Anomaly Format of Atmospheric Governing Equations with Climate as a Reference Atmosphere

To reduce numerical instability and increase forecast accuracy of a numerical weather prediction (NWP) model, one approach is to subtract a reference atmosphere from atmospheric governing equations. In the past, scientists have proposed one-dimensional, two-dimensional, and three-dimensional static (in time) reference atmospheres with respect to temperature and pressure. These three reference atmospheres were first reviewed, and their corresponding perturbation equations were derived. Then, a new four-dimensional (space and time) all-variable (temperature, pressure, wind, moisture, etc.) reference atmosphere was defined using observed climatic states. Unlike the previous three approaches, the perturbations derived from this new method are actual anomalies relative to climate and directly a part of individual weather systems in both structure and strength. By subtracting climatic states, anomaly equations were derived and analyzed. Finally, the benefits and challenges of the anomaly-equation-based NWP model were discussed. Theoretically, an anomaly model should reduce model systematic errors (bias) and should avoid model climate drift to significantly enhance a model’s performance. An example of tropical cyclone track forecasts using the Beta advection model (vorticity) was demonstrated. The separation of model physics into climatic and anomalous physics is a significant challenge if a pure anomaly-equation-based NWP model is desired. Fortunately, a model including both anomaly and climatic equations should work with current full physics. In an anomaly climate mixed model, the anomaly part needs to be predicted and the climate parts are precalculated constants. It is hoped that this study will inspire model developers to explore the approach, which could be a possible new direction in developing next-generation NWP models. A high-resolution reanalysis is also key to the success of this new approach.