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Precise Remapping

Remapping of Radar Data and its Impact on Estimated Radar Bias Hatim Sharif University of Texas at San Antonio. Introduction. Precise Remapping. Instantaneous Rain Rate.

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Precise Remapping

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  1. Remapping of Radar Data and its Impact on Estimated Radar Bias • Hatim Sharif • University of Texas at San Antonio Introduction Precise Remapping Instantaneous Rain Rate Weather Remapping of radar-rainfall estimates onto a two-dimensional Cartesian grid is commonly done using one of three methods: (1) a nearest neighbor approach or filling the grid cell collocated within a given radar bin with the value observed within the bin (e.g. Zhang et al. 2005), (2) simple averaging i.e. taking the average rainfall of all estimates of radar bins whose centers fall within the grid or area (e.g. Fulton 1998), or (3) distance-weighted averaging i.e. taking the average rainfall of all estimates of radar bins whose centers fall within the grid or area weighted by the inverse of their distance from the center of the grid (e.g. Zhang et al. 2005). We suggest simple remapping by applying knowledge of the beam geometry to define the points (2 dimensions) or planes (3 dimensions) of intersection of the Cartesian grid and collocated conical radar bins. For every Cartesian grid, the algorithm identifies the points of intersection of the grid and collocated radar bins. Here “radar bin” refers to the projection of the radar bin onto the earth's surface. Any pair of adjacent points is connected by a curve or a straight line. These lines divide the grid into a number of polygons, each representing the contribution from one radar bin. The algorism then computes the area of each polygon and multiplies it by the bin precipitation estimate and then divides the sum of the products by the bin area to compute the average grid precipitation. Problem with Traditional Methods Storm Total Rainfall Figure 6.Computed difference in grid interpolated rainfall rate between the precise method and the (a) distance-weighted average, (b) simple average, and (c) nearest-neighbor methods for S-Pol data for different grid sizes Figure 1. Two cases of the intersection of conceptualized radar bins (1 km x 1º) with 1 km x 1 km square grids. Dots represent bin centers Figure 3.Computed difference in grid interpolated storm total rainfall between the precise method and the distance-weighted average method for S-Pol data (a-d) and WSR-88D data (e-h) for different grid sizes Figure 2.Computed difference in grid interpolated storm total rainfall between the precise method and the nearest neighbor method (a-d)and the simple average method (e-h) for different grid sizes In simple averaging (e.g. Fulton 1998), all radar bins have the same weight regardless of how much of the radar bin area falls within the grid or area. This approach can introduce significant discrepancies in several situations. Figure 1 can help in visualizing that. For example, it is possible that the bin’s center falls within a particular grid with less than or just over 50% of the bin’s area contained within the grid and the simple averaging scheme will assume that 100% of the area falls within the grid. Conversely, if just less than 50% of a radar bin falls within a grid, its contribution will be ignored altogether when its center falls outside the grid. In addition, the fact that adjacent radar bins along a ray do not have exactly the same area is always ignored in this approach. The distance-weighted averaging tries to take into account the contribution from each radar bin by multiply the bin estimate by the inverse of its distance from the bin center. This approach also has some problems. For example, the bin whose center does not fall within the grid is still ignored no matter how much of its area falls within the grid. In addition, the contribution of a radar bin does not depend on its distance from the grid center only but also on the orientation of the radar bin. This can easily be understood by looking at Figure 1 and imaging that the radar bins are rotated around the grid center. Storm Total Rainfall Radar bias is typically computed by comparing gauge observation to radar estimate averaged over a certain area centered on the gauge location. Here is a look at the impact of the size of the averaging area on the bias estimate. Figure 7.Change in computed radar bias over larger grid sizes compared to bias compute for a 0.5x0.5-km square for (a) the precise interpolation, (b) simple average, and (c) distance-weighted average methods for S-Pol data for different grid sizes Conclusion In anticipation of this significant upgrade of operational weather radar, this paper investigated some sources of uncertainty that are often overlooked by researchers with the assumption that they are insignificant compared to other sources. The paper presents a new consistent and precise method for remapping radar data onto Cartesian coordinates and quantifies the potential discrepancy in computing average radar rainfall estimates when other traditional methods are used. The method is simple and more precise than commonly used methods. Results indicates that the choice of the interpolation method can have a very significant impact on the estimated radar bias. The impact of the size of the interpolation area on computed average radar rainfall for bias estimation using different methods of interpolation is also quantified. High-resolution data from a polarimetric radar are more sensitive to the remapping method and interpolation area than WSR-88D data. Figure 5.Change in computed radar bias over larger grid sizes compared to bias compute for a 0.5x0.5-km square for precise interpolation method for S-Pol data (a-d) and WSR-88D data (e-h) for different grid sizes Figure 4.Change in computed radar bias over larger grid sizes compared to bias computed for a 0.5x0.5-km square for simple average method (a-d) and distance-weighted average (e-h) for different grid sizes

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