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Edward C. D. Pope, David B. Stephenson, and David R. Jackson


Categorical probabilistic prediction is widely used for terrestrial and space weather forecasting as well as for other environmental forecasts. One example is a warning system for geomagnetic disturbances caused by space weather, which are often classified on a 10-level scale. The simplest approach assumes that the transition probabilities are stationary in time—the homogeneous Markov chain (HMC). We extend this approach by developing a flexible nonhomogeneous Markov chain (NHMC) model using Bayesian nonparametric estimation to describe the time-varying transition probabilities. The transition probabilities are updated using a modified Bayes’s rule that gradually forgets transitions in the distant past, with a tunable memory parameter. The approaches were tested by making daily geomagnetic state forecasts at lead times of 1–4 days and were verified over the period 2000–19 using the rank probability score (RPS). Both HMC and NHMC models were found to be skillful at all lead times when compared with climatological forecasts. The NHMC forecasts with an optimal memory parameter of ~100 days were found to be substantially more skillful than the HMC forecasts, with an RPS skill for the NHMC of 10.5% and 5.6% for lead times of 1 and 4 days ahead, respectively. The NHMC is thus a viable alternative approach for forecasting geomagnetic disturbances and could provide a new benchmark for producing operational forecasts. The approach is generic and is applicable to other forecasts that include discrete weather regimes or hydrological conditions (e.g., wet and dry days).

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D. B. Stephenson, K. Rupa Kumar, F. J. Doblas-Reyes, J-F. Royer, F. Chauvin, and S. Pezzulli


The Indian summer monsoon rainfall is the net result of an ensemble of synoptic disturbances, many of which are extremely intense. Sporadic systems often bring extreme amounts of rain over only a few days, which can have sizable impacts on the estimated seasonal mean rainfall. The statistics of these outlier events are presented both for observed and model-simulated daily rainfall for the summers of 1986 to 1989. The extreme events cause the wet-day probability distribution of daily rainfall to be far from Gaussian, especially along the coastal regions of eastern and northwestern India. The gamma and Weibull distributions provide good fits to the wet-day rainfall distribution, whereas the lognormal distribution is too skewed. The impact of extreme events on estimates of space and time averages can be reduced by nonlinearly transforming the daily rainfall amounts. The square root transformation is shown to improve the predictability of ensemble forecasts of the mean Indian rainfall for June 1986–89.

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