Introducing water budget constraint to improve land data assimilation performance

Data assimilation (DA) is a technique to optimally update the model with observations to estimate a better state than each alone. DA is optimum (gives the best estimate possible with the current data) provided that the underlying assumptions are fulfilled correctly (unbiased system, Gaussian white noise errors, etc.). As the nature of many hydrological processes do not fit these assumptions, simplifications are done to build a hydrological DA system (linearization of non-linear processes; block-diagonal, if not diagonal, error covariance matrices; temporally and spatially stationary error assumptions; magnitudes of observation errors; etc). These simplifications greatly affect the performance of the assimilation where wrong assumptions may result in a DA system with higher errors than that of simulations without the assimilation of observations. As a result of, DA system may not be optimum anymore. Hence several approaches are taken to improve the state estimate: 1) decreasing the observation error sources, 2) using better LSM, 3) implementing less simplifications, or 4) introducing new independent information to the system (along with the model and observations). Some studies have used innovation/analysis increment statistics as a new independent information to improve the DA performance (Reichle et al., 2008; Crow and Reichle, 2008; De Lannoy et al., 2009). Water budget closure can also be used as another independent information. Although land surface models preserve the water budget during state prediction, the analysis updates create a water imbalance which remains an unexplored problem in land data assimilation studies. In this study, a robust way is offered to improve the assimilation performance through introducing the water budget closure as a new independent source of information. This will be performed using an assimilation scheme, where the water budget closure constraint will be part of the assimilation equations. It is hypothesized that this added constraint will improve the assimilation performance.