Forecast Error Correction using Dynamic Data Assimilation by Sivaramakrishnan Lakshmivarahan, John M. Lewis, Rafal

By Sivaramakrishnan Lakshmivarahan, John M. Lewis, Rafal Jabrzemski

This publication introduces the reader to a brand new approach to information assimilation with deterministic constraints (exact pride of dynamic constraints)—an optimum assimilation approach known as Forecast Sensitivity technique (FSM), instead to the well known 4-dimensional variational (4D-Var) information assimilation approach. 4D-Var works with a ahead in time prediction version and a backward in time tangent linear version (TLM). The equivalence of knowledge assimilation through 4D-Var and FSM is confirmed and difficulties utilizing low-order dynamics make clear the method of knowledge assimilation by way of the 2 tools. the matter of go back movement over the Gulf of Mexico that incorporates upper-air observations and sensible dynamical constraints provides the reader a good suggestion of ways the FSM might be applied in a real-world scenario.

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X; t/ with respect to ˛. Differentiating both sides of the partial differential equation . 8. 18) compute and plot the variation of the Lyapunov index with respect to the parameter ˛ for the discrete time logistic model in Example 2 of Sect. 4. 1 Demonstrations Demonstration: Air–Sea Interaction Model Using the development in Example 1, Sect. 1, we solve the FSM data assimilation problem based on the dynamics of air–sea interaction. 12). The development of formulas for first and second-order sensitivities, applicable to the air–sea interaction dynamics, appears in Sect.

U; ˛/ is some (nonlinear) function of u and the scalar parameter ˛. 1 Ä i Ä 2/ are constants. x; t/ with respect to ˛. Differentiating both sides of the partial differential equation . 8. 18) compute and plot the variation of the Lyapunov index with respect to the parameter ˛ for the discrete time logistic model in Example 2 of Sect. 4. 1 Demonstrations Demonstration: Air–Sea Interaction Model Using the development in Example 1, Sect. 1, we solve the FSM data assimilation problem based on the dynamics of air–sea interaction.

12), and obtain the full quadratic approximation Q. / to f. / given by 1 eF 2 1 2 e D 2 F Q. aaT /x, where a and x are column vectors. 5 FSM: Discrete Time Formulation 37 Setting the gradient of Q. 14) is indeed a minimum provided, the Hessian of Q. 9), is given by r 2 Q. 15) is positive definite. 25) come into play. 5 FSM: Discrete Time Formulation In Sects. 2 we have illustrated the basic principles that underlie the firstorder forward sensitivity method (FSM) using a simple, scalar model in continuous time.

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