Radar rainfall estimation of stratiform winter precipitation in the Belgian Ardennes


  • P. Hazenberg,

    1. Hydrology and Quantitative Water Management Group, Centre for Water and Climate, Department of Environmental Sciences, Wageningen University,, Wageningen,, Netherlands
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  • H. Leijnse,

    1. Hydrology and Quantitative Water Management Group, Centre for Water and Climate, Department of Environmental Sciences, Wageningen University,, Wageningen,, Netherlands
    2. Now at Royal Netherlands Meteorological Institute,, De Bilt,, Netherlands
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  • R. Uijlenhoet

    1. Hydrology and Quantitative Water Management Group, Centre for Water and Climate, Department of Environmental Sciences, Wageningen University,, Wageningen,, Netherlands
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[1] Radars are known for their ability to obtain a wealth of information about spatial storm field characteristics. Unfortunately, rainfall estimates obtained by this instrument are known to be affected by multiple sources of error. Especially for stratiform precipitation systems, the quality of radar rainfall estimates starts to decrease at relatively close ranges. In the current study, the hydrological potential of weather radar is analyzed during a winter half-year for the hilly region of the Belgian Ardennes. A correction algorithm is proposed which corrects the radar data for errors related to attenuation, ground clutter, anomalous propagation, the vertical profile of reflectivity (VPR), and advection. No final bias correction with respect to rain gauge data was implemented because such an adjustment would not add to a better understanding of the quality of the radar data. The impact of the different corrections is assessed using rainfall information sampled by 42 hourly rain gauges. The largest improvement in the quality of the radar data is obtained by correcting for ground clutter. The impact of VPR correction and advection depends on the spatial variability and velocity of the precipitation system. Overall during the winter period, the radar underestimates the amount of precipitation as compared to the rain gauges. Remaining differences between both instruments can be attributed to spatial and temporal variability in the type of precipitation, which has not been taken into account.

1. Introduction

[2] Weather radars have long been recognized for their ability to obtain spatiotemporal information about storm fields at a much higher resolution than conventional rain gauge networks [Zawadzki, 1975; Joss and Lee, 1995; Smith et al., 2001; Berne et al., 2004a]. Therefore, large-scale implementation of these systems during the last decades would, in principle, make this instrument an important tool for rainfall monitoring in the framework of hydrological applications such as (flash) flood forecasting [Collier and Knowles, 1986; Joss and Waldvogel, 1990; Carpenter et al., 2001; Vivoni et al., 2006].

[3] Unfortunately, data obtained by weather radars are known to be affected by multiple sources of error. Interaction with the nearby environment can result in (partial) beam blockage and ground clutter, which especially play a dominant role in mountainous regions. This results either in an underestimation or overestimation of the amount of precipitation [e.g., Delrieu et al., 1995; Gabella and Perona, 1998; Germann and Joss, 2002; Germann et al., 2006; Dinku et al., 2002]. Other sources of error are related to temporal changes of the index of refraction [e.g., Fabry et al., 1997; Steiner and Smith, 2002], variability of the drop size distribution [e.g., Waldvogel, 1974; Berenguer and Zawadzki, 2008], and variability of the vertical profile of reflectivity (VPR) [e.g., Fabry and Zawadzki, 1995; Smyth and Illingworth, 1998; Cluckie et al., 2000].

[4] During the past decades, different techniques have been developed to correct for these types of errors, resulting in a serious improvement in the radar data quality [e.g., Kitchen and Jackson, 1993; Ciach et al., 1997; Pellarin et al., 2002; Gourley et al., 2009]. Joss and Lee [1995] implemented a stepwise algorithm identifying clutter and correcting for beam occultation, radar calibration errors, and VPR effects using either a climatological or real-time profile estimate. Anagnostou and Krajewski [1999a, 1999b] developed a similar system for an environment where topography causes no serious problems. In all of these studies, rain gauge measurements were used to correct for any final bias. A different approach was taken by Delrieu et al. [2009] for a series of extreme precipitation events within a mountainous environment in the southern part of France. Besides correcting for the errors mentioned above, the type of precipitation (convective versus stratiform) was identified as well. This resulted in a radar product of which the quality is comparable to that of rain gauge measurements.

[5] The impact of radar correction steps for stratiform precipitation systems occurring within a winter period has received less attention. During such situations, the upper part of the atmosphere consists of snow and ice particles. The melting of these particles results in a stronger return signal, known as the bright band, and causes the amount of precipitation to be overestimated by the weather radar. For the snow-ice region above the bright band, a significant decrease in the returned reflectivity signal can be observed. Especially at farther ranges, reflectivity samples originate from these two regions, which has a detrimental impact on the quality of the radar product [Fabry et al., 1992; Kitchen and Jackson, 1993; Bellon et al., 2005]. Long-term investigations of the influence of different correction mechanisms for such stratiform situations have been presented by Vignal and Krajewski [2001], Borga [2002], Germann et al. [2006], and Bellon et al. [2007]. Unfortunately, they did not attempt to verify the quality of the adjusted radar product by using it as an input to a hydrological model.

[6] The hydrological potential of weather radar has been investigated both for individual precipitation events [e.g., Hossain et al., 2004; Berne et al., 2005; Vieux and Bedient, 1998; Ogden et al., 2000; Smith et al., 2007] and on a longer-term basis [Borga, 2002; Neary et al., 2004]. Most of these identify the benefits of using radar (i.e., the ability to obtain spatial-temporal properties of the precipitation field at a high resolution). Unfortunately, only few of them corrected for all significant types of measurement errors. As a consequence, obtained results using weather radar rainfall information as an input to a hydrological model are highly dependent on the quality of the data and the environment of application.

[7] This paper addresses the importance of correcting volumetric radar reflectivity data and the applicability of these correction steps for long-term real-time hydrological purposes. The region studied is situated in the Belgian Ardennes mountain range and focuses on a winter half-year during which most of the precipitation has a stratiform character. Volumetric radar data are corrected for errors associated with attenuation, ground clutter and anomalous propagation conditions, VPR, and advection. It was decided not to correct for the remaining final bias between the amount of precipitation estimated by the radar and a rain gauge network. This decision was made to get a better understanding of the quality of the radar and because of inherent scale problems between both devices [e.g., Austin, 1987; Kitchen and Blackall, 1992; Steiner et al., 1999; Ciach and Krajewski, 1999; Morin et al., 2003].

[8] This paper is organized as follows. Section 2 will give an overview of the study area and data availability. Section 3 focuses on the different radar correction steps that have been implemented, followed by a comparison with rain gauge measurements for a series of events (section 4). Next, a whole winter period is analyzed (section 5). The different implementations are discussed in section 6, in which we will also present an application to real-time hydrological modeling at the catchment scale.

2. Study Area and Data Availability

[9] The hilly plateaus of the Ardennes, part of the Meuse basin, are situated in the eastern part of Belgium (see Figure 1) and display maximum elevations of around 650 m above sea level (asl). The hydrologic response can be classified as rain fed with some snow in winter. This results in a runoff regime that can be classified as highly variable, giving rise to low discharges in summer and high discharges in winter [Leander et al., 2005].

Figure 1.

(left) Location of the study area, with a 200 × 200 km box indicating the area shown in Figure 1 (right). (right) Topographic map of the Belgian Ardennes, where the solid lines represent the channel network. The white line indicates the Ourthe catchment (1600 km2). Also shown are the position of the radar (solid circle), catchment outlet (triangle), the meteorological station (open circle), and the position of the rain gauges (crosses).

[10] In 2001, a C-band Doppler radar was installed at an elevation of 600 m asl near the village of Wideumont, close to the border with Luxembourg. The radar has two scan sequences: one every 5 min at five different elevations and a second scan at another 10 elevations every 15 min. In this study the 5-min data were used to obtain areal information about the precipitation field. The reflectivity data from the second scan serves only to obtain an initial estimate of the VPR. A summary of the characteristics of the weather radar is presented in Table 1.

Table 1. Characteristics of the C-Band Doppler Radar at Wideumont Used in This Study
Latitude, longitude (deg)49.91, 5.51
Height (m asl)600
Frequency (GHz)5.64
Pulse repetition frequency (Hz)600
Beam width (deg)1
Antenna diameter (m)4.2
Maximum range (m)240
Scanning sequences2
Pulse length (m)250 (scan 1), 500 (scan 2)
Recurrence interval (min)5 (scan 1), 15 (scan 2)
Elevations (deg)0.3, 0.9, 1.8, 3.3, 6.0 (scan 1);
0.5, 1.2, 1.9, 2.6, 3.3, 4.0, 4.9, 6.5, 9.4, 17.5 (scan 2)

[11] Directly to the north of the radar lies the ∼1600 km2 Ourthe catchment, which has been the focus of previous studies [Berne et al., 2005; Driessen et al., 2010]. Its outlet is situated in the north near Tabreux, at approximately 60 km from the radar. Rain gauge information in the region is available for 42 rain gauges, of which 10 are directly situated inside the watershed. In addition, hourly temperature and potential evaporation data are available from the weather station near St. Hubert (see Figure 1).

[12] This study analyzes the spatial and temporal characteristics of rainstorms and the resulting catchment response of the Ourthe for the period from 1 October 2002 until 31 March 2003. During this winter half-year, most storms had a stratiform character, for which bright bands could already be observed within 1000 m from the surface. Radar data are not available for the second week of November and for one day at the end of March. These periods are left out of the analysis. For the hydrological analysis they are substituted by rain gauge data.

3. Radar Reflectivity Analysis

[13] The general measurement equation of the radar can be stated as follows:

equation image

where P(r) is the received power (W) for a given elevation at a range r (m) from the radar, C (W m5 mm-6) is the radar constant, and Zm(r) is the measured reflectivity (mm6 m-3). Both the radar reflectivity and rainfall intensity R (mm h-1) are dependent on the raindrop size distribution. The relationship between both parameters is generally assumed to follow a power law [Marshall and Palmer, 1948; Marshall et al., 1955; Battan, 1973]:

equation image

where the parameters a and b are a function of the raindrop size distribution and vary with precipitation type [Ulbrich, 1983]. Before radar data can be used for hydrological purposes, errors related to the environment and spatiotemporal atmospheric variations should be accounted for [Andrieu et al., 1997]. On the basis of the characteristics of the weather radar (see Table 1) and the Ardennes mountain range, it was therefore decided to correct the data for losses due to attenuation, artifacts due to clutter, range effects due to VPR, and potential errors due to finite sampling of rainfall. Although the radar data may be affected by other types of errors (e.g., radome attenuation, radar calibration, partial beam filling, blockage, and overshooting), these four are considered to be the main sources of error for the environment under study. Sections 3.13.5 present an in-depth overview of the different steps taken to correct for these four sources of error.

3.1. Signal Attenuation

[14] Signal attenuation can become a source of error for operational C band weather radars, especially during high rainfall intensities, and depends on both the raindrop size distribution and temperature [e.g., Delrieu et al., 1991, 1997; Berenguer et al., 2002]. One method to correct for attenuation was developed by Hitschfeld and Bordan [1954] (HB algorithm). The measured radar reflectivity is the product of two terms:

equation image

where Za(r) (mm6 m−3) is the apparent reflectivity at a given height not subject to any attenuation. In this study, it is assumed that the radar is well calibrated and there are no signal losses due to wet radome effects. Then, the amount of two-way path-integrated attenuation (PIA) (dB) is given by

equation image

where k(s) (db km−1) is the specific attenuation at a distance s (km). The relation between the reflectivity and specific attenuation can also be stated as a power law:

equation image

[15] On the basis of equations (3), (4), and (5), the apparent reflectivity can be expressed as

equation image

[16] In case of severe attenuation the denominator of equation (5) becomes small, causing the HB algorithm to become unstable. Another algorithm (originally developed for spaceborne radar [see Marzoug and Amayenc, 1994]), which is not prone to this source of error, makes use of a mountain reference [Delrieu et al., 1997; Bouilloud et al., 2009]. Unfortunately, in the current study mountainous returns are limited to a region close to the radar and cannot be applied for attenuation correction. Although it can be expected that the amount of PIA is limited for the stratiform precipitation encountered during a winter period [Delrieu et al., 1999, 2000; Uijlenhoet and Berne, 2008], the maximum amount of PIA was set to 10 dB to prevent the algorithm from becoming unstable. The parameter values of the Z-k relation (equation (5)) were estimated on the basis of drop size distributions sampled in the Netherlands [Uijlenhoet, 2008], with c = 7.34 × 105 and d = 1.344. These were assumed to originate from similar storm systems as those observed in the Ardennes region.

3.2. Anomalous Propagation and Clutter Identification

[17] Radar data in mountainous environments can be contaminated by ground clutter (GC) due to sidelobe reflections from topography and/or (partial) blockage by topography [e.g., Delrieu et al., 1995; Gabella and Perona, 1998; Pellarin et al., 2002]. Anomalous propagation (AP) occurs in situations where the vertical gradient of refractivity is large in the lower part of the atmosphere, causing the radar signal to bend down toward the surface, resulting in ground echoes [e.g., Alberoni et al., 2001; Steiner and Smith, 2002; Cho et al., 2006; Berenguer et al., 2006]. Especially at longer ranges, AP-induced GC can result in serious overestimates of the amount of precipitation [Andrieu et al., 1997].

[18] In literature, multiple GC identification techniques have been proposed, using either pulse to pulse reflectivity fluctuations [Wessels and Beekhuis, 1994], radial Doppler velocity information [Joss and Lee, 1995], spatial reflectivity information [Alberoni et al., 2001], or dual-polarization data [Giuli et al., 1991]. Other sources of data have also been used to identify GC, such as digital elevation models, temperature, or satellite information [e.g., Delrieu et al., 1995; Michelson and Sunhede, 2004; Fornasiero et al., 2006]. Currently, most GC identification algorithms make use of a classification scheme using multiple information criteria [e.g., Joss and Pittini, 1991; Joss and Lee, 1995; Steiner and Smith, 2002; Grecu and Krajewski, 2000; Berenguer et al., 2006; Cho et al., 2006]. In the framework of this study, it was decided to use the identification tree as proposed by Steiner and Smith [2002] because no radial velocity information was available. The original algorithm was extended to all elevations to identify GC pixels for the higher radar elevations as well. In the first step, a polar pixel is identified as GC if it has a minimum vertical extent less then 500 m. Next, radar pixels for which spatial variability and vertical variability both exceed a threshold value are identified as clutter. Further details of this method were presented by Steiner and Smith [2002]. Within mountainous environments, beam occultation causes a decrease in the total beam power, resulting in an underestimation by the radar [Delrieu et al., 1995]. For this type of error, no corrections were implemented because the Wideumont radar is situated at a relatively high altitude within the region. It is assumed that most of the observed GC is caused by sidelobe interception instead of direct blockage of the main beam and that therefore no beam occultation occurs.

3.3. Identification of the Vertical Profile of Reflectivity

[19] As explained in section 1, variation in the vertical structure of the precipitation field can be a serious source of error, especially for stratiform precipitation [Andrieu et al., 1997; Seo et al., 2000]. Kitchen et al. [1994] applied a correction method which updates the shape of a theoretical stratiform VPR using local meteorological characteristics. Results showed significant improvement in the estimated amount of precipitation. Germann and Joss [2002] estimate a spatially variable apparent VPR on the basis of measured volumetric weather radar data for regions up to 70 km from the radar (the meso-equation image scale). What these investigators and others [e.g., Dinku et al., 2002; Jordan et al., 2003] did not consider is the fact that the radar sampling volume increases with range.

[20] A method that does take this aspect into account is the inverse VPR identification technique of Andrieu and Creutin [1995], which was extended for volumetric radar data by Vignal et al. [1999]. The main assumptions behind this method are a spatially uniform VPR over a certain region and the decomposition of the spatial variation of the apparent reflectivity Za(r) (equation (3)) into a horizontal and vertical component:

equation image

[21] Here ZREF(x) is the reflectivity at a certain reference level at distance x from the radar, and za(y) is the apparent vertical profile of reflectivity, which is influenced by the increase of the radar beam volume as a function of range. This latter effect can be written in a simplified way as

equation image

where f is the power distribution of the radar signal, equation image is the radar beam width, and z(y) represents the actual average vertical reflectivity signal. The numerical solution discretizes z(y) into finite intervals of a few hundred meters. For each of these increments at a given range from the radar, its contribution to the total power distribution of the transmitted signal is calculated. In order to estimate the discretized profile of z(y), two types of information are needed. First, an initial estimate of the VPR, for which either a climatological profile or one estimated from the sampled volumetric data can be used. The second type of information needed is provided by the so-called ratio functions, which represent the ratio of one of the higher elevations with respect to the bottom one as a function of distance. Theoretical ratio functions are also calculated for the initial VPR using the characteristics of the radar. Then, using an inverse optimization scheme [Menke, 1989], the initial VPR is adjusted in such a way as to minimize the difference between the theoretical and measured ratio functions.

[22] This inverse method is well able to identify VPRs for stratiform situations with low-level bright bands [Borga et al., 1997]. Therefore, in this study this technique is applied to obtain a VPR estimate. During winter, most of the storm systems passing over the Ardennes have an echo top well below 6 km. The estimates of the VPR are therefore performed up to a height of 6 km at 250-m increments in the current study. The power distribution at a given distance from the radar for the different intervals was calculated on the basis of the radar characteristics. It was decided to use only the information within a 15-min window to diminish the effect of temporal changes in the VPR [Fabry et al., 1992; Bellon et al., 2005; Joss et al., 2006]. The initial VPR estimate is obtained by combining all volumetric data of both scanning sequences (see section 2) within a 15-min window for distances between 10 and 50 km from the radar. Next, on the basis of the 15-min interval volumetric data for the first scanning sequence, the ratio profiles are estimated up to a distance of 100 km. This is done by calculating the ratios of the measured reflectivity values for the four higher elevations (2–5) with respect to the bottom elevation reflectivity values. These are subsequently averaged over all polar radar cells at a given range. Once both the initial VPR estimate and the four sampled ratio profiles are obtained, the inverse optimization method is applied from which a final spatially averaged VPR is obtained.

[23] Although different studies have shown improved radar rainfall estimates when this method is applied [Andrieu et al., 1995; Anagnostou and Krajewski, 1999b; Vignal et al., 1999], a critical aspect is the assumption of a spatially uniform profile. Vignal et al. [2000] therefore identified the VPR for regions of 20 × 20 km. Delrieu et al. [2009] proposed first to select the type of precipitation system (convective, stratiform, or undefined) and then to estimate the VPR for each type separately. To analyze the option of using a local VPR, in this study a profile is also estimated on the basis of the polar reflectivity data sampled over the Ourthe catchment only. In this manner, a catchment-scale VPR is obtained, which also improves the consistency between the spatial and temporal meteorological scales [Germann and Joss, 2002]. No precipitation identification has been performed because in general, during the period of interest, most precipitation originates from stratiform systems only.

3.4. Beam Integration and Grid Conversion

[24] After correcting for the three mentioned types of error (associated with attenuation, ground clutter, and VPR, respectively), the final step is to obtain a 2-D-corrected polar reflectivity field. Similar to other radar correction algorithms operating in a mountainous environment [e.g., Joss and Lee, 1995; Germann and Joss, 2002; Delrieu et al., 2009], a weighted average was taken over the different radar elevations up to a height of 2500 m. Polar cells that were identified as GC are not taken into account. Each elevation at each point was weighted using 1/(h + 1), where h is the height (m) of the measurement, because of the assumption that lower elevations give a better estimate of the true reflectivity at the surface. The maximum measurement elevation of 2500 m was identified because most precipitation systems in this region for the period of interest have a small vertical extent. This maximum is similar to the study by Anagnostou and Krajewski [1999b]. After this aggregation step, all polar points are converted to a Cartesian grid by averaging those corresponding to a given Cartesian grid cell. When a Cartesian cell does not contain at least three corresponding polar points, interpolation with respect to the three nearest points is performed.

3.5. Storm Field Advection and Z-R Conversion

[25] Because of the temporal scanning strategy of the radar it is necessary to take the advection velocity of the precipitation field into account [e.g., Fabry et al., 1994; Jordan et al., 2000]. To correct for this source of error, a correlation-based technique is applied [e.g., Rinehart and Garvey, 1978; Tuttle and Foote, 1990; Anagnostou and Krajewski, 1999a]. The Cartesian grid is subdivided into 20 × 20 km grid blocks. For each of these, the advection direction and velocity are calculated by maximizing the correlation between two consecutive reflectivity (dBZ) fields. It is known that in the case of a spatially homogeneous precipitation field or because of the influence of residual GC, the obtained advection direction and velocity could differ from the actual ones when calculated in this manner [Tuttle and Foote, 1990; Li et al., 1995]. In order to minimize this possibility, advection directions are averaged over 40 × 40 km grid blocks, removing those values with correlation <0.7. Using the resulting advection field, the radar data are then interpolated in time at 30-s intervals. Growth and decay of the storm field are not considered here.

[26] To convert the obtained radar reflectivity to an equivalent rainfall rate (equation (2)), the Marshall-Palmer relationship Z = 200 R1.6 is applied [Marshall et al., 1955]. This relationship is known to be representative for stratiform situations [Battan, 1973]. Radar data are then averaged into hourly intervals.

[27] One problem not accounted for in the current algorithm implementation is related to possible temporal changes in the transmitted power of the weather radar in equation (1) [Ulbrich and Lee, 1999]. Steady clutter points could be used to get an indication of such changes. Results based on a few steady polar GC points for the Wideumont radar indeed showed a nonconstant backscatter. Unfortunately, it is difficult to isolate such variations from apparent changes in the refractivity or from temporal changes in vegetation and the occurrence of snow at the surface [Delrieu et al., 1995]. It was therefore decided not to take this aspect into account.

[28] In many studies, an additional step is performed to remove any residual bias with respect to rain gauge measurements [e.g., Krajewski et al., 1996; Smith and Krajewski, 1991; Ciach and Krajewski, 1999; Seo and Breidenbach, 2002; Goudenhoofdt and Delobbe, 2009]. Such a final step is not implemented here because we feel that by correcting the data on the basis of the volumetric measurements only, the full hydrological potential of weather radar in a hilly environment can be analyzed.

4. Importance of the Different Correction Steps

[29] In this section, the influence of the correction steps is analyzed by comparing 42 hourly radar–rain gauge pairs for three rainfall events typical to the region for a winter period. In order to reduce the effect of sampling differences between radar and rain gauge measurements [Joss and Lee, 1995], hourly rainfall accumulations are compared.

4.1. Event 1: A Stratiform System

[30] The first event selected was a fast-moving stratiform system which started at around 2000 UTC on 22 October 2002 and lasted for about 9 h. Average reflectivities in the range 30–43 dBZ were observed, as well as a clear bright band at around 1800 m above the radar.

[31] In Figure 2, the total event accumulation for the uncorrected (Figure 2a) and corrected radar data (Figure 2b) is presented. Comparison of both plots immediately shows the impact of both the clutter correction and advection algorithms. Not taking the former into account leads to an overestimation of the amount of precipitation, while for the latter, the observed small-scale pattern in Figure 2a does not represent reality.

Figure 2.

Total storm accumulation for (a) uncorrected and (b) fully corrected radar data for the event on 22–23 October 2002. White areas correspond to severe ground clutter leading to an overestimation. (c) Initial estimate of the vertical profile of reflectivity (VPR), the final VPR obtained using the inverse method, and a frequency plot of the measured normalized VPR (similar to the CFAD of Yuter and Houze [1995]). (d) Measured reflectivity ratios (dashed lines) and simulated reflectivity ratios (solid lines) using the obtained final VPR. Different lines represent the ratio between a given elevation and the lowest one. The data for Figures 2c and 2d correspond to a 15-min time window sampled around 2300 UTC on 22 October.

[32] For each time step, at a given polar radar pixel at 10–50 km distance, the reflectivity values sampled at one of the higher radar elevations were normalized with the lowest elevation by taking the ratio. Using these ratios for each 250-m interval up to a height of 6 km, a frequency plot was created. This frequency is indicated by the gray shading in Figure 2c. Such a frequency diagram is similar to the CFAD profile by Yuter and Houze [1995] or the meso-equation image profile by Germann and Joss [2002]. In addition to the occurrence of a bright band, it can also be observed that the distribution of VPRs is very broad.

[33] The average VPR calculated from the frequency distribution is indicated by the dotted line in Figure 2c. As explained in section 2, beam broadening was not taken into account for this profile. Together with the measured reflectivity ratios in Figure 2d (dashed lines), it serves as the initial VPR estimate. Using the inverse identification method of Andrieu and Creutin [1995], the final VPR was estimated, which is used to correct radar data for VPR effects. This profile is indicated by the black line in Figure 2c. Compared to the initial VPR obtained from the radar data, the bright band is especially more intense for the final profile. In order to indicate how well this final profile is able to represent a spatially averaged VPR, the characteristics of the radar were used to estimate the theoretical ratio functions. When compared to the observed ratio functions, it can be observed that they show a good correspondence. The differences that do occur are related to the spatial nonuniformity of the VPR as represented by the spread in the gray shaded areas in Figure 2c.

[34] The correspondence between the corrected radar rainfall estimates and the different rain gauges is shown in Figure 3. Hourly precipitation depths are well correlated in Figure 3a, although overall radar rainfall estimates are lower than those from the rain gauges. This is also confirmed by the storm accumulations in Figure 3b. Linear regression without intercept between the different radar–rain gauge pairs (gray line) confirms the underestimation by the radar. At the hourly and total event scales the regression-based underestimation was about 29% and 34%, respectively. Such large differences are not uncommon for radar–rain gauge comparisons, especially for stratiform systems.

Figure 3.

Comparison of rainfall intensities and accumulations from 42 rain gauges and the corresponding radar pixels for the event on 22–23 October 2002. Scatterplots of the (a) hourly and (b) total event rainfall accumulation for the 42 pairs. The gray lines correspond to the linear regression between the two, for which the slope is given by s. (c and d) Quality of the radar measurement as a function of range from the radar, where radar/gauge ratio was defined as equation image Radar rainfallequation image Gauge rainfall for a given gauge. NS is the Nash-Sutcliffe statistic [Nash and Sutcliffe, 1970].

[35] To investigate whether the observed errors can be related to range effects, Figures 3c and 3d show the event accumulation ratios and Nash-Sutcliffe (NS) coefficients [Nash and Sutcliffe, 1970] of the different radar–rain gauge pairs as a function of distance from the radar. A radar/gauge ratio less than 1 (Figure 3c) indicates an underestimation by the radar. In both Figures 3c and 3d, a range effect can be observed. Up to about 60 km the behavior is rather constant. At greater distances, the difference between both instruments increases. It is expected that this is due to the usage of a global VPR. The estimated profile in Figure 2c generally tends to give more weight to the reflectivity values close to the radar. For the current event, storm cells observed farther away from the radar had a slightly different average VPR than presented in Figure 2c and were therefore not always properly VPR corrected. This reveals a drawback of estimating one single VPR profile for the entire radar umbrella [Vignal et al., 1999].

[36] Table 2 presents the influence of the different correction steps on the radar–rain gauge comparison statistics. Uncorrected (raw) radar data are well able to capture the dynamic pattern of the storm system, as indicated by the large coefficient of determination equation image. However, the correspondence between these radar rainfall estimates and those from the rain gauge is poor, containing an overall positive bias and very small Nash-Sutcliffe statistic. A large improvement in the quality of the data is obtained when correcting for clutter (as can be observed from Figures 2a and 2b). Correcting for attenuation leads to a bias improvement. The implementation of the VPR correction method on average does not improve the correspondence between both types of data. As mentioned, the estimated VPR depends heavily on the data sampled close to the radar. Therefore, the benefit of the VPR correction at close ranges may be counteracted by worse results at larger distances. This latter phenomenon can also be observed in Figure 3c and 3d. For the current event, advection correction did not lead to any serious improvements in the measurement quality of the weather radar data.

Table 2. Evaluation of the Influence of the Different Radar Correction Steps for the Event on 22–23 October 2002a
  • a

    Columns are as follows: Raw, no radar correction; +Clut, correction only for clutter; +Atten, correction also for attenuation; +VPR, correction also for vertical profile of reflectivity (VPR); +Advec, correction also for advection. The GVPR and CVPR columns represent the results for the 10 gauges within the Ourthe catchment using either a global (GVPR) or catchment (CVPR) VPR estimate. The statistics were calculated on the basis of hourly information and represent the coefficient of determination equation image, the ratio equation image Radar rainfallequation image Gauge rainfall, and the Nash-Sutcliffe statistic (NS).

equation image0.850.870.860.840.850.950.95
equation image1.190.590.670.660.660.760.75

[37] In Table 2, the impact of using either a global or local VPR is presented, comparing the radar results to the 10 gauges situated inside the catchment. Estimating a VPR based on the volumetric data sampled above the Ourthe catchment only does not lead to any improvement. The main reason for this is related to the large size of the catchment and the fact that it is situated close to the radar. Both aspects result in a large overlap with the reflectivity data used to obtain the global VPR estimate. Differences in the obtained local and global VPR shapes are therefore small.

[38] Overall, it can be stated that for this event, up to about 60 km the radar was able to estimate the actual rainfall accumulation well. On average, up to these distances the bias between both instruments is about 25%. At larger distances from the radar, spatial variability of the VPR makes it impossible to obtain better results. Instead of applying one global profile estimate, a spatially varying estimate would probably improve the overall statistics for this event.

4.2. Event 2: Large-Scale Stratiform System

[39] The second event analyzed here took place on 22 December 2002 and started around 0300 UTC, lasting for about 13 h. From the volumetric radar data (not shown) a clear bright band could be observed at a height of 1800 m above the radar. The precipitation system was relatively uniform and very widespread, covering almost the full radar image with average reflectivities in the range 20–30 dBZ.

[40] The widespread character of the precipitation system causes some unwanted results for the GC and advection algorithms (Figures 4a and 4b). Although most GC is filtered out, some clutter-contaminated spots are still observed. This is related to the fairly uniform reflectivity field, which decreases the amount of spatial irregularity. Some clutter is therefore not identified. As explained in section 3.5, a spatially homogeneous precipitation field and/or residual GC might result in an incorrect identification of the advection direction [Tuttle and Foote, 1990; Li et al., 1995]. Even though we tried to correct for this, some artifacts (straight/blocky lines) of this problem can be observed Figure 4b, although their impact is small.

Figure 4.

As in Figure 2 but for the event on 22 December 2002. The data for Figures 4c and 4d correspond to a 15-min time window around 0900 UTC on 22 December.

[41] The spatial variability of the vertical profile is rather limited, as shown by the narrow frequency diagram of the normalized VPR in Figure 4c. The good correspondence between the observed and simulated ratio profiles in Figure 4d was therefore expected, giving a lot of confidence in the final VPR estimate.

[42] The radar–rain gauge comparisons in Figure 5 show an underestimation of the radar for both the hourly (Figure 5a) and total event accumulations (Figure 5b). For the hourly data, the overall spread is much larger than in Figure 3, which is due to variations in the type of precipitation, probably changing from showers into drizzle and vice versa. Especially for the latter, the Marshall-Palmer Z-R relationship is known not to be representative but to underestimate precipitation intensities [Battan, 1973], as is also clearly the case here. As a result, the radar underestimates the amount of precipitation.

Figure 5.

As in Figure 3 but for the event on 22 December 2002.

[43] The overall statistics in Table 3 reveal a poor correspondence between the 42 radar and rain gauge points. Again, the biggest improvement is made by correcting for GC. VPR correction removes the influence of the overestimation due to the bright band, resulting in an increase in the radar quality as seen by the NS. Correcting for attenuation leads to some improvements with respect to the bias in Table 3, while advection correction has no serious influence because of the moderate reflectivity variations and velocity of the observed precipitation field.

[44] The slightly worse result when using a catchment-based VPR estimate instead of the global VPR is related to a slightly larger normalized bright band size estimated on the basis of the catchment reflectivity data (not shown here). Correcting the radar data based on this VPR leads to smaller reflectivity values and rainfall estimates and thus slightly worse results.

Table 3. Evaluation of the Influence of the Different Radar Correction Steps for the Event on 22 December 2002a
  • a

    See Table 2 for explanation of the different types of correction and the statistics.

equation image0.770.790.780.830.830.870.86
equation image1.030.680.720.690.690.720.69

4.3. Event 3: Fast-Moving Frontal Stratiform System

[45] During the third event analyzed here, large overall accumulations could be observed in the Ardennes region, which resulted in the largest flood peak measured within the half-year period. The event started on 1 January 2003 around 1000 UTC and had a total duration of about 42 h. Radar images (not shown) revealed that the storm consisted of a series of fast-moving stratiform showers exhibiting considerable horizontal variability of the reflectivity field and, from time to time, well-developed bright bands at around 1500 m above the radar.

[46] Figures 6a and 6b again show the positive influence of the different radar correction steps on the overall storm accumulations. For the current event, hourly radar-gauge values line up well in Figure 7a. On average, an underestimation by the radar (29%) can be observed. A closer look at the accumulations in Figure 7b reveals that only five gauges measured much more precipitation than was estimated by the radar. These gauges are all situated to the southwest of the radar. There are three possible reasons for these differences between both instruments. As mentioned, the observed storm field was highly variable in space (Figure 6c), especially in the southwesterly direction from the radar. This resulted in some precipitation being identified as GC. Spatial variability in the VPR might have produced inappropriate corrections when using the global VPR estimate for the southwesterly region. In addition, it is possible that the usage of the Marshall-Palmer Z-R relationship was not optimal because of local variation in the type of precipitation for this region.

Figure 6.

As in Figure 2 but for the event on 1–3 January 2003. The data for Figures 6c and 6d correspond to a 15-min time window around 0900 UTC on 2 January.

Figure 7.

As in Figure 3 but for the event on 1–3 January 2003.

[47] No range effects can be observed in Figures 7c and 7d. Up to large distances from the radar both statistics stay rather constant. During this event the temporal variability in the estimated VPR was limited as compared to the October event (event 1). Therefore, using a single VPR for the whole radar umbrella was beneficial.

[48] Table 4 presents the influence of the different correction steps on the average hourly goodness-of-fit statistics of the radar–rain gauge comparisons. Except for attenuation, which does not play a serious role here, each correction step improved the quality of the data. This, on average, leads to an overall radar product quality that is comparable to that of the rain gauges.

Table 4. Evaluation of the Influence of the Different Radar Correction Steps for the Event on 22 December 2002a
  • a

    See Table 2 for explanation of the different types of correction and the statistics.

equation image0.840.860.850.860.870.900.90
equation image1.50.931.050.880.891.111.10

5. Overall Radar–Rain Gauge Comparison

[49] Results presented in section 4 showed that the impact of a given correction step strongly depends on the spatiotemporal characteristics of the precipitation system. Only the GC algorithm has a clear overall positive impact during all three storms. The next step is to have a closer look at the performance of the currently implemented radar correction algorithm for the total half-year data set. Such an overall analysis reduces the influence of the individual storm types and enables one to obtain a better understanding concerning the general quality of the algorithms.

[50] Figure 8 presents the overall ratios of daily radar-gauge accumulations on the basis of hours when both instruments measure precipitation (R ≥ 0.1 mm h−1). The average ratio values for the 42 events vary considerably in time without containing any immediate trends. The impact of changes in the transmitted power of the weather radar (equation (1)) is therefore assumed to have been small.

Figure 8.

Average ratios of the daily radar and rain gauge values for the half-year data set. Vertical bars indicate the 10th to 90th percentile range for the 42 rain gauges. The gray stars indicate the three events presented in section 4.

[51] Overall results lie close to the ratio value of 1, although from Table 5 it can be seen that on average, the underestimation is about 28%. However, for a given day, considerable variability is observed between the different gauges as indicated by the width of the bars corresponding to the 10th and 90th percentiles. The average half-year underestimation by the radar for each radar-gauge pair separately is presented in Figure 9a and varies between 5% and 45% underestimation, without showing any range effect. Range effects can be observed from the obtained half-year Nash-Sutcliffe statistics (Figure 9d), where the radar quality starts to decrease beyond 70 km from the radar. During the winter half-year, the average height of the bright band was between 1000 and 2000 m above the radar elevation. Therefore, the snow region above it starts to be sampled by the lowest radar elevation at a distance of around 70 km. Even though the correction algorithm takes the effects of VPR into account, its quality apparently decreases at these long ranges. This can be related to the fact that the estimated VPR mostly depends on the data measured close to the radar. Similar behavior could also be observed when analyzing event 1. This again shows the difficulty of taking all types of variability in the precipitation field into account. In addition, it can be expected that differences in sampling characteristics between the radar and rain gauge such as height and measurement volume will also play a greater role at larger distances [Austin, 1987; Gabella et al., 2000].

Figure 9.

Comparison between the hourly radar and rain gauge values for the half-year data set. Figures 9a and 9b correspond to Figures 3c and 3d, respectively.

Table 5. Evaluation of the Influence of the Different Radar Correction Steps for Hourly Precipitation Values of the Half-Year Data Seta
  • a

    See Table 2 for explanation of the different types of correction and the statistics.

equation image0.670.720.710.720.730.720.72
equation image5.690.770.810.770.730.750.74

[52] Table 5 presents the half-year goodness-of-fit statistics. As expected, the largest improvements in the quality of the radar data were obtained after correction for GC, followed by adjusting for VPR. Correction for attenuation only has a positive effect on the radar-gauge ratio but has a slightly negative impact on the other statistics. A possible explanation could be the usage of an inappropriate Z-k relationship for the Ardennes region, leading to incorrect estimation of the average amount of PIA. However, the influence of attenuation at C-band for this type of stratiform systems is small, as expected [Delrieu et al., 1999, 2000]. For individual, more intense events, such as the ones presented for October, this correction did have a positive impact. Correcting for advection only has a beneficial impact in the case of faster-moving storm systems of considerable variability. During the winter half-year, most stratiform storms were slow-moving, spatially homogeneous systems. Therefore, advection correction has no major impact.

[53] The implementation of a VPR estimate based on the volumetric radar data measured above the catchment does not improve results compared to applying a global VPR estimate. This could already be observed from the analysis of the individual events but is different from results obtained in other studies [Vignal et al., 2000]. As explained, a significant overlap exists between the areas used to obtain global and catchment VPR estimates. This results in almost identical profiles for both regions.

6. Discussion

6.1. Algorithm Implementation

[54] Removal of GC using the algorithm proposed by Steiner and Smith [2002] showed large improvements in the quality of the radar rainfall estimates. Analysis of the third event in section 4.3 showed that for some specific cases, it might be too sensitive. In addition, for event 2 in section 4.2 it could be observed that some isolated clutter areas cannot be identified in case of widespread and spatially homogeneous precipitation. Some pixels might have been identified as clutter, although they contained a mixture of both clutter and precipitation. The impact of removing these pixels is expected to be small because in order to obtain a 2-D polar radar estimate, a weighted average of all elevations, corrected for VPR effects, is taken. The radar data used in the current study originate from an early stage of operation. Currently, applying Doppler velocity information to discriminate clutter from precipitation has become a standard operational procedure. Unfortunately, these data were not available for the current study. Therefore, it is expected that the erroneous clutter identification and removal still observed in this study will decrease when using more recent data.

[55] Correction for attenuation showed a positive impact only for a few events but had zero or even a slightly negative impact on the overall rainfall estimation capability of the weather radar. As stated, the parameters of the Z-k relationship in equation (5) were obtained from disdrometer measurements in the Netherlands, which might not have been fully representative for the hilly environment of the Belgian Ardennes. Moreover, attenuation is not a major source of error for the Belgian winter climate at C-band in the first place. Wet radome attenuation [Germann, 1999] due to rain and snow might have resulted in additional attenuation for some events. However, it is very difficult to correct for this source of error in an operational environment. Therefore, correction for this was not attempted.

[56] The success of the VPR identification algorithm is highly dependent on the spatial variability of the storm field, as was shown by the spread of the frequency diagram of the normalized profiles in Figures 2c, 4c, and 6c. Here the reflectivity information was accumulated over 15-min intervals. Berne et al. [2004b] showed that on the basis of such aggregation periods, the estimated VPR is representative, on average, for an area of about 100 km2. In this study, the algorithm is applied at such a high temporal resolution to minimize the effect of temporal changes in the VPR. According to Bellon et al. [2005], such an implementation could give rise to a highly variable average VPR estimate, which is not representative for ranges farther from the radar. In this study, we were only interested in the quality of the radar up to a range of 100 km. Therefore, the possible detrimental effects of obtaining a VPR estimate at such a high temporal resolution were considered not to be problematic. A possible future improvement, however, might be to focus on smaller areas for VPR estimation.

[57] Such areas could either be obtained by taking only the volumetric weather radar data sampled above a certain catchment into account or by focusing more specifically on a given storm cell. Although the former method did not improve the quality of the radar data for the region inside the Ourthe catchment, it can be expected that particularly for distances farther away, such an approach would improve the impact of correcting for VPR. With respect to the latter, it could be possible to make use of a cell-tracking algorithm [Dixon and Wiener, 1993; Handwerker, 2002]. Such an approach would ensure that the obtained average VPR is representative for a given storm cell. Variability in the shape of the VPR for different storm cells as was observed for event 1 can then be taken into account. In addition, such a cell-tracking algorithm can also be applied to obtain advection direction information. Erroneous cross correlations, of which the impact for some time steps could be observed in Figure 4b, are then removed.

[58] On the basis of Figure 8 we assume that there were no serious trends in the transmitted power of the weather radar. However, in this study no specific information concerning absolute radar calibration was available. Overestimation in the amount of transmitted power can result in an underestimation of the amount of precipitation [Ulbrich and Lee, 1999] as estimated by the radar, as seen in this study. Atlas [2002] presents a historical overview on how to identify radar calibration problems. In an operational environment, Holleman et al. [2010] used the Sun to correct for this error source, while Ulbrich and Lee [1999] used disdrometer measurements to identify any resulting bias due to calibration issues. Another problem might be the choice of the Marshall-Palmer Z-R relationship, which, on average, might not be optimal for the type of precipitation in the Belgian Ardennes. This aspect will surely play a role in the temporal variability of the type of precipitation. Different types of precipitation contain different drop size distributions, resulting in variations of the Z-R relationship [Creutin et al., 1997; Uijlenhoet et al., 2003], as could also be observed during event 2. Polarimetric weather radar could result in an improved understanding of these variations.

6.2. Hydrological Potential of the Weather Radar

[59] This study analyzed the quality of the weather radar precipitation measurements on the basis of individual radar–rain gauge pairs. As explained, range effects and sampling differences complicate comparison between both devices [Austin, 1987; Kitchen and Blackall, 1992; Gabella et al., 2005]. However, it can be expected that this difference becomes smaller when aggregating over longer time periods [Borga et al., 2006] or over a catchment [Vignal et al., 2000]. One of the main benefits of using weather radar with respect to rain gauges is the fact that one obtains much more information about the precipitation field. However, for the hydrological analyses presented here, we will only use catchment-averaged rainfall information. Given the lumped model that is currently operationally used by Dutch water management authorities and given the typical response that can be observed within the Ardennes during a winter period, this is not unreasonable. The hydrological results presented in Figure 10 should be interpreted as a worst case; actually using the full potential of weather radar (i.e., high spatial resolution combined with a distributed hydrological model) is highly likely to lead to larger improvements than if only rain gauge data are used. This is subject of ongoing investigations.

Figure 10.

Observed and simulated hydrographs for the half-year data set using catchment average rain gauge and radar data.

[60] Measured and simulated hydrographs are presented in Figure 10, where both the radar and rain gauge data have been applied to simulate the discharge response of the Ourthe catchment using the operational HBV model [Bergström, 1976, 1992; Lindström et al., 1997]. This model is used by the Dutch authorities to simulate the discharge of the river Meuse for the purpose of operational water management. It has been calibrated for the Ourthe using over 30 years of data [Velner, 2000; Booij, 2002]. At the scale of the Ourthe catchment, simulation is performed using a single lumped version of the model. Therefore, weather radar data are averaged over the catchment while the rain gauge information is first interpolated before being averaged. Both model simulations are started 6 months in advance using measured catchment average rain gauge values in order to create similar initial conditions for both types of input data.

[61] From the results in Figure 10, it can be observed that the overall differences in obtained hydrographs using either rainfall source are small. The Nash-Sutcliffe values using the radar and rain gauge precipitation as an input are 0.88 and 0.89, respectively. Up to the beginning of November the simulated hydrograph based on the radar data is closer to the observed discharges than the hydrograph obtained from the rain gauge data. The discharge peak at the beginning of January 2003 is underestimated by both hydrographs. This difference is related to the lumped character of the model, which cannot take spatial variability of soil moisture into account. It should be noted that for the radar, a larger underestimation of the maximum discharge peak is observed. Evaluation of the third event in section 4 shows little difference between rainfall estimates obtained by radar and rain gauges. The observed difference in the absolute size of the simulated discharge peak therefore does not occur as a result of erroneous precipitation estimates by radar during that event. A closer inspection of Figure 10 reveals that the simulated hydrograph based on the radar data starts to underestimate observed discharges during the second half of December 2002. During this period, it can be observed from Figure 8 that the radar underestimated the amount of precipitation for several days, as could also be observed for event 2 (section 4.2). This resulted in lower storage in the catchment before the event of 1–3 January, leading to a lower simulated discharge peak. Overall, these simulations clearly reveal the potential of applying weather radar information without using any rain gauge information for operational water management.

7. Conclusion

[62] In this paper, the effects of different radar correction steps and their impact on radar rainfall estimates have been investigated for stratiform winter precipitation within a hilly environment. Especially for the more temperate regions, where discharges are largest and cause the biggest problems in winter, correct estimation of the amount of precipitation for this type of rainfall is important. On the basis of the current analysis, it could be observed that the largest improvement in the quality of the radar data was observed after GC removal. Attenuation correction, as expected, led only to an improved quality of the radar data for some of the more intense events. Overall, correcting for attenuation did not have a significant impact on the quality of the data. Correcting for advection of the precipitation field only improves the results for faster-moving precipitation systems, as presented in section 4.3. For large-scale, slow-moving systems (sections 4.1 and 4.2), taking advection into account is not necessary.

[63] The impact of correcting for the VPR is highly dependent on the spatial variability of the storm system under consideration. The implemented algorithm to obtain a global estimate of the VPR is heavily influenced by measurements taken close to the radar. Therefore, for cases with highly spatially variable storm systems, such an estimated profile does not always lead to improved results for distances farther away. Up to a distance of 70 km from the radar it could be observed that the quality of the corrected radar product became comparable to that of the rain gauges, except for a slight underestimation. At distances beyond 70 km from the radar this quality decreases, although some of this can be related to sampling differences between both instruments.

[64] Overall, the corrected radar data yield slightly lower precipitation amounts than the rain gauges. However, within the current hydrological operational environment, this does not immediately lead to erroneous rainfall-runoff simulations (Figure 10). In the future, one of the main challenges will be to take the spatial variability of the precipitation system into account. Polarimetric radars, which are gradually replacing nonpolarimetric radars all over the world, have the potential to lead to further improvements.


[65] The authors would like to thank Laurent Delobbe of the Royal Meteorological Institute of Belgium for providing the volumetric radar data and temperature and evaporation information. Philippe Dierickx of the Hydrological Service of the Walloon Region of Belgium (MET-SETHY) is thanked for providing discharge and rain gauge information. Finally, the authors would also like to acknowledge Albrecht Weerts of Deltares for providing the hydrological model. This research has been financially supported by the EU-FP6 Project FLOODsite (GOCE-CT-2004-505420), the EU-FP6 Project Hydrate (GOCE-CT-2006-037024), and the EU-FP7 Project IMPRINTS (FP7-ENV-2008-1-226555).