Horizontal organization or mesoscale variability is an important mechanism in the interaction of the boundary layer with the large-scale conditions. The development of organization in a precipitating cumulus trade-wind boundary layer is studied using large-eddy simulations with extensive horizontal domains, up to 160×160 km and fine grid resolution (40 m). The cloud fields vary between different computational domain sizes. Mean profiles and vertical velocity statistics do not vary significantly, both with respect to the domain size and when large-scale organization develops. Turbulent kinetic energy (TKE) rapidly increases when organization develops. The increase of TKE is attributed to the horizontal component, whereas the vertical velocity variance does not change significantly. The large computational domains blend the boundary between local convective circulations and mesoscale horizontal motions leading to the dependence of horizontal TKE on the LES domain size. Energy-containing horizontal length scales are defined based on the premultiplied spectra. When large-scale organization develops, the premultiplied spectra develop multiple peaks corresponding to the characteristic horizontal scales in the boundary layer. All flow variables have a small length scale of 1–2 km, which corresponds to local convective motions, e.g., updrafts and cumulus clouds. Organization development creates additional larger length scales. The growth rate of the large length scale is linear and it is about 3–4 km h−1, which agrees well with the growth rate of the cold pool radii. A single energy containing length scale is observed for vertical velocity for the entire run (even after organized convection develops) that is fairly constant with height.

No abstract

No abstract

Idealized large-eddy simulations of shallow convection often utilize horizontally periodic computational domains. The development of precipitation in shallow cumulus convection changes the spatial structure of convection and creates large-scale organization. However, the limited periodic domain constrains the horizontal variability of the atmospheric boundary layer. Small computational domains cannot capture the mesoscale boundary layer organization and artificially constrain the horizontal convection structure. The effects of the horizontal domain size on large-eddy simulations of shallow precipitating cumulus convection are investigated using four computational domains, ranging from 40×40km2 to 320×320km2 and fine grid resolution (40 m). The horizontal variability of the boundary layer is captured in computational domains of 160×160km2. Small LES domains (≤40 km) cannot reproduce the mesoscale flow features, which are about 100km long, but the boundary layer mean profiles are similar to those of the larger domains. Turbulent fluxes, temperature and moisture variances, and horizontal length scales are converged with respect to domain size for domains equal to or larger than 160×160km2. Vertical velocity flow statistics, such as variance and spectra, are essentially identical in all domains and show minor dependence on domain size. Characteristic horizontal length scales (i.e., those relating to the mesoscale organization) of horizontal wind components, temperature and moisture reach an equilibrium after about hour 30.

A computational domain translation velocity is often used in LES simulations to improve computational performance by allowing longer time-step intervals. Even though the equations of motion are Galilean invariant, LES results have been observed to depend on the translation velocity. It is found that LES results of shallow convection depend on the domain translation velocity even when a Galilean invariant formulation is used. This type of model error is named residual cross-grid flow error, to emphasize the expectation that it should be negligible or zero. The residual gross-grid flow error is caused by biases in finite difference dispersion errors. Schemes with low resolving power (typically low order of accuracy) produce larger dispersion errors that can be amplified by large-scale flow asymmetries, such as strong updrafts in cumulus-cloud layers. Accordingly, the cross-grid flow error strongly depends on the order of accuracy of the numerical scheme progressively becoming negligible as the order of accuracy is increased from second to sixth in the present simulations.