Abstract
For the primitive equations of large-scale atmosphere and ocean dynamics, we study the problem of determining by means of a variational data assimilation algorithm initial conditions that generate strong solutions which minimize the distance to a given set of time-distributed observations. We suggest a modification of the adjoint algorithm whose novel elements is to use norms in the variational cost functional that reflects the H^1-regularity of strong solutions of the primitive equations. For such a cost functional, we prove the existence of minima and a first-order adjoint condition for strong solutions that provides the basis for computing these minima. We prove the local convergence of a gradient-based descent algorithm to optimal initial conditions using the second-order adjoint primitive equations. The algorithmic modifications due to the H^1-norms are straightforwardly to implement into a variational algorithm that employs the standard L^2-metrics.
Highlights
Data assimilation is a computational technique that aims at blending a dynamical model of a physical process with observational data of this process while at the same time preserving the integrity of the model and making optimal use of the observa
Results that are similar in spirit to our work can be found in Agoshkov and Ipatova (2007), where a variational algorithm was analyzed that uses observations of sea surface temperature and of sea surface elevation to determining the control variables of heat flux and water flux that occur in the surface boundary conditions of the oceanic primitive equations
In our work here, the goal is not to introduce a regularization of the data assimilation problem but to demonstrate that optimal initial conditions for strong solutions of the primitive equations assimilation problem necessitates the use of H1norms
Summary
Journal of Nonlinear Science (2021) 31:56 tional information. It constitutes a fundamental technique for modeling real-world phenomena. In our work here, the goal is not to introduce a regularization of the data assimilation problem but to demonstrate that optimal initial conditions for strong solutions of the primitive equations assimilation problem necessitates the use of H1norms. We refer to this property as strong solvability of the data assimilation problem. The new and fundamental but decisive element in the suggested formulation of the data assimilation algorithm is to use in the cost functional metrics that are tailored to the regularity of the primitive equations. This paper describes for the primitive equations the consequences of such a choice
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
