Enhanced parallelization of the incremental 4D-Var data assimilation algorithm using the Randomized Incremental Optimal Technique

摘要

Incremental 4D-Var is a data assimilation algorithm used routinely at operational numerical weather prediction (NWP) centres worldwide. The algorithm solves a series of quadratic minimization problems (inner-loops) obtained from linear approximations of the forward model around nonlinear trajectories (outer-loops). Since most of the computational burden is associated with the inner-loops, many studies have focused on developing computationally efficient algorithms to solve the least-square quadratic minimization problem, in particular through time parallelization. This paper presents the first implementation and testing of a recently proposed method for parallelizing incremental 4D-Var, the Randomized Incremental Optimal Technique (RIOT), which replaces the traditional sequential conjugate gradient (CG) iterations in the inner-loop of the minimization with fully parallel randomized singular value decomposition (RSVD) of the preconditioned Hessian of the cost function. RIOT is tested using the standard Lorenz-96 model (L-96) as well as two realistic high-dimensional atmospheric source inversion problems based on aircraft observations of black carbon concentrations. A new outer-loop preconditioning technique tailored to RSVD was introduced to improve convergence stability and performance. Results obtained with the L-96 system show that the performance improvement from RIOT compared to standard CG algorithms increases significantly with nonlinearities. Overall, in the realistic black carbon source inversion experiments, RIOT reduces the wall-clock time of the 4D-Var minimization by a factor of 2 to 3, at the cost of a factor of 4 to 10 increase in energy cost due to the large number of parallel cores used. Furthermore, RIOT enables reduction of the wall-clock time computation of the analysis-error covariance matrix by a factor of 40 compared to a standard iterative Lanczos approach. Finally, as evidenced in this study, implementation of RIOT in an operational NWP system will require a better understanding of its convergence properties as a function of the Hessian characteristics and, in particular, the degree of freedom for signal of the inverse problem.