{
  "id": "2304.05858",
  "version": "v1",
  "published": "2023-04-12T13:42:50.000Z",
  "updated": "2023-04-12T13:42:50.000Z",
  "title": "Convergence properties of a Gauss-Newton data-assimilation method",
  "authors": [
    "Nazanin Abedini",
    "Svetlana Dubinkina"
  ],
  "categories": [
    "math.DS",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "Four-dimensional weak-constraint variational data assimilation estimates a state given partial noisy observations and dynamical model by minimizing a cost function that takes into account both discrepancy between the state and observations and model error over time. It can be formulated as a Gauss-Newton iteration of an associated least-squares problem. In this paper, we introduce a parameter in front of the observation mismatch and show analytically that this parameter is crucial either for convergence to the true solution when observations are noise-free or for boundness of the error when observations are noisy with bounded observation noise. We also consider joint state-parameter estimation. We illustrated theoretical results with numerical experiments using the Lorenz 63 and Lorenz 96 models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-12T13:42:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gauss-newton data-assimilation method",
      "convergence properties",
      "observation",
      "weak-constraint variational data assimilation estimates",
      "four-dimensional weak-constraint variational data assimilation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}