Gridded warning verification Harold E. Brooks NOAA/National Severe Storms Laboratory Norman, Oklahoma

Basic verification Match observations and forecasts –Clearly defined events Information to fill in 2x2 table

2x2 Table a = Correct fore. of events, d = Correct non-event b = False alarm, c = Missed event Ob. YesOb. NoSum Fore.Yesaba+b Fore. Nocdc+d Suma+cb+dN

Scores Probability of detection=a/(a+c) (POD) Probability of false detection=b/(b+d) (POFD) False alarm ratio (rate) = b/(a+b) (FAR) Frequency of hits=a/(a+b) (FOH=1-FAR) Detection failure ratio=c/(c+d) (DFR) F-score=2*POD*(FOH)/(POD+FOH) Odds ratio=ad/bc Threat score (CSI)=a/(a+b+c)=f(POD, FAR)

Skill scores (1) Equitable threat score –ETS=(a-CH)/(a+b+c-CH) –CH=(a+b)(a+c)/n2 Extreme dependency score –EDS=2{log([a+c]/N)/log(a/N)}-1 –Doesn’t go to zero as event becomes rare

Skill scores (2) Peirce (Hanssen-Kuipers) –(ad-bc)/[(a+c)(b+d)]=POD-POFD –(Correct-CH)/(1-CHclim) Doolittle (Heidke) –(ad-bc)/[(ad-bc)-(1/2)(b+c)] –(Correct-CH)/(1-CH) Clayton –(ad-bc)/[(a+b)(c+d)]=FOH-DFR

Current status Warnings are issued for counties (or parts) Reports are points How can we make the 2x2 table? –Correct forecast-either covers the report or report is within county –False alarm-counties without reports –Missed event-report without warning –Correct no event?

Quantities Probability of detection –Events within warning areas/total events False alarm ratio –Forecasts without events/total forecasts Other quantities can’t be calculated

Current approach Calculate POD based on events Calculate FARatio based on areas Calculate CSI from POD and FARatio

Problems Inconsistent definition, no information on d Provides little information on performance

A vision Consistency between area and event definitions Consistency with other forecast products Allow for growth

Gridding the events High resolution time/space grid –O(1-5 km, 5-15 minutes) –Grid boxes are either 0 or 1 for each location, time for all weather types Grid SPC products on the same grid

Output Series of 0,1 values (could be probabilities) –Outlooks –Watch status –Warning –Reports Doswell and Keller (1993) did this for watches on an hourly time scale, MDR block

2x2 table If you can decide what d is, you can make 2x2 tables –General thunder? –Convective outlook? –Some events may not be in table Massively large –4x4 km, 15 min-~500,000 locations, 35,000 times

Issues Traditional scores would be really different Clean up data collection Could draw warning on grid, translate to county definitions Time domain –If warning comes out in middle of time block, what to do? (Block could be smaller or 0 or 1 for this purpose)

Watch Warning Report Black Box-County

Current-1 Correct, 1 Missed Event, 1 FA POD=0.5, FAR=0.5

Grid-based-4 Correct, 1 Missed Event, 36 FA, 759 CN POD=0.8, FAR=0.9, POFD=.0013 (Watch background)

Advantages Encourages data collection (could be probabilistic events or NCAR/RAP approach) Allows for baseline comparisons –Are warnings better when watches are in effect? –Stratify by time of day, location, etc. More informative scores can be derived