21 Feb 2023
 | 21 Feb 2023
Status: this preprint is open for discussion.

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

Carl Wunsch, Sarah Williamson, and Patrick Heimbach

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.

Carl Wunsch et al.

Status: open (until 19 Apr 2023)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Carl Wunsch et al.

Carl Wunsch et al.


Total article views: 119 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
80 34 5 119 1 2
  • HTML: 80
  • PDF: 34
  • XML: 5
  • Total: 119
  • BibTeX: 1
  • EndNote: 2
Views and downloads (calculated since 21 Feb 2023)
Cumulative views and downloads (calculated since 21 Feb 2023)

Viewed (geographical distribution)

Total article views: 112 (including HTML, PDF, and XML) Thereof 112 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
Latest update: 29 Mar 2023
Short summary
Data assimilation methods that couple observations with dynamical models are essential for understanding climate change. Here, "climate" includes all sub-elements (ocean, atmosphere, ice, etc.). A common form of combination arises from sequential estimation theory, a methodology susceptible to a variety of errors that can accumulate through time for long records. Using two simple analogues, examples of these errors are identified and discussed, along with suggestions for accommodating them.