Lugar: Sala de Juntas del Instituto de Física de Cantabria (IFCA)
Título: The gig filter and its potential use in Earth-system analysis and prediction
Ponente: Craig H. Bishop, Naval Research Laboratory, Monterey, CA
Abstract: Observations and predictions of near-zero positive variables such as aerosols, water vapor, cloud, precipitation and plankton concentrations have error distributions whose standard deviations are typically proportional to the value of the variable. Many of these variables play a critical role in climate and severe-weather prediction. The Kalman filter and ensemble Kalman filter are both ill-suited to estimating distributions of these variables because they incorrectly assume that error variances are independent of the actual values of the variables. Here, we present a new tool (the gig filter) that solves the classical filtering and prediction problem for the non-linear case in which errors are proportional to the underlying magnitude of the variable being estimated rather than independent of this magnitude. In such systems, error dynamics are often non-linear. The proposed approach precisely solves Bayes’ theorem in special cases where the observation error likelihood and prior forecast error distributions are gamma and inverse-gamma (gig) distributions. Regardless of the precise form of the prior and likelihood distributions, the gig filter delivers the minimum error variance estimate as well as a posterior error covariance matrix consistent with the assumption that analysis error magnitudes are proportional to the magnitude of the analysis mean. A simple coordinate transformation allows the gig filter to simultaneously accommodate variables whose error variances are independent of variable magnitude (such as temperature). Idealized systems are used to compare and contrast the gig filter with the Ensemble Kalman filter.