Verification region selection and data assimilation for adaptive sampling

Adaptive or targeted observations supplement routine observations at a pre-specified targeting time. Adaptive observation locations are selected to supplement routine observations in an attempt to minimize the forecast error variance of a future target forecast within some predefined verification region (VR) at some predefined verification time. Ideally, the VR is placed in a location where unusually large forecast errors are likely. Here, we compare three methods of selecting VRs: a climatological method based on seasonal averages of forecast errors; an unconditioned method based on verification time ensemble spread; and a conditioned method based on an ensemble transform Kalman filter (ETKF) estimate of forecast error variance given the routine observations to be taken at the targeting time. To test the effectiveness of the three approaches, observation-system simulation experiments on a chaotic barotropic flow were performed using an imperfect model. To test the sensitivity of our results to the type of forecast error covariance model used in the data assimilation (DA) scheme, two types of DA schemes were tested: an isotropic and a hybrid scheme. For isotropic DA, correlations between vorticity forecast errors at any two points were solely a function of the distance between the points; for hybrid DA, the forecast error covariance matrix was a linear combination of the covariance matrix used in isotropic DA and the sample covariance matrix of an ETKF ensemble. For each of the three VRs, the ETKF was used to select two adaptive observations. To assess targeted-observation-induced error reductions, forecast errors with and without targeted observations were computed for the VR, the total domain and also for an empirical VR which was defined to be the VR with the largest forecast error without targeted observations. The sensitivity, to the type of DA scheme employed, of the ETKFs ability to distinguish high-impact targeted observations from low-impact observations, was also examined. Amongst other things, it was found that: conditioned VRs were more prone to large errors than the other VRs; and the targeted-observation-induced reduction in forecast error variance was largest when hybrid DA and conditioned VRs were used, as was the range of forecast impacts distinguished by ETKF predictions.