Towards the closure of momentum budget analyses in the WRF (v3.8.1) model
Abstract. Budget analysis of a tendency equation is widely utilized in numerical studies to quantify different physical processes in a simulated system. While such analysis is often post-processed when the output is made available, it is well-acknowledged that the closure of a budget is difficult to achieve without averaging. Nevertheless, the potential rise of the errors in such calculation has not been systematically investigated. In this study, an inline budget retrieval method is first developed in the WRF v3.8.1 model and tested on a 2D idealized slantwise convection case with a focus on the momentum equations. This method extracts all the budget terms following the model solver, which gives a high accuracy with a residual term always less than 0.02 % of the tendency term. Then, taking the inline values as truth, several post-processing budget analyses with different commonly-used simplifications are performed to investigate how they may affect the accuracy of the estimation of individual terms and the resultant residual. These assumptions include using a lower order advection operator than the one used in the model, neglecting the C staggering grids, or following a mathematically-equivalent but transformed format of equation. Errors in these post-processed analyses are found mostly over the area where the dynamics are the most active, impairing the subsequent physical interpretation. A maximum 99th percentile residual can reach 800 % of the concurrent tendency term, indicating the danger of neglecting the residual term as done in many budget studies. This work provides general guidance not only for applying an inline budget retrieval to the WRF model but for minimizing the errors in post-processing budget calculations.