1. Verifying Satellite Precipitation Estimates for Weather and Hydrological Applications Beth Ebert Bureau of Meteorology Research Centre Melbourne, Australia 1 st IPWG Workshop, 23-27 September 2002, Madrid

2. val. i. date ( ) tr.v. 1. To declare or make legally valid. 2. To mark with an indication of official sanction. 3. To substantiate; verify. ver. i. fy ( ) tr.v. 1. To prove the truth of by the presentation of evidence or testimony; substantiate. 2. To determine or test the truth or accuracy of, as by comparison, investigation, or reference: "Findings are not accepted by scientists unless they can be verified" (Norman L. Munn) -e The American Heritage Dictionary of the English Language. William Morris, editor, Houghton Mifflin, Boston, 1969.

3. Satellite precipitation estimates -- what do we especially want to get right? Climatologists - mean bias NWP data assimilation (physical initialization) - rain location and type Hydrologists - rain volume Forecasters and emergency managers - rain location and maximum intensity Everyone needs error estimates!

4. Short-term precipitation estimates High spatial and temporal resolution desirable Dynamic range required Motion may be important for nowcasts Can live with some bias in the estimates if it's not too great Verification data need not be quite as accurate as for climate verification Land-based rainfall generally of greater interest than ocean-based

5. Some truths about "truth" data No existing measurement system adequately captures the high spatial and temporal variability of rainfall. Errors in validation data artificially inflate errors in satellite precipitation estimates

6. Rain gauge observations AdvantagesDisadvantages True rain measurements May be unrepresentative of aerial value Verification results biased toward regions with high gauge density Most obs made once daily

7. Radar data AdvantagesDisadvantages Excellent spatial and Beamfilling, attenuation, temporal resolution overshoot, clutter, etc. Limited spatial extent TRMM PR

8. Rain gauge analyses AdvantagesDisadvantages Grid-scale quantitiesSmoothes actual rainfall Overcomes uneven values distribution of rain gauges

9. Stream flow measurements AdvantagesDisadvantages Integrates rainfall overDepends on soil conditions, a catchmenthydrological model Many accurate measure-Time delay between rain ments availableand outflow Hydrologists want itBlurs spatial distribution time Discharge (m 3 /hr) estimated observed

10. Verification strategy for satellite precipitation estimates Use (gauge-corrected) radar data for local instantaneous or very short-term estimates Use gauge or radar-gauge analysis for larger spatial and/or temporal estimates

11. Focus on methods, not results What scores and methods can we use to verify precipitation estimates? What do they tell us about the quality of precipitation estimates? What are some of the advantages and disadvantages of these methods? Will focus on spatial verification

12. Does the satellite estimate look right? Is the rain in the correct place? Does it have the correct mean value? Does it have the correct maximum value? Does it have the correct size? Does it have the correct shape? Does it have the correct spatial variability?

13. Spatial verification methods Visual ("eyeball") verification Continuous statistics Categorical statistics Joint distributions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Scale decomposition methods Entity-based methods "standard" "scientific" or "diagnostic"

14. Step 1: Visual ("eyeball") verification Visually compare maps of satellite estimates and observations Advantage: "A picture tells a thousand words…" Disadvantages: Labor intensive, not quantitative, subjective Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability Rozumalski, 2000

15. Continuous verification statistics Measure the correspondence between the values of the estimates and observations Examples: mean error (bias) mean absolute error root mean squared error skill score linear error in probability space (LEPS) correlation coefficient Advantages: Simple, familiar Disadvantage: Not very revealing as to what's going wrong in the forecast

16. Mean absolute error Measures: Average magnitude of forecast error Root mean square error Measures: Error magnitude, with large errors having a greater impact than in the MAE Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability Mean error (bias) Measures: Average difference between forecast and observed values

17. Time series of error statistics 24-hr rainfall from NRL Experimental Geostationary algorithm validated against Australian operational daily rain gauge analysis 0.25° grid boxes, tropics only

18. Linear error in probability space (LEPS) Measures: Probability error - does not penalise going out on a limb when it is justified. Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability OiOi FiFi Cumulative probability of observations CDF o Value error {

19. Correlation coefficient Measures: Correspondence between estimated spatial distribution and observed spatial distribution, independent of mean bias Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability Danger...

20. Rozumalski, 2000 AutoEstimator validated against Stage III 8x8 km grid boxes

21. Skill score Measures: Improvement over a reference estimate. When MSE is the score used in the above expression then the resulting statistic is called the reduction of variance. The reference estimate is usually one of the following (a) random chance (b) climatology (c) persistence but it could be another estimation algorithm. Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability

22. Cross-validation - useful when observations are included in the estimates where Y i * is the estimate at point i computed with O i excluded from the analysis Measures: Expected accuracy at the scale of the observations. The score is usually bias, MAE, RMS, correlation, etc. Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability

23. Categorical statistics Measure the correspondence between estimated and observed occurrence of events Examples: bias score probability of detection false alarm ratio threat score equitable threat score odds ratio Hanssen and Kuipers score Heidke skill score Advantages: Simple, familiar Disadvantage: Not very revealing

24. Estimated yes no yes hits misses no false correct alarmsnegatives Observed Estimated Observed False alarms Hits Misses Correct negatives Categorical statistics

25. Bias score Measures: Ratio of estimated area (frequency) to observed area (frequency) Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability

26. Probability of Detection Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability False Alarm Ratio Threat score (critical success index) Equitable threat score Odds ratio

27. Hanssen and Kuipers discriminant (true skill statistic) Measures: Ability of the estimation method to separate the "yes" cases from the "no" cases. Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability Heidke skill score Measures: Fraction of correct yes/no detections after eliminating those which would be correct due purely to random chance

28. Categorical verification of daily satellite precipitation estimates from GPCP 1DD algorithm during summer 2000-01 over Australia Rain threshold varies from light to heavy North (tropics) Southeast (mid-latitudes)

29. Real-time verification example 24-hr rainfall from NRL Experimental Geostationary algorithm

30. Real-time verification example 24-hr rainfall from NRL Experimental blended microwave algorithm

31. Distributions oriented view Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability Advantage: Much more complete picture of forecast performance Disadvantage: Lots of numbers

32. PREDICTED (mm/d).0--.1--.2--.5---1---2---5--10--20--50--100--200 total 0.0 | 4134 130 267 136 111 83 28 23 18 6 0 4936 0.1 | 206 25 45 42 30 15 3 4 4 1 0 375 0.2 | 281 17 52 36 25 29 12 6 3 3 0 464 0.5 | 260 6 34 17 17 31 16 20 6 3 1 411 1 | 229 13 41 28 28 61 20 26 29 4 1 480 2 | 259 22 77 50 51 55 53 43 38 6 1 655 5 | 182 21 59 37 48 76 66 68 80 15 0 652 10 | 104 21 27 47 54 106 112 127 134 27 5 764 20 | 42 6 19 13 41 96 125 158 325 127 9 961 50 | 7 1 0 0 0 1 7 8 46 45 13 128 100 | 0 0 0 0 0 0 0 0 0 8 1 9 200 total 5704 262 621 406 405 553 442 483 683 245 31 9835 OBSERVED (mm/d) 24-hr rainfall from NRL Experimental Geostationary algorithm validated against Australian operational daily rain gauge analysis on 21 Jan 2002

33. Scatterplot Shows: Joint distribution of estimated and observed values NRL geo 20020121 R=0.63

34. Probability distribution function Shows: Marginal distributions of estimated and observed values geo anal NRL geo 20020121

35. Heidke skill score (K distinct categories) Measures: Skill of the estimation method in predicting the correct category, relative to that of random chance Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability

36. Scale decomposition methods Measure the correspondence between the estimates and observations at different spatial scales Examples: 2D Fourier decomposition wavelet decomposition upscaling Advantages: Scales on which largest errors occur can be isolated, can filter noisy data Disadvantages: Less intuitive, can be mathematically tricky

37. Discrete wavelet transforms Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability Concept: Decompose fields into scales representing different detail levels. Test whether the forecast resembles the observations at each scale. Measures, for each scale: % of total MSE linear correlation RMSE categorical verification scores others...

38. Casati and Stephenson (2002) technique Step 1: "Recalibrate" forecast using histogram matching error total = error bias + error recalibrated Step 2: Threshold the observations and recalibrated forecast to get binary images

39. Step 3: Subtract to get error (difference) image Step 4: Discrete wavelet decomposition of error to scales of resolution x 2 n

40. Odds ratio Step 5: Compute verification statistics on error field at discrete scales. Repeat for different rain thresholds.

41. Multiscale statistical organization Zepeda-Arce et al. (J. Geophys. Res., 2000) Concept: Observed precipitation patterns have multi- scale spatial and spatio-temporal organization. Test whether the satellite estimate reproduces this organization. Method: Start with fine scale, average to coarser scale Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability Measures: TS vs. scale depth vs. area spatial scaling parameter dynamic scaling exponent

42. obs fcst Scale (km) Threat score + + + + + + + + Area (km 2 ) Depth (mm) obs fcst Std. dev. Scale (km) * * * * obs fcst

43. Upscaling verification of IR power law rainrate 16 September 2002, Melbourne IR radar IR radar mm hr -1

44. GMSRA validated against rain gauge analyses at different spatial scales (Ba and Gruber, 2001)

45. Entity-based methods Use pattern matching to associate forecast and observed entities ("blobs"). Verify the properties of the entities. Examples: CRA (contiguous rain area) verification Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability Advantages: Intuitive, quantifies "eyeball" verification Disadvantage: May fail if forecast does not sufficiently resemble observations

46. CRA (entity) verification Ebert and McBride (J. Hydrology, Dec 2000) Concept: Verify the properties of the forecast (estimated) entities against observed entities Method: Pattern matching to determine location error, error decomposition, event verification Verifies this attribute? Location Size Shape Mean value Maximum value Spatial variability Measures: location error size error error in mean, max values pattern error

47. Determine the location error using pattern matching: Horizontally translate the estimated blob until the total squared error between the estimate and the observations is minimized in the shaded region. Other possibilities: maximum correlation, maximum overlap The displacement is the vector difference between the original and final locations of the estimate. Observed Estimated

48. CRA error decomposition The total mean squared error (MSE) can be written as: MSE total = MSE displacement + MSE volume + MSE pattern The difference between the mean square error before and after translation is the contribution to total error due to displacement, MSE displacement = MSE total – MSE shifted The error component due to volume represents the bias in mean intensity, where and are the CRA mean estimated and observed values after the shift. The pattern error accounts for differences in the fine structure of the estimated and observed fields, MSE pattern = MSE shifted - MSE volume

49. 24-hr rainfall from NRL Experimental Geostationary algorithm validated against Australian operational daily rain gauge analysis

52. Diagnosis of systematic errors Displacement (km) NRL Experimental Geostationary algorithm 289 CRAs April 2001- March 2002

53. Diagnosis of systematic errors Estimate Analyzed NRL Experimental Geostationary algorithm 289 CRAs April 2001- March 2002

54. Tropical Rain Potential (TRaP) verification? TRaP 24 h rain from 20001208_16

55. Which methods verify which attributes?

56. Conclusions The most effective diagnostic verification method is still visual ("eyeball") verification. Categorical statistics based on yes-no discrimination are probably the least informative of all of the verification methods, although they remain very useful for quantitative algorithm intercomparison. The newer diagnostic verification methods (scale decomposition, entity-based) give a more complete and informative diagnosis of algorithm performance Need methods to deal with observational uncertainty

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