ATMOSPHERIC SCIENCE LETTERS Atmos. Sci. Let. 7: 9–14 (2006) Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/asl.122 Assessing vertical resolution requirements for operational weather radar data quality Marion P. Mittermaier,* Anthony J. Illingworth and Robin J. Hogan Department of Meteorology, University of Reading, Reading, UK *Correspondence to: Marion P. Mittermaier, Met Office, FitzRoy Rd, Exeter, EX1 3PB, UK. E-mail: marion.mittermaier@metoffice.gov.uk Received: 27 September 2005 Revised: 19 January 2006 Accepted: 26 January 2006 Abstract High-resolution, 0.28◦ beamwidth range-height-indicator (RHI) data are used to simulate the reflectivities measured at various ranges by an operational radar with a 1◦ beamwidth. It is found that the sampling is optimal when the elevation increments equal the beamwidth. Larger increments lead to an unacceptable loss of information. Copyright 2006 Royal Meteorological Society Keywords: oversampling; brightband; scan sequence 1. Background Operational radars scan in a sequence of plan position indicator (PPI) scans at different elevations producing a volume scan. The aim is to obtain information on the radar reflectivity at various heights. If the sole purpose of collecting and processing radar data were to obtain surface estimates of precipitation, then scanning in the rain at a single elevation as close to the ground as possible (without contaminating the signal with clutter) would be the solution. Very often this is not possible because at increasing ranges the low altitude level of the melting layer coupled with the earth’s curvature means that the beam is no longer in the rain, and some knowledge of the vertical profile of reflectivity (VPR) is needed to infer the rainfall rate at the ground. Multiple elevation data are essential for determining the shape of the VPR, forming the basis for VPR correction schemes that correct for melting effects and ice, assisting in the discrimination between stratiform and convective precipitation processes, determining the development stage of thunderstorms as in the GANDOLF forecasting scheme (Pierce et al., 2000) and deriving Doppler wind fields. The reflectivity at higher altitudes in the ice contains additional information. Hogan et al., (2006) reported that the error in the ice water content retrieved from radar reflectivity (taken between 10 and 40 km from the radar) is about +50%/−33% between −20 and −10 ◦ C, rising to +100%/−50% for temperatures less than −40 ◦ C. Converting these percentage errors to their logarithmic equivalents suggests that if the reflectivity Z in the ice is known to be better than 1.5 dB (rounded from 1.76 dB), it can be used to evaluate the performance of the ice parameters in operational numerical weather prediction (NWP) models, and ultimately be assimilated into such NWP models. Copyright 2006 Royal Meteorological Society The challenge of providing adequate information for downstream applications and users of radar data is one shared by all operational radar networks and is, fundamentally, a function of the underlying climatic regime, radar location relative to the terrain and also system specifications. In recent years Westrick et al. (1999) and Brown et al. (2002) discussed NEXRAD radar scan strategy needs in terms of high-altitude radar locations and obtaining accurate echo top heights. Others like Novák and Kráčmar (2002) discuss the implementation of an interlaced scan strategy, first proposed by Vasiloff et al. (1987). Still others describe the Canadian National Radar Network (Joe and Lapczak, 2002) and the South African networks (Terblanche et al., 1999), both using more than ten elevations scanning up to between 24 and 45◦ with rapid update times of the order of 5 min. In the United Kingdom, the radar network consists of 11 C-band radars (at the time of study) with a 1◦ beamwidth (Harrison et al., 2000). One of the two standard four-elevation scan strategies is used; either 0.5, 1, 1.5 and 2.5◦ (with some oversampling), or the other 0.5, 1.5, 2.5 and 4◦ (with no oversampling). In this letter we investigate the potential benefits of oversampling on data quality to provide a better representation of the VPRs for use in brightband correction schemes and to estimate ice water content in the ice. We use the UK radar network to illustrate the method. 2. Beam geometry and range effects To place the problem of sampling a varying VPR with an operational radar in perspective, we consider an idealised profile, which is a simplified version of that used by Kitchen et al. (1994) and which has a constant reflectivity of 20 dBZ in the rain, 10 M. P. Mittermaier, A. J. Illingworth and R .J. Hogan a brightband 700-m deep with a peak reflectivity of 28 dBZ and a constant reflectivity lapse rate of 3 dB·km−1 above the brightband as shown in Figure 1(a). To simulate the sampling that would be achieved by the operational Met Office radars, this profile template is convolved with a Gaussian beamwidth having a two-way full-power effective beamwidth of 1◦ , and the resulting VPRs at 20, 40, 60 and 80 km are shown. Pure beam broadening effects cause the peak value of reflectivity to fall to 36.5, 35.2, 35.3 and 33.6 dBZ , respectively. At a range of 80 km the smearing out of the echo leads to an apparent increase of 1 dB in the reflectivity of the rain at a distance of 600 m below the true bottom of the brightband. For a 12-dB brightband enhancement, the equivalent distance at this range is 850 m. Figure 1(a) was compiled with a 3 dB·km−1 slope above the brightband. Convolution with the beam pattern also introduces a constant positive bias to the resulting reflectivities above the brightband in the ice, but the magnitude is dependent on the steepness of the lapse rate of reflectivity. This bias is shown in Figure 1(b) as a function of range and for the three lapse rates of 3, 6 and 9 dB·km−1 . Steeper slopes imply a larger positive bias at progressively closer ranges. This increase appears to be nearly linear with range for smaller lapse rates, but becomes increasingly non-linear as the lapse rate increases. For small lapse rates the effect is negligible, with biases <0.15 dB, while for the steeper gradient of 6 dB·km−1 we can derive Z with the accuracy of 1.5 dB (required for estimating ice water content) out to a range of 80 km, and for gradients of 9 dB·km−1 this accuracy limit is reached at a range of 60 km. The idealised profiles in Figure 1(a) are of very high resolution (10 m), but resampling at selected heights corresponding to a few elevations and reconstructing the profiles using these few values will introduce differences between the original and the reconstructed one. The differences will depend on where the resampling is performed in height, and also on the range. 4.5 Ideal 20 km 40 km 60 km 80 km 4 Height (km) 3.5 3 2.5 2 1.5 1 0.5 14 16 18 3.5 3 Bias (dB) 20 22 24 26 28 30 Reflectivity factor (dBZ) (a) 3 db.km-1 6 db.km-1 9 db.km-1 2.5 4.1. Significant echo height distribution 1.5 1 0.5 (b) 20 A database of 981 range-height-indicator (RHI) scans sampling nine events between August and December 2000 were used. The data were collected using the 3GHz dual-polarisation Doppler weather radar located at Chilbolton (51.14 ◦ N and 1.44 ◦ W), southern England (see Goddard et al., 1994). The 25-m antenna provides a 0.28◦ beamwidth. Typically, the RHI scans have 0.1–0.2◦ elevation steps between 0–30◦ . Data are collected to a range of 90 km with a 300-m range resolution. Figure 2 shows a typical RHI from the database. Only VPRs with reflectivities greater than 12 dBZ at the lowest level, and below the freezing level, of a particular scan sequence were considered, chiefly because the main focus here is on rainfall. The threshold corresponds to a rainfall rate of 0.2 mm·h−1 (Marshall and Palmer, 1948). Freezing level height forecasts from the mesoscale version of the Met Office Unified Model (UM) were used to ensure that the lowest beam was in the rain. 4. Studying the effects of oversampling 2 0 3. Description of high-resolution radar data 30 40 50 60 Range (km) 70 80 Figure 1. (a) The Nimrod VPR template convolved with a 1◦ beam at 20, 40, 60 and 80-km range showing beam broadening effects. (b) Biases introduced in the ice due to beam pattern convolution as a function of range and VPR slope Copyright 2006 Royal Meteorological Society The echo distribution in the vertical was analysed using the RHI database. This was done to determine up to which height the radar coverage is required to capture the most important features and the maximum elevation that is required to provide this coverage. Cumulative distributions of the frequency of occurrence of significant reflectivities (≥12 dBZ in the rain) were calculated. These distributions, shown in Figure 3(a) and (b), are presented in two ways, first as a distribution in height and then as a function of elevation angle. The data are sorted into 10-km range bins of either 500-m height bins from 0 to 9 km, Atmos. Sci. Let. 7: 9–14 (2006) Vertical resolution requirements for operational weather radar data quality 11 Figure 2. Example of a high-resolution RHI for 2 November 2000 at 09 : 13 UT showing radar reflectivity factor Figure 3. Cumulative distributions of the frequency of occurrence of echoes in the RHI database exceeding 12 dBZ as a function of height in (a) and as a function of elevation in (b). Contours are every 0.1 between 0 and 1. (c) The fraction of the area within a range of 80 km, which is sampled for four different radar elevations as a function of altitude. It is desirable to sample 2 km higher than the brightband (see text) or 0.5◦ elevation bins from 0 to 30◦ . At least 90% of significant reflectivities appear to be found below 4 km at all the ranges up to 90 km from (a). From (b) it can be seen that to achieve this 90% level of coverage at 20 km, an elevation of 15◦ is required. This requirement decreases rapidly with range, and Copyright 2006 Royal Meteorological Society elevations less than 5◦ are sufficient for ranges greater than 60 km to achieve the same 90% margin. Given the wide spectrum of data included in this data set, a suggested maximum height of 5 km would come close to including most reflectivities of relevance for the VPR related applications. Atmos. Sci. Let. 7: 9–14 (2006) 12 M. P. Mittermaier, A. J. Illingworth and R .J. Hogan 4.2. Scan sequence selection 4.3. Error analysis The aim of implementing a volume scan is to gain a three-dimensional representation of the radar area. If coverage up to, say, 5-km above ground level (AGL) were required, then for a maximum elevation of 4◦ this is only possible at ranges greater than 60 km. For a maximum elevation of 2.5◦ this is only achievable beyond 100 km from the radar. Yet the 0.5◦ base scan is below 1 km up to 70 km, below 2 km up to 110 km, and below 3 km AGL up to 150 km range. Base scan is a site-specific parameter and as such will not be discussed here. On the basis of observational evidence Smyth and Illingworth (1998) showed that it is desirable to sample up to a height of at least 2 km above the brightband height to distinguish between different ice processes, and to discern whether the VPRs are convective or stratiform; an important consideration when attempting to estimate the surface rainfall rate. Aggregation gives a strong signature in the 1–2 km above the brightband for stratiform VPRs. In the United Kingdom, freezing level height forecasts (typically t + 4h forecasts) from the UM are used in the operational VPR correction scheme (Harrison et al., 2000). Their use was evaluated by Mittermaier and Illingworth (2003) and the rms of the height in the brightband was found to be less than 150 m, which is well within the specification needed for the correction scheme. Errors for the European Centre for Medium-range Weather Forecasts (ECMWF) northern hemisphere forecasts were also comparable to those obtained for the UM at longer lead times (12–36 h). To assess the impact of increasing the maximum elevation angle on radar areal coverage, consider Figure 3. The figure shows the fraction of radar area that is covered within a range of 80 km from the radar, given four different maximum elevations, 2.5, 4, 8 and 16◦ . Therefore, if the freezing level were at 1 km AGL, then a 2-km coverage above the brightband height means that the radar needs to sample up to 3 km, so for a maximum elevation of 2.5◦ and a maximum range of 80 km, only 26% of the radar area would be sampled. With a 4◦ maximum elevation 71% of the radar area is sampled. For 8◦ the area increases to 93%, and for 16◦ 98% of the area at 3 km is sampled. Notice that the incremental increases in coverage grow smaller as the maximum elevation increases. One way of studying the effect of oversampling is to nest several equally spaced scan sequences spanning the same elevation interval. Starting with a coarse sequence (effectively undersampling), each of the other sequences is nested, providing progressively finer resolution data until a resolution near that of the Chilbolton radar of 0.28◦ is reached. Here, minimum and maximum elevations of 0.5 and 4.5◦ were used. This elevation interval was then sampled at 0.33, 0.5, 0.67, 1, 1.33 and 2◦ producing scan sequences of 13, 9, 7, 5, 4 and 3 tilts, respectively. The high-resolution RHIs were convolved with a 1◦ beamwidth Gaussian beam pattern, and then resampled according to the nested sequences to investigate the effect of oversampling the same elevation angle interval. By linearly interpolating the resampled profiles back onto the original high-resolution heights, error statistics can be calculated. As all sequences are sampling the same height ranges at various resolutions, it is possible to calculate the mean root-mean-squared difference (rmsd ) in dB averaged over height; as a function of constant elevation angle separation, and for different horizontal ranges from the radar. This is plotted in Figure 4. The 95th percentile rmsd is also plotted as an indication of the maximum error. The graph yields some surprising results. It would appear that the oversampling at 0.33◦ as compared to 2◦ would result in only a very small mean decrease (∼0.4 dB) in the rmsd error. The maximum mean error is lowest when the elevation step separation is about the same as the beamwidth. The mean rmsd increases in range, but beyond 70 km the beam broadening effects produce a smoothing or damping effect for the elevation steps greater than 1◦ , so that the errors are seen to decrease slightly with elevation step separation. So why does oversampling at 0.33◦ not improve Z ? Calculating the mean over the height range does not show height intervals where the errors are greater than or less than this mean value. The brightband is typically at 1–2 km, so that at 80-km range most elevations are sampling in the ice. Values of Z in the ice above the brightband are not well related to the values of Z in the rain (e.g. Fabry et al., 1992), so for VPRs there is little to be gained from knowing Z in the ice more accurately. This was confirmed by Kitchen (1997) who showed that for VPR correction only small Copyright 2006 Royal Meteorological Society 8 Mean rmsd in height (dB) 7 20 km 40 km 60 km 80 km Max 6 5 4 3 2 1 0 0.33 0.5 0.66 1 1.33 2 Elevation step separation (°) Figure 4. The mean rmsd in dB averaged over height as a function of elevation step angle separation, for different ranges from the radar. Also shown is the 95th percentile rmsd, quoted as the maximum error Atmos. Sci. Let. 7: 9–14 (2006) Vertical resolution requirements for operational weather radar data quality 13 Figure 5. The rmsd centred on the brightband peak for different elevation step angle separations at 20, 40, 60 and 80 km gains can be made by using information from upper beams. Accordingly, the maximum error is related to how well the sampling captures features such as the brightband, which is the ‘problem area’. It is therefore useful to zoom in on the height interval 500 m on either side of the brightband peak and compute the rmsd every 100 m between the high-resolution profiles and the resampled and linearly interpolated profiles to gauge the effect of oversampling. This is plotted in Figure 5 at 20, 40, 60 and 80-km range for the six nested scan sequences. Figure 5 shows that the incremental improvements become progressively smaller with increasing overlap between successive beams. Once the angle separation is less than the beamwidth, only very small improvements are possible. It does, however, show that locally, in the ‘problem area’ around the bright band, there are benefits when oversampling and keeping the angle separation less than, or at most equal to, the beamwidth. Error reductions of 0.5 to 1 dB at ranges beyond 40 km are achievable when changing the steps from 1◦ to 0.66◦ steps, but the remaining Copyright 2006 Royal Meteorological Society error of about 4 dB cannot be reduced further by using even smaller steps. In all instances, reducing the step separation yields a progressively more accurate representation of the brightband peak. For instance, reducing the sampling volume from 1◦ to 0.66◦ , and increasing the number of elevation steps would be beneficial for the case of rain advecting into the radar domain, benefiting from both increased information (more samples in the vertical), and a reduced error. This could be important for various applications ranging from detecting severe convection to brightband correction algorithms. The errors 0.5 km above the brightband peak are more complicated, because in the aggregation zone extending 1 km above the brightband the reflectivity gradient is initially steeper and then relaxes to a lower value. As a result the interpolation between the sample at the height of the brightband maximum and at a height 2–3 km above for ranges over 60 km with the 2◦ sampling step can lead to occasional reduction in error for this coarse resolution, but on balance the net effect is still negative. Atmos. Sci. Let. 7: 9–14 (2006) 14 M. P. Mittermaier, A. J. Illingworth and R .J. Hogan 5. Concluding summary as part of various projects. We also thank the Met Office for supplying the UM output and especially Malcolm Kitchen who provided the motivation for the work. Funding for the first author was provided by the Met Office and the Environment Agency under contract PB/B3567. In the preceding sections a method for testing and comparing different scan strategies has been presented. Central to the method is the coarsening or ‘upscaling’ of high-resolution, narrow beamwidth RHI data to simulate operational radar beamwidths. The method provides flexibility in scan strategy design (the number and spacing of elevation steps between base scan and maximum elevation), constrained only by the beamwidth of the high-resolution data, in this case 0.28◦ . For this study the method was used to design nested scan sequences to test the impact of oversampling and increased information content. General conclusions include: • Elevation steps equal to the beam width appears to be the optimal solution and is acceptable in terms of data coverage. • Oversampling has very limited benefits; separating the radar beams elevations by 0.66◦ for a 1◦ beamwidth radar leads to a slight improvement in the inferred VPR, but only beyond 60-km range. • Undersampling with the elevation steps greater than the beam width leads to a rapid degradation of the inferred vertical profile and should be avoided. • The observed value of Z in the ice is generally within 1.5 dB of the true value, which is sufficient for deriving ice water content unless the vertical gradient of reflectivity exceeds 9 dB·km−1 . • Calculating a distribution of significant reflectivity (above 12 dBZ ) is helpful in determining the minimum height of the radar sampling volume. For this study at least 90% of significant reflectivities are found below 4 km at all ranges up to 90 km. This analysis is based on UK network radar specifications. Nevertheless, the figures presented may be applicable to radars with similar specifications elsewhere. In the United Kingdom, besides the benefits to the current Nimrod operational VPR correction scheme, future amendments to the scheme may require more information about the slope of reflectivity in the ice. Radar-rainfall rates have been assimilated into the UM via a latent heating scheme for several years, and this is shown to be beneficial (Jones and Macpherson, 1997). Any future plans to assimilate three-dimensional radar data, especially the assimilation of radar-derived ice water content into NWP models, would also be facilitated by increasing the information content in the ice. Acknowledgements We thank the Chilbolton Observatory, a part of the Rutherford Appleton Laboratory for use of the 3-GHz radar data collected Copyright 2006 Royal Meteorological Society References Brown R, Wood V, Barker T. 2002. 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