The spatial multi-event contingency table methodology is well suited for verifying high resolution forecasts since it gives credit to forecasts that are "close" to the truth in some way but need not be exactly correct.

The performance of a set of deterministic forecasts is often represented by a simple 2 x 2 contingency table that represents the joint distribution of forecasts and observations for a specified event criterion or threshold (for example, rain exceeding 1 mm/h).
 

	Observed yes	Observed no
Forecast yes	hits	false alarms
Forecast no	misses	correct negatives

Now, for the same observed event criterion, consider a range of K thresholds on the forecasts (for example, forecast rain exceeding 1 mm/h, 2 mm/h, 5 mm/hr, etc). These can be viewed as possible decision thresholds for taking action, such as issuing a warning. Instead of the contingency table having only a single event category it now contains multiple categories corresponding to the K forecast thresholds.
 

	Observed yes	Observed no
Forecast >= threshold1	hits1	false alarms1
Forecast < threshold1	misses1	correct negatives1
Forecast >= threshold2	hits2	false alarms2
Forecast < threshold2	misses2	correct negatives2
...	...	...
...	...	...
Forecast >= thresholdK	hitsK	false alarmsK
Forecast < thresholdK	missesK	correct negativesK

By using multiple thresholds, a deterministic forecast system can be evaluated across a range of possible decision thresholds (instead of just one) using ROC and relative value. This enables a fairer comparison against ensemble prediction systems or other probabilistic forecasts.

For an ensemble prediction system with M members, for each forecast threshold k there are now M probability categories (at least 1 member >= threshold_k, at least 2 members >= threshold_k, etc.), yielding a total of KxM categories.

An alternative to multiple intensity thresholds is multiple "closeness" thresholds, for example, forecast event within 10 km of the location of interest, within 20 km, 30 km, etc. Forecasters conceptually interpret high resolution model output in this way. The verification results can therefore be used to assess the performance of high resolution forecasts where the exact spatial matching of forecast and observed events is difficult or unimportant.

Other forecast decision criteria are possible, depending on the application.

Decision criteria can be combined to produce multi-dimensional contingency tables. The spatial multi-category contingency table described by Atger (2001) is a good example. In the case below, the number of categories would be JxK for single-model forecasts, and JxKxM for ensemble prediction systems.
 

	Forecast within distance1		...		Forecast within distanceJ
	Observed yes	Observed no	...	...	Observed yes	Observed no
Forecast >= threshold1	hits11	false alarms11	...	...	hitsJ1	false alarmsJ1
Forecast < threshold1	misses11	correct negatives11	...	...	missesJ1	correct negativesJ1
Forecast >= threshold2	hits12	false alarms12	...	...	hitsJ2	false alarmsJ2
Forecast < threshold2	misses12	correct negatives12	...	...	missesJ2	correct negativesJ2
...	...	...	...	...	...	...
...	...	...	...	...	...	...
Forecast >= thresholdK	hits1K	false alarms1K	...	...	hitsJK	false alarmsJK
Forecast < thresholdK	misses1K	correct negatives1K	...	...	missesJK	correct negativesJK

Reference:

Atger, F., 2001: Verification of intense precipitation forecasts from single models and ensemble prediction systems. Nonlin. Proc. Geophys., 8, 401-417. Click here to get the PDF (295 Kb).