Targeting Observations Using Singular Vectors

Singular vectors with maximum energy at final time inside a verification area are used to identify the target area where extra observations should be taken, at an initial time, to reduce the forecast error inside the verification area itself. This technique is applied to five cases of cyclone development in the Atlantic Ocean, with cyclones reaching the British Isles at the final time. Three verification areas centered around this region are considered. First, the sensitivity of the target area to the choice of the forecast trajectory along which the singular vectors are evolved, to the choice of the verification area where singular vector energy is maximized, and to the number of singular vectors used to define the target area is investigated. Results show little sensitivity to the choice of the verification area, but high sensitivity to the choice of the trajectory. Regarding the number of singular vectors used, results based on the first 4 or the first 10 singular vectors are shown to be very similar. Second, the potential forecast error reduction that could be achieved by taking extra observations inside the target area is estimated by contrasting the error of a forecast started from the unperturbed analysis with the error of a forecast started by subtracting so-called pseudo-inverse perturbations (estimated using the leading singular vectors) to the unperturbed analysis. Results indicate that root-mean-square errors in the verification region could be reduced by up to 13% by adding targeted observations. Overall, results suggest that linear models can be used to define the target area where adaptive observations should be taken.