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Generalized Linear Models for Site-Specific Density Forecasting of U.K. Daily Rainfall

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  • 1 Department of Engineering Science, University of Oxford, Oxford, United Kingdom
  • | 2 Saïd Business School, University of Oxford, Oxford, United Kingdom
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Abstract

Site-specific probability density rainfall forecasts are needed to price insurance premiums, contracts, and other financial products based on precipitation. The spatiotemporal correlations in U.K. daily rainfall amounts over the Thames Valley are investigated and statistical Markov chain generalized linear models (Markov GLM) of rainfall are constructed. The authors compare point and density forecasts of total rainfall amounts, and forecasts of probability of occurrence of rain from these models and from other proposed density models, including persistence, statistical climatology, Markov chain, unconditional gamma and exponential mixture models, and density forecasts from GLM regression postprocessed NCEP numerical ensembles, at up to 45-day forecast horizons. The Markov GLMs and GLM processed ensembles produced skillful 1-day-ahead and short-term point forecasts. Diagnostic checks show all models are well calibrated, but GLMs perform best under the continuous-ranked probability score. For lead times of greater than 1 day, no models were better than the GLM processed ensembles at forecasting occurrence probability. Of all models, the ensembles are best able to account for the serial correlations in rainfall amounts. In conclusion, GLMs for future site-specific density forecasting are recommended. Investigations explain this conclusion in terms of the interaction between the autocorrelation properties of the data and the structure of the models tested.

Corresponding author address: Max Little, Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom. Email: max.little@eng.ox.ac.uk

Abstract

Site-specific probability density rainfall forecasts are needed to price insurance premiums, contracts, and other financial products based on precipitation. The spatiotemporal correlations in U.K. daily rainfall amounts over the Thames Valley are investigated and statistical Markov chain generalized linear models (Markov GLM) of rainfall are constructed. The authors compare point and density forecasts of total rainfall amounts, and forecasts of probability of occurrence of rain from these models and from other proposed density models, including persistence, statistical climatology, Markov chain, unconditional gamma and exponential mixture models, and density forecasts from GLM regression postprocessed NCEP numerical ensembles, at up to 45-day forecast horizons. The Markov GLMs and GLM processed ensembles produced skillful 1-day-ahead and short-term point forecasts. Diagnostic checks show all models are well calibrated, but GLMs perform best under the continuous-ranked probability score. For lead times of greater than 1 day, no models were better than the GLM processed ensembles at forecasting occurrence probability. Of all models, the ensembles are best able to account for the serial correlations in rainfall amounts. In conclusion, GLMs for future site-specific density forecasting are recommended. Investigations explain this conclusion in terms of the interaction between the autocorrelation properties of the data and the structure of the models tested.

Corresponding author address: Max Little, Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom. Email: max.little@eng.ox.ac.uk

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