Editorial Type:
Article
Article Type:
Research Article

Improvements of the Double-Moment Bulk Cloud Microphysics Scheme in the Nonhydrostatic Icosahedral Atmospheric Model (NICAM)

Tatsuya Seiki aJapan Agency for Marine-Earth Science and Technology, Yokohama, Kanagawa, Japan

Search for other papers by Tatsuya Seiki in
Current site
Google Scholar
PubMed Close
and
Tomoki Ohno aJapan Agency for Marine-Earth Science and Technology, Yokohama, Kanagawa, Japan

Search for other papers by Tomoki Ohno in
Current site
Google Scholar
PubMed Close
Online Publication:
22 Dec 2022
Print Publication:
01 Jan 2023
DOI:
https://doi.org/10.1175/JAS-D-22-0049.1
Page(s):
111–127
Open access
View license

Abstract

This study revises the collisional growth, heterogeneous ice nucleation, and homogeneous ice nucleation processes in a double-moment bulk cloud microphysics scheme implemented in the Nonhydrostatic Icosahedral Atmospheric Model (NICAM). The revised cloud microphysical processes are tested by 10-day global simulations with a horizontal resolution of 14 km. It is found that both the aggregation of cloud ice with smaller diameters and the graupel production by riming are overestimated in the current schemes. A new method that numerically integrates the collection kernel solves this issue, and consequently, the lifetime of cloud ice is reasonably extended in reference to satellite observations. In addition, the results indicate that a reduction in graupel modulates the convective intensity, particularly in intense rainfall systems. The revision of both heterogeneous and homogeneous ice nucleation significantly increases the production rate of cloud ice number concentration. With these revisions, the new version of the cloud microphysics scheme successfully improves outgoing longwave radiation, particularly over the intertropical convergence zone, in reference to satellite observations. Therefore, the revisions are beneficial for both long-term climate simulations and representing the structure of severe storms.

Significance Statement

Very high-resolution global atmospheric models have been developed to simultaneously address global climate and regional weather. In general, cloud microphysics schemes used in such global models are introduced from regional weather forecasting models to realistically represent mesoscale cloud systems. However, a cloud microphysics scheme that was originally developed with the aim of weather forecasting can cause unexpected errors in global climate simulations because such a cloud microphysics scheme is not designed for interdisciplinary usage across spatiotemporal scales. This study focuses on systematic model biases in evaluating the terminal velocity of ice cloud particles and proposes a method to accurately calculate the growth rate of ice cloud particles. Improvements in ice cloud modeling successfully reduce model biases in the global energy budget. In addition, the internal structure of intense rainfall systems is modified using the new cloud model. Therefore, improvements in ice cloud modeling could further increase the reliability of weather forecasting, seasonal prediction, and climate projection.

Ohno’s current affiliation: Meteorological Research Institute, Tsukuba, Ibaraka, Japan.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tatsuya Seiki, tseiki@jamstec.go.jp

Abstract

This study revises the collisional growth, heterogeneous ice nucleation, and homogeneous ice nucleation processes in a double-moment bulk cloud microphysics scheme implemented in the Nonhydrostatic Icosahedral Atmospheric Model (NICAM). The revised cloud microphysical processes are tested by 10-day global simulations with a horizontal resolution of 14 km. It is found that both the aggregation of cloud ice with smaller diameters and the graupel production by riming are overestimated in the current schemes. A new method that numerically integrates the collection kernel solves this issue, and consequently, the lifetime of cloud ice is reasonably extended in reference to satellite observations. In addition, the results indicate that a reduction in graupel modulates the convective intensity, particularly in intense rainfall systems. The revision of both heterogeneous and homogeneous ice nucleation significantly increases the production rate of cloud ice number concentration. With these revisions, the new version of the cloud microphysics scheme successfully improves outgoing longwave radiation, particularly over the intertropical convergence zone, in reference to satellite observations. Therefore, the revisions are beneficial for both long-term climate simulations and representing the structure of severe storms.

Significance Statement

Very high-resolution global atmospheric models have been developed to simultaneously address global climate and regional weather. In general, cloud microphysics schemes used in such global models are introduced from regional weather forecasting models to realistically represent mesoscale cloud systems. However, a cloud microphysics scheme that was originally developed with the aim of weather forecasting can cause unexpected errors in global climate simulations because such a cloud microphysics scheme is not designed for interdisciplinary usage across spatiotemporal scales. This study focuses on systematic model biases in evaluating the terminal velocity of ice cloud particles and proposes a method to accurately calculate the growth rate of ice cloud particles. Improvements in ice cloud modeling successfully reduce model biases in the global energy budget. In addition, the internal structure of intense rainfall systems is modified using the new cloud model. Therefore, improvements in ice cloud modeling could further increase the reliability of weather forecasting, seasonal prediction, and climate projection.

Ohno’s current affiliation: Meteorological Research Institute, Tsukuba, Ibaraka, Japan.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tatsuya Seiki, tseiki@jamstec.go.jp
Keywords: Cloud microphysics; Cloud radiative effects; Climate models; Clouds

1. Introduction

Atmospheric circulation is driven by radiative energy and hence is largely modified by cloud radiative forcing. Therefore, improvement in cloud microphysics schemes is essential for climate modeling. Recently, very high-resolution general circulation models called global cloud-resolving models (GCRMs) have been developed to simultaneously address global climate and regional weather (Satoh et al. 2019; Stevens et al. 2019). The advent of GCRMs requires cloud microphysics schemes to reproduce heavy rainfall in addition to cloud optical properties. For example, GCRMs have been widely used for analyzing tropical moist convective systems such as the Madden–Julian Oscillation (Miura et al. 2007; Nasuno et al. 2009; Taniguchi et al. 2010; Miyakawa et al. 2012, 2014; Miyakawa and Kikuchi 2018; Takasuka et al. 2015, 2018; Takasuka and Satoh 2021; Matsugishi et al. 2020; Harris et al. 2020; Wedi et al. 2020) and tropical cyclones (Oouchi et al. 2009; Taniguchi et al. 2010; Yanase et al. 2010; Nakano et al. 2015, 2017; Yamada et al. 2010; Yamada and Satoh 2013; Yamada et al. 2017; Miyamoto et al. 2014; Ohno et al. 2016; Judt et al. 2021), understanding microphysical signals detected by satellite observations (e.g., Suzuki et al. 2011, 2013; Sato et al. 2018), and improving retrieval algorithms for remote sensing (e.g., Kubota et al. 2020; Hagihara et al. 2022). Currently, GCRMs are generally used with a horizontal resolution of 5 km or less (e.g., Stevens et al. 2019), although many studies have been conducted with a horizontal resolution coarser than 5 km (e.g., Kajikawa et al. 2016; Harris et al. 2020; Wedi et al. 2020).

Cloud microphysics schemes implemented in GCRMs were originally developed for regional weather forecasting models. For example, the physical package of the Weather Research and Forecasting (WRF) Model is applied to the Model for Prediction Across Scales (MPAS; Skamarock et al. 2012). However, a cloud microphysics scheme optimized for weather forecasting in the midlatitudes can cause unexpected errors in global simulations (e.g., Seiki et al. 2014; Roh and Satoh 2014; Seiki and Roh 2020). Global cloud-resolving simulations have provided us with a large sample of cloud systems across the globe (e.g., Miyamoto et al. 2013; Kajikawa et al. 2016; Hohenegger et al. 2020). As a result, the database has been utilized to reveal simulation biases in various types of cloud systems (e.g., Masunaga et al. 2008; Seiki et al. 2015a; Hashino et al. 2016; Roh et al. 2017, 2020, 2021; Seiki and Roh 2020). The development of cloud microphysics schemes for GCRMs is a challenging issue (Seiki et al. 2022).

This study particularly focuses on ice cloud microphysics related to the ice terminal velocity and ice particle size because these cloud parameters have a strong impact on the global radiation budget (e.g., Mitchell et al. 2008; Hourdin et al. 2017). In general, the terminal velocity υ in bulk cloud microphysics schemes was simplified by a power-law relation to the maximum dimension D or to the particle mass x as follows:
υ=aυDDbυDorυ=aυxxbυx.
Here, the pair of aυD and bυD and the pair of aυx and bυx are generally derived by fitting to observed values (e.g., Locatelli and Hobbs 1974; Heymsfield and Kajikawa 1987). The approximated terminal velocity was directly used in collisional growth and gravitational sedimentation and indirectly used in melting, vapor deposition/sublimation, and condensation/evaporation through the dependence of the ventilation coefficient on the Reynolds number.

In general, the use of a single pair of aυD and bυD for the power-law relation is valid only in a narrow range of the maximum dimension. Figure 1 shows the terminal velocity of various ice hydrometeors calculated by the theoretical formulation (Böhm 1989; Mitchell 1996; and see section 2a for details). The increase in terminal velocity is likely to be slowed down by larger particle sizes in any hydrometeor case. As a result, the values of the exponent bυD decrease as a particle grows. For example, bυD is theoretically assumed to be 2 for sufficiently small particles according to Stokes’s Law, and bυD approaches 0.5 for large particles. Recently, use of Eq. (1) was found to cause a nonnegligible bias in collisional growth (Seifert et al. 2014). This study examined the impact of this issue in global high-resolution simulations with a detailed cloud microphysics scheme.

Fig. 1.
Fig. 1.

Dependence of the terminal velocity υt (m s−1) on the maximum dimension D (m). Cloud ice is assumed to be hexagonal columns, snow is assumed to be the assemblages of planer polycrystals in cirrus clouds, and graupel is assumed to be lump graupel in the database compiled by Mitchell (1996).

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Accurate estimates of ice terminal velocity enable us to evaluate cloud microphysics schemes with new observation instruments and directly reduce uncertainties in cloud microphysics involving terminal velocities. Recently, Doppler radar in situ observations have been utilized to evaluate collisional growth (e.g., Ori et al. 2020; Karrer et al. 2021). Remote sensing of Doppler velocities enables us to constrain uncertainties in the ice terminal velocities. In particular, in the evaluation of collisional growth, errors originating from the power-law relation and from the aggregation efficiency are known to be comparable (e.g., Connolly et al. 2012). The Earth Clouds, Aerosol and Radiation Explorer (EarthCARE; Illingworth et al. 2015) satellite will push forward the global evaluation of ice cloud microphysics with the equipped Doppler cloud profiling radar (Hagihara et al. 2022) after its launch in 2023.

This study used a GCRM, the Nonhydrostatic ICosahedral Atmospheric Model [NICAM (Tomita and Satoh 2004; Satoh et al. 2008, 2014; Kodama et al. 2021)], for global simulations. In NICAM, a single-moment bulk cloud microphysics scheme named NSW6 [NICAM single-moment bulk cloud microphysics scheme with six water categories (Tomita 2008; Kodama et al. 2012; Roh et al. 2017)] or a double-moment bulk cloud microphysics scheme named NDW6 [NICAM double-moment bulk cloud microphysics scheme with six water categories (Seiki and Nakajima 2014; Seiki et al. 2014, 2015b)] was used as the standard numerical settings. This study subsequently revised NDW6.

NDW6 was developed by Seiki and Nakajima (2014) by reference to the cloud microphysics scheme proposed by Seifert and Beheng (2001, 2006) and Seifert (2008). The implementation of nonspherical ice particles was then extended by Seiki et al. (2014). The NICAM with NDW6 sufficiently reproduces the cirrus cloud amount near the tropopause (Seiki et al. 2015a,b). In addition, explicit coupling of the cloud microphysics scheme and radiative transfer model works to more reasonably represent cloud radiative forcing (Seiki et al. 2014, 2015a, 2022; Kodama et al. 2021). As a result, the global radiative budget in the NICAM global simulations improves by using NDW6, and consequently, warm biases in the entire troposphere due to the excessive greenhouse effect of cirrus clouds were solved (Seiki et al. 2015a). In addition, NDW6 reproduced low-level mixed-phase clouds over polar regions well (Roh et al. 2020). Recently, NDW6 has been utilized to make a reference state of cloud distributions to revise NSW6 (Seiki and Roh 2020; Noda et al. 2021). In addition, NDW6 was used for analyzing the feedback processes of droplet growth to global warming (Ohno et al. 2021). Further verification of physical processes in NDW6 makes such advanced analyses more reliable.

In this study, the terminal velocities of ice hydrometeors used for collisional growth were reevaluated based on the new theoretical formulation shown in Fig. 1 (see section 2a for details); the terminal velocities used for other microphysical processes had already been accurately modeled by Seiki et al. (2014). In addition, heterogeneous and homogeneous ice nucleation were revised because the processes starkly modified the ice number concentration. These revisions were examined in global simulations using NICAM. Demonstration of the sensitivity of cloud microphysics to the global distribution of hydrometeors and radiation budgets will motivate regional studies with more detailed cloud microphysics or laboratory experiments to advance global climate modeling.

Revisions of the current cloud microphysics scheme are described in section 2 with minor documented changes. Numerical settings are described in section 3, and the results from the new NDW6 are examined in section 4. Finally, section 5 briefly summarizes the revised NDW6 and findings from the revisions.

2. Revision of cloud microphysics

a. Terminal velocity

This study revised the evaluation of the terminal velocity used for collisional growth rates. The collisional growth rates are derived in the next subsection. In NDW6, particle shape was characterized by the power-law relationships between the particle mass x and maximum dimension D and between the maximum dimension and projected area to the flow A as follows:
x=axDbx,
A=aADbA.
For each hydrometeor category, coefficients and exponents were determined based on aircraft measurements compiled by Mitchell (1996).
The terminal velocity of ice particles is calculated according to the theory proposed by Mitchell (1996) and Böhm (1989) as follows:
υ=ηaDρδ024{[1+4δ02C01/2(2xgρD2Aηa2)1/2]1/2−1}2 ,
where δ02=5.83, C0 = 0.6, ηa is the dynamic viscosity of air, ρ is the air density, and g is the gravitational constant. With Eqs. (2) and (3), the terminal velocity was determined as a function of the maximum dimension (diameter) or particle mass. The dependence of the terminal velocity on the maximum dimension is shown in Fig. 1.

In NDW6, an accurate database of the terminal velocities of various ice hydrometeors was prepared using Eq. (4), and then the terminal velocities were approximated by fitting to the power-law relationship [Eq. (1)] to analytically evaluate the growth rate of the mass concentration and number concentration. NDW6 addresses the power-law issue of narrow particle size ranges with two pairs of aυD and bυD for different ranges of the mean mass diameter (Seiki et al. 2014). The modeled fall velocities of ice particles were evaluated by using a volume scanning video disdrometer (Kondo et al. 2021). However, the method was not applicable to collisional growth because of the complicated formulation of the collisional growth rates. In NDW6, a single pair of aυD and bυD for the power law has been used for collisional growth thus far.

b. Collisional growth

Collisional growth rates of the number concentration N and mass concentration L are generally evaluated by solving the collection equation as follows:
(∂Nj∂t)col,jk=−∫∫0∞fj(ln⁡ Dj)fk(ln⁡ Dk)K(Dj,Dk)d ln ⁡Djd ln⁡ D,
(∂Lj∂t)col,jk=−∫∫0∞xjfj(ln ⁡Dj)fk(ln⁡ Dk)K(Dj,Dk)d ln ⁡Djd ln⁡ Dk,
K(Dj,Dk)=Ejk(Dj,Dk)π4(Da,j+Da,k)2|υj(Dj)−υk(Dk)|.
Here, a hydrometeor category j is assumed to be collected by a hydrometeor category k, and f is the particle size distribution function in a logarithmic scale of D. The collection kernel K, which consists of the collection efficiency Ejk, the collisional cross section with the area-equivalent diameter Da, and the sweep distance per unit time. The integrand cannot be analytically integrated due to the dependence of the collection kernel on the terminal velocity difference. Therefore, cloud microphysics schemes generally solve the collisional growth equations [Eqs. (5) and (6)] by approximating the collection kernel or using numerical integration.
In NDW6, the collisional growth rates were derived by approximating the collection kernel as proposed by Seifert and Beheng (2006). For example, the growth rate of the mass concentration is described as follows:
(∂Lj∂t)col,jk=−Δυ¯Ejk[Dj(xj¯),D(xk¯)]∫∫0∞fj(ln ⁡Dj)fk(ln ⁡Dk)xj×π4(Da,j+Da,k)2d ln ⁡Djd ln ⁡Dk,
Δυ¯   ≡  {M[xjDa,j2Da,k2(υj−υk)2]/M(xjDa,j2Da,k2)+σj+σk}1/2,
M(α)  ≡ ∫∫0∞αfj(Dj)fk(Dk)d ln ⁡Djd ln ⁡Dk,
where x¯=L/N and σ is the variance of the terminal velocity. Following Seifert and Beheng (2006), σi = 0.2, σs = 0.2, and σc = σr = σg = 0.0 are used in NDW6. This formulation enables us to integrate the collection kernel analytically.

Recently, Seifert et al. (2014) found that nonnegligible biases arose in collisional growth with Eqs. (7) and (8). Seifert et al. (2014) alleviated the bias by using a modified formulation of the representative terminal velocity difference [Eq. (8)] with an alternative formulation of the terminal velocity. This approach is numerically efficient, but the development cost for debugging is relatively high due to the complex formulation of the analytic solution. Another approach is the use of a multidimensional lookup table to accurately estimate the collisional growth term (e.g., Milbrandt and Morrison 2016; Sulia et al. 2021). This approach can employ accurate formulations of ice terminal velocities, such as piecewise fitting curves (e.g., Heymsfield et al. 2013).

This study numerically solves the collection equation using the Gauss–Legendre quadrature as follows:
(∂Nj∂t)col,jk≈−∑njnmax∑nknmaxfj(ln⁡ Dnj)fk(ln⁡ Dnk)K(Dnj,Dnk)wnjwnk,
(∂Lj∂t)col,jk≈−∑njnmax∑nknmaxxjfj(ln⁡ Dnj)fk(ln ⁡Dnk)K(Dnj,Dnk)wnjwnk,
where Dn are the distinguished points and wn are the quadrature weights. In this formulation, the terminal velocities used in the collection kernel are accurately evaluated with Eq. (4). In general, the population of hydrometeors is densely concentrated around the mean mass diameter of their particle size distributions [D(x¯)]. Therefore, a definite integral of the collection kernel in the diameter range [D(x¯)/CGL, D(x¯)CGL] gives an accurate solution with a sufficiently large value of CGL. Note that the particle mass distribution function g(x) is basically used in NDW6, and the function is converted to particle size distribution f(lnD) in the collisional process for the Gauss–Legendre quadrature as follows:
∫0∞g(x)dx=∫0∞f(lnD)lnD.
Correspondingly, Dn and wn are defined as follows:
Dn=CGLxGLnD(x¯), (n=1,2,3,…,nmax),
wn=ln⁡(CGL)wGLn, (n=1,2,3,…,nmax),
where xGL are the Gaussian nodes in the range [−1, 1] and wGL are the Gauss–Legendre quadrature weights.
This study chose CGL = 2 with nmax = 4 for cloud water, CGL = 8 with nmax = 4 for rain, and CGL = 6 with nmax = 4 for cloud ice, snow, and graupel. These settings ensure at least approximately 90% of the integration accuracy with the normal range of the mean mass diameter. Note that the pair of CGL and nmax should be optimized depending on the shape of the particle size distribution of a hydrometeor category. Following Seifert et al. (2014), the accuracy of the solution for the collection equation was examined using normalized collision rates CN,N and CN,L, which are defined as follows:
CN,N,jk=1NjNk[Da,j(xj¯)+Da,k(xk¯)]2(∂Nj∂t)col,jk,
CN,L,jk=1LjNk[Da,j(xj¯)+Da,k(xk¯)]2(∂Lj∂t)col,jk.
Figure 2 shows the normalized collision rates in the general range of the area-equivalent diameter. Here, Ej,k = 1 was set solely to check the accuracy of the integration. The new method using the Gauss–Legendre quadrature accurately calculated the collisional growth rates in all cases. It is worth noting that the original method using the analytical formulation effectively captures the dependence of the collision rates on the area-equivalent diameter. In more detail, the normalized collision rates with the bulk method gradually deviate from the reference values at larger diameters (e.g., Da > 200 μm). In addition, the bulk method overestimates the normalized collision rates of the self-collection of cloud ice (CN,L,ii) with radii of a few tens of micrometers by up to 400%. Therefore, it is expected that heavy rainfall, in which large particles rapidly grow through collisional growth, and slow-growing cirrus clouds are more reasonably captured with the new method. Note that the use of the power-law relationships for estimating the ice terminal velocities causes large errors in the collisional growth rates, and the magnitude of the errors is comparable to the errors originating from the integration method. The errors depend on the particle sizes and the dependences are not systematic. These results are consistent with those of a previous study (Seifert et al. 2014). Use of Eq. (4) naturally solves the issue, although one may reduce the errors using an alternative approximation for estimating the ice terminal velocities (e.g., Seifert et al. 2014).
Fig. 2.
Fig. 2.

(a)–(j) The normalized mass collision rates as a function of the equivalent area diameter. Red solid and blue dashed lines indicate the collision rates calculated by the original analytical method and Gauss–Legendre quadrature method, respectively. Green dashed lines indicate the collision rates calculated by the Gauss–Legendre quadrature method with the ice terminal velocities simplified by the power-law relations. Black solid lines indicate the reference values that were calculated with the Gauss–Legendre quadrature with CGL = 20 with nmax = 30. Note that collisions between rain and cloud ice and between rain and snow result in production of graupel; hence, reduction terms of both the collected and collecting hydrometeors are shown in (d) and (e).

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

The calculation cost of the collisional growth with the Gauss–Legendre quadrature is 33 times larger than that with the analytical solution due to the dual-loop with ngmax = 4, the additional calculation for the particle size distribution, and the accurate terminal velocity [Eq. (4)]. As a result, the total calculation cost of the global simulation using the NICAM with a horizontal resolution of 14 km increases by approximately 11% on the vector supercomputer SX-Aurora TSUBASA. Therefore, the new method ensures high accuracy while maintaining high readability and extensibility of the source code with a slight increase in the calculation cost.

c. Homogeneous ice nucleation

NDW6 employs the homogeneous ice nucleation scheme proposed by Ren and MacKenzie (2005) and Kärcher et al. (2006). In the scheme, the vapor deposition rate and corresponding heating rate are required to estimate the supersaturation tendency. Therefore, in NDW6, homogeneous ice nucleation was calculated after the calculation of vapor deposition. This order of cloud microphysical procedures results in underestimation of the nucleation rate due to the decrease in the supersaturation in the vapor deposition procedure because each microphysical procedure was sequentially solved in NDW6. The sequence of procedures is illustrated in Fig. 3. This issue was expected to be alleviated when the model time step is sufficiently smaller than the characteristic time scale of the decrease in supersaturation.

Fig. 3.
Fig. 3.

The sequence of the cloud microphysical processes in NDW6. In the new version of NDW6, the order of homogeneous ice nucleation increases, and vapor deposition and sublimation are precalculated before homogeneous ice nucleation.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Following Khvorostyanov and Sassen (1998), the characteristic time scale of vapor consumption through vapor deposition τdep is estimated as follows:
∂qυ−qυsi∂t=−(qυ−qυsi)τdep,
τdep ≡ (qυ−qυsi)/(∂qi∂t)dep ,
where qυsi is the saturated specific humidity with respect to ice, and the tendency of the cloud ice mixing ratio with the subscript dep is the growth rate through vapor deposition. Here, the right-hand side of Eq. (17) does not depend on the relative humidity since qυ − qυsi in the numerator was cancelled out by the same term contained in the denominator.

Assuming the thermodynamic states of Ta = 233 K and p = 250 hPa and a monomodal ice particle size distribution with Di = 40 μm and Ni = 10–100 L−1 for a typical cirrus case, τdep ∼ 700–7000 s were derived. With NICAM, the model time step of 120 s was frequently used for global simulations with Δx = 14 km. This time step was sufficiently small in the thin cirrus case but can be comparable to relatively thick high clouds. In fact, this minor change has nonnegligible impacts on global high-resolution climate simulations. The sensitivity of this change to the ice nucleation rate is examined in section 4c.

In the new version of NDW6, the vapor deposition rate was calculated before homogeneous ice nucleation but was not used for updating the environment. The vapor deposition rate was recalculated after the nucleation processes again. Note that the computational cost of vapor deposition and sublimation was approximately 0.24% in NICAM, and therefore, their duplicated calculation costs were not a matter.

d. Heterogeneous ice nucleation

NDW6 employs the heterogeneous ice nucleation scheme proposed by Phillips et al. (2007). The scheme was based on Meyers et al. (1992) with modification based on aircraft observations organized by DeMott et al. (2003) as follows:
nin(si)=nM92exp[bM92(si−0.1)],
where the supersaturation is defined as si = qυ/qυsi − 1. This parameterization diagnoses the number concentration of the activated ice nuclei using si. Seiki et al. (2014) modified the parameterization to diagnose the ice nucleation rate as follows:
∂Ni∂t=∂nin∂si∂si∂t=∂nin∂si∂si∂zw, if ∂si∂z>0andw>0.
This formulation indicates that heterogeneous ice nucleation occurs until si reaches the maximum by adiabatic cooling in ascending motion. The new version of NDW6 clarifies the factors that affect ice nucleation as adiabatic cooling (DYN), vapor deposition (dep), and radiative cooling (RAD) assuming an ascending parcel as follows:
∂Ni∂t=∂nin∂si∂si∂t∼∂nin∂si[1qυsi(∂qυ∂t)dep−qυqυsi2(∂qυsi∂t)dep+DYN+RAD], if si>0 and ∂si∂t>0,
(∂qυsi∂t)dep=(∂qυsi∂T)ρa (∂T∂t)dep,
(∂qυsi∂t)DYN=−wg[1cp(∂qυsi∂T)p+ρa(∂qυsi∂p)T],
(∂qυsi∂t)RAD=(∂qυsi∂T)ρa(∂T∂t)RAD.

In the original method [Eq. (19)], evaluation of the vertical gradient of si strongly depends on the vertical layer thickness and the model time step. In particular, the vertical layer thickness was likely to be insufficient to resolve the vertical structure of cirrus clouds, whose thicknesses are generally 1–2 km (e.g., Seiki et al. 2015b). In addition, the vertical gradient of si is attributed to various factors other than adiabatic cooling (e.g., radiative cooling, vapor deposition, vertical diffusion, and tilting structure due to strong wind shear in the upper troposphere). Therefore, this revision was expected to have impacts on the vertical structure of cloud ice number concentration in addition to the amount of nucleated ice particles. The sensitivity of this revision to the ice nucleation rate is examined in section 4d.

e. Trivial changes and bug fixes

The NDW6 scheme, which is referred to as the current version, contains a minor change and two bug fixes after its detailed model description (Seiki and Nakajima 2014; Seiki et al. 2014, 2015b). 1) The collisional process between cloud ice and graupel, which was neglected in Seifert and Beheng (2006), was included, 2) a typo in immersion freezing of liquid droplets (Seifert and Beheng 2006) was fixed, and 3) a typo in breakup (Seifert and Beheng 2006) was fixed [see Kuba et al. (2020) for details]. In particular, change 1 is important for predicting the electric field in thunderstorms (Sato et al. 2019). All of the changes have negligible impacts on the global radiation budget, cloud distribution, and thermodynamic conditions in global simulations (not shown).

3. Numerical settings

Global simulations were performed using NICAM with Δx = 14 km and 74 vertical layers, as was used in Seiki et al. (2015b). Past studies using the NICAM have shown that the impact of cloud microphysics schemes on the global radiation budget and atmospheric states was clearly observable within 2 weeks (Seiki et al. 2015a; Seiki and Roh 2020; Roh et al. 2020). Therefore, the new version of NDW6 was tested during 10-day integration from 12 September 2016, and the simulation results during the last 5 days were analyzed. This study used the same physical processes as those used for the HighResMIP protocol (Kodama et al. 2021) except for the cloud microphysics scheme.

Note that cumulus parameterizations were not used for the NICAM simulations. Therefore, convective cloud systems were represented by cloud microphysics schemes with grid-resolved motion. Climate simulations using the NICAM have been found to be more sensitive to cloud microphysics schemes than to horizontal resolution (e.g., Kodama et al. 2021), as was shown in other GCMs (e.g., Meehl et al. 2019). In addition, climate models without cumulus parameterizations are found to better represent convective cloud systems with a horizontal resolution of less than 50 km (Vergara-Temprado et al. 2020). In terms of the sensitivity experiments, the NICAM with Δx = 14 km is sufficient for the cloud response to the NDW6 revisions, although Δx = 14 km is not sufficiently fine for global cloud-resolving simulations. Recent discussion about the validity of the horizontal resolutions for global cloud-resolving simulations are summarized in Seiki et al. (2022).

The simulated results were then processed by a satellite simulator named Joint Simulator for Satellite Sensors (Hashino et al. 2013) to be compared with the combined CloudSat–CALIPSO products from the EarthCARE Research A-Train Product Monitor (http://www.eorc.jaxa.jp/EARTHCARE/research_product/ecare_monitor_e.html). This study used a cloud flag detected by radar or lidar (the C4 cloud mask proposed by Hagihara et al. 2022) to define cirrus clouds (Seiki et al. 2019) and a 94-GHz radar echo measured by the CloudSat satellite. Cirrus clouds were defined as ice clouds with cloud base temperatures colder than 253 K. Tropical cirrus clouds were chosen for comparison because the dominant cloud microphysical processes in the cloud type, which are ice nucleation, aggregation, vapor deposition/sublimation, and gravitational sedimentation (e.g., Seeley et al. 2019; Ohno et al. 2021), are suitable for evaluating the revisions.

A series of sensitivity experiments are summarized in Table 1. Global simulations with the current version of NDW6 were referred to as CTL, and each revision was examined by individually switching it on. The CTL setting with the revised collisional method, revised order of homogeneous ice nucleation, and revised heterogeneous ice nucleation method were referred to as COL, HOM, and HET, respectively. Finally, the new version of NDW6 (NEW), in which all revisions were included, was evaluated.

Table 1

The numerical settings of the sensitivity experiments of the revised cloud microphysics.
Table 1

4. Results

a. Examination of the COL experiment

The revision of the collisional process modifies the partitioning of ice hydrometeors. Figure 4 shows the comparison of the vertical profiles of the mixing ratios of ice hydrometeors. In general, cloud ice increases and, correspondingly, snow decreases in the COL. Hereafter, the vertical profiles of cloud systems over the tropics (0°–20°N) are analyzed in detail.

Fig. 4.
Fig. 4.

Comparison of zonal mean values of mixing ratios of ice hydrometeors from the (left) CTL and (right) COL experiments.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

The revised integration method of the collection kernel drastically decreases collisional growth rates of cloud ice and, consequently, the lifetime of cloud ice increases (Fig. 5a). As a result, depositional growth largely exceeds the loss of cloud ice from collisional growth with snow in the upper troposphere in COL (Fig. 5b). Note that CN,Lii and CN,Lis were artificially limited by certain values above the altitude of 8 km in the CTL experiment because the constant variances of the ice terminal velocities σi = σs = 0.2 are empirically used based on Seifert and Beheng (2006) [see Eq. (8)]. Use of the uncertain parameters (σi and σs) affects qi as much as the change in the integration method of the collection kernel does. Therefore, it was advantageous to avoid such uncertain tuning parameters by numerically integrating the collection kernel.

Fig. 5.
Fig. 5.

(a) The averaged vertical profiles of the normalized mass collision rates and (b) major mass tendency terms over the tropics (0°–20°N, 0°–360°E). The lines PLcol indicate the reduction term of cloud ice through collisional growth to snow, and the lines PLdep indicate the production term of cloud ice through vapor deposition. The solid lines are from the COL experiment, and dashed lines are from the CTL experiment. The normalized collision rates are averaged with the weight of the denominator in Eq. (15). The vertical profile above the freezing level (approximately 5 km) is shown to avoid noisy values below the freezing level.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Interestingly, collisional growth of graupel significantly decreases in the revision (Fig. 6), whereas zonal mean values of the mixing ratio of graupel do not significantly change (Figs. 4a,d). To address this contradictory issue, we broke down rainfall cloud systems by the intensity of the surface precipitation flux P (Fig. 7). It was clearly observed that graupel production was significantly reduced in intense precipitation cases (P > 10 mm h−1) by the revision, as was expected (see section 2b). Correspondingly, the vertical velocity decreases, particularly above the freezing level (∼4 km), in intense precipitation cases. This indicated that changes in the hydrometeor interactions by the revision affect cloud dynamics.

Fig. 6.
Fig. 6.

The averaged vertical profiles of the production term of graupel through collisional growth over the tropics (0°–20°N, 0°–360°E). The solid lines are from the COL experiment, and dashed lines are from the CTL experiment.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Fig. 7.
Fig. 7.

The averaged vertical profiles of the (left) graupel mixing ratio qg (mg kg−1) and (right) vertical velocity w (cm s−1) sorted by surface precipitation P (mm h−1) on a logarithmic scale over the tropics (0°–20°N, 0°–360°E).

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Note that TRMM observations indicated that extreme rainfall events with uppermost 0.1% surface precipitation fluxes originated mainly from warm-rain processes associated with less intense convection (Hamada et al. 2015). Therefore, intense precipitation with a large graupel amount and strong updraft in the CTL simulation is presumably artificial.

b. Examination of the HOM experiment

Figure 8 shows the tropical average values of the vertical profiles of ice nucleation rates and cloud ice number concentrations in the CTL and HOM experiments. In CTL, high Ni near the tropopause powerfully suppressed homogeneous ice nucleation through vapor deposition. As a result, homogeneous ice nucleation was limited to just above the freezing level. In contrast, in HOM, homogeneous ice nucleation reasonably works in the upper troposphere and doubles Ni (Fig. 8b).

Fig. 8.
Fig. 8.

The averaged vertical profiles of (a) homogeneous ice nucleation rate (L−1 s−1) and (b) cloud ice number concentration (L−1) over the tropics (0°–20°N, 0°–360°E). The solid lines are from the HOM experiment, and dashed lines are from the CTL experiment.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

c. Examination of the HET experiment

In CTL, heterogeneous ice nucleation rates were generally low but locally very high in intense convective cores (Fig. 9a). In contrast, in HET, heterogeneous ice nucleation rates were more broadly distributed (Fig. 9b). As a result, the total amounts of nucleation rates are similar (Fig. 9c). However, the distribution of cloud ice number concentration differs significantly (Figs. 9d–f). In addition, the occurrence of heterogeneous ice nucleation was limited near the tropopause in CTL (Figs. 9a,c). This was because ice supersaturation in the middle to upper troposphere is consumed by existing cloud ice and snow through vapor deposition in tropical convective systems. Therefore, the original method, which uses the gradient of ice supersaturation [Eq. (19)], frequently misses the opportunity for ice nucleation in ascending air masses in the middle troposphere and abruptly triggers ice nucleation in the upper troposphere. In CTL, ice nucleation was more likely to be underestimated when using the coarser vertical resolution (Fig. 10), as was used for HighResMIP (Kodama et al. 2021).

Fig. 9.
Fig. 9.

Example snapshots of the vertical profiles of (top) heterogeneous ice nucleation rates (L−1 s−1) and (bottom) cloud ice number concentration (L−1) at 1200 UTC 22 Sep 2016. (c),(f) The averaged vertical profiles over the tropics (0°–20°N, 0°–360°E). The solid lines are from the HET experiment, and dashed lines are from the CTL experiment.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Fig. 10.
Fig. 10.

As in Figs. 9a–c, but that the NICAM had 38 vertical layers.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Note that upper ice clouds are sensitive to vertical resolution, as shown in Figs. 9 and 10, because radiative cooling and vertical mixing by turbulence are also modulated by increasing vertical resolution (Seiki et al. 2015b; Ohno et al. 2019). It was found that simulated cirrus clouds drastically changed from 38 layers (Δz ∼ 1500 m in the upper troposphere) to 78 layers (Δz ∼ 400 m in the upper troposphere) and almost converged with Δz ∼ 200 m in the upper troposphere (Seiki et al. 2015b; Ohno et al. 2019).

d. Examination of the new settings

Finally, global simulations with all revisions in the last 5 days were analyzed and compared to satellite observations. Ice water content (IWC) does not significantly change after the revisions to cloud microphysics except for low-level clouds in the high latitudes (Fig. 11). In the high-latitude regions (50°–90°N, 50°–90°S), the longevity of cloud ice due to the revisions slightly increases the IWC below an altitude of 4 km. Liquid water content is also insensitive to the revisions (not shown). The revision of collisional processes changes the distribution of hydrometeor mass but does not significantly change the total mass because the revision strongly works above the altitudes of 8 km where the air is thin (Fig. 5b). In contrast, the total ice number concentration significantly increases, particularly at temperatures colder than 233 K in NEW (Fig. 12), as was expected from the individual revisions.

Fig. 11.
Fig. 11.

Comparison of the zonal mean values of IWC (mg m−3). The climatological monthly mean values of IWC observations from the CloudSat products [the 2B-CWC-RO product (Austin and Stephens 2001; Austin et al. 2009)] were used to illustrate the monthly mean values in September 2016.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Fig. 12.
Fig. 12.

Comparison of the simulated total ice number concentration (Ni + Ns + Ng) (L−1).

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

In more detail, ice particle growth was evaluated using CloudSat and CALIPSO satellite observations (section 3). Here, the vertical profiles over the tropical ocean were sampled to exclude orographic clouds, in which very high ice number concentrations are frequently observed, especially in the upper troposphere (e.g., Seiki et al. 2019). Figure 13 shows the comparison of the contoured frequency of the 94-GHz radar echo by altitude diagram (CFAD). In CTL, a strong radar echo was frequently observed even near the cloud top (altitudes above 14 km) whereas the mode value of the radar echo monotonically increases toward the cloud base in the observations. The overestimation of radar echoes near the cloud top was alleviated in NEW. This indicates that the aggregation of cloud ice was efficiently suppressed in NEW by the revision (Fig. 5). In addition, slowly growing cloud ice through vapor deposition in the upper troposphere (Fig. 5b) successfully maintains the high probability of cirrus cloud occurrence at radar echoes from −30 to −20 GHz at altitudes above 12 km (Figs. 13a,c). As a result, in NEW, the cirrus cloud fraction increases by extending the lifetime of cirrus clouds and was better represented in reference to the satellite observations (Fig. 13d). However, both the CTL and NEW experiments fail to represent the distinct mode of radar echo at altitudes below 10 km, where snow particles continuously grow by aggregation and larger particles fall faster. The model error can be explained by the limitation of double-moment bulk cloud microphysics schemes in the gravitational size sorting process (e.g., Milbrandt and Yau 2005).

Fig. 13.
Fig. 13.

The contoured frequency by altitude diagram (CFAD) of the 94-GHz radar echo from (a) satellite observations, (b) CTL experiment, and (c) NEW experiment. (d) The vertical profiles of the cirrus cloud fraction defined by the C4 cloud flag and the cloud-base temperature.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

The revisions finally affect the cloud radiative properties. In the tropics, the increase in vapor deposition by the revision contributes to a slight increase in the ice mixing ratio at altitudes from 8 to 12 km (Figs. 5b and 14a). However, the ice number concentration significantly increases by the revisions at altitudes above 12 km (Figs. 8b, 9f, 12, and 14b). This change contributes to a decrease in the effective radii (Fig. 14c). Focusing on the cloud top (cloud optical depth ∼ 0.1), the ice effective radii in CTL and NEW are approximately 41 and 31 μm, respectively. As a result, the cloud optical thickness increased at altitudes from 8 to 16 km (Fig. 14d), where cirrus clouds are widely distributed (Fig. 13d). The increase in the cloud optical depth reached 0.1 near the cirrus cloud base (∼8 km) on average (Fig. 14e).

Fig. 14.
Fig. 14.

Vertical profiles of the tropical mean values of cloud microphysical parameters: (a) mixing ratios of cloud ice and snow (mg kg−1), (b) number concentration of cloud ice and snow (L−1), (c) effective radii of cloud ice and snow (μm), (d) optical thickness at a wavelength of 550 nm, and (e) optical depth from the cloud top at a wavelength of 550 nm. Here, the effective radii are calculated following Eq. (3.11) in Fu (1996) and are averaged only in cloudy grids over the tropics. In addition, the effective radii below the altitude of 5 km are masked out to avoid noisy values in the melting layer.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Now, the impact of the revision on the radiative fluxes are approximately estimated assuming a simple single cloud layer model. The increment of τdep from 0.6 to 0.7 approximately corresponds to the increment of the cirrus emissivity ε from 0.38 to 0.42 with a cirrus emissivity parameterization proposed by Fu and Liou (1993) [ε = 1 − exp (−0.79τdep)] with the visible optical depth τdep. Assuming the clear sky outgoing longwave radiation (OLR) as 280 W m−2 over the tropics, the increase in the cirrus emissivity results in the decrease in the OLR by approximately 7.5 W m−2. Similarly, the increment of τdep corresponds to the increment of the visible cloud albedo from 0.094 to 0.11 based on the two-stream method {αvis=[3 (1−g1)τdep]/[2+3 (1−g1)τdep] (Liou 2002)} with the assumption of the asymmetry factor g1 ∼ 0.8 (Seiki et al. 2014). Assuming the shortwave incident to the surface as 300 W m−2 over the tropics, the increase in the visible cloud albedo results in the increase in the outgoing shortwave radiation (OSR) by approximately 4.8 W m−2.

The rapid response of the global radiation budget to the revisions was examined during the last five days. This study uses the Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) top of the atmosphere (TOA) monthly means data Edition 4.1 data product [CERES-EBAF (Loeb et al. 2018)] for reference. Outgoing shortwave radiation slightly improves only over the narrow range of the Intertropical Convergence Zone (ITCZ) and its increment over the tropics (∼4.1 W m−2) was well explained by the simple estimation (∼4.8 W m−2) (Fig. 15). Similarly, the OLR over the subtropics to tropics clearly improves with the revisions (Fig. 16) and its increment over the tropics (∼8.3 W m−2) was explained by the simple estimation (∼7.5 W m−2) as well.

Fig. 15.
Fig. 15.

Comparison of the horizontal map of (a)–(c) OSR (W m−2) and (d) the zonal mean values of OSR (W m−2). Satellite observations from the CERES-EBAF products were used to illustrate the monthly mean values in September 2016.

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Fig. 16.
Fig. 16.

As in Fig. 15, but for OLR (W m−2).

Citation: Journal of the Atmospheric Sciences 80, 1; 10.1175/JAS-D-22-0049.1

Note that a major portion of the bias in OSR over the subtropics to tropics does not change because NICAM has long-lasting biases in low-level clouds originating from boundary layer processes (Kodama et al. 2015, 2021). The remaining biases in OLR over the tropics to subtropics were expected to improve by increasing the horizontal resolution because convective strength is known to be relatively weak in global simulations with a horizontal resolution of 14 km (Miyamoto et al. 2013; Seiki et al. 2015b; Kajikawa et al. 2016; Yashiro et al. 2016). In particular, convection over tropical land is known to be very sensitive to the horizontal resolution (Yashiro et al. 2016).

Zonal mean values of atmospheric temperature, horizontal wind, and precipitation rates do not distinctively change by the revision during the simulation period (not shown). The climate states could slowly change through the change in the radiative budget, as discussed for global warming.

5. Summary

This study revised the collisional growth, heterogeneous ice nucleation, and homogeneous ice nucleation processes in a double-moment bulk cloud microphysics scheme implemented in NICAM (NDW6).

  1. 1) Collisional growth was evaluated using the Gauss–Legendre quadrature, which contains a dual loop with a loop length of 4, to avoid numerical errors originating from the power-law formulation of the terminal velocity.
  2. 2) Heterogeneous ice nucleation was evaluated with the tendency of ice supersaturation instead of the vertical gradient of ice supersaturation.
  3. 3) The calculation order of homogeneous ice nucleation was changed.
  4. 4) The total computational cost of global simulations with a horizontal resolution of 14 km increased by approximately 11% due to the revisions.

All the revisions worked to increase the cloud ice mixing ratio and cloud ice number concentration. As a result, these revisions successfully improve the OLR, particularly over the ITCZ, in reference to the CERES satellite observations. In addition, the revision of collisional growth significantly reduces graupel production, particularly in intense rainfall systems. Therefore, the revisions were beneficial for long-term climate simulations and representing the structure of severe storms.

Acknowledgments.

The CloudSat and CERES-EBAF satellite products were obtained from the NASA Langley Research Center Atmospheric Science Data Center. The combined CloudSat–CALIPSO products were supplied by the EarthCARE Research Product Monitor (http://www.eorc.jaxa.jp/EARTHCARE/research_product/ecare_monitor.html) by the Japan Aerospace Exploration Agency (JAXA). The Joint Simulator for Satellite Sensors, which was used for the postprocess of the model results, was provided by JAXA (https://sites.google.com/site/jointsimulator/home). The authors were supported by the Integrated Research Program for Advancing Climate Models (TOUGOU) Grant JPMXD0717935457 from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. Tatsuya Seiki was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant JP21K03674 and Third Research Announcement on the Earth Observations of the Japan Aerospace Exploration Agency (JAXA). The simulations in this study were performed using the Earth Simulator. We appreciate the careful evaluation of the original manuscript and constructive comments from three anonymous reviewers.

Data availability statement.

The model output used in this study was not archived in public data storage due to its size but will be curated for 5 years and is available upon request by contacting the corresponding author. The source code availability of the NICAM and the experimental settings are documented by Kodama et al. (2021) in detail.

REFERENCES

  • Austin, R. T., and G. L. Stephens, 2001: Retrieval of stratus cloud microphysical parameters using millimeter-wave radar and visible optical depth in preparation for CloudSat: 1. Algorithm formulation. J. Geophys. Res., 106, 28 233–28 242, https://doi.org/10.1029/2000JD000293.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Austin, R. T., A. J. Heymsfield, and G. L. Stephens, 2009: Retrieval of ice cloud microphysical parameters using the CloudSat millimeter-wave radar and temperature. J. Geophys. Res., 114, D00A23, https://doi.org/10.1029/2008JD010049.

    • Search Google Scholar
    • Export Citation

  • Böhm, H. P., 1989: A general equation for the terminal fall speed of solid hydrometeors. J. Atmos. Sci., 46, 2419–2427, https://doi.org/10.1175/1520-0469(1989)046<2419:AGEFTT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Connolly, P. J., C. Emersic, and P. R. Field, 2012: A laboratory investigation into the aggregation efficiency of small ice crystals. Atmos. Chem. Phys., 12, 2055–2076, https://doi.org/10.5194/acp-12-2055-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • DeMott, P. J., D. J. Cziczo, A. J. Prenni, D. M. Murphy, S. M. Kreidenweis, D. S. Thomson, R. Borys, and D. C. Rogers, 2003: Measurements of the concentration and composition of nuclei for cirrus formation. Proc. Natl. Acad. Sci. USA, 100, 14 655–14   660, https://doi.org/10.1073/pnas.2532677100.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Fu, Q., 1996: An accurate parameterization of the solar radiative properties of cirrus clouds for climate models. J. Climate, 9, 2058–2082, https://doi.org/10.1175/1520-0442(1996)009<2058:AAPOTS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Fu, Q., and K. N. Liou, 1993: Parameterization of the radiative properties of cirrus clouds. J. Atmos. Sci., 50, 2008–2025, https://doi.org/10.1175/1520-0469(1993)050<2008:POTRPO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hagihara, Y., Y. Ohno, H. Horie, W. Roh, M. Satoh, T. Kubota, and R. Oki, 2022: Assessments of Doppler velocity errors of EarthCARE cloud profiling radar using global cloud system resolving simulations: Effects of Doppler broadening and folding. IEEE Trans. Geosci. Remote Sens., 60, 3060828, https://doi.org/10.1109/TGRS.2021.3060828.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hamada, A., Y. N. Takayabu, C. Liu, and E. J. Zipser, 2015: Weak linkage between the heaviest rainfall and tallest storms. Nat. Commun., 6, 6213, https://doi.org/10.1038/ncomms7213.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Harris, L., and Coauthors, 2020: GFDL SHiELD: A unified system for weather-to-seasonal prediction. J. Adv. Model. Earth Syst., 12, e2020MS002223, https://doi.org/10.1029/2020MS002223.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hashino, T., M. Satoh, Y. Hagihara, T. Kubota, T. Matsui, T. Nasuno, and H. Okamoto, 2013: Evaluating cloud microphysics from NICAM against CloudSat and CALIPSO. J. Geophys. Res., 118, 7273–7292, https://doi.org/10.1002/jgrd.50564.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hashino, T., and Coauthors, 2016: Evaluating arctic cloud radiative effects simulated by NICAM with A-train. J. Geophys. Res. Atmos., 121, 7041–7063, https://doi.org/10.1002/2016JD024775.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Heymsfield, A. J., and M. Kajikawa, 1987: An improved approach to calculating terminal velocities of plate-like crystals and graupel. J. Atmos. Sci., 44, 1088–1099, https://doi.org/10.1175/1520-0469(1987)044<1088:AIATCT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Heymsfield, A. J., C. Schmitt, and A. Bansemer, 2013: Ice cloud particle size distributions and pressure-dependent terminal velocities from in situ observations at temperatures from 0° to −86°C. J. Atmos. Sci., 70, 4123–4154, https://doi.org/10.1175/JAS-D-12-0124.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hohenegger, C., L. Kornblueh, D. Klocke, T. Becker, G. Cioni, J. F. Engels, U. Schulzweida, and B. Stevens, 2020: Climate statistics in global simulations of the atmosphere, from 80 to 2.5 km grid spacing. J. Meteor. Soc. Japan, 98, 73–91, https://doi.org/10.2151/jmsj.2020-005.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hourdin, F., and Coauthors, 2017: The art and science of climate model tuning. Bull. Amer. Meteor. Soc., 98, 589–602, https://doi.org/10.1175/BAMS-D-15-00135.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Illingworth, A. J., and Coauthors, 2015: The EarthCARE satellite: The next step forward in global measurements of clouds, aerosols, precipitation, and radiation. Bull. Amer. Meteor. Soc., 96, 1311–1332, https://doi.org/10.1175/BAMS-D-12-00227.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Judt, F., and Coauthors, 2021: Tropical cyclones in global storm-resolving models. J. Meteor. Soc. Japan, 99, 579–602, https://doi.org/10.2151/jmsj.2021-029.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kajikawa, Y., Y. Miyamoto, R. Yoshida, T. Yamaura, H. Yashiro, and H. Tomita, 2016: Resolution dependence of deep convections in a global simulation from over 10-kilometer to sub-kilometer grid spacing. Prog. Earth Planet. Sci., 3, 16, https://doi.org/10.1186/s40645-016-0094-5.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kärcher, B., J. Hendricks, and U. Lohmann, 2006: Physically based parameterization of cirrus cloud formation for use in global atmospheric models. J. Geophys. Res., 111, D01205, https://doi.org/10.1029/2005JD006219.

    • Search Google Scholar
    • Export Citation

  • Karrer, M., A. Seifert, D. Ori, and S. Kneifel, 2021: Improving the representation of aggregation in a two-moment microphysical scheme with statistics of multi-frequency Doppler radar observations. Atmos. Chem. Phys., 21, 17 133–17 166, https://doi.org/10.5194/acp-21-17133-2021.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Khvorostyanov, V. I., and K. Sassen, 1998: Cirrus cloud simulation using explicit microphysics and radiation. Part I: Model description. J. Atmos. Sci., 55, 1808–1821, https://doi.org/10.1175/1520-0469(1998)055<1808:CCSUEM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kodama, C., A. T. Noda, and M. Satoh, 2012: An assessment of the cloud signals simulated by NICAM using ISCCP, CALIPSO, and CloudSat satellite simulators. J. Geophys. Res., 117, D12210, https://doi.org/10.1029/2011JD017317.

    • Search Google Scholar
    • Export Citation

  • Kodama, C., and Coauthors, 2015: A 20-year climatology of a NICAM AMIP-type simulation. J. Meteor. Soc. Japan, 93, 393–424, https://doi.org/10.2151/jmsj.2015-024.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kodama, C., and Coauthors, 2021: The Nonhydrostatic Icosahedral Atmospheric Model for CMIP6 HighResMIP simulations (NICAM16-S): Experimental design, model description, and impacts of model updates. Geosci. Model Dev., 14, 795–820, https://doi.org/10.5194/gmd-14-795-2021.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kondo, M., Y. Sato, M. Inatsu, and Y. Katsuyama, 2021: Evaluation of cloud microphysical schemes for winter snowfall events in Hokkaido: A case study of snowfall by winter monsoon. SOLA, 17, 74–80, https://doi.org/10.2151/sola.2021-012.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kuba, N., T. Seiki, K. Suzuki, W. Roh, and M. Satoh, 2020: Evaluation of rain microphysics using a radar simulator and numerical models: Comparison of two-moment bulk and spectral bin cloud microphysics schemes. J. Adv. Model. Earth Syst., 12, e2019MS001891, https://doi.org/10.1029/2019MS001891.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kubota, T., S. Seto, M. Satoh, T. Nasuno, T. Iguchi, T. Masaki, J. M. Kwiatkowski, and R. Oki, 2020: Cloud assumption of precipitation retrieval algorithms for the dual-frequency precipitation radar. J. Atmos. Oceanic Technol., 37, 2015–2031, https://doi.org/10.1175/JTECH-D-20-0041.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Liou, K. N., 2002: An Introduction to Atmospheric Radiation. 2nd ed. Academic Press, 583 pp.

  • Locatelli, J. D., and P. V. Hobbs, 1974: Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79, 2185–2197, https://doi.org/10.1029/JC079i015p02185.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Loeb, N. G., and Coauthors, 2018: Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) Top-of-Atmosphere (TOA) edition-4.0 data product. J. Climate, 31, 895–918, https://doi.org/10.1175/JCLI-D-17-0208.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Masunaga, H., M. Satoh, and H. Miura, 2008: A joint satellite and global cloud-resolving model analysis of a Madden–Julian Oscillation event: Model diagnosis. J. Geophys. Res., 113, D17210, https://doi.org/10.1029/2008JD009986.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Matsugishi, S., H. Miura, T. Nasuno, and M. Satoh, 2020: Impact of latent heat flux modifications on the reproduction of a Madden–Julian Oscillation event during the 2015 pre-YMC campaign using a global cloud-system-resolving model. SOLA, 16A, 12–18, https://doi.org/10.2151/sola.16A-003.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Meehl, G. A., and Coauthors, 2019: Effects of model resolution, physics, and coupling on Southern Hemisphere storm tracks in CESM1.3. Geophys. Res. Lett., 46, 12 408–12 416, https://doi.org/10.1029/2019GL084057.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Meyers, M. P., P. J. DeMott, and W. R. Cotton, 1992: New primary ice-nucleation parameterizations in an explicit cloud model. J. Appl. Meteor. Climatol., 31, 708–721, https://doi.org/10.1175/1520-0450(1992)031<0708:NPINPI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Milbrandt, J. A., and M. K. Yau, 2005: A multimoment bulk microphysics parameterization. Part I: Analysis of the role of the spectral shape parameter. J. Atmos. Sci., 62, 3051–3064, https://doi.org/10.1175/JAS3534.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Milbrandt, J. A., and H. Morrison, 2016: Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part III: Introduction of multiple free categories. J. Atmos. Sci., 73, 975–995, https://doi.org/10.1175/JAS-D-15-0204.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Mitchell, D. L., 1996: Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities. J. Atmos. Sci., 53, 1710–1723, https://doi.org/10.1175/1520-0469(1996)053<1710:UOMAAD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Mitchell, D. L., P. Rasch, D. Ivanova, G. McFarquhar, and T. Nousiainen, 2008: Impact of small ice crystal assumptions on ice sedimentation rates in cirrus clouds and GCM simulations. Geophys. Res. Lett., 35, L09806, https://doi.org/10.1029/2008GL033552.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Miura, H., M. Satoh, T. Nasuno, A. T. Noda, and K. Oouchi, 2007: A Madden–Julian Oscillation event realistically simulated by a global cloud-resolving model. Science, 318, 1763–1765, https://doi.org/10.1126/science.1148443.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Miyakawa, T., and K. Kikuchi, 2018: CINDY2011/DYNAMO Madden–Julian Oscillation successfully reproduced in global cloud/cloud-system resolving simulations despite weak tropical wavelet power. Sci. Rep., 8, 11664, https://doi.org/10.1038/s41598-018-29931-4.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Miyakawa, T., Y. N. Takayabu, T. Nasuno, H. Miura, M. Satoh, and M. W. Moncrieff, 2012: Convective momentum transport by rainbands within a Madden–Julian oscillation in a global nonhydrostatic model with explicit deep convective processes. Part I: Methodology and general results. J. Atmos. Sci., 69, 1317–1338, https://doi.org/10.1175/JAS-D-11-024.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Miyakawa, T., and Coauthors, 2014: Madden–Julian Oscillation prediction skill of a new-generation global model demonstrated using a supercomputer. Nat. Commun., 5, 3769, https://doi.org/10.1038/ncomms4769.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Miyamoto, Y., Y. Kajikawa, R. Yoshida, T. Yamaura, H. Yashiro, and H. Tomita, 2013: Deep moist atmospheric convection in a subkilometer global simulation. Geophys. Res. Lett., 40, 4922–4926, https://doi.org/10.1002/grl.50944.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Miyamoto, Y., M. Satoh, H. Tomita, K. Oouchi, Y. Yamada, C. Kodama, and J. Kinter, 2014: Gradient wind balance in tropical cyclones in high-resolution global experiments. Mon. Wea. Rev., 142, 1908–1926, https://doi.org/10.1175/MWR-D-13-00115.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Nakano, M., M. Sawada, T. Nasuno, and M. Satoh, 2015: Intraseasonal variability and tropical cyclogenesis in the western North Pacific simulated by a global nonhydrostatic atmospheric model. Geophys. Res. Lett., 42, 565–571, https://doi.org/10.1002/2014GL062479.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Nakano, M., and Coauthors, 2017: Global 7 km mesh nonhydrostatic Model intercomparison project for improving TYphoon forecast (TYMIP-G7): Experimental design and preliminary results. Geosci. Model Dev., 10, 1363–1381, https://doi.org/10.5194/gmd-10-1363-2017.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Nasuno, T., H. Miura, M. Satoh, A. T. Noda, and K. Oouchi, 2009: Multi-scale organization of convection in a global numerical simulation of the December 2006 MJO event using explicit moist processes. J. Meteor. Soc. Japan, 87, 335–345, https://doi.org/10.2151/jmsj.87.335<