A major application of Doppler radar is to predict the incoming severe weather storms based on the reflectivity information. There are two key processes to solve this problem: first recognize the storm, measure its size and location/center and second track its trajectory over time. When it is necessary, a warning of potential damage should be issued. Yilmaz, Javed and Shah [80] presented a general survey of all the mainstream algorithms applied in object tracking in Computer Vision. They discuss the various steps of the tracking pro- cedure, such as object representation, feature selection and detection, and object tracking. The various tracking algorithms can be classified according to the object models they are using as point tracking, kernel tracking and silhouette tracking. Compared to the other pop- ular tracking objects, for example the human face, storms are only clusters of connected data points with no shape character for feature extraction. Therefore the traditional point tracking algorithm such as the “Hungarian method” [42] is widely applied in this area by NOAA and Environment Canada.
Barron and Mercer, with their students have worked in this area since the early 1990’s. The 2D work was summarized by Barronet al. [4]. In the early 2000’s, they proposed a method to detect and track the 3D storms using interval arithmetic (called “fuzzy” alge- bra) to represent deformable objects (severe storms) [53] and track them in an incremental relaxation labeling algorithm [6].
2.4.1
Storm Detection using a Flood Fill Algorithm
The severe weather storm in Doppler radar imagery is represented by high density precip- itation [59]. Therefore, when detected by a Doppler radar, a storm can be considered as a cluster of data points that have a high reflectivity value. The first step in detecting a storm is to cluster voxels with high reflectivity values into one (or a few) clusters. If the size of a cluster containing storm points is greater than some threshold, then this cluster is consid- ered a storm. An algorithm to detect adjacent storm points is based on a recursiveFlood
Fill algorithm [4, 5]. This algorithm marks a voxel as a part of a storm if it has a high reflectivity value and then applies this same process recursively to all its neighboring vox- els. In this way, 3D storms can be detected by collecting all connected neighboring voxels together into a 3D volume. The storm reflectivity threshold was set to 30 - 35 dBZ, as Qiu [56] and Tanget al. [68] did, which is widely accepted in other Meteorology research as Johnsonet al. [38] suggested.
2.4.2
Storm Representation by Fuzzy Point Algebra
Chenget al. [17] first used this flood fill algorithm in 2D. They adopted fuzzy point alge- bra (interval arithmetic) [53] and represented a storm as a 2D fuzzy point. A fuzzy point is actually a circle specified by a radius and origin coordinates. Any set of coordinates inside this circle is said to match the fuzzy point. Storms were represented by fuzzy points and fuzzy vectors were used to represent fuzzy point motion between adjacent Doppler datasets. Using this notion of fuzzy vectors, the compatibility of adjacent fuzzy vectors (using mea- sures as fuzzy magnitude and fuzzy angle definitions with interval arithmetic ranges) was determined and used in a 2D relaxation labeling tracking algorithm to compute storm tra- jectories. Because this work was 2D, it was restricted to single low elevation Doppler radar datasets. A circle does not always capture a Doppler storm (especially oblong storms) and sometimes, as a result, the storms oscillate with a potential track. Qiu’s M.Sc. thesis [56] extended fuzzy points into 3D. 3D fuzzy point algebra is now defined and applied to all elevations in 3D Doppler datasets and a 3D tracking algorithm was devised using this tool. Tang [68, 69, 70] noted that the fuzzy point extension of a 2D circle into a 3D sphere was not as appropriate as using a 3D ellipsoid. She extended 3D fuzzy algebra to use these 3D fuzzy storms by adding extra mechanisms to model the orientation of ellipsoids (not needed for 3D spheres) in the tracking algorithm. This new solution demonstrated superior tracking results. A similar representation model is also adopted by Storlie, Lee, Hanning and Nychka [22], Dixon and Wiener [66].
2.4.3
Tracking Storm by Relaxation Labeling Algorithm
Although the detection and representation of storms are simpler compared to the other tracking topics, the tracking of storms could be very challenging in some complicated cases where storm shapes are highly deformable. Different from the traditional tracking problems where objects could block each other and cause feature extraction failure [33], storms are considered as moving in the same horizontal plane that they could merge into one super storm and also split into several smaller parts. During the 1990’s, Dixon and Wiener [22], is to the author’s knowledge, the first attempt to enhance the original tracking algorithm by handling merging and splitting of storms correctly. They based their solu- tion on the combinational optimization of all the possible paths of storms. More recently, Storlie, Lee, Hanning and Nychka [66] have furthered the discussion of storm tracking in a frequent merging and splitting situation by using a statistical method called modified MHT (Multiple Hypothesis Tracking) method. Their research primarily worked on the recog- nition of merging and splitting only, other than generating smooth tracks based on this information. Besides, their algorithm focused on the enhancement of tracking results in a large coverage area such as the whole North America territory, compared to the smaller and more detailed experiment environment we use around the Great Lakes area. More recently Baldwin [2] proposed a verification framework to measure the precision of storm forecast- ing. Xu and Chandrasekar [75] developed a storm motion estimation algorithm working in Fourier domain to give steady prediction of storms moving in a temporal sequence.
The storm tracking algorithm used in our work was originally developed for the 2D case [82] in 1991. Krezeski [41] proposed a temporal relaxation labeling algorithm to track multiple storm centers using Euclidean points to represent storms. Later Cheng [16, 17] improved this algorithm by using fuzzy storm centers in the 2D Doppler datasets. Qiu [56, 57] and Tang [68, 69, 70] then extended this method into 3D and this thesis builds on that work. We note that our tracking algorithm can use 3D optical flow as one of many compatibility functions [70] when determining if two storms belong to the same track or not. This work will be fully described in the following chapters. Our optical flow algo-
rithms for single/dual/multiple Doppler radars and windprofiler radars is given in Chapters 3, 4 and 5 while our tracking algorithm is given in Chapters 6 and 7.
Velocity Retrieval with Multiple Radars
Velocity Retrieval with Optical Flow
3.1
Introduction
In this chapter we present some methods to retrieve 3D full velocity from radial velocity data using Optical Flow techniques ([13, 14, 15, 69]). Optical Flow is a technology widely applied in the Computer Vision area. The 2D Optical Flow technique estimates the 2D motion of pixels in images taken from an image sequence. A simple 3D extension to 2D Optical Flow algorithms allows the computation of the 3D volumetric motion of voxels in a sequence of 3D volumes. In meteorology applications, 3D Optical Flow is a measure of the 3D wind velocity. Generally the solution of optical flow can be divided into two classes: one uses the least squares method [48] and the other uses the global regularization method [37]. Reliable performance based on these two solutions has already been obtained on real 3D Doppler radar data (NEXRADI) in [14, 15]. Here we generalize their method and apply it to the multiple radar case.