations for threshold rain rates from 5 to 50 mm/h. Multiplying these durations by the average rain cell translation speed of 10.1 m/s yielded an equivalent distance span and hence size of the corresponding rain cell. [15] Rain cell sizes were also deduced from radar measurements comprising 66 PPI scans in 7 rain events within a 100 km range of Hampshire. The radar reflectivity field z (dbz) was converted into rain rate R (mm/h) through the relation z = 200R 1.6, which assumes a Marshall-Palmer raindrop size distribution. The contour and polyarea functions of MATLAB were employed to compute the area of rain cells of defined thresholds, and this area was then converted to cell size (i.e., diameter) in km by equating with a circular shaped region. [16] The numbers of rain cells of various rain rate thresholds obtained using rain gauge data are much lower than the numbers from radar data (Table 1). This is because the rain gauge based estimate employs the average 5of7

6 Figure 5. Cumulative distribution of rain cell sizes from radar data. rain rate in 10-s intervals at a single location whereas radar captures instantaneous rain rate values at multiple locations. The radar measurement employed covered one rain event in summer, four events in autumn and two in spring, and may therefore not have sufficient seasonal variety for the results to be reliably representative of an average year. The rain gauge data on the other hand covered all seasons of a 3-year period. The smallest cell size determined using rain gauge data was 0.61 km, so cells of size less than 0.61 km were not considered in the radar data analysis. [17] Figures 4 and 5 show the cumulative distributions of rain cell sizes derived from rain gauge and radar measurements respectively, for rain rate thresholds from 5 to 50 mm/h. The lower rain rate cells (of thresholds 5 to 10 mm/h) extend up to 65 km in diameter for results derived from rain gauge measurements using the synthetic storm technique. Intense rain cells (thresholds 20 mm/h) on the other hand have extensions around 5 to 10 km, which is in agreement with the results found in earlier studies [Yau and Rogers, 1984; Matricciani and Bonati, 1997]. It can be seen that the two methods yield comparable results for intense rain cells, whereas there is considerable difference for the lower rate cells where radar observations show cell sizes up to 25 km. The families of curves for intense cells are similar in overall appearance to those reported by Yau and Rogers [1984]. It should be noted that the accuracy of the synthetic storm technique depends on the use of correct values of storm translation speed for the different rain patterns. In our analysis, the same translation speed determined for the intense rain cells associated with highly mobile convective rain was applied to the lower rate cells of stratiform rain. This is likely to have resulted in overestimation of the spatial extent of weaker rain cells. Rain rates lower than 5 mm/h were not considered since the assumption of a circular cell shape no longer holds, as revealed by the radar observations. Very intense rain cells above 50 mm/h appeared on the radar scans as small dots whose areas could not be reliably computed, so rain intensities above 50 mm/h were excluded from the analysis. Furthermore, the sample size of intense rain cells observed using both rain gauge and radar was quite small (between 2 and 6) making their distributions unstable [Matricciani and Bonati, 1997]. In particular, distributions below 0.02% were not possible, and cell sizes indicated in Figures 4 and 5 at small percentages (<0.2%) may not accurately represent those in an average year. [18] The largest cell sizes determined from radar data (Figure 5) were around 25 to 26 km for a 5 mm/h rain rate 6of7

7 threshold. This compares well with other rain cell size distribution studies where cell sizes larger than 20 km are considered to be cell clusters controlled by air motions of scales larger than the rain cell [Sauvageot et al., 1999; Goldhirsh and Musiani, 1986; Konrad, 1978]. 6. Conclusion [19] Rain cell translation speed obtained using correlation analysis of consecutive radar PPI scans has been compared with Doppler derived wind speed and scaled ground measured wind speed. Distributions of rain cell sizes determined from both radar and rain gauge measurements were also presented. These results show that intense rain cells have sizes generally less than 10 km. The results are similar to the values found by Yau and Rogers [1984] and Matricciani and Bonati [1997]. One application of this study might be in site diversity as a rain fade mitigation technique in satellite communications, where a spacing of about 10 km between diversity stations could provide significant protection against rain-induced link outage, considering that at this spacing both stations will normally not concurrently lie within one intense rain cell. Thus in the event of a large attenuation of the satellite-to- Earth radio signal due to intense rain on the primary link, the downlink can be automatically temporarily rerouted through the secondary or diversity station. In this way diversity gains of up to about 10 db can be realized [Callaghan et al., 2008], the exact value depending on climate, link frequency and path elevation angle. [20] Rain cell size distributions from rain gauge data are found in the scientific literature where 700 mb wind speed is employed to obtain cell size distribution. In this study, a mean rain cell translation speed of 10.1 m/s obtained by cell tracking was used to determine cell size distribution. The results showed close agreement with earlier findings for intense rain cells. However, the diameters of light rain cells were 65 km which appeared to be significantly overestimated when compared to radar-derived estimates 25 km. Better agreement between rain gauge and radar estimates of cell sizes for all regimes of rain intensity was obtained by using the computed average cell translation speed of 10.1 m/s for intense cells and a trial translation speed of 4 m/s for light rain (10 mm/h). There were only a few trackable cells in the radar measurements available, so further cell tracking analysis as described in this paper is required along with higher level wind speed measurements in order to confirm the translation speed of light rain for application in the synthetic storm technique. References Battan,L.J.(1973),Radar Observation of the Atmosphere, Univ. of Chicago Press, Chicago, Ill. Browning, K. A., and R. Wexler (1968), The determination of kinematics properties of a wind field using Doppler radar, J. Appl. Meteorol., 7, Callaghan, S. A., B. Boyes, A. Couchman, J. Waight, C. J. Walden, and S. Ventouras (2008), An investigation of site diversity and comparison with ITU-R recommendations, Radio Sci., 43, RS4010, doi: /2007rs Capsoni, C., F. Fedi, C. Magistroni, A. Paraboni, and A. Pawlina (1987), Data and theory for a new model of the horizontal structure of rain cells for propagation applications, Radio Sci., 22(3), Crane, R. K. (1979), Automatic cell detection and tracking, IEEE Trans. Geosci. Electron., GE-17(14), Dixon, M., and G. Wiener (1993), TITAN Thunderstom Identification, Tracking, Analysis and Nowcasting A radar-based methodology, J. Atmos. Oceanic Technol., 10(6), Goldhirsh, J., and B. Musiani (1986), Rain cell size statistics derived from radar observations at Wallops Island, Virginia, IEEE Trans. Geosci. Remote Sens., 24, Hinterberger, H., and B. M. Bauer (1998), Discrete object detection and motion registration based on a data management approach, Proceedings of SSDBM 98, July 1 3, Capri, Italy, pp. 1 13, IEEE Press, Piscataway, N. J. Konrad, T. G. (1978), Statistical models of summer rain showers derived from fine-scale radar observations, J. Appl. Meteorol., 7, Marshall, J. S. (1953), Precipitation trajectories and patterns, J. Meteorol., 10, Matricciani, E., and A. P. Bonati (1997), Rain cell size statistics inferred from long Term point rain rate: Model and results, paper presented at Third Ka Band Utilization Conference, Eur. Space Agency, Sorrento, Italy. Sauvageot, H. (1992), Radar Meteorology, Artech House, Norwood, Mass. Sauvageot, H., F. Mesnard, and R. S. Tenorio (1999), The relation between the area average rain rate and the rain cell size distribution parameters, J. Atmos. Sci., 56, Tozer, T. C., and D. Grace (2001), High-altitude platforms for wireless communications, Electron. Commun. Eng. J., 13(3), Yau, M. K., and R. R. Rogers (1984), An inversion problem on inferring the size distribution of precipitation areas from rain gauge measurements, J. Atmos. Sci., 41(3), S. Begum and I. E. Otung, Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL, UK. (sbegum@ glam.ac.uk) 7of7

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