Kalman Filter and Analog Schemes to Postprocess Numerical Weather Predictions

Abstract

Two new postprocessing methods are proposed to reduce numerical weather prediction’s systematic and random errors. The first method consists of running a postprocessing algorithm inspired by the Kalman filter (KF) through an ordered set of analog forecasts rather than a sequence of forecasts in time (ANKF). The analog of a forecast for a given location and time is defined as a past prediction that matches selected features of the current forecast. The second method is the weighted average of the observations that verified when the 10 best analogs were valid (AN). ANKF and AN are tested for 10-m wind speed predictions from the Weather Research and Forecasting (WRF) model, with observations from 400 surface stations over the western United States for a 6-month period. Both AN and ANKF predict drastic changes in forecast error (e.g., associated with rapid weather regime changes), a feature lacking in KF and a 7-day running-mean correction (7-Day). The AN almost eliminates the bias of the raw prediction (Raw), while ANKF drastically reduces it with values slightly worse than KF. Both analog-based methods are also able to reduce random errors, therefore improving the predictive skill of Raw. The AN is consistently the best, with average improvements of 10%, 20%, 25%, and 35% with respect to ANKF, KF, 7-Day, and Raw, as measured by centered root-mean-square error, and of 5%, 20%, 25%, and 40%, as measured by rank correlation. Moreover, being a prediction based solely on observations, AN results in an efficient downscaling procedure that eliminates representativeness discrepancies between observations and predictions.

Improving PM2.5 Air Quality Model Forecasts in China Using a Bias-Correction Framework

“…The detailed approach for K t estimation can be found in Delle Monache, Nipen, Liu, Roux, and Stull [23]. Depending on the methods used in the "analog determination" step, the Kalman filter is applied in the Distance-based Kalman Filtering Analog (DIST-KF-AN) method, the CART linear model Kalman Filtering Analog (CART-LM-KF-AN) method, and the CART random forest Kalman Filtering Analog (CART-RF-KF-AN) method.…”

“…This method is chosen for its fast computation and easy implementation. The 7-day window length has also been used in previous studies on model post-correction [16,23]. The 7-Day-MA method can be regarded as a special case of the analog method, in which the 7 days prior to the forecasting cycle are the forecast analog and each day is weighted equally.…”

Characterisation of Large Changes in Wind Power for the Day-Ahead Market Using a Fuzzy Logic Approach

“…In [16], a WRF model is implemented together with the Kalman filter method for wind speed and wind power forecasting for a wind farm in China. Kalman filter approaches have also been applied in [17] and [18], as post-processing tools for correcting the bias of WRF wind speed predictions, reducing significantly the size of the training set, compared to ANN based methods. The majority of these approaches require the numerical weather prediction model to run at a very high resolution, which is time and resource consuming.…”

Insights into the deterministic skill of air quality ensembles from the analysis of AQMEII data

“…Two basic pathways exist to achieve this goal: model weighting or model sub-selecting. There are several methods to assign weights to ensemble members, such as the singular value decomposition (Pagowski et al, 2005), dynamic linear regression Djalalova et al, 2010), Kalman filtering (Delle Monache et al, 2011), Bayesian model averaging (Riccio et al, 2007;Monteiro et al, 2013) and analytical optimization (Potempski and Galmarini, 2009), while model selection usually relies on the quadratic error or its proxies in time (e.g. Solazzo et al, 2013;Kioutsioukis and Galmarini, 2014) or frequency space .…”