Identification and uncertainty estimation of vertical reflectivity profiles using a Lagrangian approach to support quantitative precipitation measurements by weather radar



[1] This paper presents a novel approach to estimate the vertical profile of reflectivity (VPR) from volumetric weather radar data using both a traditional Eulerian as well as a newly proposed Lagrangian implementation. For this latter implementation, the recently developed Rotational Carpenter Square Cluster Algorithm (RoCaSCA) is used to delineate precipitation regions at different reflectivity levels. A piecewise linear VPR is estimated for either stratiform or neither stratiform/convective precipitation. As a second aspect of this paper, a novel approach is presented which is able to account for the impact of VPR uncertainty on the estimated radar rainfall variability. Results show that implementation of the VPR identification and correction procedure has a positive impact on quantitative precipitation estimates from radar. Unfortunately, visibility problems severely limit the impact of the Lagrangian implementation beyond distances of 100 km. However, by combining this procedure with the global Eulerian VPR estimation procedure for a given rainfall type (stratiform and neither stratiform/convective), the quality of the quantitative precipitation estimates increases up to a distance of 150 km. Analyses of the impact of VPR uncertainty shows that this aspect accounts for a large fraction of the differences between weather radar rainfall estimates and rain gauge measurements.

1 Introduction

[2] The wide-scale implementation of weather radar systems over the last decades has increased our understanding of precipitation dynamics. These instruments provide information at a much higher spatial and temporal resolution than conventional rain gauge networks operated by most meteorological services [Zawadzki, 1975; Joss and Lee, 1995; Smith et al., 2001; Zhang et al., 2005; Gourley et al., 2009]. However, quantitative estimation of precipitation by weather radar is affected by many sources of error related to the physical characteristics of both the instrument, the surrounding environment, and the atmosphere [e.g., Waldvogel, 1974; Delrieu et al., 1995; Fabry et al., 1997; Gabella and Perona, 1998; Steiner and Smith, 2002; Dinku et al., 2002; Germann et al., 2006; Uijlenhoet and Berne, 2008].

[3] Over the last decades, a number of methods has been proposed to correct for these different error sources [see, e.g., Joss and Waldvogel, 1990; Andrieu et al., 1997; Villarini and Krajewski, 2010; Hazenberg et al., 2011a, and the references therein]. A dominant source of error results from vertical variations in hydrometeor properties (including their size distribution and phase) known as the vertical profile of reflectivity (VPR) [e.g., Battan, 1973; Smith, 1986; Joss and Pittini, 1991]. This especially holds for stratiform systems, where snow and ice particles at higher altitudes generally lead to smaller returned radar reflectivities as compared to the actual surface reflectivity. Around the 0° isotherm, the melting of snow gives rise to relatively large, water-coated particles. Within this region, known as the bright band (BB), the return signal is intensified because of melting snow particles with larger radar backscattering cross sections [Austin and Bemis, 1950]. Since radar beam height and beam volume both increase with distance (the so-called range effect), for stratiform precipitation, serious overestimation of the actual surface reflectivity by radar occurs when sampling within the melting layer, while above this region, underestimation takes place. Overall, this has a detrimental impact on the quality of radar precipitation estimates [Fabry et al., 1992; Kitchen and Jackson, 1993; Bellon et al., 2005]. An example of the impact of the VPR on the quality of the radar measurement for a typical stratiform profile is presented in Figures 1a and 1b.

Figure 1.

Example of the impact of the vertical profile of reflectivity (VPR) for (a–c) stratiform and (d–f) transition/neither stratiform/convective precipitation for the C-band weather radar used in the current study. Figures 1a and 1d present the average shape of the VPR, generally assumed to be spatially uniform for a given type of precipitation. Figures 1b and 1e show the impact of the VPR on the radar measurement for five different elevation angles. Figures 1c and 1f present the identified ratio profiles, defined as the ratio of one of the higher elevation angles with respect to the lowest one as a function of distance.

[4] Due to vertical mixing by intense up and down drafts, such a clear vertical segmentation of the hydrometeor size distribution is generally not observed for convective precipitation. Therefore, identification of the impact of a convective VPR on the measurement characteristics of the radar is not straightforward.

[5] In mesoscale convective systems, once the dominant convective activity decreases, the precipitation system evolves toward a stratiform type of precipitation [Yuter and Houze Jr, 1995a; Uijlenhoet et al., 2003]. During this transition phase with moderate precipitation intensities, where convective precipitation changes into stratiform precipitation without showing the clear signature of a BB, the coalescence of small raindrops generally leads to an increase of reflectivity toward the surface (see Figure 1d) [Yuter and Houze Jr, 1995b]. Therefore, rainfall intensities for this transition type of precipitation tend to be underestimated by the weather radar, especially as the range increases (Figure 1e).

[6] Historically, the physical properties of the VPR for different types of precipitation are well known [Austin and Bemis, 1950; Battan, 1973]. However, due to a dominant focus on weather radar measurements of convective precipitation, correcting for the impact of range effects and VPR in stratiform precipitation only started to receive attention since the middle of the 1970s and early 1980s [Harrold and Kitchingman, 1975; Smith, 1986; Collier, 1986].

[7] Since then, two main approaches have been developed to correct for the impact of range and VPR effects. The first approach uses an empirical range-dependent correction function for a given type of precipitation and season. This function can either be obtained from historical/climatological information [Collier, 1986] or estimated from the apparent scaling properties of the radar measurements [Chumchean et al., 2004]. However, since the height of the bright band varies over time, real-time implementation of such an approach does not immediately lead to an increase in the quality of the weather radar measurements.

[8] A second procedure is to estimate the VPR at a given point [Kitchen et al., 1994; Smyth and Illingworth, 1998] or to identify its mean profile representative for a larger region [Smith, 1986; Andrieu and Creutin, 1995; Germann and Joss, 2002]. Based on such profiles and the measurement characteristics of the radar, it is then possible to correct for the impact of VPR as a function of range. The benefit of the first approach that makes use of point corrections is that the small scale variability of the VPR is taken into account. Such small scale variability is generally also observed from in situ measurements by vertically pointing radars [Joss and Waldvogel, 1990; Fabry and Zawadzki, 1995; Cluckie et al., 2000; Berne et al., 2004; Martner et al., 2008]. However, for many precipitation systems, such local variabilities are difficult to identify by most conventional radar systems. Therefore, the second methodology to estimate the VPR provides a compromise, where a mean representative VPR is estimated for either a static fixed part of the radar umbrella [Vignal et al., 1999; Vignal et al., 2000; Seo et al., 2000; Germann and Joss, 2002; Vignal and Krajewski, 2001] or for a given type of precipitation [Delrieu et al., 2009; Kirstetter et al., 2010a].

[9] This second type of method estimates the VPR based on an Eulerian procedure without specifically taking the temporal movement and change in spatial location of the precipitation field into account. Estimation and correction of the VPR for a given precipitation region using a Lagrangian approach, to the authors' knowledge, has not been performed so far. Nevertheless, for highly dynamical systems like precipitation, such an approach would seem to be highly recommended. In the current paper a new VPR correction method is proposed that combines and extends the VPR identification methods proposed by Smith [1986] and Andrieu and Creutin [1995]. Next, this method is implemented within a newly developed Lagrangian procedure as well as by taking a traditional Eulerian approach. The Lagrangian-based VPR correction method presented here focuses on precipitation regions and their temporal evolution. Identification of different precipitation regions in principle allows the application of a specific ZR relationship, to estimate the rainfall intensities within a given precipitation region.

[10] Even though correcting weather radar measurements for range and VPR effects improves the quality of the radar surface rainfall product, considerable differences with respect to the measurements from rain gauges are still expected. These can be attributed to uncorrected error sources, resulting from scale issues when comparing the measurements of both instruments [e.g., Austin, 1987; Kitchen and Blackall, 1992; Ciach and Krajewski, 1999; Morin et al., 2003; Goudenhoofdt and Delobbe, 2009], or related to quality issues with respect to the rain gauge measurements [Steiner et al., 1999; Molini et al., 2001; Habib et al., 2001; Ciach and Krajewski, 2006]. Therefore, instead of performing bias correction of weather radar measurements using in situ rain gauge information, we believe that much more information can be obtained by focusing on weather radar rainfall uncertainty estimates. This approach is in line with Villarini and Krajewski [2010] who note that after having corrected for many of the weather radar measurement errors, the next step “we should be focusing on is the characterization of the total uncertainties associated with radar rainfall estimates of the true ground rainfall.” Over the last decade, a number of studies have tried to address this issue [e.g., Ciach et al., 2007; Villarini et al., 2009; Germann et al., 2009; Mandapaka et al., 2010; Kirstetter et al., 2010b]. However, none of these approaches identified the impact of VPR variability on radar measurement uncertainty. Such variability arises from the random nature of hydrometeor size distributions and from temporal differences between the measurements taken at different radar elevations. Since this type of uncertainty is always present in the volumetric weather radar measurement, its impact should be accounted for. Therefore, besides focusing on the correction of weather radar data for range and VPR effects, this paper also presents a method to identify radar rainfall uncertainties due to VPR variability originating from spatial and temporal changes of the hydrometeor size distribution and resulting from the scanning strategy of the radar.

[11] This paper is organized as follows. In section 2, the study area and a brief summary of a recently developed region delineation method is presented. Section 3 describes the VPR identification procedure and uncertainty estimation technique developed within this study. The impact of this approach is presented in section 4 for three precipitation events. Sections 5 and 6 present the discussion and conclusions, respectively.

2 Materials and Methods

2.1 Study Area and Radar Characteristics

[12] In this study the impact of VPR correction and uncertainty estimation is assessed using data from a C-band Doppler weather radar installed at an elevation of 600 m ASL in the Belgian Ardennes region in the eastern part of Belgium (see Figure 2). During the winter half-year, most precipitation observed in this region has a stratiform character, with BBs usually occur below 2000 m above the surface. As such, vertical variations in precipitation have a large impact on the quality of weather radar rainfall estimates. In the current study three events were selected that were observed within the region during the winter of 2002–2003. For a description of these events, the reader is referred to Hazenberg et al. [2011a].

Figure 2.

Topographic map of the Belgian Ardennes. Also shown are the location of the radar (black circle) and the location of the rain gauges (crosses). The different colors are used in later plots to discriminate between individual rain gauges. The inset shows the location of the study area, with a 200 by 200 km box indicating the area shown in the figure.

[13] The radar has two scan sequences; one every 5 min at five different elevations and a second scan every 15 minutes at another 10 elevations. In this study the 5 min data were used to obtain areal information about the precipitation field. The impact of an idealized stratiform and transition precipitation type VPR on the measurement capabilities of this weather radar are presented in Figure 1. A summary of the radar characteristics is presented in Table 1. In general, electronic radar calibration issues can have a large impact on the measurement quality of the weather radar [Ulbrich and Lee, 1999]. However, for the current period of study, no serious calibration errors were observed [see also Hazenberg et al., 2011a].

Table 1. Characteristics of the C-Band Doppler Radar at Wideumont Used in This Study
Coordinates lat/lon (°)49.91, 5.51
Height (m ASL)600
Frequency (GHz)5.64
PRF (Hz)600
Beam width (°)1
Antenna diameter (m)4.2
Radar constant (dB)63
Minimum detectable signal (dBm)−108
Maximum range (km)240
Scanning sequences2
Pulse length (m)250 (scan 1)
 500 (scan 2)
Recurrence interval (min)5 (scan 1)
 15 (scan 2)
Elevations (°)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)

[14] To assess the quality of the radar precipitation estimates, a total of 64 hourly rain gauges were used, situated up to a distance of 150 km from the radar (see Figure 2).

2.2 Precipitation Region Identification

[15] As explained in section 1, the VPR correction method presented in this paper focuses on precipitation regions in which, for each cell, the rainfall type will be identified. In order to perform such analyses, a flexible method is needed that is able to identify such regions from continuous polar-based volumetric weather radar data. For this purpose, the recently developed grid-based Rotational Carpenter Square Cluster Algorithm (RoCaSCA) was applied to the polar (r,θ) grid observed at the lowest elevation angle of the radar. RoCaSCA is able to label pixels belonging to the same region using a tracing type image segmentation method [Chang et al., 2004; Wagenknecht, 2007]. Regions or clusters are identified by delineating first their outer contours, followed by a procedure to delineate inner regions and contours in a similar manner. Such a single-pass segmentation algorithm is generally assumed to be computationally efficient [Suzuki et al., 2003; He et al., 2009; Wu et al., 2009]. However, compared to other image segmentation algorithms, RoCaSCA is not limited to linking neighboring pixels only. This latter property makes RoCaSCA highly suitable to delineate precipitation regions. Similar distance characteristics were also used in other studies to identify and track convective storm cells from weather radar images [e.g., Johnson et al., 1998; Handwerker, 2002].

[16] In Figure 3 the outer contour delineation procedure of RoCaSCA is presented for a hypothetical precipitation image with three separate regions with reflectivity values larger than a user-defined threshold. The identification is performed by rotating a carpenter square along the outer boundary of a given precipitation region. Since the sides of the carpenter square in the current hypothetical example have a size of 3, non-neighboring cells can be identified as belonging to the same precipitation region. The final outcome results in two different precipitation regions (two separate regions have been merged because of their proximity to each other) identified by RoCaSCA (see Figure 3).

Figure 3.

General technique behind the contour tracing algorithm of RoCaSCA for a hypothetical precipitation field. The color of the carpenter square indicates its direction of movement for the four different directions (i.e., red (right), blue (up), green (left), and black (down)). These directions and coloring are also indicated by the arrows on top of each subplot, where the left (right) indicates its last (next) direction. A closed (open) circle on top of a subplot indicates a(n) (anti)clockwise shift in the direction of the carpenter square, where the former (latter) indicates when a new pixel belonging to the same cluster is identified. The closed square indicates the end of the process to identify all pixels belonging to a given region. After that, each following pixel is evaluated to be part of the next precipitation region, not taking previously assessed pixels into account (pixels that are already part of a region, or pixels not belonging to any region (gray pixels)).

[17] Once a region has been delineated, each pixel is identified as stratiform [Sánchez-Diezma et al., 2000], convective [Steiner et al., 1995] or neither stratiform/convective type of precipitation before VPR estimation takes place [see also Delrieu et al., 2009]. This has been implemented by first identifying stratiform pixels using the method as presented by Sánchez-Diezma et al. [2000]. Next, the algorithm presented by Steiner et al. [1995] is used to identify convective pixels, for those points that have not been classified as stratiform precipitation. All pixels that have not been identified as either stratiform or convective precipitation, are assumed to correspond to neither of these types of precipitation. For a more detailed discussion, see Delrieu et al. [2009].

3 VPR Identification and Uncertainty Estimation

3.1 Identification of the VPR for a Given Precipitation Region

[18] The VPR identification procedure implemented in the current paper combines the characteristics of the algorithms presented by Smith [1986] and Andrieu and Creutin [1995]. Both algorithms assume the VPR to be spatially uniform over a given region. As such, it becomes possible to decompose the spatial variation of the apparent reflectivity Za(r,h) as measured by the weather radar into a horizontal and vertical component

display math(1)

[19] Here ZREF(r) is the reflectivity at the chosen reference level at distance r, and za(r,h) is the apparent vertical profile of reflectivity, which is influenced by the increase in height and volume of the radar beam as a function of range. In Smith [1986], this profile is represented by a simple piecewise linear function, similar to Figure 1a. Unfortunately, computational limitations prohibited a proper implementation of the VPR estimation proposed method by Smith [1986] until a decade later [Kitchen et al., 1994; Smyth and Illingworth, 1998].

[20] In Andrieu and Creutin [1995], the VPR follows a step profile of nz increments, where within a given height interval increment, the vertical reflectivity component Δzi is assumed to be constant. Since it is possible to calculate the proportion of the beam section within a given height increment using the characteristics of the radar, according to Andrieu and Creutin [1995] the normalized VPR can be defined as

display math(2)

where f2 is the the beam distribution of the radar signal power, θ0 is the radar half-power beam width, A is the elevation angle, inline image, and z(h) represents the actual average vertical reflectivity profile assumed to be constant over the region.

[21] To estimate the shape of the VPR for a given precipitation event, ratio profiles q(r,A1,Aj) obtained from the volumetric weather radar measurement were used (i.e., the ratio between the measured reflectivity at a higher elevation angle (elevation scan j) with respect to the lowest one (see Figure 1c, 1f)). For the VPR given by equation (2), these profiles are defined as

display math(3)

[22] In order to estimate the actual VPR, an initial discretized profile was adjusted using an inverse optimization procedure [Menke, 1989], minimizing the difference between the theoretical and observed ratio profiles. This initial a priori VPR could either be obtained from climatological information or from volumetric radar measurements.

[23] Since its first appearance, variations of the VPR estimation method of Andrieu and Creutin [1995] have been presented in a number of papers [e.g., Borga et al., 1997; Vignal et al., 1999, 2000; Seo et al., 2000; Delrieu et al., 2009; Hazenberg et al., 2011a]. The most detailed implementation was presented by Kirstetter et al. [2010a], who tried to estimate the VPR for a given type of precipitation (convective, stratiform, neither stratiform/convective). These authors also presented the limitations of this approach, focusing on the difficulties of obtaining an initial VPR from volumetric weather radar data, and the observation uncertainties influencing the estimated ratio functions. These uncertainties, together with the large degree of freedom in the parameters of the step profile, can result in erroneous estimates of the VPR.

[24] Kirstetter et al. [2010a] tried to limit the impact of these uncertainties using a range-related weighting function to estimate the initial median VPR for a given type of precipitation and employed only those reflectivity profiles for which the spatial variability at a given range was limited. In the current paper, we try to account for the impact of these measurement variabilities without performing any predefined selection. However, instead of performing an unconstrained optimization procedure with many degrees of freedom, linear constraints are introduced between the parameters of the stepwise VPR. These constraints are similar to what was originally proposed by Smith [1986]. The main benefit of this approach is that it ensures the VPR is physically realistic for a given type of precipitation (see Figures 1a and 1d), as is observed from in situ vertically pointing radar measurements [e.g., Joss and Waldvogel, 1990; Fabry and Zawadzki, 1995; Martner et al., 2008].

3.2 Theoretical Piecewise Linear VPRs in Current Paper

[25] The current paper presents a method to estimate VPRs for both stratiform and neither stratiform/convective precipitation, where the latter is assumed to contain either transition type precipitation or snow. We do not intend to identify VPRs for convective precipitation, since we feel that the horizontal variability in vertical variations of the hydrometeor properties, as explained in section 1, is too large to result in appropriate estimates of VPRs. In Figure 4 the specific piecewise linear shapes are presented, which form the basis of our estimation method. For stratiform precipitation, this representation enables one to focus on five different vertical regions comprising a total of 10 linear layers, each with slope Δ=dz/dh. These regions exhibit the following properties:

  1. [26] Layers h1h3 (rain): Vertical variation of the VPR mainly occurs due to collisional and spontaneous breakup as well as coalescence of raindrops, influenced by vertical and horizontal variation of the wind field, orographic effects, and below-BB evaporation [Austin, 1987]. Therefore, no a priori directions of the slopes Δi are defined for these layers.

  2. [27] Layers h3h5 (BB): Water-coated snow and ice particles melt completely causing their sizes to decrease. This causes a decrease in radar backscatter [Stewart et al., 1984]. Hence, within this region, the VPR is assumed to decrease toward the surface (Δi≥0).

  3. [28] Layers h5h7 (BB): The melting and aggregation of snow particles causes a liquid water coating at their surface, which results in an intensification of the returned radar reflectivity signal (the BB) [Austin and Bemis, 1950; Smith, 1986; Klaassen, 1988, 1989; Russchenberg, 1992; Steiner and Smith, 1998]. Hence, within these layers, the slopes Δ of the VPR are positive in the downward direction (Δi≤0).

  4. [29] Layer h7h8 (snow): Descending snow flakes and ice crystals aggregate, leading to a moderate increase of the returned radar signal while descending [Stewart et al., 1984; Willis and Heymsfield, 1989]. The slope is therefore assumed to be positive toward the surface (Δ8≥0).

  5. [30] Layers h8h10 (snow): Within this region, snow flakes and ice crystals are formed, which interact and slowly descend. Although, in general, reflectivities are small and slightly increasing downward, we allow for a secondary maximum to occur as a result of enhanced aggregation within the dendritic growth region (−10°C to −17°C) [Hobbs et al., 1974; Steiner and Smith, 1998]. Hence, Δ9 can have both signs, while Δ10≤0.

Figure 4.

Theoretical vertical reflectivity profiles for (a) stratiform and (b) neither stratiform/convective precipitation (e.g., transition, snow). Different height (h) and slope parameters (Δ) are optimized with respect to observed ratio profiles using a Monte Carlo optimization approach, where Δ=dz/dh.

[31] For neither stratiform/convective precipitation, less vertical variability is expected. Therefore, the VPR of neither stratiform/convective precipitation is represented by a piecewise linear shape consisting of only four linearly sloping layers. As such, it is expected that both transition type precipitation containing mostly rain drops, as well as snow can be represented by such a piecewise linear profile.

[32] For stratiform precipitation, the actual values of zi are bounded by constraining the allowed reflectivity values as well as enforcing interdependence between the piecewise linear segments (see Table 2). This approach limits the number of degrees of freedom, ensuring a physically realistic shape of the VPR. In order to reduce the number of estimated parameters for stratiform precipitation, the majority of the height parameters (h) presented in Figure 4a can be obtained directly from volumetric radar measurements (see section 3.4). The slopes (Δ) and remaining heights (h) are then estimated using a Monte Carlo optimization approach, minimizing the difference between the observed and simulated ratio profiles. Although Monte Carlo simulations are known to be time-intensive, for the current VPR parameterization, this approach gives results within an acceptable amount of time for operational practices.

Table 2. Minimum and Maximum Values of the Normalized VPR Segments Δzi (Equation (2)) at the Corner of Each Piecewise Linear Segment as Presented in Figure 4a
  Stratiform Nonstratiform
Height TypeMinMax TypeMinMax
  1. aDifferent precipitation types are rain (R), bright band (BB), and snow (S).
h1 R0.301.40 R/S0.401.40
h2 R0.201.50 R/S0.301.20
h3 R0.201.50 R/S0.201.00
h4 BBinline image2.00 R/S0.000.05
h5 BBinline image10.00    
h6 BB0.30inline image    
h7 BB0.25inline image    
h8 S0.050.50    
h9 S0.010.40    
h10 S0.000.05    

3.3 Radar Rainfall Variability Estimation From VPR Uncertainty

[33] The VPR identification method presented in the previous section can be regarded as a median field bias correction for an identified precipitation region of a given type. In practice, however, considerable local fluctuations around the median VPR are expected due to horizontal variability in vertical variations of the precipitation microstructure (size, shape, number concentration, and phase of the hydrometeors) [Joss and Waldvogel, 1990; Hazenberg et al., 2011b]. In addition, since radar measurements at different elevation angles are not performed simultaneously, temporal evolution of the VPR results in further deviations from the median profile. Therefore, besides correcting for VPR effects, we also wish to obtain an estimate of the amount of uncertainty around its median value and to assess its impact on weather radar rainfall estimation.

[34] An example of the variability in observed ratio profiles for the precipitation event described in section 4.1 is presented in Figures 5a and 5b for different percentile statistics. This figure was obtained after having identified the stratiform pixels within a precipitation region identified by RoCaSCA (see section 2.2). It can be observed that close to the radar, the median ratio profile indeed has an expected value of about 1 (see also Figure 1), although considerable deviations occur for the other percentiles. As mentioned, these deviations result from horizontal variations in the vertical variability of the precipitation microstructure, from temporal changes in the precipitation field as well as from the radar sampling properties.

Figure 5.

Variability in observed ratio profiles as represented by different percentiles for the precipitation event described in section 4.1 on 22 October 2002 at 20:30 UTC. The ratios of the weather radar measurements at elevations (a) 2 and (b) 3 with respect to the lowest one. (c and d) The ratios with respect to the median profiles are shown. Based on the mean values in Figures 5c and 5d, as a final step, the original ratio profiles presented in Figures 5a and 5b were rescaled. (e and f) The normalized ratio profiles.

[35] However, once these percentiles are scaled with respect to the median by calculating their ratio, these overall deviations become rather constant with range (Figures 5c and 5d). Similar results (not shown here) were obtained for other time steps and during other precipitation events. Therefore, based on this property, we propose to account for VPR variability by reformulating equation (3) as follows:

display math(4)

where qP is the estimated ratio profile for a given percentile value P. The factor fP is a scaling factor for a given ratio percentile, which results from the observed uniform deviation as a function of range. After rescaling the observed ratio profiles for a given percentile (qP) using this factor, the majority of the observed variability is accounted for (see Figures 5e and 5f). The remaining variability is then taken into account by identifying a normalized segmented VPR (Δzi,P) representative for the normalized ratio profiles of a given percentile (qN,P).

[36] It was decided to estimate the scaling factor fP as part of the Monte Carlo procedure explained in section 3.2 while identifying the VPR, since for some precipitation regions, it is difficult to obtain such well-defined ratio profiles as in Figure 5. Hence, for a given ratio profile percentile, both the piecewise linear segmented VPR Δzi and the scaling factor fP are estimated. By selecting a broad range of percentiles (here 20–80) based on experience obtained for the region of study, we believe that the majority of the VPR uncertainty can be identified and accounted for. Therefore, this approach enables one to study its impact on radar rainfall estimation uncertainty.

3.4 Practical Implementation

[37] The previous sections described the specific VPR identification and uncertainty estimation method used here. The complete algorithm to estimate a VPR for a given precipitation region and type is implemented as follows:

  • 1.Identify ground clutter from all pixels containing positive reflectivity values [Steiner and Smith, 2002] and remove these pixels from further analyses (see Hazenberg et al. [2011a], for further details).
  • 2.Use RoCaSCA to identify precipitation regions for the radar data obtained at the lowest elevation and track each of these regions over time. As such, the implementation follows a Lagrangian procedure.
  • 3.For each region, identify the precipitation type of each individual polar radar pixel, i.e., convective [Steiner et al., 1995], stratiform [Sánchez-Diezma et al., 2000], or neither stratiform/convective precipitation. 
  • 4.For all stratiform pixels within a given precipitation region, calculate the 20th, 40th, 50th, 60th, 80th percentiles of the estimated BB height sampled at the different polar points [Sánchez-Diezma et al., 2000]. These heights are assumed to correspond to h3, h4, h5, h6, h7, respectively, in Figure 4, which reduces the number of parameters to be estimated in the stratiform VPR optimization procedure.

[42] Then, for each precipitation region of a given type,

  • 5.Estimate the echo top, corresponding to h10 and h4 in Figure 4 for stratiform and neither stratiform/convective precipitation, respectively. The echo top was defined as the maximum elevation at which the reflectivity Z≥1 dBZ.
  • 6.Calculate the ratios between the reflectivities measured at higher elevations with respect to the lowest. Then, based on all ratio information at a given distance from the radar, obtain a number of percentiles (see Figures 1c, 1f, and 5). Here we used the 20th, 30th, 40th, 50th, 60th, 70th, and 80th percentiles. Detailed analyses (not presented here) indicated that lower or higher percentile statistics may suffer from the impact of outliers and unidentified erroneous measurements affecting the observed ratio values [see also Kirstetter et al., 2010a]. These percentile ranges were therefore excluded.
  • 7.Identify the final ratio profiles for a given percentile by aggregating temporally over a number of consecutive time steps to increase the robustness of the statistics. In the current study, all ratio information sampled within 60 min of the time step of study for the moving precipitation system was taken into account.
  • 8.Estimate the slope parameters Δ, the scaling factor fP and the remaining height parameters h based on the procedure explained in sections 3.2 and 3.3 using a Monte Carlo based optimization procedure, minimizing the sum of squared differences between the theoretical and observed ratio profile quantiles for a given percentile.
  • 9.Based on each of the identified normalized segmented VPRs (zi,P) and scaling factors fP obtained for a given ratio profile percentile, calculate VPR correction factors for each radar elevation as a function of range.
  • 10.In order to obtain a final 2-D radar reflectivity field, a weighted average of all VPR-corrected elevations is taken (for details, see Hazenberg et al. [2011a]). This approach decreases the impact and uncertainty of an individual measurement at a given elevation [Joss and Lee, 1995].
  • 11.As a final step, the reflectivity data are transformed into rainfall intensities using the Marshall-Palmer relationship Z=200R1.6 for stratiform precipitation [Marshall et al., 1955] and Z=250R1.5for neither stratiform/convective precipitation [Battan, 1973], with Z in mm6 m−3and R in mmh−1.

[50] The identification of precipitation regions by RoCaSCA was done at two different reflectivity levels, >7 and >23 dBZ, using a carpenter square of sizes 3 and 2, respectively. These reflectivity values correspond to a precipitation of >0.1 and >1.0 mm h−1, respectively, if a Marshall and Palmer Z=200R1.6relationship is assumed [Marshall et al., 1955]. In order to ensure that each precipitation region contains enough statistical information to obtain robust ratio profile estimates, each region should have a minimum area of 2500 (>7 dBZ) and 2000 (>23 dBZ) km2, respectively. These sizes are similar to the minimum areas originally proposed by Vignal et al. [1999, 2000], although for the current approach, their locations and actual sizes vary dynamically in time. Where it becomes impossible to estimate a VPR for a given pixel identified as being part of a region surpassing the higher threshold (>23 dBZ), if available, the VPR estimated for the region identified at the lower threshold level (>7 dBZ) is used.

[51] To identify and link the same precipitation region between different time steps, a different approach is taken as compared to the classical cell-tracking algorithms presented in the literature [Dixon and Wiener, 1993; Johnson et al., 1998; Handwerker, 2002], which specifically focus on tracking the center point of a given storm cell (>30 dBZ) forward in time. To link two precipitation cells observed during two different time steps as part of the same parent-child pair, generally a cost function is applied. We refer to Lakshmanan and Smith [2010] for more details on this issue. In the current manuscript, it was decided to follow a different procedure, since the interest here lies in delineating precipitation regions at much smaller reflectivity thresholds (>7 and >23 dBZ). These regions do not contain the specific cell structure as generally observed for higher intensity convective precipitation cells. Therefore, instead of focusing on tracking a specific center point, all pixels belonging to a given region are moved forward in time using the velocity estimate of the previous time step if possible, or else based on the mean wind information. The same region is observed during two time steps in case the percentage of overlapping pixels is >10%. This enables one to account for the merging and splitting of precipitation regions. The current computational possibilities enable one to implement such a procedure, where use is made of all pixels belonging to a given precipitation region.

[52] Temporal information obtained through the tracking of each region is used to increase the amount of data on which the different ratio profile statistics are based. It was decided to perform up to 1 h of temporal aggregation to obtain the ratio statistics from the volumetric data (similar to Delrieu et al. [2009] and Kirstetter et al. [2010a]), which is defined as “backward” identification. Potential problems arise for precipitation regions identified at larger distances from the radar (>100 km), for which it can be difficult to obtain any ratio information. Therefore, as a second approach, temporal aggregation of the ratio profiles, was also performed using the reflectivity information sampled both 1 h before and after a given time step (“backward/forward” identification). If a precipitation region moves closer to the radar, it is expected that the quality of the ratio profile statistics will improve. It should be noted that for real-time implementation, such an approach cannot be applied. However, this latter approach enables one to identify the potential quality improvement of the weather radar precipitation estimates observed at larger ranges, when more information on the precipitation system becomes available (as it possibly moves toward the radar).

[53] To assess the quality of the Lagrangian VPR identification method presented in this paper, VPR identification was also implemented for the entire radar volume for given precipitation type (the Eulerian perspective). This approach takes all volumetric reflectivity information sampled by the radar into account, but does not distinguish between different precipitation regions. As a last procedure, the global static Eulerian and local dynamic Lagrangian VPR identification methods were merged, where attempts are made to correct for VPR locally for each precipitation region separately, while for the remainder of the radar umbrella, the global estimate is used to correct for VPR effects. The benefit of this combined procedure is that reflectivity points that are not identified as part of a precipitation region are still VPR corrected based on global information.

4 Results

4.1 Event 1: A Stratiform System

[54] The first event presented in this paper is a fast-moving stratiform system that was first observed by the radar during the late afternoon on 22 October 2002 and lasted until the early morning of the next day. The corrected rainfall intensity field measured by the radar is presented in Figure 6 for a number of time steps. Also shown in this figure are the precipitation regions identified by RoCaSCA at >7 (red) and >23 (black) dBZ. RoCaSCA is well able to discriminate between the different precipitation regions, although at the >7 dBZ level during a number of time steps, multiple cells merge into a single region (around 19:00 h in Figure 6). This generally does not occur at the >23 dBZ level.

Figure 6.

Temporal evolution of the surface precipitation intensity field for the stratiform event as observed by the weather radar on 22 October 2002 up to a distance of 225 km. The time steps (UTC) of the different snapshots are presented in the upper right hand corner of the different panels. These results were obtained after correcting volumetric weather radar information for the impact of VPR. The boundaries of the major precipitation regions for which VPRs are estimated, as identified by the cluster algorithm RoCaSCA at >7 (red) and >23 (black) dBZ, are presented as well.

[55] The specific region characteristics for the stratiform precipitation region (>23 dBZ) that was first recognized in the South-West corner of the radar image at 18:00 UTC (see Figure 6), are presented in Figure 7. The increase in the region mean reflectivity during the first hour can be related to the high altitude of the initial radar measurements (i.e., reduction of returned signal due to snow and the possibility of overshooting, where the radar volume samples above the precipitation field). From 18:30 UTC onward, it becomes possible to estimate the median height of the BB and its uncertainty (as represented by the 20th–80th inter percentile range, see Figure 7b). Overall, the temporal variation of the BB height for this precipitation region is rather small and has a similar depth (HBB, in Figure 4) as observed in other studies [Gourley and Calvert, 2003; Zhang et al., 2008].

Figure 7.

Temporal evolution of the stratiform anti-clockwise rotating precipitation region for the 23 dBZ reflectivity threshold. Upper two panels show the region's (a) mean (black line) and median (dashed line) reflectivity and (b) estimated height of the bright band as observed by the weather radar. The uncertainty in these measurements is given by the gray contour region, representing the 20th–80th inter percentile range. The bottom three panels present the (c) estimated bright band strength (zBB,RAIN in Figure 3), (d) the spatial VPR uncertainty factor f, and (e) the goodness-of-fit between the simulated and observed ratio profiles for the lowest two elevations as represented by the Nash-Sutcliffe statistic (NS) [Nash and Sutcliffe, 1970]. These results were obtained by aggregating all ratio information observed within the previous hour (backward, solid line/red region), as well as including the information observed within the next hour (backward/forward, dashed line/green region). The uncertainty in the VPR measurements is represented by the different contour regions and defines the 20th–80th inter percentile ranges.

[56] The remaining panels of Figure 7 present the properties of the estimated VPR, obtained by aggregating the ratio profile information during the previous hour (backward, red) or from both the previous and the next hour (backward/forward, green). With the latter option, it is expected that for precipitation regions observed at further ranges from the radar, using the information obtained within the next hour, a better estimate of the VPR can be obtained.

[57] In Figure 7c, estimates of the strength of the BB are given (zBB,Rain in Figure 4). Although the results for both methods line up well, it can be observed that around 20:30 UTC, a deviation occurs. This arises from the decrease in estimated BB strength from 21:00 UTC onward. The combination of backward and forward temporal aggregation causes the volumetric radar data sampled at these time steps to be used earlier in time, as part of the ratio profile identification procedure. Since the assumption of a temporally stable VPR is clearly violated during this hour, a difference between both estimates of the BB size occurs.

[58] The total variation of the VPR scaling factor fP (Figure 7d) ranges between 60 and 140%. This indicates that the horizontal variation of the vertical precipitation structure as well as temporal differences between the different radar scans have a considerable impact on the measured ratio profile variability. The approach presented in the current paper is able to account for this overall variability. Figure 7e presents the quality of the estimated VPR to simulate the observed ratio profile between the lowest two elevations, using the Nash-Sutcliffe statistic [Nash and Sutcliffe, 1970]. Overall, the correspondence between the observed and simulated ratio profiles is good. Only during the later phase of the event (after 22:00 UTC), the quality of the fit decreases for the highest ratio percentiles. This can be related to the fact that the cell starts to decompose and looses its spatial coherence (see Figure 6), leading to an increase in ratio variability.

[59] In order to identify the spatial variability of the VPR between different precipitation systems, similar characteristics were identified for the precipitation region (>23 dBZ) observed in Figure 6 (top), which are presented in Figure 8. The sampling of this region by the weather radar has considerable temporal overlap with the region presented in Figure 7. Visual analysis of Figure 6 reveals a clear difference between both regions, where the former (Figure 8) is more elongated, while the latter (Figure 7) has a more spiral-like structure. Although the estimated height of the BB is similar for both regions, indicating a rather uniform height of the 0° isotherm, the identified strength of the BB varies considerably and is smaller for the elongated region. This clearly shows the possibilities of differentiating between different precipitation regions using an automatic procedure.

Figure 8.

As in Figure 7, but for the precipitation system first observed in Figure 6 (top).

[60] Figure 9 presents the comparison between the hourly region-based Lagrangian VPR-corrected radar rainfall accumulations and the 64 rain gauges based on the combined backward and forward obtained ratio information. It should be noted that none of the radar measurements were bias-corrected using rain gauge information. This allows an objective assessment of the true quality of corrected radar data. Although considerable variability between both instruments is observed, the corrected radar data correspond well with the gauge measurements. On average, the hourly and event-based rainfall accumulations obtained from the radar slightly underestimate the precipitation amounts sampled by the gauges (see Figures 9a and 9b). The impact of range effects is strongly reduced once the weather radar data is corrected for VPR effects, as reflected by the rather constant bias as a function of range in Figure 9c (see also Table 3). It should be noted that the hourly deviations between both instruments increases with distance (Figure 9d). This can be explained by the increase in measurement height difference between both instruments and the possible impact of wind drift [Gabella and Perona, 1998; Seo et al., 2000; Gabella et al., 2000, 2005].

Figure 9.

Comparison of rainfall accumulations obtained from 64 rain gauges and sampled by the corresponding radar pixels above, using the ratio information obtained within the previous and next hour (backward/forward), for the event on 22–23 October 2002. For all 64 pairs, the top panels show scatter plots of the (a) hourly and (b) total event rainfall accumulation. The correspondence between the weather radar corrected using the median VPR (square) with respect to the rain gauges is given by the red line with slope s, obtained from linear regression. Figures 9c and 9d show the quality of the radar measurement as a function of range from the radar, where radar/gauge ratio is defined as inline image Radar rainfall / inline image Gauge rainfall. NS is the Nash-Sutcliffe statistic [Nash and Sutcliffe, 1970]. The uncertainty in the radar rainfall estimates as a result of VPR variability and uncertainty is indicated by the error bars (20th–80th percentiles). Different colors correspond to the gauges as shown in Figure 2.

Table 3. Impact of the Different VPR Identification Methods on the Quality of Hourly Radar Rainfall Estimates Compared to the 64 Rain Gauges at Different Ranges, for the Event on 22–23 October a
   E(R/G) inline image NS
  1. aRow headers correspond to N - no VPR correction, R - region-based VPR identification, G - global VPR identification, and G&R - global and region-based VPR identification. The latter were estimated using the ratio information obtained within the previous hour (backward) or both the previous and next hour (backward/forward). The quality is assessed using the hourly bias E(R/G) between the radar and rain gauge measurement, the total event bias inline image and the Nash-Sutcliffe statistic (NS).
 (km) 0–5050–100100–150 0–5050–100100–150 0–5050–100100–150
 N 0.760.590.49 0.790.680.57 0.790.470.25
 R 0.900.800.61 0.970.930.77 0.830.400.24
 G 0.900.840.81 0.980.980.98 0.820.510.44
 G&R 0.890.850.89 0.981.001.04 0.840.490.39
 R 0.920.820.71 0.980.940.83 0.820.380.33
 G 0.910.860.82 0.981.001.00 0.830.490.42
 G&R 0.900.880.86 0.981.031.08 0.840.480.42

[61] In Table 3 the quality of the region-based VPR correction (R) is compared to the implementation of a global estimation of the VPR (G), and a combination of both approaches (G&R). For completeness, the impact of not correcting for VPR is also given (N). In general, VPR correction leads to a large improvement in radar rainfall estimation quality. The quality of the region-based VPR-corrected radar measurements (R), based on the ratio information from the previous hour (backward) decreases considerably beyond 100 km. This can be related to visibility problems if a region is still located far away. By taking the volumetric data of the next hour into account as well (backward/forward), VPR correction also leads to improved results at these distances (see also first hour in Figure 7).

[62] When compared to the global VPR-corrected radar measurements (G), the region-based technique (R) performs less well. This is because not all radar measurements are VPR corrected with the latter approach, as well as the difficulty to identify a VPR for a region located at longer distances from the radar. The combination of applying region-based VPR correction for pixels belonging to a precipitation cell and a global VPR correction elsewhere (G&R), gives a slight improvement in both the hourly and event-based bias statistics beyond 50 km when compared with the global correction (G). However, the latter observation is not reflected by the Nash-Sutcliffe statistic.

[63] Besides the impact of median VPR radar rainfall correction, the impact of VPR uncertainty on the radar measurements is also presented in Figure 9. As explained in section 3.3, this uncertainty was obtained using the ratio profiles for different percentiles. It can be observed that the overall variability as a result of VPR effects is considerable. What is striking about this figure is that, when compared with the rain gauge accumulations, the majority of the difference between radar-gauge pairs can be attributed to the uncertainty in the estimated VPR.

[64] In Figure 10, the impact of VPR uncertainty on the quality of the three different identification approaches is assessed using the ratio profile information obtained during the previous hour (backward identification). From Figures 10a and 10b, it can be observed that the overall impact of VPR uncertainty increases with range, as was also reflected by the decrease of the Nash-Sutcliffe statistic in Table 3. Close to the radar (<50 km) the overall VPR uncertainty is similar for the three different approaches. This can be related to the relatively large size of the different precipitation zones observed during this event and the fact that most ratio information is obtained close to the radar. Therefore, the global VPR estimates (G) for the type of precipitation field observed during the current event are quite similar to the region-based VPR estimates (R). Further from the radar, the overall uncertainty of the region-based VPR-estimate increases. With the other two approaches (G and G&R) similar radar rainfall uncertainty estimates are obtained. For these ranges the differences between R, on the one hand, and G and G&R, on the other hand, may be caused by the fact that for the first approach, no VPR correction is applied and hence no uncertainty is attributed.

Figure 10.

Impact of radar rainfall estimation uncertainty on hourly accumulations for the radar pixels above the 64 rain gauge locations for four different distance intervals from the radar, as given and represented by a Box-Whisker plot. In the upper panels box plots present the ratios between the (a) maximum and (b) minimum with respect to the median VPR-corrected radar event accumulation. In the lower panels, the (c) maximum and (d) minimum VPR-corrected event accumulations are compared to the measurements obtained from the rain gauges. The different colors correspond to the three different VPR correction implementations performed in this paper and are given in Figure 10c.

[65] Comparing these results with the rain gauge measurements, it can be observed that for all three approaches, the majority of the maximum rainfall accumulations are higher than those estimated by the gauges, whereas the minimum accumulations are lower than the gauge accumulations. This result again confirms that the majority of the precipitation differences between both instruments can be attributed to VPR variability. Only for the region-based approach (R) at longer distances from the radar (>100 km), the maximum precipitation intensities are still underestimated by the radar compared to the gauges, which results from the fact that a VPR could not be estimated for precipitation regions observed at these distances during all time steps. Therefore, data observed during these time steps were not VPR corrected using the region-based approach only.

4.2 Event 2: Large-Scale Stratiform System

[66] As a second example to present the possibilities of region-based VPR identification and uncertainty estimation, a large-scale precipitation system observed on 22 December 2002 was analyzed. In Figure 11, the rainfall intensity field as observed by the radar is presented. Compared to the event described in section 4.1, precipitation intensities for the current event are much smaller. Generally, such widespread precipitation is expected to be drizzle.

Figure 11.

As in Figure 6, but for the large-scale stratiform precipitation system observed on 22 December 2002.

[67] The characteristics of the precipitation region as identified by RoCaSCA (>7 dBZ) are shown in Figure 12. Also for the current event, the mean cell reflectivities increase while moving closer to the radar (i.e., influence of overshooting and the measurement of snow). However, even once its location is close to the radar (beyond 5:00 UTC) the reflectivity field still intensifies. Similar behavior is also observed for the estimated height of the BB, which increases as well. The explanation for this is that both occur as a result of increased solar activity during the morning, resulting in an influx of energy. At around 9:00 UTC, it can be observed from Figure 12b that the variability in the estimated BB-height changes. Detailed analyses (not presented here) show that this resulted from a situation of two BB heights (with 200 m height difference) at different horizontal locations. Unfortunately, due to the widespread character of this event, the current implementation of RoCaSCA was unable to distinguish between both regions. This can also be observed from Figure 12c where for about an hour (09:00–10:00 UTC), considerable differences between both aggregation methods (backward and backward/forward) occur, reflecting the situation of two different BB heights.

Figure 12.

As in Figure 7, but for the large-scale stratiform precipitation system observed on 22 December 2002.

[68] The impact of the two different BB levels for a period of about 2 h can also be observed in Figure 13. In general, the radar underestimates the amount of precipitation as compared to the gauges. However, the identification of a single spatially uniform VPR is unable to account for all horizontal variability of the vertical precipitation variability in a situation with two different BB levels. Hence, this leads to an overestimation of the rainfall intensities for a number of gauges, while at other locations, an underestimation is observed. This is further reflected by the variability of the Nash-Sutcliffe statistic, which does not show a clear tendency with range.

Figure 13.

As in Figure 9, but for the large-scale stratiform precipitation system observed on 22 December 2002.

[69] In Table 4, the quality of the region-based VPR-corrected radar measurements are presented as a function of range. As a result of the large-scale character, only a single precipitation region at both intensity levels was identified for the majority of the event. Therefore, it was decided to present only the results for region-based VPR (R), since both the global (G) and the combined (G&R) approach make use of the same reflectivity data. VPR correction results in a large improvement in the quality of the radar rainfall estimates. However, making use of the weather radar data observed during the next hour (backward/forward) does not lead to a quality improvement. This can be attributed to the widespread character of the current system, from which it is possible to obtain proper ratio information based on reflectivity data from the previous hour alone.

Table 4. As in Table 3, but for the Large-Scale Stratiform Precipitation System Observed on 22 December a
 E(R/G) inline image NS
  1. aNote that R = G = R & G.
(km) 0–5050–100100–150 0–5050–100100–150 0–5050–100100–150
N 0.660.620.41 0.660.620.44 0.490.300.03
Rbackward 0.780.770.68 0.780.790.72 0.590.420.50
Rbackward/forward 0.780.760.66 0.770.780.71 0.600.440.46

[70] Although the uncertainty in the identified VPR explains some of the variability between the radar and gauge accumulations, considerable differences between both instruments are still observed. The main part of this event probably consisted of drizzle, as mentioned above. Therefore, application of the Marshall-Palmer relationship resulted in an underestimation of the rainfall intensity. Hence, for the current event, it is expected that the majority of the difference between the radar-gauge pairs can be related to the characteristics of the DSD, which deviate from standard stratiform precipitation for this event.

4.3 Event 3: Fast-Moving Frontal Stratiform System

[71] As a last example, the performance of the VPR identification and uncertainty estimation procedure is tested for a fast-moving frontal precipitation system. The event started on 1 January 2003 around 10:00 UTC and had a total duration of about 42 h. The precipitation region identified by RoCaSCA (not shown here) was much smaller in size and better defined than for the event of October 2002 (see section 4.1 and Figure 6). Therefore, a clearer deviation can be expected between the results obtained using the region-based VPR-estimate and applying a global VPR-estimate.

[72] In Figure 14, the quality of the region-based VPR-corrected radar rainfall estimates are presented. Although on average the radar slightly underestimates the amount of precipitation, the majority of the radar-gauge pairs match well. Only for a number of gauges situated in the South at relatively close distance (within 60 km, light blue points) the underestimation by the radar is considerable during a number of hours. Since these gauges are situated in the same region, it is expected that the observed underestimation results from other sources of error not taken into account here (e.g., DSD variability). From Figures 14c and 14d, it can be observed that the impact of range effects is well accounted for using the region-based VPR estimates. In addition, the variability in the hourly estimates for the different radar-gauge pairs is rather constant, as can be observed from the relatively large values of the Nash-Sutcliffe statistic. Hence, after correcting, the current event was well captured by the radar.

Figure 14.

As in Figure 9, but for the fast-moving frontal stratiform system observed on 1–3 January 2003.

[73] In Table 5 the impact of the region-based VPR identification (R) is again compared to identification in a global (G) or combined (G&R) manner. Up to 100 km the region-based estimate is well able to estimate the amount of precipitation based on the information obtained during the previous hour (backward) and gives better results compared to applying a global VPR identification procedure. The quality of the region-based VPR-corrected radar data increases, when the volumetric information observed within the next hour is also taken into account (backward/forward). Again, this can be attributed to the visibility problems affecting a precipitation region which is located at further range from the radar.

Table 5. As in Table 3, but for the Fast-Moving Frontal Stratiform System Observed on 1–3 January 2003
   E(R/G) inline image NS
 (km) 0–5050–100100–150 0–5050–100100–150 0–5050–100100–150
 N 0.840.870.52 0.630.770.51
 R 0.921.040.77 0.660.700.64
 G 0.931.120.92 1.181.301.00 0.640.660.71
 G&R 0.931.050.82 0.660.730.67
 R 0.921.050.83 0.660.740.70
 G 0.931.120.92 1.181.311.02 0.640.690.72
 G&R 0.921.060.84 0.650.740.73

[74] However, by applying the combined procedure (G&R), a major part of the radar-gauge difference can be accounted for using the precipitation data obtained during the previous hour alone. This is an important result, since this procedure can be implemented in real-time operational weather radar applications.

[75] Also for the current event, the major part of the variability in the observed radar-gauge difference can be accounted for by taking the uncertainty in the estimated VPR into account (see Figures 14c, 15c, and 15d). The impact of VPR uncertainty for the three different approaches is further demonstrated in Figure 15. Close to the radar, region-based VPR correction leads to smaller uncertainties as compared to a global estimate. This is a direct consequence of the fact that, with the former procedure, spatial variability in the characteristics of the VPR between different zones is accounted for. With the latter approach, all variability is combined, leading to an increase of the VPR uncertainty. The combined procedure estimates a VPR using the region-based estimate if available, and applies the global estimate elsewhere. As a result, the overall variability lies between the other two approaches.

Figure 15.

As in Figure 10, but for the fast-moving frontal stratiform system observed on 1–3 January 2003.

5 Discussion

[76] The constrained piecewise linear VPR identification procedure presented in the current paper results in improved quantitative precipitation estimates by weather radar. This holds for both the Lagrangian and Eulerian implementation of the newly presented VPR identification method, where both implementations lead to similar improvements in the quality of the weather radar precipitation estimates. The new Lagrangian procedure presented here focuses specifically on identifying and tracking precipitation regions of a given type. The importance of such an implementation has been addressed in a number of papers [Fabry et al., 1992; Vignal et al., 1999; Delrieu et al., 2009]. These authors recognized the necessity to estimate the VPR within a region of uniform precipitation with limited spatial variability regarding vertical variations of the precipitation microstructure. We believe the Lagrangian approach presented here provides a way forward in reaching this goal.

[77] For the three precipitation events presented in the current paper, results reveal that up to distances of about 100 km, proper identification of the VPR for a given precipitation region can be achieved. Unfortunately, beyond this distance, visibility problems prevent proper identification of the ratio profiles. It is expected that these ranges are extended during summer conditions and in warmer climates (i.e., larger vertical extent of precipitation and higher level of the BB). It should be noted that the Eulerian implementation (G) provides similar results as compared to the combined implementation (G&R). We believe this can be related to the uniform character of the precipitation events presented in this paper. Because spatially more heterogeneous situations often occur, we recommend using the combined global and regional VPR. Although this approach is computationally more intensive, experience has shown that it can be implemented in real time. In addition, the results presented here show that, up to distances of 150 km, this combined procedure provides proper quantitative precipitation estimates.

[78] For regions closer to the radar, thresholding at >7 dBZ results in relatively large regions, although the delineation of precipitation regions has a positive impact on the quality of the estimated VPR. Hence, it was decided in this study to add a second threshold of >23 dBZ, similar to what was historically proposed as part of many storm cell identification and tracking procedures [Dixon and Wiener, 1993; Johnson et al., 1998; Handwerker, 2002]. In its current implementation, these thresholds therefore function to delineate uniform precipitation regions. For the type of systems observed within the Ardennes region, this assumption holds rather well for the second threshold level (>23 dBZ). However, the results of this study have shown that considerable variability is still encountered within a given delineated region (see section 4.2), and this uncertainty can have an impact on the identified VPR. Therefore, as a next step, the identification of precipitation regions could be improved further by making use of multiple variables such as reflectivity, BB height, and echo top information. These properties can all be obtained from conventional volumetric radar measurements. The use of polarimetric radar data provides even more possibilities [Seliga and Bringi, 1976; Doviak and Zrnic, 1993]. In principle, RoCaSCA should be able to take multiple properties into account, although its current two-dimensional implementation should then be extended.

[79] Even if such an extension would provide the possibility to further discriminate between precipitation regions, the random nature of hydrometeor interactions and the temporal differences between the measurements at different radar elevations will always result in uncertainty and variability in the observed ratio profiles. The VPR uncertainty identification method presented here provides a manner to take this variability into account. For all three precipitation events, results have indicated that the overall uncertainty due to the VPR can be considerable and is able to account for a large part of the observed radar-gauge differences. Such an approach, therefore, provides a direct way to take VPR uncertainty into account and should be identified together with other radar rainfall uncertainty identification procedures [Villarini and Krajewski, 2010]. The importance of the latter aspect could also be observed from the analyses presented in section 4.2.

[80] The current uncertainty identification procedure is not able to discriminate deviations of the true DSD from “standard” stratiform conditions. Such deviations can have a large impact on the rainfall measurement capabilities of the radar. The possibility of being able to discriminate between different precipitation regions, as presented in the current paper, could also provide extra information that is usable to identify such situations. Detailed analyses of the different precipitation regions and their physical properties (e.g., BB height and depth, vertical structure) could for instance result in the identification of a region specific ZR relationship. Another option would be to make use of real-time rain gauge networks, which nowadays have similar temporal resolutions as radar. Merging the obtained precipitation region identification procedure with measurements from rain gauges would allow estimation of region specific ZR relationships. This would then further improve radar rainfall estimates.

6 Conclusion

[81] In this study a new method was presented to estimate the vertical profile of reflectivity from volumetric weather radar data. This method was implemented in both the traditional Eulerian manner as well as in a newly proposed Lagrangian procedure. Although the dynamic nature of precipitation suggests the use of such a procedure, such an approach has not been implemented before, to the author's knowledge. For the three different precipitation events analyzed here, the developed tracing type cluster identification algorithm RoCaSCA is well able to delineate precipitation regions at different levels of intensity, without focusing on linking neighboring pixels only. By tracking each of these regions in time, it is possible to extract the reflectivity ratio information in a Lagrangian manner. The VPR is then identified by combining and extending the methods originally proposed by Andrieu and Creutin [1995] and Smith [1986] for two different piecewise linear profiles discriminating between stratiform and neither stratiform/convective precipitation.

[82] For the Lagrangian implementation, results presented in this paper show that for the region of study, up to a distance of 100 km, the VPR identification method is able to correct for range effects. Beyond this distance, reduced visibility of the radar due to overshooting and sampling within the snow region decreases the possibility to obtain proper ratio information. The identification of a representative VPR therefore becomes difficult. For the Eulerian implementation, correcting for VPR improves the quality of the weather radar data up to a distance of 150 km.

[83] Two methods are proposed to increase the effective VPR identification range of the Lagrangian implementation. The first approach uses data observed within the next hour as well. During this second hour, some of the precipitation regions move closer to the radar, leading to an increase in the quality of the ratio data. However, for precipitation regions moving away from the radar, this obviously does not lead to improved results of the estimated VPR. Also for situations where the assumption of a temporally stable VPR is violated, the quality of the estimated VPR is not improved by taking a second hour into account. As a second approach, the Lagrangian region-based procedure was combined with a Eulerian global VPR identification approach. This latter option enables one to estimate a VPR for all positive reflectivity pixels that were not used in the Lagrangian approach. Results show that this approach is able to generate proper quantitative precipitation estimates up to a distance of 150 km. Since this procedure only takes the precipitation information of the previous hour into account, another benefit of this procedure is that it can be implemented in real time. As such, this latter approach provides better possibilities as compared to the former, while still being able to discriminate between different precipitation regions.

[84] In general, considerable spatial variability in the characteristics of the VPR are observed. Therefore, besides implementing a region-based median VPR estimation procedure, this paper also presents an approach to identify the impact of VPR uncertainty on weather radar measurements. To the authors' knowledge, such a procedure to estimate radar rainfall uncertainty resulting from VPR identification uncertainty has not been presented before. Analyses of two precipitation events showed that this type of uncertainty is able to account for the majority of radar-gauge differences. Although this partly holds for another event analyzed here as well, further deviations between the measurements of both instruments are caused by variations of rainfall microstructure.

[85] The current paper only presents the results for three different precipitation events. In future contributions, we will test the newly presented approach on a longer data set. We have not tried to implement any bias correction mechanisms to account for such deviations. In the future, we believe it will be possible to identify these situations by performing extended analyses on the characteristics of the identified precipitation regions (e.g., size, velocity, characteristics of the delineated VPR). As such, we hope to be able to recognize such variations in the DSD from volumetric radar data. Polarimetric radars, which are gradually replacing nonpolarimetric radars all over the world, could provide even more possibilities. Such an approach would allow the corrected weather radar data to be directly applicable for hydrological applications, using the rain gauge information only for verification. These results have not been presented here, but will be the focus of future contributions.


[86] The authors would like to thank Laurent Delobbe of the Royal Meteorological Institute of Belgium for providing the volumetric radar data, 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. This research has been financially supported by the EU-FP7 Project IMPRINTS (FP7-ENV-2008-1-226555), while the first author was financially supported by a United States Department of Energy research grant DE-SC0006773.