Application of a New Adjoint Newton Algorithm to the 3-D ARPS Storm Scale Model Using Simulated Data
Zhi Wang, Kelvin K. Droegemeier, L. White, I.M. Navon
The adjoint Newton algorithm (ANA) is based on the first- and second-order adjoint techniques allowing one to obtain the ``Newton line search direction" by integrating a ``tangent linear model" backward in time (with negative time steps). Moreover, the ANA provides a new technique to find ``Newton line search direction" without using gradient information. The error present in approximating the Hessian (the matrix of second order derivatives) of the cost function with respect to the control variables in the quasi-Newton type algorithm is thus completely eliminated, while the storage problem related to storing the Hessian no longer exists since the explicit Hessian is not required in this algorithm. The ANA is applied here, for the first time, in the framework of 4-D variational data assimilation to the adiabatic version of the Advanced Regional Prediction System (ARPS), a 3-dimensional, compressible, nonhydrostatic storm-scale model. The purpose is to assess the feasibility and efficiency of the ANA as a large scale minimization algorithm in the setting of 4-D variational data assimilation. Numerical results using simulated observations indicate that the ANA can efficiently retrieve high quality model initial conditions. It improves upon the efficiency of the usual adjoint method employing the LBFGS algorithm by more than an order of magnitude in terms of both CPU time and number of iterations for our test problems. Numerical results also show that the ANA obtains a fast linear convergence rate.