RADAR STORM MOTION ESTIMATION AND BEYOND: A SPECTRAL ALGORITHM AND RADAR OBSERVATION BASED DYNAMIC MODEL

Gang Xu* and V. ChandrasekarColorado State University

Fort Collins, CO 80523, USA

Abstract

Storm motion tracking using a temporal sequence of radar images is an important step in computer-aided operational nowcasting. There exist three commonly used approaches for radar storm tracking. The first approach is based on motion field that is identified by employing cross-correlation technique over two local blocks in two successive radar images. The second approach is referred to as “centroid tracking”, such as the storm cell identification and tracking (SCIT) algorithm developed by Johnson et al (1998). The third approach is based on identification of storm’s position, size, mergers and splits that was implemented in the TITAN algorithm, referring to thunderstorm identification, tracking, analysis and nowcasting, developed by Dixon and Wiener (1993). Various improved methods have been developed based on local pattern matching and cross-correlation techniques. For example, Wolfson et al (1999) recently have developed a technique commonly referred as “growth-decay storm tracker” (GDST). The “growth-decay storm tracker” employs an elliptically shaped spatial filter such as to enable tracking systematic growth-decay propagations of the larger scale component in storms.

We present the development of a new algorithm developed in spectral domain for estimating the motion field of storms. It is a global algorithm in the sense that it does not employ local block windows in radar images. The estimated motion field can be globally constructed over the whole spatial region where radar images are rendered. The smoothness of estimated motion field is controlled by the choice of the Fourier coefficients for each dimension. The motion-flow equation for radar images has been formulated and solved in the spectral domain. A global optimal solution in the least-square sense is guaranteed and the numerical computation for solving linear inversion problem is efficient. The performance of the new algorithm is evaluated using both simulated data and observed radar images. For observed radar data, we compared the motion-tracking based nowcasting using the spectral algorithm with the “growth-decay storm tracker”.

Formal Formulation and Spectral Algorithm

• General motion-flow model for radar observation field F(x, y, t) is solved in spectral domain.

•F(x, y, t) is the radar observation field modeled as a spatiotemporal process; •U(x, y) is the x-direction motion velocity and V(x, y) is the y-direction motion velocity;•S(x, y, t) includes all other dynamic mechanisms.

Nowcasting scores for observed radar data collected by the WSR-88D radar (Melbourne, FL; 21:02, 08/23 - 00:57, 08/24, 1998. The spectral algorithm is compared with the GDST. CSI is

the critical success index. POD is the detection rate. FAR is the false alarm rate.

Conclusions

• We have developed a new algorithm in Fourier domain for radar observation based storm motion estimation. A linear dynamic model was developed along with the spectral algorithm that can be easily implemented for radar observational data.

• Using simulations we have demonstrated that the spectral algorithm has the ability to mitigate the influence of local growth-decay mechanisms on motion estimation.

• The spectral algorithm is applied to nowcasting up to one hour ahead, using observational data from the WSR-88D radar (Melbourne, FL). Results reveal that the spectral algorithm performs equally well or slightly better than the “growth-decay storm tracker”.

* Contact e-mail: xgang@lamar.colostate.edu.

• Global algorithm - no local block size issue, minimal “aperture-effect”, smoothness of motion field via reduced Fourier-coefficients

• Capability of modeling and separating other mechanisms from storm motion - mitigating influence of other mechanisms

• Reduced coefficients and linear inversion algorithm – fast and efficient

Steady S-term in simulation 2 Estimate Steady S-term using spectral algorithm

Estimated motion field near growth center without S-term (simulation 2)

Estimated motion field near growth center with S-term added (simulation 2)

Nowcasting Using Observational Data

),,(

)

tyxS

F(x,y,ty

V(x,y)F(x,y,t)x

U(x,y)F(x,y,t)t

Some Results from Simulations

• In simulation 2, a localized steady source, S(x, y, t)S(x,y), is added along with passive advection terms (motion field is simulated and used for validation).

• We compare two different ways to apply the spectral algorithm to motion field estimation:

1. Without S-term in Eq. (1);2. With S-term added in Eq. (1).

(1)

Comparison of observation and motion-tracking based nowcast

Acknowledgement: this research was supported by the NSF-ITR Program and the CASA-ERC (NSF award number 0313747)