3D Estimates of Analysis and Short-Range Forecast Error Variances
Jie Feng
ESRL
Noon Feb 10 in Room 2155
Abstract:
Accurate estimates of analysis and short-range forecast error variances
are critical for successful data assimilation and ensemble forecasting
applications. Pena and Toth (2014, PT14) introduced a statistical
minimization algorithm for the unbiased estimation of the variance
between “truth” interpolated to a Numerical Weather Prediction (NWP)
model grid and the NWP analysis or forecast (i.e., “true” errors). The
method uses variances between NWP forecasts and analyses (i.e.,
“perceived” forecast errors) and assumptions about the growth and
correlation of errors. After demonstrating in simple model experiments
that the method produced unbiased error variance estimates, PT14
estimated the mean of true analysis and forecast error variances for
NWP systems over large domains.
The present study expands on PT14 by (a) fitting variances between
different lead-time forecasts valid at the same time as additional
constraints of cost function, (b) using a suitable minimization
algorithm, the L-BFGS (Byrd et al. 1995), and by (c) deriving
3-dimensional gridpoint-based error variance estimates via the L-BFGS
algorithm. The 3-dimensional error variance estimates were examined in
a simulated forecast environment with a quasi-geostrophic model where
the analyses were generated using the Ensemble Kalman Filter (EnKF)
scheme. It is found that the method can reproduce the area-average true
analysis and forecast error within confidence intervals. Moreover, the
estimated analysis errors at the gridpoint level has a high correlation
with the distribution of the true analysis errors. The estimations were
more accurate than those obtained from the EnKF ensemble spread. Based
on these encouraging results, our next step is to apply this enhanced
method to the Global Forecast System (GFS) and to compare with the
error variances generated in operations