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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.
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.
Abstract
An algorithm to consistently couple a conservative semi-Lagrangian finite-volume transport scheme with a spectral element (SE) dynamical core is presented. The semi-Lagrangian finite-volume scheme is the Conservative Semi-Lagrangian Multitracer (CSLAM), and the SE dynamical core is the National Center for Atmospheric Research (NCAR)’s Community Atmosphere Model–Spectral Elements (CAM-SE). The primary motivation for coupling CSLAM with CAM-SE is to accelerate tracer transport for multitracer applications. The coupling algorithm result is an inherently mass-conservative, shape-preserving, and consistent (for a constant mixing ratio, the CSLAM solution reduces to the SE solution for air mass) transport that is efficient and accurate. This is achieved by first deriving formulas for diagnosing SE airmass flux through the CSLAM control volume faces. Thereafter, the upstream Lagrangian CSLAM areas are iteratively perturbed to match the diagnosed SE airmass flux, resulting in an equivalent upstream Lagrangian grid that spans the sphere without gaps or overlaps (without using an expensive search algorithm). This new CSLAM algorithm is not specific to airmass fluxes provided by CAM-SE but applies to any airmass fluxes that satisfy the Lipshitz criterion and for which the Courant number is less than one.
Abstract
An algorithm to consistently couple a conservative semi-Lagrangian finite-volume transport scheme with a spectral element (SE) dynamical core is presented. The semi-Lagrangian finite-volume scheme is the Conservative Semi-Lagrangian Multitracer (CSLAM), and the SE dynamical core is the National Center for Atmospheric Research (NCAR)’s Community Atmosphere Model–Spectral Elements (CAM-SE). The primary motivation for coupling CSLAM with CAM-SE is to accelerate tracer transport for multitracer applications. The coupling algorithm result is an inherently mass-conservative, shape-preserving, and consistent (for a constant mixing ratio, the CSLAM solution reduces to the SE solution for air mass) transport that is efficient and accurate. This is achieved by first deriving formulas for diagnosing SE airmass flux through the CSLAM control volume faces. Thereafter, the upstream Lagrangian CSLAM areas are iteratively perturbed to match the diagnosed SE airmass flux, resulting in an equivalent upstream Lagrangian grid that spans the sphere without gaps or overlaps (without using an expensive search algorithm). This new CSLAM algorithm is not specific to airmass fluxes provided by CAM-SE but applies to any airmass fluxes that satisfy the Lipshitz criterion and for which the Courant number is less than one.
