An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. The authors consider a nudging-based approach for data assimilation that constructs an ap...An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. The authors consider a nudging-based approach for data assimilation that constructs an approximate solution based on a feedback control mechanism that is designed to account for observations that have been blurred by a moving time average. Analysis of this nudging model in the context of the subcritical surface quasi-geostrophic equation shows, provided the time-averaging window is sufficiently small and the resolution of the observations sufficiently fine, that the approximating solution converges exponentially fast to the observed solution over time. In particular,the authors demonstrate that observational data with a small blur in time possess no significant obstructions to data assimilation provided that the nudging properly takes the time averaging into account. Two key ingredients in our analysis are additional boundedness properties for the relevant interpolant observation operators and a non-local Gronwall inequality.展开更多
基金supported by NSF Grants DMS-1418911,DMS-1418928,ONR Grant N00014-15-1-2333the Einstein Stiftung/Foundation-Berlin+1 种基金the Einstein Visiting Fellow Programthe John Simon Guggenheim Memorial Foundation
文摘An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. The authors consider a nudging-based approach for data assimilation that constructs an approximate solution based on a feedback control mechanism that is designed to account for observations that have been blurred by a moving time average. Analysis of this nudging model in the context of the subcritical surface quasi-geostrophic equation shows, provided the time-averaging window is sufficiently small and the resolution of the observations sufficiently fine, that the approximating solution converges exponentially fast to the observed solution over time. In particular,the authors demonstrate that observational data with a small blur in time possess no significant obstructions to data assimilation provided that the nudging properly takes the time averaging into account. Two key ingredients in our analysis are additional boundedness properties for the relevant interpolant observation operators and a non-local Gronwall inequality.
