Capturing Nonlinearities with the Naval Research Laboratory's Global and Mesoscale 4DVar Data Assimilation Systems

Abstract:

Numerical weather prediction models and observation (forward) operators are important components of modern data assimilation systems. They are inherently nonlinear or even highly nonlinear at times. These nonlinearities can be handled through an iterative procedure, often referred to as the “outer loop” / ”inner loop” formulation in 3D/4DVar data assimilation. In the “inner loop”, one typically minimizes a cost-function around a previous 3D/4D state that is already a good approximation of the true nonlinear state. Additional “outer loops” are then used to account for the missing nonlinearity in both the NWP model and the observation operator. There is no formal proof of convergence in the aforementioned iterative procedure in general. However, it can be formally shown that the procedure can converge under certain condition (e.g. the Gauss-Newton algorithm). In practice, the iterative procedure works quite well due to the fact that the NWP model and the observation operators are generally quite good in capturing majority of the nonlinearity in dynamical process.

The NRL global and mesoscale 4DVar systems use the Accelerated Representer (AR) formulation to solve the analysis equations in observation space. The dual formulation has several strategic advantages, but also present additional challenges unique to this formulation. This presentation will describe various methods used within the NRL Accelerated Representer 4DVar formulations to extend the solution methods to weakly nonlinear problems. These include ocean surface wind speed assimilation, assimilation of water vapor sensitive radiances, the multiple outer loop formulation, and the inclusion of linearized physics in the tangent linear and adjoint models.