Large sample evaluation of cumulative rainfall amounts in the Alps using a network of three radars

Atmospheric Research 77 (2005) 256 – 268 www.elsevier.com/locate/atmos

Large sample evaluation of cumulative rainfall amounts in the Alps using a network of three radars M. Gabellaa,T, M. Bolligerb, U. Germannb, G. Peronaa a

Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy b Osservatorio Ticinese, Swiss Meteorological Institute, Switzerland Received 31 March 2004; received in revised form 3 September 2004; accepted 24 October 2004

Abstract Quantitative precipitation estimation in complex terrain is surely a challenge. Many papers have been published on the use of radar measurements to estimate surface rainfall during intense events lasting a few days, but little work has been dedicated to large data sets spanning several months and tens of thousands of km2. This paper presents the analysis of 2 years of radar and gauge data measured in Switzerland (from December 2000 to November 2002). The analysis is based on the operational MeteoSwiss radar product RAIN, which combines radar measurements from a total of 20 elevations, to obtain the best estimate of surface precipitation in real time. The resolution is 5 min and 1 km. The data processing includes automatic calibration, 7-step clutter elimination, correction for partial shielding and profile effects, as well as long-term radar–gauge adjustment. The root mean square areal difference between the radar and in situ measurements, rms(AD), is of the order of 1700 mm (the average gauge total of the 2-year period is 3031 mm). This figure is an average of a 39,500 km2 area (427 gauges) that includes mountainous areas with bad radar visibility. A bulk adjustment reduces the rms(AD) to ~900 mm. If an adjustment based on a non-linear weighted multiple regression (WMR) is used, the rms(AD) decreases to ~700 mm. A modified form of the WMR is able to further reduce the rms(AD) to ~400 mm. The results of this and other studies have been used to modify the RAIN algorithm in March 2003 and February 2004, and thus better radar–gauge agreement is expected for the year 2004. D 2005 Elsevier B.V. All rights reserved. Keywords: Meteorological radar; Large rainfall data set evaluation; The Alps; Rain gauge network

T Corresponding author. Tel.: +39 11 5644105; fax: +39 11 5647959. E-mail address: [email protected] (M. Gabella). 0169-8095/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2004.10.014

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

257

1. Introduction For more than five decades researchers have been trying to quantitatively assess rainfall amounts on the ground using radar echoes aloft. Literature is full of analyses on (intense) precipitation events observed by radar (several hours; several thousands of square kilometers). Analysis of larger data sets (weeks, months or even years) over spatial scales (tens of thousands of square kilometers) involving a network of radars are certainly much more unusual (Grecu and Krajewski, 2000; Krajewski and Vignal, 2001; Nelson et al., 2003; Vignal and Krajewski, 2001), especially in Europe (Michelson and Koistinen, 2000). This paper presents the results of an analysis of 2 years of data from the MeteoSwiss network of C-band Doppler radars. It is well known that rain gauge observations represent local effects and not areal quantities. Therefore, for hydrological applications, in which areal precipitation measurements are required, their main drawback is the lack of representativeness (Kitchen and Blackall, 1992) or under-sampling of the spatial variability, i.e. there are not enough observations to describe the variability of the precipitation field. Rain gauges are usually considered to provide accurate bpointQ measurements (a description of the main sources of errors that affect bhigh-resolutionQ rain gauges can be found e.g. in Nystuen et al., 1996; Nesˇpor and Sevruk, 1999; Steiner et al., 1999; Duchon and Essenberg, 2001; Habib et al., 2001; Ciach, 2003). In this context, bpointQ means a gauge cross-section that is usually 200 cm2 (and a sampling volume of the order of ~30 m3 every 5 min, assuming, for instance, 1 mm diameter raindrops). Because of the spatial variability of rainfall (especially during intense, convective events), it is obvious that bpointQ measurements could under-sample the precipitation fields, even though the measurements themselves were correct (Krajewski and Smith, 2002; Krajewski et al., 2003). Radar measurements can add the desired information on the areal distribution of precipitation fields. Several methods have been developed in recent years (e.g. Seo et al., 2000; Michelson and Koistinen, 2000) to operationally merge radar estimates with gauge measurements, so as to obtain quantitatively accurate and spatially continuous radar-derived precipitation fields. Many of these analyzed the Radar-to-Gauge ratio (e.g. Wilson, 1970; Brandes, 1975; Koistinen and Puhakka, 1981; Collier et al., 1983) while others applied optimal interpolation techniques (e.g. Krajewski, 1987; Smith and Krajewsky, 1991). The probability matching of radar reflectivity and the rain rate was first introduced on a long-term basis (of the order of a year) by Calheiros and Zawadzki (1987), and then proposed as an bafter-the-factQ adjustment technique during observation periods of about 3 weeks by Rosenfeld et al. (1993). A well-known technique that has been used in Europe to combine radar and gauge data, particularly in complex orography regions, is that of a non-linear Weighted Multiple Regression (Gabella et al., 2000), which was developed in cooperation with radar meteorologists from the Swiss Confederation and the Czech and Slovak Republics (Boscacci, 1999; Kracmar et al., 1999; Gabella et al., 1999). The WMR-adjustment was successfully applied to the most (severe/extreme) events that occurred in the 1994–2001 period on the southern side of the Western Alps (Gabella and Notarpietro, 2004; Gabella, 2004). This and other adjustment-techniques performances are here compared using a blargeQ (2-year long) data set. Section 2 presents the study area, the sensor locations, the instrumentation and the measurement characteristics. Section 3 introduces the WMR and

258

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

the other techniques. Section 4 describes the tuning and analyzes the resulting coefficients. Section 5 shows the results of the evaluation.

2. Geographic, instrumentation and data description This study is based on 24 months (from December 2000 to November 2002) of data obtained from the MeteoSwiss C-band radar network and from two networks of gauges located in Switzerland (resulting in a very dense network of in situ observations: 427 rain gauges in ~39,500 km2): one network is telemetered and equipped with 69 tipping-bucket rain gauges with 0.1 mm resolution; rain amounts are recorded every 10 min and transmitted, in real time, to the operation center. Fig. 1 shows a (300
300 km2) digital elevation map of the region and the telemetered rain gauge locations. The other gauge network operates 358 daily rainfall-measuring stations, whose locations are shown in Fig. 2. All the gauges lie within the Swiss boundaries in a 39,500 km2 area. Trained part-time

Fig. 1. Digital elevation model of Switzerland and location of the telemetered stations (bANETZ Q network), which are equipped with tipping-bucket rain gauges with a 0.1 mm resolution. The Cartesian axes show the Swiss National (kilometric) coordinates that result from a conformal mapping from the Earth surface to a (nontransverse) cylindrical surface.

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

259

Fig. 2. Location of the daily rainfall-measuring rain gauges (bNIMEQ network) and of the three bmountainousQ Doppler radars: Albis (681E, 238N, 928 m), near Zurich; Dole (497E, 142N, 1680 m), near Geneve; and Lema (708E, 100N, 1625 m), near the Verbano lake.

observers operate many of these stations and professional staff operates some of them. Cumulative daily precipitation amounts are read every day at 0600 UTC. The MeteoSwiss radar network consists of three bmountainousQ C-band Doppler radars. The radar sites are shown in Fig. 2 using a cross within an octagon; their geographic coordinates are: Albis (681E, 238N, 928 m), near Zurich; Dole (497E, 142N, 1680 m), near Genevra; and Lema (708E, 100N, 1625 m). Each radar scans the full volume with a 18 beam at 20 elevations. The 18
18
80 m clutter-free range bins are averaged and resampled on a Cartesian grid. An bOVERVIEWQ product that contains full volume reflectivity information is updated every 5 min. It is well known that it is not sufficient to simply take reflectivity aloft and then use some Z–R relations to derive the rainfall rate on the ground. MeteoSwiss has in fact been working hard in recent years to improve the operational radar estimation of precipitation. These efforts have led to the RAIN product, where the bbestQ estimate of precipitation at ground level is retrieved through a weighted mean of all the radar observations aloft. The weighting function is derived from an average vertical profile of radar reflectivity observed within 70 km from the radar (Germann and Joss, 2002). A maximum of 288 bRAINQ maps were used each day to derive the collocated radar amounts above the gauges: the raw data were converted into precipitation intensities

260

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

Table 1 Statistical characteristics of the 427 radar–gauge couples: height of the gauges above sea level, HG; height of visibility above the gauges, HV (i.e. height a weather target must reach to be visible from the radar site); distances between the radar and the gauges, D; logarithm of the distances normalized to 1 km (same logarithmic dimension used in the non-linear Weighted Multiple Regressions) Height of the gauges, HG Height of visibility, HV Radar–gauge distance, D Log10(D)

Average

Median

Standard deviation

Min.

Max.

0.82 km 1.86 km 64.9 km 1.74

0.70 km 1.44 km 61.4 km 1.79

0.45 km 1.29 km 33.2 km 0.30

0.20 km 0.51 km 1.1 km 0.04

3.32 km 4.93 km 155 km 2.19

The 427 rain gauge locations are shown in Figs. 1 and 2. They have been installed in a ~39,500 km region (almost the whole Helvetic Confederation).

using a Z–R power-law relationship (Z = aR b ) with b = 1.5 and a = 316. A detailed description of the radars can be found e.g. in Joss et al. (1998), while a detailed characterization of the hostile orography can be found in Germann and Joss (2004). For a large-sample evaluation of the operational quantitative precipitation estimates based on the RAIN product, the reader can refer to Germann et al. (2004). In this paper, the radar–gauge comparison involves one radar (out of three) which has the best (blowestQ) height of visibility, HV. The distribution of the radar–gauge distance (also on the logarithmic scale used in the regression) and the HV, according to this criterion, is shown in Table 1 (the equivalent earth’s radius that is used is 8000 km). Table 1 also shows the height of the ground, HG, which is used together with HV and Log(D) as an explanatory variable in the weighted multiple regression.

3. Gauge-adjustment of radar-based precipitation estimates 3.1. A simple (one-coefficient) bulk adjustment A simple remedy that can be used to compensate at least the bias is the so-called bulk adjustment. This consists in multiplying radar estimates by the ratio between the Gauges and Radar total (overall total, in time and space). 3.2. An adjustment based on a non-linear Weighted Multiple Regression (WMR) The WMR method, as many other gauge adjustment techniques, analyzes the Radar-toGauge ratio. Using the same terminology introduced by Collier et al. (1983), let us call Assessment (or Adjustment) Factor (AF) the ratio between the time-cumulated radarderived rain amount, t R, and the corresponding time-cumulated gauge amount, t G. First of all, in order to reduce the fluctuations of the AF, caused not only by changes in storm microphysics, but most of all by intrinsically different sampling modes as well as mismatches in time and space of the radar and gauge instruments, we consider timeintegrated and non-instantaneous values of the AF. When comparing radar and gauges, it is in fact wise to integrate in time (e.g. Zawadzki, 1975). The WMR method considers the AF as a model of the bmultiplicative errorQ that affects radar measurements taken at a

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

261

certain altitude with respect to the corresponding precipitation values taken on the ground. It tries to bexplainQ its variability in terms of the following three independent variables: (1) D, the distance between the radar and the gauges, which reflects non-homogeneous beam filling, the altitude of the beam, beam broadening and, to some extent, attenuation; (2) HV, the height a meteorological target must reach over the gauge-pixel to be visible to the radar, taking shielding effects into consideration (this reflects the influence of the vertical profile of reflectivity); (3) HG, the height of the gauge (corresponding to the altitude of the terrain; this reflects the depth of the layer where precipitation increases related to orography can occur). The variability of the AF (dependent variables) is analyzed on a decibel scale. The adopted non-linear, multiple regression for each radar–gauge data couple is written as:
 AFdB ¼ 10d log t R=t G ¼ a0 þ aD d logðDÞ þ aHV d HV þ aHG d HG: ð1Þ Unlike an ordinary multiple regression, a weighted multiple regression should be used to correct the radar estimates: this means that the four regression coefficients in Eq. (1) are determined by minimizing the weighted sum of square errors instead of an ordinary sum of square errors. The bphilosophyQ behind Eq. (1), the weights to be used as well as the explanation of why a logarithmic dimension of AF and D allows optimum performance, is described in Section 4 of Gabella et al. (2001). 3.3. A (two-coefficient) adjustment based on a non-linear Simple Regression (SR) This adjustment is based on a power-law Simple Regression (SR) between the timeaveraged radar observations (i.e. the components of the column-matrix t R) and the physical quantity we would like to retrieve (i.e. the column-matrix t G, whose components are the time-cumulated precipitation amounts at the ground at each site). On a logarithmic decibel scale: t GdB

¼ ad t RdB þ v

ð2Þ

With respect to the bulk adjustment (Section 3.1), there is one additional coefficient to be tuned: the exponent-coefficient a (in addition to v). 3.4. An adjustment based on a modified Weighted Multiple Regression (mWMR) Let us write the non-linear WMR expression (Eq. (1)) in a slightly different form, namely: t GdB

 t RdB ¼  a0  aD d logðDÞ  aHV d HV  aHG d HG:

ð3Þ

The remotely sensed observable (i.e. the radar reflectivity, Z, above a rain gauge) has been related to the instantaneous rainfall intensity, R, through a power-law, Z = ad R b . The timecumulated radar-derived rain amount, t R, involves the average of N echoes (dozens or hundreds in a rainy day, thousands in the bclimatologicalQ approach here presented); in formula: N X 1 1=b R¼ Z : ð4Þ N d a1=b i¼1 i

262

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

If, as in Section 3.3, we allow an adjustment based on an exponent-coefficient a, Eq. (4) becomes: !a  a N X 1 1=b Ra ¼ d Zi : ð5Þ N d a1=b i¼1 If this new term is arbitrarily moved to the right side, Eq. (2) becomes: 1st order adjustment

t GdB

2nd order adjustment

zfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflffl{ zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ ¼ ad t RdB þ vdB  aD Logð DÞ  aHV d HV  aHG d HG :

ð6Þ

In this modified form of the WMR (mWMR), the ratio between the (time-cumulated) radar and gauge amounts no longer represents the dependent variable; rather, the timecumulated precipitation on the ground, t G, is directly explained: ! as a function of the Remotely sensed estimate, R, as in Section 3.3; this 1st part of the regression has a greater influence on the adjustment process than the 2nd one; ! as a function of three additional variables (D, HV, HG), which bstatistically explainQ part of the difference between the radar observations aloft and the gauge values (Section 3.2); this second part of the regression plays a minor role, as shown by the values of the retrieved coefficients in Section 4 (Eq. (9)).

4. Tuning the radar–gauge adjustment techniques The underestimation of precipitation using radar often occurs in the presence of high orography. This is due to the increasing illuminated volume with range as well as the effect of a decreasing vertical profile of radar reflectivity with height, combined with beam shielding and/or occultation by orography. These effects are in turn complicated by an increased non-homogeneous beam filling effect. From the 3rd column of Table 2, it is evident that the bulk-adjustment coefficient derived from 427 radar–gauge couples for the 2-year period is of the order of 2.0 (3 dB). Actually, it is derived using a bcross-validationQ approach: the idea is to exclude one Table 2 Results of the verification in terms of root mean square of the radar–gauge areal differences of precipitation amounts cumulated over 2 years P P Type of radar data R/ G FSE Root mean square of the radar–gauge areal differences Raw data Bulk-adjusted data WMR-adjusted data SR-adjusted data MWMR-adjusted data

0.50 1.00 0.94 0.98 0.99

0.57 0.47 0.39 0.22 0.19

1685 mm 857 mm 707 mm 454 mm 416 mm

The study area (~39,500 km2) is in Switzerland and is covered by a network of three C-band radars and of 427 daily rain gauges. The 2-year average precipitation measured by the gauges is 3031 mm. The Fractional Standard Error (FSE) is defined as the root mean square of the 427 radar–gauge differences normalized to the average precipitation measured by the gauges.

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

263

observation at a time when deriving the bulk adjustment while in the evaluation the resulting coefficient is used to evaluate the excluded data point. The same approach has been used with the other adjustment techniques (which are based on more than one coefficient): we have 427 sub-samples made of 426 radar–gauge couples from which 427 sets of coefficients are derived; in the evaluation process (next section), each of these sets of coefficients is used to predict and then evaluate the excluded data point. For instance, the average values (out of 427 regressions) of the WMR-derived coefficients are: GdB  RdB ¼  AFdB ¼ þ 0:86 þ 0:64d LogD þ 1:37d HV  1:75d HG:

ð7Þ

The explained variance (i.e. the square of the multiple correlation coefficient) is ~35%. The values of the coefficients are somewhat artificial, since they depend on the units that are used in the regression (the distances from the radar are measured in kilometers) and on the reference system (the heights above mean sea level are also expressed in kilometers). As expected and obtained so far in the course of several storms in the Western Alps (e.g. Gabella and Notarpietro, 2004; Gabella, 2004), both coefficients a HV and a D are always negative, indicating that the radar underestimates precipitation for higher sampling volumes and longer distances. In past WMR analyses, the buncertaintyQ affecting a HG was so large that it spanned both negative and positive values. Those analyses also referred to the Western Alps, but to ~50 radar–gauge couples (during a storm): the smaller sample was probably insufficient to reveal an orographic influence on the Radar-to-Gauge ratio, AF. Here the sign of a HG reveals that, on average, the AF increases with increasing height of the ground. The average values (out of 427 regressions) of the power-law relationship between the 2-year in situ values and the corresponding remotely sensed estimates are:

 Log t G ¼ þ 0:26d Log t R þ 2:67: ð8Þ The explained variance is only ~32%. If we consider a brainyQ season with higher (on average) 08 isotherms (for instance, spring 2001, during which the average precipitation over the whole Switzerland was greater than 700 mm) the explained variance increases to 45%, a increases from 0.26 to 0.44 and v decreases from 2.67 to 1.47. Finally, the average m-WMR adjustment coefficients are (as in Eq. (7), D, HV and HG are again expressed in km; as in Eq. (8), t R and t G are expressed in mm):

 Log t G ¼ þ 0:32d Log t R þ 2:46  0:06d LogD þ 0:04d HV þ 0:03d HG; ð9Þ and the resulting explained variance is ~55%. The values of the first two coefficients (in Eq. (8) as well) tell us that the radar practically sees only a very small part of the variability of precipitation on the ground. Unfortunately, this is exactly what happens! In this part of the Western Alps most of the radar echoes are in fact backscattered by solid precipitation (the radar cannot see the liquid phase below).

5. Evaluation and results The areal estimate of precipitation is of major interest for hydrology. The agreement between radar-derived and in situ rainfall estimates can however only be checked at some points (with some reasonable and representative information from the gauges). The

264

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

variability of the precipitation field and the extreme differences in sampling modes are relevant when comparing measurements from radar and rain gauges (Ciach and Krajewski, 1999; Habib and Krajewski, 2002). A radar samples a volume high up in the sky (a volume which increases in size with distance) once every 5 min, while a rain gauge continuously records at a single point on the ground. With an average rainfall velocity of ~5 m/s, the gauge would sample ~30 m3 in 5 min. Even on a 2-year basis, this volume is no larger than 105 m3, a value that is still far from the volume of the thousands of radar samples measured aloft, whose order of magnitude is, on average, approximately 109 m3 for each individual sample of instantaneous backscattered measurement. Consequently, we less than 1500 mm 1500 - 2000 mm 2000 - 2500 mm 2500 - 3000 mm 3000 - 3500 mm 3500 - 5000 mm 5000 - 9000 mm more than 9000 mm

Grisons

Valais

Valle d’ Aosta

less than 1500 mm 1500 - 2000 mm 2000 - 2500 mm 2500 - 3000 mm 3000 - 3500 mm 3500 - 5000 mm 5000 - 9000 mm more than 9000 mm

295

240

185

130

735

675

615

555

495

75

Fig. 3. Two-year radar-derived precipitation amounts measured to the north, south and over the Graian, Pennine and Leponitne Alps using the MeteoSwiss network of three C-band Doppler radars (white marks). The upper left and lower right Swiss National coordinates of the selected area are (495E, 310N) and (795E, 10N). The upper left picture is simply bthe averageQ of more than two hundred thousand 5-min radar maps (acquired from December 2000 to November 2002) multiplied by 2.0 (bulk adjustment). This btwo-year radar averageQ, in the upper right picture, has been adjusted using an estimated assessment factor that is a function of the distance, height of visibility and the height of ground (WMR-adjustment, see Eq. (7)). The bradar averageQ, in the lower left picture, has been adjusted using a Simple Regression (SR-adjustment, see Eq. (8)). The precipitation on the ground, in the lower right picture, is bpredictedQ using, in addition to the radar observations, the topography combined with the distance and height of the radar echoes (mWMR-adjustment, see Eq. (9)). This kind of adjustment shows the best performance in terms of root mean square of the radar–gauge differences (see Table 2).

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

265

decided not to compare each individual bpointQ measurement and the corresponding radar estimate; we instead opted for areal estimates over rectangular patches of 60
55 km2 (see lower left picture in Fig. 3). All the gauges lie in 18 of these patches. We then derived an array of 18 Areal Differences and to summarize the results, we opted for the root mean square of these 18 Areal-integrated Differences, rms(AD), which is shown in the last column of Table 2. Even a simple bulk adjustment leads to an improvement in terms of rms(AD). The corresponding 2-year radar-derived, bulk-adjusted, rainfall amounts are shown in the upper left picture of Fig. 3, where in practice, the original (raw) radar estimates are simply multiplied by a factor of 2 (see the 3rd column of Table 2, first line). It is evident that all the three radars are bblindQ in part of the Valais, Valle d’Aosta, Grisons and western Piedmont regions. An adjustment based on a WMR further reduces the rms(AD); a qualitative visual inspection of the corresponding WMR-adjusted rainfall map (upper right picture of Fig. 3) shows the improved situation both in the region of poor visibility (originally greatly underestimated) and in the vicinity of the radars (originally overestimated). Smaller values of rms(AD) are found using a purely empirical simple regression (last line of Table 2). However, this regression squeezes the radar signal dynamics: the rainfall amounts on the ground are proportional to R b , where b (Eq. (9)) is as small as 0.26 (instead of 1!) This fact is visible in the lower left picture (Fig. 3) that shows the corresponding adjusted map using this simple (power law) regression. The image shows little contrast and variability, the precipitation field seems indeed to be too uniform. The lowest value of rms(AD) is obtained using a modified WMR (4th line, Table 2): the corresponding mWMR-adjusted image of the 2-year cumulated precipitation field is shown in the lower right picture of Fig. 3. Radial and concentric artifacts are present in all the pictures; the (upper) lower right pictures depict the spatial variability of Alpine precipitation at a resolution that has never been reached before and with a reasonable accuracy: the root mean square areal difference is ~420 mm (~710 mm), i.e. 14% (23%) of the 2-year average precipitation measured by the 427 rain gauges.

6. Summary and concluding remarks In this study, the radar estimate of precipitation on the ground is not simply obtained by taking a (single) reflectivity value aloft (the most common operational radar products are: the maximum echo along the vertical or the lowest useful elevation echo). It is instead retrieved through a weighted mean of all the overlying radar observations (full volume, up to 20 elevations). The weighting function is derived from an average vertical profile of radar reflectivity observed within 70 km from the radar. This post-processing is performed operationally and in real time for the MeteoSwiss network of radars and the results are stored in the so-called bRAINQ product, which has been used in this study. In spite of all these efforts, which include (since the beginning of 2001) the introduction of meso-beta profiles of reflectivity (Germann and Joss, 2002), it can be seen from the 1st line of Table 2 that during the 2-year period (3031 mm of average precipitation) the root mean square of the Areal Differences, rms(AD), is still as high as ~1700 mm (and the bias is 3 dB in rainfall amounts, i.e. of the order of 4.5 dBZ in terms of radar reflectivity, Z). This often happens in a hostile mountainous terrain, where the radar sees precipitation only thousands

266

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

of meters above the ground. However, for the 2001–2002 period, even a purely empirical, single-coefficient bulk adjustment reduces the rms(AD) from ~1700 to ~900 mm. Other adjustments, which relate 2-year radar and gauge amounts on a logarithmic scale and are based on 2 or more coefficients, remarkably reduce the rms(AD). The best results are obtained using a non-linear Weighted Multiple Regression to bpredictQ precipitation on the ground as a function not only of the radar observations alone, but also of the topography, distance and height of the radar echoes: in this case the rms(AD) results to be as small as ~400 mm. A significant improvement (down to ~705 mm) is also obtained using a nonlinear Weighted Multiple Regression (WMR) to explain the Radar-to-Gauge ratio. This adjustment factor is derived as a function of the distance and height of visibility from the radar site (in addition to the topography). If classification is used according to meteorological classes, it is hoped in the future to be able to find weather-dependent coefficients that can be applied consistently with the actual meteorological situation. However, the application of the WMR method is not restricted to prognosis; it is also an important tool for the diagnosis of the accuracy of radar rainfall estimates in mountainous terrain. It can be used to diagnose the influence of beam broadening with distance (and non-homogeneous beam filling), of the height of visibility and of the ground: the fact that ~40% of the variability of the 2-year Radar-to-Gauge ratio in the Alps can be explained as function of these three explanatory variables tells us that this is an indicator of the quality or the radar product. In the meantime MeteoSwiss has made several improvements to the algorithms for quantitative precipitation estimation. The first results, which are based on a large-sample evaluation, are promising: the overall bias, scatter, probability of detection, false alarm ratio, critical success index and equivalent threat score all show a significant improvement. In 2003 (and the first 6 months of 2004) the bias for well-visible areas is below 10%, while for most of Switzerland, including several shielded valleys at relatively far ranges (~100– 150 km), is below 25%. For details see Germann et al. (2004). Acknowledgments This research was co-funded by the European Commission as part of the VOLTAIRE project (Contract EVK2-CT-2002-00155). The authors wish to thank Gianmario Galli and Ju¨rg Joss for the interesting discussions and the two anonymous reviewers for their comments and suggestions. References Boscacci, M., 1999. Quality checks for elaborate radar measures. In: Collier, G.C. (Ed.), COST-75 Final International Seminar on Advanced Weather Radar Systems, Locarno, Switzerland. Commission of the European Communities, Brussels, Belgium, pp. 280 – 287. Brandes, E.A., 1975. Optimizing rainfall estimates with the aid of radar. J. Appl. Meteorol. 14, 1339 – 1345. Calheiros, R.V., Zawadzki, I., 1987. Reflectivity–rain rate relationships for radar hydrology in Brazil. J. Appl. Meteorol. 26, 118 – 132. Ciach, G.J., 2003. Local random errors in tipping-bucket rain gauge measurements. J. Atmos. Ocean. Technol. 20 (5), 752 – 759.

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

267

Ciach, G.J., Krajewski, W.F., 1999. Radar–rain gauge comparisons under observational uncertainties. J. Appl. Meteorol. 38 (10), 1519 – 1525. Collier, C.G., Larke, P., May, B., 1983. A weather radar correction procedure for real-time estimation of surface rainfall. Q. J. R. Meteorol. Soc. 109, 589 – 608. Duchon, C.E., Essenberg, G.R., 2001. Comparative rainfall observations from pit and aboveground rain gauges with and without wind shields. Water Resour. Res. 37, 3253 – 3263. Gabella, M., 2004. Improving operational measurement of precipitation using radar in mountainous terrain: Part II. Verification and applications. IEEE Geosci. Remote Sens. Lett. 1, 84 – 89. Gabella, M., Notarpietro, R., 2004. Improving operational measurement of precipitation using radar in mountainous terrain: Part I. Methods. IEEE Geosci. Remote Sens. Lett. 1, 78 – 83. Gabella, M., Galli, G., Ghigo, O., Joss, J., Perona, G., 1999. Clutter elimination and agreement between hourly precipitation amounts as measured by two radars and a network of gauges. In: Collier, G.C. (Ed.), COST-75 Final International Seminar on Advanced Weather Radar Systems, Locarno, Switzerland. Commission of the European Communities, Brussels, Belgium, pp. 102 – 113. Gabella, M., Joss, J., Perona, G., 2000. Optimizing quantitative precipitation estimates using a non-coherent and a coherent radar operating on the same area. J. Geophys. Res. 105, 2237 – 2245. Gabella, M., Joss, J., Perona, G., Galli, G., 2001. Accuracy of rainfall estimates by two radars in the same Alpine environment using gage adjustment. J. Geophys. Res. 106, 5139 – 5150. Germann, U., Joss, J., 2002. Mesobeta profiles to extrapolate radar precipitation measurements above the Alps to the ground level. J. Appl. Meteorol. 41, 542 – 557. Germann, U., Joss, J., 2004. Operational measurement of precipitation in mountainous terrain (Chapter 2). In: Meischner, P. (Ed.), Weather Radar: Principles and Advanced Applications. Physics of Earth and Space Environment, vol. XVII. Springer Verlag, Heidelberg, Germany, pp. 52 – 77. Germann, U., Galli, G., Boscacci, M., Bolliger, M., Gabella, M., 2004. Quantitative precipitation estimation in the Alps: where do we stand? Third European Conference on Radar Meteorology ERAD 2004, Visby, Sweden, pp. 33 – 37. Grecu, M., Krajewski, W.F., 2000. A large-sample investigation of statistical procedures for radar-based shortterm, quantitative precipitation forecasting. J. Hydrol. 239 (1–4), 69 – 84. Habib, E., Krajewski, W.F., 2002. Uncertainty analysis of the TRMM ground validation radar-rainfall products: application to the TEFLUN-B field campaign. J. Appl. Meteorol. 41 (5), 558 – 572. Habib, E., Krajewski, W.F., Kruger, A., 2001. Sampling errors of fine resolution tipping-bucket rain gauge measurements. J. Hydrol. Eng. 6 (2), 159 – 166. Joss, J., Schadler, B., Galli, G., Cavalli, R., Boscacci, M., Held, E., Della Bruna, G., Kappenberger, G., Nespor, V., Spiess, R., 1998. Operational Use of Radar for Precipitation Measurement in Switzerland. Hochschulverlag AG an der ETH, Zurich. Kitchen, M., Blackall, R.M., 1992. Representativeness errors in comparisons between radar and gauge measurements of rainfall. J. Hydrol. 134, 13 – 33. Koistinen, J., Puhakka, T., 1981. An improved spatial gauge-radar adjustment technique. Preprints. 20th Conf on Radar Meteorology Amer. Meteor. Soc., pp. 179 – 186. Kracmar, J., Joss, J., Novak, P., Havranek, P., Salek, M., 1999. First steps towards quantitative usage of data from Czech weather radar network. In: Collier, G.C. (Ed.), COST-75 Final International Seminar on Advanced Weather Radar Systems, Locarno, Switzerland. Commission of the European Communities, Brussels, Belgium, pp. 91 – 101. Krajewski, W.F., 1987. Cokriging radar-rainfall and rain gauge data. J. Geophys. Res. 92, 9571 – 9580. Krajewski, W.F., Smith, J.A., 2002. Radar hydrology: rainfall estimation. Adv. Water Resour. 25, 1387 – 1394. Krajewski, W.F., Vignal, B., 2001. Evaluation of anomalous propagation echo detection in WSR-88D data: a large sample case study. J. Atmos. Ocean. Technol. 18 (5), 807 – 814. Krajewski, W.F., Ciach, G.J., Habib, E., 2003. An analysis of small-scale rainfall variability in different climatological regimes. Hydrol. Sci. J. 48 (2), 151 – 162. Michelson, D.B., Koistinen, J., 2000. Gauge-radar network adjustment for the Baltic Sea experiment. Phys. Chem. Earth, Part B 25, 915 – 920. Nelson, B.R., Krajewski, W.F., Kruger, A., Smith, J.A., Baeck, M.L., 2003. Archival precipitation data set for the Mississippi River Basin: algorithm development. J. Geophys. Res. 108 (D22), 8857.

268

M. Gabella et al. / Atmospheric Research 77 (2005) 256–268

Nesˇpor, V., Sevruk, B., 1999. Estimation of wind-induced error of rainfall gauge measurements using a numerical solution. J. Atmos. Ocean. Technol. 16, 450 – 464. Nystuen, J.A., Proni, J.R., Black, P.G., Wilkerson, J.C., 1996. A comparison of automated rain gauges. J. Atmos. Ocean. Technol. 13, 62 – 73. Rosenfeld, D., Wolff, D.B., Atlas, D., 1993. General probability-matched relations between radar reflectivity and rain rate. J. Appl. Meteorol. 32, 50 – 72. Seo, D.J., Breidenbach, J.P., Fulton, R., Miller, D., O’Banon, T., 2000. Real time adjustment of range dependent biases in WSR-88D rainfall estimates due to non-uniform vertical profile of refractivity. J. Hydrometeorol. 1, 222 – 224. Smith, J.A., Krajewsky, W.F., 1991. Estimation of the mean field bias of radar rainfall estimates. J. Appl. Meteorol. 30, 397 – 412. Steiner, M., Smith, J.A., Burges, S.J., Alonso, C.V., Darden, R.W., 1999. Effect of bias adjustment and rain gauge data quality control on radar rainfall estimation. Water Resour. Res. 35, 2487 – 2503. Vignal, B., Krajewski, W.F., 2001. Large sample evaluation of two methods to correct range-dependent error for WSR-88D rainfall estimates. J. Hydrometeorol. 2 (5), 490 – 504. Wilson, J.W., 1970. Integration of radar and gage data for improved rainfall measurements. J. Appl. Meteorol. 9, 489 – 497. Zawadzki, I., 1975. On radar–rain gage comparison. J. Appl. Meteorol. 14, 1430 – 1436.