Longterm assessment of bias adjustment in ... - Wiley Online Library

WATER RESOURCES RESEARCH, VOL. 38, NO. 11, 1226, doi:10.1029/2001WR000555, 2002

Long-term assessment of bias adjustment in radar rainfall estimation Marco Borga and Fabrizio Tonelli Department of Land and Agroforest Environments, University of Padova, Legnaro, Italy

Robert J. Moore Centre for Ecology and Hydrology, Wallingford, UK

Herve´ Andrieu Division Eau, Laboratoire Central des Ponts et Chausse´es, Bouguenais, France Received 26 March 2001; revised 15 February 2002; accepted 15 March 2002; published 9 November 2002.

[1] A comprehensive analysis of precipitation estimation by weather radar operated over

hilly terrain is performed. The study is based on a nearly continuous 3-year database of weather radar observations and hourly rain accumulations from a dense rain gauge network located in southwest England. Radar rainfall processing scenarios associated with correction for systematic and range dependent errors are investigated. The focus of the study is in demonstrating the impact of radar range effects at short to medium (less than 70 km) distances and determining the significance of coupling mean-field and range-related bias adjustment in radar rainfall estimation. The investigation is performed on the basis of climatological radar rainfall statistics for selected radar sectors and radar-rain gauge comparisons over a densely instrumented medium size (135 km2) basin located at 35–40 km from the radar. The application of the combined adjustment is shown to reduce overall error over the catchment by 24%. The analysis suggests that gauge-based radar adjustment can be properly applied only when homogeneity in the accuracy of the radar rainfall INDEX TERMS: 1854 estimates with respect to range and scanning elevation is ensured. Hydrology: Precipitation (3354); 3360 Meteorology and Atmospheric Dynamics: Remote sensing; 3394 Meteorology and Atmospheric Dynamics: Instruments and techniques; KEYWORDS: precipitation, rainfall estimation, weather radar, accuracy, rain gauge Citation: Borga, M., F. Tonelli, R. J. Moore, and H. Andrieu, Long-term assessment of bias adjustment in radar rainfall estimation, Water Resour. Res., 38(11), 1226, doi:10.1029/2001WR000555, 2002.

1. Introduction [2] Radar enables three-dimensional observation of precipitation with excellent areal coverage (104 km2) and high spatial (1 –5 km2) and temporal (minutes to hourly accumulations) resolution, which makes it an ideal tool for hydrological applications. Nevertheless, radar rainfall estimates suffer from several types of errors, caused mainly by the need to transform measurements made aloft to a corresponding surface rainfall rate value, which includes the highly variable and nonlinear reflectivity-to-rainfall rate (Z-R) conversion. [3] Current understanding has identified three broad categories of radar error sources [Creutin et al., 2000]: (1) lack of electronic stability and miscalibration of the radar system, with an emphasis on the concept of repeatability rather than of absolute calibration [Joss and Lee, 1995]; (2) the radar detection environment, which includes issues related to beam geometry, beam broadening with distance, clutter and anomalous propagation, and visibility effects; (3) fluctuations of the atmospheric conditions including the Copyright 2002 by the American Geophysical Union. 0043-1397/02/2001WR000555

variability in time and space of the vertical profile of reflectivity, the beam power attenuation, and issues related to the microphysics of precipitation. [4] Current radar correction methods rely on rain gauge measurements to resolve and correct differences between radar rainfall estimates and surface rain rates. Examples of gauge-based adjustment approaches include the studies of Collier [1986], Krajewski [1987], Moore et al. [1994], and Seo [1998]. Schemes that are based on radar-gauge comparisons suffer from the problem of sensor sampling differences, which combined with the significant small-scale rainfall variability introduce representativeness errors in the statistical comparisons [Kitchen and Blackall, 1992; Anagnostou et al., 1999]. Studies have shown that the rain gauge areal rainfall representativeness error may explain a significant fraction of the radar-gauge rainfall difference variance at an hourly time step [Creutin et al., 1997] and even at scales of multiday accumulations [Ciach and Krajewski, 1999]. An advantage of gauge-adjustment schemes is that by relating the radar estimates to measurements of surface precipitation, an attempt is made to deal with all sources of radar errors in a single process; errors which include those due to beam height above the ground, deviation of the Z-R relationship from that assumed, and

8-1

8-2

BORGA ET AL.: LONG-TERM ASSESSMENT OF BIAS ADJUSTMENT

imperfect radar calibration. This characteristic may prove to be a major limitation when error sources exhibit differential time and space variability, making extrapolation of the adjustment to nearby places uncertain. [5] Research studies by Joss and Lee [1995], Andrieu et al. [1997], Borga et al. [2000], and Seo et al. [2000], among others, have reported approaches for addressing this issue. Most of the studies agree on a three-stage radar rainfall correction approach: (1) the preliminary identification of the radar detection environment, (2) radar data-based adjustment of range-related errors associated with the vertical profile of reflectivity (VPR) and beam attenuation, and (3) rain gauge-based estimation of mean-field bias (hereinafter referred to as MFB) associated with systematic and drift errors in the radar calibration and biased Z-R relationship. There are several issues related to this combined correction approach. First, there is a need to understand the significance of VPR-based range-related error correction (mainly with respect to ensuring unbiasedness of radar rainfall estimates) for varying beam elevation angles. Furthermore, the question is raised regarding the effectiveness and reliability of radar-gauge comparisons for MFB estimation and its dependence on the proposed approach, gauge density, and rain regime. Finally, the use of combined error correction approaches should be properly verified by investigating the significance of VPR adjustment in improving the transferability of MFB estimates across a range of radar distances and beam elevations. [6] This paper offers a comprehensive investigation of the above issues. A variety of radar rainfall processing scenarios are studied based on a long period (3 years) of hourly rainfall accumulations from a weather radar and a dense network of rain gauges over hilly terrain in southwest England. A detailed analysis is reported for range effects at short to middle ranges (less than 70 km) and mean-areal rainfall estimates over a catchment (135 km2) covered with a very dense network of 49 tipping-bucket recording rain gauges installed as part of the Hydrological Radar Experiment (HYREX) [Moore et al., 2000].

2. Study Area and Data Resources [7] The radar data used in this study are from the C-band non-Doppler, Wardon Hill weather radar. Figure 1a shows the position of the radar, which is located at an elevation of 255 m above mean sea level (AMSL), and the surrounding topography. The radar data are collected every 5 min up to a range of 210 km for four elevation scans with elevation angles of 0.5, 1.0, 1.5, and 2.5. The 3 dB radar beam width is 1. Correction for partial beam blocking by intervening obstacles is applied for certain sectors of the two lowest scans. The radar data are archived in Cartesian coordinates with 2-km (lowest scan) and 5-km (all four scans) grid resolution. Because of the need for upper scans in this study, only the 5-km resolution data are used. A description of the signal processing used to produce these data (including a Marshall-Palmer Z-R conversion) is given by Brown et al. [1991] and Kitchen and Jackson [1993]. [8] The study area comprises a medium size (135 km2) basin (the Brue catchment) located at 30– 40 km from the radar (Figure 1b) and is equipped with a dense network of 49 rain gauges which record the time-to-tip of 0.2 mm buckets [Moore et al., 2000]. For the lowest scan elevation

Figure 1. (a) Location of the Wardon Hill radar and the Brue catchment in southwest England. The radius of the circle is 75 km. (b) Rain gauge sites in the Brue catchment and the radar pixel resolution (5 km 5 km). (0.5) the radar beam height above the Brue catchment is approximately 0.4 km. The catchment is located in a radar sector free of beam blocking and ground clutter for all four scans. A near-continuous record of radar and rain gauge data is available over the 39-month period October 1993 to December 1996. The radar data gaps are about 18% of the total hours. Careful quality control of the rain gauge data is known to be a crucial step in radar-rain gauge comparison [Steiner et al., 1999]. The occasional malfunctioning of tipping bucket rain gauges was commonly caused by plant or soil debris and animal interference [Wood et al., 2000]. The integrity of the database has been checked and suspected readings have been eliminated. The basin-area reference rainfall estimates were computed by averaging the quality controlled rain gauge reports [Wood et al., 2000]. Over the study period, the accumulated basin-area reference rainfall amounts to 2487 mm. Basin-averaged radar rainfall estimates were obtained as weighted averages of radarrainfall values for all the grids covering the Brue catchment and using proportions of squares within the catchment to compute the weights. Figure 1b shows that using a 5-km radar grid may lead to some uncertainty in the location of rainfall, thus affecting the comparison between basinaveraged rain gauge and radar rainfall. A further comparison with basin-averaged radar rainfall computed on the basis of the 2-km radar grid showed that differences between 2-km


and 5-km radar grid basin averaged estimates are negligible. Finally, hourly temperature data from a number of weather stations under the radar umbrella were used to estimate the 0C isotherm altitude, information utilized in the radar correction procedure presented here.

3. Error Sources and Correction Procedures [9] The major factors affecting radar rainfall estimation in the study area are nonuniform VPR, orographic enhancement of precipitation, anomalous propagation of the radar beam (AP), radar calibration stability effects, and uncertainty in Z-R conversion. In this study we attempt to combine procedures for correcting systematic and rangedependent errors associated with the above factors. Specifically, the procedures investigated include algorithms for AP detection, identification and correction for a spatially uniform VPR, and adjustment of the MFB. For consistency with the hydrological analysis constituting a second stage of the present study [Borga, 2002], hourly rainfall accumulations are considered. A summary of the procedures investigated is provided below. 3.1. Range-Dependent Radar-Rainfall Bias due to Nonuniform VPR [10] The primary source of range-related radar errors is the vertical variability of reflectivity, especially for radars scanning over hilly terrain [e.g., Joss and Waldvogel, 1990]. For mainly stratiform precipitation, overestimation up to a factor of 10 may result due to bright band effects at close and intermediate ranges [Smith, 1986; Fabry and Zawadzki, 1995; Borga et al., 1997; Cluckie et al., 2000], while at longer ranges underestimation due to cloud overshooting is likely to occur. This study focuses on range-related biases that arise from short to medium radar ranges (30 – 70 km) associated with relatively high elevation scans (1.5– 2.5) used to avoid ground effects and beam occlusion. [11] The procedure of Vignal et al. [1999] is used to estimate the vertical reflectivity profile from radar measurements. The approach, which is a generalization of the method developed by Andrieu and Creutin [1995], accounts for spatiotemporal variations in the VPR. It evaluates for discrete sectors and range intervals the average ratio of radar data between each elevation and the lowest scan (called ‘‘ratio curves’’). An inverse method is used to retrieve VPR profiles at different radar sectors from these ratio values using a single initial VPR estimate (the ‘‘a priori VPR’’). [12] The method is applied at the hourly time step to detect fluctuations of the VPR within a rain event. The VPR is identified based on reflectivity data at 1.0, 1.5, and 2.5 scan elevations. The area chosen for VPR identification covers the radar sector with radar azimuth between 45 and 45 at ranges between 5 and 70 km. The limited number of elevation scans available in this study allows only estimation of a spatially uniform VPR. The definition of the ‘‘a priori’’ VPR is inspired from the method proposed by Kitchen et al. [1994]. The ‘‘a priori’’ VPR is computed at every hour based on (1) the available surface wet bulb temperature data and a standard lapse rate to derive 0C heights, (2) a bright band intensity and depth defined equal to 5 dB and 300 m, respectively, the profile above the bright band vanishing at 3 km. In summary, the retrieval of VPRs starts from the physically based approach suggested by

8-3

Kitchen et al. [1994], which is corrected according to the local observations of VPRs provided by ratio curves. [13] The implementation of the algorithm requires selection of values for a number of parameters [Andrieu and Creutin, 1995]. Important parameters are those characterizing the a priori information, which is formed by the vector of the a priori VPR and its associated covariance matrix. It contains the initial knowledge of the parameters to identify (i.e., the VPR) and the level of confidence that can be ascribed to this knowledge. A sensitivity analysis was performed to choose the values of the covariance matrix of the a priori VPR (standard deviation sz and distance decorrelation Dz). The quality of the results was evaluated by calculating the deviation between the identified ratio curves and the observed ones. On the basis of this analysis, the values of sz and Dz were set to 0.8 dBz and 0.2 km, respectively. This approach is prone to biasing the results toward a solution which gives more weight to the radar measurements and less to the a priori information. Nevertheless, this solution appears consistent with the nature of the problem at hand. In fact, the availability of two ratio curves in the range 5 –70 km may be considered enough to allow a correct sampling of the lower part of the VPR (altitudes less than 2 – 3 km), which is of interest here. 3.2. Anomalous Propagation [14] Strong vertical temperature and moisture gradients in the lower atmosphere, quite typical in anticyclonic conditions, can cause the beam to superrefract and produce echoes from ground targets that may be misrepresented as rainfall [Steiner and Smith, 1997]. An automated quality control procedure, called a tilt test, designed to remove the deleterious overestimation caused by AP, has been implemented. The tilt test is a vertical echo continuity check, which uses knowledge that the areal extent of AP often rapidly decreases as the antenna elevation steps up to higher angles. It has been implemented in the computation of the ratio curves used for VPR correction. The procedure discards the lowest two scans when more than 60% of the 1.5/ 1.0 ratio values in the range of 20– 70 km is less than 0.005 and, instead, uses data from the VPR-adjusted 1.0 scan (both thresholds are adaptable parameters). [15] This vertical continuity procedure, although simple, has proven effective in removing AP in situations where rainfall does not exist. For instance, on a total of 14,886 hours characterized by zero mean-areal reference rainfall over the Brue catchment during the study period (not considering radar faults), AP-related mean-areal radar rainfall exceeding 0.032 mm/h occurred for 1058 (613) hours at 0.5 (1.0) scan, generating 257.8 (145.9) mm of fictitious rainfall. Applying the proposed AP correction method reduces these errors to 333 (185) hours at 0.5 (1.0) scan, whereas fictitious rainfall is reduced to 106.9 (52.4) mm. However, it is in the more challenging situations when rain and AP coexist (i.e., part of the return is from the ground and part is from the rain) that the tilt test is more likely to fail. Research is under way to evaluate the accuracy of the algorithm in these situations. 3.3. Mean-Field Radar Rainfall Bias [16] The range-related bias adjustment procedure discussed in section 3.1, which is based solely on radar data,

8-4


cannot resolve systematic errors due to Z-R relationship uncertainties and system calibration errors. Typically radar rainfall estimates are compared against rain gauge data at a certain accumulation timescale to estimate a mean-field bias coefficient, which is subsequently applied uniformly to the whole radar domain to adjust its rainfall estimates [Anagnostou et al., 1998; Seo et al., 1999]. It is noteworthy that this procedure only accounts for the uncertainty in the mean areal Z-R relationship, with particular reference to the prefactor of that relationship. In this study the mean field bias is calculated at the daily scale as Ns P

MFB ¼ i¼1 Ns P

Gi ð1Þ

; Ri

i¼1

where Gi and Ri are the corresponding rain gauge and 5-km radar cell daily rainfall values (both exceeding 0.5 mm) for gauge station i, and Ns is the number of stations for a given day. To avoid sampling errors, MFB is calculated for Ns greater than 4; otherwise it is set equal to 1. Bias removal has been implemented on the basis of daily rainfall accumulations and not in a real-time fashion to avoid additional uncertainty due to time and space mismatching of the radar and gauge samples at shorter time intervals. However, the procedure could be easily accommodated to the real-time requirements, using rainfall values accumulated in a 24-hour running temporal window. [17] The MFB is computed based on a set of 20 rain gauge stations located within 30-km radar range to avoid rangerelated effects and using radar data from 1.5 scan to minimize interception by the ground of the secondary lobes (see Figure 2). The mean field bias evaluated for the whole data period is 1.22, which means that there is a 22% underestimation associated with Z-R and radar calibration effects. This bias is expected to vary both within and between storms.

4. Algorithm Evaluation [18] Quantitative analyses of radar error sources and evaluation of the proposed adjustment procedures are performed on the basis of (1) climatological range-dependent radar rainfall statistics; (2) long-term range-dependent radar-rain gauge rainfall difference statistics; and (3) mean basin average radar-rain gauge rainfall comparisons. Two criteria have been selected for statistical evaluation: Mean relative error (MRE) Nt P

MRE ¼ i¼1

ðPi Oi Þ Nt P

;

ð2Þ

;

ð3Þ

Oi

i¼1

Mean absolute error (MAE) Nt P

MAE ¼ i¼1

jPi Oi j Nt P i¼1

Oi

Figure 2. Locations of the rain gauge stations used for the calculation of the mean-field bias (MFB) (crosses) and of rain gauges selected for comparison (circles). where Oi is the reference variable for the ith time step, Pi is the corresponding predicted variable, and Nt is the number of time steps in the period of evaluation. 4.1. Range-Dependent Radar Rainfall Statistics [19] The following azimuthally averaged range-dependent radar rainfall statistics are evaluated: (1) probability of rainfall, (2) conditional mean rainfall, and (3) unconditional mean rainfall. The probability of rainfall, or rainfall frequency, is simply the fraction of hours with rainfall greater than a given threshold, while the conditional mean rainfall is the corresponding average rainfall. The threshold was set to 0.032 mm h1, based on previous analysis by Kitchen et al. [1994], which showed that the value is slightly higher than the radar detection threshold. Analyses are split into warm season (April – September) and cold season (October –March) periods, and results are reported for 1.5 and 2.5 scans (which are reasonably free from ground returns), before and after applying VPR adjustment. The area chosen for the comparisons overlaps the domain chosen for VPR identification. [20] This statistical analysis aims to assess the degree of interelevation homogeneity achieved from the VPR-based adjustment technique. The expectation is that the adjustment would minimize the range dependence and interelevation bias seen in the unadjusted data statistics, which is an effect of the nonuniform VPR described earlier. Demonstrating a successful elimination of the range dependence for the different elevation scans is crucial for the proper application of MFB adjustment across a range of radar distances and beam elevations, particularly in complex terrain. In areas prone (or suspected to be prone) to ground effects, it would allow to replace the adjusted estimate from the lowest unobstructed elevation angle by an upper elevation angle free from ground echoes. [21] Figure 3 shows azimuthally averaged range-dependent variations of the above statistics for both cold and warm


8-5

Figure 3. Range-dependent radar rainfall statistics for the cold season (October –March) and warm season (April – September) and for both unadjusted and vertical profile of reflectivity (VPR) adjusted radar estimates. Statistics include (a) probability of precipitation, (b) conditional mean hourly precipitation (mm h1), and (c) unconditional mean hourly precipitation (mm h1). seasons and for unadjusted and VPR-adjusted radar estimates. There is a decrease with range apparent in the precipitation frequency derived from the unadjusted data of the two upper scans. An isolated peak in frequency exhibited for 1.5 scan at around 47-km range is probably related to ground returns from areas of elevated topography rather than enhanced orographic precipitation. The adjustment affects slightly the frequency of precipitation. [22] The peak at 35 km in conditional mean of 2.5 scan during the warm season is due to the interception with the melting layer; beyond 35 km the conditional mean decreases sharply. The peak does not appear at 1.5 scan because at this

elevation the interception with the melting layer occurs at further ranges (between 40 and 100 km, in average terms), where the beam sampling volume is large enough to smooth out the bright band overestimation with the reduced reflectivity aloft. For the cold season, the conditional mean at 1.5 (2.5) scan decreases sharply beyond 40 km (20 km), where the radar beam samples the frozen hydrometeors above the melting layer. Figure 3b indicates that the VPR adjustment removes a significant portion of the range dependence and of the interelevation bias in the conditional mean statistics (i.e., when precipitation is detected by the radar). The residual errors associated with the adjustment around the bright band

8-6


Figure 4. Average daily rainfall accumulations versus range for both cold (October – March) and warm (April – September) seasons from rain gauge measurements and from (a) unadjusted radar data, (b) radar data adjusted for VPR, and (c) radar data adjusted for both VPR and MFB. peak are possibly related to the use of 5-km radar grids in the correction. [23] The unconditional mean rain statistics in Figure 3c mirror the principal features of the conditional mean at short range. In the cold season, the unadjusted mean rainfall at 70 km for 1.5 scan is about 3 times greater than for 2.5 scan, while in the warm season the ratio is around 2. The VPR adjustment reduces considerably these biases: Residual underestimation at 2.5 scan with respect to 1.5 scan amounts to 24% and 18% for the cold and warm seasons, respectively. Comparison against the other statistics shows that this residual bias is almost completely due to

radar rain detection failures, which cannot be corrected by the VPR adjustment. [24] The peak in probability at 47 km is cancelled by the dip in conditional mean, which is consistent with the view that this feature is due to ground returns from elevated topography that generate frequently spurious rainfall rates (slightly exceeding the threshold) on the 5-km radar grid. 4.2. Range-Dependent Radar-Rain Gauge Statistics [25] A radar-rain gauge comparison is carried out to investigate the impact of VPR and MFB effects on radar


8-7

Figure 5. MAE between rain gauges and radar-derived daily accumulations versus range for both cold and warm seasons for (a) unadjusted radar data, (b) radar data adjusted for VPR, and (c) radar data adjusted for both VPR and MFB.

rainfall errors and the efficiency of the combined correction approach described in section 3. Daily rainfall accumulations from 12 rain gauges aligned northward (see Figure 2) from the radar have been selected for this analysis. Daily accumulations of unadjusted, VPR-only adjusted, and combined VPR-MFB adjusted radar data (from 1.5 and 2.5 scans) are compared against data from collocated rain gauge in terms of seasonal average daily values (Figure 4) and MAE statistics (Figure 5). This is in contrast with the comparisons reported in section 4.1, where azimuthally averaged range dependent variations were considered. Several features are worth noting in Figure 4. First, the rain gauge accumulations show a peak around 45– 50 km from the radar site, for both cold and warm seasons, which

is due to orographic influences and is almost entirely missed by the radar estimates. This is quite expected, since over the area both elevation scans sample the atmosphere at altitudes that are missing the low level orographic growth. The range-dependence structure of the average radar rainfall from 1.5 and 2.5 scans is very similar to that analyzed in section 4.1. Radar estimates from 2.5 scan show severe underestimation at ranges exceeding 40 –45 km, particularly in the cold season. VPR-adjustment brings both beam estimates at the same level, even though a residual underestimation at ranges exceeding 50 km remains at 2.5 scan with respect to 1.5 scan. The residual bias, almost independent of range, is further decreased by applying the MFB adjustment. Since this adjustment mag-

8-8


nifies (in this study) the radar estimates, it is expected to inflate also the residual interelevation bias. The underestimation at 40– 60 km, due to orographic influence and not specifically addressed by the adjustment procedures, still remains after correction. [26] Figure 5a shows that at close ranges MAE is less in the cold season than in the warm season, for both elevations. However, at 2.5 scan the increase in MAE is sharper in the cold than in the warm season, whereas at 1.5 scan MAE shows striking influences from the orographic features. The VPR-adjustment greatly reduces the MAE increase with range, particularly at 2.5 scan. As expected, the application of the MFB adjustment yields a further reduction of MAE. For example, at 70 km MAE is reduced from 76% (80%) to 56% (52%) for 2.5 scan in the warm (cold) season, while the improvement is only slightly less important for 1.5 scan. 4.3. Basin Average Radar-Gauge Rainfall Comparisons [27] Comparisons of basin average hourly rainfall derived from radar and the rain gauge network of the Brue catchment are considered next for all four scan elevations. Results obtained for the upper two elevation scans may be deemed representative of results that would have been obtained when lower scans were blocked or too polluted by ground effects, or for a more distant catchment at a lower radar scan. Figures 6 –8 show cold season, warm season, and overall MAE and MRE statistics, by applying separate adjustments for combined VPR and AP, for MFB only, and for combined VPR, AP, and MFB.

Figure 6. Comparison between hourly rain gauge and radar-derived mean-areal rainfall over the Brue catchment for the cold season: (a) mean absolute error (MAE), (b) mean relative error (MRE).

Figure 7. Comparison between hourly rain gauge and radar-derived mean-areal rainfall over the Brue catchment for the warm season: (a) MAE, (b) MRE. [28] Several features are worth noting from this analysis. First, there is a distinct seasonal error structure associated with the unadjusted radar estimates. In the cold season, MAE increases with beam elevation (from 0.51 at 0.5 scan to 0.56 at 2.5 scan) due to the significant influences of MFB and VPR. Warm season estimates exhibit a much more pronounced impact from AP, even though MFB and VPR are still important error sources. In fact, MAE has a maximum value at 0.5 scan (0.72) and a minimum at 1.5 scan (0.53). The pattern of MRE mirrors these characteristics: In the warm season and at 0.5 and 1.0 scans, AP compensates for MFB-related systematic underestimation. In the cold season, a similar compensation is exerted by bright band at 1.0 and 1.5 scans. [29] Combined adjustment for AP and VPR is effective in reducing MAE. At 0.5 and 1.0 scans the improvement is due most to AP correction and less to VPR adjustment. The opposite is true for 1.5 and 2.5 scans. In the cold season, residual bright band effects remain after VPR adjustment, resulting in an overestimation for 1.0 to 2.5 scan elevations. [30] Adjustment for MFB only produces overall detrimental results for all beam elevations, with the exception of the lowest scan. It is slightly more effective when considering the warm season, where it improves over ‘‘no correction’’ for the first three scans. Conversely, combined correction for AP, VPR, and MFB results in significant improvement in the accuracy of the estimates. The overall MAE at the first scan decreases by 24% when the combined correction is applied, with a marked seasonal effect giving reductions of 16% and 33% in the cold and warm seasons, respectively. The improvement decreases with increasing


8-9

the low-level orographic growth, may lead to further improvements with respect to this error source.

5. Conclusions and Future Research Recommendations

Figure 8. Overall comparison between hourly rain gauge and radar-derived mean-areal rainfall over the Brue catchment: (a) MAE, (b) MRE.

scan elevation, MAE reducing at 2.5 scan by about 9% and 11% in the cold and warm seasons, respectively. The striking difference between MFB-adjusted radar estimates and those adjusted jointly for AP, VPR, and MFB show that MFB adjustment can only be properly applied when homogeneity in the accuracy of the radar rainfall estimates with respect to range and scan elevation is ensured. Overall MAE for the combined VPR and AP correction equals that for VPR, AP, and MFB for 1.5 and 2.5 scans, even though MRE is lower, in absolute value, for the complete adjustment. [31] Radar-gauge residuals after adjustment are still relatively large, even for 0.5 scan: in terms of MAE, they range from 0.42 in the cold season to 0.48 in the warm season. There are at least two reasons for these errors. First, AP contamination during rainy periods and more generally interaction of the radar beam with orographic features is still a major problem, particularly for the warm season. Improvement in this case might be sought using texturebased algorithms [see, for example, Wessels and Beekhuis, 1995; Grecu and Krajewski, 2000]. Use of a Doppler velocity test [see, for example, Joss and Lee, 1995] provides another possible avenue for improvement. Second, the complex terrain that makes radar measurements more difficult also has a profound impact on precipitation patterns [Hill et al., 1981; Barros and Lettenmaier, 1994]. It is well known that in this climatic and geographic setting the orographic enhancement may be only partially detected or entirely missed by the radar, even at ranges of about 50 km [Kitchen et al., 1994]. A physically based adjustment scheme [Kitchen et al., 1994], able to take into account

[32] The principal conclusions of this study are summarized as follows: Range-dependent biases have been shown to affect radar rainfall estimates for ranges less than 70 km and beam elevations that are required operationally to avoid ground returns and beam occlusion. Effects of bright band are recognizable at close ranges, while at farther ranges the effects of beams sampling the ice region leads to strong underestimation. This is due both to the different dielectric properties of the frozen hydrometeors and to the problem of precipitation detection. [33] Improvement obtained by applying the VPR adjustment procedure is significant and leads to a remarkable reduction of interelevation systematic differences. Nevertheless, the variability of the interelevation differences, although also reduced, still remains considerable. This is due to several limitations of the correction procedures, which call for further investigations. First, the 5-km radar grid used in the study is too coarse to handle sharply varying VPR values. Better radar data resolution may lead to significant improvements in this regard. Second, the assumption made here of horizontal VPR homogeneity may lead to inefficiencies of the algorithm. However, it remains to be seen whether the information available from multiscan radar volume data warrants a more spatially detailed reconstruction of the VPR. A third question arises from the need for more precise information when initializing the VPR estimation algorithm. It is likely that the use of measurements from a vertically pointing radar as ‘‘a priori’’ information would lead to significant improvement, particularly in handling very sharp bright band peaks at low altitudes. Furthermore, it has been shown that detection failures make a relatively large contribution to residual biases between VPR-adjusted accumulations obtained from different elevation scans. These failures impose a critical limit to the adjustment available from VPR information. [34] The MFB effect is clearly recognizable and is shown to explain around 20% of the underestimation for this specific study. It has been shown also that even a simple algorithm such as that proposed here can be effective in reducing MFB effects, provided that VPR correction is applied first. Indeed, the analysis suggests that gauge-based radar adjustment can be properly applied only when homogeneity in the accuracy of the radar rainfall estimates with respect to range and scanning elevation is ensured. AP remains a major problem for situations where AP is embedded with precipitation. Developing more complex AP algorithm (such as texture-based classification procedures) that could work more effectively for rain cases is expected to offer significant improvements in radar rainfall estimation. [35] Acknowledgments. The authors are grateful to E. N. Anagnostou (University of Connecticut) for his suggestions and discussions and to Enrico Frank for early elaboration of the data. We also wish to thank two anonymous reviewers for their useful comments. This work was in part supported by the European Commission, DGXII, Environment Programme (contract ENV4-CT96-0290) and by the Italian National Research Council grant 93.02975.PF42. The Natural Environment Research Council (UK) is thanked for making the HYREX data set available.

8 - 10


References Anagnostou, E. N., W. F. Krajewski, D.-J. Seo, and E. R. Johnson, Meanfield radar rainfall bias studies for WSR-88D, ASCE J. Hydrol. Eng., 3(3), 149 – 159, 1998. Anagnostou, E. N., W. F. Krajewski, and J. Smith, Uncertainty quantification of mean-field radar-rainfall estimates, J. Atmos. Oceanic Technol., 16(2), 206 – 215, 1999. Andrieu, H., and J. D. Creutin, Identification of vertical profiles of radar reflectivities for hydrological applications using an inverse method, part 1, Formulation, J. Appl. Meteorol., 34, 225 – 239, 1995. Andrieu, H., J. D. Creutin, G. Delrieu, and D. Faure, Use of weather radar for the hydrology of a mountainous area, part I, Radar measurement interpretation, J. Hydrol., 193, 1 – 25, 1997. Barros, A. P., and D. P. Lettenmaier, Dynamic modeling of orographically induced precipitation, Rev. Geophys., 32(3), 265 – 284, 1994. Borga, M., Accuracy of radar rainfall estimates for streamflow simulation, J. Hydrol., 267, 26 – 39, 2002. Borga, M., E. N. Anagnostou, and W. Krajewski, A simulation approach for validation of a brightband correction method, J. Appl. Meteorol., 36, 1507 – 1518, 1997. Borga, M., E. N. Anagnostou, and E. Frank, On the use of real-time radar rainfall estimates for flood prediction in mountainous basins, J. Geophys. Res., 105, 2269 – 2280, 2000. Brown, R., G. P. Sargent, and R. M. Blackall, Range and orographic corrections for use in real-time radar data analysis, in Hydrological Applications of Weather Radar, edited by I. D. Cluckie and C. G. Collier, pp. 219 – 228, Ellis Horwood, Chichester, England, 1991. Ciach, G. J., and W. F. Krajewski, On the estimation of radar rainfall error variance, Adv. Water Resour., 22, 585 – 595, 1999. Cluckie, I. D., K. A. Tilford, R. J. Griffith, and A. Lane, Radar hydrometeorology using a vertically pointing radar, Hydrol. Earth Syst. Sci., 4, 565 – 580, 2000. Collier, C. G., Accuracy of rainfall estimates by radar, I, Calibration by telemetering rain gauges, J. Hydrol., 83, 207 – 223, 1986. Creutin, J. D., H. Andrieu, and D. Faure, Use of a weather radar for the hydrology of a mountainous area, 2, Radar data validation, J. Hydrol., 193, 26 – 44, 1997. Creutin, J. D., M. Borga, and J. Joss, Hydrometeorology: Storms and flash floods, in Mountainous Natural Hazards, edited by F. Gillet and F. Zanolini, pp. 349 – 366, Cemagref Edt., Grenoble, France, 2000. Fabry, F., and I. Zawadzki, Long-term radar observations of the melting layer of precipitation and their interpretation, J. Atmos. Sci., 52, 838 – 850, 1995. Grecu, M., and W. F. Krajewski, An efficient methodology for detection of anomalous propagation echoes in radar reflectivity data using neural networks, J. Atmos. Oceanic Technol., 17(2), 121 – 129, 2000. Hill, F. F., K. A. Browning, and M. J. Bader, Radar and rain gauge observations of orographic rain over south Wales, Q. J. R. Meteorol. Soc., 107, 643 – 670, 1981. Joss, J., and R. Lee, The application of radar-gauge comparisons to operational precipitation profile corrections, J. Appl. Meteorol., 34, 2612 – 2630, 1995. Joss, J., and A. Waldvogel, Precipitation measurements and hydrology, in Radar in Meteorology, edited by D. Atlas, pp. 577 – 606, Am. Meteorol. Soc., Boston, Mass., 1990. Kitchen, M., and R. M. Blackall, Representativeness errors in comparison

between radar and gauge measurements of rainfall, J. Hydrol., 134, 13 – 33, 1992. Kitchen, M., and P. M. Jackson, Weather radar performance at long range— Simulated and observed, J. Appl. Meteorol., 32, 975 – 985, 1993. Kitchen, M., R. Brown, and A. G. Davies, Real time correction of weather radar for the effects of bright band, range and orographic growth in widespread precipitation, Q. J. R. Meteorol. Soc., 120, 1231 – 1254, 1994. Krajewski, W. F., Co-kriging radar-rainfall and rain gage data, J. Geophys. Res., 92, 9571 – 9580, 1987. Moore, R. J., B. C. May, D. A. Jones, and K. B. Black, Local calibration of weather radar over London, in Advances in Radar Hydrology: Proceedings of the International Workshop, Lisbon, Portugal, 11 – 13 November 1991, edited by M. E. Almeida-Teixeira et al., pp. 186 – 195, Rep. EUR 14334 EN, Eur. Commiss., Brussels, Belgium, 1994. Moore, R. J., D. A. Jones, D. R. Cox, and V. S. Isham, Design of the HYREX rain gauge network, Hydrol. Earth Syst. Sci., 4, 523 – 530, 2000. Seo, D. J., Real-time estimation of rainfall fields using radar rainfall and rain gage data, J. Hydrol., 208, 37 – 52, 1998. Seo, D. J., J. P. Breidenbach, and E. R. Johnson, Real-time estimation of mean-field bias in radar rainfall data, J. Hydrol., 223, 131 – 147, 1999. Seo, D. J., J. P. Breidenbach, R. Fulton, and E. R. Johnson, Real-time adjustment of range-dependent biases in WSR-88D rainfall estimates due to nonuniform vertical profile of reflectivity, J. Hydrometeorol., 1, 222 – 240, 2000. Smith, C. J., The reduction of errors caused by bright band in quantitative rainfall measurements made using radar, J. Atmos. Oceanic Technol., 3, 129 – 141, 1986. Steiner, M., and J. A. Smith, Anomalous signal propagation—An assessment of its potential to occur and ways to mitigate the problem in operational radar data, in 13th Conference in Hydrology, pp. 117 – 120, Am. Meteorol. Soc., Boston, Mass., 1997. Steiner, M., J. A. Smith, S. J. Burges, C. Alonso, and R. W. Darden, Effect of bias adjustment and rain gauge data quality control on radar rainfall estimation, Water Resour. Res., 35(8), 2487 – 2503, 1999. Vignal, B., H. Andrieu, and J. D. Creutin, Identification of vertical profiles of reflectivity from volume scan data, J. Appl. Meteorol., 38, 1214 – 1228, 1999. Wessels, H. R. A., and J. H. Beekhuis, Stepwise procedure for suppression of anomalous ground clutter, in COST 75: Weather Radar Systems, International Seminar, Brussels (B), 20 – 23 September 1995, edited by C. G. Collier, pp. 271 – 277, Rep. EUR 16013, Eur. Commiss., Brussels, Belgium, 1995. Wood, S. J., D. A. Jones, and R. J. Moore, Accuracy of rainfall measurement over scales of hydrological interest, Hydrol. Earth Syst. Sci., 4, 531 – 543, 2000.

H. Andrieu, Division Eau, Laboratoire Central des Ponts et Chausse´es, B.P. 19, 44340 Bouguenais, France. M. Borga, and F. Tonelli, Department of Land and Agroforest Environments, University of Padova, IT-35020, Legnaro, Italy. (marco. [email protected]) R. J. Moore, Centre for Ecology and Hydrology Wallingford, OX10 8BB, UK.