Extending logistic regression to provide full‐probability‐distribution MOS forecasts

Abstract

Statistical post-processing of dynamical forecasts, using the Model Output Statistics (MOS) approach, continues to be an essential component of weather forecasting. Even in the current era of ensemble forecasting, ensemble-MOS methods are used to transform raw ensemble forecasts into well-calibrated probability forecasts. Logistic regression has been found to be an especially useful method for this purpose for predictands, such as precipitation amounts, that are distinctly non-Gaussian. However, the usual implementation of logistic regression fits separate forecast equations for different predictand thresholds, yielding finite sets of threshold probabilities rather than full forecast probability distributions. Furthermore, these individual threshold probabilities are not constrained to be mutually consistent, so that negative probabilities may be implied for some ranges of the predictand. In this paper, logistic regressions are extended to yield full continuous, and coherent, probability distribution forecasts by including the predictand threshold itself as an additional predictor in the forecast equation. The procedure is illustrated using 6-10 day precipitation forecasts for a sample of locations in the U.S., drawn from the GFS reforecast dataset.

Improving Stochastic Modelling of Daily Rainfall Using the ENSO Index: Model Development and Application in Chile

“…Sometimes this approach is also adopted for the simulation of precipitation intensity, especially when the aim is to represent rainfall values that are clearly non-Gaussian [32]. The use of GLM Stochastic weather models, or weather generators (WGs), are algorithms to generate synthetic series of climate variables, preserving the main statistical parameters of the observed series.…”

“…Sometimes this approach is also adopted for the simulation of precipitation intensity, especially when the aim is to represent rainfall values that are clearly non-Gaussian [32]. The use of GLM was first proposed by Stern and Coe [33] and later, further developed by Yang et al [34] and Chandler [35].…”

Relative effects of statistical preprocessing and postprocessing on a regional hydrological ensemble prediction system

“…HCLR is selected since it offers the advantage, over other regression-based preprocessors (Wilks, 2009), of obtaining the full, continuous predictive probability density function (pdf) of precipitation…”

“…The development of the HCLR follows the logistic regression model initially proposed by Hamill et al (2004) as well as the extended version of that model proposed by Wilks (2009). The extended logistic regression of Wilks (2009) is used to model the probability of binary responses such that…”

Understanding the predictability of the Arctic climate

“…Roulston and Smith, 2003;Raftery et al, 2005;Schmeits and Kok, 2010), full ensemble calibration has so far not been applied to seasonal forecasts of Arctic sea ice. We use two recently developed methods, namely extended logistic regression (ELR) (Wilks, 2009) and heteroscedastic ELR (HELR) (Messner et al, 2014). Third, we apply these advanced methods to different regions in the Arctic to assess the regional differences in skill.…”