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  • View in gallery
    Fig. 1.

    WSR-88D sampling distributions for VCP 21 assuming a beam propagation model under standard atmospheric refraction conditions

  • View in gallery
    Fig. 2.

    WSR-88D radar power density function for (a) VCP 11 and (b) VCP 21. The brighter white areas indicate higher power densities

  • View in gallery
    Fig. 3.

    WSR-88D data resolutions in azimuthal and elevational directions for VCP 21

  • View in gallery
    Fig. 4.

    (a) Composite reflectivity and range–height indicator (RHI) reflectivity plots along (b) 263° and (c) 122° azimuths. The data are from KIWX (North Webster, IN) radar valid at 2036 UTC 25 Jun 2002. The thin white lines in (a) indicate constant ranges (every 50 km) and azimuths (every 45°). The bold white lines in (a) indicate where the RHIs in (b) and (c) were obtained

  • View in gallery
    Fig. 5.

    (a) Composite reflectivity and RHI reflectivity plots along (b) 0° and (c) 270° azimuths. The data are from KIWA (Phoenix, AZ) radar valid at 0859 UTC 15 Feb 1998. The bold white lines in (a) indicate where the RHIs in (b) and (c) were obtained

  • View in gallery
    Fig. 6.

    Horizontal cross section of reflectivity analysis at 1.9 km above the radar using the RBVM method. The data are from KIWA and are valid at 0859 UTC 15 Feb 1998

  • View in gallery
    Fig. 7.

    Horizontal cross section of the reflectivity analysis at 4.7 km above the radar using the RBVM method. The data are from KIWX and are valid at 2036 UTC 25 Jun 2002. The red arrows indicate an arc-shaped discontinuity in the trailing stratiform region as a result of RBVM

  • View in gallery
    Fig. 8.

    (a) An RHI plot along 263° azimuth and (b) a horizontal cross section at 4.7 km above the radar of the reflectivity analysis using the VI scheme. The data are for the convective case. The red arrows in (b) indicate places where arc-shaped discontinuities resulted from the RBVM approach but not from the VI

  • View in gallery
    Fig. 9.

    (a) An RHI plot along 0° azimuth and (b) a horizontal cross section at 1.9 km above the radar of the reflectivity analysis using the VI scheme. The data are for the winter stratiform case. The red arrows in (a) indicate places where reflectivity values above and below the bright band are used to interpolate the reflectivity in the gaps

  • View in gallery
    Fig. 10.

    An illustration of the VHI scheme. The grid point is indicated by +, and numbers 1–4 indicate the four radar bins where the observations are used to compute the analysis value at the grid point

  • View in gallery
    Fig. 11.

    Same as in Fig. 9 except for the VHI scheme. The red arrows in (a) indicate places where artifacts due to the vertical part of the interpolation scheme remain but to a much lesser degree than in the VI scheme

  • View in gallery
    Fig. 12.

    Echo-top fields (in km above radar level) derived from the 3D reflectivity analyses (KIWA, 0859 UTC 15 Feb 1998) using the (a) RBVM and (b) VHI approaches

  • View in gallery
    Fig. 13.

    Same as in Fig. 9a except for the VHI scheme. Note that artifacts (indicated by the red circle) are introduced by the horizontal interpolation

  • View in gallery
    Fig. 14.

    Composite reflectivity fields observed by the (a) KLOT and (b) KIWX radars for the same region at 2036 UTC 25 Jun 2002 and the mosaicked composite reflectivity fields using the (c) flat and (d) steep mosaic weighting functions shown in Fig. 15. The red lines in (a) and (b) indicate the equidistant line between the two radars

  • View in gallery
    Fig. 15.

    Two examples of mosaic weighting functions

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Constructing Three-Dimensional Multiple-Radar Reflectivity Mosaics: Examples of Convective Storms and Stratiform Rain Echoes

Jian ZhangCooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma

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Kenneth HowardNational Severe Storms Laboratory, Norman, Oklahoma

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J. J. GourleyCooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma

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Abstract

The advent of Internet-2 and effective data compression techniques facilitates the economic transmission of base-level radar data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) network to users in real time. The native radar spherical coordinate system and large volume of data make the radar data processing a nontrivial task, especially when data from several radars are required to produce composite radar products. This paper investigates several approaches to remapping and combining multiple-radar reflectivity fields onto a unified 3D Cartesian grid with high spatial (≤1 km) and temporal (≤5 min) resolutions. The purpose of the study is to find an analysis approach that retains physical characteristics of the raw reflectivity data with minimum smoothing or introduction of analysis artifacts. Moreover, the approach needs to be highly efficient computationally for potential operational applications. The appropriate analysis can provide users with high-resolution reflectivity data that preserve the important features of the raw data, but in a manageable size with the advantage of a Cartesian coordinate system.

Various interpolation schemes were evaluated and the results are presented here. It was found that a scheme combining a nearest-neighbor mapping on the range and azimuth plane and a linear interpolation in the elevation direction provides an efficient analysis scheme that retains high-resolution structure comparable to the raw data. A vertical interpolation is suited for analyses of convective-type echoes, while vertical and horizontal interpolations are needed for analyses of stratiform echoes, especially when large vertical reflectivity gradients exist. An automated brightband identification scheme is used to recognize stratiform echoes. When mosaicking multiple radars onto a common grid, a distance-weighted mean scheme can smooth possible discontinuities among radars due to calibration differences and can provide spatially consistent reflectivity mosaics. These schemes are computationally efficient due to their mathematical simplicity. Therefore, the 3D multiradar mosaic scheme can serve as a good candidate for providing high-spatial- and high-temporal-resolution base-level radar data in a Cartesian framework in real time.

Corresponding author address: Jian Zhang, NSSL, 1313 Halley Circle, Norman, OK 73069.Email: jian.zhang@noaa.gov

Abstract

The advent of Internet-2 and effective data compression techniques facilitates the economic transmission of base-level radar data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) network to users in real time. The native radar spherical coordinate system and large volume of data make the radar data processing a nontrivial task, especially when data from several radars are required to produce composite radar products. This paper investigates several approaches to remapping and combining multiple-radar reflectivity fields onto a unified 3D Cartesian grid with high spatial (≤1 km) and temporal (≤5 min) resolutions. The purpose of the study is to find an analysis approach that retains physical characteristics of the raw reflectivity data with minimum smoothing or introduction of analysis artifacts. Moreover, the approach needs to be highly efficient computationally for potential operational applications. The appropriate analysis can provide users with high-resolution reflectivity data that preserve the important features of the raw data, but in a manageable size with the advantage of a Cartesian coordinate system.

Various interpolation schemes were evaluated and the results are presented here. It was found that a scheme combining a nearest-neighbor mapping on the range and azimuth plane and a linear interpolation in the elevation direction provides an efficient analysis scheme that retains high-resolution structure comparable to the raw data. A vertical interpolation is suited for analyses of convective-type echoes, while vertical and horizontal interpolations are needed for analyses of stratiform echoes, especially when large vertical reflectivity gradients exist. An automated brightband identification scheme is used to recognize stratiform echoes. When mosaicking multiple radars onto a common grid, a distance-weighted mean scheme can smooth possible discontinuities among radars due to calibration differences and can provide spatially consistent reflectivity mosaics. These schemes are computationally efficient due to their mathematical simplicity. Therefore, the 3D multiradar mosaic scheme can serve as a good candidate for providing high-spatial- and high-temporal-resolution base-level radar data in a Cartesian framework in real time.

Corresponding author address: Jian Zhang, NSSL, 1313 Halley Circle, Norman, OK 73069.Email: jian.zhang@noaa.gov

1. Introduction

The deployment of the Weather Surveillance Radar-1988 Doppler (WSR-88D; http://www.roc.noaa.gov/;) network has provided meteorologists critical information toward the issuance of warnings for tornadoes, severe storms, and flash floods. Spherical coordinates are most commonly used to store the raw radar observations. While a spherical coordinate system accommodates the data collection method (i.e., scan strategies) of the WSR-88Ds, it becomes inconvenient when coanalyzing radar data with other observational data sources (e.g., satellite data) or when combining data from multiple radars. Numerous approaches and techniques have been developed for gridding WSR-88D and other ground-based or airborne radars' observations in Cartesian space. The commonly used interpolation techniques include 1) nearest neighbor (e.g.,Jorgensen et al. 1983), 2) linear interpolation (e.g.,Fulton 1998; Mohr and Vaughn 1979; Miller et al. 1986), 3) the Cressman weighting scheme (e.g., Weygandt et al. 2002a), and 4) the Barnes or exponential weighting scheme (e.g., Shapiro et al. 2003; Askelson et al. 2000). Software packages, such as the Sorted Position Radar Interpolator (SPRINT; Miller et al. 1986) and REORDER (http://www.atd.ucar.edu/rdp/home/reorder.html), that were developed at the National Center for Atmospheric Research included one or more of the aforementioned analysis schemes and provide many researchers (e.g., Bluestein and Gaddy 2001; Ziegler et al. 2001; Wurman and Gill 2000) tools for radar data analysis.

Smoothing and filtering characteristics of these simple schemes are studied in Trapp and Doswell (2000) and Askelson et al. (2000) using theoretical approximations and observation system simulation experiments. More sophisticated analysis schemes include statistical (Heymsfield 1976) and variational (Gao et al. 1999) approaches. A majority of the Cartesian interpolation schemes were developed for specific research applications whereby the parameters in the analysis schemes are usually dependent on the applications' objective. For example, some degree of smoothing in analyses is necessary for reducing errors in single-Doppler wind retrievals (Zhang and Gal-Chen 1996; Gao et al. 1999). This type of smoothing, however, may be undesirable for severe storm applications, such as storm cell tracking. The purpose of this study is to find a scheme that can generate a radar reflectivity analysis on a three-dimensional (3D) high-resolution Cartesian grid that satisfies the following criteria.

  1. The gridded reflectivity data must retain, as much as possible, the important convective-scale storm structures evident in the raw radar data with minimal smoothing.

  2. The analyses should be physically realistic with minimal induced artifacts.

  3. The scheme must be computationally efficient and economic for real-time operational applications.

With these criteria, the analyses should provide end users with high-resolution radar reflectivity data fields that are comparable to the raw data with the advantage of a Cartesian coordinate system. A Cartesian coordinate system provides a common framework in which other observational datasets can be merged and cross-correlated. This facilitates the creation of multisensor algorithms and applications that use the strength of individual observations collectively to provide more physically and scientifically sound depictions of meteorological phenomena than a single observing system.

The transformation of radar data from a spherical coordinate to a Cartesian grid provides a more direct approach of combining multiple radars onto a common grid. Forecasters are often responsible for areas that encompass multiple-radar umbrellas [e.g., the National Weather Service (NWS) County Warning Areas and the Federal Aviation Administration (FAA) Air Route Traffic Control Centers]. Moreover, the life cycle of an individual storm or storm system may span a region that requires observations from two or more radars to adequately monitor the evolution of storm and associated characteristics. The Collaborative Radar Acquisition Field Test (CRAFT; Droegemeier et al. 2002) project successfully demonstrated the feasibility of transmitting full-volume scan data from all radars in the NWS WSR-88D network to a center facility economically and in real time. This provides the ability to integrate the full-resolution base-level data from multiple radars onto a common 3D framework. The 3D mosaic grid can benefit forecasters, meteorologists, and researchers with a wide variety of products and displays, including flexible horizontal or vertical cross sections in addition to regional rainfall maps. High-resolution reflectivity analyses can also serve as an important source in data assimilations for convective-scale numerical weather modeling (e.g., Zhang 1999; Weygandt et al. 2002b) over large domains and for merging conventional datasets (e.g., lightning strike information, objectively analyzed rawinsonde observations, numerical forecast simulation fields, etc.) with the radar data.

A radar reflectivity observation is not simply a point observation. It is an integrated electromagnetic power return from scatters in a radar sample volume (Rinehart 2001) or resolution volume (Doviak and Zrnic 1993). The sample volume is also referred to as a radar data bin in this paper. Due to the spherical geometry of radar sampling, the size of radar sample volumes increases with increasing range while the sample resolution decreases with increasing range. Figure 1 shows the range height coverage for the WSR-88D volume coverage pattern (VCP) 21 (OFCM 2003) for standard atmospheric refractive conditions. Within ∼20 km of the radar, centers of radar data bins are less than 1 km apart, while at ranges of ∼150 km, data are spaced more than 50 km horizontally (between points A and A′) and more than 2.5 km vertically (between B and B′). This nonuniformity in data spacing makes the choice of an interpolation scheme and associated filter somewhat dependent on the objective of the application. Trapp and Doswell (2000) evaluated the error characteristics of nearest-neighbor, Barnes-type, and Cressman-type interpolation schemes using simulated radar fields. Their results show that a nearest neighbor scheme gives the smallest root-mean-square (rms) errors between the analysis and the observations, but the spatial scales of the error fields are nonuniform. A heavy Barnes filter based on the poorest resolution of the reflectivity data results in an error field of uniform spatial scales but with significantly less high-resolution information (Askelson et al. 2000) than in the raw data. This is not desirable for severe storm tracking applications, nor for convective-scale numerical weather assimilation applications because higher-resolution information available at shorter ranges is discarded.

This paper explores various objective analysis methods applied to WSR-88D data across a spectrum of weather regimes with comparisons between nearest-neighbor and two linear interpolation schemes. Results from several mosaicking techniques, including nearest neighbor, maximum value, and distance-weighted mean, are presented for comparison.

The following section provides an overview of WSR-88D scan strategies and the associated beam geometry. The objective analysis schemes mentioned above are illustrated and contrasted in section 3. Strategies for combining data from multiple radars are presented in section 4, and a summary is provided in section 5.

2. WSR-88D data resolution

The WSR-88Ds pulse electromagnetic energy into the atmosphere along a conical beam as the antenna scans azimuthally in specified elevation angle steps. The resultant volume scan is in spherical (r, ϕ, θe) coordinates, where r is the slant range, ϕ is azimuth angle from north, and θe is elevation angle from the horizon. The electromagnetic power distribution in a beam follows a Bessel function of second order (Doviak and Zrnic 1993):
i1520-0426-22-1-30-e1
where α is the angular distance from the beam axis, J2 is the Bessel function of second order, D is the diameter of the antenna reflector, and λ is the wavelength.
The operational WSR-88Ds scan in four different modes, each of which has prespecified elevation angles (Table 1). Figure 2 shows vertical cross sections of beam propagation paths and power density distributions for the VCP11 and VCP21 scan modes. The propagation of the beams is assumed to follow the 4/3-effective earth radius model (Doviak and Zrnic 1993):
i1520-0426-22-1-30-e2
i1520-0426-22-1-30-e3
i1520-0426-22-1-30-e4
where a represents the earth's radius, ae represents the 4/3-effective earth radius, h is the height of the center of the radar beam, and s is the distance between the radar and the projection of the bin along the earth surface. All the computations in this paper assume this standard atmospheric beam propagation model.

Equation (1) shows that the radar power peaks along the center of the beam and decreases in the azimuthal and elevational directions. An observation in a given radar bin is an integrated returned power from all scatters within the sampling volume of the bin, with the scatters near the beam center weighted more than the scatters near the beam edges. At each range bin, the variance of the returned power is reduced to ∼1 dB by averaging a number of independent pulses (Sirmans and Doviak 1973). The spatial density of radar data can be discussed in terms of the distance between centers of adjacent radar bins. In the radial direction the data spacing of the WSR-88D reflectivity data is fixed at 1 km. In the azimuthal and elevational directions, however, the data spacing is a function of range (Fig. 2). The azimuthal data spacing is calculated by assuming that radials are 1° apart and evenly distributed. Therefore, the distance between centers of adjacent radials is simply r1 − cos(ϕ), where Δϕ = 1°. The azimuthal data spacing is 1 km at a range of approximately 75 km and increases linearly with range (Fig. 3a). The elevational data spacing is calculated in a similar way, but the angle differences are those between two adjacent tilts (prescribed by VCPs). Since adjacent tilt angles are not uniform (Table 1), the elevational data spacing varies not only with range but also with elevation. The large gaps between higher tilts in VCP21 result in very poor vertical coverage (Fig. 3b). The data spacing is >1 km beyond a range of 30 km (15 km) above the fifth (sixth) tilt. Significant data voids exist between higher tilts as well as below the lowest tilt and above the highest tilt (see black regions in Figs. 2a,b). These factors significantly impact the spatial fidelity of the radar data, which is apparent before and after the radar data have been objectively analyzed to a grid.

3. Remapping radar data to Cartesian space

a. Case description

Approximately 50 cases from different geographical regions and within each season were examined using the various analysis schemes. This section presents the results from two representative cases, a convective storm event that occurred on 25 June 2002 in Indiana (Fig. 4) and a wintertime stratiform precipitation event that occurred on 15 February 1998 in Arizona (Fig. 5). These two cases represent different weather regimes occurring on dissimilar spatial scales, as is evident in their radar depictions. The convective storm case shows strong upright convective cells with horizontal scales on the order of 10–100 km with vertical scales up to 15 km (Figs. 4b,c). The winter case, in contrast, shows much more horizontally homogeneous echoes (often termed “stratiform” rain) with large horizontal extents of 300–400 km (Fig. 5a), yet the height of precipitating echo is only approximately 7.5 km (Figs. 5b,c). A radar bright band [resulting from melting hydrometeors (Atlas and Banks 1950)] is apparent at ∼1.7 km above radar, where reflectivity is ∼45 dBZ at the center of the bright band and decreasing to ∼30 dBZ within 250 m below and above (Figs. 5b,c).

b. Radar bin volume mapping

Four interpolation schemes were evaluated for remapping radar data from their native spherical coordinates to Cartesian coordinates. The first scheme, radar bin volume mapping (RBVM), simply fills in grid cells collocated within a given radar bin with the value observed within the bin. A grid cell is determined to be within a radar bin if the center of the grid cell is contained inside the volume of the radar bin. The volume of radar bins is assumed to be 1 km × 1° × 1°. Αll grid cells that are not encompassed by any radar bin volume are flagged as missing (e.g., grid cells in the black regions in Fig. 2). Figures 4b, 4c, 5b and 5c show vertical cross sections of RBVM analyses from the two cases using a very fine Cartesian grid (50 m × 50 m × 10 m). Using this fine grid, the RBVM scheme depicts radar beam propagation and data distributions (assuming 4/3-effective earth radius model) and the radar sampling limitations of the VCP 11 and VCP 21 scanning strategies. A more complete depiction of convective reflectivity structure is accomplished using VCP11 (Figs. 4b,c) as compared to VCP 21 (Figs. 5b,c).

A horizontal cross section taken at 1.9 km above the radar for the winter storm case shows ring-shaped artifacts as a result of the relatively poor vertical sampling (Fig. 6). Radar bin sizes increase with range rapidly from an approximate diameter of 0.3 km at a range of 25 km to 2.5 km at a range of 150 km (Fig. 5b). The 1.9-km height intersects different rays at different distances. Sometimes grid points at the 1.9-km level are within radar bins that are strongly affected by the bright band, while other times grid points are within radar bins that are not strongly affected by the bright band. The high-reflectivity rings are associated with radar bins that are centered near the bright band, while the low-reflectivity rings are associated with radar bins that are centered above or below the bright band.

Horizontal plots of reflectivity for the convective case provide a smooth depiction of the reflectivity field (Fig. 7). Nevertheless, arc-shaped discontinuities similar to the winter brightband case can be present in the trailing stratiform region (Fig. 7). The black rings near the radar in both Figs. 6 and 7 indicate that gaps between the higher tilts are related to the individual scan strategy.

c. Nearest-neighbor mapping

The second scheme being examined, nearest neighbor mapping (NNM), assigns the value of the closest radar bin to grid cell, where distance is evaluated using the location of the centers of the radar bins. The nearest-neighbor approach results in a horizontal cross section (not shown) that is very similar to that produced by the RBVM method but with the characteristic of filling in data voids near the radar. Therefore, it suffers from many of the same artifacts as the RBVM approach (e.g., the ring-shaped artifacts). The ring artifacts of the RBVM and NNM analysis schemes are not surprising because these schemes are simply moving observation values instead of estimating from trends in the data. The problem is more pronounced in the vertical than in horizontal because the scales of atmospheric phenomena are much smaller in the vertical than in the horizontal.

d. Vertical interpolation

The third scheme examined is a linear interpolation scheme in the elevational direction combined with the nearest neighbor scheme in the azimuthal and range directions. The vertical interpolation (VI) approach has been used quite successfully in airborne Doppler radar applications (Jorgensen et al. 1996) where the antenna makes vertical scans. For small elevation angles (<20°), the elevational direction is approximately vertical (hence the schemes name). The procedure for computing the analysis value fai at a given grid cell i is as follows.
  1. Find the range, azimuth, and elevation at the center of the grid cell i.

  2. Find two observations, fo1 and fo2, on the two adjacent tilts below and above the grid cell, respectively, and at the same range and azimuth as the grid cell.

  3. Compute the analysis value fai using

i1520-0426-22-1-30-e5
Here w1 and w2 are the interpolation weights given to the reflectivity observations below and above the grid cell, respectively. The weights are determined by
i1520-0426-22-1-30-e6
i1520-0426-22-1-30-e7
where θi, θo1, and θo2 represent elevation angles of the grid cell and the radar bins below and above, respectively.

By performing a linear interpolation in the elevational direction, the vertical gradients are better preserved than with nearest-neighbor mapping. The vertical structure of convective storm cells is more coherent than in the RBVM (Fig. 8a versus Fig. 4b) and with NNM analyses. Moreover, the ring-shaped discontinuities in the brightband layer have been alleviated, except at ranges corresponding to gaps between tilts in VCP 21 (Figs. 9a,b versus Figs. 5b and 6), where the VI scheme relies on reflectivity observations above and below the bright band to fill in the data voids. As a result of the VI, low reflectivity rings appear in these gaps on the horizontal cross sections (Fig. 9b). To better preserve brightband layer structures, a fourth scheme is employed and subsequently evaluated.

e. Vertical and horizontal interpolation

The fourth scheme uses the VI scheme plus a horizontal interpolation between adjacent tilts that are more than 1° apart. The analysis formula for the vertical and horizontal interpolation (VHI) scheme is the following:
i1520-0426-22-1-30-e8
Here fo3 and fo4 represent the two reflectivity observations along horizontal directions on the two adjacent tilts below and above the grid cell (see Fig. 10); and w3 and w4, the interpolation weights given to the two observations fo3 and fo4, respectively, are determined by
i1520-0426-22-1-30-e9
i1520-0426-22-1-30-e10
Here si represents horizontal distance between the radar (at the origin in Fig. 10) and the grid cell i; and so3 and so4 represent horizontal distances between the radar and data bins “3” and “4,” respectively (Fig. 10).

The horizontal interpolation, when applied in the data voids, recovered the brightband layer and further alleviated the ring-shaped artifacts on horizontal cross sections (Fig. 11). The 3D reflectivity analyses generated using the VHI approach also produce more realistic echo-top fields (Fig. 12). Ring artifacts often appear in echo-top fields derived from reflectivity in spherical coordinates (Howard et al. 1997; Maddox et al. 1999; Brown et al. 2000). They also exist in the reflectivity analysis using the RBVM (Fig. 12a) and the NNM (not shown) approaches. The VHI approach, which makes uses of trends (with a linear approximation) in the data, is able to alleviate the ring-shaped discontinuities significantly (Fig. 12b).

It was discovered that the VHI scheme is not as well suited for the convective echoes characterized by significant variability in the horizontal. As shown in Fig. 13, for example, the VHI approach produces unwanted artifacts near the edges of the upright convective cores. Based on the experiments above and the detailed examination of several cases (convective and stratiform), the VI approach is suitable for most situations. The exception is the occurrence of a bright band, where the VHI approach preserves more of the continuous nature of the brightband layer and avoids ring-shaped artifacts in the analysis. Therefore, the objective analysis approach requires adaptation to the spatial scales (horizontal and vertical) of the observed weather. Objective brightband identification schemes such as the one developed by Gourley and Calvert (2003) can be used to determine the existence of a bright band and thus determine a proper objective analysis approach in real time.

4. Mosaic schemes

a. Multiradar mosaic

Through utilization of one or more of the objective analysis approaches discussed in the previous section, the reflectivity fields from individual radars are remapped onto a common Cartesian grid. The remapped reflectivity fields from multiple radars are then combined, or “mosaicked,” to produce a unified 3D reflectivity grid. There are many areas across the United States, especially at mid- to upper levels of the troposphere, where multiple radars overlap in coverage (Maddox et al. 2002). The reflectivity value for each grid cell in a mosaicked grid i is obtained by
i1520-0426-22-1-30-e11

Here fm(i) is the mosaicked reflectivity value at the grid cell, i; fan(i) is an analysis value at the grid cell from the nth radar; αn is a weight given to the analysis value fan(i); and Nrad represents the total number of radars that have an analysis value at the grid cell. If Nrad = 0, then the grid cell is not covered by any radar and a missing flag is assigned to fm(i). If Nrad = 1, then the grid cell is covered by one radar only and the analysis value from that radar is assigned to the grid cell [i.e., fm(i)=fa1(i)]. If Nrad > 1, then a weighted mean of multiple-radar analysis values is assigned to the grid cell. Several weighting methods are considered and tested to determine an optimal weighting methodology for combing radar data.

The first mosaic weighting method is the “nearest neighbor,” in which the analysis value from the closest radar is assigned to the grid cell. The nearest-neighbor method does not impose any smoothing when creating a mosaic from multiple radars. However, discontinuities may appear at the equidistant lines between radars in the mosaicked field. Figures 14a and 14b show composite reflectivity fields for two adjacent radars (KIWX at North Webster, Indiana, and KLOT at Romeoville, Illinois) that share a common area and were valid near the same time. The KIWX composite reflectivity values are significantly higher than those of KLOT in the majority of the domain shared by both radars (Figs. 14a,b). The mean difference (KIWX − KLOT) computed at the equidistant grid cells along the red line in Fig. 14 between the two fields is +7 dBZ. Gourley et al. (2003) has shown that calibration differences among WSR-88Ds often exceed 5 dBZ. The calibration differences result in discontinuities in the nearest-neighbor mosaic along the equidistant lines, making the nearest-neighbor scheme suboptimal for mosaicking reflectivity from multiple radars. Discontinuities could also arise from other causes, such as the presence of a bright band that is sampled differently by the two radars.

The second mosaicking method simply uses the maximum reflectivity value among the multiple observations that cover the same grid cell. This method does not involve smoothing and it retains the highest reflectivity intensities in the data fields. The method possibly mitigates attenuation losses due to intervening regions of intense rainfall. Therefore, it is better suited for creating derivative products such as composite reflectivity fields. However, this method would provide a biased estimate toward radars that provide higher reflectivity values as a result of calibration differences.

The third mosaic method considered is a weighted mean, whereby the weight is based on the distance between an individual grid cell and the radar location. Two weighting functions were tested; both monotonically decrease with range (Fig. 15). The weighting function reflects the confidence level that the radar observation is representative of the convective-scale storm structure. Due to the beam spreading, the size of the radar resolution volume increases squarely with range. Subsequently, the reflectivity fields have less finescale structure at far ranges than at ranges closer to the radar. Therefore, the observations at far range should receive smaller weights than those from near the radar when mosaicking. The first weighting function has a characteristically steep shape (dashed line in Fig. 15) where the weight decreases with range very rapidly. In contrast, the second weighting function (solid line in Fig. 15) is relatively flat, so that more weight is given to observations from distant radars. Mosaicked composite reflectivity fields from KIWX and KLOT radars were derived using the two weighting functions (Figs. 14c,d). The mosaicked composite reflectivity field using the flat weighting function scheme (Fig. 14c) showed much lower reflectivities than those depicted in the KIWX observations (Fig. 14b), especially in regions near the KIWX radar. The lesser reflectivity intensities in this analysis are due to the fact that lower reflectivity values from the KLOT radar received significant weights during the mosaicking analysis. In addition, due to the beam spreading, reflectivity observations at far ranges contain features with coarser scale than reflectivity observations close to the radar. If a flat weighting function is applied, the far-range observations can dampen the finescale gradients associated with near-range observations. Conversely, the steep weighting function retains more details on reflectivity structures by allowing more contributions from near-range observations. The latter scheme is thus preferred in this case for mosaicking reflectivity data from multiple radars due to its capability of representing finescale storm structures while preserving their magnitudes.

b. Data voids

Figure 2 shows the existence of gaps between the higher tilts as well as the data voids above the highest beam (i.e., the “cone of silence”) and below the lowest beam. All the spherical-to-Cartesian remapping schemes discussed in section 4 do not extrapolate reflectivity values into the data void regions below the beam coverage shown in Fig. 2. While multiple-radar mosaic can fill in the upper part of one radar's “cone of silence” using observations from other radars nearby, significant data voids still exist in the lower altitudes (Maddox et al. 2002). Without filling in the data voids, the application of the 3D mosaic grid to numerical weather models is limited since the information near the surface is critical to model initialization. An additional radar network, such as the FAA Terminal Doppler Weather Radar (TDWR) network, can potentially reduce the data voids in areas near airports and large metropolitan areas (Vasiloff 2001). Vertical profiles of reflectivity (VPRs; e.g., Joss and Waldvogel 1990; Berne et al. 2004) can be derived from the observations at the close ranges. The profiles can be used to approximate vertical reflectivity structures at far ranges down to the earth's surface.

5. Summary

Four interpolation approaches and three mosaic methods are evaluated in this paper. These techniques are candidates for converting radar reflectivity data from multiple sources in their native (spherical) coordinates onto a multiradar, mosaicked 3D Cartesian grid. Approximately 50 cases from different geographical regions and different seasons were evaluated and examples of two common weather regimes (spring/summer convective storms and wintertime stratiform precipitation systems) are presented. Based on extensive case studies, it was found that the vertical interpolation scheme provides the most physically realistic mosaic for convective storms. For stratiform precipitation with the presence of a bright band, an additional horizontal interpolation scheme is required to reconstruct the horizontally extended layers in the data voids, especially between upper tilts, as in VCP 21. When combining multiple-radar reflectivity fields onto a single 3D grid, a distance-weighted mean scheme is preferred to produce a continuous and representative field. The shape of the weighting function is important for retaining the spatial reflectivity gradients and intensities.

By using the vertical interpolation and vertical/horizontal interpolation approaches together with a distance-weighted mosaicking scheme, multiple-radar reflectivity fields can be integrated onto a common 3D Cartesian grid. These mosaics contain high-resolution features of the raw data, but in a manageable size with the advantage of a Cartesian coordinate system. The high-resolution mosaic grid provides useful datasets for further applications, such as quantitative precipitation estimation, severe storm detection algorithms, and data assimilation for convective-scale numerical weather predictions.

The VI and VHI schemes have the advantage of low computational costs. However, the resultant reflectivity analyses are not very suited for applications that require high-order derivatives of the analyses. This is due to the fact that linear interpolations used in the scheme can introduce discontinuities in derivative fields of the analyses. A smoothing or filtering of the mosaic grid data is recommended before such applications. With the Cartesian grid, filtering of the data is straightforward in comparison to spherical coordinates.

Even with the interpolations and multiple-radar mosaic, data voids still exist such as with the cone of silence above the radar and in regions below the lowest beam. To reduce the data voids, the FAA TDWR data will be integrated into the mosaic for better lower-atmosphere coverage, especially over metropolitan areas. New studies are under way to assess the potential of using vertical profiles of reflectivity to extrapolate reflectivity observations at far ranges down to the earth's surface. Future research also includes development of a synchronization scheme for handling time and sampling differences among multiple radars' observations. These studies will enhance the 3D mosaic grid and increase its usefulness for forecasters and for the inclusion of high-resolution 3D mosaic fields in numerical models.

Acknowledgments

The authors would like to thank Dr. Dave Jorgensen and Dr. Robert Maddox and the reviewers for their comments that helped immensely in the preparation of this manuscript. Major funding for this research was provided under the Aviation Weather Research Program NEXRAD Algorithms Product Development Team (NAPDT) MOU, and partial funding was provided under NOAA-OU Cooperative Agreement NA17RJ1227.

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Fig. 1.
Fig. 1.

WSR-88D sampling distributions for VCP 21 assuming a beam propagation model under standard atmospheric refraction conditions

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 2.
Fig. 2.

WSR-88D radar power density function for (a) VCP 11 and (b) VCP 21. The brighter white areas indicate higher power densities

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 3.
Fig. 3.

WSR-88D data resolutions in azimuthal and elevational directions for VCP 21

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 4.
Fig. 4.

(a) Composite reflectivity and range–height indicator (RHI) reflectivity plots along (b) 263° and (c) 122° azimuths. The data are from KIWX (North Webster, IN) radar valid at 2036 UTC 25 Jun 2002. The thin white lines in (a) indicate constant ranges (every 50 km) and azimuths (every 45°). The bold white lines in (a) indicate where the RHIs in (b) and (c) were obtained

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 5.
Fig. 5.

(a) Composite reflectivity and RHI reflectivity plots along (b) 0° and (c) 270° azimuths. The data are from KIWA (Phoenix, AZ) radar valid at 0859 UTC 15 Feb 1998. The bold white lines in (a) indicate where the RHIs in (b) and (c) were obtained

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 6.
Fig. 6.

Horizontal cross section of reflectivity analysis at 1.9 km above the radar using the RBVM method. The data are from KIWA and are valid at 0859 UTC 15 Feb 1998

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 7.
Fig. 7.

Horizontal cross section of the reflectivity analysis at 4.7 km above the radar using the RBVM method. The data are from KIWX and are valid at 2036 UTC 25 Jun 2002. The red arrows indicate an arc-shaped discontinuity in the trailing stratiform region as a result of RBVM

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 8.
Fig. 8.

(a) An RHI plot along 263° azimuth and (b) a horizontal cross section at 4.7 km above the radar of the reflectivity analysis using the VI scheme. The data are for the convective case. The red arrows in (b) indicate places where arc-shaped discontinuities resulted from the RBVM approach but not from the VI

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 9.
Fig. 9.

(a) An RHI plot along 0° azimuth and (b) a horizontal cross section at 1.9 km above the radar of the reflectivity analysis using the VI scheme. The data are for the winter stratiform case. The red arrows in (a) indicate places where reflectivity values above and below the bright band are used to interpolate the reflectivity in the gaps

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 10.
Fig. 10.

An illustration of the VHI scheme. The grid point is indicated by +, and numbers 1–4 indicate the four radar bins where the observations are used to compute the analysis value at the grid point

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 11.
Fig. 11.

Same as in Fig. 9 except for the VHI scheme. The red arrows in (a) indicate places where artifacts due to the vertical part of the interpolation scheme remain but to a much lesser degree than in the VI scheme

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 12.
Fig. 12.

Echo-top fields (in km above radar level) derived from the 3D reflectivity analyses (KIWA, 0859 UTC 15 Feb 1998) using the (a) RBVM and (b) VHI approaches

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 13.
Fig. 13.

Same as in Fig. 9a except for the VHI scheme. Note that artifacts (indicated by the red circle) are introduced by the horizontal interpolation

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 14.
Fig. 14.

Composite reflectivity fields observed by the (a) KLOT and (b) KIWX radars for the same region at 2036 UTC 25 Jun 2002 and the mosaicked composite reflectivity fields using the (c) flat and (d) steep mosaic weighting functions shown in Fig. 15. The red lines in (a) and (b) indicate the equidistant line between the two radars

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Fig. 15.
Fig. 15.

Two examples of mosaic weighting functions

Citation: Journal of Atmospheric and Oceanic Technology 22, 1; 10.1175/JTECH-1689.1

Table 1.

Elevation angles (°) used in the four NWS operational VCPs for WSR-88Ds

Table 1.
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