The formation of shallow cumulus cloud streets was historically attributed primarily to dynamics. Here, we focus on the interaction between radiatively induced surface heterogeneities and the resulting patterns in the flow. Our results suggest that solar radiative heating has the potential to organize clouds perpendicular to the sun's incidence angle.

To quantify the extent of organization, we performed a high-resolution large-eddy
simulation (LES) parameter study. We varied the horizontal wind
speed, the surface heat capacity, the solar zenith and azimuth
angles, and radiative transfer parameterizations (1-D and
3-D). As a quantitative measure we introduce a simple algorithm
that provides a scalar quantity for the degree of organization and
the alignment. We find that, even in the absence of a horizontal
wind, 3-D radiative transfer produces cloud streets perpendicular to
the sun's incident direction, whereas the 1-D approximation or
constant surface fluxes produce randomly positioned circular
clouds. Our reasoning for the enhancement or reduction of
organization is the geometric position of the cloud's shadow and its
corresponding surface fluxes. Furthermore, when increasing
horizontal wind speeds to

The advent of airborne and satellite observations allowed for a bird's
eye view of the atmosphere and, ever since, meteorologists have been
fascinated by the striped patterns often evident in cloud systems.

Overall, we can summarize that the formation of cloud streets has been extensively explored from theoretical and observational perspectives. The abovementioned studies shed light on the various aspects of interaction with the cloud field but either lack a realistic representation of surface processes, neglect 3-D radiative transfer effects or do not examine the relationship concerning the background wind speed.

In this study we strive to overcome these shortcomings and determine the prerequisites for the formation of cloud streets, while our main focus is on dynamic heterogeneities and (3-D) radiative transfer. We try to disentangle the underlying processes with a rigorous parameter study using large-eddy simulations (LES).

Section

The LES were performed with the UCLA-LES
model. A description and details of the LES model can be found
in

The TenStream is a MPI-parallelized solver for the full 3-D radiative
transfer equation. Similarly to a two-stream solver, the TenStream
solver computes the radiative transfer coefficients for up- and
downward fluxes and additionally for sideward streams. The coupling
of individual boxes leads to a linear equation system which is written
as a sparse matrix and is solved using parallel iterative methods from
the Portable, Extensible Toolkit for Scientific Computation

The most pronounced difference between 1-D and 3-D radiative transfer
solvers, pertaining the setup here, is the displacement of the sun's shadow
at the surface. In the case of 1-D radiative transfer, the shadow of a cloud
is by definition always directly beneath it (so-called independent pixel or
independent column approximation). Contrarily, 3-D radiative transfer allows
the propagation of energy horizontally and correctly displaces the clouds
shadow depending on the sun's position. The features of 3-D radiative
transfer in the thermal spectral range are an increased cooling on cloud
edges and a smoothed distribution of surfaces fluxes. While we compute
thermal radiative transfer in a 3-D fashion, we expect these effects to be
less important for this setup because feedbacks on the dynamics appear to
happen only on longer timescales of a day

The spectral integration is performed using the correlated

The base setup of the UCLA-LES simulates a
domain of

The focus of this study is to determine the interplay of radiation with the
atmosphere, the surface, and the clouds and finally take a closer look on the
formation of cloud streets. To that end we run the simulations with five free
parameters, namely the heat capacity of the surface skin layer
(

Parameter space for the LES simulations: the mean west wind (

Virtual photograph of LES simulations at a cruising altitude of 15

The time it takes the simulations to form the first clouds depends on the
choice of the parameters. Foremost the solar zenith angle determines the
energy input into the atmosphere and the surface (lower positioned sun thus
leads to a later onset of cloud development). To compare the heterogeneous
simulations we limit the following analysis to the time steps (output every
5 min) where the cloud fraction is between 10 and
50 %

Figure

Volume rendered liquid water mixing ratio (LWC) and surface latent and sensible heat flux (

The panels exemplarily depict the autocorrelation coefficients of the cloud distribution in the
three simulations presented in Fig.

Since we do not deal with towering and tilted or multilayer clouds we can use the cloud mask as a proxy to separate individual clouds.
We derive the cloud mask as the binary field of the liquid water path (

Next, we use the transects of the correlation coefficient along the

This definition would miss cloud streets in diagonal direction which,
however, is no limitation for our analysis. For one, we know that the
background wind induces cloud streets along the mean wind direction, i.e.,
here in the west–east component

The correlation ratio reduces a cloud field snapshot into a scalar which yields

As an example for the evolution of convective organization,
Fig.

To reduce the information of convective organization into a single scalar
value, we compute the mean correlation ratio

Time evolution of the correlation ratio

Correlation ratio for simulations with a variable surface skin heat capacity (

The basis for the following analysis is the evaluation of mean correlation
ratios as a function of the five free parameters,

We will first focus on panel

The three simulations presented in Sect.

Sketch from an aerial view depicting surface fluxes in the vicinity of a cloud with a tilted solar incidence.
The cloud casts a shadow on the westward surface pixels (blue dots).
The available convective energy is directly proportional to latent and sensible heat release of the surface in the vicinity of the convective updraft.
Arrows illustrate the confluence of near-surface air masses from adjacent pixels in a thermally driven updraft event.
Convective tendencies will be weaker on pixels that are adjacent to shaded patches, e.g., at

To explain the concept of why 3-D RT creates rolls, we set up a short
thought experiment. First start with the assumption that there already is a
single cloud which will cast the shadow along the sun's incident angle. The
surface fluxes for latent sensible heat will be smaller in the shadowy area
and hence we expect the next convective plume to rise in sun-lit areas.
Figure

It is also clear from the horizontal axis of Fig.

Simulations with 1-D radiative transfer or constant

Three-dimensional radiation calculations with high or low solar zenith angles also show a reduced production of cloud streets. This is (a) because low zenith angles (sun above head) practically behave just as 1-D radiative transfer and (b) because large zenith angles (low sun, smaller heating rates) have a weaker potential to create surface heterogeneities.

Figure

So far we have discussed only the simulations with constant

Let us consider a case in which there is a dynamically induced cloud street
along the mean background wind, i.e., from west to east. Quasi-1-D radiation
(1-D and 3-D if the sun is close to zenith) casts a shadow onto the cloud's
updraft region and therefore hinders further development of the cloud. This
results in values for the correlation ratio of

In contrast, for 3-D radiative transfer with solar incidence perpendicular to
the mean wind, i.e., sun from south or north, and permitted that the sun's
zenith angle allows it to illuminate the surface beneath the cloud (

As mentioned previously in Sect.

A stronger background wind profile of 10

The formation of cumulus cloud streets was historically attributed primarily
to dynamics. This work aims to document and quantify the generation of
radiatively induced cloud street structures. To that end we performed 192 LES
simulations with varying parameters (see Table

We find that, in the absence of a horizontal wind, 3-D radiative transfer produces cloud streets perpendicular to the sun's incident direction whereas
the 1-D approximation or constant surface irradiance produce randomly positioned circular clouds.
Our reasoning for this is the geometric position of the cloud's shadow and the corresponding feedback on surface fluxes
which enhances or diminishes convective tendencies (see Fig.

We find that if solar radiation illuminates the surface beneath the cloud, i.e., when the sun is positioned orthogonal to the mean wind field
and the solar zenith angle is larger than 20

Given the results of this study we expect that simulations including shallow cumulus convection will have difficulties producing cloud streets if they employ 1-D radiative transfer solvers or may need unrealistically high wind speeds to excite cloud street organization.

An interesting future topic would be the influence atmospheric heating rates
on the evolution of cloud shapes, particularly the corresponding timescales
and how the introduced asymmetry and shear changes the local flow. Moving
forward, we will examine whether the relationship between radiative transfer and
convective cloud streets also applies to the real world with all the
complexities of a diurnal cycle or static surface heterogeneities combined
with complex wind fields. Several studies perform detailed analyses on the
footprint of static surface heterogeneities in windy conditions, i.e., how
upstream heterogeneities influence the characteristics of boundary layer
dynamics

The UCLA-LES model is publicly available at

To obtain a copy of the TenStream code, please contact one of the authors. This study used the TenStream model at git revision 5e0a2d5.

For the sake of reproducibility we provide the input parameters for the here mentioned UCLA-LES computations along with the TenStream sources.

The authors declare that they have no conflict of interest.

This work was funded by the Federal Ministry of Education and Research (BMBF) through the High Definition Clouds and Precipitation for Climate Prediction (HD(CP)2) project (FKZ: 01LK1208A, 01LK1507D). Many thanks to Cathy Hohenegger, Bjorn Stevens, and the DKRZ, Hamburg, for fruitful discussions and for providing us with the computational resources to conduct our studies. Special thanks are also due to Alois Dirnaichner and the anonymous reviewers who improved this paper by proofreading and commenting on the original manuscript. Edited by: Philip Stier Reviewed by: two anonymous referees