Data Assimilation and Applications in Forecasting

Abstract

The work presented here spans two projects which are connected by data assimilationand specifically the ensemble Kalman filter (EnKF). The first explores how spatial localization, an important method commonly used in the EnKF, can be extended to multiscale problems. Rather than using a single length scale when localizing, we construct a localized covariance matrix through the estimation of eigenvectors. Specifically, we estimate the leading large-scale eigenvectors from a sample covari- ance matrix calculated from a spatially smoothed ensemble with spatial localization applied with a long localization distance. We then create projection matrices from these eigenvectors which allows us to calculate the space orthogonal to these initial large scales. This process can then be repeated for multiple scales if required. We present numerical experiments using this localization method using both simplified examples in which the correct covariance matrix is known and cycling experiments with the Lorenz Model III. The second project explores an application of the EnKF. We use the EnKF as part of a system to forecast cloud cover. Cloud cover forecasts are useful when forecasting solar power generation because clouds are the primary driver of reducing irradiance and therefore solar power generation. Our method uses satellite images, optical flow, and numerical weather prediction (NWP) in conjunction with an EnKF to estimate cloud motion vectors (CMVs) which are then used to advect cloud index (CI) fields using a 2-D advection scheme. This system produces an ensemble forecast which can be used to produce deterministic forecasts. We explore the effectiveness of these forecasts over Tucson, AZ.