  The use of tiered warnings and multicategorical forecasts are ubiquitous in
meteorological operations. Here, a flexible family of scoring functions is
presented for evaluating the performance of ordered multicategorical forecasts.
Each score has a risk parameter $\alpha$, selected for the specific use case,
so that it is consistent with a forecast directive based on the fixed threshold
probability $1-\alpha$ (equivalently, a fixed $\alpha$-quantile mapping). Each
score also has use-case specific weights so that forecasters who accurately
discriminate between categorical thresholds are rewarded in proportion to the
weight for that threshold. A variation is presented where the penalty assigned
to near misses or close false alarms is discounted, which again is consistent
with directives based on fixed risk measures. The scores presented provide an
alternative to many performance measures currently in use, whose optimal
threshold probabilities for forecasting an event typically vary with each
forecast case, and in the case of equitable scores are based around sample base
rates rather than risk measures suitable for users.
