Kinetic Energy Spectra, Backscatter, and Subgrid Parameterization Analysis in Radiative-Convective Equilibrium

Abstract

This thesis explores how energy is distributed and transferred across scales in convective-permitting radiative-convective equilibrium (RCE) simulations and how these processes can be more accurately represented in numerical models through improved subgrid parameterizations. Aggregation steepens the horizontal kinetic energy spectra by enhancing the large-scale energy, which results in horizontal kinetic energy spectra in both the upper troposphere and lower stratosphere that are close to the mesoscale -5/3 spectrum. In the upper troposphere, spectral energy budget analysis indicates that this is the result of the balance between buoyancy flux and vertical energy flux, rather than a classic direct energy cascade. In the lower stratosphere, there is inverse energy transfer, which may be explained by wave-mean-flow-interaction. Subfilter energy transfer analysis is performed on an idealized RCE simulation by filtering 1-km high-resolution simulation to a horizontal scale of 4 km. The net subfilter energy transfer rate is dissipative in the upper troposphere and backscattering in the lower stratosphere, which are consistent with the direction of energy transfer in the nonlinear transfer energy flux. The stochastic backscatter TKE scheme, a stochastic backscatter-allowing subgrid turbulence scheme created by adding a zero-mean stochastic forcing to the eddy viscosity of the TKE scheme, is proposed and tested on idealized RCE simulations. The stochastic backscatter TKE scheme improves the subgrid local energy transfer when compared to a common stochastic backscatter scheme and the standard TKE scheme without backscatter. Despite the fact that backscatter is still weaker than dissipation in the lower stratosphere in the stochastic backscatter TKE simulations, the kinetic energy spectra are closer to the -5/3 spectrum when compared to the standard TKE simulation. This study advances our understanding of the interscale distribution and transfer of energy in RCE, and the introduction of the stochastic backscatter TKE scheme provides a more realistic representation of dissipation and backscatter by matching the distribution of subfilter energy transfer rate from a high-resolution simulation.