Adjoint Derived Adaptive Observation Network based on the Retrospective Optimal Interpolation

Forecast sensitivity to observation (FSO) is a diagnostic tool to estimate the observation impact and design the observing network. The adjoint of the data assimilation process is needed to evaluate the effect of observations on forecasts. In this research, the reduced-rank retrospective optimal interpolation was used as the data assimilation algorithm. The retrospective optimal interpolation (ROI) is a new data assimilation scheme which was derived from the quasi-static variational assimilation (QSVA) algorithm and introduced by Song et al. (2009).

The Kalman gain of the reduced-rank ROI includes the tangent linear of the forecast model and the adjoint of the forecast model. Therefore, using the Kalman gain of the reduced-rank ROI, the four dimensional distribution of optimal observations can be estimated properly. In addition, because the Kalman gain of the reduced-rank ROI is defined in a low dimension subspace, it is easy to calculate the transpose of the Kalman gain matrix. Experiments are performed with the Lorenz 40-variable model. 

Key words: adaptive observation, forecast sensitivity to observation, retrospective optimal interpolation.