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Radiosonde data provide in situ measurements of atmospheric environmental variables, including temperature, pressure, RH, wind speed, and wind direction, which is recognized to be able to derive the overlapping pattern of cloud in the vertical direction. The China radiosonde network (CRN) consists of 120 radiosonde sites across China, in which the high-resolution (5−8 m) sounding balloon is launched twice per day at 0800 LST (LST = UTC + 8) and 2000 LST (Guo et al., 2016, 2019). Based on these fine-resolution radiosonde measurements, the CBHs are calculated for the summer (June−August) during the period from 2010 to 2018 using the improved relative humidity (RH) threshold method (Zhang et al., 2018). Coincidently, up to two additional soundings are launched occasionally at 1400 LST and 0200 LST in summer during certain intensive observing periods at selected stations (Guo et al., 2016; Lou et al., 2019). Given the spatial inhomogeneity, the CBHs from all sites are interpolated onto a regular 5° × 5° grid, following the method by Zhang et al. (2018). The significant diurnal variation of summertime clouds in China (Chen et al., 2018) justifies the use of the 1400 LST soundings to derive CBHs unless otherwise noted. This is expected to better match with the CTH products from MODIS onboard Aqua, one of the polar-orbiting satellites.
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The MODIS instrument, an important payload of both Terra and Aqua satellites, can observe the Earth with a total swath width of 2300 km, with a revisit cycle of one to two days, depending on the location (Remer et al., 2005). The MODIS has 36 spectral bands ranging from 0.4 to 14.2 μm (Salomonson et al., 1989), providing global coverage of cloud optical and physical parameters at both granule and grid levels (Platnick et al., 2003). As one of important cloud optical properties, cloud optical depth (τ) can affects the shortwave CRF by reflecting the attenuation of radiation intensity by cloud in the transmission path (Chen et al., 2019b). As the global gridded product, the level-3 cloud products of MODIS are made publicly available on a grid size of 1° × 1° at daily, 8-day, and monthly timescales (Menzel et al., 2008).
Therefore, the MODIS level-3 daily cloud products onboard Aqua (MYD08_D3) are used in this study to characterize the optical and physical properties of cloud tops. In order to be collocated with the CBHs derived from the 1400 LST radiosonde data, the MODIS cloud products, including the CTH (ht), the daily averaged liquid and ice COD (τc), liquid and ice cloud effective radius (rc), as well as cloud fraction (ƒc), are resampled to 5° latitude× 5°longitude grid by simply averaging out the original MODIS products.
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The MODIS albedo product (MCD43) could provide both white-sky albedos and black-sky albedos for spectral and broad bands. The MCD43 is a daily product, obtained by the surface reflectance observations built up over a 16-day period (Schaaf et al., 2002). As a climate modeling grid product, MCD43C3 provides albedo d ata at a spatial resolution of 0.05° latitude× 0.05° longitude grid. In the present study, a climatology of daily-averaged surface albedo (α) data was built using nine years (2010−18) of MCD43C3 black-sky visible albedo, in which only those α values with a quality flag less than or equal to two were used.
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The Clouds and the Earth's Radiant Energy System (CERES) instrument directly measures global radiance at the TOA. By combining the MODIS and GEOS-derived cloud properties, CERES could also provide the radiance at the surface (Wielicki et al., 1996). The high accuracy and robustness of the CERES radiance products in revealing Earth’s energy imbalance have been adequately verified (Loeb et al., 2012; Allan et al., 2014; Trenberth et al., 2014). As such, the CERES Synoptic TOA and surface fluxes and clouds (SYN) products under the clear-sky and all-sky conditions with a spatial resolution of 1° × 1° are used here as “ground-truth” to validate the SWCRF estimated by the radiative transfer model. Prior to its application in the following analysis, we first calculate the CERES SWCRFTOA and SWCRFSUR using the clear-sky and all-sky incoming and outgoing SW flux at the TOA and surface, respectively. Then, the CERES-derived SWCRF are resampled from a 1° × 1° to 5° × 5° latitude/longitude grid.
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The shortwave rapid radiative transfer model (RRTM_SW) has been used to calculate both atmospheric radiative fluxes and heating rates for the spectral wavenumber of 820−50 000 cm−1 (Clough et al., 2005). By utilizing the correlated-k approach, the fluxes provided by RRTM SW are accurate, computationally efficient, and fast. Due to its high accuracy and efficiency, the RRTM_SW has been widely applied to those studies associated with atmospheric radiative transfer and general circulation models (GCMs) (e.g., Thampi and Roca, 2014; Verlinden and de Szoek, 2018).
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Here, the SWCRF (ΔF; W m−2) is defined as the difference of net solar flux between an environment with clouds and one without clouds present at the surface, at the TOA, or in the atmosphere, which can be expressed as:
where i represents the surface, TOA, and the ATM, respectively,
$ {F_{{\rm{net}},i}} $ represents the net flux with clouds, and$ {F'_{{\rm{net}},i}}$ represents the net flux without clouds.$ {F_{{\rm{net}},i}} $ can be calculated as the difference between the downwelling flux with cloud ($ {F}_{\downarrow,i} $ ) and upwelling flux with cloud ($ {F}_{\uparrow,i} $ ), which is formulated as:Similarly,
$ {F'_{{\rm{net}},i}} $ denotes the difference between the downwelling flux without cloud ($ {F'_{ \downarrow,i}} $ ) and the upwelling flux without cloud ($ {F'_{ \uparrow,{\rm{i}}}} $ ), which can be formulated as follows:Combining Eqs. (1)−(3), we obtain the following expression:
Since the downward flux at the top of the atmosphere is independent of the presence of clouds (i.e.,
$ {F_{ \downarrow,{\rm{TOA}}}} = {F'_{ \downarrow,{\rm{TOA}}}} $ ), the SWCRF at TOA (ΔFTOA) can be derived as:Meanwhile, the SWCRF in the atmosphere (ΔFATM) is defined as:
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Normally, the vertical distribution of COD is assumed to be uniform in the current climate model. Here, we define four scenarios regarding the vertical distribution of COD, including a two-point distribution (Scenario 1), a uniform distribution (Scenario 0 & Scenario 2), and a normal distribution (Scenario 3), which are described as follows:
(1)Two-point distribution
The two-point distribution assumes the total COD is concentrated in only two cloud layers. Thus, the COD for each cloud layer is 1/2 of the total COD. In addition, we define the two heights of the cloud layer to be 1/4 and 3/4 of the total cloud height. The distribution can be formulated as follows:
where the
${\tau _{\rm{t}}}$ and${\tau _i}$ stands for the total COD and the COD of the ith cloud layer, respectively. ht and hb represent the cloud-top height and cloud-base height, respectively, and hi stands for the height of the ith cloud layer.(2)Uniform distribution
The uniform distribution assumes that the total COD is uniformly distributed across the cloud layers in the vertical, and the COD of the ith cloud layer is expressed as follows:
where the hi,t, and hi,b stand for the top and base height for the ith cloud layer, respectively, and N represents the number of the cloud layer.
(3)Normal distribution
The symmetrical distribution of many natural processes and phenomena is the normal distribution. In this study, we assume the vertical distribution of COD is a normal distribution. For the given interval [μ ± 3σ], the probability of the actual COD falling within that interval is nearly 1.0 (Mishra and Datta-Gupta, 2018). Thus, the COD of the ith cloud layer can be described as follows:
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To calculate the upward flux reaching the top-of-atmosphere (
$ {F'_{ \uparrow,{\rm{TOA}}}} $ and$ {F_{ \uparrow,{\rm{TOA}}}} $ ) and the downward flux reaching the surface ($ {F'_{ \downarrow,{\rm{SUR}}}} $ and$ {F_{ \downarrow,{\rm{SUR}}}} $ ), we employ the RRTM_SW model. A tropical standard atmosphere model is chosen for the model set up, with the vertical atmospheric profiles of pressure and temperature set to their default values. The model differentiates between ice and liquid clouds. As key input parameters of the RRTM_SW model, MODIS-derived cloud physical parameters, such as cloud fraction, liquid droplet effective radius, and cloud effective radius of ice, have been directly incorporated into the model simulation. The cloud water path is calculated using the COD from MODIS. The vertical profiles of the COD are calculated by the CBH, CTH, and the total COD, using the method described in section 2.2.2. The profiles of cloud fraction and cloud effective radius are assumed to be invariant with the height h and set equal to fc and rc, respectively. For the surface albedo, the climatological mean values derived from MODIS have been utilized. It is noteworthy that aerosol properties are not included in the input file for the RRTM_SW model since the radiative effect induced by aerosol-cloud interaction is more complicated and beyond the scope of this study.Besides the CBH, it is well known that the SWCRF is influenced by the vertical profile of the COD. In order to investigate the impact of CBH on the SWCRF, we assume two main scenarios: (1) the SWCRF is calculated from only the CTH with the CBH unknown (Scenario 0), and (2) the SWCRF is calculated from both the CTH and CBH (Scenarios 1−3), the details of which are summarized in Table 1. Schematically shown in Fig. 1 is an example of the vertical profile of the COD as a function of the normalized total COD.
Scenarios Vertical profile pattern of COD Number of cloud layers (N) Scenario 0 Uniform 1 Scenario 1 two-point 2 Scenario 2 Uniform true cloud layer Scenario 3 Normal true cloud layer Table 1. Summary for the vertical profile scenarios of cloud optical depth (COD) assumed in the calculation of cloud optical depth, which is an important input for the calculation of cloud radiative forcing.
Figure 1. The normalized cloud optical depth (COD;
${\tau }_{{\rm{c}}}$ ) shown as a function of normalized cloud height (km) for three different vertical profile Scenarios of COD: (a) Scenario 1, (b) Scenario 2, and (c) Scenario 3, based on the assumption of the true number of the cloud layer is equal to 10 and the height of cloud is uniform. -
We perform a sensitivity analysis to better understand the impact of CBH on the SWCRF. This consisted of a series of experiments on the CRF estimation, that have been conducted by running the RRTM_SW with varying CBH values, under different cloud vertical profile patterns of COD. In an ideal experiment, the liquid effective particle radius is set to be uniform at 15 μm, whereas the solar zenith angles (SZA) are set to 0°, 30°, and 60°, respectively. The CBH values are set to increase from 0.5 km upwards until 5.0 km at 0.5 km intervals, and the increase in CBH each time is defined as Δhb. The total COD is constant, and the vertical profile of COD is calculated using the cloud-top height (ht) and the changed cloud-base height (hb + Δhb).
Scenarios | Vertical profile pattern of COD | Number of cloud layers (N) |
Scenario 0 | Uniform | 1 |
Scenario 1 | two-point | 2 |
Scenario 2 | Uniform | true cloud layer |
Scenario 3 | Normal | true cloud layer |