Radiative forcing of the tropical thick anvil evaluated by combining TRMM with atmospheric radiative transfer model

The presences of anvil clouds significantly affect the tropical mean radiation budget and increase the uncertainty of climate model simulations. In this study, the climatological mean distributions of thick anvil parameters, such as top, bottom, occurrence, cloud effective radius (CER) and cloud optical depth (COD) in the tropics (20°S–20°N) are investigated by Tropical Rainfall Measuring Mission's (TRMM) precipitation radar (PR) and visible and infrared scanner (VIRS) from 1998 to 2007. The thick anvil radiative forcing at shortwave (0.2 ∼ 4 µm) and longwave (4 ∼ 50 µm) length, i.e. Shortwave radiative forcing (SRF) and Longwave radiative forcing (LRF) and their net effects at different altitudes are simulated with Santa Barbara DISORT Atmospheric Radiative Transfer Model (SBDART). The results show that thick anvils present higher top/bottom, smaller CER, and thicker COD over land than those over ocean. At the top of atmosphere (TOA), net radiative effects of thick anvils are positive warming, which means the earth‐atmosphere system obtains energy forced by thick anvils. At earth surface, net radiative effects of thick anvils are positive warming at land surface and negative cooling at ocean surface, respectively. In general, anvil SRF, LRF and net effects vary with different geographical locations and also present large land–ocean differences in the tropics, due to different anvil properties forced by the surface heating and topography. All spatial patterns of stronger anvil SRF, LRF and net effects are well matched with the places where exist higher fractions of anvils, such as Asian monsoon zone, the Intertropical Convergence Zone (ITCZ), the South Pacific Convergence Zone (SPCZ), tropical Africa, Mid‐America and South America. In addition, the present work provides an evidence that it is an effective approach to calculate quantitatively the grid‐cell SRF and LRF of cloud at a large scale by using the SBDART model with inputs from satellite observations.


Introduction
It has been estimated that clouds cover more than 50% of the globe (Liou, 2002), which are very important in regulating atmospheric radiative transfer via their greenhouse versus albedo effects (Stephens and Webster, 1981;Stephens, 2005;Waliser et al., 2009;Zhang et al., 2013;Hong and Liu, 2015). As a typical non-precipitating cloud, thick anvil closely associated with deep convection is one of the most important cloud types in the tropics. Previous studies pointed out that the presences and longevity of anvil clouds may have a significant impact on the tropical circulation through significantly affecting the tropical mean radiation budget, which can increase the uncertainty of climate model simulations (Webster and Stephens, 1980;Machado and Rossow, 1993;Yao and Del Genio, 1999;Colman, 2003;Clement and Soden, 2005).
Using a single-or multi-satellite observation, therefore, many previous studies have revealed the geographical distributions of anvil occurrence, threedimensional structures (e.g. top/bottom/thick) of anvil clouds (Schumacher and Houze, 2006;Cetrone and Houze, 2009;Fu et al., 2010;Yuan and Houze, 2010;Li and Schumacher, 2011;Yuan et al., 2011;Young et al., 2012) and their corresponding spectral characteristics (e.g. visible/infrared radiance) (Machado and Rossow, 1993;Fu et al., 2010;Young et al., 2013;Yang et al., 2015) in a regional or tropics-wide scale. For example, high occurrences of thick anvils located most frequently over Asia monsoon region, equatorial Africa, the Maritime Continent, and Panama (Cetrone and Houze, 2009;Yuan and Houze, 2010;Li and Schumacher, 2011). Especially, based on observation of precipitation radar (PR) aboard on the Tropical Rainfall Measuring Mission (TRMM) satellite, Li and Schumacher (2011) found that thick anvils have an average 17-dBZ echo top of ∼8.5 km and an average thickness of ∼2.7 km in the tropics, which were usually higher and thicker over land compared to ocean. Recently, by using the advantage in near synchronization observation of merged PR and VIRS, Yang et al. (2015) further explored that visible/infrared reflectance and the equivalent brightness temperature of a Radiative forcing of the tropical thick anvil 223 blackbody at different wavelengths for thick anvils in the tropical-wide regions, and their spectral signals implied that thick anvils cloud presents thinner optical depth and their cloud tops consists many more smaller-ice droplets over land than those over ocean. In contrast, the radiative forcings of thick anvils were provided by few studies, which only focused on their general radiative characteristics of tropical anvil (Webster and Stephens, 1980;Ackerman et al., 1988;Machado and Rossow, 1993). However, the geographical distribution of radiative forcing climatology of thick anvil is limited in their ability to measure anvils vertical structure and their spectral signals and microphysical properties at the same time with a radiative transfer model simulation, leaving large gaps in our comprehensive understanding of radiative characteristics of thick anvils.
For this purpose, in this study, PR and VIRS onboard TRMM are firstly used to capture thick anvil occurrence, top/bottom, and their spectral signals during -2007, following Yang et al. (2015. Moreover, cloud effective radius (CER) and cloud optical depth (COD) of thick anvils are retrieved by the bispectral reflectance (BSR) algorithm (Nakajima and Nakajma, 1995;Fu, 2014), using the visible and infrared reflectance of VIRS with Santa Barbara DISORT Atmospheric Radiative Transfer Model (SBDART) (Ricchiazzi et al., 1998). Finally, the thick anvil radiative forcings at shortwave (0.2 ∼ 4 μm) and longwave (4 ∼ 50 μm) lengths, i.e. Shortwave radiative forcing (SRF) and Longwave radiative forcing (LRF), and their net effects at the top of atmosphere (TOA)/earth surface are simulated by SBDART with input of anvil occurrence, geometrical (top and bottom) and microphysical parameters (CER and COD).

Data and methods
The launch of the TRMM presents an unique opportunity to comprehensively understand the precipitation types and three-dimensional rainfall structures with their corresponding spectral signals (Iguchi et al., 2000;Fu et al., 2003;Kodama and Tamaoki, 2002;Awaka et al., 2009;Liu and Fu, 2010;Yang et al., 2015;Fu et al., 2017).TRMM PR 2A25 version 7 and VIRS 1B01 (hereafter referred to as 2A25 and 1B01) datasets from 1998 to 2007, provided by Goddard Space Flight Center, will be used in this study. A merged dataset at PR spatial resolution was established by collocating 2A25 and 1B01 products with a weight-averaged method, which picks the mean value of VIRS at PR pixels (Yang et al., 2015).
In the 2A25, original radar reflectivity profile is used to identify rain classifications and their tops (Awaka et al., 1998Iguchi et al., 2009;Chen et al., 2016). The thick anvils are defined as echo with a rain type: equal to 160 -'Maybe stratiform, but rain hardly expected near surface. Bright band may exist but is not detected'; 170 -'Maybe stratiform, but rain hardly expected near surface. Bright band hardly expected. Maybe cloud only'; or 300 -'Other'. In addition, anvil reflectivity must be greater than 17 dBZ and have an echo base higher than 3 km (Li and Schumacher, 2011;Yang et al., 2015). The errors for the retrieval of bottom and top mainly depend on the detection sensitivity of PR. Here, only single-layer thick anvils, whose vertical profiles present sequential reflectivities of >17 dBZ, are considered to calculate their radiative forcings. Anvil thickness is defined as the difference between the top and base. The reflectance at 0.63 and 1.6 μm from 1B01 products (hereafter referred to as RF1 and RF2, respectively) are used to retrieve cloud parameters (CER and COD) using the BSR method (Fu, 2014), whose the retrieval errors for CER/COD is less than 10% for most cases of realistic clouds under realistic conditions (Nakajima and Nakajma, 1995).
Because of the large pixel samples from orbital-level data (2A25 and 1B01), probability density distribution, which is defined as the ratio of the samples at each anvil property (top/CER/COD) interval to the sum samples of all intervals for each anvil property, is used herein to reveal detailed differences of anvil property over different underline surfaces. In addition, the orbital data are grouped into 0.5 ∘ × 0.5 ∘ grid boxes in which total observations, anvil samples, top/bottom and their vertical profiles with spectral signals over the global Tropics domain (20 ∘ S-20 ∘ N). The occurrence frequency (i.e. fraction) of thick anvil is defined as the ratio of the number of identified anvil pixels to the total number of observation pixels within each 0.5 ∘ grid.
The SBDART model is intended for the calculation of radiative transfer problems covering a wide spectral range. It runs with 33 altitude layers and 4 radiation streams. Users can define about 60 initial parameters and 12 output options including cloud properties, aerosol characteristics and surface types, according to the research purpose. Cloud radiative forcing (CRF) is defined as the net radiation flux under all sky minus that under clear sky at TOA, surface and any other height. In this study, climatic mean anvil parameters (anvil top, bottom and fraction, CER and COD) are input to SBDART for calculating anvil SRF, LRF, and their net effects (i.e. SRF plus LRF) at surface and TOA in each 0.5 ∘ grid, while other input parameters come from the tropical climatic mean database in SBDART.

Vertical structure of thick anvil
Anvil geometric and physical parameters (e.g. top, bottom, thick, CER and COD) and fractions, as key input parameters to SBDART, played key roles in determining the process of thick anvil radiative forcing. The Contoured Frequency by Altitude Diagram (CFAD) is an effective method to analyze the characteristics of vertical structure of thick anvil, as suggested by previous studies (Yuter and Houze, 1995;Fu et al., 2003;Qin and Fu, 2016). The distribution can reflect the thick anvil characteristics with different echo reflectivities and heights. The vertical structure of thick anvil over land and ocean is, respectively, extracted as shown in Figures 1(a) and (b), which presents a uniform shape over both land and ocean. Differently, the maximum frequency appears at approximately 6 ∼ 9 km over land, while approximately 5 ∼ 8 km over ocean. Moreover, the peak height over land is higher than that over ocean, and the maximum reflectivity (24 dBZ) mainly corresponds to a height of 6 km over land, which is also higher than that over ocean (∼5.5 km). Furthermore, the Bi-parameter probability density distribution pattern of thick anvils in two-dimensional space consisting of anvil top height (ATH) and CER/COD over land and ocean (Figures 1(d)-(f)). Over land, ATH of 5∼10.5 km is mainly concentrated between 8 and 22 μm for CER, whereas ATH of 4.5∼9 km is mainly concentrated between 10 and 25 μm for CER over ocean. Similarly, over land, ATH of 5∼10.5 km is mainly concentrated between 40 and 110 for COD, whereas ATH of 4.5∼9 km is mainly concentrated between 35 and 110 for COD. In general, as expected, thick anvils are usually higher/thicker over land than over ocean by 0.5 ∼ 1 km, and also anvil physical parameters (e.g. CER and COD) are intimately tied to its geometric parameters (e.g. top and height).

Spatial distributions of anvil parameters
To reveal the differences in geographical distribution of anvil, Figure 2 shows spatial distributions of climatologies for the above parameters over global tropical areas during 1998-2007. In general, all these parameters present clear land-ocean differences. In detail, anvil tops/bottoms are higher over land (8.5 ∼ 10 km/5.5 ∼ 6.5 km) than those over ocean (7 ∼ 8.5 km/4.5 ∼ 5.5 km) (Figures 2(a) and (b)). Previous studies showed that convection were usually higher and thicker over land compared with ocean, which is probably attributed to the surface heating and topography (Stanley and Carlson, 1986;Nesbitt et al., 2006;Chen et al., 2016). Because anvil properties were closely tied to the properties of the parent convection, it can imply that the land-forcing effect can make anvils higher and thicker.
Moreover, smaller CER/thicker COD mostly occurred over land (16 ∼ 19 μm/85 ∼ 110 μm), while not over ocean (19 ∼ 22 μm/60 ∼ 95 μm) (Figures 2(c) and (d)), which suggests that anvil tops consist many more smaller-ice droplets and thicker vertical layers over land than those over ocean, due to land-forcing effects. Finally, higher fractions of anvils mainly appear over the Asian Monsoon Region, the Intertropical Convergence Zone (ITCZ), the South Pacific Convergence Zone (SPCZ), regions between the South America and the North America, and the Tropical Africa, where fractions vary between 0.4 and 0.6% (Figure 2(f)). While over most other areas, anvil fractions are less than 0.3%. Based on these, therefore, it should be checked that whether regional differences in tropical thick anvil parameters can modulate different earth-atmosphere energy budgets at surface and TOA.

Radiative forcing of thick anvil
CRF and its net radiative effect are key factors to evaluate the energy balance modulated by clouds. Figure 3 shows that geographical distributions of climatological mean SRF and LRF of thick anvil and their net radiative effect at TOA, respectively. At TOA, thick anvils induce weakly positive SRF over land, ranging from 0.05 to 0.15 W m −2 , while negative SRF over ocean, ranging from −1.8 to −0.2 W m −2 (Figure 3(a)). It means that thick anvils mainly induce very weak shortwave heating and shortwave cooling at TOA over land and ocean, respectively. The weakly positive SRFs of thick anvils at the TOA over land are probably ascribed to the enhanced absorption effects of ice or water droplets in thick anvils. As well known, ice and water droplets will absorb certain radiation at near-infrared wavebands, meanwhile thick anvils over land contain many more smaller-ice or water droplets than those over ocean (Yang et al., 2015; also seen in Figure 2(c)), which is probably related to the enhancement of shortwave radiation absorption effect over land. Moreover, compare to low-albedo ocean surface, land surface represents higher albedo that will cause much more shortwave radiation reabsorbed by thick anvils through multiple reflections. Over land, therefore, there will be less outgoing shortwave radiation in the condition of the existence of thick anvils than that in clear-sky condition, which presents weakly positive SRF at TOA. As it should be, many more experimental observations combined with model simulations are needed to validate the above supposition regarding the weakly positive SRF at TOA caused by thick anvils over land.
Differently, thick anvil-induced LRF are positive heating over both land and ocean, where the values of LRFs are 0.4∼4 W m −2 (Figure 3(b)). Further, net radiative effect of thick anvil at TOA is positive warming over both land and ocean (Figure 3(c)), which means the earth-atmosphere system obtains energy forced by thick anvils, ranging from 0.2 to 5 W m −2 . In addition, the larger shortwave/longwave heating or cooling values at TOA mainly locate over the Asian Monsoon Region, ITCZ, SPCZ and the Tropical Africa, all of these regions present higher fractions of anvils (Figure 2(f)).
Similarly, Figure 4 shows that geographical distributions of climatological mean SRF and LRF of thick anvils and their net radiative effect at surface, respectively. At earth surface, anvil SRFs are negative cooling in both land and ocean, ranging from −2 to −0.05 W m −2 (Figure 4(a)), while LRFs are positive heating in both land and ocean, varying between 0 and 1.2 W m −2 (Figure 3(b)). While those at earth surface are positive warming over land and negative cooling over ocean, respectively. In contrast, SRFs at TOA (positive heating) are opposite with those   at surface (negative cooling) over land, while SRFs at both TOA and surface are positive with similar heating values over ocean (Figures 3(a) and 4(a)). LRFs at TOA are stronger than those at surface by more than two times (Figures 3(b) and 4(b)), and both of which present obvious longwave heating. Therefore, thick anvil-induced net radiative effects at earth surface are positive warming (0.04∼0.3 W m −2 ) over land and negative cooling (−1 ∼ −0.1 W m −2 ) over ocean, respectively. It means that the land surface temperature is increased by 0.02 ∼ 0.5 K, while the sea surface temperature is decreased by 0.05 ∼ 0.5 K, according to the equation on the relationship between radiative forcing changes and global surface temperature changes (Dickinson, 1982;Cess et al., 1993). In addition, the regions of larger SRFs/LRFs at surface are also well matched with those of higher fractions of anvils.    means the earth-atmosphere system obtains energy forced by thick anvils. Thirdly, at earth surface, anvil SRFs (LRFs) are negative cooling (positive heating) over both land and ocean. Accordingly, net radiative effects of thick anvils are positive warming at land surface and negative cooling at ocean surface, respectively. Finally, anvil SRF, LRF and their net effects vary with different geographical locations in the tropics, and also exist significant land-ocean differences, due to different anvil properties forced by the surface heating and topography. All spatial patterns of anvil SRF, LRF and net effects are well matched with those of anvil fractions. This paper focuses mainly on geographical distribution of radiative forcing climatology for thick anvil using the approach for quantitatively calculating the grid-cell radiative forcing at a large scale based on SBDART model with TRMM observations. Taking thick anvil as an example, generally, the present work may prove useful in improving our understanding of cloud climate effects in the earth-atmosphere system. However, because the detection of thinner cloud by PR is limited to its long wavelength (2.2 cm), thinner anvils are usually missed. Nevertheless, such thin anvils can be effectively detected by Cloud Profiling Radar (CPR) onboard CloudSat (Yuan et al., 2011;Young et al., 2013). In addition, it is not considered in our present work that the effects of overlapping or multi-layer clouds on anvil radiative forcing (Zhang and Jing, 2010;Zhang et al., 2013). Therefore, more detailed research on all the anvils and their radiative forcings are still undergoing, using the combinations of TRMM and CloudSat observations in the horizontal and vertical directions.