PUBLICATIONS. Journal of Advances in Modeling Earth Systems. Global climate impacts of stochastic deep convection parameterization in the NCAR CAM5

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1 PUBLICATIONS Journal of Advances in Modeling Earth Systems RESEARCH ARTICLE /2016MS Key Points: The Plant-Craig stochastic deep convection parameterization is implemented into CAM5.3 Global climate impacts of stochastic deep convection scheme are investigated The simulated climate is improved by the stochastic deep convection scheme Correspondence to: G. J. Zhang, Citation: Wang, Y., and G. J. Zhang (2016), Global climate impacts of stochastic deep convection parameterization in the NCAR CAM5, J. Adv. Model. Earth Syst., 8, , doi: / 2016MS Received 7 JUL 2016 Accepted 23 SEP 2016 Accepted article online 29 SEP 2016 Published online 19 OCT 2016 Global climate impacts of stochastic deep convection parameterization in the NCAR CAM5 Yong Wang 1 and Guang J. Zhang 2,3 1 Center for Earth System Science, Tsinghua University, Beijing, China, 2 Scripps Institution of Oceanography, La Jolla, California, USA, 3 Center for Earth System Science, Tsinghua University, Beijing, China Abstract In this study, the stochastic deep convection parameterization of Plant and Craig (PC) is implemented in the Community Atmospheric Model version 5 (CAM5) to incorporate the stochastic processes of convection into the Zhang-McFarlane (ZM) deterministic deep convective scheme. Its impacts on deep convection, shallow convection, large-scale precipitation and associated dynamic and thermodynamic fields are investigated. Results show that with the introduction of the PC stochastic parameterization, deep convection is decreased while shallow convection is enhanced. The decrease in deep convection is mainly caused by the stochastic process and the spatial averaging of input quantities for the PC scheme. More detrained liquid water associated with more shallow convection leads to significant increase in liquid water and ice water paths, which increases large-scale precipitation in tropical regions. Specific humidity, relative humidity, zonal wind in the tropics, and precipitable water are all improved. The simulation of shortwave cloud forcing (SWCF) is also improved. The PC stochastic parameterization decreases the global mean SWCF from W/m 2 in the standard CAM5 to W/m 2, close to W/m 2 in observations. The improvement in SWCF over the tropics is due to decreased low cloud fraction simulated by the stochastic scheme. Sensitivity tests of tuning parameters are also performed to investigate the sensitivity of simulated climatology to uncertain parameters in the stochastic deep convection scheme. VC The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. 1. Introduction Moist convection can affect dynamical and thermodynamic processes in the atmosphere by transporting momentum, moisture and heat vertically. However, due to the coarse resolution ( km) in general circulation models (GCMs), convection within a GCM gird box cannot be resolved, and must be parameterized using a convective parameterization scheme. Since there are typically many clouds in the GCM grid box, the parameterization represents the ensemble mean effects of subgrid-scale convective processes on grid-scale fields. Currently, all GCMs use this type of deterministic convective schemes. Owing to representing only the ensemble mean responses of moist convection in a GCM grid box provided by the deterministic parameterizations, the variability in each grid box caused by individual subgrid-scale convective clouds is neglected. As the GCM resolution increases, this missing variability becomes more prominent because the fluctuations around the ensemble mean responses get larger [Jones and Randall, 2011]. Therefore, the traditional deterministic convection parameterizations should be improved not only to reproduce the ensemble mean of convection but also to capture the variability of subgrid scale convective states. To address this issue, Buizza et al. [1999] introduced stochastic components to perturb the convective parameterization tendency. Their work was the prelude of the development of stochastic parameterizations. Palmer [2001] confirmed that the variability associated with subgrid processes can be improved by utilizing stochastic parameterizations. Similar approaches, namely, random perturbations, were explored by Bright and Mullen [2002] for the trigger function of a deterministic convective parameterization and by Lin and Neelin [2003] for convective available potential energy (CAPE)-based closure of the Zhang and McFarlane [1995] (hereafter ZM) deep convective parameterization. In recent years, more state-of-the-art stochastic parameterizations have been developed [Suselj et al., 2012, 2014; Ajayamohan et al. 2013; Deng et al., 2015; Sanchez et al., 2016]. Based on their earlier work [Majda and Khouider, 2002; Khouider et al., 2003; Khouider and Majda, 2006], Khouider et al. [2010] developed a stochastic multicloud model (SMCM) to describe the WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1641

2 evolution (i.e., life cycle) of an ensemble of different cloud types, incorporating the probabilistic transitions among clear sky, congestus clouds, deep cumulus and stratiform anvil clouds [Frenkel et al., 2013; Peters et al., 2013] and successfully implemented it into an aquaplanet GCM with various idealized sea surface temperature (SST) configurations [Deng et al., 2015, 2016; Ajayamohan et al., 2016]. Dorrestijn et al. [2012] further extended it to include shallow cumulus clouds. Different from the SMCM using the conditional Markov chain (CMC), a parameterization framework based on statistical mechanics was developed by Cohen and Craig [2006] and Craig and Cohen [2006] for noninteracting clouds in statistical equilibrium using cloudresolving model (CRM) simulations. In their work, an exponential probability distribution function (PDF) of mass flux for individual clouds was assumed based on results from cloud resolving model simulations. The number of clouds contributing to a given mass flux was expressed as a Poisson distribution. These two PDFs were incorporated to describe the chance of producing the number of clouds with a given cloud base mass flux in each grid box. The local fluctuations around the large-scale equilibrium state are reflected by those clouds randomly initialized from the PDF. A stochastic convective parameterization scheme was later formally developed by Plant and Craig [2008], and applied in numerical weather predication (NWP) models [Groenemeijer and Craig, 2012; Keane et al., 2016] and a GCM under aquaplanet setting [Keane et al., 2014]. Sakradzija et al. [2015] further applied Craig and Cohen [2006] work to shallow convection. Recently, Wang et al. [2016] implemented the Plant-Craig stochastic deep convection scheme into the National Center for Atmospheric Research Community Atmosphere Model (NCAR CAM5.3) in an effort to improve the tropical precipitation characteristics including intensity, frequency and variability. In their work, the original deterministic Kain-Fritsch scheme [Kain, 2004] used in the Plant-Craig stochastic parameterization was replaced by the ZM deterministic scheme. They found that after introducing the Plant-Craig stochastic deep convection scheme, the tropical precipitation intensity and variability were greatly improved in CAM5. In particular, the frequency of extreme precipitation in the tropics from observations was reproduced very well. In this study, we further examine the impacts of Plant-Craig stochastic convection scheme on global climatology of precipitation, clouds and radiation systematically and explore the causes leading to these changes. In addition, sensitivity tests to uncertain parameters and different averaging strategies of input quantities to PC scheme are conducted to better understand its performance and interaction with other processes (e.g., shallow convection) in CAM5. The paper is organized as follows. The CAM5 model and implementation of the PC stochastic deep convective scheme are described in section 2. Experiment setup, model configuration and evaluation data are also given in this section. The impacts of stochastic deep convection scheme on global climatology are presented in section 3. Section 4 shows the results of sensitivity tests. A summary is given in section Model and Evaluation Data The model used in this paper is the NCAR CAM5.3 in standard configuration, with a horizontal resolution of and a vertical resolution of 30 levels. Although a higher resolution version of CAM5 ( ) is available, we decided to use the standard publicly released version so that the simulation using stochastic deep convection parameterization can be compared with well-documented CAM5 climatology. The deep convection parameterization uses the Zhang-McFarlane (ZM) scheme [Zhang and McFarlane, 1995], with dilute CAPE modification by Neale et al. [2008]. Shallow convection is parameterized using Park and Bretherton [2009], and the boundary layer moist turbulence processes are parameterized following Bretherton and Park [2009]. The two-moment stratiform cloud microphysics parameterization scheme by Morrison and Gettelman [2008] is used for large-scale microphysics. The radiative transfer calculations follow the Rapid Radiative Transfer Model (RRTM) of Iacono et al. [2008]. The Plant and Craig [2008, hereinafter PC08] scheme is implemented into the CAM5 and coupled with the ZM scheme. At each model grid point, the ensemble mean (or expected) cloud base mass flux <M> is determined by the closure in the ZM deterministic convection scheme using spatially (over 9 neighboring grid points for 28 resolution) and temporally (trailing average over 3 h at each time step) averaged vertical profiles of temperature and moisture. In PC08, two PDFs form the most essential elements of the scheme. First, the probability of having a particular mass flux m for a cloud is assumed to follow an exponential distribution: WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1642

3 Table 1. List of Simulations Simulation a Length (Years) Description CTL 20 ( ) Standard CAM5 with the deterministic ZM deep convection scheme EXP 20 ( ) As in CTL, but coupling the PC stochastic deep convection scheme with the deterministic ZM deep convection scheme (<m> kg s 21 and the random number is updated every day) R1H 10 ( ) As in EXP, but with random number updated every 1 h R6H 10 ( ) As in EXP, but with random number updated every 6h SAO 10 ( ) As in EXP, but with spatial averaging only TAO 10 ( ) As in EXP, but with temporal averaging only EM4 10 ( ) As in EXP, but with <m> kg s 21 EM8 10 ( ) As in EXP, but with <m> kg s 21 a All simulations are atmosphere-only simulations, using fully prognostic atmosphere and land models with specified observed sea surface temperatures and sea ice extent, at a horizontal resolution of and a vertical resolution of 30 levels using finite volume dynamical core. pm ð Þdm5 1 = <m>dm; (1) <m> e2m where <m> is the ensemble mean mass flux of a cloud, which is set to kg s 21 [Groenemeijer and Craig, 2012; Wang et al., 2016]. The integral of this PDF over all values of mass flux is 1, meaning probability one that every cloud has a mass flux between zero and infinity. A second PDF is for the number of clouds for each mass flux interval. For a given cloud type having mass flux between m and m1dm and given grid box and time step in GCM, the probability of having n clouds is drawn from a Poisson distribution. p dnðmþ n ð Þ5 dn ðm n! Þn e 2dn ðmþ Here dn ðmþis the average number of clouds with mass flux m, and is given by: for n50; 1; 2;... (2) dn ðmþ5 < N > pm ð Þdm5 <N > <m> e2 <m> m dm (3) where <N> is the ensemble mean number of clouds at each grid point. Normalization of equation (2) is that the sum of the probabilities over all n equals one, i.e., probability one that some number between zero and infinity of clouds will be triggered in this grid box at this time step with mass flux in this interval. The special case of having one cloud (i.e., n 5 1) with mass flux in the range (m, m1dm) is sampled based on the joint distribution of the aforementioned two PDFs: p dn ðmþ ð1þ5dn ðm Þe 2dn m ð Þ <N > <m> e2 <m> m dm (4) The approximation is obtained for small dn ðmþ. Then, whether to initiate one cloud with mass flux m randomly is achieved by comparing its occurrence probability p dn ðmþ ð1þ to a random number between zero and unity (if p dnðmþ ð1þ is larger than a random number, then this cloud will be generated; otherwise, it will not). The probability of having more than one cloud with mass flux between m and m1dm is O(dn ðmþ 2 ), thus negligible for small dn ðmþ. The total cloud base mass flux at each grid point is the sum of mass fluxes from those clouds successfully launched, multiplied by a factor <N> 5 <M> / <m> to scale to the mass flux of all clouds. Therefore, at a grid point during a model time step, the total cloud base mass flux is a random variable. However, over a long time period and/or a large enough spatial domain, the cloud base mass flux from the stochastic parameterization approaches that of the deterministic convection scheme. Details of the implementation of PC08 in CAM5, including settings of uncertain parameters and other modifications, are given in Wang et al. [2016]. Several simulations are carried out. First, a control (CTL) simulation is conducted using the default deterministic ZM deep convection parameterization. This serves as a reference for evaluating the impact of the PC stochastic scheme. Second, an experiment (EXP) simulation after the implementation of the PC stochastic convection scheme is performed. Finally, six additional simulations are conducted to test the sensitivity of model simulations to uncertain parameters associated with the PC stochastic scheme. Table 1 lists the relevant information of each simulation. The simulations of CTL and EXP are run for 21 years from 1980 to 2000, WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1643

4 and the last 20 years are used for analysis. Other sensitivity simulations are run for 11 years from 1990 to 2000, and the last 10 years are used for analysis. Longer integrations in CTL and EXP simulations are used for performing statistical significance test. The following reanalysis and observation data are used in this paper for model evaluation: the Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA-Interim, ERA-I) [Simmons et al., 2007], the Global Precipitation Climatology Project (GPCP) observations ( ) [Adler et al., 2003] for total precipitation, the Tropical Rainfall Measurement Mission (TRMM) 3A12 observations ( ) for convective and stratiform precipitation [Kummerow et al., 2001], the National Aeronautics and Space Administration (NASA) Water Vapor Project (NVAP) observations ( ) [Randel et al., 1996] for precipitable water and liquid water path, and the Clouds and Earth s Radiant Energy Systems Energy Balanced and Filled (CERES-EBAF) observations ( ) [Loeb et al., 2009] for shortwave and longwave cloud radiative forcing. 3. Results 3.1. Precipitation Figure 1 shows the total annual mean surface precipitation from simulations and GPCP observations as well as their differences. The overall geographical distribution of global precipitation between the CTL and EXP is comparable. Both overestimate tropical precipitation. Compared to CTL, there are some modest improvements by EXP: the double intertropical convergence zone (ITCZ) over the central and eastern Pacific south of the Equator is alleviated; the underestimated precipitation in Amazonia (especially for boreal winter; see Wang et al. [2016, Figure 1]) and the overestimated precipitation in Asian monsoon region are improved; the fictitious precipitation center in the Arabian Peninsula desert is reduced. There are also some degradations. For instance, there is too much ITCZ precipitation in the Pacific (especially South East Pacific), as compared to CTL and GPCP observations. Figure 2 shows the partitioning between convective and large-scale precipitation and comparison with the TRMM data. In TRMM observations, convective precipitation is larger than large-scale precipitation, but Figure 1. Total annual surface precipitation rates for (a) GPCP (2.67), (b) CTL (3.00), and (c) EXP (3.07), and their differences for (d) CTL-GPCP, (e) EXP-GPCP, and (f) EXP-CTL. The numbers in the parentheses are global means in units of mm/d. The stippled areas indicate that the difference between CTL and EXP is statistically significant at the 0.05 level. WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1644

5 Figure 2. Convective (a-c) and large-scale (d-f) precipitation rates for TRMM (3A12), CTL and EXP, respectively. overall they are comparable in the tropical region (3 4 mm/d for the large scale precipitation and 5 6 mm/ d for the convective precipitation). In CTL, there is very little large-scale precipitation (<1 mm/d) in the tropics and precipitation is dominated by convective precipitation (>8 mm/d). With the inclusion of stochastic deep convection parameterization, EXP significantly increases the large-scale precipitation to a level comparable to TRMM observations although convective precipitation is also increased slightly. This is beneficial to the model as deficient grid-scale precipitation in the tropics has been a long-standing bias in CAM5 and its predecessors. Figure 3 breaks convective precipitation down into contributions from deep and shallow convection parameterizations, respectively. In the CTL run, deep convection is the dominant contributor to the total convective precipitation, with shallow convection contributing to < 0.5 mm/d in tropical and subtropical regions. In EXP, the contribution from deep convection is reduced while the contribution from shallow convection is increased significantly with the maximum shallow convective precipitation over the eastern equatorial Pacific, resulting in a slight increase in net convective precipitation in EXP (Figure 2c). Therefore, the enhanced total precipitation over the equatorial Pacific (Figure 1f) is due to increases of large-scale precipitation (Figure 2f) and convective precipitation from shallow convection Moisture and Zonal Wind The inclusion of stochastic convective parameterization also improves the simulation of thermodynamic structure and circulation of the atmosphere, particularly in the tropics. Figure 4 shows the annual mean vertical cross sections of specific humidity, relative humidity and zonal wind in the global belt of 208 S 208 N from simulations and ERA-I reanalyses as well as their differences. For specific humidity, CTL produces mostly positive biases in the entire troposphere except over longitudes corresponding to landmasses, where there are dry biases in the lower troposphere below 600 hpa (Figure 4d). With the inclusion of the stochastic deep convection parameterizaion, EXP, compared to CTL, simulates lower specific humidity above 800 hpa and higher specific humidity below 800 hpa for most of longitudes, leading to a significant improvement above 600 hpa as well as all altitudes for longitudes between 0 o E and 30 o E but a degradation between 900 hpa and 600 hpa for longitudes between 60 o E and 180 o E (Figure 4j). In the simulation of relative humidity (RH), an obvious decrease of RH in EXP can be found at the middle altitude with the maximum decrease at 500 hpa around 150 o E (Figure 4k), alleviating the positive biases of RH produced in CTL. Consistent WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1645

6 Figure 3. Convective precipitation from deep convection and shallow convection for (top) CTL and (bottom) EXP. improvements at all altitudes and longitudes can be seen in the simulation of zonal wind where EXP alleviates the positive biases above 200 hpa for longitudes between 150 o E and 08, and negative biases especially between the surface and 400 hpa for longitudes between 180 o W and 08 and above 600 hpa for longitudes between 0 o E and 120 o E in CTL (Figure 4l). The global distributions of total annual mean column water vapor from NVAP observations, simulations and their differences are shown in Figure 5. The column water vapor is overestimated in CTL in comparison with the NVAP observations. EXP, with inclusion of the stochastic deep convection scheme, greatly reduces the positive biases of column water vapor in the tropics, particularly over the northwestern Pacific, western Indian Ocean and the double intertropical convergence zone (ITCZ) over the eastern Pacific south of the Equator (Figure 5f), although there is still too much column water vapor in these regions. On global average, the global-mean column water vapor is reduced from mm in CTL to mm in EXP, resulting in a better agreement with mm in NVAP observations Cloud Properties To understand the causes of changes in precipitation and water vapor, we first investigate the large-scale precipitation. In CAM5, large-scale precipitaion from stratiform clouds is determined by microphysical processes associated with cloud liquid water and ice. Figure 6 shows the total annual mean cloud liquid water path (LWP) from simulations and NVAP observation as well as their differences, and Figure 7 shows the difference of IWP between EXP and CTL. In Figure 6, the NVAP observations show a global-mean LWP (ocean) of g/m 2 with large values of LWP over eastern equatorial Pacific, northern Pacific Ocean and Southern Ocean, while in CTL it is g/m 2 with dramatically underestimated LWP in the above regions. The LWP in EXP is increased to a global mean (ocean) of g/m 2. Large increase of LWP in EXP mainly occurs over the equatorial oceans, particularly in the Pacific and Atlantic (Figure 6f), making it more comparable with the NVAP observations. In addition to the improvement over the equatorial oceans, there is also a slight increase in LWP in the Southern Ocean (5 10 g/m 2 ) and the Northern Hemisphere storm tracks. For IWP (Figure 7), the global-mean IWP in EXP increases by 0.47 g/m 2. The major regions of IWP increase are WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1646

7 Figure 4. The annual meridional-mean cross sections of (a, d, g, j) specific humidity, (b, e, h, k) relative humidity and (c, f, i, l) zonal wind in the global belt of 20 o S 20 o N for (a c) ERA-I and differences for (d f) CTL ERA-I, (g i) EXP ERA-I and (j-l) EXP CTL. The stippled areas indicate that the difference between CTL and EXP is statistically significant at the 0.05 level. equatorial Pacific and Atlantic, and midlatitude storm tracks in both northern and southern hemispheres. Overall, the regions of increase of LWP and IWP correspond well with regions of increased large-scale precipitation (Figure 2f). As the modifications are made to the deep convection shceme only, a key process that bridges LWP and IWP in large-scale stratiform clouds and convective clouds is the detrained liquid water and ice water from deep and shallow convection. Figure 8 shows the differences of detrained liquid water (DLW) between EXP and CTL in the global belt of 20 o S 20 o N (tropics) and 70 o S 30 o S (Southern Ocean) from deep convetion and shallow convection, respectively. There is a large increase in DLW from shallow convection and a slight decrease in DLW from deep convection in both regions. In CAM5, the DLW from convection is partitioned into cloud water and cloud ice according to cloud top temperature and supplied to the cloud microphysical parameterization [Morrison and Gettelman, 2008] as sources for large-scale cloud ice and water. As a result, the increase in toal DLW from convection leads to increase of LWP and IWP, which in turn increase largescale precipitation. In particular, over the Southern Ocean the DLW from shallow convection is the WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1647

8 Journal of Advances in Modeling Earth Systems /2016MS Figure 5. Total annual column water vapor for (a) NVAP (24.60), (b) CTL (25.52), and (c) EXP (25.19), and their differences for (d) CTL - NVAP, (e) EXP - NVAP, and (f) EXP - CTL. The numbers in the parentheses are global means in units of mm. The stippled areas indicate that the difference between CTL and EXP is statistically significant at the 0.05 level. Figure 6. Total liquid water path (LWP) for (a) NVAP (79.86), (b) CTL (43.04), and (c) EXP (48.96) and their differences for (d) CTL - NVAP, (e) EXP - NVAP, and (f) EXP - CTL. The numbers in the parentheses are global means in units of g/m2. The stippled areas indicate that the difference between CTL and EXP is statistically significant at the 0.05 level. WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1648

9 Figure 7. Difference of ice water path (IWP) for EXP CTL (0.47). The number in the parentheses is the global mean, in units of g/m 2. The stippled areas indicate that the difference between CTL and EXP is statistically significant at the 0.05 level. dominant contributor to LWP compared to other process (e.g., vertical diffusion and microphysics) [Kay et al., 2016]. Therefore, the significantly increased DLW from shallow convection helps to reduce the long-standing negtive bias of LWP in CAM5 although it also further overestimates cloud ice content over the Southern Ocean [Xie et al., 2013]. The changes of DLW are due to changes in convective mass flux. There is a large increase of shallow convection and a slight decrease in deep convection from CTL to EXP (not shown). The chages in shallow and deep convection result in corresponding changes in precipitation (i.e., reduced precipiation from deep convection and ehnhaced precipiation from shallow convection; Figure 3). The increase in shallow convection is porbably due to its interaction with deep convection: the reduced deep concection favors the buildup of CAPE and more frequent shallow convection [Zhang and Mu, 2005], which serves to precondition the lower troposhere for MJO [Zhang and Song, 2009; Cai et al., 2013; Zermeo-Daz et al. 2015]. Wang et al. [2016] showed that MJO simulation is improved in the EXP as compared to CTL. In addition to cloud hydrometeor changes, there are also changes in cloud cover. Figure 9 shows the differences of high, middle, and low clouds as well as the total cloud fraction between EXP and CTL. In most of the tropical regions high, middle and low clouds are all reduced in EXP, particularly the middle clouds, which are reduced by 20% over the South Pacific Convergence Zone (SPCZ). As the magnitude of decrease in middle clouds is larger than others, it dominates the pattern of changes in total clouds. This result can be attributed to a large decrease of relative humidity (RH) occurring in the middle level (Figure 4k). Although Figure 8. Differences of detrained liquid water (DLW) in the global belt of (left) 20 o S 20 o N and (right) 70 o S 30 o S from deep convection (blue) and shallow convection (red) between EXP and CTL (EXP - CTL). The black dashed line represents the reference for zero. WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1649

10 Figure 9. Differences between EXP and CTL (EXP - CTL) in annual-mean (a) high-level (21.98), (b) midlevel (22.32), (c) low-level (21.97), and (d) total clouds (22.64). The numbers in the parentheses are global mean values, in units of %. The stippled areas indicate that the difference between CTL and EXP is statistically significant at the 0.05 level. the amount of low cloud is decreased over most of tropical regions, the EXP produces more low clouds in the eastern Pacific, leading to an improvement to underestimated low clouds over these regions in CAM5 [Cheng and Xu, 2015] Cloud Radiative Forcing Changes in cloud LWP/IWP and cloud fraction eventually influence the cloud radiative forcing. Figure 10 shows the shortwave cloud forcing (SWCF) from simulations and observations as well as their differences. The global-mean SWCF from CERES-EBAF observations is W/m 2. Compared to observations, the global mean SWCF from the CTL ( W/m 2 ) is somewhat excessive. Almost all negative biases from the observed SWCF are in the tropics. Thayer-Calder et al. [2015] attributed it to cloud liquid water not precipitating out sufficiently by deep convective microphysics. We note that the global mean SWCF from the Earth Radiation Budget Experiment (ERBE) observations is W/m 2 [Harrison et al. 1990]. In this sense, the SWCF from CTL is within the observational uncertainty. However, even in this case there are still negative SWCF biases in the tropics (not shown). With the PC stochastic deep convection scheme in EXP, the globalmean SWCF ( W/m 2 ) is close to that in observations. Compared to CTL, the positive changes in SWCF in the tropics, especially over the western Pacific and western Indian Oceans as well as eastern Africa (Figure 10f) help to alleviate the negative biases in the CTL. Additionally, the stochastic deep convection parameterization slightly mitigates the positive biases of the simulated SWCF in CAM5 over the Southern Ocean mainly due to more cloud liquid water (Figure 6) from enhanced DLW (Figure 8) from shallow convection. The longwave cloud forcing (LWCF) for simulations is compared to observations in Figure 11. Both CTL and EXP simulate smaller LWCF than observations. One notable degradation in EXP is that it further underestimates LWCF over the Southern Pacific Convergence Zone. Although the global-mean LWCF in EXP is underestimated (21.80 W/m 2, compared to W/m 2 in CTL and W/m 2 in observations), there are notable regional improvements. For example, the overestimated LWCF over the central and eastern Pacific and the western Indian Ocean in CTL is improved. WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1650

11 Journal of Advances in Modeling Earth Systems /2016MS Figure 10. Shortwave cloud forcing (SWCF) for (a) CERES-EBAF (247.16), (b) CTL (252.25), and (c) EXP (248.86) and its differences for (d) CTL - CERES-EBAF, (e) EXP - CERES-EBAF, and (f) EXP - CTL. The numbers in the parentheses are global means in units of W/m2. The stippled areas indicate that the difference between CTL and EXP is statistically significant at the 0.05 level. Figure 11. Longwave cloud forcing (LWCF) for (a) CERES-EBAF (26.06), (b) CTL (24.01), and (c) EXP (21.80) and its differences for (d) CTL - CERES-EBAF, (e) EXP - CERES-EBAF, and (f) EXP CTL. The numbers in the parentheses are global means in units of W/m2. The stippled areas indicate that the difference between CTL and EXP is statistically significant at the 0.05 level. WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1651

12 4. Sensitivity Tests The PC stochastic convection scheme contains several tuning parameters. The results presented in the last section use a set of default parameter values. In this section, we carry out a suite of experiments to test the sensitivity of model simulation to these tuning parameters. There are three uncertain parameters: 1) updating frequency of random numbers used to generate clouds in the PC scheme, 2) spatial and temporal averaging of input fields to the PC scheme, and 3) mean mass flux of a cloud. At each GCM grid point, a random number is generated to determine if a cloud with occurrence probability obeying the exponential PDF should be launched. This random number is updated once a day to crudely account for the memory or lifetime of organized convection. To test the sensitivity, two experiments are performed, with a random number updating frequency of every 1 h (R1H) and every 6 h (R6H), respectively. The PC scheme assumes that convective quasi-equilibrium holds in a statistical sense over an area larger than the GCM grid box. Therefore, averaging over such an area is required for input fields (e.g., temperature, moisture) into the host convective parameterization scheme (the ZM scheme in the case of CAM5). In our implementation, temporal averaging is also performed [Wang et al., 2016]. For sensitivity test, two additional simulations are conducted, one with spatial averaging only (SAO) and the other with temporal averaging only (TAO). In the PC scheme, the mass flux of a cloud follows the exponential probability distribution, with the mean mass flux per cloud <m> specified as a constant of kg s 21. Here two more sensitivity tests are conducted, with <m> set to kg s 21 (EM4) and kg s 21 (EM8), respectively. Specifics of all these sensitivity tests are listed in Table 1. Figure 12 shows the vertical profiles of mass flux from deep convection in the global belt of 20 o S 20 o N for different simulations. By increasing the update frequency of random numbers to 6 h (the R6H run) and 1 h (the R1H run), the mass flux in deep convection increases to become closer to that in the CTL run. This is understandable. When the random numbers are updated more frequently, it is more likely that all cloud base mass flux values per cloud (particularly those clouds with large cloud base mass flux values having small probabilities to launch) in a grid box will be encountered, resulting in an ensemble mean mass flux from the stochastic deep convection scheme closer to the deterministic result (Figure 12a). The spatial averaging decreases the cloud base mass flux (compare TAO with EXP, Figure 12b). This is because spatial averaging smoothes out spatial variability of temperature and moisture, and thus reduces the frequency of occurrence of large CAPE values. To demonstrate this, Figure 13 shows frequency distributions of CAPE in the global belt of 20 o S 20 o N for SAO and TAO based on the daily mean output. For each experiment, CAPE from each GCM grid point with and without averaging (spatial in SAO and temporal in (a) (b) (c) Figure 12. Vertical profiles of mass flux from deep convection in the global belt of 20 o S 20 o N for different simulations. Blue and red solid lines in each frame are for CTL and EXP, respectively. (a) Purple and green lines are for updating random numbers every hour (R1H) and every 6 h (R6H), (b) temporal averaging only (TAO) and spatial averaging only (SAO), and (c) the ensemble mean mass flux of 8x10 7 kg/s (EM8) and 4x10 7 kg/s (EM4) per cloud, respectively. WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1652

13 Figure 13. Frequency distributions of CAPE in the global belt of 20 o S 20 o N for (blue) EXP but with spatial averaging only (SAO) and (red) EXP but with temporal averaging only (TAO) based on the daily mean simulation data. The solid line represents the CAPE without any averaging in SAO and TAO simulations and the dashed line represents the averaged CAPE in SAO and TAO simulations. TAO) is plotted. For SAO, spatial averaging significantly reduces the frequency of occurrence of large CAPE values (compare solid and dashed blue lines in Figure 13). Through the CAPEbased closure in the ZM scheme, cloud base mass flux is decreased. On the other hand, the effect of temporal averaging on the frequency of occurrence of CAPE is small (compare solid and dashed red lines in Figure 13). As such, temporal averaging has little effect (compare SAO and EXP, Figure 12b) on cloud base mass flux. Finally, the sensitivity tests show that the total cloud mass flux has little sensitivity to the mean mass flux per cloud (Figure 12c). A possible reason is that the probability of triggering a cloud in a given cloud base mass flux interval changes minimally. With increasing <m> [Wang et al., 2016, equation (1)], <N> m <m> decreases while e2<m> and dm increase, resulting in opposite effects which mostly cancel out. 5. Summary and Discussions This paper extends the work of Wang et al. [2016] to further evaluate the impact of Plant-Craig stochastic deep convection parameterization on global climate simulation in the NCAR CAM5. With implementation of PC stochastic deep convection scheme, deep convection is suppressed, which promotes more shallow convection. As a result, convective precipitation from deep convection decreases and that from shallow convection increases accordingly. As the increase of detrained liquid water (DLW) from shallow convection overwhelms the slight decrease of that from deep convection, more large-scale cloud ice and liquid water are simulated, which enhances the large-scale precipitation in CAM5, making it in better agreement with TRMM observations. Moisture, zonal wind, cloud fraction and cloud radiative forcing are also investigated. With the inclusion of the stochastic deep convection scheme, a drier condition in midtroposphere is simulated and thus fewer middle clouds are produced, which dominates the change of the total cloud fraction. Some encouraging improvements are noted: (1) zonal wind at all altitudes and longitudes in the global belt of 208 S 208 Nis simulated better; (2) the positive biases of column water vapor in the Tropics are reduced; (3) the overestimated SWCF in the standard CAM5 is alleviated, yielding better agreement observations, and the biases of SWCF over the Tropics, and the Southern Ocean to some extent, are reduced; (4) the overestimated LWCF in central and eastern equatorial Pacific and the western Indian Ocean is reduced. Overall, the climate impacts of stochastic deep convection scheme in CAM5 are positive. In this study, the stochastic process is introduced into the deep convection scheme only. However, shallow convection is also affected due to its interaction with deep convection. More shallow convection in the simulation exerts positive impacts on cloud liquid water and shortwave radiation over eastern equatorial Pacific and the Southern Ocean where shallow convective clouds are the primary cloud type. Although use of the PC stochastic parameterization of deep convection in CAM5 results in important improvements in simulated climatology, there are also degradations, e.g., more excessive precipitation in the eastern Pacific ITCZ. As discussed in Berner et al. [2016], a stochastic parameterization, while able to reduce systematic errors and improve numerical models from a particular process perspective, often fails to compensate for other model errors which are typically achieved by tuning uncertain parameters in the model to gain the best mean state. Thus, we are hopeful that further tuning would lead to additional improvement in model simulation. WANG AND ZHANG CLIMATE IMPACTS OF PC SCHEME IN CAM5 1653

14 For instance, precipitation from shallow convection is excessive after deep convection is reduced in our simulation. One possible way to improve it is to tune down conversion rate from cloud water to rainwater in shallow convection to allow more liquid water detrainment for large-scale condensation and precipitation in the equatorial Pacific ITCZ region. Sensitivity tests are performed to examine the sensitivity of model simulation to uncertain tuning parameters, including the updating frequency of random numbers, spatial and temporal averaging of input fields and the mean mass flux of a cloud <m>. It is found that the updating frequency of random numbers and the spatial averaging of vertical profiles of temperature and moisture are important. On the other hand, the simulation is not sensitive to temporal averaging and mean mass flux of a cloud <m>. In addition to the mean climate state evaluated in this study, Wang et al. [2016] showed that the Plant-Craig stochastic deep convection scheme also improved the representation of tropical intraseasonal variability associated Madden-Julian oscillation (MJO). The stochastic scheme enhanced the intraseasonal variability and successfully simulated the eastward propagating intraseasonal oscillation (ISO). This was attributed to the fact that the stochastic parameterization of convection was able to capture spatial variability due to unresolved convective processes and better represent their influence on large-scale flow. However, the intraseasonal signals are still not as coherent as in observations. Weisheimer et al. [2014] also found that the stochastically perturbed backscatter (SPBS) scheme and the stochastically perturbed physical tendencies (SPPT) scheme in the European Centre for Medium-Range Weather Forecasts (ECMWF) coupled seasonal forecasting model failed to do so. This study uses the AMIP-style atmosphere-only simulations to examine the effect of stochastic convective parameterization. Thus, its effect on interannual variability such as ENSO cannot be evaluated. A recent study by Christensen et al. [2016] showed that including stochastic forcing in the NCAR CCSM4 greatly improved the ENSO simulation in both its amplitude and periodicity. We plan to perform coupled simulations with the Plant-Craig stochastic scheme in the future to determine if it can achieve similar effect on ENSO simulation. The Plant-Craig stochastic deep convection scheme has only been evaluated at resolution in NCAR CAM5.3 standard configuration. Overall, the mean climate state and variability at this resolution are improved. As shown in Wang et al. [2016], the frequency of occurrence of intense precipitation is simulated much better with the PC stochastic scheme incorporated. This will likely improve the simulation of extreme precipitation in both present climate and future climate projection, a subject of great societal interest. With increasing resolution in GCMs, perturbations from unresolved convective processes will be more pronounced [Jones and Randall, 2011] and the assumption of convective quasi-equilibrium will break down [Plant and Craig, 2008]. In this situation, it will become even more important to incorporate stochastic convective parameterization in GCMs. Berner et al. [2016] provide an excellent overview of progress and current status of stochastic parameterization in this regard. 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