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.)

Definitions:

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

where:

A (bove),

N (ear Normal) ; not used here

B (elow)

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 individual month

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.

NOTE:

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.