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Modeling the Distribution of Precipitation Forecasts from the Canadian Ensemble Prediction System Using Kernel Density Estimation

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  • 1 Meteorological Research Division, Environment Canada, Toronto, Ontario, Canada
  • | 2 Meteorological Research Division, Environment Canada, Dorval, Québec, Canada
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Abstract

Kernel density estimation is employed to fit smooth probabilistic models to precipitation forecasts of the Canadian ensemble prediction system. An intuitive nonparametric technique, kernel density estimation has become a powerful tool widely used in the approximation of probability density functions. The density estimators were constructed using the gamma kernels prescribed by S.-X. Chen, confined as they are to the nonnegative real axis, which constitutes the support of the random variable representing precipitation accumulation.

Performance of kernel density estimators for several different smoothing bandwidths is compared with the discrete probabilistic model obtained as the fraction of member forecasts predicting the events, which for this study consisted of threshold exceedances. A propitious choice of the smoothing bandwidth yields smooth forecasts comparable, or sometimes superior, to the discrete probabilistic forecast, depending on the character of the raw ensemble forecasts. At the same time more realistic models of the probability density are achieved, particularly in the tail of the distribution, yielding forecasts that can be optimally calibrated for extreme events.

Corresponding author address: Syd Peel, 4905 Dufferin St., Toronto, ON M3H 5T4, Canada. Email: syd.peel@ec.gc.ca

Abstract

Kernel density estimation is employed to fit smooth probabilistic models to precipitation forecasts of the Canadian ensemble prediction system. An intuitive nonparametric technique, kernel density estimation has become a powerful tool widely used in the approximation of probability density functions. The density estimators were constructed using the gamma kernels prescribed by S.-X. Chen, confined as they are to the nonnegative real axis, which constitutes the support of the random variable representing precipitation accumulation.

Performance of kernel density estimators for several different smoothing bandwidths is compared with the discrete probabilistic model obtained as the fraction of member forecasts predicting the events, which for this study consisted of threshold exceedances. A propitious choice of the smoothing bandwidth yields smooth forecasts comparable, or sometimes superior, to the discrete probabilistic forecast, depending on the character of the raw ensemble forecasts. At the same time more realistic models of the probability density are achieved, particularly in the tail of the distribution, yielding forecasts that can be optimally calibrated for extreme events.

Corresponding author address: Syd Peel, 4905 Dufferin St., Toronto, ON M3H 5T4, Canada. Email: syd.peel@ec.gc.ca

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