APPLICATION OF A NEW ADJOINT NEWTON ALGORITHM TO THE 3D ARPS STORM-SCALE MODEL USING SIMULATED DATA

The adjoint Newton algorithm (ANA is based on the first-and second-ord er 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 techniqu e to find Newton line search direction without using gradient informat ion. The error present in approximating the Hessian (the matrix of sec ond-order derivatives) of the cost function with respect to the contro l variables in the quasi-Newton-type algorithm is thus completely elim inated. while the storage problem related to storing the Hessian no lo nger exists since the explicit Hessian is not required in this algorit hm. The ANA is applied here, for the first time, in the framework of 4 D variational data assimilation to the adiabatic version of the Advanc ed Regional Prediction System, a three-dimensional, compressible. nonh ydrostatic 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 usi ng simulated observations indicate that the ANA can efficiently retrie ve high quality model initial conditions. It improves upon the efficie ncy of the usual adjoint method employing the LBFGS algorithm by mom t han an order of magnitude in terms of both CPU time and number of iter ations for test problems presented here. Numerical results also show t hat the ANA obtains a fast linear convergence rate.