Sato et al. Progress in Earth and Planetary Science (2015) 2:23
DOI 10.1186/s40645-015-0053-6

RESEARCH ARTICLE

Open Access

Impacts of cloud microphysics on tradewind cumulus: which cloud microphysics
processes contribute to the diversity in alarge eddy simulation?
Yousuke Sato*, Seiya Nishizawa, Hisashi Yashiro, Yoshiaki Miyamoto, Yoshiyuki Kajikawa and Hirofumi Tomita

Abstract
This study investigated the impact of several cloud microphysical schemes on the trade wind cumulus in the large
eddy simulation model. To highlight the differences due to the cloud microphysical component, we developed afully compressible large eddy simulation model, which excluded the implicit scheme and approximations as muchas possible. The three microphysical schemes, the one-moment bulk, two-moment bulk, and spectral bin schemes
were used for sensitivity experiments in which the other components were fixed. Our new large eddy simulation
model using a spectral bin scheme successfully reproduced trade wind cumuli, and reliable model performancewas confirmed. Results of the sensitivity experiments indicated that precipitation simulated by the one-momentbulk scheme started earlier, and its total amount was larger than that of the other models. By contrast, precipitation
simulated by the two-moment scheme started late, and its total amount was small. These results support those of aprevious study. The analyses revealed that the expression of two processes, (1) the generation of cloud particles
and (2) the conversion from small droplets to raindrops, were crucial to the results. The fast conversion from cloudto rain and the large amount of newly generated cloud particles at the cloud base led to evaporative cooling andsubsequent stabilization in the sub-cloud layer. The latent heat released at higher layers by the condensation ofcloud particles resulted in the development of the boundary layer top height.
Keywords: Large eddy simulation; Shallow clouds

BackgroundThe effect of clouds is one of the most uncertain factors
in climate projection and numerical weather prediction.
Shallow clouds (e.g., stratus, stratocumulus, shallow cumulus) play particularly important roles in the energy
budget of the earth through radiation process because
they cover a broad area of the earth (e.g., Randall et al.
1984). The 5th Intergovernmental Panel on Climate
Change (IPCC) report suggested that the uncertainties
with regards to shallow clouds should be reduced for reliable assessments (IPCC AR5, Stocker et al. 2013).
In global scale models (e.g., general circulation model(GCM)) and regional models with coarse grid spacing,shallow clouds are usually expressed by parameterizations* Correspondence: yousuke.sato@riken.jp
RIKEN Advanced Institute for Computational Science, 7-1-26
Minatojima-Minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan(e.g., Tiedtke 1993; Considine et al. 1997; Kain 2004), butthese parameterizations have not been able to effectively
simulate the shallow cloud cover observed from satellites(e.g., Chepfer et al. 2008; Naud et al. 2010).
To improve the expression of shallow cloud, the results of large eddy simulation (LES) models have beenutilized. For example, Bretherton and Park (2009) used
the results of an LES model to develop a new moist turbulent parameterization. Suzuki et al. (2004) and Posselt
and Lohmann (2008) introduced an autoconversion
parameterization that was typically used in an LES
model (Khairoutdinov and Kogan 2000) into a global
scale model. Many studies using LES models have been
conducted to determine the characteristics of shallow
cloud and improve large-scale modeling (e.g., Wang andFeingold 2009; Xue et al. 2008, Savic-Jovcic and Stevens
2008, Yamaguchi and Randall 2012). However, the© 2015 Sato et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to
the Creative Commons license, and indicate if changes were made.

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

results of LES models are diverse, as indicated by several
LES model intercomparison studies targeting shallow
cloud (e.g., Stevens et al. 2005; Ackerman et al. 2009;van Zanten et al. 2011; Siebesma et al. 2003). It has beensuggested that the difference in the microphysical schemes
used in LES models is one of the reasons for the diversity
in the results (Ackerman et al. 2009; van Zanten et al.
2011). However, it is difficult to investigate the exact effectof the different cloud microphysical schemes (i.e., the effect on the results that comes from changing the cloud
microphysical scheme while keeping all other components
fixed), because each LES model uses a different scheme,
not only in cloud microphysics but also many other components (e.g., governing equation, turbulent scheme, advection scheme, and others). Thus, it is also difficult todetermine which microphysical processes contribute mostto the diversity of the LES results. Sensitivity experiments,
which change only the cloud microphysical scheme, arerequired to better understand the exact effects of thecloud microphysical scheme.
The kinematic driver (KiD) model developed by Shipway
and Hill (2012) enables us to conduct sensitivity simulations by changing only the cloud microphysics. Using
KiD, we can consider the exact effects of the differencesin cloud microphysical schemes. However, KiD ignores
feedbacks to the atmosphere, even though the feedbacks of microphysics can affect the microphysicalproperties of shallow clouds and the turbulent structure of the boundary layer (e.g., Stevens et al. 1998;
Wang et al. 2010). It is necessary to consider the feedback of microphysical processes on the dynamics when
determining which process causes the diversity in the
results of LES models. We should use the model that
excludes approximation and implicit schemes as muchas possible, because these features also affect the cloud
microphysical properties simulated by the model.
This study developed a model that satisfies these requirements. Using the model, we attempted to reproduce the diversity in the results of the LES model usedin van Zanten et al. (2011) and to determine impact ofthe various cloud microphysical schemes. Three types ofcloud microphysical schemes (one-moment bulk, twomoment bulk, and spectral bin schemes) were consideredin this study, because these three schemes have been usedin previous intercomparison studies.
Of the several types of shallow cloud, we focused on
trade wind cumulus because their variability in the results of LES models was larger than that of other typesof shallow clouds. For example, the variability of surface
precipitation in an intercomparison of trade wind cumulus (van Zanten et al. 2011) was larger than that in anintercomparison of stratocumulus (Ackerman et al.
2009). van Zanten et al. (2011) proposed that one of thereasons for the diversity in the microphysical properties

Page 2 of 16

of trade wind cumuli was the different cloud microphysical models. They interpreted that a simple (one-momentbulk) microphysical scheme produced large amounts ofprecipitation (i.e., Table 3 of van Zanten et al. (2011)) andliquid water simulated by one-moment bulk schemestended to be distributed in the lower layer. By contrast,
the liquid water was located in the higher layer, and theprecipitation flux was small in most of the two-moment
schemes (i.e., Figure 6a of van Zanten et al. (2011)). In thisstudy, we confirmed the validity of their interpretation
through a simulation using our new fully compressible
LES model and determined the main processes contributing to the diversity in the results of LES model intercomparison studies.

Methods
Experimental setup, dynamic framework, turbulencemodel, and external forcing

This section describes the common parts of the modelwith its experimental setup (i.e., the dynamic framework,
turbulence model, and external forcing). The different
parts of the microphysical schemes are highlighted in
the subsequent section.
The dynamic model used in this study is an LES
model that is included in the Scalable Computing for
Advanced Library and Environment library (SCALE).
Henceforth, we call this LES model SCALE-LES. The
details of SCALE-LES are found at http://scale.aics.riken.jp/.
A fully compressible system is adopted for the governing equation of SCALE-LES. The prognostic variables
are the three-dimensional momentum (ρu, ρv, ρw), total
density (ρ), mass-weighted potential temperature (ρθ),
and mass concentration of tracers (ρqs), where qs includes specific humidity, ratio of mass, and number concentration ratio of hydrometeors to total mass. Explicit
time integration is used in all directions. Furthermore,
the fourth-order central difference scheme is adopted
for spatial discretization to avoid the numerically implicit diffusion that would be induced by odd-ordered difference schemes. The three-step Runge–Kutta scheme isadopted. To retain stability of the model, fourth-ordersuperviscosity/diffusion is applied for all prognostic variables. Using SCALE-LES, developed as described above,
we exclude the effects of approximation in the governing
equation system and implicit diffusion as far as possible,
enabling a consideration of the effects of the target component (i.e., cloud microphysics in this study).
To guarantee monotonicity, the flux-corrected transport (FCT) scheme (Zalesak 1979) is applied for all
prognostic variables except for density. The effects of
sub-grid scale turbulence are calculated using a
Smagorinsky-type scheme based on Brown et al. (1994)
and Scotti et al. (1993).

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

The experimental setup is almost the same as that ofthe previous Global Energy and Water Exchange project (GEWEX) Cloud System Study (GCSS) intercomparison of Rain in Cumulus over the Ocean (RICO)(van Zanten et al. 2011). The calculation domain covers
12.8 × 12.8 km2 horizontally with a double periodic
boundary condition and 4.0 km vertically. The horizontal
and vertical grid intervals are 100 and 40 m, respectively.
Rayleigh damping is applied for three-dimensional momentum over the upper atmosphere of z > 3.5 km. The
strength of the numerical diffusion is set as 1.25 ×
105 m4 s−1, which is determined by the sensitivity experiment (the results of the sensitivity experiment are shownin Appendix 1 of this paper). The simulations are conducted for 24 h with time steps (Δt) of 0.05, 0.15, and
0.5 s for dynamics, cloud microphysics, and other physics.
The Δt for cloud microphysics is determined as the largest
time step to avoid artificial noise, and the ratio of Δt for
dynamics to Δt for other physics is set to 10 based on thesensitivity experiments (see Appendix 2 of this paper for
details of the sensitivity experiment).
The external forcing of the radiation, the surface flux,
and the large-scale horizontal advection are applied in thesame way as in van Zanten et al. (2011). The forcing of thelarge-scale subsidence is applied for all prognostic variables including density, except for u and v. In nature,large-scale subsidence generates a divergence of total
density, which makes the air mass flow out from the domain. However, it cannot flow out in the compressiblemodel using the configuration of van Zanten et al. (2011)
due to the periodicity in the lateral boundary condition.
Although this problem can be ignored in the anelastic
and Boussinesq systems due to the fixed density, it isnecessary to consider this problem in the compressible
system. Although no description is available for thisproblem in van Zanten et al. (2011), the density ofeach layer should be reduced according to the divergence. The density reduction rate and the equation
system with large-scale forcing are given below.
Large-scale subsidence (wLS) was given by van Zanten
et al. (2011) as:8< − 0:005 z ðz < 2260mÞ
2260
wLS ¼
:
−0:005 ðz ≥ 2260 mÞ
where z is the height. Instead of this formulation, wegive the subsidence formulated directly to vertical momentum as:8< − 0:005 z ðz < 2260 mÞ
2260
ρwLS ¼:−0:005 ðz ≥ 2260mÞ
Consequently, the density reduction rate (D) is given as:

Page 3 of 16

8
0:005
ðz < 2260mÞ
∂ðρwLS Þ < −
2260
¼
D≡
:
∂z
0 ðz ≥ 2260mÞ
The continuous equation modified with the subsidence
term is given by∂ρ ∂ðρuÞ ∂ðρvÞ ∂ðρðw þ wLS ÞÞ
þ
þ
þ
¼D
∂t
∂x
∂y
∂z

ð1Þ

The density reduction derived from the divergence by
the large-scale subsidence is added in the right-hand side(rhs) of Eq. (1). Note that this equation is identical to theequation without large-scale subsidence. The Lagrangian
conservation equation of the scalar quantities (ϕ) is
given as:
ρ

∂ϕ
∂ϕ
∂ϕ
∂ϕ
þ ρu
þ ρv
þ ρðw þ wLS Þ
¼0
∂t
∂x
∂y
∂z

ð2Þ

The prognostic variable of SCALE-LES is a massweighted value, and the equation of mass-weighted
values is derived from Eqs. (1) and (2) as:∂ðρϕ Þ ∂ðρuϕ Þ ∂ðρvϕ Þ ∂ðρðw þ wLS Þϕ Þ
þ
þ
þ
¼ Dϕ
∂t
∂x
∂y
∂z

ð3Þ
As shown in the rhs of Eq. (3), the scalar quantities(ϕ) flow out from each layer of the system by subsidence. The equation for the vertical momentum is modified, as is that of the scalar quantities. The vertical flux
ρwLSϕ at the top boundary can be determined so thatsuch additional convergence of the flux is canceled withDϕ at the top layer.
Three microphysical schemes

To reproduce the diversity in the results of the RICO
study, three types of cloud microphysical scheme areused for this study: the one-moment bulk microphysicalscheme (Tomita 2008), the two-moment bulk scheme(Seiki and Nakajima 2014), and the spectral bin microphysical scheme (Suzuki et al. 2010). The one-momentbulk scheme and the two-moment bulk scheme arebased on Berry (1968) and Seifert and Beheng (2001), respectively. Both of the original bulk schemes were usedin the RICO study.
The essential difference among the three schemes istheir treatment of the size distribution of the number ofhydrometeor particles. The one-moment bulk scheme
expresses this value by the Marshall–Palmer distribution, with the assumption of a constant total number ofparticles. By this assumption, only the mass concentration is needed to determine the size distribution. Although the two-moment bulk scheme conceptuallytreats the size distribution almost the same way, it differs

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

from the one-moment bulk scheme in the assumption
about the type of size distribution function and in theprocess of its determination. The two-moment bulk
scheme assumes the generalized gamma distribution as
the size distribution function, and the size distribution
itself is determined not only by the mass concentration
but also by the number concentration. In this sense, thetwo-moment bulk scheme is more sophisticated thanthe one-moment bulk scheme. The spectral bin scheme
is an intrinsically sophisticated method compared withthe others. It explicitly predicts the size distribution. To
compensate for the detailed expression of size distribution, the spectral bin scheme requires about four- to
fivefold larger number of prognostic variables comparedwith the other two schemes.
Although the three microphysical schemes treat bothwarm and ice phase cloud, the ice phase was not calculated because the temperature at the model top is
greater than 273.15 K. In this case, the categorizationof hydrometeors for each scheme is as follows. The
one-moment and two-moment bulk schemes address
two types of hydrometeors: cloud droplet and raindrop
for warm rain process. The spectral bin scheme
addresses only a type of water drop, which covers theparticle size of both cloud droplets and raindrops. For
the spectral bin scheme, the radius of newly generated
cloud particles by nucleation is set to 3 μm (Suzuki etal. 2006). The size distribution of hydrometeors is discretized to 33 bins; its configuration has been establishedby several previous studies (e.g., Khain and Sednev
1996; Iguchi et al. 2008). The center of mass of ith bin(mi) is set by using the i-1-th bin (mi-1) as mi = 1.874
mi-1. m1 is the mass of cloud particles whose radius is
3 μm.
All three schemes consider the generation of cloud
droplets, condensation, evaporation, and sedimentationof cloud hydrometeors. Although the two-moment bulk
scheme also considers the breakup of cloud droplets,
this difference is minor based on sensitivity experiments
examining the breakup process (figure not shown). Sedimentation is calculated by the first-order upwind scheme
for all three schemes.
Since the generation of new cloud droplets is one of
the critical processes in this experiment, the differencein this process among the schemes should be noted.
The mass of newly generated cloud droplets is calculated by saturation adjustment in the one-moment bulk
scheme, which was also used in some one-moment bulk
schemes in the RICO study. By contrast, it is calculatedby the nucleation schemes in the two-moment bulk andspectral bin schemes. The number concentration of thecloud droplets (Nc,nucl) generated by the nucleation
process is calculated as follows (e.g., Pruppacher and
Klett 1997):

Page 4 of 16

N c;nucl ¼ N 0 S w k ;ð4Þ

where Sw is supersaturation over water. The constants
N0 and k are set as N0 = 100 × 106 m−3 and k = 0.462.
This scheme was also used in several models used in the
RICO study. The growth of cloud droplets into raindrops is another key issue for this experiment, as well as
the underlying creation process. In the bulk scheme, thisis expressed as autoconversion and accretion. To investigate the strength of the impact of the autoconversion
and accretion processes, we conducted the same simulation with autoconversion and accretion ratios that weretwice as large (0.067-fold smaller) as the two-moment(one-moment) scheme. The autoconversion rate (Pauto)in the one-moment bulk scheme is calculated as inTomita (2008), which was based on Berry (1968):
1
3:6  10−5 N c;T08
2
Pauto ¼ 16:7  ðρqc Þ 5 þ
Dd ρqcρ
‐1 ‐1 ;kg kg sð5Þ
where Dd = 0.1456−5.964 × 10−2 log (Nc,T08/2000), qc isthe cloud water mixing ratio, and Nc,T08 is the number
concentration of cloud droplets. In Tomita (2008),
Nc,T08 was set as 50 cm−3, but in this study, Nc,T08 was
set as 70 cm−3 based on the experimental setup in the
RICO study (van Zanten et al. 2011). Another autoconversion scheme from Khairoutdinov and Kogan (2000)
was implemented into the one-moment bulk scheme because it had performed better than the scheme of Berry(1968) in a GCM (Suzuki et al. 2004). The scheme wasalso adopted in some models used in the RICO study.
Pauto in the Khairoutdinov and Kogan (2000) scheme iscalculated as:
Pauto ¼ 1350  qc2:47  N −1:79
kgkg‐1 s‐1
ð6Þ
c;T08
Using the schemes shown above, we attempted toreproduce the diversity of the LES results in the RICO
study.

Results and discussion
Basic performance of SCALE-LES

The validity of SCALE-LES was confirmed throughcomparison with a previous study (van Zanten et al.
2011). The results of the spectral bin scheme wereregarded as a reference solution of SCALE-LES, because
it is the most sophisticated scheme of the three. First,
the results of the reference solution were compared withthe previous study. As shown in Figs. 1 and 2, the resultsof our model (SCALE-LES) are within the range between
the maximum and minimum of the intercomparison
study in terms of temporal evolution and vertical profile

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

(a)Page 5 of 16

(b)

(c)

Fig. 1 Comparison of the time evolution between SCALE-LES and a previous intercomparison study. Time evolution of the a liquid water path,b vertically integrated turbulence kinetic energy, and c boundary layer top height averaged over the entire calculation domain simulated by(black line) SCALE-LES, with the spectral bin scheme. The blue line, dark gray shading, and light gray shading indicate the median, range between
the first and third quartiles, and range between the maximum and minimum values, respectively, of the previous intercomparison study(van Zanten et al. 2011)

for several quantities. This indicates that our model
could reproduce the shallow cumulus simulated by the
LES models used in the previous study.
As well as the physical performance, the computational performance and the scalability of SCALE were
investigated. The elapsed time for a time step (Δt) andthe performance efficiency are shown in Table 1. The
elapsed time and performance of SCALE-LES do notchange when it is used with a large number of Message
Passing Interface (MPI) processes (e.g., over 10,000 MPI
processes). This indicates that SCALE-LES has excellent
scalability and a reasonable performance in massive parallel computing.
Impacts of cloud microphysical scheme on simulation
results

Second, we show the results of the same simulation(RICO) by using three microphysical schemes for investigating the impacts of the cloud microphysical scheme.
Figure 3 indicates the differences among the threeschemes. The precipitation flux simulated by the twomoment bulk scheme is small, and its peak value is distributed in the upper layer. By contrast, the precipitation
flux by the one-moment bulk scheme is large and thepeak value locates in the lower layer. The precipitationby the spectral bin scheme is between the other two(Fig. 3a). The trend is consistent with the previous study(Figure 6a of van Zanten et al. 2011).
The impacts of the different cloud microphysicalschemes on the vertical distribution of the precipitation
flux, the liquid water mixing ratio (ql), and cloud fraction
are clearly shown in Fig. 3a–c. The ql in the onemoment bulk scheme is distributed in the lower layer(the peak value is represented at z ~ 900 m). Table 2
shows the surface precipitation averaged during the last

4 h for the three schemes. The precipitation amount in
the one-moment bulk scheme is the largest, and the precipitation begins earliest among the three. The surface
precipitation over 0.1 W m−2 starts at 1.8 h in the onemoment bulk scheme, at 10.05 h in the two-momentbulk scheme, and at 2.63 h in the spectral bin scheme.
The liquid water simulated in the two-moment bulk
scheme is located in the upper layer (the peak value islocated at z ~ 2400 m), and only trace amounts of precipitation reach the surface (Table 2). The cloud fractionof the one-moment scheme is located in the lower layer
and is small in the upper layer. On the other hand, thepositive cloud fraction in the two-moment bulk scheme
reaches a higher layer. The spectral bin scheme simulates an intermediate value between the other two, withthe same trend as the RICO study. These results are
consistent with the result of the previous study (vanZanten et al. 2011).
The large amount of precipitation in the onemoment bulk scheme carries a large amount of liquidwater to the lower layer. As shown in Fig. 3d, the total
water mixing ratio (qt) of the lower layer (i.e., z <1500 m) in the one-moment bulk scheme is larger thanthat in the others. Despite the difference in the vertical
distribution of liquid water, the liquid water path
(LWP) shows the same value (Fig. 3e). By contrast, thecloud coverage of the one-moment scheme is smaller
than in the other scheme (Fig. 3f ). This implies thatthe amount of cloud that extends horizontally at the
top of boundary layer is small in the one-moment
scheme, which is because of the liquid water removed
from the cloud layer earlier by precipitation. This isalso found in Fig. 3c, where the peak of the cloud fraction does not appear around the top of the boundary
layer (i.e., z ~ 2000 m).

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

Page 6 of 16

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Fig. 2 Comparison of vertical profiles between SCALE-LES and a previous intercomparison study. Horizontally averaged profile of the a liquidwater potential temperature (θl) and total water mixing ratio (qt), b liquid water mixing ratio (ql), c precipitation flux, d cloud fraction, e verticalvelocity in cloud core, f variance of resolved w’, g w’θl’, h w’qt’, and i horizontal wind velocity, averaged during the last 4 h. The solid line indicatesthe results of SCALE-LES. The dashed line, heavy gray shading, and light gray shading indicate the median, range between the first and third
quartiles, and range between the maximum and minimum values, respectively, of the previous intercomparison study (van Zanten et al. 2011)

The impacts of cloud microphysics appear not only on
the precipitation and vertical distribution of liquid water,
but also the turbulent properties such as the turbulencekinetic energy (TKE), the variance in resolved verticalvelocity (w’), and boundary layer top height. The boundary layer top height in the two-moment bulk scheme isthe highest among the three schemes, whereas the onemoment bulk scheme simulates the lowest boundary

layer height. This trend in boundary layer height continues to the end of the simulation time, as shown in
Fig. 4a, and the difference among the schemes gradually
becomes large. The variance in w’ (Fig. 4c) and TKE(Fig. 4d) in the two-moment bulk scheme attributes alarger value to the upper layer. By contrast, those in the
one-moment scheme are smaller in the upper layer. Vertically integrated TKE tends to be large and small in theSato et al. Progress in Earth and Planetary Science (2015) 2:23

Page 7 of 16

Table 1 Computational performance of SCALE-LES
32,768 131,072 663,552a

Number of core16

2048 8192(Number of MPI
process)(2)(256) (1024) (4096) (16,384) (82,944)

Elapsed time (s step−1) 2.528 2.172 2.443

2.017

1.995

2.113

Performanceefficiency (%)

6.8

6.9

6.5

5.5

6.3

5.6

Elapsed time (s step−1) and performance efficiency (%) of SCALE-LES measured
using the two-moment bulk microphysical scheme. The performance wasmeasured through an experiment in which the number of grids for each MPI
process was the same (weak scaling test) on the K computeraThis test used all nodes of the K computer

two-moment and the one-moment bulk schemes, respectively (Fig. 4b).
From the results shown above, we concluded that the
turbulent properties of the boundary layer as well as thecloud microphysical properties of cumulus are significantly affected by the different microphysical schemes
when other components are unchanged. These results

support the proposal of van Zanten et al. (2011) that theuse of different cloud microphysical schemes is one of
the main reasons for the diversity among LES models.
We have confidence in this conclusion because direct effects other than the cloud microphysical schemes were
excluded in our experiments.
Reasons for the differences among the results of thethree schemes

The impacts of the cloud microphysical schemes areclearly indicated by the differences in the boundary layer
top height, vertical distribution of liquid water, and theprecipitation flux, as shown in the previous section. The
reasons for these differences will be discussed in thissection.
Since the impacts of each cloud microphysical scheme
originate from the expression of the liquid water in eachscheme, an examination of the tendency of ql and potential temperature (θ) in the cloud microphysical process

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 3 Comparison of the three cloud microphysical schemes. Horizontally averaged profile of the a precipitation flux, b liquid water mixing ratio,
c cloud fraction, d total water mixing ratio and liquid water potential temperature, and time evolution of e the liquid water path and f cloud
cover. The red, green, and sky-blue lines show results of the spectral bin scheme, the two-moment bulk scheme, and the one-moment bulk
scheme, respectively, and the black line, dark gray shading, and light gray shading indicate the median, range between the first and third quartiles,
and range between the maximum and minimum values, respectively, of the previous intercomparison study (van Zanten et al. 2011). The small
figure in d indicates the extension of the profile of liquid water potential temperature below 1000 m

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

Page 8 of 16

Table 2 Comparison of surface precipitation flux. The surface
precipitation flux averaged over the whole calculation domain
during the last 4 h of calculation
SchemeOne-moment bulk Two-moment bulk Spectral bin

Precipitation flux 22.89(W m−2)

0.174

13.17

is helpful for understanding the differences among the results. We first investigate the difference during t = 3−4 hof the calculation, because the effects of feedbacks ofcloud physics to dynamics is not large and it is easy tointerpret the difference. The tendencies at each heightaveraged during t = 3 h to t = 4 h are shown in Fig. 5a, b.
The results from t = 0 h to t = 3 h were removed to ignore
the effects of spin-up. The effect of sedimentation wasomitted from the tendencies. The generation of liquidwater at the cloud base in the one-moment bulk scheme
is more active than that in the others (Fig. 5a). This is attributed to the difference in the mechanism for generating

cloud particles. In the one-moment bulk scheme, newly
generated cloud particles are calculated by saturation
adjustment, whereas in the other schemes, they are calculated based on Eq. (4). Because the saturation adjustment does not permit supersaturation, it can generatelarger amounts of liquid water at the cloud base thanthat can be generated by the scheme based on Eq. (4),which allows for supersaturation. This large amount ofliquid water generation results in a large heat release at
the cloud base (Fig. 5b) and subsequently a strong verticalvelocity (Fig. 5c).
In addition to the large amount of liquid water generated in the one-moment bulk scheme, it is clear fromthe particle size distribution that the conversion fromcloud to rain is fast. Size distributions at the lower partof cloud (i.e., z = 1000 m) are shown in Fig. 5d. The generation of drizzle and raindrops (i.e., particles over
40 μm in radius) in the lower part of the cloud is activein the one-moment bulk scheme, whereas small cloud

(a)

(b)

(c)

(d)

Fig. 4 Comparison of turbulence properties between the three schemes. Time evolution of the a boundary layer top height and b verticallyintegrated turbulence kinetic energy (grid resolved + sub-grid scale) and horizontally averaged profile of c the variance of resolved w’ and d grid-resolved
turbulence kinetic energy averaged during the last 4 h of calculation

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

3500

2500

2500

2000
1500

2000
0
-2e-5

1500

-1e-5

0

1e-5

2000
1500

1000

1000

500

500

500

0

0.02

0.04

0.06

0.08

0.1

0.12

0
-0.0001 -5e-05

Tendency of mixing ratio [mg/kg/s]

05e-05 0.0001 0.00015 0.0002 0.00025

3500

(d)

z = 1000m
z = 1500m

100.02 0.04 0.06 0.08 0.1

3000

(e)

3000

Height [m]Height[m]

(f)

2500

2500
2000
1500

2000
500

1500

1e-06

1e-08

1e-10

1

10

100

1000

10000

Radius [µm]Spectral bin scheme

1000

1000

500

500

0

0

0.12 0.14 0.16 0.18

w'w’ [m2/s2]
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0.00010

Tendency of potential temperature [K/s]100

Number density (n(log m)) [# cm-3]

2500

250

1000

0
-0.04 -0.02

(c)

3000

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3000

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(b)

(a)
3000
Height[m]Height[m]3500

Page 9 of 16

250

0
296

2

4
6
8
Precipitation flux [W/m2]

2-moment bulk scheme

10

12

298

300

0
296 298 300 302 304 306 308 310 312 314

Liquid water potential temperature [K]1--moment bulk scheme

Fig. 5 Profiles and size distribution function averaged during t = 3~4 h. Horizontally averaged profile of the a tendency of the liquid water,b tendency of potential temperature, c variance of w’, e precipitation flux, and f liquid water potential temperature averaged during t = 3 to
4 h. d Number density distribution (n (log m)) averaged over the whole cloudy grid at (solid) z = 1000 m and (dashed) z = 1500 m, where nand m are the number concentration and mass of liquid water, respectively. The red, green, and sky-blue lines show results of the spectralbin, two-moment bulk, and one-moment bulk schemes, respectively. The extended figures in b and f show the tendencies of potential
temperature and liquid water potential temperature below 500 m, respectively

particles are dominant in the two-moment bulk schemes.
This indicates that the conversion from cloud to rain in
the one-moment bulk scheme is faster than that in theothers, and larger numbers of raindrops are generated in
the lower part of the cloud by the one-moment bulk
scheme.
The generation of large raindrops leads to the fast terminal velocity of the hydrometeors and a large precipitation flux in the one-moment bulk scheme (Fig. 5e),which, in turn, leads to the large precipitation flux atthe surface and the fast onset of surface precipitation.
Figure 5a, b also show that the peak negative tendencyof ql and θ near the cloud top (z ~ 1700 m), which corresponds to the evaporation of cloud droplets at the
top of the boundary layer, is located in a lower layer inthe one-moment scheme than in the others. This indicatesthat the large precipitation volume and large cloud size inthe one-moment bulk scheme restrain the cloud particles
from reaching the upper layer. Therefore, the boundary

layer top height of the one-moment bulk scheme becomes
lower (Fig. 4a).
The large amount of raindrops in the one-moment
scheme creates feedback for the thermodynamic structure below the cloud. The water loading due to raindrops leads to active evaporative cooling below thecloud (shown in the negative tendency of ql and θ below
the cloud as shown in Fig. 5a, b and the lower potential
temperature below the cloud shown in Fig. 5f ). Thisevaporative cooling stabilizes the boundary layer andsuppresses the heat transfer from the ground to theupper part of the boundary layer, which is shown in thefact that the positive tendency of θ in the one-momentbulk scheme does not reach z > 1200 m but reaches z ~1400 m in the other scheme. This supports Stevens et al.
(1998), who indicated that precipitation suppresses cloud
growth and entrainment. This suppression can limit thedevelopment of the boundary layer and results in a morestable boundary layer.

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

difference in the timing of the surface precipitation all originate from the variety of microphysical schemes used inthis study. The differences in each scheme would not always appear when the results of other one-moment, twomoment, and spectral bin schemes are compared. By contrast, the evaporative cooling and subsequent stabilizationof the sub-cloud layer and the suppression of the development of boundary layer height, which appeared in the results of the one-moment scheme used in this study, canbe expected if the fast conversion from cloud to rain or
the active generation of cloud particles at the cloud baseoccurs as a result of natural phenomena, regardless ofwhich scheme is used. The active latent heat release andhigh boundary layer, which appeared in the two-moment
scheme used in this study, can also be expected. The results are commonly expected for trade wind cumulus.
Speed of conversion from cloud to rain

The analyses in the previous sections hint that the performance of the bulk microphysical schemes could be
modified by changing the nucleation schemes and theconversion speed from cloud to rain. In the bulk scheme,
autoconversion and accretion are the main processes involved in the conversion from cloud to rain. To obtain information for the modification of the parameterization ofthese two processes, a comparison of the autoconversion
and accretion rates among the three schemes is helpful.
Figure 6 shows the autoconversion and accretion rates

3500
Autoconversion rate
Accretion rate

3000
2500
Height[m]The difference between the two-moment bulk and thespectral bin schemes in the tendency of ql and θ are relatively small. However, the difference in size distributionfunction between the two schemes is clearly apparent(Fig. 5d). A larger amount of raindrops (r > 100 μm) were
present in the spectral bin scheme than in the case in
the two-moment bulk scheme. It is indicated that theconversion from cloud droplets to raindrops is slow inthe two-moment bulk scheme. Because the amount oflarge raindrops is small in the two-moment bulk
scheme (shown as green lines in Fig. 5d), liquid wateris carried to the upper layer more easily than in theother schemes. The liquid water evaporates at the topof the boundary layer. This is shown by the negative
tendency of ql, and by θ locating in a higher layer in thetwo-moment bulk scheme than in the others (Fig. 5a, b).
The presence of larger particles in the spectral bin
scheme subsequently increases the rate of collisions withother particles, which leads to more rapid growth of particles and earlier precipitation in the spectral bin scheme
than in the two-moment bulk scheme. This provides
feedback due to the large amount of precipitation, whichis the same feedback that occurs in the one-momentbulk scheme.
With the feedback, the differences among the threeschemes increase with the integration time. The difference in the boundary layer top height in the threeschemes becomes large as the integration time increases(Fig. 4a), and the difference in the liquid water potential
temperature below clouds during the last 4 h (Fig. 3d) islarger than at t = 3–4 h (Fig. 5f ). The differences in thetendencies of θ and ql shown above also become clear(figure not shown).
In summary, the one-moment bulk scheme creates alarger amount of precipitation, because the saturation
adjustment was adopted in the one-moment bulk scheme,
and raindrops are subsequently produced by the fast conversion from cloud to raindrops. This results in earlier onset and larger amounts of surface precipitation. The
evaporative cooling by raindrops, which occurs actively
below the cloud, stabilized the boundary layer in the onemoment bulk scheme.
The two-moment scheme creates raindrops more slowly,
resulting in a smaller amount of precipitation comparedwith the other schemes. The smaller amount of precipitation results in an active latent heat release in the higher
layer (shown in Fig. 5b) and a high boundary layer. The
spectral bin scheme shows an intermediate rate of conversion and creates an intermediate amount of precipitation,with values between those of the two-moment and onemoment bulk schemes.
The large number of cloud particles newly generated at
the cloud bottom by saturation adjustment, the differencein the speed of conversion from cloud to rain, and thePage 10 of 16

2000
1500
1000
500
0

0

1e-09 2e-09 3e-09 4e-09 5e-09 6e-09
Autoconversion and Accretion rates [kg/kg/s]
Spectral bin scheme
1-moment scheme(Original)
2-moment scheme
1-moment scheme(KK)

Fig. 6 Autoconversion and accretion rate averaged during t = 3~4 h.
The horizontally averaged (solid line) autoconversion rate and(dashed line) accretion rate simulated by the spectral bin scheme(red), two-moment scheme (green), one-moment scheme (sky blue),and one-moment scheme with the Khairoutdinov and Kogan (2000)
scheme (pink), averaged during t = 3~4 hSato et al. Progress in Earth and Planetary Science (2015) 2:23

Page 11 of 16

averaged during t = 3~4 h. The autoconversion rateof the spectral bin scheme is regarded as the rate ofincreasing mass of raindrops (defined as liquid particles whose radius is larger than 40 μm) generated by
the coagulation between cloud particles (defined asliquid particles whose radius is smaller than 40 μm).
The accretion rate of the spectral bin scheme is determined as the increasing rate of mass due to the
coagulation between cloud particles and raindrops.
Figure 6 shows that the autoconversion rate of theone-moment scheme is about 15 times larger thanthat of the spectral bin scheme. By contrast, the accretion rate of the two-moment scheme is 1.5~2
times smaller than that of the spectral bin scheme.
Based on these results, the sensitivity of these twoprocesses in each scheme was investigated and is discussed in the next section.

Sensitivity of the autoconversion to the one-moment bulk
schemeAs shown above, the one-moment bulk scheme overestimates the conversion speed from cloud droplet to raindrop. We first investigated the difference between theoriginal autoconversion scheme of Tomita (2008) andthat of Khairoutdinov and Kogan (2000) shown in Eq. (6).
The results of the one-moment bulk scheme with the
Khairoutdinov and Kogan (2000) scheme are more similar
to the results of the spectral bin scheme and the previous
study than those calculated by Eq. (5) (Fig. 7). This indicates that the conversion speed calculated by Eq. (5) is too
fast for shallow clouds because the validity of the onemoment bulk scheme with Eq. (5) was confirmed throughexperiments with deep convective clouds (Tomita 2008).
In addition to the experiment with the Khairoutdinov
and Kogan (2000) scheme, other sensitivity experiments

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3000

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1500

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0

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-2

Precipitation flux [W m ]
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18

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10

(d)

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Total water mixing ratio [g/kg]

0.005

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0.04

Liquid water mixing ratio [g/kg]

Previous inter-comparison
Spectral bin scheme

0.06

0.08

0.1

0.12

Cloud Fraction

2-moment scheme
1-moment scheme(Original)

1-moment scheme(KK)

Fig. 7 Cloud microphysical properties simulated by Khairoutdinov and Kogan’s auto conversion scheme. Horizontally averaged profile of thea precipitation flux, b total water mixing ratio (qt), c liquid water mixing ratio, and d cloud fraction averaged during the last 4 h. The red,green, sky-blue, and pink lines show results by the spectral bin scheme, the two-moment bulk scheme, the one-moment bulk scheme, andone-moment bulk scheme using the Khairoutdinov and Kogan (2000) autoconversion rate, respectively. The black line, dark gray shading, andlight gray shading indicate the median, range between the first and third quartiles, and range between the maximum and minimum values,
respectively, of the previous intercomparison study (van Zanten et al. 2011)

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

Page 12 of 16

were conducted by reducing the autoconversion rate.
Based on the analyses in Fig. 6, a 0.067-fold (i.e., 1/15)
smaller autoconversion rate than the default value wasused for the sensitivity experiment. Another sensitivity
experiment with an accretion rate that was 0.067-foldsmaller than the default value was also conducted. Figure 8
shows the profile of ql and the precipitation flux, whichwere calculated using the smaller autoconversion and accretion rate. It can be seen that a small autoconversion
rate results in liquid water locating in the upper layer,
whereas it does not locate in the upper layer when theaccretion rate was reduced to the same extent as the
autoconversion rate. Hence, the autoconversion process
is more sensitive to the production of raindrops.
Sensitivity of the accretion to the two-moment bulk scheme

Contrasting the one-moment bulk scheme, the twomoment bulk scheme underestimates the conversion
speed from cloud to raindrop. We speculate that the faster conversion from cloud droplet to raindrop in thetwo-moment scheme produced similar results using thespectral bin scheme. Sensitivity experiments were conducted by changing both the autoconversion and accretion rates of the two-moment scheme. Based on theanalyses in Fig. 6, a twofold increase in the accretion rate
was used, and a twofold increase of the autoconversion
rate was also used for the sensitivity experiment. Figure 9shows the results of these experiments. In the twomoment bulk scheme, both the precipitation rate and ql
increase when the autoconversion rate is doubled. However, doubling the autoconversion rate does not result ina peak value of ql and a precipitation flux in the lower
layer as simulated by the one-moment bulk scheme. By
contrast, the precipitation flux simulated when the accretion rate is doubled is considerably larger than both
the default and when the autoconversion rate is doubled.
This indicates that the accretion process was the major
contributor to the creation of liquid water in the lower
layer in the two-moment bulk scheme.
In short, the sensitivity of the accretion and the autoconversion processes to the cloud microphysical properties differ between the schemes.
Component level intercomparison

In this study, we investigated the exact effects of thevarious cloud microphysical schemes on model simulations of trade wind cumulus. If we change components
other than the cloud microphysical scheme (e.g., dynamical core, turbulence scheme, advection scheme), the response of the cloud microphysical properties wouldchange as suggested by van Zanten et al. (2011). It is necessary to conduct sensitivity experiments by changing
each component while keeping all other components
fixed, as we did when targeting the cloud microphysicalscheme in this study. We refer to these sensitivity experiments as a “Component level intercomparison”.
Grabowski (2014) suggested a piggyback approach tobetter understand the exact effects of cloud microphysics and the interaction between microphysics and dynamics. This approach can be also applied to the othercomponents. Using a component level intercomparison
and the piggyback approach, we can discuss the effects

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(b)

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0

0.005

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25

30

35

40

Fig. 8 Cloud microphysical properties simulated in the sensitivity experiment with a varying conversion ratio in the one-moment scheme.
Horizontally averaged profile of the a liquid water mixing ratio (ql) and b precipitation flux averaged during the last 4 h. The solid sky-blue,
dashed sky-blue, and dotted sky-blue lines show the results using the one-moment bulk scheme with the default autoconversion rate, one-moment bulk
scheme with an autoconversion rate 0.067-fold (i.e., 1/15) smaller, and one-moment bulk scheme with accretion ratio 0.067-fold smaller, respectively.
The black line, dark gray shading, and light gray shading indicate the median, range between the first and third quartiles, and range between
the maximum and minimum values, respectively, for a previous intercomparison study (van Zanten et al. 2011)

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

Page 13 of 16

3500

3500

(a)

3000

(b)
3000

2500

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1500

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1000

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500

0

0

0.005

0.01

0.015

0.02

0.025

0

0

5

10

15

20

25

30

35

40

Fig. 9 Cloud microphysical properties simulated in the sensitivity experiment with a changing conversion ratio in the two-moment scheme. The
horizontally averaged profile of the a liquid water mixing ratio (ql) and b precipitation flux averaged during the last 4 h. The solid green, dashedgreen, and dotted green lines show the results using the two-moment bulk scheme with the default autoconversion rate, two-moment bulk
scheme with an autoconversion rate twice as large as the default, and two-moment bulk scheme with an accretion ratio twice as large as thedefault. The black line, dark gray shading, and light gray shading indicate the median, range between the first and third quartiles, and the range
between the maximum and minimum values, respectively, for a previous intercomparison study (van Zanten et al. 2011)of each component separately and obtain knowledge thatwould improve the parameterization of global scalemodels or regional models with coarse resolution.

Conclusions
In this study, we developed a large eddy simulation
model (SCALE-LES), which excludes approximations
and implicit schemes as much as possible. The results ofa benchmark test indicated that SCALE-LES effectively
reproduces the trade wind cumuli simulated in a previous LES intercomparison study (van Zanten et al. 2011).
Using SCALE-LES, we investigated the impacts of cloud

microphysical schemes on shallow cumulus and investigated which processes were critical for the diversity observed in previous LES intercomparison studies. Threetypes of cloud microphysical scheme, the one-momentbulk scheme of Tomita (2008), the two-moment bulk
scheme of Seiki and Nakajima (2014), and the one-moment
spectral bin scheme of Suzuki et al. (2010), were implemented with SCALE-LES for the sensitivity experiments.
The results indicated that the precipitation at the surface increases, in order, from the two-moment bulk
scheme to the spectral bin scheme and the one-momentbulk scheme. Surface precipitation begins first in theFig. 10 Cloud microphysical properties in the sensitivity experiment of NDT (=Δtmicrophy/Δtdyn). Hourly averaged profile of the a buoyancy
production, b shear production, and c transport terms averaged over the entire calculation domain during the last hour of each simulation. The
red, green, pink, black, and orange lines represent the results of NDT = 1, 5, 10, 20, and 30, respectively. The blue line, dark gray shading, and lightgray shading indicate the mean, standard deviation, and the range between the maximum and minimum values, respectively, from a previous
intercomparison study (Stevens et al. 2005)

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

Page 14 of 16

Table 3 List of non-dimensional coefficient for sensitivity
experiment

Appendix 1
Sensitivity of the ratio of the physical time step to the
dynamical time step. In this study, the time step of dynamics (Δtdyn), cloud microphysics (Δtmicrophy), andother physics (Δtphy) were set as 0.05, 0.15, and 0.5 s, respectively. The time step of dynamics was determined by
the Courant–Friedrichs–Lewy (CFL) condition for the
acoustic wave. The time step for physics (except forcloud microphysics) was set as 10 × Δtdyn based on thesensitivity experiment (Nishizawa et al., 2015). The
Δtmicrophy was determined in sensitivity experiments
examining the ratio of Δtmicrophy to Δtdyn. The resultsof the sensitivity experiments examining the ratio NDT(=Δtmicrophy/Δtdyn) are shown in this section. For thissensitivity test, the experimental setup of the second
Dynamics and Chemistry of Marine Stratocumulus Research Flight 1 (DYCOMS-II RF01) (Stevens et al. 2005)
was used. In this study, the experimental setup of the
RICO study was used in most cases, but the effects of theacoustic wave appeared more clearly in the DYCOMS-II
case (figure not shown). Consequently, the ratio (NDT)
was determined using the DYCOMS-II RF01 experimental
setup. For this sensitivity experiment, Δtdyn was set as0.01 s and NDT was swept from 1 to 30 (i.e., Δtmicrophy wasset from 0.01 to 0.3 s).
The results of the sensitivity experiment indicated thatthe effects of NDT were mostly small (figures not shown),
except for the TKE budget. Figure 10 shows the profile ofthe buoyancy production term, shear production term, andtransport term of TKE production. The transport term wasquite noisy when NDT was large (NDT > 10). Noise is alsopresent in the shear production term. This noise was derived from the acoustic wave that was generated at every
time step of the microphysical processes. When NDT was

γ = 10−3

Non-dimensional coefficient (γ)
The strength of the numerical filter4

γ = 10−551.25 × 10

γ = 10−731.25 × 10

1.25 × 101−1

The value of the numerical filter (m s ) for each experimentone-moment bulk scheme, followed in order by thespectral bin and two-moment bulk schemes. These results
support the suggestion of a previous intercomparison
study (van Zanten et al. 2011)
Our analyses confirmed that the differences between
the schemes were derived mainly from the generation ofcloud particles and the speed of conversion from cloud
droplets to raindrops. The differences in the two processes
originated from the differences in the microphysicalschemes used. By contrast, the phenomena generated bythis variety, i.e., evaporative cooling and stabilization
below the cloud and a low boundary layer, active latent
heat release, and a high boundary layer can be expected
regardless of the scheme used, if the active conversion
from cloud to rain and the active generation of new cloudparticles occur in nature.
The sensitivity of the autoconversion and accretion
processes to the cloud microphysical properties simulated by the bulk microphysical schemes was also investigated. In the two-moment bulk scheme the accretion
process was more sensitive to the cloud microphysicalproperties, whereas the autoconversion was more sensitive in the one-moment bulk scheme. These results indicate that the tuning method of the microphysicalscheme differs from scheme to scheme, and a component level intercomparison is useful to obtain the exact
method for each scheme.

Fig. 11 Results of a sensitivity experiment of the strength of numerical diffusion. Time evolution of the a vertically integrated turbulence kinetic
energy averaged over the whole calculation domain and the profile of the b liquid water mixing ratio and c cloud fraction averaged over thewhole calculation domain during the last 4 h. The red, green, and sky-blue line shows the results with the coefficient (γ) as 10−3, 10−5, and 10−7,
respectively. The black line, thick gray shade, and thin gray shade indicate the median, range between the first and third quartiles, and range
between the maximum and minimum values of a previous intercomparison study, respectively (van Zanten et al. 2011)

Sato et al. Progress in Earth and Planetary Science (2015) 2:23

large, the variation of θ at each step of the microphysicalprocesses was also large. The large variation in θ generates
an acoustic wave, which produced the noise. This indicates that NDT should be smaller than 5 to render theeffects of the acoustic wave negligibly. From these results
and for safety, NDT was set as 3 for the RICO experiment(i.e., Δtmicrophy = 3 × Δtdyn).

Appendix 2
Numerical filter. This section describes the sensitivity
experiments of the strength of the numerical diffusion.
The nth ordered superviscosity/diffusion is defined as:23∂ 4 ∂n−1 f 5
f ∈fu; v; w; θ; qs g:νρ n−1∂x∂x
2
3∂ 4 ∂n−1 ρ5ν∂x ∂xn−1
The v is written as:nν ¼ ð−1Þ2þ1 γ

Δxn
2n Δt

where γ is a non-dimensional coefficient, Δx is the grid
spacing, and n is the order of the numerical filter. This
study adopted a fourth-order numerical diffusion (i.e.,n = 4) to dampen the artificial noise. n was set as 4 because of the computational efficiency.
To investigate the sensitivity of the strength of thenumerical diffusion, simulations of the RICO study wereconducted while changing the strength of the numerical
diffusion. Based on the rough estimation of Nishizawa etal. (2015), the non-dimensional coefficient (γ) should besmaller than O (10−3)–O (100) for n = 4. Thus, γ was changed from 10−3 to 10−7. The strength of the numerical diffusion for each γ is shown in Table 3. The two-moment bulk
scheme was used for the sensitivity experiment. As a resultof the numerical diffusion, one-dimensional sinusoidal
two-grid noise will decay to 1/e with a 1/γ time step.
Figure 11 shows the results of the sensitivity experiment. The vertically integrated TKE increased with aweakening of the numerical filter, even though the TKE
of all experiments was located in the range between the
maximum and minimum of the previous studies. This isbecause a strong numerical diffusion can efficiently
dampen small-scale turbulence. As well as the TKE, theliquid water mixing ratio of all the sensitivity experiments was also located in the range of previous intercomparison studies regardless of the strength of thenumerical diffusion. However, the cloud fraction simulated with a small numerical diffusion (i.e., γ ≤ 10−5)
was much larger than that of the intercomparison
study, and the cloud fraction was completely outside

Page 15 of 16

the range of the inter comparison studies. The cloud
fraction, core fraction, and variance of w’ were also
outside the range of the inter comparison studies
when γ was smaller than 10−5 (figure not shown).
The temporal evolution of the cloud fraction indicates that the large cloud fraction, with small numerical diffusion, seems to originate from artificial noise.
However, it is difficult to identify the reason for thelarge cloud fraction being artificial noise. The same
experiment must be conducted with a fine grid resolution to divide all of the elements of the wave intoa physically meaningful wave and artificial noise.
However, computational limitations prevented us
from conducting these experiments. Consequently, γ
was determined using the results of the intercomparison study (van Zanten et al. 2011) as a reference solution, and γ was set as 10−3 (i.e., the strength of thenumerical diffusion is 1.25 × 105 m4 s−1).
Abbreviations
DYCOMS: Dynamics and Chemistry of Marine Stratocumulus; GCSS: GEWEXCloud System Study; GEWEX: Global Energy and Water Exchange project;
KiD: the kinematic driver; LES: large eddy simulation; LWP: liquid water path;
MPI: Message Passing Interface; RICO: Rain in Cumulus over the Ocean;
SCALE: Scalable Computing for Advanced Library and Environment;
TKE: turbulence kinetic energy.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
YS implemented the cloud microphysical schemes in the SCALE library,
designed this study, conducted the numerical simulations, analyzed theresults of the simulations, and developed the manuscript. SN, HY, and YM
developed the main frames of the SCALE library. YK collaborated with thecorresponding author in the creation of the manuscript. HT proposed thedevelopment of the SCALE library. All authors read and approved the final
manuscript.
Acknowledgement
Part of the results is obtained by the K computer at the RIKEN Advanced
Institute for Computational Science. This work was supported by FOCUS
Establishing Supercomputing Center of Excellence. SCALE-LES developed byTeam-SCALE of the RIKEN Advanced Institute for Computational Sciences.
The data from GCSS intercomparison studies used in several figures were
downloaded from http://www.knmi.nl/samenw/rico/.
Received: 23 February 2015 Accepted: 6 August 2015

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