Linear Diagnostics to Assess the Performance of an Ensemble Forecast System

Abstract

The performance of an ensemble prediction system is inherently flow dependent. This dissertation investigates the flow dependence of the ensemble performance with the help of linear diagnostics applied to the ensemble perturbations in a small local neighborhood of each model grid point location ℓ. A local error covariance matrix Pℓ is defined for each local region and the diagnostics are applied to the linear space Sℓ defined by the range of the ensemble based estimate of Pℓ. The particular diagnostics are chosen to help investigate the ability of Sℓ to efficiently capture the space of true forecast or analysis uncertainties, accurately predict the magnitude of forecast or analysis uncertainties, and to distinguish between the importance of different state space directions. Additionally, we aim to better understand the roots of the underestimation of the magnitude of uncertainty by the ensemble at longer forecast lead times. Numerical experiments are carried out with an implementation of the Local Ensemble Transform Kalman Filter (LETKF) data assimilation system on a reduced (T62L28) resolution version of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS). Both simulated observations under the perfect model scenario and observations of the real atmosphere are used in these experiments. It is found that (i) paradoxically, the linear space Sℓ provides an increasingly better estimate of the space of forecast uncertainties as the time evolution of the ensemble perturbations becomes more nonlinear with increasing forecast time, (ii) Sℓ provides a more reliable linear representation of the space of forecast uncertainties for cases of more rapid error growth, (iii) the E-dimension is a reliable predictor of the performance of Sℓ in predicting the space of forecast uncertainties, (iv) the ensemble grossly underestimates the forecast error variance in Sℓ, (v) when realistic observation coverage is used, the ensemble typically overestimates the uncertainty in the leading eigen-directions of ˆP ℓ and underestimates the uncertainty in the trailing directions at analysis time and underestimates the uncertainty in all directions by the 120-hr forecast lead time, and (vi) at analysis time, with a constant covariance inflation factor, the ensemble typically underestimates uncertainty in densely observed regions and overestimates the uncertainty in sparsely observed regions.