Overshooting problem in radar radial velocity analysis

One important observation studied in this research is radar radial velocity observation that can be distributed in high density and cause overshooting problems. In this section, the ARPS 3DVAR analysis is used to analyze simulated radar radial velocity observations and results are used to estimate the extent of the overshooting problem in the analysis.

The first situation simulated assumes many radial velocity observations concentrated on a certain area. For that purpose, 100 U observations with same value of 10 m s-1 and distributed one grid point by one grid point in a square-shaped area are created and analyzed via the ARPS 3DVAR with 0 background field. The result from the analysis without the recursive filter gives analysis value of 6.92 m s-1 in each grid point that has an observation in it (not shown). The analysis using the recursive filter with the horizontal decorrelation scale, R, set to 1 and 3 grid spacing is shown in Fig. 2.4a and b, respectively. We can see that the analyzed U values in the observation area have been increased by 1.99 m s-1 for R = 1 and 3.05 m s-1 for R = 3 comparing to the analysis values without the recursive filter.

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Umax=8.91 ,Umin=0.458E-05,Vmax=0.00 ,Vmin=0.00 Min=0.00 Max=0.00 Contour interval=0.00

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Umax=9.97 ,Umin=0.131 ,Vmax=0.00 ,Vmin=0.00 Min=0.00 Max=0.00 Contour interval=0.00

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Umax=9.30 ,Umin=0.621E-04,Vmax=0.00 ,Vmin=0.00 Min=0.00 Max=0.00 Contour interval=0.00

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Umax=10.5 ,Umin=0.530 ,Vmax=0.00 ,Vmin=0.00 Min=0.00 Max=0.00 Contour interval=0.00

(b) (a)

(c) (d)

Fig. 2.4 3DVAR analysis is applied to 100 U observations concentrated on an area like radar radial wind. The observation values are 10 m s-1 and background field is set to 0. The recursive filter is used to model background error correlation. a) Analysis of a square-shaped observation area with the horizontal decorrelation scale set to 1 grid spacing. b) Similar to a) but with the horizontal decorrelation scale set to 3 grid spacings. c) Analysis of four square-shaped observation areas that have 2 grid spacing missing observations or holes among them. The horizontal decorrelation scale set to 1 grid space. d) Similar to c) but with the horizontal decorrelation scale set to 3 grid spacings. e) Analysis of four square-shaped observation clusters that observed U directions in each cluster are opposite to its nearby cluster. The horizontal decorrelation scale set to 1 grid spacing. f) Similar to e) but with the horizontal decorrelation scale set to 3 grid spacings.

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Umax=9.20 ,Umin=-9.20 ,Vmax=0.00 ,Vmin=0.00 Min=0.00 Max=0.00 Contour interval=0.00

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Umax=11.8 ,Umin=-11.8 ,Vmax=0.00 ,Vmin=0.00 Min=0.00 Max=0.00 Contour interval=0.00

(e) (f)

Fig. 2.4 Continued

The second situation assumes that some holes exist in a radial velocity observation area. This time we construct four observation clusters to form a big square- shaped area like the first situation and with 25 U observations in each cluster. Between these four clusters are 2 grid spacing wide missing observations or holes. The same 3DVAR analysis is applied in this observation situation and results are shown in Fig. 2.4c and d. The same as the first situation, analyzed U values in the observation area are increased by 2.38 m s-1 for R = 1 and 3.58 m s-1 for R = 3, a little larger than those in the first situation. Fig. 2.4d also shows that the holes between four observation areas have been filled by the recursive filter with a large horizontal decorrelation scale.

The third situation assumes radial velocity observations with shear and divergence among them. Using same four U observation clusters and put them together form a large square-shaped area but observed U directions in each cluster are opposite to its nearby clusters. Therefore, between these four clusters, there is a shear line in x-direction and a

divergence line and a convergence line in y-direction. Fig. 2.4e and f show the 3DVAR analysis with the horizontal decorrelation scale set to 1 and 3 grid spacing, respectively. It is found that the 3DVAR analysis correctly gives the existence of shear, divergence, and convergence lines but the overshooting problem can be severe along those lines when a large horizontal decorrelation scale is used (Fig. 2.4f). The results of this experiment indicate that the overshooting problem has been limited under a low level in most situation of the radial velocity analyses in the ARPS 3DVAR.

In further experiments, several observations are set in one grid box, which is how radial velocity observations are used in most current storm-scale simulations. Although, in the ARPS 3DVAR, both reflectivity and radial velocity data have been interpolated to the grid point via a preprocessing procedure that makes observation operator of the 3DVAR analysis much simpler, it is worthwhile to take a look at the situation where the resolution of radial velocity observations is higher that that of analysis space. In this experiment, 4 observations are put into the same grid box and totally 400 observations are distributed in 100 grid boxes that form a square-shaped observation area. The background is set to 0. The observations are set to 10 m s-1_{. The 3DVAR analysis without}

the recursive filter is shown in Fig. 2.5a. The most of analysis values are larger than the observation values even without space correlation in the background error covariance. When the 3DVAR analysis with the recursive filter of the horizontal decorrelation scale set to 1 and 3 grid spacing is applied, the recursive filter does not cause overshooting problem in this situation and, interestingly, it can mitigate the overshooting problem induced by high resolution observations as demonstrated in Fig. 2.5b and c.

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Umax=10.4 ,Umin=0.190 ,Vmax=0.00 ,Vmin=0.00 Min=0.00 Max=0.00 Contour interval=0.00

(a) (b)

(c)

Fig. 2.5 3DVAR analysis is applied to 400 U observations concentrated on an area like radar radial wind. Each grid box has 4 observations in it. The observation values are 10 m s-1 _{and background field is set to 0. The recursive filter is used to model background error}

correlation. a) Analysis without the recursive filter. b) Analysis using the recursive filter with the horizontal decorrelation scale set to 1 grid spacing. c) Similar to b) but with the horizontal decorrelation scale set to 3 grid spacing.