Abstract
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 temporal and/or spatial averaging. Nevertheless, the development of errors in such calculations 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 0.1 % of the tendency term. Then, taking the inline values as truth, several offline 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 grid staggering, or following a mathematically equivalent but transformed format of the governing equations. Errors in these post-processed analyses are found mostly over the area where the dynamics are the most active, thus impairing the subsequent physical interpretation. A maximum 99th percentile residual can reach >50 % 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 budget diagnoses with the WRF model but also for minimizing the errors in post-processed budget calculations.
Highlights
The atmosphere is a complex system with different scales of motion
Budget analysis has been performed on diverse properties of many systems on various scales, including the Madden– Julian oscillation (MJO; e.g., Kiranmayi and Maloney, 2011; Andersen and Kuang, 2012), tropical cyclones (e.g., Zhang et al, 2000; Rios-Berrios et al, 2016; Huang et al, 2018), squall lines (e.g., Sanders and Emanuel, 1977; Gallus and Johnson, 1992; Trier et al, 1998), supercell thunderstorms (e.g., Lilly and Jewett, 1990), and so on
Aside from Coriolis force (COR), the absolute errors in the tendency, ADV and pressure gradient force (PGF) can exceed 6 × 10−4 m s−2, the former two of which are more than 50 % of the magnitude of their true values locally
Summary
The atmosphere is a complex system with different scales of motion. Its dynamics are governed by a set of fluid equations based on the fundamental laws of physics. The equation set cannot be solved analytically, numerical models can be used to simulate the observed weather and climate systems to improve our understanding of the atmosphere. Due to the complexity and nonlinearity of the numerical models, budget analysis is often employed to interpret the results by quantifying the contribution of each term (i.e., physical process) in a tendency equation that governs the evolution of a certain quantity in the simulated system. The accuracy of a given budget analysis can be estimated from the residual term, defined as the difference between the tendency term on the left-hand side (lhs) of the equation and the summation of all the forcing terms on its right-hand side (rhs). Budget analysis has been performed on diverse properties (e.g., momentum, temperature, water vapor, vorticity) of many systems on various scales, including the Madden– Julian oscillation (MJO; e.g., Kiranmayi and Maloney, 2011; Andersen and Kuang, 2012), tropical cyclones (e.g., Zhang et al, 2000; Rios-Berrios et al, 2016; Huang et al, 2018), squall lines (e.g., Sanders and Emanuel, 1977; Gallus and Johnson, 1992; Trier et al, 1998), supercell thunderstorms (e.g., Lilly and Jewett, 1990), and so on
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