The nature of adjoint sensitivities with respect to model parameters and their use in adaptive data assimilation
The predictability of the atmosphere depends, in part, on the accuracy of the initial states of numerical weather prediction models. Adjoints of numerical weather prediction models are used to produce initial condition sensitivities of some chosen forecast metric, quantifying such predictability. Previous studies investigating the nature of such sensitivities have used forecast metrics which typically diagnose cyclogenesis. Localized, uphear-tilted, subsynoptic scale sensitivity structures which maximize in the middle to lower troposphere are common results of these studies. However, due to the requirement of significant computational resources, these studies have typically been performed with simplified physics, coarse resolution, and other approximations used within the adjoint models. With modern computational resources, the work in this thesis extends the understanding of initial condition sensitivity computed at coarse resolution with simplified physics to that at higher resolution with more advanced physics, which more accurately characterizes real-time modern numerical weather prediction. It is found that sensitivity structures vary significantly with different model physics, basic-state trajectories, and resolution. The most pronounced variations occur with respect to model horizontal resolution, as sensitivity structures decrease in scale, increase in magnitude, and decrease in tangent-linear accuracy as horizontal grid spacing decreases from 216-km to 24-km resolution.An alternative measure, ensemble sensitivity, is introduced and is defined as the slope of the linear regression of a forecast metric onto each initial-time model state variable within an ensemble of forecasts. These ensemble sensitivities are shown to be a product of the initial-time covariance statistics of the ensembles and the initial-time adjoint sensitivity of the same forecast metric calculated about the forecast begun from the ensemble-mean initial condition under tangent-linear assumptions. Ensemble sensitivities reflect a statistical and dynamical understanding of the flow, and can also be used to develop computationally efficient measures of data impact and targeting strategies by exploiting their relationship to adjoint sensitivities. The flexibility of the forecast metric also allows for investigation of data impact and targeting strategies associated with high-impact weather events.
- Atmospheric sciences