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PUBLICATIONS Journal of Advances in Modeling Earth Systems RESEARCH ARTICLE 10.1002/2015MS000469 Key Points:  MMF is a valuable test bed for evaluating microphysical schemes globally  A 4ICE scheme agrees better with CloudSat/CALIPSO products than earlier 3ICE schemes  Cloud ice and snow highly depend on microphysics yet must balance with radiation globally

Correspondence to: J.-D. Chern, [email protected]

Citation: Chern, J.-D., W.-K. Tao, S. E. Lang, T. Matsui, J.-L. F. Li, K. I. Mohr, G. M. Skofronick-Jackson, and C. D. PetersLidard (2016), Performance of the Goddard multiscale modeling framework with Goddard ice microphysical schemes, J. Adv. Model. Earth Syst., 8, 66–95, doi:10.1002/ 2015MS000469. Received 13 APR 2015 Accepted 11 DEC 2015 Accepted article online 15 DEC 2015 Published online 28 JAN 2016

Performance of the Goddard multiscale modeling framework with Goddard ice microphysical schemes Jiun-Dar Chern1,2, Wei-Kuo Tao1, Stephen E. Lang1,3, Toshihisa Matsui1,2, J.-L. F. Li4, Karen I. Mohr5, Gail M. Skofronick-Jackson1, and Christa D. Peters-Lidard6 1

Mesoscale Atmospheric Processes Laboratory, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA, 2Earth System Science Interdisciplinary Center, University of Maryland, College Park, Maryland, USA, 3Science Systems and Applications, Inc., Lanham, Maryland, USA, 4Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA, 5Earth Sciences Division—Atmospheres, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA, 6 Earth Sciences Division—Hydrospheric and Biospheric Sciences, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA

Abstract The multiscale modeling framework (MMF), which replaces traditional cloud parameterizations with cloud-resolving models (CRMs) within a host atmospheric general circulation model (GCM), has become a new approach for climate modeling. The embedded CRMs make it possible to apply CRM-based cloud microphysics directly within a GCM. However, most such schemes have never been tested in a global environment for long-term climate simulation. The benefits of using an MMF to evaluate rigorously and improve microphysics schemes are here demonstrated. Four one-moment microphysical schemes are implemented into the Goddard MMF and their results validated against three CloudSat/CALIPSO cloud ice products and other satellite data. The new four-class (cloud ice, snow, graupel, and frozen drops/hail) ice scheme produces a better overall spatial distribution of cloud ice amount, total cloud fractions, net radiation, and total cloud radiative forcing than earlier three-class ice schemes, with biases within the observational uncertainties. Sensitivity experiments are conducted to examine the impact of recently upgraded microphysical processes on global hydrometeor distributions. Five processes dominate the global distributions of cloud ice and snow amount in long-term simulations: (1) allowing for ice supersaturation in the saturation adjustment, (2) three additional correction terms in the depositional growth of cloud ice to snow, (3) accounting for cloud ice fall speeds, (4) limiting cloud ice particle size, and (5) new size-mapping schemes for snow and graupel. Despite the cloud microphysics improvements, systematic errors associated with subgrid processes, cyclic lateral boundaries in the embedded CRMs, and momentum transport remain and will require future improvement.

1. Introduction

C 2015. The Authors. V

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.

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The representation of cloud and convection processes in traditional atmospheric general circulation models (GCMs) with relatively coarse resolution (100 km) has been a long-standing challenge (see Arakawa [2004] for a review). Since resolving cloud dynamics explicitly require grids of a few hundred meters and time scales of just a few seconds, traditional GCMs need to rely on cloud parameterizations to represent these subgrid processes empirically. Cloud parameterizations have been empirically formulated using parameters resolved at GCM grid scales and usually include simple one-dimensional cloud plume models, closure assumptions, and ad hoc trigger criteria to close the system. These lead to great uncertainty in both weather forecasting and climate simulations. With recent advancements in computational technology, a new breed of GCMs with horizontal grids fine enough to resolve (or ‘‘permit’’) large convective clouds have been developed to break the conventional cloud parameterization deadlock [Randall et al., 2003; Randall, 2013]. Though computationally very expensive (approximately a million times more than a traditional GCM), global cloud-resolving models (GCRMs) with horizontal resolutions of about 3.5–14 km are already being run for multiyear simulations [Tomita et al., 2005; Miura et al., 2007, 2009; Nasuno et al., 2009; Putman and Suarez, 2011; Satoh et al., 2008, 2011, 2012]. Another less computationally demanding (approximately a few hundred times more than a conventional GCM) approach is the multiscale modeling framework (MMF) or superparameterization (SP) that replaces conventional cloud parameterizations with a 2-D cloud-resolving model

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(CRM) within each GCM grid column [Grabowski and Smolarkiewicz, 1999; Khairoutdinov and Randall, 2001; Randall et al., 2003]. The first MMF (called SP-CAM) was developed at Colorado State University using the Community Atmosphere Model (CAM) as a host GCM and the System for Atmospheric Modeling (SAM) as the CRM component [Khairoutdinov and Randall, 2001; Randall et al., 2003]. The MMF has been used to study a wide range of phenomena such as the mean climatology [Khairoutdinov et al., 2005; Marchand et al., 2009a], subtropical low clouds [Blossey et al., 2009; Wyant et al., 2006, 2009], interannual variability [Stan et al., 2010], subseasonal variability and the Madden-Julian Oscillation (MJO) [Khairoutdinov et al., 2008; Thayer-Calder and Randall, 2009; Benedict and Randall, 2009, 2011; Kim et al., 2011], monsoons [DeMott et al., 2011; Goswami et al., 2011], the diurnal cycle [Khairoutdinov et al., 2005; Zhang et al., 2008; Pritchard and Somerville, 2009], ocean heat transport [DeMott et al., 2010], and climate change [Wyant et al., 2012; Stan and Xu, 2014]. In addition, new MMFs have been fostered at different research institutes such as the Goddard MMF [Tao et al., 2009a] with a completely different GCM and CRM, the SPCAM-IPHOC [Cheng and Xu, 2011, 2013; Xu and Cheng, 2013a,b; Cheng and Xu, 2014] with higher-order turbulence closure (HOC), the PNNL-MMF aerosol climate model [Wang et al., 2011a,b], the SPCAM5-CLUBB [Wang et al., 2015] with a different HOC called Cloud Layers Unified By Binormals (CLUBB) [Golaz et al., 2002; Larson et al., 2012] and more are currently under development. One advantage of GCRMs and MMFs with grids of only a few kilometers is that more complete cloud microphysical schemes developed for CRMs and/or mesoscale models can be directly implemented into these models. However, most such schemes are typically developed and evaluated using special field campaign data sets or short-term case study simulations. How well these schemes perform in a global environment with a variety of cloud systems, complicated scale interactions, and nonlinear feedback among different physical processes for long-term climate simulations is still uncertain and requires comprehensive evaluation. Tremendous effort has been recently devoted to evaluating and improving the microphysical schemes in the Nonhydrostatic Icosahedral Atmospheric Model (NICAM), a GCRM [Tomita et al., 2005; Masunaga et al., 2008; Satoh et al., 2010; Inoue et al., 2010; Kodama et al., 2012]. Inoue et al. [2010] found that NICAM with the Grabowski [1998] microphysical scheme produced too little cloud ice and too much snow in the upper troposphere. Because testing and improving physical schemes is a painstaking process that requires many iterative cycles, it is impractical to use GCRMs with 3.5 km resolution for this kind of work. Most of the assessments and sensitivity experiments were done using the 14 km NICAM but the results may not be applicable to GCRMs with grid spacing of a few kilometers. Satoh and Matsuda [2009] and Noda et al. [2010] found that upper-level cloud cover is sensitive to model grid spacing. Tao et al. [2009b] proposed to develop a multiscale modeling system that consists of a CRM, a mesoscale model, and an MMF with unified physics packages (e.g., microphysics, radiation, aerosol, land, etc.) to provide a common platform for rigorous evaluation and development of model physics. The goal of a multiscale modeling system is to develop universal physics packages that can be applied to all local, regional, and global CRMs with the same sets of model parameters. The MMF is used to bridge the gap between CRMs and GCMs and to provide a computationally feasible way for parameter optimization. This study presents the efforts of developing a universal microphysical scheme using an MMF as an additional test bed. The main objectives of this study are: (1) to evaluate the performance of the Goddard MMF with three existing versions of the Goddard three-ice class (cloud ice, snow, and graupel) one-moment bulk microphysics, (2) to develop and evaluate a new four-ice class (cloud ice, snow, graupel, and frozen drops-hail) universal scheme suitable for all local, regional, and global CRMs with grid sizes of a few hundred meters to a few kilometers, and (3) to assess the impact of specific physical processes newly improved in the four-ice scheme on the MMF performance. The paper has the following organization. Section 2 describes the Goddard MMF, the Goddard microphysical schemes, and the validation data sets. Section 3 presents the results of the MMF control experiments with different microphysics schemes. Section 4 shows the results of the sensitivity experiments assessing the impact of key upgraded processes. Section 5 offers a summary and conclusions.

2. Model and Validation Data 2.1. The Goddard Multiscale Modeling Framework (GMMF) The GMMF is based on a coupling of the cloud-resolving Goddard Cumulus Ensemble model (GCE) and the Goddard Earth Observing System (GEOS) global atmospheric model. Version 1.0 of the GMMF and its

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differences with SP-CAM have been documented in detail in Tao et al. [2009a]. Briefly, the subgrid cloud parameterizations in the GEOS model have been replaced with a two-dimensional (x-z) GCE [Tao et al., 2003]. The GEOS model was configured to run with 28 3 2.58 (latitude 3 longitude) horizontal grid spacing with 32 vertical layers stretching from the surface to 0.4 hPa. Within each GEOS grid column, there is a 64column GCE with a horizontal spacing of 4 km, using cyclic lateral boundaries, a 10 s time step, and 28 vertical layers. Because the GEOS terrain-following vertical coordinate differs from the GCE height (z) coordinate, a finite-volume piecewise parabolic mapping (PPM) that conserves mass, momentum, and moist static energy is used for vertical interpolation between these two coordinates. The GEOS-GCE coupling time is 1 h, the same as the GEOS model time step. In GMMF v1.0, radiation was called from the GEOS model with cloud properties provided by the embedded GCE [Tao et al., 2009a]. This version has been evaluated using NASA high-resolution satellite data [Waliser et al., 2009; Chen et al., 2011; Li et al., 2012], improved with the addition of a land surface model [Mohr et al., 2013], and computationally enhanced for high impact weather studies [Shen et al., 2013]. In this study, GMMF v2.0 is used. Vertical layers within the GEOS model and GCE are increased to 48 and 44, respectively, to improve resolution in the lower atmosphere (17 layers below 700 hPa). The GCE model top height is extended, moving the lowest damping level upward from 16 to 20 km to avoid interference with deep convection. Fully compressible dynamics [Klemp and Wilhelmson, 1978] are used instead of the anelastic flow [Ogura and Phillips, 1962] used in GMMF v1.0. Radiation is called from the GCE to have better cloudradiation interaction at the natural temporal and spatial resolution of the CRM. The longwave radiation parameterization follows GMMF v1.0 [Chou et al., 1999] and includes all major (water vapor, CO2, O2) and most of the minor trace gas (N2O, CH4, and CFCs) absorption as well as clouds and aerosols. The solar radiation model [Chou and Suarez, 1999] in GMMF v1.0 is replaced by the parameterization of Chou et al. [2002] to account for mixed ice particle species. It includes the absorption due to water vapor, O3, O2, CO2, clouds, and aerosols as well as scattering by clouds, aerosols, molecules (Rayleigh scattering), and the surface. Fluxes are integrated over almost the entire spectrum, from 0.175 to 10 mm, including eight bands in the ultraviolet and visible region and three in the infrared region. For a cloud layer, instead of computing longwave and shortwave cloud optical properties and thickness [Sui et al., 1998; Fu and Liou, 1993] outside the radiation scheme as in GMMF v1.0, optical thickness is parameterized as a function of cloud condensate mixing ratio and effective particle size for each shortwave and longwave band and the single-scattering albedo and asymmetry factor as a function of the effective particle size. Cloud ice effective size follows Sun [2001] as a function of cloud ice amount and temperature. The scheme for the effective size of cloud water [Kiehl et al., 1994] accounts for the size difference over land and ocean. The effective particle sizes of precipitating condensates (snow, graupel, hail-frozen drops, and rain) are formulated consistent with each particle size distribution and density used in the Goddard microphysical schemes. Aerosols in GMMF v2.0 correspond to the 15 species of dust, carbon, sulfate, and sea salt currently used in the Goddard Chemistry Aerosol, Radiation, and Transport (GOCART) aerosol model [Chin et al., 2002]. The aerosol amount and effective size for each species are specified input parameters together with a function that computes optical thickness, single-scattering albedo, and asymmetry factor for each spectral band. The model aerosol amounts are prescribed from the temporal interpolation of the MERRA Aerosol Reanalysis monthly mean data [Buchard et al., 2014]. 2.2. Goddard Microphysical Schemes The original Goddard two-class liquid (cloud water, rain) and three-class ice (3ICE) one-moment bulk microphysics scheme developed and coded at Goddard [Tao and Simpson, 1993] was mainly based on Rutledge and Hobbs [1983, 1984] with additional processes from Lin et al. [1983]. This scheme has undergone several progressive revisions; the three major releases used in this study were documented in Tao et al. [2003, hereafter referred to as T2003], Lang et al. [2007, hereafter referred to as L2007], and Lang et al. [2011, hereafter referred to as L2011]. T2003 has an option to use hail as the third ice class; however, more recently, a fourice class (cloud ice, snow, graupel, and frozen drops/hail) bulk microphysics scheme has been developed [Lang et al., 2014, hereafter referred to as L2014] and further improved (W.-K. Tao et al., High-resolution NUWRF simulations of a deep convective-precipitation system during MC3E: Further improvements and

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Table 1. Major Successive Improvements to the Microphysical Processes in Three Versions of the Goddard Three-Ice Class One-Moment Bulk Microphysics (3ICE) Schemes and the New Four-Ice Class One-Moment Bulk Microphysics (4ICE) Scheme From the Original Rutledge and Hobbs [1983, 1984] and Lin et al. [1983] Based Schemes Scheme Name, Type, Reference T2003, 3ICE, Tao et al. [2003]

L2007, 3ICE, Lang et al. [2007] L2011, 3ICE, Lang et al. [2011]

L2014, 4ICE, Lang et al. [2014] and T2015

Summary of Major Improvements 1. Options to choose either graupel or hail as the third class of ice 2. New saturation technique 3. Use of a larger time scale for an ice crystal to grow from 20 to 100 mm to reduce the cloud ice depositional growth rate 1. Eliminate dry collection by graupel 2. Lower the collection efficiency of cloud water by snow 1. Explicitly parameterize cloud ice fall speed 2. Introduce FRH and FSZ correction factors in cloud ice depositional growth term PSFI 3. Reduce the time scale of PSFI term (time to grow ice crystal from 40 to 55 mm) 4. Relax the saturation scheme to allow for ice supersaturation 5. Add snow and graupel size mapping (snow and graupel intercepts are parameterized as functions of temperature and mass) 6. Replace the Fletcher [1962] curve with the Meyers et al. [1992] curve to determine the number concentration of active ice nuclei 7. Add contact nucleation and immersion freezing terms 8. Add a simple Hallett-Mossop rime splintering parameterization 1. Add frozen drops hail as the fourth class of ice and its related microphysical processes 2. Add water vapor diffusivity correction term in all processes related to water vapor 3. Replace the Meyers curve [Meyers et al., 1992] with the Cooper curve [Cooper, 1986] and limit the mean size of cloud ice particles 4. Introduce a rain evaporation correction term based on bin-microphysics results [Li et al., 2009] 5. Improve the snow and graupel size mappings 6. Add a snow density mapping [Brandes et al., 2007] 7. Change the time scale for an ice crystal depositional growth rate (from 35 to 50 mm) 8. Allow peak ice supersaturation to linearly increase from 5% to 21% based on updraft intensity in the saturation scheme 9. Include the effect of snow breakup via interactions with graupel and hail 10. Add a simple hail size mapping as a function of temperature and hail mass 11. Increase autoconversion of cloud ice to snow by lowering the autoconversion threshold

comparisons between Goddard microphysics schemes and observations, submitted to Journal of Geophysical Research, 2015, hereafter referred to as T2015). The fourth ice category encompasses the spectrum of particles from smaller frozen drops to larger hailstones that have a high density (~0.9 g cm23). This four-ice class (4ICE) scheme has the ability to simulate more intense convection with intense radar echoes and precipitation without the need to switch schemes (i.e., from 3ICE-graupel to 3ICE-hail) a priori. Since graupel and frozen drops/hail can simultaneously occur in nature both in the same storm and in different storm systems at different locations, a 4ICE scheme is necessary to simulate a variety of cloud systems over the entire globe. Major improvements to the 3ICE and 4ICE schemes are listed in Table 1. For minor improvements and detailed descriptions, please refer to the original papers (i.e., T2003, L2007, L2011, L2014, and T2015). The new 4ICE scheme is the first to use the multiscale modeling system, which consists of the GCE [Tao et al., 2014], the NASA Unified-Weather Research and Forecasting model (NU-WRF) [Peters-Lidard et al., 2015], and the GMMF, during its developing stage. While each specific improvement was developed primarily within the context of one specific model, each improvement is implemented into all of these models and evaluated under different weather systems and climate regimes using a variety of validation matrices. The goal is to develop a comprehensive and well-tested universal scheme with the same microphysics parameters suitable for all local, regional, and global CRMs with horizontal resolutions of a few hundred meters to a few kilometers. In L2014, the new 4ICE scheme was tested in the GCE for an intense, midlatitude, continental squall line and a moderate, less-organized continental case in the Tropics. Simulated PDFs of radar echoes and peak radar reflectivity profiles were improved both in intensity and shape for both cases. In T2015, the same 4ICE scheme was applied and further improved in the regional-scale NU-WRF to study an intense mesoscale convective system that occurred on 20 May 2011 in central Oklahoma during the Midlatitude Continental Convective Clouds Experiment (MC3E) [Jensen et al., 2015]. The simulated radar reflectivity, rainfall intensity, and cloud organization and structure are in better agreement with

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observations than NU-WRF simulations with the Goddard 3ICE microphysics schemes. The 4ICE scheme produced more erect convective cores and a more horizontally stratified trailing stratiform region with a broad, more coherent light rain area. The NU-WRF-simulated radar reflectivity distributions were consistent with and generally superior to those simulated by the GCE for the same storm case due to the less restrictive open lateral boundaries. This paper now assesses the Goddard 3ICE and 4ICE schemes within the GMMF using global validation data described in the next section. 2.3. Validation Data Sets As discussed, recent improvements to the Goddard microphysics schemes focus on ice-phase processes (Table 1). To evaluate their performance in the GMMF, global cloud ice products from CloudSat [Stephens et al., 2008] and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) [Winker et al., 2010] are used as the primary validation. CloudSat/CALIPSO cloud fractions [Kay and Gettelman, 2009] and other satellite data, namely the Global Precipitation Climatology Project (GPCP) [Adler et al., 2003], Tropical Rainfall Measuring Mission (TRMM) [Simpson et al., 1996] product 3B43 [Huffman et al., 2007, 2010], Clouds and the Earth’s Radiant Energy System (CERES) [Wielicki et al., 1996], and NASA’s Water Vapor Project (NVAP) [Randel et al., 1996], are used to assess the model’s global energy and hydrological cycles. CloudSat and CALIPSO are part of the A-Train constellation of satellites [Stephens et al., 2002] with the same sun-synchronous orbits and equatorial crossing time of 1:30 P.M. solar time. CloudSat provides reflectivity profiles from its 94 GHz cloud profiling radar (CPR) at a vertical resolution of 480 m and footprint sizes of 1.7/1.3 km along/across track [Stephens et al., 2008]. CALIPSO lidar measures parallel and perpendicular backscatter at 532 nm and total backscatter at 1064 nm. CALIPSO’s vertical and along-track resolutions vary from 60 m and 1.0 km between 8.2–20.2 km to 30 m and 0.33 km below 8.2 km, respectively. These two active sensors provide an unprecedented global view of vertical cloud structures, and their products have been used to validate global atmospheric models [Bodas-Salcedo et al., 2008, 2011; Chepfer et al., 2008, 2010; Marchand et al., 2009b; Gettelman et al., 2010; Delano€e et al., 2011; Kodama et al., 2012; Li et al., 2012; Hashino et al., 2013; Xu and Cheng, 2013a,b; Dodson et al., 2013, and many others]. In this study, three ice water content (IWC) products, the CloudSat radar-only 2B-CWC-RO Release 4 [Austin et al., 2009], CloudSat/ CALIPSO 2C-ICE Release 4 [Deng et al., 2010], and the DARDAR (raDAR/liDAR) product [Delano€e and Hogan, 2008, 2010; Stein et al., 2011], are used to validate the model simulations and account for observational uncertainties. For a detailed description of these products, please refer to Li et al. [2012]. Comparison of the three IWC products with in situ measurements show their average biases are typically less than 30–40% for high-altitude ice clouds [Heymsfield et al., 2008; Austin et al., 2009; Deng et al., 2010, 2013]. However, the retrievals likely have even larger biases when the IWC is small or when the lidar beam is heavily attenuated. Uncertainties in the algorithms arise from a variety of sources [Deng et al., 2010]. The treatment of cloud particle habits is particularly important and can produce a 50% difference in the DARDAR IWC [Stein et al., 2011]. In general, microphysical assumptions, empirical relationships, and a priori data are based largely on Northern Hemisphere midlatitude data, and there may well be larger biases in the tropics, at high latitudes and in the Southern Hemisphere. In this study, CloudSat retrievals are assumed to represent total ice water content (TIWC), that is, the total mass of cloud ice, snow, graupel, and hail. The so-called FLAG approach is used to estimate cloud ice water content (CIWC) [Li et al., 2012]. In the FLAG approach, retrieval profiles that are identified as precipitating at the surface or classified as ‘‘deep convection’’ or ‘‘cumulus’’ (from CloudSat 2B-CLDCLASS data set) are excluded from the calculation of IWC. Of course, precipitating ice that is not spatially collocated with surface precipitation is being included in the FLAG estimates. The technique also effectively assumes that profiles of cloud ice outside of precipitation and convective areas are representative of cloud ice overall, which is likely problematic at warmer temperatures. It is hard to gauge the effectiveness of the FLAG approach. Nonetheless, Chen et al. [2011] suggest that CIWC should be 25–40% of TIWC based on a drop-sizedistribution partitioning approach using the 2B-CWC product–a result that compares favorably with the FLAG approach. Despite their uncertainties, these data sets remain the most valuable source of information for evaluating the model-simulated TIWC and IWC globally as in situ measurements are few and far apart. Figure 1 (left) shows the 2 year (2007 and 2008) mean total IWP (TIWP, the vertical integral of the TIWC) from three different CloudSat products. Because CloudSat and CALIPSO follow the A-Train orbit, their data only cover 808S–808N. Despite averaging the level-2 CloudSat pixel products to the GMMF grids (28 3 2.58),

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Figure 1. Annual mean (left) total and (right) cloud ice water path (g m22) from three different CloudSat products: (first row) 2B-CWC, (second row) 2C-ICE, and (third row) DARDAR, and (fourth row) their zonal mean for 2007–2008.

there is still considerable noise due to the small CPR footprint. The three retrievals exhibit the same key large-scale dynamical features like the relatively high TIWP values over the Tropical Western Pacific (TWP), Inter-Tropical Convergence Zone (ITCZ), South Pacific Convergence Zone (SPCZ), tropical Indian Ocean, tropical continental regions, and midlatitudes storm tracks and low values over the subtropical subsidence regions and deserts. The two CloudSat/CALIPSO products are very close to each other except DARDAR has slightly larger values; however, the 2B-CWC has consistently lower values (averaged about 30–40%) over most of the cloudy areas (Figure 1g). In contrast, cloud IWPs (CIWPs) from the corresponding FLAG data set (Figure 1, right) all have similar geographical distribution patterns, and 2B-CWC CIWPs are only slightly (10–15%) less than those of 2C-ICE and DARDAR (Figure 1h), indicating the difference in TIWPs mainly comes from the estimated amount of precipitating particles. Zonal TIWC and CIWC distributions (Figure 2) are in good agreement among the three retrievals with relatively high values over the tropics and midlatitudes and low values over subtropical subsidence regions. The IWC patterns over the tropics are asymmetric with a stronger northern branch. The 2B-CWC has considerably less TIWC and slightly less CIWC than the other two products. Data below 900 hPa are excluded to eliminate surface clutter. The vertical distribution of TIWC and CIWC do show some degree of difference among the three products. Local TIWC and CIWC maxima as well as the lowest level to which cloud ice reaches are located at higher altitudes in 2B-CWC. This may come from the 2B-CWC algorithm retrieving

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Figure 2. Annual zonal mean (left) total and (right) cloud ice mixing ratio (1026 g g21) from three different CloudSat products: (top) 2B-CWC, (middle) 2C-ICE, and (bottom) DARDAR for 2007–2008.

both the liquid and ice separately before combining them into a composite profile using a linear temperature scheme between 2208 and 08C. The scheme has been used in some models for estimating the cloud ice and cloud liquid amount or contribution. However, this method is questionable for estimating total ice and liquid amounts since maximum snow and graupel mixing ratios are usually located just above the freezing level due to their large fall speed. Both 2C-ICE and DARDAR do not use the temperature relationship and seem to produce better vertical distribution of total ice than 2B-CWC.

3. MMF Control Experiment Results Four GMMF control experiments are carried out with four different versions of the Goddard microphysical schemes from 1 December 2006 to 31 December 2008. Table 2 lists all GMMF control and sensitivity experiments presented in this paper. The first month is considered as spin-up, and only results from 2007 to 2008 are depicted in this paper. These 2 years are chosen to match the currently available FLAG cloud ice data set. Sea surface temperatures (SSTs) in the GMMF were prescribed using NOAA OI weekly SSTs [Reynolds et al., 2007], while the initial atmospheric conditions came from the ECMWF ERA-Interim reanalysis [Dee et al., 2011] at 0000 UTC 1 December 2006. The overall global annual mean atmospheric state parameters such as precipitation rate, hydrometeor water paths, cloud fractions, and radiative fluxes from the four GMMF control experiments are listed in Table 3. The corresponding observations and their uncertainties whenever available are also listed in Table 3. The four control experiments were run without any tuning to achieve radiative balance; therefore, there are small imbalances (21.26 to 2.59 W m22) at the top of the atmosphere (TOA) for the 2 year integrations. However, most of the atmospheric state variables are in reasonable agreement with observations and there is no detectable climate drifting from the time series of daily mean global quantities (not shown) in the control experiments. Large climate drifting associated with positive cloud-radiation feedbacks does occur in one of the sensitivity experiments (see section 4.3). Some selected fields in Table 3 from four control experiments are compared with observations and shown in Figures 3–11.

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Table 2. List of Numerical Experimentsa Experiment Name T2003 L2007 L2011 L2014 NO_FRH NO_FDWV_PSFI NO_FDWV NO_ICEFALL NO_SGMAP NO_SSI NO_ICESZMX MEYERS NO_HAIL a

Microphysical Scheme

Duration

3ICE [Tao et al., 2003] 3ICE [Lang et al., 2007] 3ICE [Lang et al., 2011] 4ICE [Lang et al., 2014; T2015] 4ICE but turn off FRH 4ICE but turn off FDWV in PSFI term 4ICE but turn off FDWV in all processes 4ICE but turn off ice fall speed 4ICE but turn off snow and graupel size mappings 4ICE but not allowing for ice supersaturation in the saturation adjustment 4ICE but turn off maximum size limit for cloud ice particles 4ICE but use Meyers curve instead of Cooper curve 4ICE but turn off hail processes

Jan 2007 to Dec 2008 Jan 2007 to Dec 2008 Jan 2007 to Dec 2008 Jan 2007 to Dec 2008 Jan 2007 Jan 2007 Jan 2007 Jan 2007 Jan 2007 Jan 2007 Jan 2007 Jan 2007 Jan 2007

The first four experiments are control simulations; the remainder are sensitivity experiments with the new 4ICE scheme.

Figure 3 shows the geographical distributions of simulated annual mean precipitation from the four control simulations, along with the corresponding observations from the GPCP version 2 and TRMM 3B43 products [Huffman et al., 2007, 2010]. In general, given the observed SST forcing, the observed annual mean precipitation patterns can be realistically simulated by the GMMF for extratropical storm tracks and the Tropics. Interestingly, the four GMMF simulations exhibit similar precipitation patterns and amounts (global means from 2.874 to 2.955 mm/d) despite the many differences in the microphysical schemes (Table 1). The correlation coefficient (CORR) ranges from 0.803 to 0.817 and the root-mean-square error (RMSE) from 1.67 to 1.74; all are quite similar. The simulated annual mean global precipitation rates are higher than that from GPCP (2.66 mm/d) and there are visible biases in all of the simulations. For example, precipitation in the Pacific and Atlantic ITCZs, the SPCZ, and western India Ocean is overestimated while precipitation in the

Table 3. Annual Global Mean Hydrometeor, Cloud, and Radiation Parameters From the GMMF Simulations and Observations for the Years 2007–2008 Parameters (unit)

T2003

L2007

L2011

L2014

Observation

Precipitation rate (mm) Total column water vapor (mm) Total ice water path (g m22) Cloud ice water path (g m22) Cloud liquid water path (g m22) Rain water path (g m22) Snow water path (g m22) Graupel water path (g m22) Hail water path (g m22) Low cloud fraction (%) Middle cloud fraction (%) High cloud fraction (%) Total cloud fraction (%) Shortwave cloud forcing (W m22) Longwave cloud forcing (W m22) Net all sky shortwave radiation at TOA (W m22) Net clear sky shortwave radiation at TOA (W m22) Net all sky longwave radiation at TOA (W m22) Net clear sky longwave radiation at TOA (W m22) Net radiation balance at TOA (W m22)

2.91 24.62 68.8 10.0 47.2 24.2 24.5 34.3 NA 51.69 26.66 26.82 64.54 242.9 18.9 247.04 290.00 244.44 263.38 2.59

2.87 24.95 96.9 18.1 50.9 24.6 69.6 9.2 NA 51.46 26.09 25.32 63.72 246.3 21.2 243.64 289.98 242.09 262.50 1.56

2.94 24.37 70.5 4.5 46.1 24.5 63.4 2.6 NA 49.68 23.49 29.02 64.39 241.6 16.4 248.39 290.05 246.67 263.03 1.72

2.93 24.20 78.0 27.7 51.3 20.9 46.8 3.2 0.17 48.66 25.24 32.79 65.73 249.6 22.7 240.32 289.97 241.59 264.28 21.26

2.66a 24.60b 74.6–120.2c 23.0–26.7d 22.4e,31.6f, 58g 26.7e NA NA NA 42.92h, 50.3i 32.21h, 27.4i 40.32h, 30.7i 66.74h, 68.0i 247.2j 1 3.0k 26.02j 1 4.0k 240.14j 1 2.0k 287.29j 239.56j 1 3.3k 265.58j 1 3.3k 0.57j

a

GPCP version 2.2 [Adler et al., 2003]. NASA’s Water Vapor Project (NVAP) [Randel et al., 1996]. c CloudSat Products: 2B-CWC Release 4, 2C-ICE Release 4, and DARDAR [Li et al., 2012]. d CloudSat FLAG Products: 2B-CWC, 2C-ICE, and DARDAR [Li et al., 2012]. e CloudSat FLAG 2B-CWC Product [Li et al., 2008]. f MODIS low-cloud-filtered data set over ocean [Lebsock and Su, 2014]. g AMSR-E low-cloud-filtered data set over ocean [Lebsock and Su, 2014]. h CloudSat/CALIPSO cloud fraction [Kay and Gettelman, 2009]. i CloudSat, CALIPSO, CERES and MODIS (C3M)-derived cloud fraction [Kato et al., 2011; Xu and Cheng, 2013a]. j CERES-EBAF radiation fluxes [Loeb et al., 2009]. k The uncertainties for the radiation fluxes come from Stephens et al. [2012]. b

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Figure 3. Annual mean precipitation rates (mm/d) from (a) GPCP and (b) TRMM observations, GMMF simulations using the (c) T2003, (d) L2011, (e) L2007, and (f) L2014 microphysics, and the zonal mean differences between the GMMF simulations and (g) GPCP and (h) TRMM 3B43.

Amazon and central Africa is underestimated. The annual mean precipitation averaged over the Tropics (308S–308N) is about 30% more than the TRMM observations (Figure 3h). Figures 3g and 3h show the TRMM mean precipitation rate tends to be higher in the Tropics and lower in the Southern Hemisphere midlatitudes near the edge of the satellite orbits than that of the GPGP. Appling different microphysics in the GMMF does not seem to affect these model systematic biases. Khairoutdinov et al. [2005] suggested the use of 2-D CRMs with cyclic lateral boundaries, which do not allow deep convective systems to propagate to neighboring GCM grid boxes, thereby prolonging their lifetime, is a possible cause for the positive precipitation bias in MMFs. Cheng and Xu [2014] showed the orientation of the 2-D CRM and momentum transport are important to mitigate this bias. The subsidence associated with the outflow of excessive precipitation over tropical oceans may suppress convection over surrounding land areas. Due to considerable noise in observed global distributions of TIWP and CIWP (Figure 1), all simulated and observed TIWP and CIWP data sets were averaged to 48 3 58 for computing the differences and statistics as suggested in Li et al. [2012]. Although there are only small differences in global precipitation among the four GMMF control simulations, the annual mean TIWP and CIWP (Figures 4 and 5) show substantial differences in the ice-phase condensates. Global distributions of TIWP (Figure 4b), such as the midlatitude storm tracks and the convective region in the Tropics, are in good agreement with the CloudSat 2C-ICE product (Figure 4a). However, the global mean amounts in all four GMMF experiments are comparable to that of the

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Figure 4. Annual mean total ice water path (g m22) from (a) 2C-ICE and (b) the L2014 simulation, (c–f) the differences between the GMMF simulations and 2C-ICE observations, and (g) their zonal means and (h) zonal mean differences.

2B-CWC but underestimated by about 15–40% when compared with the two CloudSat/CALIPSO products even though radar-lidar retrievals are thought to be more accurate. The simulated TIWP amount from the PNNL-MMF also showed this same discrepancy [Zhang et al., 2014, Figure 10b]. The global annual mean TIWP differences between the GMMF control simulations and 2C-ICE observations are shown in Figures 4c–4f. A major improvement from T2003 to L2007 (Figures 4c and 4e) is the elimination of dry collection processes by graupel, which reduces the unrealistic amount of graupel in the simulated anvils while increasing cloud ice and snow amounts. Because snow and cloud ice fall speeds are smaller than that of graupel, the TIWP increases (Figure 4e) and precipitation decreases (Figure 3e). The overall patterns and amplitudes of the L2007 scheme are quite reasonable and better than the other control simulations (Figures 4g and 4h). The scheme was implemented into GMMF v1.0 in Tao et al. [2009a] and Mohr et al. [2013]. Many important microphysical processes were upgraded in the L2011 scheme (Table 1), and the scheme was successfully applied in GCE and NU-WRF case studies [Tao et al., 2013; Shi et al., 2014; L2011]. The global annual mean CIWPs from the 2C-ICE product and four GMMF simulations are depicted in Figure 5. The new 4ICE scheme (L2014) produces the best CIWP in both amount and spatial distribution (Figures 5b and 5f).

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Figure 5. Same as Figure 4 except for cloud ice water path (g m22).

However, CIWP amounts in the Tropical Western Pacific warm pool and in midlatitudes are overestimated in the 4ICE scheme (Figures 5f–5h) while all GMMF simulations underestimate the CIWP over South America and central Africa to varying degrees. Surprisingly, the CIWP in the L2011 simulation (Figure 5d) is significantly diminished with a mean bias of 221.6 g m22, RMSE of 25.31 g m22, and CORR of 0.666 due mainly to its allowance of a fixed 10% ice supersaturation that reduces the production rate of cloud ice from water vapor (see section 4.5 for more details), a reasonable and conservative value for local conditions but one that is too high globally. In both GCE and NU-WRF simulations of convective systems, this scheme was shown to reduce the bias in the overly deep penetration of 40 dBZ echoes to higher altitudes and produce better reflectivity probability distributions. Because the number of case studies in GCE or NU-WRF is limited, it is vital to test schemes globally using the GMMF to cover a broad variety of environments over a longer period. The annual zonal mean TIWC and CIWC from the 2C-ICE observations and the four GMMF control experiments are depicted in Figure 6. The GMMF TIWC zonal patterns (Figures 6b–6e) have relative maxima in the Tropics in agreement with 2C-ICE, though the magnitudes tend to be too low. The values associated with midlatitude storm tracks are relatively similar but too low compared to the 2C-ICE (Figure 6a). The asymmetric patterns with a stronger northern branch in the Tropics are also consistent with the satellite estimates. Furthermore, the southern midlatitudes have more ocean surface and produce more ice

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Figure 6. Annual zonal mean (left) total and (right) cloud ice mixing ratio (1026 g g21) from (first row) 2C-ICE, and the GMMF simulations using the (second row) T2003, (third row) L2007, (fourth row) L2011, and (fifth row) L2014 microphysics.

condensate than the northern. The TIWCs in all four GMMF runs are underestimated compared to the 2CICE but close to the 2B-CWC values. The vertical distribution of total ice in the GMMF simulations is similar to 2C-ICE except the model cloud tops are not as high as the 2C-ICE in high-latitude regions. This may indicate that the vertical resolution of the model is inadequate for simulating the thin cirrus clouds observed by CALIPSO. L2014 is superior in terms of its mean zonal cloud ice vertical structure and amount among the four schemes (Figures 6e and 6j). In contrast to the other GMMF simulations, which have high cloud ice bases near 400–500 hPa in the Tropics, CIWCs extend down to the freezing level near 600 hPa in L2014 (Figure 6j) in good agreement with the 2C-ICE and DARDAR products. The better simulation is mainly due to the improvements in cloud ice depositional growth and snow/graupel size mappings and will be discussed in more detail in sections 4.1 and 4.4. Although the simulated TIWC in the lower atmosphere at high latitudes is smaller than all of the CloudSat products, the CIWC in these regions is overestimated in L2014 when compared with the FLAG 2C-ICE cloud ice product (Figure 6f). Observational uncertainty is arguably larger at high latitude, and the FLAG method inevitably classifies cloud ice as precipitating particles when there is surface precipitation.

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Figure 7. Taylor diagrams of annual mean (a) total ice water path, (b) cloud ice water path, (c) zonal mean total ice mixing ratio, and (d) zonal mean cloud ice mixing ratio.

To further quantify and synthesize the performance of the GMMF experiments as well as the uncertainty among the three CloudSat products, Taylor diagrams [Taylor, 2001] are used to summarize the degree of similarity in the spatial patterns of total and cloud ice. The similarity between two patterns is quantified in terms of their spatial correlation, centered root-mean-square error, and normalized standard deviation. These statistics are calculated using the 2C-ICE as the reference. Taylor diagrams of simulated and observed horizontal global patterns of annual mean TIWP and CIWP are shown in Figures 7a and 7b. The CloudSat estimates are plotted as circles and the GMMF simulations as squares. Not surprisingly, both CloudSat/CALIPSO products are more correlated than the radar-only product (2B-CWC), and the retrieval products have a higher correlation than the model simulations. L2007 and L2014 have higher normalized standard deviations than that of 2B-CWC (Figure 7a) and outperform T2003 and L2011 in standard deviations of both TIWP and CIWP (Figure 7b). For the zonal mean patterns of total ice, L2014 and L2007 have higher spatial correlations with 2C-ICE than T2003, L2011, and the other two CloudSat products (Figure 7c). The mean total ice amount and normalized standard deviations of 2B-CWC and the GMMF model results are smaller than those of 2C-ICE and DARDAR. The FLAG cloud ice products are very similar to each other, and L2007 and L2014 again have better statistics than T2003 and L2011 (Figure 7d). Among the GMMF simulations, L2014 has the best zonally averaged cloud ice vertical spatial correlation (0.86) and normalized standard deviation (1.03). In addition to the evaluation of spatial distributions of total ice-phase condensates and cloud ice as previously discussed, the contribution from individual ice- and liquid-phase condensates is critical for understanding and improving microphysics schemes. Figure 8 shows the domain and time-averaged hydrometeors over the Tropics (308S–308N), midlatitudes (308S/N–608S/N), and high latitudes (608S/N–908S/ N) from the four GMMF experiments. The annual mean hydrometeor profiles are substantially different over

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Figure 8. Annual mean hydrometeor profiles from the GMMF experiments: (first row) T2003, (second row) L2007, (third row) L2011, and (fourth row) L2014 over the (left) tropics (308S–308N), (middle) midlatitudes (308S/N–608S/N), and (right) high latitudes (608S/N–908S/N). The 2C-ICE FLAG cloud ice profiles are also presented in the fourth row.

the three climate zones because different cloud systems flourish in each zone. The profiles represent ensemble means of all cloud systems and can be very different from those of individual cloud systems studied in either NU-WRF or the GCE. In the Tropics, most ice-phase hydrometeors prevail below freezing and melt into rain or cloud water at warm temperatures, thus rarely reaching the ground. The amplitudes of the hydrometeor profiles are also smaller than at midlatitudes because the tropical band includes subtropical subsidence regions and deserts. Ice-phase hydrometeors can reach the surface in midlatitudes especially during winter. Low-level liquid water clouds prevail in midlatitudes, especially during summer. The reduction of liquid-phase clouds is also apparent in high latitudes. In Figure 8, there are disparities in the hydrometeor profiles among the different microphysics schemes. The T2003 scheme includes graupel dry collection and produces abundant amounts of graupel in all latitude zones. When dry collection is eliminated in the succeeding schemes, graupel amounts diminish significantly and snow becomes the dominant ice-phase hydrometeor. Many cloud ice source and sink terms were modified in L2011. Cloud ice amounts, however, are unreasonably low and suggest that those source and sink terms (e.g., the global 10% ice supersaturation) are not in balance for MMF applications. Although

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Figure 9. Annual mean low cloud fraction (%) from (a) CloudSat/CALIPSO and the (b) L2014 simulation, (c–f) the differences between the GMMF simulations and the CloudSat/CALIPSO observations, and (g) their zonal means and (h) zonal mean differences.

there are reasonable amounts of cloud ice for individual convective storms in GCE and NU-WRF case studies [Tao et al., 2013; Shi et al., 2014] and even in the GMMF simulations, this scheme as is may not be suitable for other types of cloud systems in different environments. The new 4ICE scheme (L2014) has more cloud ice and less snow when compared with the L2007 and L2011 simulations. The 2C-ICE FLAG cloud ice profiles are also presented in Figure 8 (fourth row). The amount of cloud ice in L2014 is in good agreement (within 10%) with observations in the Tropics and at midlatitudes in the upper atmosphere but is overestimated at lower levels in midlatitude and high latitude. L2014 has the least amount of rain among the schemes, although it has the most low-level cloud water in midlatitude and high latitude. The contribution of frozen drops/hail is negligible in the annual mean total mass of hydrometeors. However, as shown in T2015, it is absolutely essential for generating intense simulated convective systems. Components of the annual mean global water budget are summarized in Table 3. Simulated global annual mean precipitation (2.87–2.94 mm/d) is larger than that of GPCP (2.66 mm/d). However, recent satellite measurements suggest that the global mean precipitation is likely higher than the GPCP estimates

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Figure 10. Annual mean TOA shortwave radiative cloud forcing (W m22) from (a) CERES-EBAF observations and the (b) L2014 simulation, (c–f) the differences between the GMMF simulations and the CERES-EBAF observations, and (g) their zonal means and (h) zonal mean differences.

[Stephens et al., 2012]. The simulated global total column of water vapor (24.20–24.95 mm) is in good agreement with the NVAP estimate (24.60 6 1.9 mm) [Randel et al., 1996] and the SPCAM-IPHOC (24.2 mm) [Xu and Cheng, 2013a] but slightly drier than SPCAM (25.1 mm) [Khairoutdinov et al., 2008] and SPCAM5-CLUBB (25.1–25.9 mm) [Wang et al., 2015]. Using 2C-ICE as the reference for TIWP, L2014 is about 32% less but within the nominal CloudSat uncertainty estimates of 30–40%. The L2014 amount (78 g m22) is less than that of L2007 (96.9 g m22) due mainly to its allowance of ice supersaturation. The CIWC in L2014 (27.7 g m22) is very close to that of the 2C-ICE amount (within 6%) and significantly better than the factors of 2–10 difference between the CMIP5 GCMs and observations as reported in Li et al. [2012]. The CIWC in SPCAM5CLUBB ranges from 11.3 to 47.1 g m22. Currently, the disagreement in retrieved cloud liquid water paths (CLWP) from passive and active satellite sensors is too large to provide useful constraints on global models [Li et al., 2008; Lebsock and Su, 2014]. Simulated CLWPs (46.1–51.3 g m22) are larger than the CloudSat FLAG product (22.4 g m22) and MODIS low-cloud-filtered ocean only product (31.6 g m22) but smaller than the

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Figure 11. Same as Figure 10 except for annual mean TOA longwave radiative cloud forcing (W m22).

AMSR-E low-cloud filtered ocean only product (58.0 g m22). There is also large disagreement in CLWPs among SPCAM5-CLUBB (42.5–89.7 g m22), SPCAM-IPHOC (98 g m22), and SPCAM (93 g m22). The simulated global rain water path (20.9–24.6 g m22) is less than the CloudSat FLAG product (26.7 g m22). The contribution of graupel and hail to the global annual mean ice mass is quite small (about 4% and 0.2%, respectively); however, they are crucial for reproducing intense radar echoes (L2014; T2015). Monthly CloudSat/CALIPSO global (828S–828N) cloud fraction data sets [Kay and Gettelman, 2009], which included layered, low (z < 2.75 km), mid (2.75 km < z < 7.0 km), and high (z > 7.0 km) as well as total cloud cover, are used to evaluate cloud amounts in the GMMF simulations. CloudSat data in the bottom 720 m above ground level are excluded due to surface clutter in the observed low cloud fraction but not the CALIPSO data. Unlike many passive satellite estimates of cloud amount, radar and lidar are active instruments that can penetrate cloud and detect multiple cloud layers as long as the upper-level cloud does not attenuate the radar or lidar signal. The Goddard Satellite Data Simulator Unit (SDSU) [Masunaga et al., 2010; Matsui et al., 2013] was applied to the MMF results to provide a more consistent evaluation between model and satellite measurements. The CRM data that go into the SDSU include snapshots of air temperature,

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moisture, hydrometeor mixing ratios, and particle size distributions [Masunaga et al., 2010]. Each CRM grid point is determined to be cloudy when the simulated radar reflectivity (including the effect of all precipitating and nonprecipitating hydrometeors) exceeds 230 dBZ or the lidar-scattering ratio (SR), defined as the ratio of the simulated 532 nm attenuated backscattered (ATB) profile and the molecular ATB profile, is greater than 5 [Chepfer et al., 2010]. To be consistent with the observed cloud fraction data sets, the modelsimulated CloudSat cloud fraction in the bottom 720 m is also excluded. Figure 9 shows the global distribution of annual mean low-level cloud fraction (%) from the CloudSat/ CALIPSO estimates and the L2014 simulation as well as the difference between the observations and the four MMF simulations along with the zonal means. The global pattern of low clouds is well simulated with correlation coefficients from 0.80 to 0.83. However, the model simulations overestimate the global mean low-level cloud fraction (42.9% from CloudSat/CALIPSO) by 5.7%–8.8%. The model simulations produce too much low cloud cover over tropical oceans and midlatitude storm tracks while underestimating the low cloud amount in the cool, subtropical regions west of the continents. Among the four schemes, L2014 is superior in terms of mean bias and RMSE. To account for observational uncertainties in cloud fractions, the CloudSat, CALIPSO, CERES, and MODIS (C3M) merged data product is also provided in Table 3. The global mean low cloud fraction in C3M is about 50.3%, which is higher than the CloudSat/CALIPSO product. The L2014 low cloud fraction (48.66%) is within the uncertainties of the observations. Table 3 also shows that the GMMF-simulated annual global mean middle (23.5–26.7%), high (25.3–32.8%), total (63.7–65.7%) cloud fractions are underestimated, except for the L2014 high cloud fraction (32.79%), which is within the uncertainties of the observations (30.7–40.32%). The GMMF-simulated cloud fractions are comparable to the results from other MMFs except that the low cloud fractions are higher and are possibly due to higher vertical resolution in the boundary layer in the 48-layer GMMF (17 layers below 700 hPa versus 5 layers in SPCAM and 12 layers in SPCAM-IPHOC). This 48-layer GMMF produces about 3% more global mean low cloud fraction (with an increase of 2% in subtropical stratocumulus regions and 8% in tropical oceans) than the 32-layer GMMF (10 layers below 700 hPa). However, the cloud fraction diagnostics from other MMFs is different from that of the satellite simulator, making it difficult for direct comparisons. Cloud radiative effects are best illustrated by the longwave (LWCF) and shortwave cloud forcing (SWCF). The annual mean SWCF at the TOA from CERES-Energy Balanced and Filled (EBAF) observations [Loeb et al., 2009] and the four GMMF simulations are shown in Figure 10. In the GMMF, radiative fluxes are calculated on the GCE grid with the Goddard radiation transfer scheme. Partial cloudiness is not used in the GCE; the model grid is either overcast or clear. The global distribution patterns of SWCF are overall in good agreement (CORR 5 0.78–0.83) with observations, but the simulations all overestimate SWCF over the tropical Indian Ocean, the western Pacific warm pool, and the eastern Pacific and Atlantic ITCZs, consistent with the systematic excessive precipitation biases in these regions. The global mean SWCF value of L2007 (246.3 W m22) and L2014 (249.6 W m22) are closer to the observed value (247.1 W m22) than that of T2003 (242.9 W m22) and L2011 (241.6 W m22). Additional cloud ice simulated in the extratropical storm tracks in L2014 (Figure 5f) increases SWCF values only slightly too much over the North Pacific but overcompensates over the southern oceans (Figure 10f). A common deficit appears in all simulations due to the lack of low-level clouds in the cool subtropical ocean regions west of the continents where stratocumulus clouds prevail (Figures 10c–10f). The SWCF shows this deficiency more clearly than the simulated low-cloud fractions (Figure 9) and suggests that the optical thickness of low clouds is also underestimated. The GMMF with embedded CRMs at 4 km resolution cannot resolve planetary boundary layer (PBL) turbulence and small cloud-scale circulations, causing an inadequate simulation of low-level clouds. This is a common problem for MMFs with a simple PBL turbulence parameterization [Khairoutdinov et al., 2008; Marchand and Ackerman, 2010; Cheng and Xu, 2011]. Replacing a simple PBL scheme with a higher-order turbulence closure in the embedded CRM can allow MMFs to simulate more realistic structures and amounts of low-level clouds over the subtropical oceans [Cheng and Xu, 2011; Xu and Cheng, 2013a; Bogenschutz and Krueger, 2013; Wang et al., 2015]. The annual mean observed and simulated LWCF at the TOA are shown in Figure 11. All simulations underestimate the LWCF in the Amazon and central Africa, consistent with the systematic underestimation of cloud amount and precipitation in these regions. The L2014 simulation has the best global mean value (22.69 W m22) and root-mean-square error (8.413 W m22) among all control simulations. The observed global mean LWCF (26.10 W m22) is about 3.4 W m22 larger than that of L2014, with part of this deficit likely due to different definitions of clear-sky

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flux between the model and observations. Sohn et al. [2010] showed that models underestimate the LWCF by about 10% due to this definition difference. The observed uncertainty of global mean SWCF and LWCF is 63 and 64 W m22, respectively [Stephens et al., 2012] and the biases of L2014 are within these ranges. Table 3 shows that the L2014-simulated net all-sky/clear-sky shortwave and longwave radiation at the TOA are all in good agreement with observations and superior to the other GMMF simulations.

4. MMF Sensitivity Experiment Results To understand why the GMMF 4ICE produces better results than 3ICE simulations and which newly improved microphysical processes contribute to its success, a series of sensitivity experiments (Table 1) were conducted by removing selected process in the 4ICE scheme. All are initialized at 0000 UTC 1 December 2006 and integrated for 2 months. The first month is for spin-up; only results from January 2007 are used. A 2 month period is used because the direct impact of microphysics changes is captured as well as any short-term indirect feedback. If a positive indirect feedback exists, a small change may grow over time and become significant. Such a process is crucial for long-term global climate modeling but difficult to detect using short-term CRM or mesoscale model simulations. 4.1. Cloud Ice Depositional Growth (PSFI) The vapor depositional growth of cloud ice into snow (PSFI) was parameterized in Lin et al. [1983] as PSFI 5qi =Dt;

where qi is cloud ice mixing ratio, Dt the time scale for an ice crystal to grow from 40 to 50 mm in radius, which is somewhat artificial. The growth rate of a single crystal is parameterized as a function of temperature at water saturation [Koenig, 1971]. This is a key process for converting cloud ice to snow [Li et al., 2002, 2005] but it is often problematic and ambiguous in applications. Pinto and Curry [1995] found this term is too efficient and reduced it to 20% for an Arctic environment. Krueger et al. [1995] suggested using a larger time scale for an ice crystal to grow from 40 to 100 mm to reduce the growth rate (0.1 3 PSFI) and improve the simulation of anvil clouds for a tropical squall line. T2003 followed the same approach but used an even larger time scale (i.e., from 20 to 100 mm). The depositional growth rate of an ice crystal parameterized in Koenig [1971] is for a water-saturated environment. However, it is routinely applied to water subsaturated environments in schemes that follow Lin et al. [1983]. Krueger et al. [1995] hypothesized that PSFI in this case acts like a crude fall-speed parameterization for cloud ice since cloud ice does not fall but snow does in Lin et al. [1983]. Cloud ice fall speed is explicitly parameterized in L2011, so a correction factor (FRH) is needed for the PSFI term at water subsaturation [Ikawa and Saito, 1991; Reisner et al., 1998; Wang, 2001]. The factor is defined as: FRH 5

qv 2qsi ; qsw 2qsi

where qv is water vapor mixing ratio, and qsw and qsi are the saturation water vapor mixing ratios with respect to water and ice, respectively. Figure 12a shows the FRH correction factor as a function of temperature and ice supersaturation (SSI). FRH is less than 0.2 at low temperatures and low SSIs and is consistent with the studies of Pinto and Curry [1995] and Krueger et al. [1995]. Wang [2001] argued that the FRH correction, which has a large value in mixed phase clouds and a small value in anvil clouds, is a better approach than a constant reduction in the growth rate. The PSFI term was further improved in L2014 as follows: PSFI

NEW 5FRH 3FSZ 3FDWV 3PSFI ;

where PSFI_NEW is the new PSFI term, FSZ the cloud ice particle size correction term, and FDWV the water vapor diffusivity correction term (see the next section for a detailed description). FSZ accounts for a longer time scale needed for a small ice crystal to grow from its mean size to the minimum snow size (i.e., 50 mm). When the Cooper [1986] curve is used to determine the number concentration of active ice nuclei, FSZ is a function of temperature, cloud ice mass, and pressure. Figure 12b shows the FSZ factor only applies for cloud ice mixing ratios less than 1025 g/g, and the overall effect is small. Monthly zonal mean TIWC and CIWC differences between 2C-ICE and the control run for January 2007 are depicted in Figures 12c and 12d. The TIWC is significantly underestimated while CIWC is underestimated in

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the upper atmosphere and overestimated in the lower atmosphere. The simulated bias is similar to the 2 year L2014 simulation but with more noise due to only 1 month of 2C-ICE sampling. Figures 12e and 12f show the impact of the FRH correction factor on the GMMF-simulated monthly mean zonal snow and cloud ice mixing ratios. It plays a critical role in the successful simulation of cloud ice and snow amounts; without it, global mean cloud ice amount decreases by 62% and snow increases by 15%. The cloud-scale feedback to the large-scale circulation is also evident in Figure 12e as the strength of the Hadley circulation is enhanced due to this correction. As a result, there is more snow in the ascending branch (458N–608N) and less in the descending branches over the Arctic and subtropics (308N–458N). The direct effect can be locally overshadowed by the indirect effect on the global simulation. 4.2. Water Vapor Diffusivity Atmospheric water vapor diffusivity (Dv) was a constant (2.26 3 1025 m2 s21) in Rutledge and Hobbs [1984], T2003, L2007, and L2011. In the new 4ICE scheme, it is formulated as a function of temperature and pressure following Massman [1998]:  1:81   T Po Dv 5Do ; P To where D0 is the water vapor diffusivity (2.18 3 1025 m2 s21) at STP (i.e., temperature T0 5 273.15 K and pressure P0 5 1013.25 hPa). Figure 13a shows Dv increases with temperature and decreases with pressure and is about 3–7 times larger than the STP value aloft for temperatures of 260 to 2308C. A correction factor (FDWV) is introduced to scale diffusional growth rates based on the constant STP value. FDWV was applied to all diffusion processes that involved water vapor and condensates (both liquid and solid phases), including the PSFI term. Figure 13b shows growth rates can increase 3–6 times aloft between 260 and 2308C. In general, FDWV is greater than one except in the lower troposphere when temperatures are below freezing. Two sensitivity experiments were performed: one without the correction for the PSFI term only (NO_FDWV_PSFI) and the other without it in all processes involving water vapor diffusion (NO_FDWV). Figures 13c and 13d show global mean cloud ice increases by 13.6% while snow decreases by 4.7% in the NO_FDWV_PSFI simulation. Most of the cloud ice increase occurs aloft consistent with Figure 13b. When FDWV is turned off in all the corresponding source and sink terms, the net cloud ice amount is reduced by 7.1% and the net snow amount by 1.9% (not shown). 4.3. Cloud Ice Fall Speed Instead of the PSFI term acting as a crude cloud ice fall-speed parameterization as in T2003 and L2007, cloud ice fall speed is explicitly formulated [Hong et al., 2004] and its effects on the appropriate sweep volumes included in L2011 and L2014. When cloud ice fall speed is turned off (NO_ICEFALL), cloud ice is not efficiently removed and dramatically expands into the upper troposphere, stratosphere, and the Arctic regions due to strong positive cloud-radiation feedback (Figure 14b). As a result, the troposphere becomes warmer (Figure 14c), moist (Figure 14d), and stable. Vertical velocities in the NO-ICEFALL (Figure 14f) experiment are much weaker than the control (Figure 14e), sharply reducing snow amounts in the Tropics and midlatitudes (Figure 14a). Cloud ice fall speed plays a critical role not only in the simulation of hydrometeor amounts but also the climate state. These results demonstrate the importance of nonlinear feedbacks in global climate models and the need for rigorously evaluating microphysical schemes using an MMF. 4.4. Snow and Graupel Size Mappings The size-mapping schemes for snow and graupel were introduced in L2011 and further improved in the new 4ICE scheme in tandem with the addition of the frozen drops/hail category. In the mappings, the intercepts of snow and graupel are formulated as functions of temperature and mixing ratio, lowering particle sizes at colder temperatures but allowing larger particles near the melting level and at higher mixing ratios. An associated snow density mapping was also introduced as a function of snow size [Brandes et al., 2007] in L2014. Graupel density is divided into low and moderate based on a simple mixing ratio threshold. The snow and graupel size-mapping factors in the new 4ICE scheme are depicted in Figures 15a and 15b. The snow (graupel) intercept is scaled up by over 800 (100) at cold temperatures and low mixing ratios. These snow/graupel size mappings reduced overly strong echoes in the middle and upper troposphere in GCE simulations of a weakly organized continental case and an oceanic mesoscale convective system (L2011) as well as improve stratiform radar echoes for an intense midlatitude squall line (L2014). Figures 15c and 15d

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Figure 12. Correction factor for (a) FRH and (b) FSZ in the cloud ice depositional growth (PSFI) term. Monthly zonal mean (c) total and (d) cloud ice mixing ratio (1026 g g21) difference between 2C-ICE and the control run for January 2007. Monthly zonal mean (e) snow and (f) cloud ice mixing ratio (1026 g g21) difference between the NO_FRH sensitivity and control runs for January 2007.

show substantially reduced snow (19.3%) and cloud ice (41.9%) amounts when the mapping factors are turned off (NO_SGMAP). As snow particle size increases, snow fall speed and snow accretion of cloud ice increase. The depositional growth of snow, however, decreases due to the reduction in snow surface area. The size mappings are indispensable for simulating both radar reflectivity and hydrometeor amount.

4.5. Supersaturation The saturation adjustment scheme converts water vapor supersaturated with respect to ice into cloud ice and is the primary production term for cloud ice. There is a delicate balance between it and key cloud ice sink terms such as the PSFI, autoconversion, and snow collection terms [Li et al., 2002, 2005]. With the introduction of the FRH correction factor in PSFI, the PSFI term becomes a function of ice supersaturation in the 4ICE scheme. If ice supersaturation is not allowed in the saturation adjustment as in T2003 and L2007, the PSFI term is effectively turned off and more cloud ice is produced. Figures 16a and 16b show global mean cloud ice increases by 41.8% and snow decreases by 7.5% in the NO_SSI experiment. Ice supersaturations are commonly observed on the order of tens of percent [Jensen et al., 2001; Stith et al., 2002; Garrett et al., 2005]. L2011 allowed a 10% ice supersaturation, which is reasonable on small scales but is too large and produces too little cloud ice for a global application like the GMMF. Ice supersaturation varies from a background 5% to a maximum of 20% based on vertical velocity in the 4ICE scheme and performs well in GCE, NU-WRF, and GMMF simulations.

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Figure 13. (a) The ratio of water vapor diffusivity as a function of temperature and pressure relative to a constant water vapor diffusivity at STP, and (b) the ratio of the diffusion growth rate when water vapor diffusivity is a function of temperature and pressure relative to that of a constant water vapor diffusivity at STP. Monthly zonal mean (c) snow and (d) cloud ice mixing ratio (1026 g g21) difference between the NO_PSFI_FDWV sensitivity and control runs for January 2007.

4.6. Number of Active Ice Nuclei The Meyers et al. [1992] curve for the number of active ice nuclei (IN) was replaced by the Cooper curve [Cooper, 1986] in the 4ICE scheme. The Meyers curve is based on supersaturation amount while the Cooper curve is a function of temperature. Being a single moment scheme, the previous ice number concentration is not stored, which, when using the Meyers curve, results in the number of IN decreasing as excess vapor is absorbed. In conjunction with this change, the IN number concentration is constrained such that the mean cloud ice particle size cannot exceed the specified minimum snow size (i.e., 50 mm in radius). Figures 16c and 16d show the importance of this constraint; cloud ice decreases by 36.8% and snow increases by 5.1%. Figure 17 shows the impact of all the GMMF sensitivity experiments on hydrometeor amounts except the NO_ICEFALL experiment that has extreme values (cloud ice and cloud water increases by 309% and 27% while snow, graupel, hail, and rain decreases by 59%, 84%, 89%, and 31%, respectively) due to the positive cloudradiation feedback. The biggest impacts on cloud ice (Figure 17a) include NO_FRH, NO_SSI, NO_ SGMAP, and NO_ICESZMX; the remainder (Figure 17b) change cloud ice from 22.2% to 13% but are still important considering that the overall 4ICE scheme bias is about 6%. The snow/graupel size mappings greatly increase the amount of condensates (except rain) at the expense of water vapor while hail-related processes only play a minor role regarding cloud ice and snow amounts. It is apparent that the cloud ice fall speed, ice supersaturation in the saturation adjustment, and FDWV correction in the PSFI term are three key sink terms for cloud ice while the remainder are cloud ice production terms. It is critical to achieve the correct balance between cloud ice sources and sinks for long-term global simulations. The percentage difference in TIWP and CIWP between 2C-ICE and the control run is also depicted in Figure 17a. The CIWC difference is quite small (28%) and almost all processes contribute to achieve this balance. On the other hand, the difference in TIWP still remains large (48%), only NO_SSI, NO_SGMAP, NO_ICESZMX, and possibly the NO_ICEFALL processes show some change in TIWP but none has the same amplitude as the observed difference.

5. Summary and Conclusions The MMF and GCRM are two new approaches to representing cloud processes in atmospheric global models with horizontal grids fine enough to resolve (or permit) large convective clouds and mesoscale

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Figure 14. Monthly mean zonal (a) snow and (b) cloud ice mixing ratio (1026 g g21), (c) temperature (K), (d) water vapor mixing ratio (g kg21) difference (NO_ICEFALL minus CNTRL) for January 2007 and the vertical velocity (0.01 Pa s21) for the (e) CNTRL and (f) NO_ICEFALL experiments.

circulations. More complete cloud microphysical schemes originated from CRMs can be directly implemented into these models. However, most CRM schemes have yet to be tested in a global environment for long-term climate simulation. In this study, the GMMF in conjunction with satellite observations is used for the rigorous evaluation and continued improvement of microphysics schemes developed at Goddard, demonstrating that testing microphysical schemes at the global scale is an important part of their development. The advantages of global MMF testing include: (1) allowing for the simultaneous, long-term simulation of a variety of cloud systems in different climate regions, (2) accounting for the nonlinear interaction between cloud-scale and global circulations, (3) permitting complicated cloud-radiation and cloud-surface process feedbacks, and (4) being far less computationally demanding than a GCRM. Four versions of the Goddard one-moment microphysical schemes are implemented into the GMMF. Twoyear (2007–2008) simulations are then validated against three CloudSat/CALIPSO cloud ice products and other satellite products. Mean annual global precipitation is very similar in both amplitude and pattern among the four schemes despite the differences in their microphysics. The geographical distributions of precipitation from all four schemes agree well with TRMM and GPCP, except for having excessive precipitation in the Pacific and Atlantic ITCZs, the SPCZ, and western India Ocean and less precipitation in the Amazon and central Africa. This result suggests microphysics may not be the main source of this systematic precipitation bias in MMFs with prescribed SSTs. The cyclic boundary conditions of the embedded CRMs and the momentum transport are believed to be possible causes [Khairoutdinov et al., 2005; Cheng and Xu, 2014]. Despite only small differences in precipitation, simulated ice-phase condensates show considerable disparities among the four schemes. Their horizontal and vertical patterns of simulated TIWC agree well with CloudSat products; however, in terms of amount, three simulations (T2003, L2011, and L2014) are within

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Figure 15. Size-mapping factor for (a) snow, (b) graupel as a function of temperature and mass. Monthly mean zonal (c) snow and (d) cloud ice mixing ratio (1026 g g21) difference between the NO_SGMAP sensitivity and control runs for January 2007.

4–8% of 2B-CWC values but are 30–40% too low in comparison to the two CloudSat/CALIPSO products. Disparities in CIWP and CIWC among the four schemes are even more striking; in spite of many upgrades to its microphysical processes, L2011 produces far too little cloud ice due mainly to a maximum of 10% ice supersaturation being applied globally and without any constraint on the maximum cloud ice particle size. GMMF performance is further synthesized using Taylor diagrams, which show L2007 and L2014 are superior to the other two schemes (T2003 and L2011). Horizontal distributions tend to score lower than vertical mainly due to the cloud ice and snow associated with systematic precipitation biases as previously discussed. Though L2007 performs quite well in terms of total ice, in general the new 4ICE scheme performs the best among the four schemes, especially with regards to cloud ice. It has horizontal spatial correlation coefficients of 0.69 and 0.79 for CIWP and TIWP and vertical spatial correlation coefficient of 0.86 and 0.91 for CIWC and TIWC. Its global mean TIWP (CIWP) is within 5% (20%) and 32% (6%) of the 2B-CWC and 2C_ICE values, respectively. These errors are within or close to the nominal CloudSat uncertainty estimates of 30–40%. Furthermore, the global mean biases in the total column of water vapor, TOA radiation fluxes, TOA SWCF, and TOA LWCF, where again the 4ICE performs quite well, are also within the observed uncertainty. The ambiguity of the cloud ice depositional growth term (PSFI) in Lin et al. [1983] is clarified with three correction factors (FRH, FDWV, and FSZ). GMMF sensitivity experiments show both FRH and FDWV play important roles in the production/depletion of cloud ice/snow. Other important processes include ice supersaturation, the snow/graupel size mappings, and limiting the cloud ice maximum size. Turning off cloud ice fall speed in the 4ICE scheme tends to produce excessive clouds in the upper troposphere and lower stratosphere due to cloud-radiation feedbacks, which alters the Earth’s climate after just 2 months of simulation. Although the global mean mass of hail is small, the hail-related processes are important for achieving the correct balance between cloud ice sources and sinks. As part of a multiscale modeling system, the GMMF with its global, long-term application represents another critical component in the evaluation of the new Goddard 4ICE scheme in addition to the previous development and evaluation in the GCE [Lang et al., 2014] and NU-WRF [T2015]. The prognostic hydrometeor equations in one-moment microphysics schemes are based on mass conservation principles. It is vital to constrain the mass to within the uncertainty of the observations in addition to the remote sensing signals, which are sensitive to particle size, shape, and phase. Cloud ice and total ice in the new 4ICE scheme

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Figure 16. Monthly mean zonal snow and cloud ice mixing ratio (1026 g g21) difference (sensitivity run minus control) for two GMMF sensitivity experiments: (a, b) NO_SSI and (c, d) NO_ICESZMX.

have been evaluated and therefore constrained using CloudSat/CALIPSO retrieval products; however, highquality global data sets of other hydrometeor species for model evaluation are still lacking [Li et al., 2008; Lebsock and Su, 2014]. The approach of using satellite simulators to simulate satellite signals from the model

Figure 17. Percentage change in global monthly mean total ice and individual hydrometeor water paths for (a) four dominant and (b) five secondary processes. The percentage difference between the observed and control run total and cloud ice water path is also presented in Figure 17a.

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output against the corresponding raw satellite observations is invaluable for the next phase of model evaluation and beyond the scope of this paper. Despite the overall success of the GMMF simulations, systematic deficits still exist. The simple turbulence parameterization must be upgraded to a higher-order closure scheme and a shallow convection parameterization is also required in the CRM to better simulate low clouds and reduce the precipitation biases over tropical ITCZs, the SPCZ, and tropical continents. Taking the uncertainties of satellite retrieval and the separation method between cloud ice and snow into consideration, the apparent overestimation of cloud ice in the lower atmosphere over polar areas indicates cloud ice may be not converted into snow efficiently enough in L2014. From sensitivity experiments, the major contributions to cloud ice amount in the polar region come from the FRH, SGMAP, and ICESZMX terms.

Acknowledgments This research was supported by the NASA Modeling, Analysis, and Prediction (MAP) Program and the NASA Precipitation Measurement Missions (PMM). The authors are grateful to David B. Considine and Ramesh Kakar at NASA HQ for their support of this research. Acknowledgment is also made to the NASA Goddard Space Flight Center and NASA Ames Research Center computing facilities and to Tsengdar Lee at NASA HQ for the computational resources used in this research. CloudSat data were acquired through the CloudSat Data processing Center at Colorado State University (http:// cloudsat.cira.colostate.edu). CloudSat/ CALIPSO cloud fractions were obtained from https://climatedataguide.ucar. edu and. CERES-EBAF data were acquired from the NASA Langley Research Center (http://ceres-tool.larc. nasa.gov). GPCP Precipitation data were provided by the NOAA/OAR/ESRL from their web site at http://www.esrl. noaa.gov/psd/.

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