SOLA, 2015, Vol. 11, 75−79, doi:10.2151/sola.2015-019

75

Horizontal Distance of Each Cumulus
and Cloud Broadening Distance Determine Cloud Cover
Yousuke Sato, Yoshiaki Miyamoto, Seiya Nishizawa, Hisashi Yashiro, Yoshiyuki Kajikawa,
Ryuji Yoshida, Tsuyoshi Yamaura, and Hirofumi Tomita
RIKEN Advanced Institute for Computational Science, Kobe, Hyogo, Japan

Abstract
We examine how cloud cover is determined in shallow-cloudareas by using large-eddy simulation with an extremely wide
domain, which covers the transition phase from cumulus-understratocumulus to shallow-cumulus regimes. The relationshipbetween two distances is critical to cloud cover. One characteristic
distance is the horizontal distance between cumulus clouds, andthe other is the broadening distance of anvil-like stratiform cloudat the top of the boundary layer. High cloud cover occurs with along distance of broadening and short distances between cumuli.
In contrast, low cloud cover appears with a short distance ofbroadening and a long distance between cumuli. The contrast of
the two distances is rooted in aerosol amount and the strength of
the surface heat flux. The relationship between these two distances
can be applied to estimating the cloud cover below sharp inversions.
(Citation: Sato, Y., Y. Miyamoto, S. Nishizawa, H. Yashiro,
Y. Kajikawa, R. Yoshida, T. Yamaura, and H. Tomita, 2015: Horizontal distance of each cumulus and cloud broadening distancedetermine cloud cover. SOLA, 11, 75−79, doi:10.2151/sola.2015019.)

1. Introduction
Clouds have a marked effect on the energy budget of the
Earth (Trenberth et al. 2009). Among the several types of cloud,shallow clouds (e.g., stratus, stratocumulus, and shallow cumulus)
play particularly important roles in the energy budget throughradiation processes because they cover a broad area of the Earth(e.g., Randall et al. 1984). In climate prediction, the effects ofclouds on the radiation budget are usually estimated throughthe radiative properties, for example, cloud optical thickness,
effective radius, cloud fraction, cloud cover (e.g., Stephens 2005);
therefore, shallow cloud cover is an important property that mustbe estimated correctly to improve climate prediction. Shallow
clouds have been expressed by parameterizations in global-scalemodels (e.g., Tiedtke 1993; Considine et al. 1997). However,the parameterizations have not been able to simulate the shallow
cloud cover observed from satellite (e.g., Chepfer et al. 2008;
Naud et al. 2010); thus, it is necessary to improve understandingof the characteristics and parameterizations of shallow clouds toreduce uncertainties in climate prediction.
Shallow clouds are often generated off the west coast ofcontinents under a sharp inversion of potential temperature (Klein
and Hartmann 1993), and a transition from high cloud cover tolow cloud cover often appears from the coast to the open oceanarea. During the transition, solid stratus deck, cumulus under stratocumulus, and shallow cumulus are observed from the coast to
the open ocean (Klein et al. 1995). High cloud cover occurs in theformer two regimes, and cloud cover is low in the latter. The cloud
cover below the sharp inversion changes drastically around thetransition from cumulus under stratocumulus to shallow cumulus.
In this paper, we target this phase to investigate the characteristics
Corresponding author: Yousuke Sato, RIKEN Advanced Institute for Computational Science, Kobe, Hyogo, Japan. E-mail: yousuke.sato@riken.jp.
©2015, the Meteorological Society of Japan.

of shallow cloud cover.
In the cumulus-under-stratocumulus regime, anvil-like stratiform clouds broaden horizontally at the top of the boundary layer(e.g., Kropfli et al. 1995). The wide broadening of the clouds
enlarges the area of cloud coverage by stratiform cloud (Stevens
et al. 2001). These results indicate that the extent of this broadening (lifetime of the stratiform cloud) is one of the key scales forcloud cover. Henceforth, we refer to this broadening as “cloudbroadening,” and we refer to the distance of cloud broadening
as “broadening distance.” In addition to cloud broadening froma single cumulus, the existence of multiple cumuli can affect thecloud cover. Cloud cover can be high when broadening clouds
reach neighboring cumuli (Miller and Albrecht 1995). Cloud covercan also be high when individual cumuli are close to each other,even if the distance of cloud broadening is small. This suggeststhat the horizontal distance between cumuli is another key scale
for cloud cover. Henceforth, we refer to this distance as “cumulus
distance.”
To examine shallow cloud, many previous studies have used
the large eddy simulation (LES) model (e.g., Bretherton et al.
1999; Stevens et al. 2001; Stevens et al. 2005; Xue et al. 2008;
Ackerman et al. 2009; Sandu and Stevens 2011; Chung et al.
2012). However, their calculation domains were limited to several
square kilometers due to a lack of computational resources. Thisdomain size is too small to examine the effects of cloud broadening and multiple cumuli on cloud cover change because thehorizontal distance of cloud broadening (i.e., several tens of kilometers; Wood 2012) is larger than the domain size. To investigate
the relationship between these two distances and cloud cover, an
experiment using an LES model with an extremely wide calculation domain covering several tens or hundreds of kilometers is
required. The recent evolution of the supercomputer has facilitatedsuch a large-scale simulation.
The purpose of this study was to (1) simulate the transition
from cumulus under stratocumulus to shallow cumulus in the
single-calculation domain, (2) investigate the relationship between
the two distances, and (3) explore their contribution to determining shallow cloud cover.

2. Methodology
2.1 Model and experimental setup
The model used in this study was a fully compressible Large
Eddy Simulation (LES) model in the Scalable Computing for
Advanced Library and Environment library (SCALE-LES). The
details of the LES model are described at http://scale.aics.riken.
jp/. Subgrid-scale turbulence and microphysical processes were
calculated using a Smagorinsky-type scheme (Scotti et al. 1993;
Brown et al. 1994) and a two-moment bulk cloud microphysicalscheme (Seiki and Nakajima 2014), respectively. We implemented
a simple parameterization of radiative cooling based on an intercomparison study of the Second DYnamics and Chemistry Of
Marine Stratocumulus (DYCOMS-II) first research flight (RF01)(Stevens et al. 2005), which was originally created from the δ-four
stream radiative transfer model of Fu and Liou (1993).
The calculation domain in this study covered 768 × 28 × 2 km3with a horizontal grid interval (Δx and Δy) of 50 m and a verticalinterval (Δz) of 5 m. An open boundary condition was imposedin the x direction, in the regions of 0 < x < 247 km and 545 < x <76Sato et al., Two Distances Determine Shallow Cloud Cover

768 km. The grid spacing in the x direction was stretched in theseregions. In the z direction, a sponge layer was included in z >1200 m in the same manner. In these regions, Rayleigh damping,which enforces the initial values, was applied for all prognostic
variables to avoid artificial wave reflection. The damping coefficient increased linearly to the lateral boundary and model top.
The damping time scale of horizontal and vertical direction was
300 and 10 s, respectively. These time scales were derived fromsensitivity experiments (results not shown). The boundary condition in the y direction was periodic. The horizontally uniform
initial profiles of potential temperature (θ), vapor mixing ratio(qv), and liquid water mixing ratio (ql) were the same as those in
DYCOMS-II RF02 (Ackerman et al. 2009). For the wind profile,a uniform horizontal velocity of 5.0 m s−1 in the x direction was
imposed in the whole calculation domain. The integration timewas 16 h. We mainly discuss the snapshot of t = 15.5 h because
the airmass located at x = 247 km (upwind lateral boundary) was
carried to the downwind lateral boundary by the initial horizontal
velocity at this time. The effects of spin-up are negligible aroundthis time.
We configured the experiment so that the upwind region (x =0 km) was a region of high cloud cover, as is often observed near
the coastal area. In contrast, the downwind area (x = 768 km)
mimicked a region of low cloud cover over the open ocean. To
imitate an increase in sea surface temperature from the coastal
region to the open-ocean region, surface latent heat (LH ) flux, andsurface sensible heat (SH ) flux were increased from upstream todownstream as LH (x) = 93 + 0.1365 x Wm−2 and SH (x) = 15 +0.03062 x Wm−2, respectively. These fluxes at x = 0 were the same
as for DYCOMS-II RF02, which were derived from observations
off the coast of California.

The number concentration of cloud condensation nuclei(CCN) (Nccn) was a constant value during the simulation, Nccn (x) =250 exp(−7.0433 × 10−3 x) cm−3, in which the unit of x is km. ThisCCN setting imitates the decreasing trend of aerosol amount fromthe coastal area to the open ocean. The CCN number concentration at x ~ 330 km was 25 cm−3, which was the threshold between
high- and low cloud cover simulated by a previous study using
SCALE-LES (Sato et al. 2014). A forcing of large-scale subsidence (wLS = Dz) was given for all prognostic variables (ϕ) as−ρwLS ¶¶fz based on Ackerman et al. (2009). The D was set to 1.33 ×
10−6 s−1, the same as that used in Berner et al. (2011), ρ is total
density whose unit is kg m−3, and the unit of z is meters. We
ignored the forcing of the Coriolis effect. The surface flux of
momentum was the same as that in DYCOMS-II RF02. Random
perturbations of θ (0.1 K) and qv (2.5 × 10−6 kg kg−1) were given
below the boundary layer top (~795 m) at t = 0 to drive the turbulence. We expected that the above configurations of surface heat
flux and CCN would simulate the transition from the cumulus-under-stratocumulus regime to the cumulus regime as in the observation.
2.2 Definition of the distance of cloud broadening and thecumulus distance
To analyze the distance of cloud broadening and the cumulus
distance, we divided the whole calculation domain into nine
regions, as shown in Fig. 1. We estimated these two distances ineach region as follows. The distance of cloud broadening wasestimated as the distance to which the anvil-like stratiform cloud
extends from the convection center. The origin of the broadening
distance was taken as the convection center because the stratiform

Fig. 1. Spatial distribution of the liquid water path at (a) t = 5.5 h, (b) t = 7.5 h, (c) t = 10 h, (d) t = 12 h, (e) t = 14 h, and (f) t = 16 h, and x−z slice of (contour)
the liquid water mixing ratio (ql = qc + qr) and (shaded) vertical velocity in (g) region 1 and (h) region 8 at y = 15 km at t = 16 h. The contour lines in (g) and (h)correspond to 0.25, 0.5, 0.75, and 1.0 g kg−1, respectively.

SOLA, 2015, Vol. 11, 75−79, doi:10.2151/sola.2015-019
clouds broaden horizontally around the top of each cumulus. The
convection center was defined as the point at which the absolutevalue of vertical velocity (w) at z = 500 m and t = 15.5 h waslarger than 3σ, in which σ is the standard deviation of w to thehorizontally averaged w. Because several convection centers wereextracted in each region, we created the mean radius–height distribution of ql for each region. The ending point of cloud broadening
was defined as the point at which ql is smaller than the thresholdvalue, ql, t (= 2.2 × 10−4 kg kg−1). To calculate ql, t , we assumed thatthe liquid water mixing ratio increased linearly with height (i.e.,the cloud was adiabatic) and that the cloud geometrical thickness
was 300 m, which was the initial geometrical thickness of clouds
in the LES simulation.
The LES reproduced the transition from the closed cell structure in the cumulus-under-stratocumulus regime to the open cellstructure in the shallow cumulus regime. The cumulus distancewas determined as the distance between cells. The distance wasestimated from the spectra of ql averaged over 5 min around t =15.5 h. We calculated the spectra at z = 500, 600, and 700 m by
the Fourier transformation. The cumulus distance was definedas the average of the wavelength of peak power among the threeheights. The details of the methods are shown in Supplemental
material.

3. Results and discussion
Figure 1 shows the temporal evolution of the liquid water pathfrom t = 5.5 h to t = 16 h and an x‒z slice of ql and w in regions
1 (270 km < x < 300 km) and 8 (480 km < x < 510 km) at y = 15 km
and t = 16 h. The contrast in cloud cover between the upwind anddownwind regions becomes clear as the integration time increases.
The cloud cover is high in the upwind regions (i.e., regions 1, 2,
and 3), where a weak surface flux and large CCN concentration
were given. In contrast, low cloud cover is apparent in the downwind regions (i.e., from regions 6 to 9), with strong surface flux
and low CCN concentration. The x–z slice indicates that cumuli
are generated in both the high- and low cloud cover areas. In thehigh cloud cover regions, stratiform cloud exists at the top of theboundary layer (Fig. 1g), whereas “shallow cumulus” dominatesin the low cloud cover region (Fig. 1h). The cloud top height,
which corresponds to the boundary layer top, in regions 1 and 8 isabout 840 and 910 m, respectively. The difference in the cloud top
height between high and low cloud cover regions is smaller thanthat observed in the in situ measurements. One of the reasons forthe difference would be the horizontally uniform initial condition.
An experiment using the initial condition, in which the top of
the boundary layer gradually increases to the downwind region,

77

would reproduce a transition that is more realistic. However, weused horizontally uniform initial conditions to focus on the effectsof CCN and surface heat flux in this study. We will conduct experiments using more realistic experimental setups in the future.
Figure 2 shows the vertical profiles of the total water mixing
ratio (qt = ql + qv), ql , liquid water potential temperature (θl),
precipitation flux, and third moment of grid resolved w′ (= w −−, in which w− is the horizontal average of w) averaged duringw
t = 15.5 to 16 h. In the high cloud cover regions, both qt and θlhave a small vertical gradient below the top of the boundary
layer. The precipitation flux at the surface is about 1 mm day−1.
The third moment of w′ is positive, which indicates the existenceof strong upward motion within a narrow area. These results
indicate that cumulus-under-stratocumulus driven by the surface
flux is successfully simulated. In the low cloud cover regions, theprecipitation flux is larger than that in the high cloud cover region.
Heavy precipitation removes liquid water from the atmosphere.
Consequently, the peak value of ql is small. The differences in
qt and θl between the ground and the top of the boundary layer
are larger than those in the high cloud cover regions. It is worth
simultaneously reproducing these aspects in a single calculation
domain including the transition from the cumulus-under-stratocumulus regime to the shallow cumulus regime.
The horizontal wind field indicates that airmasses elevatedby the updraft in the convection center diverge at the top of theboundary layer irrespective of the region (figure not shown).
However, the distance of stratiform cloud broadening is wide onlyin the high cloud cover regions. The differences in the distance ineach region can be interpreted as follows. In the low cloud coverregions, strong surface flux induces active convection and the low
CCN concentration leads to fast conversion from cloud droplets toraindrops. Both effects contribute to generate strong precipitation.
The strong precipitation removes liquid water from cumuli, andcloud broadening is confined to a narrow area. On the other hand,in the high cloud cover regions, convection is less active due tothe weak surface flux. High CCN concentration suppresses the
autoconversion process. They lead to weak precipitation andmaintain liquid water in the cloud layer longer. Consequently,
stratiform clouds tend to broaden more at the top of the boundary
layer.
Figure 3 shows the distance of the cloud broadening, half ofthe cumulus distance, and cloud cover averaged over each region.
The cumulus distance increases from the upwind region to thedownwind region. The discontinuity of the distance from regions 5
to 6 occurs because the long-wavelength resolution is insufficient
for resolving in the Fourier transform analysis. In contrast, the distance of the cloud broadening decreases from upwind to the downwind region. The distance in regions 1, 2, and 3 is not plotted. In

Fig. 2. Horizontally averaged vertical profile of (a) liquid water potential temperature (θl) (dot-dashed), total water mixing ratio (qt = qc + qr + qv) (solid),
and tenfold liquid water mixing ratio (ql) (dashed); (b) precipitation flux of cloudy columns, the liquid water path for which is larger than 20 g m−2, and (c)third moment of w′ normalized by w′ variance to the power of 1.5 (áw′w′w′ñ/áw′w′ñ1.5), averaged during the last 30 min (i.e., from t = 15.5 h to t = 16 h). To
calculate the horizontally and temporally averaged vertical profile model outputs, data with 1-min intervals were used.

78

Sato et al., Two Distances Determine Shallow Cloud CoverFig. 3. The distance of cloud broadening (triangle), half-distance between
cumuli (circle), and cloud cover (square) derived from the LES model
result.

these regions, cloud broadens more widely than in other regions,and the distance of the cloud broadening is not explicitly determined because of the contamination of several clouds. However,analyses performed by using an ideal parcel model demonstratethat the distance of the cloud broadening increases on the order ofregion 3 < region 2 < region 1, and that the broadening distanceexceeds or is comparable to half the cumulus distance in regions 1
and 2 (as shown in the supplemental material). Thus, the distanceof the cloud broadening is longer than the cumulus distance in the
upwind region, and vice versa in the downwind region.
In the upwind regions, the stratiform clouds broaden widely
and the cumulus distance is short. In this case, the stratiform
clouds can reach the stratiform clouds from neighboring cumuli
before water droplets fall or are evaporated. Therefore, the cloud
cover tends to be high (i.e., regional average of cloud coveris above 0.7). In the downwind regions, the cloud broadening
distance is shorter than the cumulus distance. In this case, thestratiform cloud disappears until it extends to neighboring clouds.
As a result, the cloud cover tends to be low (i.e., smaller than 0.5).
Thus, the relationship between the distance of cloud broadening
and the cumulus distance determines the cloud cover.

4. Concluding remarks and future work
We clarified that the relationship between the broadening
distance of anvil-like stratiform clouds and the horizontal distance
between cumuli determines shallow cloud cover. We clarified thisby using a high-resolution LES model with an extremely wide
domain. These two distances are important for determining shallow cloud cover in the transition phase from cumulus under stratocumulus to shallow cumulus. Figure 4 is a conceptual illustrationof our interpretation of the relationship between cloud cover andthe two distances. In the cumulus-under-stratocumulus regime, thedistance between cumuli is smaller than the broadening distanceof stratiform clouds at the top of the boundary layer. Each stratiform cloud can extend to its neighboring clouds. High cloud cover
over 0.7 appears in this case (Fig. 4a). In the shallow-cumulus
regime, a cloud cannot extend to the next cloud for two reasons:(1) the long distance between cumuli, and (2) the small extent
of cloud broadening. In this case, cloud cover is low (Fig. 4b).
Thus, the relationship between the distance between cumuli andthe broadening distance of the stratiform clouds determines theshallow cloud cover.
Long (short) broadening distance of the anvil-like stratiform
clouds occurs with weak (strong) surface heat flux and large (small)Fig. 4. Schematic illustration of an overhead and a side view of (a) thehigh cloud cover (cumulus-under-stratocumulus) region and (b) the low
cloud cover (shallow-cumulus) region.

amounts of aerosol. In contrast, long (short) distance between
cumuli appears when the surface heat flux and aerosol amounts
are strong and small (weak and large), respectively. We can apply
the relationship between the two distances to estimate shallow
cloud cover in global-scale models with coarse grid resolution.
This result contributes to improvement of the parameterizationsof shallow clouds and to reduction of the uncertainties of climate
prediction caused by shallow clouds. For actual improvementof shallow cloud parameterization, it is a key to incorporate thedependency of cloud cover to the cloud broadening distance anddistance between cumuli into the parameterization scheme. We
will attempt to incorporate it in the near future.
In this study, the contrast of these distances between high- andlow cloud cover regions was generated by the differences of CCN
and surface flux. Sensitivity experiments with separately changing
CCN concentrations and surface heat flux are required to quantitatively evaluate the contribution of each factor.
In addition to the sensitivity experiment, an experiment covering a large calculation domain for both the x and y directions
is also required, because the cumulus distance in the downwind
region (e.g., regions 8 and 9) would be limited by the domain sizein the y direction. To make our suggestion more robust, we willconduct these experiments in the near future.

Acknowledgements
Part of the results is obtained by the K computer at the RIKEN
Advanced Institute for Computational Science. (AICS teamresource, and resource from proposal number hp140046). Figure
1 was created by Grid Analysis and Display System (GrADS).
Figures 2 and 3 were created by the Gnuplot. The authors would
like to thank to S. A. Adachi, our colleagues, and anonymous
reviewers for fruitful discussions.

SOLA, 2015, Vol. 11, 75−79, doi:10.2151/sola.2015-019

Supplement
Supplement 1 indicates the sensitivity experiment of aerosol
amount to the cloud broadening distances using a parcel model.
Supplement 2 describes the method to estimate the distance ofcloud broadening and cumulus distance.

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Manuscript received 10 March 2015, accepted 9 May 2015
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