Patent Publication Number: US-6340946-B1

Title: Method for determining storm predictability

Description:
GOVERNMENT INTEREST 
     The subject matter described herein was supported in part by the Federal Aviation Administration under contract No. DTFA01-91-Z-02036. The government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to a method and apparatus for determining the predictability of elements in a weather radar image. In particular, the invention relates to a method for generating a predictability score indicative of the predictability for a pixel in the weather radar image. 
     BACKGROUND OF THE INVENTION 
     Short term (e.g., 30-120 minutes) weather predictions of the location of storms are extremely important to many sectors of the population. For example, aviation systems, traffic information systems, power companies and commuters realize important safety and economic benefits from accurate predictions of organized storms. Unfortunately, the classic weather problem of determining the motion of organized storms has not led to accurate automated forecasts for the short term time scale. 
     Organized storms are large scale meteorological events, often resulting from frontal discontinuities or cyclonic disturbances. Organized storms include clusters or groups of cells which occur alone or in larger line storms, hurricanes, tropical storms or in association with low pressure centers. Large single cells, including hailstorms, tornadic cells and supercells, are also considered organized storms due to their longer lifetime and broader geographic range. Conversely, airmass storms are small-scale, unorganized convective elements of limited duration and geographic range. Any convective element (i.e., cell) can be categorized as part of an organized storm or an individual airmass storm. 
     The storm tracking community has attempted for years to determine not only storm advection (i.e., the horizontal motion due to air currents) but also the growth and decay of the organized storm with no significant success. The lifetime of individual cells within the organized storm can be 20 minutes or less. New cells frequently grow near old decaying cells, but not necessarily along the direction of motion of the old cells. As a result of this discrete propagation (i.e., growth and decay process), storm motion can appear to deviate from cellular advection. For short term predictions (e.g., 20 minutes or less), the tracking of cell motion yields accurate predictions. Longer term predictions (e.g., greater than 20 minutes) based on the tracking of cell motion are considerably less accurate. 
     Tracking the large scale motion, or envelope, of the organized storm is one method that have been used to improve short term forecast accuracy. See, for example, U.S. Pat. No. 5,959,567 in which the method for tracking organized storms is based on the principle that large scale storms tend to decorrelate less rapidly with time. The method includes applying an image filter to a weather radar image to obtain only the large scale features within the image. The large scale features are tracked to determine the motion of the envelope and to generate a predicted image. Image filters that approximate the storm envelope are preferred because they typically yield predicted images with higher accuracy. 
     SUMMARY OF THE INVENTION 
     Although predicted images are useful for determining the future location of organized storms, it is desirable to determine the predictability, or likelihood, that the specific features within the predicted image will occur. Predictability can provide a level of confidence for reliance on the predicted image for planning future activities. 
     The invention relates to a method and apparatus for determining the predictability of a selected element within a weather radar image. The method is an improvement on known methodologies for tracking large scale features in weather radar images, and can be implemented using various image processing techniques. The images generated by the method of the present invention provide an indication of the predictability, or likelihood, that the features in predicted weather radar images will happen. The method is based on the principle that large scale storms tend to decorrelate less rapidly with time. By taking weather radar data and filtering it to obtain only the large scale features, the envelope of the organized storm can be determined. Thus, elements in a weather radar image that correspond to elements within the envelope of the organized storm in the filtered image are generally more predictable than other elements within the weather radar image. The predictability of a selected element can be generated from its filtered value and the variation in the values of the element and its neighboring elements. 
     The method includes receiving a selected element and neighboring elements from a weather radar image and processing the selected and neighboring elements to generate a processed selected element value. The weather radar image can be a reflectivity image and/or an image derived from weather radar image data. In one embodiment, the derived image is the correlation of two other weather radar images representing two different times. In one embodiment, the processing includes filtering the selected element and the neighboring elements. Optionally, filtering includes iteratively rotating an image filter in coordinate space and applying the filter to the selected element and the neighboring elements. 
     The method also includes the steps of determining a variability from the selected element and the neighboring elements and generating the predictability of the selected element from the processed selected element value and the variability. The variability can be the standard deviation or the variance of the selected element and the neighboring element. According to one embodiment, the predictability is proportional to a power of the processed element. In other embodiments, the method also includes displaying the predictability. 
     The apparatus for determining a characteristic of a selected weather radar image element includes an input module for receiving the selected element and neighboring elements, a prediction module and an output module for displaying the characteristic. The prediction module includes a rotation module for iteratively rotating a filter in coordinate space and a filter module for applying each rotated filter to the selected element and its neighboring elements. The prediction module also includes a processor module for determining the characteristic from the selected filtered element values and the sets of filtered element values. In one embodiment, the characteristic is a predictability value. In another embodiment, the output module is a graphical display. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a known apparatus for predicting the motion of an organized storm. 
     FIGS. 2 a  and  2   b  are prior art image filter kernel elements for an elliptical template at 0° and 45°, respectively. 
     FIG. 3 is an illustration of an unfiltered weather radar image. 
     FIG. 4 is an illustration of a weather radar image after application of a prior art image filter. 
     FIG. 5 is a graphical representation of track vectors generated by an image tracker. 
     FIG. 6 is an illustration of a predicted weather radar image generated by known prediction methods. 
     FIG. 7 is a flowchart representation of a prior art method for predicting the motion of an organized storm. 
     FIG. 8 is a block diagram of an apparatus for determining the predictability of a weather radar image according to the present invention. 
     FIG. 9 is a flowchart representation of a method for determining predictability values for a weather radar image according to an embodiment of the invention. 
     FIG. 10 is a flowchart representation of a method for determining predictability values for a weather radar image according to an embodiment of the invention. 
     FIGS. 11A and 11B are illustrations of an unfiltered weather radar image and a corresponding predictability image, respectively, generated according to an embodiment of the invention. 
     FIGS. 12A and 12B are illustrations of an unfiltered weather radar image and a corresponding predictability image, respectively, generated according to an embodiment of the invention. 
     FIG. 13 is an illustration of a time lagged autocorrelation surface of a low predictability weather radar image. 
     FIG. 14 is an illustration of a time lagged autocorrelation surface of a weather radar image having a high predictability feature. 
    
    
     DETAILED DESCRIPTION 
     The present invention relates to an improvement in the methods of tracking storms in weather radar images. The improvement includes determining the predictability of features in the weather radar image. FIGS. 1 to  7  are substantially the same as the corresponding figures in U.S. Pat. No. 5,959,567, which describes a method for tracking organized storms. These figures are included for a more thorough understanding of the underlying technology upon which the present invention can be based. FIGS. 8 to  14  relate to the inventive aspects of the invention. 
     FIG. 1 shows a functional block diagram of an apparatus for predicting the motion of an organized storm. An input module  10  receives weather radar image data from a weather radar image source  16 . The input module  10  provides the image data to a processor module  20  which generates a predicted weather radar image available at an output module  30 . 
     The input module  10  includes an acquisition module  12  and a memory module  14  to receive and store weather radar images for processing by the processor module  20 . The acquisition module  12  initiates transfer of weather radar images from the image source  16  (e.g., remote computer system, satellite receiver and processor, Internet server or other device capable of transmitting weather radar images). The memory module  14  is any device capable of temporary or permanent storage of the weather radar image. 
     A processor module  20  includes a filter module  22 , a tracker module  24  and an advection module  26 . The processor module  20  receives multiple weather radar images from the memory module  14  and generates a predicted weather radar image available at output module  30 . The filter module  22  applies an image filter  50  (FIGS. 2 a - 2   b ) to each weather radar image received from memory module  14  to create a filtered image. The filtered images are transferred to the tracker module  24  which generates track information on the motion of successive local image areas. An advection module  26  applies the track information to one of the unfiltered weather radar images stored in the memory module  14  to generate a predicted weather radar image. The predicted image is available at the output module  30 . 
     FIG. 2 a  shows an example of an image filter  50  having an elliptical template  52  with an aspect ratio of about 4:1 as defined by pixels  54 . The image filter  50  can employ other template forms, however, the selected template is closely matched to the envelope of the organized storm. Because storms often organize into lines, the utilization of an elliptical template  52  is often advantageous. The template  52  can be rotated within the image filter  50 , resulting in a rotated template  56  as depicted in FIG. 2 b.  Rotation is typically necessary to achieve a template orientation that is matched to the orientation of the envelope of the organized storm. 
     Referring to FIG. 3, an unfiltered weather radar image  60  indicates regions of varying intensity  62 ,  63  and  64 . Intensity values typically represent vertical integrated liquid water (VIL), but can also represent other forms of radar reflectivity (e.g., raw reflectivity, composite reflectivity, etc.). Low intensity regions  62  have VIL values less than 1 kg/m 2  and indicate insignificant precipitation. Moderate intensity regions  63  have VIL values between 1 kg/m 2  and 10 kg/m 2 . Precipitation in these regions would be noticeable. High intensity regions have VIL values greater than 10 kg/m 2  and indicate heavy precipitation. The high intensity regions (or cells)  64  correspond to areas of convective activity with lifetimes typically 20 minutes or less. The image filter  50  is applied to each pixel in the weather radar image  60  for a series of template orientations defined by an incremental rotation angle. For example, an increment of 10° can be used resulting in 18 different elliptical template orientations. The image filter  50  is designed to return a large value when the underlying image nearly matches the elliptical template  56 . The maximum value at each pixel resulting from the application of all orientations of the template  56  is retained. 
     FIG. 4 shows a filtered weather image  70  defined by the array of maximum pixel values returned by the filtering process. The filtered image  70  includes regions of moderate intensity  72  and light intensity  74 . The boundary  76  of the light intensity region  74  approximates the envelope of the storm, however, the small scale high intensity features  64  of the unfiltered image  60  are no longer apparent. Once the image filter  50  has been applied to each weather radar image  60 , the resulting filtered image  70  is passed to the tracker module  24 . 
     FIG. 5 shows an array  80  of track vectors  82  describing the local motion of the storm occurring during the time interval between images  60 . The array  80  generated by the tracker module  24  is the result of correlating a local subimage  79  of a prior filtered image  70  with a subimage  79  of a more recent filtered image  70 . Referring to FIG. 6, the track vectors  82  are applied by the propagation module  26  to one of the unfiltered weather radar images  60  to generate a predicted weather radar image  90  of the organized storm. Pixel values in the predicted weather radar image  40  are more likely to correctly predict storm conditions in a geographical location when the corresponding pixel lies with a region (i.e., an envelope) representative of an organized storm. Small scale, high intensity features  42  in the predicted weather radar image  90  which exist in isolation, however, are generally less likely to occur at their respective geographical location at the predicted time. 
     The flowchart in FIG. 7 describes one implementation of a known method as a series of method steps. At step  100 , a request for transfer of a weather radar image is made to an image provider and, at step  102 , a weather radar image is received. Step  104  determines if additional images must be obtained. If additional images are required, steps  100  and  102  are repeated. At step  106 , the method is applied to the first unfiltered image pixel p. At step  108 , the filter orientation angle θ is initialized at 0° (i.e., no rotation with respect to the unfiltered image) and the filtered image is initialized at all points to a physically unrealizable value (e.g., −1000). In step  110 , the filter oriented at θ is applied to the current point p in the unfiltered image and a value VAL is calculated. At step  112 , VAL is compared with the previously stored maximum value MAX_VAL for the point in the unfiltered image and the greater of the two values is saved as MAX_VAL. At step  114 , the filter orientation angle θ is increased by an incremental angle Δ. At step  116 , if θ is less than 180°, the method returns to step  110 . However, if θ is at least 180°, the method proceeds to step  118  and MAX_VAL is saved as the value for the corresponding pixel p′ in the filtered image. In step  120 , the method is directed back to step  106  if there are still unprocessed pixels in the unfiltered image. However, if all pixels in the unfiltered image have been processed, the method continues to step  122  where an array of track vectors is generated from the previous and current filtered images. At step  124 , the array of track vectors is applied to one of the unfiltered images to advect the unfiltered image to a future time (i.e., generate a predicted image). At step  126 , the predicted weather radar image is provided to an output device for viewing or transmission. 
     FIG. 8 shows a block diagram of an apparatus for determining the predictability of a weather radar image. The input module  10  includes an acquisition module  12  and a memory module  14 . A request for a weather radar image is transmitted by the acquisition module  12  to an image source  16 . In response, the image source  16  transmits a weather radar image back to the acquisition module  12  which stores the image in a memory module  14 . The processor module  20 ′ includes a filter module  22  and a predictability module  27 . The filter module  22  generates a filtered image for a weather radar image retrieved from the memory module  14 . The filtered images from the filter module  22  are transferred to the predictability module  27  which generates predictability values (i.e., predictabilities) for pixels in the weather radar image. The predictabilities are available at the output module  30 ′ for display or subsequent processing. Optionally, the processor module  20 ′ also includes a tracker module  24 , an advection module  26  and/or an output module  30  capable of providing a predicted weather radar image (see FIG.  1 ). 
     FIG. 9 depicts a method for determining predictability values for a weather radar image according to one embodiment of the invention. At step  130 , a selected element in a weather radar image and neighboring elements are received. In step  132 , a processed selected element value is generated from the values of the selected element and the neighboring elements. In one implementation of the method, neighboring elements include pixels which lie within the template  52  of an image filter  50  applied to the selected pixel. In step  134 , a variability is determined from the values of the selected element and neighboring elements. The variability can be the standard deviation, variance or any quantity characterizing the variation in element values. At step  136 , the predictability of the selected element is determined from the processed selected element value and the variability. In one embodiment the predictability of the selected element is high if the processed selected element value is high and/or the variability is low. In a further embodiment the predictability is based on a ratio of the processed selected element value and the variability. In step  138 , the predictability is displayed. In one embodiment, the predictability is displayed on a graphical display unit. In a further embodiment, the predictability is displayed as a color according to a predetermined color-coded format. 
     FIG. 10 depicts a method for generating a predictability image from a weather radar image according to an embodiment of the invention. At step  150 , a weather radar image P is received and, at step  152 , a pixel P(x,y) selected for processing (i.e., the first pixel for a new image  60 ) is identified. Variables used to determine the predictability value PRVAL(x,y) for the pixel P(x,y) are initialized in step  154 . Initialization includes setting the filter orientation angle θ to 0° and setting the variables and the predictability value PRVAL(x,y) to a physically unrealizable value (e.g., −1000). In step  156 , the filter  50  oriented at θ is applied to the current pixel P(x,y) in the unfiltered weather radar image  60 . A filtered image value AVG_VAL(x,y) equal to the average value of all pixel values within the filter  50  is calculated. At step  158 , AVG_VAL(x,y) is compared with the previously stored maximum value MAX_VAL(x,y) for the current pixel P(x,y) in the unfiltered image  60 . At step  160 , if AVG_VAL(x,y) exceeds MAX_VAL(x,y) then MAX_VAL(x,y) is assigned a new value equal to AVG_VAL(x,y) and the standard deviation STD_DEV(x,y) of the pixels inside the image filter  50  is determined. However, if AVG_VAL(x,y) does not exceed MAX_VAL(x,y), the values of MAX_VAL(x,y), and STD_DEV(x,y) are not changed. At step  162 , the filter orientation angle θ is increased by an incremental angle Γ. At step  164 , if θ is less than 180°, the method returns to step  156  to apply the image filter  50  at the new filter orientation angle θ. At step  164 , if θ is at least 180°, the method proceeds directly to step  166  where the predictability value PRVAL(x,y) for the pixel P(x,y) is calculated using the following equation:                PR_SCORE        (     x   ,   y     )       =           (     AVG_VAL        (     x   ,   y     )       )     2       STD_DEV        (     x   ,   y     )         .             (   1   )                         
     In step  168 , if it is determined that there is at least one more predictability value to calculate, the method returns to step  152 . If all predictability values have been determined, a predictability map is generated from all values of PRVAL(x,y) in step  170 . 
     In other embodiments, the predictability value PRVAL(x,y) is generated from other functional relationships based on MAX_VAL(x,y) and the statistical distribution of pixel values within the template  52  of the image filter  50  for the orientation θ where MAX_VAL(x,y) is at a maximum. In one embodiment, the image filter  50  is isotropic and no filter rotation is performed for the calculation of MAX_VAL(x,y). 
     Typically, a pixel&#39;s predictability is high if neighboring pixels fill the template  52  of the image filter  50  with substantially uniform values. For example, a pixel in an unfiltered weather radar image  60  which lies well within the envelope of an organized storm will have a high predictability because its neighboring pixels located in the template  52  of the image filter  50  have relatively high intensity values and the variations between pixel values within the image filter  50  are small. Conversely, a pixel located in a small-scale high intensity feature (e.g., an isolated convective cell or airmass storm) of an unfiltered weather radar image  60  has a relatively low predictability even if it has a high intensity value. 
     FIG. 11A shows an exemplary unfiltered weather radar image  180  indicating an organized storm  182  having an organization (i.e., spatial structure) indicative of longevity and several airmass storms  184 . The location of the organized storm  182  is more predictable than the location of the other storms  184  in longer term predictions (e.g., one hour). FIG. 11B shows the predictability image  190  generated from the unfiltered weather radar image  180 . Except for a small region  192  of high predictability corresponding to the organized storm  182 , low predictability is indicated. 
     FIG. 12A shows an unfiltered weather radar image  200  corresponding to the same geographical location as the weather radar images  180  and  190  in FIGS. 11A and 11B, respectively. The image  200  indicates the presence of an organized storm  202  having high intensity values organized in a substantially linear distribution oriented from the southwest (lower left) to the northeast (upper right). A stratiform shield  204  having associated moderate intensity values is situated to the north of the line storm  202 . The corresponding predictability image  210  is shown in FIG.  12 B. An extended linear region  212  of high predictability is substantially coincident with the high intensity pixels of the line storm  202 . Moderately high predictability values are also evident in regions  214  corresponding to the stratiform shield  214 . Thus, these regions  212  and  214  can be predicted to persist at least one hour. 
     FIG. 13 depicts a correlation surface  220  generated by autocorrelating a time lagged pair of weather radar images. The source weather radar images (not shown) include spotty air mass cells but contain no large scale features indicative of organized storms. As a result, the correlation surface  220  includes multiple spikes  222  of relatively low values. Thus, the numerator of Equation (1) is small, even in the neighborhood of the spikes  222 , and the denominator of Equation (1) is large due to the high standard deviation for any pixel on the correlation surface  220 . As a result, the predictability values of the pixels in the corresponding weather radar image are low. 
     FIG. 14 shows a correlation surface  230  also generated by autocorrelating a time lagged pair of weather radar images. The source images (not shown) include a more predictable line storm feature than the source images corresponding to FIG.  13 . The pixel values for the correlation surface  230  are relatively high and the surface  230  is relatively smooth. Thus, for most pixels the numerator of Equation (1) is large and the denominator of Equation (1) is small, resulting in relatively high predictability values for most pixels on the surface  230 . 
     Equivalents 
     While the invention has been particularly shown and described with reference to specific preferred embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.