Development of a tangent linear model (version 1.0) for the High-Order Method Modeling Environment dynamical core

摘要

We describe development and validation of a tangent linear model for theHigh-Order Method Modeling Environment, the default dynamical core in theCommunity Atmosphere Model and the Community Earth System Model that solves aprimitive hydrostatic equation using a spectral element method. A tangentlinear model is primarily intended to approximate the evolution ofperturbations generated by a nonlinear model, provides a computationallyefficient way to calculate a nonlinear model trajectory for a short timerange, and serves as an intermediate step to write and test adjoint models,as the forward model in the incremental approach to four-dimensional variationaldata assimilation, and as a tool for stability analysis. Each module in thetangent linear model (version 1.0) is linearized by hands-on derivations, andis validated by the Taylor–Lagrange formula. The linearity checks confirmall modules correctly developed, and the field results of the tangent linearmodules converge to the difference field of two nonlinear modules as themagnitude of the initial perturbation is sequentially reduced. Also,experiments for stable integration of the tangent linear model (version 1.0)show that the linear model is also suitable with an extended time step sizecompared to the time step of the nonlinear model without reducing spatialresolution, or increasing further computational cost. Although the scope ofthe current implementation leaves room for a set of natural extensions, theresults and diagnostic tools presented here should provide guidance forfurther development of the next generation of the tangent linear model, thecorresponding adjoint model, and four-dimensional variational data assimilation,with respect to resolution changes and improvements in linearized physics anddynamics.