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--> --> -->Cloud droplet relative dispersion (ε), defined as the ratio of the standard deviation to the mean droplet radius, increases with an increasing cloud droplet number concentration due to increasing anthropogenic aerosols, because the larger number of small droplets formed in polluted clouds compete for water vapor and broaden the droplet size distribution, as compared with clean clouds having fewer droplets and less competition (Liu and Daum, 2002). This enhanced ε reduces the changes induced by aerosols in the R e and the liquid water path, exerts a warming effect, and in turn partly offsets the cooling of aerosol indirect radiative forcing (Liu and Daum, 2002; Xie et al., 2017). Hence, parameterizations of R e and A r considering the dispersion effect have been proposed to investigate aerosol indirect effects (Liu and Daum, 2002, 2004; Peng and Lohmann, 2003; Rotstayn and Liu, 2003; Liu et al., 2007, 2008; Xie and Liu, 2009, 2013). (Liu and Daum, 2002) related R e to ε and further parameterized ε in terms of an empirical relationship with cloud droplet number concentration and showed that the magnitude of aerosol indirect radiative forcing can be reduced significantly when considering the dispersion effect. Implementation of this parameterization of R e with ε into various GCMs, including CSIRO Mk3.0 (Rotstayn and Liu, 2003) and ECHAM4 (Peng and Lohmann, 2003), largely confirmed the results reported by (Liu and Daum, 2002). The A r determines the onset of the surface precipitation associated with warm clouds, and its parameterization has always attracted much attention. In recent years, one-moment mass content schemes (e.g., Planche et al., 2015; Lee and Baik, 2017) and two-moment mass content and droplet concentration schemes (e.g., Sednev and Menon, 2012; Kova?evi? and ?uri?, 2014; Michibata and Takemura, 2015) of autoconversion have been applied to numerical models of different scale. Additionally, (Liu and Daum, 2004) developed an analytical autoconversion rate for mass content that accounts explicitly for ε using the generalized mean value theorem of integrals into the general collection equation. Extension of this theoretical expression to include the autoconversion threshold and autoconversion rate for cloud droplet number concentration were derived by Liu et al. (2006, 2007) and (Xie and Liu, 2009). The parameterization of A r in mass content with ε has been used in CSIRO Mk3.0 (Rotstayn and Liu, 2005) and in the Weather Research and Forecasting model (Xie and Liu, 2011, 2015; Xie and Liu, 2013). Recently, cloud microphysical schemes with two-moment A r and R e with ε have been successfully implemented into the Community Atmosphere Model, version 5.1 (CAM5.1), significantly reducing the aerosol indirect forcing——especially over the Northern Hemisphere (Xie et al., 2017).
The latest version (version 4.1) of the IAP's AGCM (IAP AGCM 4.1), which is also the atmospheric component of the Chinese Academy of Sciences' Earth System Model, is described in (Zhang et al., 2013) and (Lin et al., 2016). IAP AGCM 4.1 adopts a physical package with a two-moment bulk stratiform cloud microphysics scheme from CAM5.1, as described by (Morrison and Gettelman, 2008), but has a different dynamical core (Zhang et al., 2009, 2013). Although the CAM5.1 microphysics schemes consider the dispersion effect on R e with different expression from (Liu and Daum, 2002), they do not include the dispersion effect on the A r (Xie et al., 2017). Hence, a cloud microphysical scheme including two-moment A r and R e schemes with ε is implemented in IAP AGCM 4.1, following (Xie et al., 2017) for CAM5.1. To demonstrate the superiority of the new schemes, we evaluate the performance and improvement of IAP AGCM 4.1 by comparing results with observations and CAM5.1 simulations——in particular, for cloud shortwave and longwave radiative forcings (SWCF and LWCF, respectively) and surface precipitation.
This paper is an extension to the preliminary study of (Xie et al., 2017) and is structured as follows: Section 2 describes the inclusion of the two-moment A r and R e with ε in the cloud microphysics of IAP AGCM 4.1, along with the configuration of the simulation experiments. Section 3 evaluates the simulated cloud fields and surface precipitation in IAP AGCM 4.1 with different cloud schemes against observations and CAM5.1 results. The main conclusions and further discussion are presented in section 4.
2.1. Description of IAP AGCM 4.1
IAP AGCM 4.1 can reproduce the observed climatology in a generally successful manner (Sun et al., 2012; Yan et al., 2014; Lin et al., 2016). It is a global grid-point model using a finite-difference scheme with a terrain-following σ coordinate. Its horizontal resolution is approximately 1.4°× 1.4° and it has 30 vertical levels with a model top at 2.2 hPa. The dynamical core of IAP AGCM 4.1 is described in detail by Zhang et al. (2009, 2013). The physical processes in IAP AGCM4.1 mostly derive from the CAM5 (Neale et al., 2010), including a two-moment bulk stratiform cloud microphysics scheme coupled with a three-mode version of the modal aerosol model, which enables the investigation of aerosol direct and semi-direct effects, as well as indirect effects (Morrison and Gettelman, 2008; Ghan et al., 2012; Liu et al., 2012). Parameterizations of all microphysical processes (Morrison and Gettelman, 2008) are adopted in this model, including the activation of cloud condensation nuclei or nucleation on ice nuclei to form cloud droplets or cloud ice, condensation/deposition, evaporation/sublimation, autoconversion of cloud droplets and ice to form rain and snow, accretion of cloud droplets and ice by rain, accretion of cloud droplets and ice by snow, heterogeneous freezing of cloud droplets to form ice, homogeneous freezing of cloud droplets, sedimentation, melting, and convective detrainment. The autoconversion process is parameterized by (Khairoutdinov and Kogan, 2000), which we refer to as the KK parameterization.2
2.2. Newly implemented parameterizations for R e and A r
The R e is parameterized via the following expression based on the assumption of the cloud droplet size distribution following a gamma distribution (Liu and Daum, 2002; Xie and Liu, 2013): \begin{equation} \label{eq1} R_{\rm e}=\left(\dfrac{3}{4\pi\rho_{\rm w}}\right)^{\frac{1}{3}}\dfrac{(1+2\varepsilon^2)^{\frac{2}{3}}}{(1+\varepsilon^2)^{\frac{1}{3}}} \left(\frac{L_{\rm c}}{N_{\rm c}}\right)^{\frac{1}{3}} ,\ \ (1) \end{equation} where L c (g cm-3) and N c (cm-3) represent the liquid water mass content and cloud droplet number concentration for clouds, respectively; and ρ w is the density of liquid water. The two-moment scheme of A r with ε can be easily derived from the analytical formulas (Xie and Liu, 2009). The number and mass autoconversion rates (PN and PL, respectively) can be written as \begin{align} \label{eq2} P_N&=1.1\times 10^{10}\frac{\Gamma(\varepsilon^{-2},x_{\rm cq})\Gamma(\varepsilon^{-2}+6,x_{\rm cq})}{\Gamma^2(\varepsilon^{-2}+3)}L_{\rm c}^2 , \ \ (2a)\end{align} \begin{align} \label{eq3} P_L&=1.1\times 10^{10}\frac{\Gamma(\varepsilon^{-2})\Gamma(\varepsilon^{-2}+3,x_{\rm cq})\Gamma(\varepsilon^{-2}+6,x_{\rm cq})}{\Gamma^3(\varepsilon^{-2}+3)}N_{\rm c}^{-1}L_{\rm c}^3 ,\tag{2b} \end{align} where \begin{align} \label{eq4} x_{\rm cq}&=\left[\frac{(1+2\varepsilon^2)(1+\varepsilon^2)}{\varepsilon^4}\right]^{\frac{1}{3}}x_{\rm c}^{\frac{1}{3}} ,\tag{2c}\ \ \\ \label{eq5} x_{\rm c}&=9.7\times 10^{-17}N_{\rm c}^{\frac{3}{2}}L_{\rm c}^{-2} .\tag{2d} \end{align} The Gamma function and the incomplete Gamma function can be represented as the following two formulas: \(\Gamma(n)=\int_0^\infty x^n-1\exp(-x)dx\) and \(\Gamma(n,a)=\int_a^\infty x^n-1 \exp (-x)dx\), respectively. The PN and PL both increase with L c and ε, but decrease with N c (Liu et al., 2007; Xie and Liu, 2009). The above cloud microphysical schemes of R e and two-moment A r have been successfully implemented in CAM5.1 (Xie et al., 2017). Here, we implement these cloud schemes into IAP AGCM 4.1, where the Rotstayn-Liu relationship of ε=1-0.7exp(-0.003N c) is adopted in our model (Rotstayn and Liu, 2003) instead of the default relationship of ε=0.0005714N c+0.271 (Morrison and Gettelman, 2008). The default relationship is based on a small number of measurements (ε=0.43 for "polluted continent" and ε=0.33 for "clean ocean"), whereas the Rotstayn-Liu relationship is derived from more measurements, as described by (Liu and Daum, 2002). Note that the KK parameterization is fitted by applying the least-squares method based on the results from a large-eddy simulation, which does not include the ε. However, our autoconversion parameterizations with ε are analytically derived by applying the generalized mean value theorem for integrals to the general collection equation (Xie and Liu, 2009). These autoconversion parameterizations used here are more reliable physically, and have been extended from one-moment (Liu and Daum, 2004) to two-moment schemes (Xie and Liu, 2009).2
2.3. Configuration of simulations
We run IAP AGCM 4.1 for the years 1979-2005 with historical sea-ice concentrations and SST derived from (Hurrell et al., 2008), and with historical greenhouse gases and anthropogenic aerosol emissions (Lamarque et al., 2010). Natural aerosols including sea salt and dust are predicted during this period. To examine the influences of the different cloud microphysical schemes on cloud microphysical fields and surface precipitation, two numerical experiments are performed——one with the standard and one with the new cloud microphysical schemes. The standard experiment (STANDARD) uses the default cloud microphysical scheme of IAP AGCM 4.1; the new experiment (NEW) is conducted by using the complete cloud schemes of R e (2) and two-moment A r (2) with the Rotstayn-Liu relationship between ε and the cloud droplet concentration.
Figure1. (a) Autoconversion rates from the KK scheme and the new autoconversion parameterizations for a fixed cloud droplet concentration of 100 cm-3. (b) Difference in the autoconversion rates (units: 10-9 kg kg-1 s-1) from STANDARD and NEW (NEW minus STANDARD).Observational cloud radiative forcings including SWCF and LWCF are derived from the CERES-EBAF satellite product from 2000 to 2010, as described by (Loeb et al., 2009), and the ERBE data from 1985 to 1989, as described by (Barkstrom and Hall, 1982). The simulated annual global mean SWCFs are -51.49 W m-2 inSTANDARD and -48.31 W m-2 inNEW, showing that the global mean SWCF inNEW is lower than that inSTANDARD. The main reason for this is that lower cloud liquid water exists at low levels over low latitudes inNEW, leading to smaller SWCF. These two values fall within the observational range given by CERES-EBAF (-47.07 W m-2) and ERBE (-54.16 W m-2). The simulated LWCFs are 22.78 W m-2 inSTANDARD and 23.56 W m-2 inNEW, which are lower than the observational values from (Loeb et al., 2009) and (Barkstrom and Hall, 1982). However, the value of LWCF inNEW is much closer to the observational range of 26.48-30.36 W m-2 compared to that inSTANDARD. The increased LWCF inNEW is due to a larger high-cloud fraction compared toSTANDARD. The observational total precipitation rate is derived from GPCP data from 1979 to 2009 (Adler et al., 2003) and CMAP data from 1979 to 1998 (Xie and Arkin, 1997). The simulated annual global mean tota l precipitation rates are similar forSTANDARD (2.95 mm d-1) andNEW (2.97 mm d-1), which are larger than that from the observational results (2.67-2.69 mm d-1) taken from the GPCP and CMAP observations.
The annual global mean AODs derived fromSTANDARD andNEW are 0.092 and 0.090, respectively (Table 1). Because the same anthropogenic emissions (black carbon, organics and sulfate) from (Lamarque et al., 2010) are adopted in the two experiments, non-significant differences exist in the simulated AODs ofSTANDARD andNEW, likely because of the differences in the meteorological conditions. Both simulated AODs are significantly lower than that from composite satellite remote sensing data (around 0.15) (Kinne et al., 2006), showing that IAP AGCM 4.1 significantly underestimates AOD. The main reason for the underestimation of AOD is that the coverage period of the simulated AODs (1979-2005) differs from that of the satellite observations (2000-present) Additionally, the anthropogenic aerosol emissions derived from (Lamarque et al., 2010) are substantially underestimated, especially over South Asia and East Asia (Liu et al., 2012).
To further explore the differences between the effects of using different cloud microphysical schemes, we further compare the annual and seasonal zonal means and global spatial distributions of SWCF, LWCF and surface precipitation in the following subsections.
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3.1. SWCF
Figure 2 shows the zonal means of SWCF from observations (CERES-EBAF and ERBE) and IAP AGCM 4.1 (STANDARD andNEW) for the whole year, for summer (June-July-August; JJA), and for winter (December-January-February; DJF). The annual zonal-mean tendencies of SWCF fromSTANDARD andNEW are in good agreement with CERES-EBAF and ERBE. Both simulated SWCFs are greatly overestimated at low latitudes and greatly underestimated at middle and high latitudes (Fig. 2a). Over the low-latitude regions, the simulated SWCF ofNEW is significantly reduced compared toSTANDARD, and is clearly closer to CERES-EBAF and ERBE observations; whereas,STANDARD andNEW show non-significant influences on
Figure2. The (a) annual, (b) JJA and (c) DJF zonal mean SWCF (positive represents cooling) derived from observations (CERES-EBAF estimates from 2000 to 2010 and ERBE data from 1985 to 1989) and IAP AGCM 4.1 (STANDARD and NEW).SWCF over the mid- and high-latitude regions. Of note is that the autoconversion rate of mass content (2) is a cubic function of cloud liquid water content, whereas it is 2.47 power of cloud liquid water content (Morrison and Gettelman, 2008). Hence, the autoconversion rate used here is larger than the autoconversion rate of CAM5.1, especially for larger quantities of cloud water (Fig. 1), which leads to less liquid cloud and smaller SWCF over low-latitude regions. Similar to the annual zonal-mean SWCF, the simulated seasonal results inNEW are also significantly reduced at low latitudes, which are in better agreement with the two sets of observational results shown in Figs. 2b and c. Also of note is that a significant difference exists in the SWCF between the two sets of observational data in Fig. 2a, with the zonal mean value from ERBE being much larger than that from CERES-EBAF.
Figure3. Annual mean global spatial distribution of SWCFfrom (a) CERES-EBAF estimates from 2000 to 2010, and (b, c) IAP AGCM 4.1 [(b) STANDARD; (c)New]. (d, e) Model SWCF biases from (d)STANDARD and (e)NEW.Figure 3 shows the annual mean global spatial distribution of SWCF from CERES-EBAF for the years 2000-10, that ofSTANDARD andNEW, and SWCF model biases. The simulated annual mean SWCFs fromSTANDARD (Fig. 3b) andNEW (Fig. 3c) can both reproduce the spatial distribution of CERES-EBAF (Fig. 3a). In Figs. 3d and e, over low latitudes, the simulated SWCFs fromSTANDARD andNEW are considerably overestimated; and over middle and high latitudes, the SWCF is greatly underestimated, compared with CERES-EBAF. The model bias in the annual mean SWCF forNEW is significantly reduced over low-latitude regions, where this reduced bias of SWCF is also found for JJA and DJF (not shown). Additionally, Table 2 summarizes some statistical results regarding the global mean SWCF, the difference in global means between observational estimates and model results, spatial pattern correlations, and RMSEs for the whole year, JJA and DJF. The results show that the annual, JJA and DJF global mean SWCF inNEW is much closer to the CERES-EBAF estimates than that ofSTANDARD. The spatial pattern correlation is slightly increased in the results for the whole year, as well as for JJA and DJF, and the RMSE (12.92, 15.26 and 18.20 W m-2 for the whole year, JJA and DJF, respectively) all decrease substantially inNEW, compared to that (15.54, 18.32 and 20.19 W m-2) inSTANDARD.
These results indicate that, compared to the standard cloud scheme, the new cloud schemes with ε can better simulate the SWCF, which effectively reduces the low-latitude SWCF and is much closer to satellite observations.
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3.2. LWCF
The annual, JJA and DJF zonal mean LWCF from CERES-EBAF and ERBE, and from IAP AGCM 4.1, are displayed in Fig. 4. The results show that, compared to the SWCF, the influence of the new cloud schemes on LWCF is much smaller. The simulated mean LWCF inNEW is slightly enhanced due to an increased high-cloud fraction, and closer to observations at all latitudes, compared toSTANDARD, for the whole year (Fig. 4a), JJA (Fig. 4b) and DJF (Fig. 4c). For the annual (Fig. 5) and seasonal (not shown) mean global spatial distribution of LWCF, the simulated results can also reproduce the observational spatial distribution. However, notably, the differences in the LWCF spatial distribution between STANDARD and NEW are non-significant.
Figure4. The (a) annual, (b) JJA and (c) DJF zonal mean LWCF (positive represents warming) from observations (CERES-EBAF estimates from 2000 to 2010 and ERBE data from 1985 to 1989) and IAP AGCM 4.1 (STANDARD andNEW).Table 2 shows that, compared to STANDARD, the model biases in the annual and seasonal global means of LWCF in NEW against CERES-EBAF are significantly reduced. Additionally, the spatial pattern correlation is slightly increased for the annual and seasonal means in NEW, and the RMSE is reduced. Hence, the above results show that the new cloud scheme improves the simulation of LWCF by increasing it slightly.
Figure5. Annual mean global spatial distribution of LWCF from (a) CERES-EBAF estimates from 2000 to 2010, and (b, c) IAP AGCM 4.1 [(b) STANDARD; (c) NEW]. (d, e) Model LWCF biases from (d)STANDARD and (e) NEW.2
3.3. Surface precipitation
Figure 6 presents the annual and seasonal zonal mean total precipitation rates and corresponding large-scale precipitation rates from GPCP and CMAP observations and IAP AGCM 4.1 (STANDARD and NEW). Both STANDARD and NEW reproduce the annual and seasonal zonal mean changes in total precipitation from GPCP and CMAP (Figs. 6a, 6c and e). Furthermore, the simulated mean total precipitation rate in NEW changes non-significantly from that in STANDARD, both on an annual and seasonal (JJA and DJF) basis. The differences in the global spatial distribution of the model biases for annual and seasonal total precipitation between STANDARD and NEW are also marginal (figures not shown). Additionally, Table 2 shows that the model biases in annual and seasonal global mean total precipitation, the spatial pattern correlation, and the RMSE, change non-significantly from STANDARD to NEW. Hence, the results from IAP AGCM 4.1 show that the different cloud microphysical schemes do not affect the total surface precipitation significantly.
Figure6. The (a, b) annual, (c, d) JJA and (e, f) DJF zonal mean PRECT and larger-scale PRECL from observations (GPCP, 1979-2009; CMAP, 1979-98) and IAP AGCM 4.1 (STANDARD and NEW).Figures 6b, d and f show that the effect of the cloud schemes on large-scale precipitation is stronger than the effect on total precipitation. The new scheme displays more large-scale precipitation than the standard scheme, for annual and seasonal means alike, especially over low-latitude regions. This is because the autoconversion rate used here is larger than the autoconversion rate of CAM5.1, especially at higher cloud liquid water (Fig. 1), leading to considerably more large-scale precipitation over low-latitude regions. These results regarding enhanced large-scale precipitation in NEW are also reflected by the information presented in Table 3. Taken together, the results presented in Fig. 6 provide further indication that the total precipitation is determined by convective precipitation where no aerosol indirect effects are considered.
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3.4. Comparison between IAP AGCM 4.1 and CAM5.1
Results from IAP AGCM 4.1 (Table 2) and CAM5.1 (Table 4) show that the simulated SWCFs with the new cloud schemes over low-latitude regions are significantly reduced and are much closer to satellite observations, as compared to the standard cloud scheme, which decreases the model bias in mean SWCF, increases the spatial pattern correlation, and decreases the RMSE, on the global scale. Here, we also compare the simulated SWCF from IAP AGCM 4.1 and CAM5.1 with the new cloud scheme (Tables 2 and 4). IAP AGCM 4.1 with the new scheme shows smaller bias in global mean SWCF for the whole year (-1.23 W m-2), for JJA (-3.24 W m-2), and for DJF (0.79 W m-2), than that (-3.94 W m-2, -7.14 W m-2 and -1.37 W m-2, respectively) in CAM 5.1. This model also has a higher spatial pattern correlation with CERES-EBAF (0.85, 0.90, and 0.90 for the whole year, for JJA and for DJF, respectively) than CAM5.1 (0.77, 0.84 and 0.83). Additionally, the RSMEs for IAP AGCM 4.1 (12.92, 15.26 and 18.20 W m-2 for the whole year, for JJA and for DJF, respectively) are smaller than those of CAM5.1 (15.74, 20.69 and 21.62 W m-2). Furthermore, IAP AGCM 4.1 with the new schemes improves the simulated LWCF, as discussed in subsection 3.2, but no such improvement is found in CAM5.1 with the new schemes. Although IAP AGCM 4.1 with the new schemes shows a larger global mean LWCF bias, it exhibits higher spatial pattern correlations (0.90, 0.89 and 0.92 for the whole year, for JJA and for DJF) than CAM5.1 (0.88, 0.85 and 0.89), and lower RMSEs (6.83, 9.00 and 8.29 W m-2 for the whole year, for JJA and for DJF, respectively, in IAP AGCM 4.1 versus 7.12, 10.45 and 9.38 W m-2 in CAM5.1).Compared to the standard scheme, the large-scale precipitation and its ratio to total precipitation can be effectively enhanced in the new scheme, for both GCMs (Table 3). Note that, although the ratio of large-scale precipitation to total precipitation from both GCMs in the tropics (30°S-30°N) is much lower than that from TRMM observational estimates (Dai, 2006), these two GCMs with the new schemes produce much higher large-scale precipitation, and larger ratios of large-scale precipitation to total precipitation, which is clearly closer to the TRMM observational estimates. Additionally, IAP AGCM 4.1 displays substantially more large-scale precipitation and higher ratios of large-scale precipitation to total precipitation than CAM5.1.
The dispersion effect on aerosol indirect forcing in CAM5.1 has been reported from differences between simulations with present-day and pre-industrial aerosol emissions in (Xie et al., 2017), showing that the corresponding aerosol indirect forcing with the dispersion effect considered can be reduced substantially by a range of 0.10-0.21 W m-2 at the global scale, and by a much bigger margin of 0.25-0.39 W m-2 for the Northern Hemisphere. The dispersion effect on aerosol indirect forcing in IAP AGCM 4.1 will be reported from present-day and pre-industrial experiments in a future study. Finally, it is noted that the choice of the Rotstayn-Liu relationship of ε-N c in the cloud microphysical schemes with ε used in this study (Rotstayn and Liu, 2003) may have implications. Different empirical formulas have been presented to stand for ε with respect to N c, since ambient atmospheric factors and aerosol chemical and physical properties may influence the ε significantly (Liu et al., 2008; Xie and Liu, 2013, 2017). The effect of different ε-N c relationships on the results from IAP AGCM4.1 will also be examined in future work.
