Potential Artifacts in Conservation Laws and Invariants Inferred from Sequential State Estimation

Abstract. In sequential estimation methods often used in oceanic and general climate calculations of the state and of forecasts, observations act mathematically and statistically as forcings. For purposes of calculating changes in important functions of state variables such as total mass and energy, or volumetric current transports, results are sensitive to mis-representation of a large variety of parameters, including initial conditions, prior uncertainty covariances, and systematic and random errors in observations. Here toy models of a mass-spring oscillator and of a barotropic Rossby-wave equation are used to demonstrate many of the issues. Results from Kalman-filter estimates, and those from finite interval smoothing are analyzed. In the filter (and prediction) problem, entry of data leads to violation of conservation and other invariant rules. A finite interval smoothing method restores the conservation rules, but uncertainties in all such estimation results remain. Convincing trend and other time-dependent determinations in "reanalysis" -like estimates require a full understanding of both models and observations.