Do Shallow Cumulus Clouds have the Potential to Trigger Secondary Circulations Via Shading?

Abstract

The effects on the convective boundary layer (CBL) of shading due to shallow cumulus clouds are investigated. The main question is to see whether clouds are able to produce secondary circulations by shading of the surface (dynamic heterogeneities) and how these dynamic heterogeneities interact with static heterogeneities in terms of the production of secondary circulations. Also the effects of cloud shadows on cloud-field characteristics are analyzed. The effects are studied using large-eddy simulations of a cloud-topped CBL with an idealized surface. Over a homogeneous surface, shadows trigger secondary circulations with different strengths depending on the solar zenith angle $\vartheta$, with large $\vartheta$ favouring the development of secondary circulations. Over a static heterogeneous surface with a simple striped pattern, the strength of secondary circulations is effectively reduced by dynamic heterogeneities at small $\vartheta$. At large $\vartheta$, however, the effect on secondary circulations depends on the orientation of the striped static heterogeneities to the shadow-casting direction of the clouds. The influence of shadows is only small if they are cast perpendicular to the striped heterogeneity, but if stripes and the shadow-casting direction are parallel, secondary circulations are reduced in strength also for large $\vartheta$. Shadow effects on the cloud-field characteristics vary with $\vartheta$ as well. The results show that small $\vartheta$ favours the development of small clouds with a reduced lifetime while large $\vartheta$ promotes the development of larger clouds with an extended lifetime compared to non-shading clouds.

Appendix 1

The additional shading effect on the near-surface latent heat flux $\textit{LE}$ has only a minor impact on the boundary-layer dynamics. In order to confirm this, we performed an additional simulation considering shading effects on $\textit{LE}$ above a homogeneous surface at a solar zenith angle of $\vartheta =60^\circ$. According to Lohou and Patton (2014) $\textit{LE}$ is reduced by 50% on shaded surfaces, accounted for by

$$\begin{aligned} \textit{LE}^{\mathrm {c}}_{\mathrm {ho}}(x,y) = \textit{LE}_{\mathrm {ho}}(x,y) \frac{ 0.5 e^{-\tau (x,y)} + 0.5 }{\left\langle 0.5 e^{-\tau (x,y)} + 0.5 \right\rangle }, \end{aligned}$$

(11)

as in Eq. 6 for the sensible heat flux H. Figure 15a–c show the vertical profiles of $\overline{u'^2}$, $\overline{v'^2}$, and the liquid water content $\overline{q_l}$, respectively, for a simulation with varying $\textit{LE}$ due to shading and a reference simulation with constant $\textit{LE}$. Modifying $\textit{LE}$ due to shading results only in a minor increase of $\overline{u'^2}$ and $\overline{v'^2}$ inside the boundary layer. Thus, the contribution of a heterogeneous distribution of $\textit{LE}$ to the formation of secondary circulations is only minor as compared to the effects of heterogeneities in H. Although heterogeneities in $\textit{LE}$ enter into the buoyancy term, density changes due to changes in the humidity can be generally neglected for the small absolute humidity levels present in the simulations. The influence on the clouds is also very limited as shown by the small differences in the profiles of $q_l$ (Fig. 15c) between the simulations. The cloud onset and development is mainly determined by the initial humidity profile, and because the surface $\textit{LE}$ contributes little to the mean humidity profile, a heterogeneously distributed $\textit{LE}$ has only minor effects on the cloud layer.

Fig. 15

Profile of the variance of the a x-velocity component u, b y-velocity component v, and c the profile of the liquid water content $q_l$ for simulations with the homogeneous surface with constant and varying $\textit{LE}$ and $\vartheta =60^\circ$. Profiles are averaged over the last 30 min of the simulation. Grey shaded areas represent the cloud layer