The Optimality of Potential Rescaling Approaches in Land Data Assimilation

It is well-known that systematic differences exist between modeled and observed realizations of hydrological variables like soil moisture. Prior to data assimilation, these differences must be removed in order to obtain an optimal analysis. A number of rescaling approaches have been proposed for removing systematic differences between models and observations. These methods include rescaling techniques based on: matching sampled temporal statistics (i.e. variance), minimizing the least-squares distance between observations and models, and the application of triple collocation. Here we evaluate the optimality and relative performances of these rescaling methods both analytically and numerically and find that a triple collocation-based rescaling method results in an optimal solution whereas variance matching- and least squares-regression approaches result in only approximations to this optimal solution.