caa a22 4500 469052589 CHVBK 20180323132834.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF01025501 doi (NATIONALLICENCE)springer-10.1007/BF01025501 The second order adjoint analysis: Theory and applications [Elektronische Daten] [Zhi Wang, I. Navon, F. Le Dimet, X. Zou] Summary: The adjoint method application in variational data assimilation provides a way of obtaining the exact gradient of the cost functionj with respect to the control variables. Additional information may be obtained by using second order information. This paper presents a second order adjoint model (SOA) for a shallow-water equation model on a limited-area domain. One integration of such a model yields a value of the Hessian (the matrix of second partial derivatives, ∇2 J) multiplied by a vector or a column of the Hessian of the cost function with respect to the initial conditions. The SOA model was then used to conduct a sensitivity analysis of the cost function with respect to distributed observations and to study the evolution of the condition number (the ratio of the largest to smallest eigenvalues) of the Hessian during the course of the minimization. The condition number is strongly related to the convergence rate of the minimization. It is proved that the Hessian is positive definite during the process of the minimization, which in turn proves the uniqueness of the optimal solution for the test problem. Numerical results show that the sensitivity of the response increases with time and that the sensitivity to the geopotential field is larger by an order of magnitude than that to theu andv components of the velocity field. Experiments using data from an ECMWF analysis of the First Global Geophysical Experiment (FGGE) show that the cost functionJ is more sensitive to observations at points where meteorologically intensive events occur. Using the second order adjoint shows that most changes in the value of the condition number of the Hessian occur during the first few iterations of the minimization and are strongly correlated to major large-scale changes in the reconstructed initial conditions fields. Springer-Verlag, 1992 Wang Zhi Department of Mathematics and Supercomputer Computations Research Institute, Florida State University, 32306, Tallahassee, Florida, USA aut Navon I. Department of Mathematics and Supercomputer Computations Research Institute, Florida State University, 32306, Tallahassee, Florida, USA aut Le Dimet F. Grenoble, Laboratoire de Modelisation et Calcul, B.P. 53X, F-38041, Grenoble Cedex, France aut Zou X. Supercomputer Computations Research Institute, Florida State University, 32306, Tallahassee, Florida, USA aut Meteorology and Atmospheric Physics Springer-Verlag 50/1-3(1992-03-01), 3-20 0177-7971 50:1-3<3 1992 50 703 https://doi.org/10.1007/BF01025501 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01025501 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Zhi Department of Mathematics and Supercomputer Computations Research Institute, Florida State University, 32306, Tallahassee, Florida, USA aut NATIONALLICENCE 700 1- Navon I. Department of Mathematics and Supercomputer Computations Research Institute, Florida State University, 32306, Tallahassee, Florida, USA aut NATIONALLICENCE 700 1- Le Dimet F. Grenoble, Laboratoire de Modelisation et Calcul, B.P. 53X, F-38041, Grenoble Cedex, France aut NATIONALLICENCE 700 1- Zou X. Supercomputer Computations Research Institute, Florida State University, 32306, Tallahassee, Florida, USA aut NATIONALLICENCE 773 0- Meteorology and Atmospheric Physics Springer-Verlag 50/1-3(1992-03-01), 3-20 0177-7971 50:1-3<3 1992 50 703 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer