  We investigate the effect of statistical post-processing on the probabilistic
skill of discomfort index (DI) and indoor wet-bulb globe temperature (WBGTid)
ensemble forecasts, both calculated from the corresponding forecasts of
temperature and dew point temperature. Two different methodological approaches
to calibration are compared. In the first case, we start with joint
post-processing of the temperature and dew point forecasts and then create
calibrated samples of DI and WBGTid using samples from the obtained bivariate
predictive distributions. This approach is compared with direct post-processing
of the heat index ensemble forecasts. For this purpose, a novel ensemble model
output statistics model based on a generalized extreme value distribution is
proposed. The predictive performance of both methods is tested on the
operational temperature and dew point ensemble forecasts of the European Centre
for Medium-Range Weather Forecasts and the corresponding forecasts of DI and
WBGTid. For short lead times (up to day 6), both approaches significantly
improve the forecast skill. Among the competing post-processing methods, direct
calibration of heat indices exhibits the best predictive performance, very
closely followed by the more general approach based on joint calibration of
temperature and dew point temperature. Additionally, a machine learning
approach is tested and shows comparable performance for the case when one is
interested only in forecasting heat index warning level categories.
