The outlook and observations are categorized in three equal classes,
based on 1961-90 period. We use 102 CDs. The heidke skill score is calculated for the
A&B classes combined; we don't issue N forecasts a-priori. The outlook is regarded as
falling in the A or B class if the amplitude is half the tercile limit. This is done
because the forecast is usually damped, and we want some 60% coverage or so. Even if SS1
were 100, SS2 would be 100*coverage, about 60. (This largely explains why even at negative
lead the w30 forecasts (= self specification) do not yield SS2=100.)
Heidke score - general definition for 3 equal classes
SS = 100* (H - E) / (T - E) = 100* (H - T/3) / (T - T/3) = 100*(H - T/3) / (2/3 T)
Score on non-CL stations:
SS1 = 100 * (H1 - E1) / (T1 - E1) = 100 * (H1 - T1 /3) / (2/3 T1)
For a score on all stations, assume that 1/3 of the CL forecasts are
right, 2/3 is wrong, i.e. H = H1 + (T-T1)/3. Then:
SS2 = (H - T/3) / (2/3 T) *100 = (under above assumption) = SS1 * C
N (ear Normal) ; not used here
CL =climatological probabilities
A, B and N occurred 33.333% of the time during 1961-90. Skill measures
the improvement over CL as a 'forecast' everywhere all the time.
T = Total # of forecasts = # of stations * # of seasons = 102 for
H = # of hits
E = # of hits expected by chance = T/3
T1 = Total # of forecasts for non-CL (= combined area of A&B) forecasts
H1 = # of hits at non-CL stations
E1 = # of hits expected at non-CL stations = T1/3
C = coverage = T1 / T; C*100 is percentage of non-CL stations.
You don't start to count skill (SS) as positive unless and until more
than 1/3rd of the forecasts are categorically correct. 1/3rd is the 'zero' skill level.
Pointing at a case (here and there) where your method was right is dangerous, particularly
when done after the fact and when SS-overall <=0.