The Ensemble Tangent Linear Model Applied to Nonorographic Gravity Wave Drag

Abstract An essential component of four-dimensional variational data assimilation is the tangent linear model (TLM), which is a linearized version of the full nonlinear forecast model. A relatively new approach to calculating the TLM is a regression model called the Ensemble Tangent Linear Model (ETLM). Here we validate the ETLM for linearizing a nonorographic gravity wave drag (NGWD) sub-grid scale model. The regression is applied to an ensemble created by perturbing the atmospheric state and calculating one time step of the NGWD model. The ETLM is validated using independent perturbations based on archived analysis increments. We examine how the skill of the NGWD ETLM depends on the choice of ensemble perturbation, ensemble size, amount of ensemble inflation/deflation, and the size of the localization stencil. After examining the nearly perfect results using a large ETLM ensemble (100,000 members), optimal tuning is then performed for 150 - 500 members. For smaller ETLM ensembles, spurious noise due to sampling error could be reduced either by downscaling the perturbations or by localizing the ETLM. The impact of localization decreases as the ETLM ensemble size increases. We then validate the ETLMs using one year of archived DA analysis increments. The skill varies over time with percentage errors relative to persistence forecasts (where 100% is no skill, 0% is a perfect forecast) generally ranging from ~50-90% (~40-80%) for ETLMs with 150 (500) members. The ETLM is also shown to propagate small increments (1% of the size of analysis increments) with fractional errors of ~10%.