Data Mining Storm Attributes

Transcription

1 Data Mining Storm Attributes VA L L I A P PA L A K S H M A N A N N AT I O N A L S E V E R E S T O R M S L A B O R AT O R Y / U N I V E R S I T Y O F O K L A H O M A L A K S H M A O U. E D U AT C I T Y U N I V E R S I T Y O F N E W Y O R K N O V E M B E R

2 Data Mining Storm Attributes What is data mining? A usable definition: Statistics + Computer Science + Large data sets What questions can data mining answer? How many days of 2 hail does a location experience? What is the likelihood of rainfall at X given that it rained at Y? What is the average US population affected by 2 hail every year? Given a climate forecast, what is the expected economic cost of damage? How about these questions? What is the likelihood that a supercell will produce a tornado? What is the likelihood of 2 hail from a squall line? What is the likelihood of a NYC tunnel flooding from a tropical storm? How is the second set of questions different from the first? 2

3 Key Challenges Storms do not have rigid boundaries Have to identify storms from remotely sensed images The definition of a storm is dependent on scale (supercell/squall line) Storms move over time Need to track and associate storms across multiple images Have to do this in multiple scales Need to classify storm types For probabilistic guidance 3

4 Example: SCAN in United States 4

5 Example: COTREC in Switzerland 5

6 Limitations SCAN is not multiple-scale Centroid-based tracking Useful in interactive use, but not for large-data analysis COTREC is an image forecast ( nowcast ) Also single-scale No storm identification or classification 6

7 Data Mining Storm Attributes Introduction Storm Identification Storm Association Extracting Storm characteristics Estimating Motion 7

8 Identifying Storms Simple idea: Areas of high reflectivity or low infrared temperature Area = contiguous range gates (or pixels, if Cartesian) Key pre-decisions: What field to use? Base reflectivity? Reflectivity at -10C Infrared temperature? Brightness count? Lightning flash density? Need to quality control the data first Clutter, sun-spikes, biological echoes, etc. Smooth the data Which smoothing filter? Gaussian/Median filters most common 8

9 Single Threshold A single threshold is problematic Could be too high, and miss initiating storms Could be too low and storms end up being unrealistically large 50 dbz 20 dbz There is no perfect threshold Threshold just right Threshold too low 30 dbz Threshold too high

10 Enhanced Watershed Storm = contiguous pixels above t2 that have at least one pixel above t1 t2 = highest value that will allow objects be at least N pixels 40 dbz 10 px 40 dbz 5 px Change N to get multi-scale 30 dbz 10 px 30 dbz 5 px 10

11 Vector quantization via K-Means clustering [1] Quantize the image into bands using K-Means Vector quantization because pixel value could be many channels Like contouring based on a cost function (pixel value & discontiguity) 11

12 Mathematical Description: Clustering Each pixel is moved among every available cluster and the cost function E(k) for cluster k for pixel (x,y) is computed as d E m xy Distance in measurement space (how similar are they?) ( k) d ( k) (1 ) d ( k) m, xy c, Discontiguity measure (how physically close are they?) n, xy ( k) k I d ( ) (1 ( )) xy c, xy k Sij k ij N xy xy Weight of distance vs. discontiguity (0 λ 1) Mean intensity value for cluster k Pixel intensity value Courtesy: Bob Kuligowski, NESDIS Number of pixels neighboring (x,y) that do NOT belong to cluster k 12

13 Tuning vector quantization (-d) The K in K-means is set by the data increment Large increments result in fatter bands Size of identified clusters will jump around more (addition/removal of bands to meet size threshold) Subsequent processing is faster Limiting case: single, global threshold Smaller increments result in thinner bands Size of identified clusters more consistent Subsequent processing is slower Extremely local maxima The minimum value determines probability of detection Local maxima less intense than the minimum will not be identified 13

14 Storm Cell Identification: Characteristics Cells grow until they reach a specific size threshold Cells are local maxima (not based on a global threshold) Optional: cells combined to reach size threshold 14

15 Enhanced Watershed Algorithm [2] Starting at a maximum, flood image Until specific size threshold is met: resulting basin is a storm cell Multiple (typically 3) size thresholds to create a multiscale algorithm 15

16 Tuning watershed transform (-d,-p) The watershed transform is driven from maximum until size threshold is reached up to a maximum depth 16

17 Data Mining Storm Attributes Introduction Storm Identification Storm Association Extracting Storm characteristics Estimating Motion 17

18 Associating Storms Suppose you identify a set of storms in one image And have the set of storms identified in previous image Need to associate the two sets of storms Methods: Find centroids and associate the closest centroid Project the centroid at previous time to its new expected location Associate the closest centroid (within some sanity limits) Use cost function that weights distance and storm characteristics Minimize cost function: this is a linear optimization problem called the Munkres or Hungarian algorithm Greedy optimization Rank storms based on importance (so that stronger, longer-lived storms get associated first, for example) 18

19 Difficulties in storm association Misidentification Storm splits and merges 19

20 Unique matches; size-based radius; longevity; cost [4] Project cells identified at t n-1 to expected location at t n Sort cells at t n-1 by track length so that longer-lived tracks are considered first For each projected centroid, find all centroids that are within sqrt(a/pi) kms of centroid where A is area of storm If unique, then associate the two storms Repeat until no changes Resolve ties using cost fn. based on size, intensity or 20

21 Resolve ties using cost function Define a cost function to associate candidate cell i at t n and cell j projected forward from t n-1 as: Location (x,y) of centroid Area of cluster Peak value of cluster Max Magnitude For each unassociated centroid at t n, associate the cell for which the cost function is minimum or call it a new cell 21

22 Data Mining Storm Attributes Introduction Storm Identification Storm Association Extracting Storm characteristics Estimating Motion 22

23 Storm characteristics Identified storm cells have an area Can extract statistics of other spatial grids within those areas Track properties over time Alternately, extract stats in neighborhood of centroid Things to think about: Is outline of object exact? Impact of using watershed approach on spatial properties Impact of using thresholds on initiation/intensification properties Problem of core vs. periphery Use properties + data mining to make predictions 23

24 Geometric, spatial and temporal attributes [3] Geometric: Number of pixels -> area of cell Fit each cluster to an ellipse: estimate orientation and aspect ratio Spatial: remap other spatial grids (model, radar, etc.) Find pixel values on remapped grids Compute scalar statistics (min, max, count, etc.) within each cell Temporal can be done in one of two ways: Using association of cells: find change in spatial/geometric property Assumes no split/merge Project pixels backward using motion estimate: compute scalar statistics on older image Assumes no growth/decay 24

25 Specifying attributes to extract (-X) Attributes should fall inside the cluster boundary C-G lightning in anvil won t be picked up if only cores are identified May need to smooth/dilate spatial fields before attribute extraction Should consider what statistic to extract Average VIL? Maximum VIL? Area with VIL > 20? Fraction of area with VIL > 20? Should choose method of computing temporal properties Maximum hail? Project clusters backward Hail tends to be in core of storm, so storm growth/decay not problem Maximum shear? Use cell association Tends to be at extremity of core 25

26 26 Initiation Forecast

27 Data Mining Storm Attributes Introduction Storm Identification Storm Association Extracting Storm characteristics Estimating Motion 27

28 Estimating Motion Three ways to estimate motion: Object based: use object association to find velocity of each object Interpolate motion field between objects Works best for small objects; size changes problematic Optical flow Consider a rectangular window centered around each pixel Move window around in previous frame and maximize cross-correlation or some other measure of matching skill Can also be done using phase correlation Works well for large objects; subject to aperture problem Hybrid Identify objects and move object around in previous frame to minimize mean absolute error (does not depend on associating objects) 28

29 Cluster-to-image cross correlation [1] Pixels in each cluster overlaid on previous image and shifted The mean absolute error (MAE) is computed for each pixel shift Lowest MAE -> motion vector at cluster centroid Motion vectors objectively analyzed Forms a field of motion vectors u(x,y) Field smoothed over time using Kalman filters 29

30 Motion Estimation: Characteristics Because of interpolation, motion field covers most places Optionally, can default to model wind field far away from storms The field is smooth in space and time Not tied too closely to storm centroids Storm cells do cause local perturbation in field 30

31 Cluster-to-image cross correlation [1] The pixels in each cluster are overlaid on the previous image and shifted, and the mean absolute error (MAE) is computed for each pixel shift: Number of pixels in cluster k Summation over all pixels in cluster k MAE k ( x x, y y) 1 n k xy k I t ( x, y) I t t ( x x, y y) Intensity of pixel (x,y) at current time Intensity of pixel (x,y) at previous time To reduce noise, the centroid of the offsets with MAE values within 20% of the minimum is used as the basis for the motion vector. Courtesy: Bob Kuligowski, NESDIS 31

32 Interpolate spatially and temporally After computing the motion vectors for each cluster (which are assigned to its centroid, a field of motion vectors u(x,y) is created via interpolation: Motion vector for cluster k Sum over all motion vectors u( x, y) k k u k w w k k ( x, ( x, The motion vectors are smoothed over time using a Kalman filter (constant-acceleration model) y) y) w k ( x, y) Nk xy c Number of pixels in cluster k Euclidean distance between point (x,y) and centroid of cluster k k

33 Data Mining Storm Attributes Introduction Storm Identification Storm Association Extracting Storm characteristics Estimating Motion WDSS-II w2segmotionll 33

34 segmotion is a general-purpose algorithm Segmentation + Motion Estimation Segmentation --> identifying parts ( segments ) of an image Here, the parts to be identified are storm cells segmotion consists of image processing steps for: Identifying cells Estimating motion Associating cells across time Extracting cell properties Advecting grids based on motion field segmotion is part of WDSS-II Can be downloaded from Can be applied to any uniform spatial grid Has been applied to radar, satellite, model grids, 2D/3D lightning Some applications interested only in advection; others only on attribute extraction 34

35 Try things out Download WDSS-II from Follow Quick Start to learn how to run algorithms Download radar data from NCDC Convert to netcdf using ldm2netcdf Use c option to create composite Run w2segmotioncg on ReflectivityComposite Experiment with various options as described on the following slides Try applying QC/smoothing to data first w2qcnn w2smooth (or k option to w2segmotioncg) 35

36 Tuning motion estimation (-O) Motion estimates are more robust if movement is on the order of several pixels If time elapsed is too short, may get zero motion If time elapsed is too long, storm evolution may cause flat crosscorrelation function Finding peaks of flat functions is error-prone! 36

37 Preprocessing (-k) affects everything The degree of pre-smoothing has tremendous impact Affects scale of cells that can be found More smoothing -> less cells, larger cells only Less smoothing -> smaller cells, more time to process image Affects quality of cross-correlation and hence motion estimates More smoothing -> flatter cross-correlation function, harder to find best match between images 37

38 Evaluate advected field using motion estimate [1] Use motion estimate to project entire field forward Compare with actual observed field at the later time Caveat: much of the error is due to storm evolution But can still ensure that speed/direction are reasonable 38

39 Evaluate tracks on mismatches, jumps & duration Better cell tracks: Exhibit less variability in consistent properties such as VIL Are more linear Are longer Can use these criteria to choose best parameters for identification and tracking algorithm 39

40 Extrapolating images Extrapolation of radar echoes Intuitive approach: put Take current echoes Move them forward in time (advect) by their motion field put is subject to holes in the created images get results in the wrong motion field being used Simple put followed by get Move echoes forward, fill in gaps via interpolation Results in ghost echoes Smarter approach: Advect the motion field, interpolating within gaps Now, do get using advected motion field 40

41 Example 41

42 WDSS-II w2segmotionll References Algorithm for identifying and tracking cells from spatial grids Identify cells using vector quantization and watershed transform [2] Estimate motion using cross-correlation and interpolation [1] Track cells: longevity, size-based search radius and cost function [4] Extract attributes: geometric, spatial and temporal [3] How to evaluate algorithm: Evaluate cell tracks using mismatches, jumps & duration [4] Evaluate motion field using advected products [1] 1) V. Lakshmanan, R. Rabin, and V. DeBrunner, ``Multiscale storm identification and forecast,'' J. Atm. Res., vol. 67, pp , July ) V. Lakshmanan, K. Hondl, and R. Rabin, ``An efficient, general-purpose technique for identifying storm cells in geospatial images,'' J. Ocean. Atmos. Tech., vol. 26, no. 3, pp , ) V. Lakshmanan and T. Smith, ``Data mining storm attributes from spatial grids,'' J. Ocea. and Atmos. Tech., vol. 26, no. 11, pp , ) V. Lakshmanan and T. Smith, ``An objective method of evaluating and devising storm tracking algorithms,'' Wea. and Forecasting, vol. 25, no. 2, pp ,

43 WDSS-II Programs w2segmotionll Multiscale cell identification and tracking: this is the program that much of this talk refers to. w2advectorll w2scoreforecast Uses the motion estimates produced by w2segmotionll (or any other motion estimate, such as that from a model) to project a spatial field forward The program used to evaluate a motion field. This is how the MAE and CSI charts were created w2scoretrack The program used to evaluate a cell track. This is how the mismatch, jump and duration bar plots were created. 43