Application of observability Gramian to targeted observation in WRF data assimilation

The optimal observation placement in weather forecast and research (WRF) data assimilation is investigated using a sensitivity analysis method. The method quantifies the sensitivity of observation location to assimilated results as an unobservability index. The empirical observability Gramian matrix composed from a time series of WRF model outputs is used to obtain the unobservability index in the WRF domain. A three-dimensional variational data assimilation (3 D-VAR) method is employed in the WRF model to assimilate the observations of horizontal winds, whose locations are selected based on the unobservability index. The results from the identical-twin experiments show a correlation between improvement in the assimilated wind field and the magnitude of unobservability index. The temporal variation of the vertical component of vorticity is strongly related to the unobservability index, which confirms that an observation location exhibiting a high unobservability index contributes to error reduction in the data assimilation owing to the reduction in the uncertainty caused by the strong vorticity changes.