1. 1 Verification Introduction Holly C. Hartmann Department of Hydrology and Water Resources University of Arizona hollyoregon@juno.com RFC Verification Workshop, 08/14/2007

2. 2 General concepts of verification Think about how to apply to your operations Be able to respond to and influence NWS verification program Be prepared as new tools become available Be able to do some of their own verification Be able to work with researchers on verification projects Contribute to development of verification tools (e.g., look at various options) Avoid some typical mistakes Goals

3. 3 1.Introduction to Verification -Applications, Rationale, Basic Concepts -Data Visualization and Exploration -Deterministic Scalar measures 2. Categorical measures – KEVIN WERNER -Deterministic Forecasts -Ensemble Forecasts 3. Diagnostic Verification -Reliability -Discrimination -Conditioning/Structuring Analyses 4. Lab Session/Group Exercise - Developing Verification Strategies - Connecting to Forecast Operations and Users Agenda

4. 4 Why Do Verification? It depends… Administrative: logistics, selected quantitative criteria Operations: inputs, model states, outputs, quick! Research: sources of error, targeting research Users: making decisions, exploit skill, avoid mistakes Concerns about verification?

5. 5 Need for Verification Measures Verification statistics identify -accuracy of forecasts -sources of skill in forecasts - sources of uncertainty in forecasts - conditions where and when forecasts are skillful or not skillful, and why Verification statistics then can inform -improvements in terms of forecast skill and decision making with alternate forecast sources (e.g., climatology, persistence, new forecast systems) Adapted from: Regonda, Demargne, and Seo, 2006

6. 6 Skill versus Value Assess quality of forecast system i.e. determine skill and value of forecast A forecast has skill if it predicts the observed conditions well according to some objective or subjective criteria. A forecast has value if it helps the user to make better decisions than without knowledge of the forecast. Forecasts with poor skill can be valuable (e.g. extreme event forecasted in wrong place) Forecasts with high skill can be of little value (e.g. blue sky desert) Credit: Hagedorn (2006) and Julie Demargne

7. 7 Common across all groups Uninformed, mistaken about forecast interpretation Use of forecasts limited by lack of demonstrated forecast skill Have difficulty specifying required accuracy Unique among stakeholders Relevant forecast variables, regions (location & scale), seasons, lead times, performance characteristics Technical sophistication: base probabilities, distributions, math Role of of forecasts in decision making Common across many, but not all, stakeholders Have difficulty distinguishing between “good” & “bad” products Have difficulty placing forecasts in historical context Stakeholder Use of HydroClimate Info & Forecasts

8. 8 Forecast evaluation concepts All happy families are alike; each unhappy family is unhappy in its own way. -- Leo Tolstoy (1876) All perfect forecasts are alike; each imperfect forecast is imperfect in its own way. -- Holly Hartmann (2002) What is a Perfect Forecast?

9. 9 “Today’s high will be 76 degrees, and it will be partly cloudy, with a 30% chance of rain.” Deterministic Categorical Probabilistic Different Forecasts, Information, Evaluation

10. 10 “Today’s high will be 76 degrees, and it will be partly cloudy, with a 30% chance of rain.” Deterministic Categorical Probabilistic Categorical Deterministic How would you evaluate each of these? Different Forecasts, Information, Evaluation Rain No rain 30% 76°

11. 11 “Today’s high will be 76 degrees, and it will be partly cloudy, with a 30% chance of rain.” Deterministic Categorical Probabilistic Different Forecasts, Information, Evaluation Standard hydrograph Deterministic

12. 12 ESP Forecasts: User preferences influence verification From: California-Nevada River Forecast Center

13. 13 ESP Forecasts: User preferences influence verification From: California-Nevada River Forecast Center

14. 14 ESP Forecasts: User preferences influence verification From: California-Nevada River Forecast Center

15. 15 ESP Forecasts: User preferences influence verification From: California-Nevada River Forecast Center

16. 16 Deterministic Bias Correlation RMSE Standardized RMSE Nash-Sutcliffe Linear Error in Probability Space Categorical Hit Rate Surprise rate Threat Score Gerrity Score Success Ratio Post-agreement Percent Correct Pierce Skill Score Gilbert Skill Score Heidke Skill Score Critical Success index Percent N-class errors Modified Heidke Skill Score Hannsen and Kuipers Score Gandin and Murphy Skill Scores… Probabilistic Brier Score Ranked Probability Score Distributions- oriented Measures Reliability Discrimination Sharpness So Many Evaluation Criteria!

17. 17 RFC Verification System: Metrics CATEGORIESDETERMINISTIC FORECAST VERIFICATION METRICS PROBABILISTIC FORECAST VERIFICATION METRICS 1. Categorical (predefined threshold, range of values) Probability Of Detection (POD), False Alarm Ratio (FAR), Probability of False Detection (POFD) Lead Time of Detection (LTD), Critical Success Index (CSI), Pierce Skill Score (PSS), Gerrity Score (GS) Brier Score (BS), Rank Probability Score (RPS) 2. Error (accuracy) Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Error (ME), Bias (%), Linear Error in Probability Space (LEPS) Continuous RPS 3. Correlation Pearson Correlation Coefficient, Ranked correlation coefficient, scatter plots 4. Distribution Properties Mean, variance, higher moments for observation and forecasts Wilcoxon rank sum test, variance of forecasts, variance of observations, ensemble spread, Talagrand Diagram (or Rank Histogram) Source: Verification Group, courtesy J. Demargne

18. 18 RFC Verification System: Metrics CATEGORIESDETERMINISTIC FORECAST VERIFICATION METRICS PROBABILISTIC FORECAST VERIFICATION METRICS 5. Skill Scores (relative accuracy over reference forecast) Root Mean Squared Error Skill Score (SS- RMSE) (with reference to persistence, climatology, lagged persistence), Wilson Score (WS), Linear Error in Probability Space Skill Score (SS-LEPS) Rank Probability Skill Score, Brier Skill Score (with reference to persistence, climatology, lagged persistence) 6. Conditional Statistics (based on occurrence of specific events) Relative Operating Characteristic (ROC), reliability measures, discrimination diagram, other discrimination measures ROC and ROC Area, other resolution measures, reliability diagram, discrimination diagram, other discrimination measures 7. Confidence (metric uncertainty) Sample size, Confidence Interval (CI) Ensemble size, sample size, Confidence Interval (CI) Source: Verification Group, courtesy J. Demargne

19. 19 Accuracy - overall correspondence between forecasts and observations Bias - difference between average forecast and average observation Consistency - forecasts don’t waffle around Possible Performance Criteria Good consistency

20. 20 Accuracy - overall correspondence between forecasts and observations Bias - difference between average forecast and average observation Consistency - forecasts don’t waffle around Sharpness/Refinement – ability to make bullish forecast statements Not Sharp Sharp Possible Performance Criteria

21. 21 What makes a forecast “good”? Forecasts should agree with observations, with few large errors Accuracy Forecast mean should agree with observed meanBias Linear relationship between forecasts and observations Association Forecast should be more accurate than low-skilled reference forecasts (e.g., random chance, persistence, or climatology) Skill Adapted from : Ebert (2003)

22. 22 What makes a forecast “good”? Binned forecast values should agree with binned observations (agreement between categories) Reliability Forecast can discriminate between events & non- events Resolution Forecast can predict with strong probabilities (i.e., 100% for event, 0% for non-event) Sharpness Forecast represents the associated uncertaintySpread (Variability) Adapted from : Ebert (2003)

23. 23 False AlarmsSurprises warning without eventevent without warning No fire “False Alarm Ratio”“Probability of Detection” A forecaster’s fundamental challenge is balancing these two. Which is more important? Depends on the specific decision context… Forecasting Tradeoffs Forecast performance is multi-faceted

24. 24 Skill Score: (0.50 – 0.54)/(1.00-0.54) = -8.6% ~worse than guessing~ Skill Score = S Forecast – S Baseline S Perfect – S Baseline How Good? Compared to What? What is the appropriate Baseline? = 1 - S Forecast S Baseline

25. 25 Graphical Forecast Evaluation

26. 26 Historical seasonal water supply outlooks Colorado River Basin Basic Data Display Morrill, Hartmann, and Bales, 2007

27. 27 Historical seasonal water supply outlooks Colorado River Basin Scatter plots Morrill, Hartmann, and Bales, 2007

28. 28 Historical seasonal water supply outlooks Colorado River Basin Histograms Morrill, Hartmann, and Bales, 2007

29. 29 IVP Scatterplot Example Source: H. Herr

30. 30 Empirical distribution of forecast probabilities for different observations categories Goal: Widely separated CDFs Cumulative Distribution Function (CDF): IVP Cat 1 = No Observed Precipitation Cat 2 = Observed Precipitation (>0.001”) Source: H. Herr, IVP Charting Examples, 2007

31. 31 Probability Density Function (PDF): IVP Cat 1 = No Observed Precipitation Cat 2 = Observed Precipitation (>0.001”) Empirical distribution for 10 bins for IVP GUI Goal: Widely separated PDFs Source: H. Herr, IVP Charting Examples, 2007

32. 32 “Box-plots”: Quantiles and Extremes Based on summarizing CDF computation and plot Goal: Widely separated box-plots Cat 1 = No Observed Precipitation Cat 2 = Observed Precipitation (>0.001”) Source: H. Herr, IVP Charting Examples, 2007

33. 33 Scalar Forecast Evaluation

34. 34 Bias Mean forecast = Mean observed Correlation Coefficient Variance shared between forecast and observed (r 2 ) Says nothing about bias or whether forecast variance = observed variance Pearson correlation coefficient: assumes normal distribution, can be + or – (Rank r: only +, non-normal ok) Root Mean Squared Error Distance between forecast/observation values Better than correlation, poor when error is heteroscedastic Emphasizes performance for high flows Alternative: Mean Absolute Error (MAE) fcst obs Observed Forecast Standard Scalar Measures

35. 35 1943-99 April 1 Forecasts for Apr-Sept Streamflow at Stehekin R at Stehekin, WA Forecast (1000’s ac-ft) Observed (1000’s ac-ft) 1954-97 January 1 Forecasts for Jan-May Streamflow at Verde R blw Tangle Crk, AZ Bias = 22 Corr = 0.92 RMSE = 74.4 Bias = -87.5 Corr = 0.58 RMSE = 228.3 Standard Scalar Measures (with Scatterplot)

36. 36 IVP: Deterministic Scalar Measures ME: smallest; + and – errors cancel MAE vs. RMSE: RMSE influenced by large errors for large events MAXERR: largest Sample Size: small samples have large uncertainty Source: H. Herr, IVP Charting Examples, 2007

37. 37 IVP: RMSE – Skill Scores Skill compared to Persistence Forecast Source: H. Herr, IVP Charting Examples, 2007