Introduction to signal variance

Signal Variance map

The ET KF attempts to predict the covariance of signal realizations produced by Q possible deployments of supplementary observations (e.g. the WSR drops). A signal realization is defined by the difference between analyses (or forecasts) initialized with and without the targeted observations. An example of the square of an NCEP signal realization at time ti+M is shown in Fig.1 for a flight at 0000 UTC 11 February 2000. It represents the square of the difference between two NCEP 3DVAR analyses: one using the fully supplemented observational network, and the other using data only from the routine network. The NCEP signal attains its highest magnitudes in regions close to the observation sites. The time evolution of operational forecast signals is an important test of the success of a deployment of targeted observations.
For a detailed reference, please refer to:
Majumdar, S.J., C.H.Bishop, B.J.Etherton, and Z.Toth, 2002: Adaptive Sampling with the Ensemble Transform Kalman Filter. Part II: Field Program Implementation. Mon. Wea. Rev., 130, 1356-1369.

Fig. 1. (a) Squared NCEP signal in J kg-1 at targeting time 0000 UTC 11 Feb 2000, averaged over the 850-, 500-, and 200-hPa pressure levels. It is calculated as (1/2)[(uq - ur)2 + (vq - vr)2] + 3.346 (Tq - Tr)2, where (uq, vq, Tq) and (ur, vr, Tr) represent NCEP analyses of horizontal wind components and temperature with and without the targeted observations, respectively. Dots represent locations at which GPS sondes were released. (b) ET KF signal variance at 0000 UTC 11 Feb 2000. Units are J kg.1 for all signal variance plots. A combined ensemble of 25 ECMWF members (generated +36 h prior to the targeting time) and 7 NCEP members (+24 h, +36 h) is used in this calculation