Impacts of Numerical Advection Schemes and Turbulence Modeling on Gray-Zone Simulation of a Squall Line

Abstract With increasing computational power, atmospheric simulations have approached the gray-zone resolutions, where energetic turbulent eddies are partly resolved. The representation of turbulence in the gray zone is challenging and sensitive to the choices of turbulence models and numerical advection schemes. Numerical advection schemes are typically designed with numerical dissipation to suppress small-scale numerical oscillations. However, at gray-zone resolutions, the numerical dissipation can damp both numerical and physical oscillations. In this study, we first evaluate the impact of advection schemes on the simulation of an idealized squall line at two gray-zone resolutions (1 and 4 km). We found that at the 4-km resolution, the numerical dissipation from advection schemes can be unfavorable because it damps convective cells greatly and weakens the front-to-rear flow, producing an underestimated convective precipitation maximum and excessive stratiform precipitation. At the 1-km resolution, the numerical dissipation is essential because, without it, excessive spurious numerical oscillations disrupt the squall-line structure. The dynamic reconstruction model (DRM) of turbulence is designed to model both forward- and backscatter having the potential to counter the effect of numerical dissipation from the advection schemes. Our findings demonstrate that DRM enhances squall-line simulations at the 4-km resolution, improving both the squall-line structure and precipitation distribution. However, at the 1-km resolution, DRM fails to improve simulation accuracy, likely due to its influence on triggering spurious convections. Significance Statement This work investigates the effects of numerical mixing arising from numerical advection schemes and physical mixing from turbulence schemes on an organized deep convective system in the gray zone. The numerical mixing is found to be critical in shaping the deep convective system structure and the corresponding precipitation distribution. Meanwhile, the role of numerical mixing varies with gray-zone resolutions. The numerical mixing is necessary when it primarily acts on spurious numerical oscillations but unfavorable when it mainly acts on physical convections. Turbulence schemes that allow backscatter can reduce the impact of numerical mixing, which helps improve the accuracy of simulations at certain gray-zone resolutions.