A Revised Approach to Ice Microphysical Processes for the Bulk Parameterization of Clouds and Precipitation

a. Sedimentation of falling ice crystals

b. Ice mass, diameter, and number concentration relationship

We believe it is important to distinguish between the number concentration of ice nuclei, as formulated by Fletcher (1962), for instance, and the activated ice crystal number concentration that depends not only upon the local availability of ice nuclei but also on the history of the air parcel carrying the ice crystals. Two-moment schemes predict number concentration as an independent variable and can therefore incorporate such information directly, but we chose to continue with a one-moment scheme. Double-moment schemes such as Ferrier (1994) and Reisner et al. (1998) are beyond the scope of this study and often have complex numerical issues associated with separately advecting mass and number concentration fields. More recent observations [than Fletcher (1962)] reported in Ryan (2000) show that the relation between ice crystal number concentration and cloud temperature is not consistent from case to case [see Fig. 5 of Ryan (2000)], but there are measurements from several field programs that show a correlation between ice mass and number concentration (A. Heymsfield 2002, personal communication). The ice mass is affected by processes including ice initiation, deposition, sublimation, accretion, autoconversion, advection, and sedimentation. By relating number concentration to ice mass these processes also indirectly affect number concentration, which is realistic and addresses a perceived deficiency in one-moment schemes that parameterize number concentration solely in terms of local thermodynamic variables.

The resulting mass, diameter, and number concentration relationships developed in this study are as follows:

View Expanded

where again all units are in MKS. We slightly changed the coefficients for the mass–diameter relation for simplicity. The mass versus diameter formula has a square power as in RH83. Recall that Eq. (5c) ensures that the mean terminal velocity, V_I, is the same as that of Heymsfield and Donner (1990) [Eq. (1)] for a given cloud ice amount when this relation is used in conjunction with a velocity–diameter relation (5a) derived by Heymsfield and Iaquinta (2000). The current scheme allows for consistent ice crystal sizes to be used for both sedimentation and ice microphysical processes, which is an improved aspect compared to the old scheme. Existing schemes implicitly ignore this connection unless they relate the fall speed of ice crystals to a mean diameter that is also used in the microphysics.

c. Intercept parameter for snow (n_0S)

RH83 and D89 treat the spectral intercept parameter for snow (n_0S) as a constant (2 × 10⁷ m⁻⁴) despite its strong dependency on temperature in nature (Ryan 1996). Based on Houze et al. (1979), n_0S can be expressed as

View Expanded

The above formula indicates an increase of the n_0S as the temperature decreases. The computed values are given an upper bound of 2 × 10⁸ m⁻⁴ since there is no observational evidence at cloud temperatures below −35°C (Ryan 1996). With this formula, the slope parameter of the size distributions for snow, λ_S = (πρ_Sn_0S/ρq_S)^1/4, where ρ_S is the density of snow and q_S is the mixing ratio of snow, increases from 10³ m⁻¹ to 10⁴ m⁻¹ as cloud temperature decreases for typical snow concentrations of 0.1 × 10⁻³ to 1 × 10⁻³ kg kg⁻¹. This formula implicitly represents broadening of the snow spectra at higher temperature that is well documented in observational studies (Houze et al. 1979; Ryan 1996).

The value of 2 × 10⁷ m⁻⁴ of RH83 and D89 corresponds to that at T = −19.5°C in Eq. (6). The increase of n_0S at colder temperatures means an increase of snow number concentration, which enhances the rate of accretion of ice and sublimation/deposition of snow and reduces the sedimentation of snow through the reduced mean size of snow aggregates.

d. Initiation of cloud ice crystal (Pgen)

For RH83 and D89, the initiation rate of cloud ice from water vapor when T < 0°C and the air is supersaturated with respect to ice under the no ice condition was given by

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where Pgen ≥ 0, Δt is the time step, q is the water vapor mixing ratio, q_SI is its saturated value with respect to ice, q_I0 is M_I0N_I0/ρ, and M_I0 is the initial mass of cloud ice that corresponds to 10⁻¹² kg. It can be seen that given the N_I0 of Fletcher (1962), N_I0M_I0/ρ is usually greater than q_I in the upper troposphere, which leads to a bounded value of Pgen at (q − q_SI)/Δt. For example, M_I0N_I0/ρ is 0.1 × 10⁻³ kg kg⁻¹ for T = −38.5°C, and 1.0 × 10⁻³ kg kg⁻¹ for T = −42.5°C. For temperatures below −43°C, Pgen assumes the supersaturated amount of water vapor with respect to ice, and all the supersaturation is removed immediately.

e. Vapor deposition of a small ice crystal (Pisd)

For RH83 and D89, the growth rate of ice crystals by deposition of water vapor, when the air is supersaturated with respect to ice, was given by using the mean mass of an ice crystal (M_I = ρq_I/N_I) and the mass–diameter relation in Eq. (5b),

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where S_I is the ice saturation (q_SI/q), A_I and B_I are thermodynamic functions (see, e.g., D89). Here, D_Icon is 11.9 instead of 16.3, used by RH83 and D89. Because of the new formulation of N_I that generally implies larger crystals, Pisd is slower at colder temperatures, as it should be, whereas Pisd was unrealistically active at colder temperatures in RH83 (Fig. 3). Our formula for Pgen is more active at colder temperatures than Pisd, which is more active at warmer temperatures. The formulation Pgen is responsible for the initiation of small ice crystals in favorable conditions where few or none existed before while the further growth of crystals is taken into account by the deposition process, but this also has an implicit initiation because of the mass–number relation that is assumed to always hold. For RH83, both processes are more active at cold temperatures because of the use of higher number concentrations implying smaller crystals.

f. Accretion of cloud ice by snow (Pacr)

The accretion rate of cloud ice by snow is parameterized as in RH83 and D89 and is given by

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in which the accretion efficiency, E_SI, is a constant at 0.1, b_S = 0.41 is the exponent, and a_S = 11.72 is the multiplier in the snowfall-speed formula. Note that as in LFO83 and D89, Eq. (10) was derived without considering the effect of cloud ice sedimentation. The effect of ice sedimentation in the accretion of cloud ice by snow can be adopted in the future (M. Gilmore 2003, personal communication). Based on physical justification, accretion of cloud ice by snow is more active at higher temperature (LFO83), so a new efficiency function is expressed by

E_SITT₀(11)

where T₀ is the freezing temperature (273.15K). The formula in (11) is similar to a temperature-dependent efficiency in LFO83 but has a more rapid decrease of the efficiency at colder temperatures. On the other hand, an opposing effect at colder temperatures is expected because of the increase of n_0S in (6).

g. Conversion of ice crystals to snow (Paut_I)

h. Sublimation and depositional growth of snow/evaporation of rain (Pres)

The evaporation of rainwater is calculated if the air is subsaturated with respect to water, and the formula [Eq. (B14) in D89] is very similar to that for snow sublimation given below. For snow, however, the formula is with respect to ice saturation, where both subsaturation and supersaturation may occur. As in RH83 and D89, the continuous growth equation is given by

View Expanded

where S_c is the Schmidt parameter and μ is the dynamic viscosity of air. Compared to the process with n_0S = 2 × 10⁷ m⁻⁴ in RH83 and D89, the formula for n_0S in this study (6) produces larger (smaller) Pres at colder (warmer) temperatures, consistent with the assumed broadening of the snow size spectrum.

i. Autoconversion of cloud water to rain (Paut_C)

Autoconversion is the process whereby cloud droplets form raindrops through collisions with each other. Following Kessler (1969), the autoconversion rate of cloud water to rain may be written as

⁻¹⁻¹αq_Cq_C0(15)

in which the autoconversion rate from cloud water, q_C, to rain depends on a critical liquid water content for cloud water (q_C0). Here an autoconversion parameterization with a stronger physical basis (Tripoli and Cotton 1980, hereafter TC80) is adopted and can be expressed by

View Expanded

where μ is the dynamic viscosity of air (1.718 × 10⁻⁵ kg m⁻¹ s⁻¹), ρ_w is the density of water, N_C is the droplet concentration (3 × 10⁸ m⁻³), g is the acceleration due to gravity, E_c is the mean collection efficiency (0.55). Also, H(x) is the Heaviside unit step function, which suppresses the autoconversion processes until cloud water reaches a critical mixing ratio (q_C0),

View Expanded

where r_cr is the critical mean droplet radius at which the autoconversion begins.

The formula of TC80 is more physically based than Kessler's (1969). It can be shown that the TC80 scheme represents a similar conversion rate to that of Kessler for q_C less than 1 × 10⁻³ kg kg⁻¹ and a faster conversion for larger droplets. However, for typical values of q_C less than 1 × 10⁻³ kg kg⁻¹, the two formulas convert the cloud droplets similarly despite the complexity in TC80. As pointed out by LFO83, the critical mixing ratio is important in the Kessler formula. This value has been tuned to a smaller value of 0.5 × 10⁻³ or 0.7 × 10⁻³ kg kg⁻¹, relative to the original value of 1 × 10⁻³ kg kg⁻¹ in LFO83 to produce raindrops realistically on a mesoscale grid. Likewise, r_cr is an important parameter in the TC80 formula. We set the value to 8 μm instead of 10 μm used in TC80. With a value of 10 μm, the threshold value for conversion is 1.28 × 10⁻³ kg kg⁻¹, which is similar to the threshold used in the LFO83. In addition, the TC80 formula is consistent with the autoconversion of ice to snow in Eqs. (12)–(13) through the introduction of number concentration of cloud droplets. The number concentration of cloud droplets is also a tunable parameter that may be larger in unpolluted and marine environments.

a. Idealized thunderstorm experiment

The idealized thunderstorm simulation is a present option for the WRF model. We chose a 2D domain in the x direction. The grid in the x direction is 201 points with a 250-m grid spacing. The number of vertical layers is 80. The model is integrated for 60 min with a time step of 3 s. The initial condition has a warm bubble that has a radius of 4 km and a maximum perturbation of 3 K at the center of the domain. A 12 m s⁻¹ wind is applied in the positive x direction at the surface, decreasing to zero at 2.5 km above the ground, with no wind above. Open boundary conditions are applied, and there is no Coriolis force or friction. The only physical parameterization is the microphysical scheme. This experiment serves to show the behavior of the microphysics in a quasi-steady setting that simplifies the interpretation of the results. After an hour simulation, the thunderstorm started to move in the x direction within the periodic lateral boundaries.

Figure 4 compares the condensate fields from Exp4 to those from the PLS experiment. The PLS experiment is referred to as a reference run since it predicts cloud water, cloud ice, snow, graupel, and rainwater explicitly. Despite the simplified representation of ice processes in Exp4, the scheme shows its capability of simulating fundamental features of a well-organized thunderstorm. The general structure of the thunderstorm, such as the cloud/ice water in the updraft region near the storm center and anvil clouds, is well simulated. Cloud condensate reaches a maximum in the middle troposphere in the area of the updraft for both experiments. A wider area of the rain shaft in the PLS experiment may be due to higher fall speed of precipitation due to the inclusion of graupel. The overall resemblance of the results from the cloud 3 and Purdue Lin schemes assures us that the simplified ice microphysical processes are reasonable for even this high resolution of 250 m in the horizontal. The basic features of the simulated storm are unchanged from Exp1 to Exp4, but the detailed structure is different, as shown below.

Figure 5 compares profiles of domain-averaged condensate and precipitation mixing ratios for Exp1–Exp4. Overall, the impact of sedimentation of falling ice is small without considering our modifications of microphysics since the use of Fletcher's (1962) formula for diagnosing both N_I0 and N_I allows too many small ice crystals to be generated and persist in the upper troposphere, and these do not grow into snow crystals at a significant rate. Only a slight reduction of q_I in the anvil centered at the 10-km level is visible (Fig. 5; cf. Exp1 and Exp2). It is apparent that the distribution of cloud ice is more uniform in the vertical through the incorporation of ice microphysics introduced in this study (cf. Exp1 and Exp3). The average cloud content at upper levels is decreased by more than a factor of 2. An increase of ice is also distinct in the lower part of the ice clouds below 8 km. The ice crystal mixing ratio in the anvil ranges from 0.1 × 10⁻³ to 1 × 10⁻³ kg kg⁻¹ in Exp1, whereas the range is from 0.01 × 10⁻³ to 0.1 × 10⁻³ kg kg⁻¹ in Exp3. This smaller magnitude of q_I in Exp3 is closer to some observations in cold cloud ice shields (HI2000). As compensation, there is an increase of snow at the colder temperatures and a decrease at warmer temperatures.

The distribution characteristics of ice and snow are a combined effect of the modifications in the ice microphysics described in section 2. The reduction of ice and the increase of snow at colder temperatures are due mostly to the increase of n_0S and non-temperature-dependent ice number concentration. The increase of n_0S at colder temperatures enhances the rate of accretion of ice and sublimation/deposition of snow. The new formulas for ice nucleation [Eqs. (7)–(8)] also reduce (increase) the initial generation of ice at temperatures cooler than −38°C (warmer than −38°C) when ice does not exist. The rate of ice deposition (9) is also decreased because of smaller ice number concentrations at colder temperatures but is more active at warmer temperatures. Accretion of ice particles onto snow (10)–(11) is active at midcloud layers, together with the effect of n_0S. The conversion process from ice to snow (12) is less active at warmer temperatures and more active at colder temperatures (see Fig. 2). The reduction of cloud water below 4 km is found to be due to an indirect impact of ice microphysics rather than the change of autoconversion following TC80. The effect of the inclusion of ice sedimentation is still small compared to the changes in microphysics but more distinct when the new microphysics is employed (cf. Exp3 and Exp4). The introduction of sedimentation of ice particles reduces the ice amount in the upper part of ice shields but does not affect the snow distribution.

Modifications in the ice microphysical processes reduce the ice crystals and increase the snow at colder temperatures and does alleviate a discontinuity of ice and snow distributions seen in vertical soundings by also increasing the ice and decreasing the snow at warmer temperatures.

b. Heavy rainfall case experiment

A heavy rainfall event is selected in this study to investigate the impact of the new parameterization on the simulated precipitation and upper-atmospheric large-scale properties. A significant amount of precipitation was recorded in Korea on 25 July 1997 (Fig. 6), with a local maximum of about 170 mm in the west-central part of South Korea and another of about 90 mm at the southeastern flank of the peninsula. Most of the rainfall was observed during the 12-h period from 0000 to 1200 UTC 25 June 1997. Before the onset of heavy precipitation at 0000 UTC 25 June, moderate rain was observed at the southwestern part of Korea, with less than 40 mm between 1200 UTC 24 June and 0000 UTC 25 June 1997. Associated with the heavy rainfall over Korea, there was a low pressure system centered over the Yellow Sea, with a warm front to the east and a cold front to the southwest, that was embedded within a monsoon circulation (Fig. 7a). Associated with this low pressure system, convective activity is visible both to the south of the cold front and to the north of the warm front (Fig. 7b).

From the upper-level analyses (not shown), it is found that a southerly low-level jet (LLJ), which was associated with a cyclonic circulation centered over the low system and an anticyclonic circulation along the western flank of a subtropical high, brought moisture northward. As the low pressure system moved northeastward and the subtropical high further extended to the west, the LLJ south of a monsoon front was intensified. The enhanced LLJ brought moisture to the Korean peninsula. The upper-level circulation shows intensification of a thermal ridge over the peninsula and a trough to the west of the surface low system centered over the Yellow Sea. These LLJ and upper-level patterns satisfy the synoptic circulation favorable for developing heavy precipitation over the Korean peninsula (Lee et al. 1998; Chen et al. 1999).

Initial and boundary conditions are based on the global analysis and prediction system that is routinely produced operationally at NCEP. Incorporating information from upper-level sounding data through the MM5 analysis system further enhances initial conditions, and these files are then adapted for input to the WRF system using the MM52WRF converter program. The 48-h experiments start at 1200 UTC 23 June 1997, 36 h prior to the onset of heavy precipitation in the Korean peninsula. The model is run at 45-km grid spacing in the horizontal on a Lambert-conformal conic projection with 23 levels in the vertical. The number of horizontal grid points in both x and y directions is 80, centered on the Korean peninsula covering the area of Fig. 7a. A higher-resolution experimental setup is desired, but the current version of the WRF model does not have a nesting capability. The PLS experiment will only briefly be discussed in the final section since this graupel scheme was not designed for such large grid sizes.

Table 2 shows the statistics of simulated precipitation over South Korea and the domain-averaged 300-hPa temperature. The number of surface observation stations over South Korea is 72, which is about 35-km horizontal resolution. The 24-h accumulated observed precipitation data are linearly interpolated on the WRF grid by using a simple objective analysis (Cressman 1959) to compute the statistics. The spatial pattern correlation coefficient is computed between simulated and observed precipitation on the WRF grids for each experiment. The bias score for precipitation for each experiment is the ratio of the area-averaged simulated precipitation over the observed value. The 300-hPa temperature is verified over the NCEP reanalysis that is used to provide the lateral boundary data. The bias and rms values averaged over the model domain are the difference and root-mean-square error values between simulation and reanalysis, respectively.

It is clear that Exp4 improves the precipitation scores over Korea by enhancing the precipitation activity in both cloud 3 and cloud 5 schemes. Meanwhile, the improvement of the 300-hPa mean temperature is distinct in Exp4. The improvement of precipitation scores by enhanced precipitation and reduced warm bias in Exp4 are not only due to the improvement of microphysics, but are also due to a better cloud–radiation feedback, which is an indirect effect of the new scheme and which will further be discussed at the end of this section.

Overall, the impact of the microphysics for the heavy rainfall case follows the scenario revealed in the idealized experiments but with a larger impact in the upper part of cloud shields because of the incorporation of a radiation feedback in the 3D model framework (Fig. 8). The impact of the changes in microphysics and the ice sedimentation on simulated ice clouds follows the characteristics analyzed in the idealized experiments (Fig. 8a) but with sedimentation having more impact possibly because of the longer time scale of this simulation. For example, the decrease of ice in the upper part of clouds is distinct in going from Exp1 to Exp2 and from Exp3 to Exp4. The increase of ice at warmer temperatures is pronounced, as in the idealized experiments. The monotonic decrease of the sum of ice and snow in Exp4 with decreasing temperature is consistent with the results from Ryan (2000). The combined effect of improved microphysics and sedimentation of ice provides a significant effect on the cloud and precipitation particles. In Exp3 and Exp4, coexisting ice and snow are seen at warmer temperatures below 13 km, whereas there is negligible ice at these levels in Exp1 and Exp2. On the other hand, the sensitivity of the distribution of snow/rain is different from the behavior revealed in the idealized experiments. The impact of the changes in the microphysics alone on the snow/rain distribution follows that in the idealized case above z = 4 km. However, unlike in the idealized case, the addition of sedimentation also has a significant impact, considerably increasing the snow/rain within the entire troposphere below 13 km.

Both schemes relate sedimentation to ice mass by HD90 (Exp2 and Exp4), but Fig. 8 shows that there is a stronger effect when sedimentation of ice is added to the new microphysics. This is mostly due to an enhanced conversion to snow when sedimentation is activated, while the former scheme's snow amount is unaffected by adding sedimentation (Exp2). This happens because when the ice mass is reduced at a high level by sedimentation the new scheme (Exp4) also reduces the number of ice crystals through (4), while the old scheme, where the number is only a function of temperature following Fletcher [1962; Eq. (3)] would unrealistically assume the same number to be distributed in the smaller remaining mass. Hence sedimentation in the new scheme leads to fewer crystals that still easily convert to faster falling snow, thereby enhancing the fallout, while the old scheme implies many smaller crystals that cannot convert, and thus the slower HD90 sedimentation rate continues to apply.

In Fig. 9, the 24-h accumulated precipitation amounts during the heavy precipitation period from Exp1 and Exp4 are shown. The resulting point values of accumulated precipitation, due to the changes of microphysics and inclusion of sedimentation, are increased by 20 mm over Korea. The enhanced precipitation seen in Exp4 is closer to what was observed (Table 2), owing to better areal coverage of the heavy rain. However, we note that many more case studies are needed to determine whether the improvements in Exp4 give forecasts that are consistently closer to the observed rainfall. An increase of precipitation was evident in Exp2 and Exp3 over Korea but was much smaller than that from Exp4. Note that the increased portion of precipitation over Korea is mostly due to the grid-resolvable precipitation physics. The convective parameterization scheme is responsible for less than 2 mm of the accumulated precipitation (not shown) during the 24-h period of precipitation in Fig. 9. This is due to that fact that heavy rainfall over Korea is linked with a nearly saturated atmospheric structure up to the middle troposphere embedded in the east Asian summer monsoon front (Hong and Lee 1994; Lee et al. 1998; Chen et al. 1999). It is interesting to note that major features of simulated precipitation remain unchanged by the introduction of the new physical processes and the inclusion of sedimentation of cloud ice (Fig. 9), despite some improvement of precipitation forecast skill scores (Table 2). The distribution of simulated precipitation was similar to that in Exp4 when the Purdue Lin scheme is introduced (not shown). This implies that the heavy rainfall case selected in this study is synoptically organized, as is typical for heavy rainfall in Korea (Lee et al. 1998).

The time evolution of domain-averaged precipitation amounts due to subgrid-scale (implicit) processes from the convective parameterization scheme and the grid-resolvable (explicit) processes from the cloud microphysics is shown in Fig. 10. Note that most of the precipitation over Korea in Fig. 9 is due to microphysics, as explained in the previous paragraph. Most of the implicit rain in Fig. 10 appears in southern China, where convective instability is a key mechanism (not shown). Consistent with the sensitivity of precipitation mixing ratio in Fig. 8, the increase of surface rain is pronounced in Exp4, particularly during the heavy precipitation period over Korea from the 30- to 48-h forecast time. The domain-total implicit rain experiences a distinct diurnal variation because of the nature of the Kain–Fritsch convective parameterization. Enhanced convective activity is found during the late afternoon in Exp4, which is an indirect effect of the microphysical process on large-scale features. This issue will be further addressed at the end of this section.

In Fig. 11, we show the vertically integrated ice/cloud water mixing ratio at 0000 UTC 25 June 1997. In the figure, rain/snow is identified over the precipitation areas in southern China, Korea, and northern Manchuria (not shown). It is apparent that too much cloud condensate is simulated in Exp1 when the modifications in section 2 are not considered (cf. Figs. 11a and 7b). Large amounts of cloud over the ocean south of Japan are spurious. As stated in the discussion of Fig. 8, the microphysics plays a more significant role than the sedimentation of ice in reducing the spurious ice in the upper atmosphere. For example, the spurious ice shields over the oceans south of Japan still exist in Exp3, with a smaller amount than in Exp1 and Exp2 (not shown).

The amount of cloud ice/water keeps increasing with time, being greatest in Exp1, followed by Exp2 and Exp3, while Exp4, with the new scheme, shows the slowest increase after the initial adjustment for a few hours (Fig. 12a). This monotonic increase of cloudiness with time in Exp1–Exp3 was reported in the previous literature. Manning and Davis (1997) showed such an increase of clouds when the sedimentation of ice particles is not considered, whereas Hong et al. (1998) demonstrated that the same trend was observed when a diagnostic precipitation process is employed or when horizontal advection of clouds is not considered. The improvement in large-scale mean temperature is striking (Fig. 12b). Exp4 is capable of suppressing the synoptic-scale drift of the simulated large-scale temperature. Compared to the sensitivity of cloudiness, the impact of either sedimentation of ice or microphysics only is much smaller than the combined effect. The same improvement was obtained for moisture fields by suppressing the monotonic increase of moisture with time. The correction of the large-scale bias is also found below 400 hPa, but with a smaller magnitude than in the upper troposphere.

Additional experiments were conducted to reveal the cause of the 300-hPa warm bias in Exp1. The NORA, NOLW, and NOSW experiments are the same as Exp1 but exclude the radiative effects of short- and longwave heating due to ice particles. In other words, the NORA, NOLW, and NOSW experiments exclude both short and longwave heating, longwave heating, and shortwave heating due to ice, respectively. From Fig. 13, it can be seen that, while the effect on cloud amount is quite small, the removal of longwave–cloud interaction cools the troposphere below the cirrus, while the removal of shortwave–cloud interaction has a warming effect there. It can be inferred that excessive longwave radiation heating, due to trapping by too much ice cloud above, is the cause of the warm bias in Exp1. A reduction of shortwave heating in the troposphere due to cirrus shading is an opposite effect to that from the longwave, but has a much smaller impact. The absence of the ice cloud–radiation interaction increases surface precipitation (Table 3); this means that more (less) ice cloud decreases (increases) surface precipitation (Fig. 13a). Note again that precipitation over Korea is mostly due to explicit microphysics, whereas most of the implicit (convective) rain is simulated in southern China. It is evident that neglecting the shortwave–ice cloud interaction affects the amount of implicit rain due to parameterized convection, whereas the longwave radiation influences the explicit rain due to microphysical processes significantly. Having more implicit rain in the NOSW experiment is found to be due to the fact that more shortwave heating near the surface increases the moist static energy, which in turn leads to an increase in the convective available potential energy. Meanwhile, more explicit rain in the NOLW experiment is likely due to the fact that a colder temperature in the absence of longwave–ice cloud interaction increases the relative humidity in the upper troposphere.