The Heidke Skill score is in the usual skill score format,
Skill = (score value – score for the standard forecast) / (perfect score – score for the standard forecast)
For the HSS, the "score" is the number correct or the proportion correct.
The "standard forecast" is usually the number correct by chance or the proportion correct by chance.
Thus using the proportion correct,
HSS = {(a+d)/n – [(a+b)(a+c)+(b+d)(c+d)]/n
2
}/{1 – [(a+b)(a+c) +(b+d)(c+d)]/n
2
}
This can be simplified into,
The HSS measures the fractional improvement of the forecast over the standard forecast.
Like most skill scores, it is normalized by the total range of possible improvement over
the standard, which means Heidke Skill scores can safely be compared on different datasets.
The range of the HSS is -∞ to 1.
Negative values indicate that the chance forecast is better, 0 means no skill,
and a perfect forecast obtains a HSS of 1.
The HSS is a popular score, partly because it is relatively easy to compute and perhaps
also because the standard forecast, chance, is relatively easy to beat.
Other standard scores are possible, such as persistence or climatology,
but these require additional information to compute, in the form of a separate contingency table.
Now let’s analyse the skill of the gale and tornado forecasts.
Loading Questions
...
For which set of forecasts is the proportion correct by chance greater?
(see if you can figure this out by inspecting the equation and tables)
Yes. Because there are so many non-events, many of these will be correct by chance –
the proportion works out to 94.8% which doesn’t leave much room for improvement.
No. The proportion of gale forecasts correct by chance is 75.4%,
but the proportion for tornados is even higher.
Without doing the calculations, do you think the tornado forecasts are skilful?
Correct. Actually, it is skilful. The proportion correct is 96.8%,
which is 2% higher than the standard score, which leads to a positive HSS.
Incorrect. It is tempting to think that the standard score of 94.8% is hard to beat,
but all those correct non-occurrences also count towards the proportion correct of the forecast.
See the other button for the exact percentage.
