Information Synthesis Across Scales in Atmospheric State Estimation: Theory and Numerical Experiments

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This thesis studies the benefits of simultaneously considering system information from different sources when performing ensemble data assimilation. In particular, in Chapter 2 we consider ensemble data assimilation using both a global dynamical model and climatological forecast error information, and, in Chapters 3 and 4, using both a global dynamical model and at least one higher-resolution limited-area dynamical model. Focus is given to applying data assimilation for atmospheric state estimation. Introductory material on ensemble forecasting is given in Chapter 1.

In Chapter 2, I first investigate how the forecast background-error climatology can be used to help improve state estimates, and subsequent forecasts initialized from those state estimates. ``Climatological perturbations'' derived from an estimate of the background-error covariance matrix are added to the dynamic ensemble that has been forecasted from the previous analysis time, enlarging the space of possible analysis increments. Numerical experiments on a one-dimensional toy model test this method and illustrate that climatologically augmenting the dynamical forecast ensemble during the analysis has a positive impact on state estimation and forecast accuracy.

Chapter 3 studies data assimilation that considers state information from various spatial scales. In practice, it is common for regional-scale weather forecasts to be created using limited-area atmospheric models which have relatively high spatial resolution. Limited-area model forecasts require lateral boundary conditions, which often come from a lower resolution forecast model (with different model physics) defined over a larger, often global, domain. Here I describe how data assimilation may be performed on a composite forecast state containing information from all available forecast models, and show results from numerical experiments that detail the benefits of this approach.

Chapter 4 of this thesis explores forecast model bias, which is the result of uncertain, unknown or incorrect model physics. I adapt a strategy for correcting forecast model bias to use when performing data assimilation using the composite state method described in Chapter 3. In numerical experiments, I test this bias correction strategy for differently biased global and limited-area models, and observe that analysis and forecast accuracy is dramatically improved when compared to forecasts made without bias correction.