Preprints
https://doi.org/10.5194/gmd-2021-171
https://doi.org/10.5194/gmd-2021-171

Submitted as: methods for assessment of models 20 Jul 2021

Submitted as: methods for assessment of models | 20 Jul 2021

Numerically consistent budgets of energy, momentum and mass in Cartesian coordinates: Application to the WRF model

Matthias Göbel1, Stefano Serafin2, and Mathias Walter Rotach1 Matthias Göbel et al.
  • 1Department of Atmospheric and Cryospheric Sciences, University of Innsbruck, Innsbruck, Austria
  • 2Department of Meteorology and Geophysics, University of Vienna, Vienna, Austria

Abstract. Numerically accurate budgeting of the forcing terms in the governing equations of a numerical weather prediction model is hard to achieve. Because individual budget terms are generally two to three orders of magnitude larger than the resulting tendency, exact closure of the budget can only be achieved if the contributing terms are calculated consistently with the model numerics.

We present WRFlux, an open-source software that allows precise budget evaluation for the WRF model, as well as transformation of the budget equations from the terrain-following grid of the model to the Cartesian coordinate system. The theoretical framework of the numerically consistent coordinate transformation is also applicable to other models. We demonstrate the performance and a possible application of WRFlux with an idealized simulation of convective boundary layer growth over a mountain range. We illustrate the effect of inconsistent approximations by comparing the results of WRFlux with budget calculations using a lower-order advection operator and two alternative formulations of the coordinate transformation. With WRFlux, the sum of all forcing terms for potential temperature, water vapor mixing ratio and momentum agrees with the respective model tendencies to high precision. In contrast, the approximations lead to large residuals: The root mean square error between the sum of the diagnosed forcing terms and the actual tendency is one to three orders of magnitude larger than with WRFlux. Furthermore, WRFlux decomposes the resolved advection into mean advective and resolved turbulence components, which is useful in the analysis of large-eddy simulation output.

Matthias Göbel et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2021-171', Anonymous Referee #1, 17 Aug 2021
    • AC1: 'Reply on RC1', Matthias Göbel, 20 Aug 2021
      • RC2: 'Reply on AC1', Anonymous Referee #1, 20 Aug 2021
  • RC3: 'Comment on gmd-2021-171', Anonymous Referee #2, 03 Sep 2021
    • AC2: 'Reply on RC3', Matthias Göbel, 17 Sep 2021
  • RC4: 'Comment on gmd-2021-171', Anonymous Referee #3, 06 Sep 2021
    • AC3: 'Reply on RC4', Matthias Göbel, 17 Sep 2021

Matthias Göbel et al.

Data sets

WRFlux: v1.2.1 Matthias Göbel, Stefano Serafin https://doi.org/10.5281/zenodo.4726600

Simulation setup for "Numerically consistent budgets of energy, momentum and mass in Cartesian coordinates: Application to the WRF model" Matthias Göbel, Stefano Serafin https://doi.org/10.5281/zenodo.4724415

Matthias Göbel et al.

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Short summary
We present WRFlux, an open-source software that allows numerically consistent budget evaluation of prognostic variables for the numerical weather prediction model WRF, as well as transformation of the budget equations from the terrain-following grid of the model to the Cartesian coordinate system. We demonstrate the performance and a possible application of WRFlux and illustrate the detrimental effects of approximations that are inconsistent with the model numerics.