A Comparison between Bayesian Model Averaging, and Extended Logistic Regression for Calibration of Probabilistic Precipitation Forecasts over Iran

Precipitation forecasting is an essential tool for optimal management of water resources and flood forecasting. The numerical weather prediction (NWP) models play a major role in weather forecasting. They predict the future state of the weather by mathematical modeling of the atmosphere behavior, based on its current condition. However, the accuracy of the NWP models is still a challenging issue and its improvement is the main goal of the operational prediction centers. In weather forecasting by using NWP models, there are several resources of uncertainty such as intrinsic chaotic behavior of atmosphere dynamic system, errors in observational data and initial conditions which are almost impossible to remove. Ensemble systems are used to quantify these uncertainties. Instead of only one deterministic forecast, an ensemble system is created by several forecasts obtained from perturbation of the initial conditions, physical schemes or dynamical core of the NWP models. Ensemble systems are widely used by the meteorological communities especially for medium-range weather forecasts, short range and even ultra-short range weather prediction. A probabilistic forecasting of flood and extreme precipitation can be produced by an Ensemble Prediction System (EPS). However in practice, ensemble forecasts are generally under-dispersive and thus are not calibrated, especially for meteorological parameters near the ground level. Several statistical methods have been proposed to post-process the EPS outputs. After post-processing the EPS outputs, the biases in both location and dispersion are removed using a historical database of ensemble forecast errors, and then a predictive probability density function (PDF) can be estimated. The most popular ensemble post-processing methods are Bayesian Model Averaging and Ensemble Model Output Statistics. In BMA method, based on the error statistics of each member during a training period, a PDF is first fitted to every ensemble member forecast. Then the predictive PDF is estimated by weighted averaging of members' PDFs. Logistic regression is a nonlinear regression method that is well suited to probability forecasting, i.e. situations where the predictand is a probability rather than a mea- surable physical quantity Logistic regression is a nonlinear regression method that is well suited to probability forecasting, i.e. situations where the predictand is a probability rather than a mea- surable physical quantity Logistic regression is a nonlinear regression method that is well suited to probability forecasting, i.e. situations where the predictand is a probability rather than a mea- surable physical quantity Logistic regression is a nonlinear regression method that is well suited to probability forecasting, i.e. situations where the predictand is a probability rather than a mea- surable physical quantity Logistic regression is a nonlinear regression method that is well suited to probability forecasting, i.e. situations where the predictand is a probability rather than a mea- surable physical quantity Logistic regression is a nonlinear regression method that is well suited to probability forecasting, i.e. situations where the predictand is a probability rather than a mea- surable physical quantity LR was among the first statistical methods that were used to post-process the EPS output. Logistic Regression (LR) was extended to provide a full continuous predictive PDF. In the extended Logistic regression (ELR), the predictions and thresholds are used as additional predictor variables. In this study, an EPS was developed using eight different configurations of the WRF model to produce probabilistic precipitation forecast over Iran. Initial and boundary conditions for WRF were provided from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) forecasts with a horizontal resolution of 0.5. The BMA and ELR methods were used to calibrate the probabilistic forecasts of rainfall in the fall and winter of 2016-2015 over Iran. The data were separated to two parts of equal periods. The first and second parts of the data were used for training and test respectively. The calibrated probabilistic forecasts were assessed using reliability and Relative Operating Characteristic Curve (ROC) diagrams, ROC Skill Score, Ranked Probability Score (RPS) and Ranked Probability Skill Score RPSS at the thresholds of 0.1, 2.5, 5, 10, 15 and 25 mm. For ensemble probabilistic forecasting, BMA was used as a statistical technique that combines inferences and predictions based on individual ensemble members, so as to yield a more skillful and reliable probabilistic prediction. It was assumed that the forecast PDF of a weather variable y is conditional on the ensemble member forecast f_k: p_k=(y|f_k). The BMA ensemble forecast is essentially an average of forecasts based on individual members weighted by the likelihood that an individual forecasting model is correct given the observations. LR was used as a nonlinear regression method that is well suited to probability forecasting, i.e. situations where the predicted is a probability rather than a measurable physical quantity. The mathematical form of the LR equation yields ‘S-shaped’ prediction functions that are strictly bounded on the unit interval (0<p< 1).