Introduction
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.
presented some early pictures of cloud
streets from rocket and aircraft instruments. Descriptions of cloud
streets date back as far as ,
who gave a detailed description of a long-distance glider flight, and
, who investigated the soaring patterns of
seagulls. Scientific literature documenting the existence and
explaining the prerequisites for the formation of cloud streets is
plentiful. , ,
, and provide a thorough review
of past observations and theoretical frameworks. The above literature
suggests two prominent effects to be responsible for such vortices,
namely inflection-point instabilities (e.g., from cross-roll wind
components in a Ekman boundary layer) and thermal
instabilities (buoyancy driven). Purely buoyancy-driven convection,
without any horizontal wind or shear, produces a random pattern of
updrafts. Introducing a linear wind shear, the convective elements
become stretched out along-wind. Following
, “At some point (increasing
the wind speed/shear) the shearing becomes strong enough so that
dynamic instability may interact with buoyancy to produce a hybrid
roll vortex/convective cell mechanism. As the shear becomes
stronger, shearing instability or roll vortex motion is
predominant.” In this work, we will focus on the radiative impact,
the most prominent effect of which being cloud shadows which modulate
surface fluxes and consequently build up surface heterogeneities.
These induced surface heterogeneities are the link between radiative
transfer and buoyancy-driven convection . Our focus is therefore more
on buoyancy-driven roll vortices in a linear shear
environment and less so on inflection-point
instabilities. To that end, we omit cross-wind shear by neglecting
Coriolis force and correspondingly neglect the horizontal turning of
the wind as it would be the case in an Ekman boundary layer.
Several studies investigated the role of surface fluxes on the
development of such boundary layer circulations. Here the literature
distinguishes between static heterogeneities – i.e., differences in
land-surface parameters such as vegetation, surface roughness or
surface albedo – and dynamic heterogeneities, such as moisture budget or
temperature fluctuations. Static heterogeneities in conjunction with
shallow cumulus clouds and cloud streets have been examined for
example by , ,
and . In contrast, ,
, , and
investigated the influence of dynamic heterogeneities in surface
shading and even considered 3-D radiative effects (i.e., the
displacement of the shadow). However, they did not include a
realistic surface model but rather adjusted the surface fluxes
instantaneously. This does not allow us to study the timescales on which
radiation and dynamics may interact. Others investigated the influence
of shading coupled to an interactive surface
model .
However, one particularly questionable issue with those studies was
the application of 1-D radiative transfer solvers, which are known to
introduce large spatial error in surface heating
rates .
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 briefly outlines the LES model, explains the
setup of the simulations, and introduces a scalar metric to quantify
the organization in cloud streets. In Sect. we
interpret the magnitude of cloud street formations in the parameter
space spanning surface properties, background wind speeds, and the
sun's angles. Section finally summarizes key
findings of the parameter study.
Methods and experiments
LES model
The LES were performed with the UCLA-LES
model. A description and details of the LES model can be found
in . The land-surface model included in
the UCLA-LES follows the implementation of the Dutch Atmospheric
Large-Eddy Simulation code . The
simulations presented here use warm microphysics formulated in
, in which the formation of rain is turned off to
prevent any further complications such as cold pool dynamics. The
radiative transfer calculations are performed with the TenStream
package , which includes a 1-D Schwarzschild (thermal
only), a δ-Eddington two-stream (solar and thermal), and
the 3-D TenStream (solar and thermal) solver.
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 PETSc; framework. In
, we extensively validated the TenStream
by comparison with the exact Monte Carlo code MYSTIC .
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 and, more
importantly, because it does not cause any asymmetries in the heating or
cooling pattern.
The spectral integration is performed using the correlated k method following .
The coupling of the TenStream solver to the UCLA-LES follows the description in .
One exception is the Monte Carlo spectral
integration ,
which we do not use because of limitations with regards to computations involving
interactive surface models .
Model experiment setup
The base setup of the UCLA-LES simulates a
domain of 50km×50 km with a horizontal grid length
of 100 and 50 m vertically. The simulations start from a well-mixed
initial background profile with a constant virtual potential temperature
(292 K) in the lower 700 m and increases by
+6 Kkm-1 above. Water vapor near the surface amounts to
9.5 gkg-1, decreasing with -1.3 gkg-1km-1.
The surface model has four layers which have the same initial temperature of
291 K, are stripped of vegetation, and are soaking wet (saturated
clay with 30 % water volume mixing ratio). The surface albedo for
shortwave radiation is set to 7 %. The land-surface model solves the
surface energy balance equation for an imaginary skin layer which often has
no heat capacity. We vary the heat capacity of the surface skin layer
Cskin to mimic a water layer covering the surface. The heat
capacities are chosen to be representative for situations ranging from
continental land surfaces to a well-mixed ocean. The thickness of this
imaginary water layer lends the simulations and the radiative transfer a
memory on the surface. All other parameters of the land-surface model such as
surface resistances or roughness lengths for momentum or heat are kept
constant in order to focus on these memory effects.
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
(Cskin), the background wind (u, i.e., west winds), the
solar zenith (θ) and azimuth (φ) angle, and
different radiative transfer approximations (see
Table ). The coupling of radiative transfer to the
land-surface model is realized in four ways. We either compute the net
surface irradiance Qnet with a 1-D δ-Eddington two-stream
solver or employ the 3-D TenStream solver, with two azimuth angles.
Additionally, we conducted experiments in which Qnet is set to a
prescribed constant value (spatial and temporal average of the surface
irradiance of the corresponding 1-D simulation).
Parameter space for the LES simulations: the mean west wind (u), the solar azimuth
and zenith angle (φ, θ), the surface skin heat capacity (Cskin) as a water column
equivalent,
and three settings for the computation of net radiative surface fluxes (Qnet).
The radiative transfer computations are done either with a 1-D δ-Eddington two-stream method,
with the 3-D TenStream solver or simulations with constant mean net irradiance.
Variations of the solar azimuth φ are only applied for 3-D radiative transfer.
Values of Qnet in case of simulations without interactive radiative transfer were set to
the mean surface irradiance of the 1-D simulations.
In total there are 192 simulations.
u
0, 5, 10
m s-1
φ
90, 180
∘
θ
20, 40, 60, 75
∘
Cskin
1, 10, 100, 1000
cm
Qnet
constant, 1-D, 3-D
Virtual photograph of LES simulations at a cruising altitude of 15 km.
Top panel: cloud formation of a simulation driven by 3-D radiation (TenStream with sun in the east, i.e., right; φ=90∘).
Lower panel: cloud formation of a simulation which was performed with 1-D radiation (two stream).
The specific model setup is the same as referenced in Fig. , i.e., no background wind and a continental land surface.
The simulations differ with respect to cloud size distributions and the organization in cloud streets,
the cloud fraction though is the same (27 %).
The visualization was performed with a physically correct
rendering with MYSTIC MonteCarlo solver in libRadtran;.
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 % typical for shallow cumulus convection;
e.g., . Most simulations produce clouds after about 1 h and show an increase in cloud cover up to and beyond 50 % in the
first 6 h. Simulations with low positioned sun took longer and were hence
run for a longer period of 12 h. Our analysis is mostly independent of the
specific, individual course of each simulation as we find robust signals
across the various groups of parameters. The interested reader, however, is
referred to Sect. 3.2 for further details (e.g., liquid
water path, cloud fraction, mean cloud size distribution) on the evolution of
a typical simulation.
Figure shows a photo rendering of the LES cloud field
for two simulations with differing options for the radiative transfer solver.
In the top panel, 3-D radiative transfer is considered with the sun
positioned in the east (zenith θ=60∘); in the bottom
panel the 1-D solver is applied where the shadow is by definition always
cast directly beneath the clouds. In the former the organization in cloud
streets perpendicular to the sun's incident angle is evident whereas the
latter does not seem to organize in any way. Figure
presents the liquid water content and the surface heat flux for the same two
simulations plus one 3-D simulation where the sun is in the south. This time
we look at volume rendered liquid water content and surface heat fluxes for
the full domain. In Figs. and , simulations
with 3-D radiative transfer show organization in cloud streets with length
scales of up to 20 km, perpendicular to the sun's incident angle. We can
clearly identify these coherent cloud structures with the naked eye. However,
to solidify our claims, we present a quantitative measure for the cloud
distribution.
Volume rendered liquid water mixing ratio (LWC) and surface latent and sensible heat flux (L+H) for three simulations.
The cloud scene of the left and middle panel have already been presented in Fig. .
In the left panel, radiative transfer calculations are performed with the TenStream solver and the sun is positioned in the east (φ=90∘).
The simulation in the middle panel is driven by a 1-D two-stream solver,
whereas the right panel simulation also employs the TenStream solver but with the sun shining from the south (φ=180∘).
The solar zenith angle is in all three simulations θ=60∘, the mean background wind speed is
0 ms-1,
and the surface skin heat capacity is set to an equivalent of 1 cm water depth (representative for continental land surface).
The snapshot shows the simulations after 3 h model time at a cloud fraction of 27 %.
Volume rendered plots were created with VISIT .
The panels exemplarily depict the autocorrelation coefficients of the cloud distribution in the
three simulations presented in Fig. .
The upper panels show the normalized 2-D autocorrelation coefficient with two intersection lines in the
north–south (vertical) and the east–west (horizontal) direction.
The markers pinpoint the distance in N–S (red) and E–W (blue) direction, where the
autocorrelation coefficient reaches a zero value
and therefore denotes the distance where it becomes less likely to find a cloud.
The lower panels follow the black line cuts and further describe the two transects depicting the correlation
function's root points from which we derive the correlation ratio.
Simulations with 3-D radiative transfer (a, c, d, f) show, in
contrast to 1-D radiative transfer (b, e), a distinct asymmetry perpendicular to the solar incidence angle.
The organization of clouds and their alignment is represented by values of the correlation ratio Rc
that are less than or greater than 1 for alignment along the y or x axis, respectively.
Correlation ratio
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 (LWP>0).
We then use the normalized 2-D auto correlation function of the cloud mask to analyze the spatial distribution
of cloudy and clear-sky patches.
The three upper panels of Fig. illustrate the 2-D correlation coefficient for the
three simulations presented in Fig. .
Next, we use the transects of the correlation coefficient along the x and y axis (indicated as a black line).
The lower panels in Fig. show the linearly interpolated
line cuts of the discrete autocorrelation function.
The location where the normalized correlation coefficients goes to zero defines the mean distance from a
cloudy pixel where it is more likely to find a clear-sky pixel.
We use the north–south and the east–west distances dNS and
dEW, respectively, to define the correlation ratio
Rc as
Rc=dNS/dEW.
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 see, e.g.,.
At the same time we hypothesize that radiatively induced effects will be
either along or perpendicular to the incident solar beam, i.e., follow the
surface inhomogeneities see, e.g.,. The two
major directions should therefore capture the dominant effects of dynamically
and radiatively induced cloud dynamics.
The correlation ratio reduces a cloud field snapshot into a scalar which yields Rc=1 for symmetrically distributed clouds,
Rc<1 for organized cloud fields along the north–south direction, and Rc>1 if cloud features are arranged east to west.
Results and discussion
As an example for the evolution of convective organization,
Fig. illustrates the correlation ratio
Rc over time for one of the earlier introduced
simulations (depicted in Fig. ). In the simulation, first
cumulus clouds occur after about half an hour with the clouds being oriented
randomly. The resulting shadowing of these clouds introduces surface
temperature heterogeneities which in turn act on the flow through changes in
latent and sensible heat fluxes. About 1 h after the onset of clouds, we
find the convection to organize into bands from north to south (Rc<1). To further highlight the involved timescales, we restart the
simulation from 2 h onwards with a 90∘ rotated sun and find that
convection changes from a north to south orientation to bands from east to
west in approximately 1 h. This example yields a 1/e timescale for
convective organization of half an hour. This timescale will, however, depend
on several factors – most certainly on the solar zenith angle and the surface
heat capacity, which determine the timescales at which surface heterogeneities
can be introduced.
To reduce the information of convective organization into a single scalar
value, we compute the mean correlation ratio Rc‾ as the
arithmetic mean of Rc calculated at all output time steps (every
5 min) where the cloud fraction is between 10 and 50 %. The aim
of the cloud fraction filtering is to allow a comparison of simulations with
varying temporal evolutions due to different energy inputs (solar zenith
angles) and heat sinks (Cskin).
Time evolution of the correlation ratio Rc (e.g., as in Fig. ).
The solar zenith angle is θ=40∘; there is no mean background wind speed (u=0ms-1)
and the surface skin heat capacity is set to an equivalent of 1 cm water depth (representative for continental land surface).
The radiative transfer is computed with the TenStream solver and the sun is positioned in the east (φ=90∘).
The first shallow cumulus clouds develop with a random orientation (Rc=1).
The radiative response (i.e., surface shadows) changes the organization of convection to bands from north to south Rc<1 in about 1 h.
Additionally, to examine the timescales of radiatively induced organization of convection, we perform a
restart of the simulation with the sun positioned in the south (φ=180∘).
Once the sun is rotated, it takes the simulation again about 1 h to change the orientation of convection into bands from east to west (Rc>1).
Correlation ratio for simulations with a variable surface skin heat capacity (Cskin),
solar zenith angle (θ), and three wind velocities (panels a to c).
Shaded areas group simulations with a constant Cskin according to their respective
values, while the horizontal spread inside a group is merely to separate data points visually.
Wind component u is always from west to east while the individual markers denote simulations
where the surface irradiance Qnet is set to a constant value or is computed
either with a 1-D two-stream solver or with the 3-D TenStream, where the sun is either shining
from the south (180∘) or from the east (90∘).
The correlation ratio is averaged over all time steps where the cloud fraction is between 10 and 50 %.
The basis for the following analysis is the evaluation of mean correlation
ratios as a function of the five free parameters, u,φ,θ,
and
Cskin, and the radiative transfer solver (for details, see
Table ). Figure shows the mean
correlation ratio Rc‾ for each of the 192
simulations. The three panels show results for different horizontal
background wind speeds: 0, 5, and 10 ms-1. Each panel's
x axis is divided into four categories for the surface skin heat capacity
and the color bar describes the solar zenith angle. Additionally, four
different markers denote the various options concerning the radiative
transfer solvers while the rotation of triangle markers (3-D RT) denotes the
azimuth angle.
We will first focus on panel a, which shows the correlation ratios for the
simulations without any background wind and later move on to simulations with wind.
In other words, we start by focusing on purely radiative effects and their influence on the
organization of convection and eventually add dynamically induced cloud streets to the discussion.
Without wind: u=0ms-1
The three simulations presented in Sect. are located on panel
a of Fig. with a surface skin heat capacity
equivalent of 1 cm water column (furthest to the left-most shaded
area). Correspondingly, the markers for 3-D radiative transfer are shown as
triangle markers in light blue (zenith angle of 60∘). The upward
triangle represents the sun positioned in the south and yields a mean
correlation ratio of 1.5 (rolls produced west to east). In contrast, the
left rotated triangle presents a sun positioned in the east and shows a mean
correlation ratio of 0.7 (rolls produced south to north). The simulation with
1-D radiative transfer is presented with a diamond shaped marker and shows a
mean correlation ratio of ≈1 (no organization).
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 (a).
In contrast, pixels that are surrounded by sun-lit patches, e.g., (b), are likely to show enhanced convective motion.
This pattern favors the organization of cumulus convection in stripes perpendicular to the sun's incident.
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 illustrates the concept for a single cloud and the
resulting pattern for surface fluxes. The schematic only constrains
convection to be less favorable on the shadowy side but it does not
necessarily favor the perpendicular directions over the direction towards the
sun. However, if a cloud would evolve on the sun-facing side, the resulting
shadow would in turn lead to a faster dissipation of the initial cloud and is
thereby an unstable environment for persistent cloud patterns. Following
this, we expect the convection to occur favorably perpendicular to the sun's
incident angle purely from geometric reasoning.
It is also clear from the horizontal axis of Fig. that higher
heat capacities lead to less pronounced formations of cloud streets, which is
to be expected because it weakens the radiative impact and consequently
reduces the dynamically induced surface heterogeneities. However, though weaker,
we still find an impact in 3-D radiative transfer simulations even for a
water column equivalent of 10 m. In this case, with such high
surface heat capacities, the simulations do not exhibit any variability in
surface fluxes and radiation solely acts through atmospheric heating. We also
find this behavior in simulations with a fixed sea surface
temperature or with constant latent and sensible surface fluxes (not shown).
In Fig. 3.22, we show that the asymmetric heating of
the cloud sides or similarly in for displaced surface
shadows introduces a secondary
circulation by lifting the sun-lit side and enhancing subsidence on the
shadowy side. This asymmetry introduces a wind shear component consisting of
a horizontal wind away from the sun at cloud height and towards the sun near
the surface. Given that the effects of atmospheric heating is much smaller
and happens on longer timescales compared to the surface feedback, we will
explore this
interpretation at another time.
Simulations with 1-D radiative transfer or constant Qnet do not produce cloud
streets, which is reflected by correlation ratios Rc≈1.
If we apply the same geometric reasoning from Fig. for these simulations,
where the shadow is either directly beneath the cloud or with no heterogeneity at all,
it is clear that there can be no preferential direction for convective organization.
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.
Medium wind: u=5ms-1
Figure b presents the correlation ratios for
simulations with a horizontal background wind of 5 ms-1. If we
first shift our attention to the simulations with constant surface irradiance
Qnet (round markers), it is evident that the introduction of a
mean wind profile leads to the formation of cloud streets (R‾c>1), irrespective of radiatively induced surface
heterogeneities. The fact that we also find cloud streets without any
radiation is not surprising and is expected from the literature on the
formation of buoyancy-driven cloud streets (introduced in Sect. ). Furthermore, we find a
spread in the development of cloud streets depending on the magnitude of the
prescribed Qnet, with correlation ratios ranging from 1 to 5.
The fact that buoyancy-driven cloud street organization is favored in
slightly unstable conditions (low sun) compared to stronger
instabilities (high sun) agrees well with
observations e.g.,.
So far we have discussed only the simulations with constant Qnet.
When we look at land surfaces that are coupled to radiative transfer calculations (1-D and 3-D markers in Fig. ),
we find that radiative heating may either enhance the organization (R‾c up to 13) or counteract it (R‾c<1).
The following paragraph examines the superposition of dynamically and radiatively induced tendencies to organize the clouds.
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 R‾c≈1. Similarly, 3-D radiation where the azimuth is in the same
direction as the wind (here east, φ=90∘, left-rotated
markers) also inhibits the formation of cloud streets or may even oppose the
dynamically induced organization and produce correlation ratios R‾c<1.
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 (θ>20∘), we find that the radiative tendency to organize the clouds
amplifies the dynamical one. This synergistic behavior results in
correlation ratios R‾c between 5 and 13.
As mentioned previously in Sect. , we again find a generally diminished
influence of surface radiative heating in simulations with larger surface heat capacities.
Strong wind: u=10ms-1
A stronger background wind profile of 10 ms-1 principally shows
similar behavior as the case that was presented with medium wind speeds (see
panel c of Fig. ). The mean correlation ratios of purely
dynamically induced cloud streets (simulations with constant
Qnet, i.e., circle markers) cover an increasingly large range of
ratios from 2 to 14. Strong solar radiation coupled with small surface
heat capacities still manage to efficiently suppress the formation of cloud
streets (i.e., R‾c consistently smaller than purely
dynamic values), whereas illumination perpendicular to the wind direction
(φ=180 and θ>20∘) again greatly amplifies the
occurrence of cloud streets. This is surprising when we consider that
horizontal wind should indeed smooth out the impact of radiative surface
heating. , for example, also suggest that wind speeds
of 10 ms-1 may decouple the effects of dynamically induced
surface heterogeneities from the evolution of clouds. However, when we consider
that the dynamically induced cloud streets have typical length scales of
50 km , then, as far as radiative heating at the
surface is concerned, the cloud appears to be standing still. In other words,
when a dynamically induced cloud feature aligns in such a way that it
persistently shades a surface region for an extended period of time, we
expect that the radiatively induced surface heterogeneities in turn interact
with the flow. It is this intricate linkage between dynamically induced cloud
structures and (3-D) radiative transfer that may enable or prohibit the
formation of cloud streets.
Summary and conclusions
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 ) for
the horizontal wind speed, the surface heat capacity, the solar zenith and
azimuth angle, and different radiative transfer solvers
(Sect. ). As a quantitative measure for the
development of cloud streets, we introduce a simple algorithm using the
autocorrelation function on the cloud mask
(Sect. ), which provides a scalar quantity for the
degree of organization in cloud streets and the alignment along the cardinal
directions.
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. for details).
While the simulations indicate that there exists an influence due to atmospheric heating rates,
we find that the differences between 1-D and 3-D radiation stem predominantly from surface heating,
i.e., the horizontal displacement of cloud shadows.
Furthermore, with increasing horizontal wind speeds of 5 or 10 ms-1, we observe the
development of dynamically induced cloud streets.
The dynamical formation of cloud streets is not particularly surprising, but it does lead to the questions of if and
how radiative transfer interacts with the organization of convection.
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∘,
the cloud-radiative feedback may significantly enhance the tendency to organize in cloud streets.
In contrast, in the case of the 1-D approximation (or also 3-D if the sun is aligned with the mean wind),
the tendency to organize in cloud streets is weaker or even prohibited because the shadow is cast directly beneath the cloud, weakening the cloud's updraft.
The timescale of the convective organization through radiative transfer is found to happen on the order of 1 h (see Fig. ).
The radiative feedback, which creates surface heterogeneities, is generally diminished for large surface heat capacities.
We therefore expect radiative feedbacks to be strongest over land surfaces and less so over the ocean.
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 e.g.,.
It may very well be worth revisiting their analyses and particularly focus on
static and dynamic (radiative) heterogeneities. A promising start is an
analysis of the simulations within the
HDCP2 project , which will allow us to test
the interpretations proposed here in a more realistic setup.