.[1] We investigate the potential for skillfully predicting the number of daily temperature extremes over 3 month (seasonal) periods. We use retrospective forecasts from the Met Office seasonal forecasting system, GloSea4, nominally initialized 1 month ahead of the target season. Initially, we define daily extremes to be events outside either the upper or lower deciles of the daily temperature distribution from the relevant season. This definition provides a threshold that is sufficiently "extreme" to be of interest to many users but moderate enough to allow a sufficient sample for verification and to be of regular use to users. We show that skill reduces slightly at more extreme thresholds. Correlations of predicted and observed numbers of upper or lower decile extreme days over a season are significantly greater than zero over much of the globe and, in general, are better than a persistence forecast. Forecast skill for seasonal mean temperature is similar to, but generally greater than, the skill of predictions of the number of extreme days. Observations have a strong relationship between the seasonal mean and the number of extreme days. We show that the skill in predicting the number of extreme days is largely a consequence of this relationship and occurs primarily through a shift in the distribution of the daily data rather than a change of its shape. The ability to predict the El Niño-Southern Oscillation and climate change are both significant contributors to the skill in predicting temperature extremes. In summer, significant skill also comes from initializing soil moisture.
[1] The predictability of daily temperature and precipitation extremes is assessed out to a decade ahead using the Met Office Decadal Prediction System. Extremes are defined using a simple percentile based counting method applied to daily gridded observation data sets and corresponding model forecasts. We investigate moderate extremes, with a 10% probability of occurrence, ensuring they are frequent enough for robust skill analysis while having sizable impacts. We quantify the predictability of extremes, assess the impact of initialization, and compare with the predictability of the mean climate. We find modest but significant skill for seasonal predictions of temperature extremes in most regions (global area-average correlation of 0.3) and for precipitation extremes over the USA (area-average correlation of 0.2). The skill of both temperature and European rainfall extremes improves for multiyear forecast periods, as longer averaging periods reduce the impact of unpredictable short-term variations, capitalizing on predictable trends from external forcings. For 5 year periods out to a decade ahead, root-mean square temperature errors are reduced by 20% compared to use of climatology in most regions, apart from the southeastern USA. Initialization improves forecast skill for temperature and precipitation extremes on seasonal timescales in most regions. However, there is little improvement beyond the first year suggesting that skill then arises largely from external forcings. The skill for extremes is generally similar to, but slightly lower than, that for the mean. However, extremes can be more skillful than the mean, for example, USA cold nights, where trends in extremes are greater than for the mean.
In this paper we develop a methodology for defining stopping rules in a general class of global random search algorithms that are based on the use of statistical procedures. To build these stopping rules we reach a compromise between the expected increase in precision of the statistical procedures and the expected waiting time for this increase in precision to occur.
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