## Abstract

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 4D variational data assimilation to the adiabatic version of the Advanced Regional Prediction System, a three-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 4D 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 test problems presented here. Numerical results also show that the ANA obtains a fast linear convergence rate.

*Corresponding author address:* Dr. Zhi Wang, 100 E. Boyd, EC 1110, Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, OK 73019.

Email: dwang@tornado.gcn.uoknor.edu