Verification of nowcasts and very short range forecasts

1. Verification of nowcasts and very short range forecasts Beth Ebert BMRC, Australia WWRP Int'l Symposium on Nowcasting and Very Short Range Forecasting, Toulouse, 5-9 Sept 2005

2. Why verify forecasts? • To monitor performance over time  summary scores • To evaluate and compare forecast  continuous and systems categorical scores • To show impact of forecast  skill & value scores • To understand error in order to  diagnostic methods improve forecast system The verification approach taken depends on the purpose of the verification

3. Verifying nowcasts and very short range forecasts

4. Observations – issues for nowcasts Thunderstorms and severe weather (mesocyclones, hail, lightning, damaging winds) • Spotter observations may contain error • Biased observations • More observations during daytime & in populated areas • More storm reports when warnings were in effect • Cell mis-association by cell tracking algorithms Precipitation • Radar rain rates contain error • Scale mismatch between gauge observations and radar pixels Observation error can be large but is usually neglected  more research required on handling observation error

5. point-to-grid grid-to-point Matching forecasts and observations • Matching approach depends on • Nature of forecasts and observations • Scale • Consistency • Sparseness • Other matching criteria • Verification goals • Use of forecasts • Matching approach can impact verification results • Grid to grid approach • Overlay forecast and observed grids • Match each forecast and observation Forecast grid Observed grid

6. First rule of forecast verification – look at the results! Forecast Quality Definitions Wilson subjective categories 1 – forecast and observed almost perfect overlap. 2 – majority of observed and forecast echoes overlap or offsets <50 km 3 – forecast and observed look similar but there are a number of echo offsets and several areas maybe missing or extra. 4 – the forecasts and observed are significantly different with very little overlap; but some features are suggestive of what actually occurred. 5 – there is no resemblance to forecast and observed.

7. Systematic verification – many cases Aggregation and stratification • Aggregation • More samples  more robust statistics • Across time - results for each point in space • Space - results for each time • Space and time - results summarized across spatial region and across time • Stratification • Homogeneous subsamples  better understanding of how errors depend on regime • By location or region • By time period (diurnal or seasonal variation)

8. Real-time nowcast verification • Rapid feedback from latest radar scan • Evaluate the latest objective guidance while it is still "fresh" • Better understand strengths and weaknesses of nowcast system • Tends to be subjective in nature • Not commonly performed! Real time forecast verification system (RTFV) under development in BMRC

9. Post-event verification POD • More observations may be available • verification results more robust • No single measure is adequate! • several metrics needed • distributions-oriented verification • scatter plots • (multi-category) contingency tables • box-whisker plots • Confidence intervals recommended, especially when comparing one set of results with another • Bootstrap (resampling) method simple to apply Frequency bias CSI FAR

10. Estimated yes no yes H = hits M = misses no F = false CR = correct alarms rejections forecast M H Observed F observations CR Accuracy – categorical verification Standard categorical verification scores PC = (H + CR) / N proportion correct (accuracy) Bias = (F + H) / (M + H) frequency bias POD = H / (H + M) probability of detection POFD = F / (CR + F) probability of false detection FAR = F / (H + F) false alarm ratio CSI = H / (H + M + F) critical success index (threat score) ETS = (H – Hrandom) / (H + M + F – Hrandom) equitable threat score HSS = (H + CR – PCrandom) / (N – PCrandom) Heidke skill score HK = POD – POFD Hanssen and Kuipers discriminant OR = (H * CR) / (F * M) odds ratio

11. Accuracy – continuous verification Standard continuous verification scores (scores computed over entire domain) bias = mean error MAE = mean absolute error RMSE = root mean square error r = correlation coefficient Forecast F Observations O Domain

12. Accuracy – probabilistic verification Standard probabilistic verification scores/methods Reliability diagram Brier score Brier skill score Ranked probability score Relative operating characteristic (ROC)

13. 0.6 Hanssen & Kuipers score > 0 mm 0.5 > 1 mm > 5 mm 0.4 0.3 0.2 0.1 ____ Nowcast _ _ _ Extrapolation........ Gauge persistence 0 -0.1 30 60 90 120 150 180 Forecast (min) 0 -0.2 -0.4 Skill w.r.t. gauge persis. -0.6 -0.8 -1 30 60 90 120 150 180 Forecast (min) ____ Nowcast _ _ _ Extrapolation Skill A forecast has skill if it is more accurate than a reference forecast (usually persistence, cell extrap-olation, or random chance). Skill scoresmeasure the relative improvement of the forecast over the reference forecast: Strategy 1: Plot the performance of the forecast system and the unskilled reference on the same diagram Strategy 2: Plot the value of the skill score

14. Practically perfect hindcast – upper bound on accuracy Approach: If the forecaster had all of the observations in advance, what would the "practically perfect" forecast look like? • Apply a smoothing function to the observations to get probability contours, choose an appropriate yes/no threshold • Did the actual forecast look like the practically perfect forecast? • How did the performance of the actual forecast compare to the performance of the practically perfect forecast? Convective outlook was 75% of the way to being "practically perfect" SPC convective outlook CSI = 0.34 Practically perfect hindcast CSI = 0.48 Kay and Brooks, 2000

15. "Double penalty" Event predicted where it did not occur, no event predicted where it did occur Big problem for nowcasts and other high resolution forecasts Ex: Two rain forecasts giving the same volume fcst fcst obs obs 10 10 3 10 High resolution forecast RMS ~ 4.7 POD=0, FAR=1, CSI=0 Low resolution forecast RMS ~ 2.7 POD~1, FAR~0.7, CSI~0.3

16. fcst obs fcst obs Value A forecast has value if it helps a user make a better decision Value scoresmeasures the relative economic value of the forecast over some reference forecast: The most accurate forecast is not always the most valuable! Expense depends on the cost of taking preventative action and the loss incurred for a missed event Small or rare events with high losses, value maximized by over-prediction Events with high costs and displacement error likely, value maximized by under-prediction Baldwin and Kain, 2004

17. Exact match vs. "close enough" Need we get a high resolution forecast exactly right? Often "close" is still useful to a forecaster • YES • High stakes situations (e.g. space shuttle launch, hurricane landfall) • Hydrological applications (e.g. flash floods) • Topographically influenced weather (valley winds, orographic rain, etc.) • NO • Guidance for forecasters • Model validation (does it predict what we expect it to predict?) • Observations may not allow standard verification of high resolution forecasts Standard verification methods appropriate (POD, FAR, CSI, bias, RMSE, correlation, etc.) "Fuzzy" verification methods, diagnostic methods verify attributes of forecast

18. Sydney t - 1 t Frequency t + 1 Forecast value "Fuzzy" verification methods • Large forecast and observed variability at high resolution • Fuzzy verification methods don't require an exact match between forecasts and observations to get a good score • Vary the size of the space / time neighborhood around a point • Damrath, 2004 • Rezacova and Sokol, 2004 * • Theis et al., 2005 • Roberts, 2004 * • Germann and Zawadski, 2004 • Also vary magnitude, other elements • Atger, 2001 • Evaluate using categorical, continuous, probabilistic scores / methods * Giving a talk in this Symposium Forecasters don't (shouldn't!) take a high resolution forecast at face value – instead they interpret it in a probabilistic way.

19. single threshold Spatial multi-event contingency table Verify using the Relative Operating Characteristic (ROC) • Measures how well the forecast can separate events from non-events based on some decision threshold Decision thresholds to vary: • magnitude (ex: 1 mm h-1 to 20 mm h-1) • distance from point of interest (ex: within 10 km, .... , within 100 km) • timing (ex: within 1 h, ... , within 12 h) • anything else that may be important in interpreting the forecast Can apply to ensembles, and to compare deterministic forecasts to ensemble forecasts ROC curve for varying rain threshold ROC curve for ensemble forecast, varying rain threshold Atger, 2001

20. fcst obs Do Df 8 clusters identified in x-y-p space Cf Co Af Bo Bf Ao MM5 Object- and entity-based verification • Consistent with human interpretation • Provides diagnostic information on whole-system properties • Location • Amplitude • Size • Shape • Techniques • Contiguous Rain Area (CRA) verification (Ebert and McBride, 2000) • NCAR object-oriented approach* (Brown et al., 2004) • Cluster analysis (Marzban and Sandgathe, 2005) • Composite method (Nachamkin, 2004) NCAR

21. Obs Fcst Contiguous Rain Area (CRA) verification • Define entities using threshold (Contiguous Rain Areas) • Horizontally translate the forecast until a pattern matching criterion is met: • minimum total squared error • maximum correlation • maximum overlap • The displacement is the vector difference between the original and final locations of the forecast. • Compare properties of matched entities • area • mean intensity • max intensity • shape, etc. Ebert and McBride, 2000

22. Error decomposition methods • Attempt to quantify the causes of the errors • Some approaches: • CRA verification (Ebert and McBride, 2000) MSEtotal = MSEdisplacement + MSEvolume + MSEpattern • Feature calibration and alignment (Nehrkorn et al., 2003) E(x,y) = Ephase(x,y) + Elocal bias(x,y) + Eresidual(x,y) • Acuity-fidelity approach (Marshall et al., 2004) minimize cost function: J = Jdistance + Jtiming + Jintensity + Jmisses from both perspectives of forecast (fidelity) and observations (acuity) • Error separation (Ciach and Krajewski, 1999) MSEforecast = MSEtrue + MSEreference

23. SATELLITE l=0 MODEL l=1 RADAR l=2 RAIN GAUGES l=3 Scale separation methods • Measure correspondence between forecast and observations at a variety of spatial scales • Some approaches: • Multiscale statistical prop-erties (Zepeda-Arce et al., 2000; Harris et al., 2001) • Scale recursive estimation (Tustison et al., 2003) • Intensity-scale approach* (Casati et al., 2004)

24. Summary • Nowcasts and very short range forecasts present some unique challenges for verification • High impact weather • High resolution forecasts • Imperfect observations • There is still a place for standard scores • Historical reasons • When highly accurate forecasts are required • Useful for monitoring improvement • Must use several metrics • Please quantify uncertainty, especially when intercomparing forecast schemes • Compare with unskilled forecast such as persistence

25. Summary (cont'd) • Evolving concept of what makes a "good" forecast • Recognizing value of "close enough" • Probabilistic view of deterministic forecasts • Exciting new developments of diagnostic methods to better understand the nature and causes of forecast errors • Object- and entity-based • Error decomposition • Scale separation

26. http://www.bom.gov.au/bmrc/wefor/staff/eee/verif/verif_web_page.html