The previous two-dimensional simple adjoint method for retrieving horizontal wind field from a time sequence of single-Doppler scans of reflectivity and/or radial velocity is further developed into a new method to retrieve both horizontal and vertical winds at high temporal and spatial resolutions. This new method performs two steps. First, the horizontal wind field is retrieved on the conical surface at each tilt (elevation angle) of radar scan. Second, the vertical velocity field is retrieved in a vertical cross-section along the radar beam with the horizontal velocity given from the first step. The method is applied to phased array radar (PAR) rapid scans of the storm winds and reflectivity in a strong microburst event and is shown to be able to retrieve the three-dimensional wind field around a targeted downdraft within the storm that subsequently produced a damaging microburst. The method is computationally very efficient and can be used for real-time applications with PAR rapid scans.
Updrafts and downdrafts are the essential components of storms. Their strengths often determine the type and evolution stage of storms. Quickly detecting updrafts and downdrafts and estimating their strengths in storm wind fields will make timely and accurate assessments of hazardous weather conditions. It is thus desirable to develop an efficient method to retrieve both the horizontal and vertical winds, including updrafts and downdrafts, in real time from phased array radar (PAR) rapid scans of storms. A key advantage of PAR over Weather Surveillance Radar 1988-Doppler (WSR-88D) is the capability to rapidly and adaptively scan storms. With its agile electronic beam steering, the PAR scan strategy can be optimized on particular weather phenomena with the volume scan time reduced from minutes to seconds (Zrnic et al. [
Since Doppler radar observations are limited mainly to reflectivity and radial-component velocity (along the radar beam) and there is no direct measurement of the remaining two wind components perpendicular to the radar beam, a two-dimensional simple adjoint (2D-SA) method was developed by Qiu and Xu [
To reduce the computational cost, the horizontal and vertical winds will be retrieved separately in two steps. In the first step, the 2D-SA method is used to retrieve the horizontal winds on each conical surface of the radar scans in a targeted domain of convective scale, while the mesoscale background horizontal wind field is provided by the existing radar wind analysis system that was developed based on the statistic interpolation for real-time applications with the operational WSR-88D radars (Xu et al. [
The 2D-SA method is used in the first step to estimate the incremental time-mean quasi-horizontal velocity
The first term in (
The second term in (
The third and fourth terms in (
The last term in (
The gradients of the first cost-function term
The gradients of the subsequent three cost-function terms in (
The gradient of the background term in (
The second step retrieves the time-mean vertical crossbeam velocity component
The first cost-function term
Sketch of geometric relationship between the components of
The
The gradients of the first cost-function term
The gradients of
The gradient of the background term
The multimission PAR, located at the National Weather Radar Testbed (NWRT), Norman, Oklahoma, is a research radar using a converted U.S. Navy SPY-1A phased array antenna. This PAR has essentially the same wavelength (9.4 cm in S band) and range resolution (250 m) as the WSR-88D radars, and it can mimic WSR-88D volume coverage patterns (VCPs) and collect data at similar pulse repetition intervals. The most significant difference between the PAR and the WSR-88D is that the phased array antenna forms each beam electronically by controlling the phases of transmit-receive elements and thus can scan storms rapidly and adaptively. With its rapid scan capability, the PAR captured the rapid evolution of a severe storm produced microburst at the 20 km radial range to the south-southwest during the early evening of July 10, 2006. The PAR applied a beam multiplexing scanning strategy to volume coverage pattern 12 (VCP12) for a 90° sector scan, so each volume scan contained up to 53 tilts (with the elevation angles from 0.51° to 41°) and is completed in just 34 seconds. Since the retrieval domain is small and not very close to the PAR, only 14 tilts (from 0.51° to 19.5°) are intercepted by the retrieval domain and will be used for the retrievals in this paper. The storm and its produced microburst were fully sampled in time and space by the PAR. In particular, the PAR detected a reflectivity core aloft between 19 : 40 : 21 and 19 : 42 : 20 UTC at about 6 km above ground level. This reflectivity core produced a strong downdraft maximized around 19 : 49 : 07 UTC as shown in Figure
Reflectivity images from 20 consecutive PAR 90° sector scans of a severe microburst event from 19 : 41 : 12 to 19 : 53 : 19 UTC on July 10, 2006. Each panel consists of two subpanels: (i) the range height indicator (RHI) display along the 210.7° azimuth on the left side and (ii) the plan position indicator (PPI) display at 0.51° elevation on the right side. For the RHI display, the radial range is leftward from
As mentioned in Section
Background wind fields (shown by white arrows) produced by the radar wind analysis system at 19 : 40 : 42 UTC at (a)
The nested horizontal domain on the conical surface of each tilt of PAR scan is centered at the radial range of
The weights and decorrelation length scales used by the cost function in (
The weights and decorrelation length scales used by the cost function in (
Figures
Quasi-horizontal (
From Figures
On the other hand, as we can see from Figures
Figures
Reflectivity source fields (for the
Time series of retrieved
In the upper level (around
As another by-product, the horizontal turbulent diffusivity coefficient
Figures
Note that the vertical advection term is explicitly considered in (
Reflectivity source field (for the
As another by-product, the vertical turbulent diffusivity coefficient
As mentioned in the introduction, the retrieval errors can be reduced if the reflectivity and radial velocity fields are scanned more rapidly than the operational WSR-88D radar scans (Qiu and Xu [
Figures
As in Figure
The difference fields obtained by subtracting the
The 1 min time-mean wind fields retrieved in the benchmark experiment are less smeared in time and therefore expected to be more accurate than the 10 min time-mean wind fields retrieved in Expt-5 min. However, since the true fields are not known, it is difficult to directly evaluate whether and how much the retrieval accuracy is improved by rapid scans. To overcome this difficulty, we resort to the square root of the first (or second) cost-function term
Figure
(a) As in Figure
For the particular case considered in this paper, the targeted retrieval domain is small and the mesoscale background velocity
The terms
As in Figure
In this paper, the simple adjoint method (Qiu and Xu [
The above severe storm was scanned not only by the PAR but also by the operational KTLX radar (about every 5 minutes per volume) and the terminal Doppler weather radar (also about every 5 minutes per volume). These two operational radars, however, are all located in the same northeast quadrant as the PAR relative to the storm, so real dual-Doppler observations are not available for quantitative verifications of the single-Doppler retrievals obtained in this paper. Nevertheless, the method used in the first step is a refinement of the previous 2D-SA method, and the previous method has been tested for many real cases with the retrieved wind fields well verified by dual-Doppler analyses (Xu et al. [
Note that the 2D-SA can be also formulated in the polar coordinates centered at the radar (instead of the local Cartesian coordinates as shown in Figure
The authors are thankful to Dr. Alan Shapiro and anonymous reviewers for their comments and suggestions that improved the representation of the results and to GuangYu Wang for his help in editing Figure