On the dual advantage of placing observations through forward sensitivity analysis

Details

• Journal Title:
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Personal Author:
  Ahmed, S. E. ; San, O. ; Lakshmivarahan, S. ; Lewis, J. M.
• NOAA Program & Office:
  OAR (Oceanic and Atmospheric Research) ; NSSL (National Severe Storms Laboratory)
• Description:
  The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning the minimum number and placement of observations. To answer this question, we demonstrate the dual advantage of placing the observations where the square of the sensitivity of the model solution with respect to the unknown control variables, called forward sensitivities, attains its maximum. By following this approach, we can force the observability Gramian to be of full rank, which in turn guarantees efficient recovery of the optimal values of the control variables, which is the first of the two advantages of this strategy. We further show that the proposed strategy of placing observations has another inherent optimality: the square of the sensitivity of the optimal estimates of the control with respect to the observations (used to obtain these estimates) attains its minimum value, a second advantage that is a direct consequence of the above strategy for placing observations. Our analytical framework and numerical experiments on linear and nonlinear systems confirm the effectiveness of our proposed strategy.
• Keywords:
  General Engineering General Mathematics General Physics And Astronomy General Physics And Astronomy General Physics And Astronomy
• Source:
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2274)
• DOI:
  https://doi.org/10.1098/rspa.2022.0815
• ISSN:
  1364-5021 ; 1471-2946
• Format:
  PDF
• Publisher:
  The Royal Society
• Document Type:
  Journal Article
• License:
  https://creativecommons.org/licenses/by/4.0/
• Rights Information:
  CC BY
• Compliance:
  Submitted
• Main Document Checksum:
  urn:sha256:eae998fe301970cf0e400951d46416d5c2347ed49a0f21103e7ed64675346a09
• Download URL:
  https://repository.library.noaa.gov/view/noaa/51178/noaa_51178_DS1.pdf
• File Type:
  [PDF - 6.13 MB ]