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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Discussion papers
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: development and technical paper 23 Oct 2019

Submitted as: development and technical paper | 23 Oct 2019

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This discussion paper is a preprint. It is a manuscript under review for the journal Geoscientific Model Development (GMD).

Towards the closure of momentum budget analyses in the WRF (v3.8.1) model

Ting-Chen Chen, Man K. Yau, and Daniel J. Kirshbaum Ting-Chen Chen et al.
  • Atmospheric and Oceanic Sciences Department, McGillUniversity, Montreal, H3A0B9, Canada

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.

Ting-Chen Chen et al.
Interactive discussion
Status: open (until 19 Dec 2019)
Status: open (until 19 Dec 2019)
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Ting-Chen Chen et al.
Model code and software

WRFV3.8.1_inline_budget_retrieval: Inline budget retrieval tool for 3D momentum components and potential temperature T.-C. Chen

Ting-Chen Chen et al.
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Latest update: 18 Nov 2019
Publications Copernicus
Short summary
Budget analysis helps to quantify the contribution of different terms in a selected prognostic equation within a numerical simulation. However, it is well acknowledged that non-negligible errors generally exist if such equations are analyzed in model post-processing. Here, we develop an inline budget retrieval method within the WRF model to give a high accuracy budget closure. We also compare the inline and post-processed budgets to investigate the potential sources of errors in the latter. 
Budget analysis helps to quantify the contribution of different terms in a selected prognostic...