Nonlinearity in data assimilation applications: A practical method for analysis

A new method to quantify the nonlinearity of data assimilation problems is proposed. The method includes the effects of system errors, measurement err ors, observational network, and sampling interval. It is based on computati on of the first neglected term in a "Taylor'' series expansion of the error s introduced by an extended Kalman filter, and can be computed at very litt le cost when one is already applying a second-order (or higher order) Kalma n filter or an ensemble Kalman filter. The nonlinearity measure proposed he re can be used to classify the "hardness'' of the problem and predict the f ailure of data assimilation algorithms. In this manner it facilitates the c omparison of data assimilation algorithms and applications. The method is applied to the well-known Lorenz model. A comparison is made between several data assimilation algorithms that are suitable for nonlinea r problems. The results indicate significant differences in performance for more nonlinear problems. For low values of V, a measure of nonlinearity, t he differences are negligible.