X. Wu, K. A. Balmes , Q. Fu Article · 2021. 1. 25. · Corresponding author: K. A. Balmes, [email protected] {1{Accepted Article This article has been accepted for publication and undergone

manuscript submitted to JGR: Atmospheres

Aerosol direct radiative effects at the ARM SGP and1

TWP Sites: Clear skies2

X. Wu, K. A. Balmes∗, Q. Fu3

Department of Atmospheric Sciences, University of Washington, Seattle, WA, USA4

Key Points:5

• Clear-sky aerosol direct radiative effects were estimated based on multi-year ground-6

based observations at the ARM SGP and TWP sites7

• Modeled clear-sky surface downwelling shortwave fluxes using observed inputs agreed8

well with surface radiometer observations9

• The annual mean clear-sky aerosol direct radiative effects at the top of the atmo-10

sphere are -3.00 W m−2 at SGP and -2.82 W m−2 at TWP11

Corresponding author: K. A. Balmes, [email protected]

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This article has been accepted for publication and undergone full peer review but has not been throughthe copyediting, typesetting, pagination and proofreading process, which may lead to differences betweenthis version and the Version of Record. Please cite this article as doi: 10.1029/2020JD033663.

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https://doi.org/10.1029/2020JD033663

https://doi.org/10.1029/2020JD033663

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Abstract12

The clear-sky aerosol direct radiative effect (DRE) was estimated at the Atmospheric13

Radiation Measurement (ARM) Southern Great Plains (SGP) and Tropical Western Pa-14

cific (TWP) sites. The NASA Langley Fu-Liou radiation model was used with observed15

inputs including aerosol vertical extinction profile from the Raman lidar; spectral aerosol16

optical depth (AOD), single-scattering albedo and asymmetry factor from Aerosol Robotic17

Network (AERONET); temperature and water vapor profiles from radiosondes; and sur-18

face shortwave spectral albedo from radiometers. A radiative closure experiment was con-19

ducted for clear-sky conditions. The mean differences of modeled and observed surface20

downwelling shortwave total fluxes were 1 W m−2 at SGP and 2 W m−2 at TWP, which21

are within observational uncertainty. At SGP, the estimated annual mean clear-sky aerosol22

DRE is -3.00 W m−2 at the top of atmosphere (TOA) and -6.85 W m−2 at the surface.23

The strongest aerosol DRE of -4.81 (-10.77) W m−2 at the TOA (surface) are in the sum-24

mer when AODs are largest. The weakest aerosol DRE of -1.28 (-2.77) W m−2 at the25

TOA (surface) are in November-January when AODs and single-scattering albedos are26

lowest. At TWP, the annual mean clear-sky DRE is -2.82 W m−2 at the TOA and -10.3427

W m−2 at the surface. The strongest aerosol DRE of -5.95 (-22.20) W m−2 at the TOA28

(surface) are in November (October) due to the biomass burning season’s peak. The weak-29

est aerosol DRE of -0.96 (-4.16) W m−2 at the TOA (surface) are in March (April) when30

AODs are smallest.31

1 Introduction32

Aerosols directly modulate the radiative energy budget by scattering and absorb-33

ing radiation, which is referred to as the aerosol direct radiative effect (DRE). More re-34

cently, the DRE is also referred to by the Intergovernmental Panel on Climate Change35

(IPCC) as the radiative effect due to aerosol-radiation interactions (REari) (Boucher et36

al., 2013). The DRE varies with aerosol optical properties (e.g., aerosol extinction pro-37

file, optical depth, single-scattering albedo, and asymmetry factor), solar zenith angle38

and environmental characteristics (e.g., clouds, surface albedo, and relative humidity).39

Aerosol DREs occur under both clear-sky and cloudy conditions (J. M. Haywood40

& Shine, 1997; Chand et al., 2009; Peters et al., 2011; De Graaf et al., 2012; Vuolo et41

al., 2014). The importance of the latter has been underscored by a continuum transi-42

tion in aerosol and cloud optical depth going from clear-sky to cloudy conditions (Calbo43

et al., 2017; Balmes & Fu, 2018). Furthermore, the impact of clouds on the aerosol DRE44

caused by absorbing aerosols can switch the cooling to a warming effect over the regions45

with a low surface albedo (Chand et al., 2009; Keil & Haywood, 2003; Podgorny & Ra-46

manathan, 2001). The quantification of aerosol DRE requires both aerosol and cloud op-47

tical depths and their individual vertical extinction distributions in the same atmospheres48

(Liao & Seinfeld, 1998; J. M. Haywood & Shine, 1997; Podgorny & Ramanathan, 2001;49

Keil & Haywood, 2003). This study, however, solely focuses on the aerosol DRE in the50

absence of clouds (i.e., clear-sky). This is the first part of our effort to quantify aerosol51

DREs at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP)52

and the Tropical Western Pacific (TWP) sites under all-sky conditions based on the ARM53

ground-based aerosol, cloud, radiation, and atmospheric state measurements, which has54

not been done before.55

Clear-sky global-mean estimates of the shortwave (SW) aerosol DRE at the top of56

the atmosphere (TOA) range between -2 to -7 W m−2 (e.g., Henderson et al., 2013; Ma-57

tus et al., 2015, 2019; Myhre et al., 2007; Reddy et al., 2005; Yu et al., 2006; Christo-58

pher & Zhang, 2002; Remer & Kaufman, 2006; T. X. Zhao et al., 2008; T. X.-P. Zhao59

et al., 2011; Thomas et al., 2013; Boucher et al., 2013). However, many of these stud-60

ies are limited to satellite observations with passive sensors (e.g., Myhre et al., 2007; Christo-61

pher & Zhang, 2002; Remer & Kaufman, 2006; T. X. Zhao et al., 2008) or may use in-62

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struments that do not detect all radiatively significant aerosols (e.g., CALIPSO) (Thorsen63

& Fu, 2015b; Thorsen et al., 2017). In contrast, the high-quality ground-based obser-64

vations at the ARM sites allow the opportunity to quantify the aerosol DRE with all aerosol,65

cloud, radiation and atmospheric state quantities available from observations. The es-66

timated clear-sky aerosol DREs at the ARM SGP and TWP sites should be useful to67

compare and validate the global estimates over these two regions.68

The ARM ground-based observations provide reliable information on the aerosol69

and environmental conditions necessary to determine the aerosol DRE. Paired with a70

radiative transfer model, the regional aerosol DRE can be determined by considering an71

atmosphere with and without aerosols. The ground-based Raman lidars (RL) (Ferrare72

et al., 2006; Goldsmith et al., 1998; Newsom, 2009) at the ARM sites provide aerosol ver-73

tical detection and extinction profile (Balmes et al., 2019; Balmes & Fu, 2018; Thorsen74

& Fu, 2015a; Thorsen et al., 2015; Thorsen & Fu, 2015b; Thorsen et al., 2017). In ad-75

dition, the Aerosol Robotic Network (AERONET) operates collocated Cimel sun pho-76

tometers, which provides aerosol optical depth, single-scattering albedo and asymme-77

try factor at several wavelengths (Holben et al., 1998; Giles et al., 2019). The synergy78

of aerosol observations can then be inputted into the NASA Langley Fu-Liou radiative79

transfer (RT) model (Fu & Liou, 1992, 1993; Fu, 1996; Fu et al., 1998; F. G. Rose & Char-80

lock, 2002; F. Rose et al., 2006) to determine the clear-sky aerosol DRE.81

In this study, the observations from ground-based ARM RLs, AERONET sun pho-82

tometers, radiosondes, and spectral radiometers along with the RT model are utilized83

to investigate the clear-sky aerosol DRE at the ARM SGP and TWP sites. The surface84

SW downwelling fluxes are compared between surface radiometer observations and the85

RT model for clear-sky conditions. The daily mean, monthly mean and seasonal cycle86

of the clear-sky aerosol DRE is quantified.87

Section 2 presents the aerosol optical properties from the RL and AERONET and88

the extension of spectral aerosol optical properties outside the observational spectra range.89

Section 3 describes the RT model and other datasets used in this study. Section 4 shows90

the radiative closure experiment that compares simulated surface downwelling SW fluxes91

using observed inputs with surface radiometer observations. Section 5 details the clear-92

sky aerosol DREs from the daily to seasonal scale at the SGP and TWP sites. Section93

6 quantifies the uncertainties associated with the estimated aerosol DREs and simulated94

downward SW fluxes. Section 7 summarizes and discusses all findings presented and pro-95

vide some conclusions.96

2 Aerosol Optical Properties97

The ARM RL operates at 355 nm. The vertically resolved profiles of aerosol ex-98

tinction are retrieved using the feature detection and extinction (RL-FEX) retrieval al-99

gorithm (Balmes et al., 2019; Balmes & Fu, 2018; Thorsen et al., 2015; Thorsen & Fu,100

2015a; Thorsen et al., 2017). The RL AOD at 355 nm is obtained by vertically integrat-101

ing all aerosol extinction within a profile. In this study, we use the RL data with 10-minute102

temporal resolution and 30 meter vertical resolution from 1 August 2008 to 31 August103

2016 at the SGP site (36.6◦N, 97.49◦W) and from 15 December 2010 to 1 January 2015104

at the TWP site (12.4◦S, 130.89◦E). Lidar retrievals near the surface are difficult due105

to incomplete overlap of the emitted laser beam and the receiver’s field of view (Thorsen106

et al., 2015; Thorsen & Fu, 2015a). To avoid unphysical aerosol extinction near the sur-107

face, the extinction for the first two vertical bins from the surface to 60 m was obtained108

by extrapolating the extinctions from the two vertical bins between 60 to 120 m.109

Figure 1 shows the monthly climatology of the aerosol extinction profile from the110

RL over SGP and TWP. During the winter months at SGP, the aerosols remain quite111

low to the surface but during the other seasons the aerosols can reach quite high in the112

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Figure 1. Monthly climatology of the aerosol extinction profiles for each month from the Ra-

man lidar at 355 nm at the (top) Southern Great Plains (SGP) site from August 2008 to August

2016 and at the (bottom) Tropical Western Pacific (TWP) site from December 2010 to January

2015. The mean is denoted as a line and the shading refers to the 25th to 75th percentiles.

troposphere (Turner et al., 2001), especially from May to September, corresponding to113

larger monthly-mean AOD (Fig. 6). At TWP, the aerosols can be distributed high from114

September to January, especially in October with the largest monthly-mean AOD as-115

sociated with the biomass burning (Fig. 6).116

We also use the Aerosol Robotic Network (AERONET) Version 3 (V3) Level 2 AEROSOL117

OPTICAL DEPTH and Level 1.5 AEROSOL INVERSIONS datasets for spectral AOD,118

column-mean single-scattering albedo, and asymmetry factor (Giles et al., 2019). The119

aerosol optical properties from the AERONET are only available under clear-sky con-120

ditions. The AEROSOL OPTICAL DEPTH dataset provides AOD at 7 wavelengths (340,121

380, 440, 500, 675, 870, and 1020 nm) at the SGP site and 8 wavelengths (340, 380, 440,122

500, 675, 870, 1020, and 1640 nm) at the TWP site. The AEROSOL INVERSIONS dataset123

provides aerosol single-scattering albedo and asymmetry factor at 4 wavelengths (440,124

675, 870, and 1020 nm).125

2.1 Comparison of AOD between the RL and AERONET126

In order to compare the AOD at the same wavelength, the AERONET AOD at 355127

nm is derived by AOD(λ) = cλ−α, where λ is the wavelength and constants c and α (i.e.,128

the Angstrom exponent) are determined by the two AERONET AODs at the two clos-129

est wavelengths (i.e., 340 and 380 nm). AERONET AODs with an Angstrom exponent130

within ±3 standard deviations of the mean are used, following the screening threshold131

of AERONET data quality control program (Smirnov et al., 2000). The RL and AERONET132

AODs are collocated in time for comparison. The RL temporal resolution is 10 minutes,133

therefore, all AERONET AODs within each 10-minute time period are averaged. Only134

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Figure 2. Comparison of aerosol optical depth (AOD) at 355 nm between the Raman lidar

(RL) and Aerosol Robotic Network (AERONET) for collocated times at the (a) Southern Great

Plains (SGP) site from August 2008 to August 2016 and the (b) Tropical Western Pacific (TWP)

site from December 2010 to January 2015. The colors represent the number of occurrences di-

vided by the total number of observations. The 1-to-1 line is shown in dashed black. The sample

size (N), the correlation coefficient (r), the mean relative difference of the RL AOD compared

to the AERONET AOD (MD), and the mean RL (AODRL) and AERONET (AODAERONET )

AODs are also given.

transparent RL profiles are considered in this comparison (i.e., the lidar beam does not135

fully attenuate). We also only consider AODs less than 1 as a quality control.136

Figure 2 shows the comparison of RL and AERONET AOD for all collocated times.137

The RL (AERONET) mean AOD is 0.19 (0.19) at the SGP site and 0.23 (0.24) at the138

TWP site. The relative differences are -3.9% and -0.7% at SGP and TWP, respectively.139

The RL and AERONET AODs were compared in Thorsen and Fu (2015a) and they found140

a better agreement at SGP (-0.3%). This better agreement is due to the time period con-141

sidered (i.e., August 2008 through July 2013), which is related to a cancellation of a pos-142

itive and negative AOD difference over time. The mean RL AOD is smaller than the AERONET143

AOD prior to 2011, but larger after 2011.144

Of all collocated data, 22% and 61% of the RL profiles detect clouds at the SGP145

and TWP sites, respectively. Therefore, there are times when the AERONET determines146

the sky to be clear but the RL profile detects clouds. In order to investigate the impact147

of clouds on the RL and AERONET comparison, we also compare the RL and AERONET148

AODs separately for cases when the RL detects no clouds and when the RL detects clouds149

(Fig. 3). The mean AODs from both AERONET and RL under cloudy conditions at SGP150

are higher than those under cloud-free conditions, by 15.4% and 20.0%, respectively, which151

does not show the role of cloud contamination but suggests that the AOD could be higher152

when clouds are present. At the TWP site, the percentage differences between cloudy153

and cloud-free conditions are smaller for both AERONET (4.8%) and the RL (0.8%) but154

indicate potential small cloud contamination in the AERONET AOD due to high thin155

cirrus clouds (Smirnov et al., 2000; Huang et al., 2011; Chew et al., 2011) that occur fre-156

quently in the tropics (e.g., Fu et al., 2007; Balmes & Fu, 2018; Balmes et al., 2019; Thorsen157

& Fu, 2015a).158

In estimating aerosol DREs in this study, we use the aerosol extinction coefficient159

profile from the RL at 355 nm, scaled to the AERONET AOD. Below we describe the160

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Figure 3. Mean aerosol optical depth (AOD) at 355 nm of Aerosol Robotic Network

(AERONET; blue) and Raman lidar (RL; orange) for all collocated times (AOD355nm), collo-

cated times when the RL detects no clouds (AOD355nm,RL no cloud) and collocated times when

the RL detects clouds (AOD355nm,RL cloud) at the (a) Southern Great Plains (SGP) site from

August 2008 to August 2016 and the (b) Tropical Western Pacific (TWP) site from December

2010 to January 2015.

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Figure 4. Spectral distribution of (a) aerosol optical depth (AOD), (b) aerosol column single-

scattering albedo and (c) aerosol column asymmetry factor at the Southern Great Plains (SGP)

site from August 2008 to August 2016. The means of AERONET observations are denoted by

red solid lines and the shading refers to the 25th percentile through the 75th percentile. The

AOD at wavelengths outside the AERONET spectral range is extrapolated using the power law

with the AERONET-derived Angstrom exponent, as shown by the dotted red line with shading

in (a). The single-scattering albedo and asymmetry factor outside the AERONET spectral range

are obtained by a combination of 84% urban aerosol type plus 16% sulfate droplets, as shown as

solid black lines in (b) and (c), which fit the observed means best.

spectral aerosol optical depth, single-scattering albedo and asymmetry factor in the en-161

tire solar spectrum, constrained by the observations, which are required by the radia-162

tive transfer model to estimate aerosol DREs (Michalsky et al., 2006; Magi et al., 2008).163

2.2 Spectral aerosol optical depth, single-scattering albedo and asym-164

metry factor165

The AOD at any wavelength within the AERONET spectral range (i.e., 340 nm166

to 1020 nm at SGP and 340 nm to 1640 nm at TWP) is obtained by the logarithmic in-167

terpolation using the AERONET-observed AODs at the two nearest wavelengths for each168

AERONET observation in time. At a wavelength outside the AERONET spectral range169

(i.e., less than 340 nm and greater than 1020 nm at SGP and less than 340 nm and greater170

than 1640 nm at TWP), the AOD is obtained from a power law with the Angstrom ex-171

ponent derived by considering the AERONET-observed AODs at all wavelengths. Fig-172

ures 4a and 5a show the spectral distributions of the mean AOD and its 25th to 75th173

percentile range at the SGP and TWP, respectively.174

In order to mitigate the wavelength limitation of measurements (Magi et al., 2007),175

we also leverage AERONET observations to specify the spectral dependence of single-176

scattering albedo and asymmetry factor required by the radiative transfer model. The177

single-scattering albedo and asymmetry factor at a wavelength within the AERONET178

spectral range between 440 and 1020 nm are obtained using the linear interpolation with179

the observations at the two closest wavelengths. The AERONET retrievals of single-scattering180

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Figure 5. The same as Fig. 4 except at the Tropical Western Pacific (TWP) site from Decem-

ber 2010 to January 2015, and that the single-scattering albedo and asymmetry factor outside

the AERONET spectral range are obtained by a combination of 87% water soluble aerosols and

13% soot aerosols.

albedo and asymmetry factor are not available as often as the AERONET AOD obser-181

vations. When the AERONET AOD is available but the single-scattering albedo and asym-182

metry factor are not, the single-scattering albedo and asymmetry factor observation clos-183

est in time are used. At SGP, 50% of the single-scattering albedo and asymmetry fac-184

tor observations are within ∼25 minutes of the AOD observations and 90% are within185

∼1.5 days. At TWP, 50% of the single-scattering albedo and asymmetry factor obser-186

vations are within 15 minutes of the AOD observations and 90% are within 1.5 hours.187

The observed mean single-scattering albedo and asymmetry factor between 440 and 1020188

nm are shown in Figures 4b&c and 5b&c at SGP and TWP, respectively. Since the ob-189

servations of single-scattering albedo and asymmetry factor are column-mean values, we190

neglect their vertical dependences in this study.191

We extend the single-scattering albedo and asymmetry factor at the wavelengths192

outside the observational range by using aerosol optical properties of common aerosol193

types (D’Almeida et al., 1991; Hess et al., 1998). They include the spectral extinction194

coefficient, single-scattering albedo, and asymmetry factor for various relative humidi-195

ties. Briefly, the spectral optical properties profiles for the common aerosol types are first196

derived for the given relative humidity profile (see 3.1) with the extinction scaled by the197

RL extinction vertical distribution. The column-mean single-scattering albedo and asym-198

metry factor are then derived. We identify the combination of two aerosol types to best199

fit the AERONET-observed spectral single-scattering albedo averaged for all data col-200

located with the RL observations. Five common aerosol types are considered, which are201

continental, urban, water soluble, soot, and sulfate droplets (D’Almeida et al., 1991; Hess202

et al., 1998). It is found that the best combinations of two aerosol types are 84% urban203

and 16% sulfate droplets at SGP and 87% water soluble and 13% soot at TWP. The per-204

centage represents the fraction of the AOD at 355 nm from the two aerosol types. Fur-205

ther details on the fitting methodology are provided in Appendix A. The single-scattering206

albedo and asymmetry factor at the wavelengths outside the observational wavelength207

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range are then obtained from the best-fit aerosol type combination, which are shown in208

Figs. 4b&c and 5b&c.209

Figure 6 shows the monthly climatology of the AOD, Angstrom exponent, single-210

scattering albedo, and asymmetry factor at 500 nm from observations over the SGP and211

TWP sites. The AOD monthly climatology is constructed from the AERONET AOD212

at 500 nm and the RL AOD scaled by a monthly mean scaling factor between the AERONET213

and RL to increase the sample size. The Angstrom exponent is derived considering all214

AERONET wavelengths. The single-scattering albedo and asymmetry factor are from215

AERONET observations, which are linearly interpolated to 500 nm. A large monthly216

mean AOD is seen over SGP in the summer with a value of about 0.2, but over TWP217

in the spring with a value of 0.2 to 0.35. The monthly mean Angstrom exponent at SGP218

is between about 1.1 and 1.5 with smaller values in the spring. The mean Angstrom ex-219

ponent at TWP is smaller than one from December to May but is ∼1.2 from June to Novem-220

ber, indicating smaller aerosol particle sizes related to biomass burning (see the discus-221

sion below). The single-scattering albedo at TWP has a large seasonal cycle, ranging from222

∼0.83 in June to ∼0.97 in January.223

The seasonal cycle for the dry season (April-November) at TWP is characterized224

by a range of single-scattering albedos and AOD due to the biomass burning. At the start225

of the biomass burning season (June), the AOD is smaller with smaller single-scattering226

albedos (i.e., higher absorption). The wildfires are closest to Darwin in June (Beringer227

et al., 1995; Carr et al., 2005; Haverd et al., 2013), which corresponds to a larger frac-228

tion of the smoke comprising of fresh smoke and consequently the lowest single-scattering229

albedos (Eck et al., 2003; Carr et al., 2005; Qin & Mitchell, 2009). However, the biomass230

burning is at the peak of area burned for Australia in October when the AOD is the largest,231

but the fires are more dispersed (Kanniah et al., 2010). Therefore, a portion of the biomass232

burning aerosols are aged, which results in higher single-scattering albedo (i.e., lower ab-233

sorption) compared to the fresh smoke’s lower single-scattering albedo.234

3 Radiative Transfer Model and Other Data Used235

The NASA Langley Fu-Liou radiative transfer model (Fu & Liou, 1992, 1993; Fu,236

1996; Fu et al., 1998; F. G. Rose & Charlock, 2002; F. Rose et al., 2006) is used in this237

study. This model employs the delta-four stream scheme for radiative transfer and the238

correlated k-distribution method for non-gray gaseous absorption for 18 SW bands and239

12 longwave bands. Herein we only consider the SW components since we are interested240

in the aerosol DRE and its LW component is often considerably smaller in magnitude241

for the aerosol types taken into account here (e.g., Reddy et al., 2005). The SW upwelling242

and downwelling fluxes at the TOA and surface from the model are used. The total down-243

welling surface SW flux (F ↓total) is further separated into the direct (F ↓direct) and diffuse244

(F ↓diffuse) components in the radiative closure experiment.245

The input for the radiative transfer model is all based on observations. In addi-246

tion to aerosol optical properties (Section 2), other observational data including atmo-247

spheric temperatures and composition concentrations and surface albedo for the radia-248

tive transfer model input are briefly described below. Also described are the SW sur-249

face downwelling direct (F ↓direct) and diffuse (F ↓diffuse) fluxes from the radiometers which250

are used in the radiative closure experiment.251

3.1 Atmospheric temperature and water vapor profiles and other gaseous252

concentrations253

Temperature and relative humidity profiles were from radiosondes, which were in-254

terpolated to match RL-FEX vertical and temporal resolution (i.e., 10 min/30 m) for255

the retrieval processing (Thorsen et al., 2015; Thorsen & Fu, 2015a). Therefore, tem-256

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Figure 6. Seasonal cycle of (a)&(b) AOD, (c)&(d) Angstrom exponent, (e)&(f) single-

scattering albedo, and (g)&(h) asymmetry factor over the (left) Southern Great Plains (SGP)

site from August 2008 to August 2016 and at the (right) Tropical Western Pacific (TWP) site

from December 2010 to January 2015. The AOD, single-scattering albedo and asymmetry fac-

tor are for 500 nm. The monthly means are denoted as dots and the shading refers to the 25th

percentile through the 75th percentile. Annual mean values are given in each plot.

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perature and water vapor profiles are available for all RL profiles. The microwave radiome-257

ter (MWR) provides integrated water vapor measurements every 20 seconds (Turner et258

al., 2007; Morris, 2019), which for the 2-minute interval centered on the RL time are used259

to scale water vapor profiles. Water vapor profiles have an impact on solar radiation not260

only through the absorption but also through aerosol single-scattering albedo and asym-261

metry factor that change with the relative humidity.262

The temperature and water vapor profiles are smoothed by using a running aver-263

age of ±300 m (i.e., average of 20 vertical bins). The smoothed temperature and water264

vapor profiles extend from the surface until 16 km at SGP and 18 km at TWP, which265

are the highest heights for the RL retrievals. For the radiative transfer model input, the266

smoothed temperature and water vapor profiles are extended to 1 hPa using the seasonal267

climatology profiles over the SGP and TWP sites as derived from the European Cen-268

tre for Medium-Range Weather Forecasts (ECMWF) reanalysis product, ERA-Interim269

(Dee et al., 2011), which are blended with the observed profile following Yang et al. (2008).270

The ERA-Interim seasonal climatology profiles of ozone are used. The concentra-271

tions of CO2, N2O, CH4, and CFCs are the corresponding annual global mean concen-272

trations from the National Oceanic and Atmospheric Administration (NOAA) Earth Sys-273

tem Research Laboratory (ESRL) observations.274

3.2 Surface albedo275

The aerosol DRE is affected by the surface albedo (Yu et al., 2006; Chand et al.,276

2009; Keil & Haywood, 2003; Podgorny & Ramanathan, 2001). We use the MODIS MCD43C1277

Version 6 Bidirectional Reflectance Distribution Function (BRDF) and Albedo Model278

Parameters dataset (Schaaf et al., 2002; Roesch et al., 2004), which has a resolution of279

0.05◦x0.05◦. The monthly mean surface albedo from 7 spectral bands are used, which280

are linearly interpolated to model wavelengths. The spectral surface albedo for model281

wavelengths outside the observational range use the value from the closest observational282

wavelength. The black-sky surface albedo is calculated considering the solar zenith an-283

gle dependence (Schaaf et al., 2002). The total albedo is obtained by combining the black-284

sky and white-sky albedos weighted with the diffuse fraction that is initially guessed from285

an empirical equation as a function of the solar zenith angle (Roesch et al., 2004). The286

radiative transfer model is then run to determine the diffuse fraction for the observed287

atmospheric conditions including aerosols. The spectral surface albedo is determined based288

on the recalculated diffuse fraction. The monthly mean climatology MODIS spectral sur-289

face albedos at a solar zenith angle of 60◦ are plotted in Figs. 7b-e.290

At the SGP site, we also consider the ARM Surface Spectral Albedo (SURFSPECALB)291

value-added product (McFarlane et al., 2011) to derive the spectral surface albedo in each292

SW band in the radiative transfer model (Fig. 7a). The SURFSPECALB product con-293

structs the spectral surface albedo by combining observations from the multifilter radiome-294

ters (MFRs) and the multifilter rotating shadowband radiometers (MFRSRs). We equally295

weight the 10-m and 25-m tower spectral surface albedo (Kassianov et al., 2014; Mlawer296

& Turner, 2016) and then group by the solar zenith angle to maintain the solar zenith297

angle dependence of the surface albedo. The SURFSPECALB product is not available298

at the TWP site.299

The ground-based observation of the spectral surface albedo should be more ac-300

curate than satellite observations but might be less representative for a region. We uti-301

lize the satellite surface albedo observations in deriving the aerosol DRE that would be302

more representative for a region, which also facilitates the comparison of the aerosol DRE303

between SGP and TWP. However, we also calculate the aerosol DRE using the ground-304

based albedo observations and compare the results with those using the satellite surface305

albedo observations. In general, the ground-based surface albedos are larger than those306

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from the satellite (Fig. 7). The dependence of surface albedo on the solar zenith angle307

was explicitly considered in deriving the aerosol DRE.308

3.3 Surface shortwave fluxes309

The ARM QCRAD value-added product provides data quality-controlled surface310

flux measurements at the ARM sites (Long & Shi, 2006, 2008). The QCRAD data prod-311

uct combines radiometer observations and a data quality analysis to determine the best-312

estimate of the surface fluxes. The F ↓total is obtained as the summation of the downward313

direct (F ↓direct) and diffuse (F ↓diffuse) fluxes at the horizontal surface. The simulated down-314

welling surface SW fluxes are compared with observed downwelling surface SW fluxes315

to test the radiative closure under clear-sky conditions.316

4 Radiative Closure Experiment317

We compare simulated surface solar broadband radiative fluxes including down-318

welling direct, diffuse and total fluxes with ground-based observations at the SGP and319

TWP sites to test and validate the radiative transfer model with the observed inputs.320

This radiative flux closure method has been extensively used to quantify the retrieval/observation/model321

uncertainty in derived radiative fluxes (e.g., Mace et al., 2006; Michalsky et al., 2006;322

Mather et al., 2007; Miller & Slingo, 2007; Comstock et al., 2013; Shupe et al., 2015; Mc-323

Comiskey & Ferrare, 2016). Only clear-sky conditions when collocated AERONET and324

RL observations are available and both detect no clouds are considered. The inputs for325

the radiative transfer model include the instantaneous atmospheric temperature and wa-326

ter vapor and aerosol optical properties and monthly mean spectral surface albedo, as327

described in Sections 2 and 3.328

To avoid possible cloud contamination or other instrument issues, we applied a thresh-329

old by comparing the model fluxes to the observation after doubling and halving the AOD.330

After doubling the AOD, if the modeled F ↓direct (F ↓diffuse) flux was larger (smaller) than331

the observed F ↓direct (F ↓diffuse) flux, the profile was no longer considered. After halving332

the AOD, if the modeled F ↓direct (F ↓diffuse) flux was smaller (larger) than the observed333

F ↓direct (F ↓diffuse) flux, the clear-sky profile was no longer considered. These thresholds334

exclude 20.3% and 7.0% of the clear-sky profiles at SGP and TWP sites, respectively.335

Figure 8 shows the comparison of simulated and observed downwelling surface SW fluxes336

at the SGP and TWP sites.337

At the SGP site, the mean differences in F ↓total, F↓direct and F ↓diffuse are 1.18, 1.24,338

and -0.05 W m−2, respectively, corresponding to relative differences of ∼0.2%, 0.3%, and339

-0.1%. The correlation coefficients between modeled fluxes and observations are greater340

than 0.99 for F ↓total and F ↓direct, and 0.98 for F ↓diffuse. Noting the measurement uncer-341

tainty of ±2% for the F ↓total and ±3% for the F ↓diffuse in the 95% confidence interval (Michalsky342

& Long, 2016), the simulated F ↓total and F ↓diffuse agree with observations within instru-343

ment uncertainty.344

At the TWP site, the mean differences in F ↓total, F↓direct and F ↓diffuse are 2.38, 2.19,345

and 0.19 W m−2, respectively, corresponding to relative differences of ∼0.5%, 0.5%, and346

0.2%. Similar to the SGP site, the differences are within the measurement uncertainty.347

The correlation coefficients between model and observations are larger than 0.99 for F ↓total348

and F ↓direct, and 0.98 for the F ↓diffuse.349

The overall excellent agreement between modeled and observed SW downwelling350

surface fluxes validates the radiative transfer model along with the observed inputs used351

in the simulations. We will discuss the impact of the uncertainties associated with the352

model inputs on the simulated surface downwelling SW fluxes in Section 6.353

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Figure 7. The spectral (a) surface (SFC) albedo from the ARM observation at the South-

ern Great Plains (SGP) site, (b)&(d) black-sky surface albedo and (c)&(e) white-sky surface

albedo from MODIS at the SGP and Tropical Western Pacific (TWP) sites, respectively, for a

solar zenith angle of 60◦. The lines represent the monthly mean climatology for December (black

solid), January (black dashed), February (black dotted), March (blue solid), April (blue dashed),

May (blue dotted), June (red solid), July (red dashed), August (red dotted), September (brown

solid), October (brown dashed), and November (brown dotted). The observed spectral surface

albedos are interpolated to model wavelengths.

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Figure 8. Downwelling surface shortwave (SW) fluxes for (a, d) the total downwelling surface

SW fluxes, F ↓total, (b, e) the direct downwelling surface SW fluxes, F ↓direct, and (d, f) the diffuse

downwelling surface SW fluxes, F ↓diffuse, from the model versus observations at the Southern

Great Plains (SGP) site (top row) and the Tropical Western Pacific (TWP) site (bottom row).

Clear-sky profiles of collocated Raman lidar (RL) and Aerosol Robotic Network (AERONET)

observations are considered from August 2008 to August 2016 for SGP site and from December

2010 to January 2015 for TWP site. The regression lines are shown as solid black lines. The

mean difference (diff) and correlation coefficient (r) between model and observation are given in

the top of each plot. Mean value of observations (obs) is shown in lower-right corner of each plot.

The sample size is given in the lower-right corner of each plot in the left column.

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5 Clear-sky aerosol direct radiative effect354

The instantaneous aerosol DRE at the top of the atmosphere (TOA) and surface355

(SFC) is defined as:356

357

DRE(TOA) = [F ↓(TOA)− F ↑(TOA)]aerosol − [F ↓(TOA)− F ↑(TOA)]no aerosol,358

(1)359

and360

361

DRE(SFC) = [F ↓(SFC)− F ↑(SFC)]aerosol − [F ↓(SFC)− F ↑(SFC)]no aerosol,362

(2)363

where F ↓ is the downward flux and F ↑ is the upward flux. The aerosol DRE is derived364

for a given atmospheric profile by running the radiative transfer model with and with-365

out aerosols. We consider the daily, monthly and annual mean aerosol DREs.366

The daily mean aerosol DRE, DRE, can be expressed as:367

368

DRE = 1tday

∫ sunsetsunrise

DRE(t)dt,369

(3)370

where DRE(t) is the instantaneous DRE at given time t and tday is the time in a day371

(i.e., 86400 seconds). To adequately capture the diurnal variation of the solar zenith an-372

gle and its effect on the DRE, a time step of 30 minutes is used (Yu et al., 2004, 2006).373

The difference between the daily insolation calculated using a time step of 30 minute and374

the reference value is only ∼0.25 W m−2 (less than 0.1%). The sunrise and sunset are375

determined with 1 second resolution for each day so that the first and last time steps could376

be slightly less than 30 minutes. The time step is centered on the hour mark (e.g., 0:00)377

and half hour mark (e.g., 0:30) to align with the observation’s time steps. The solar zenith378

angle is determined by considering the effects of refraction (Vignola et al., 2012). The379

monthly mean is the average of daily means in each month (e.g., all daily means in Jan-380

uary 2011). Monthly mean climatology is derived by averaging all monthly means for381

a given month in multiple years, and the annual mean climatology is the average of the382

twelve monthly-mean climatology. Because of large gaps in data availability at TWP site,383

we only derive the monthly and annual mean climatology there. At the TWP site, the384

monthly mean climatology is derived by averaging all available daily means for a given385

month regardless of the year.386

5.1 Daily- and monthly-mean time series of clear-sky aerosol DREs at387

SGP388

To determine the daily mean clear-sky aerosol DRE, the instantaneous clear-sky389

aerosol DRE is calculated at each 30-minute time step. However, observations are not390

always available at each time step for every day of the 8-year time period considered at391

SGP (e.g., during the cloudy periods). Therefore, we find the closest clear-sky observa-392

tions in time to fill in time steps without observations. We refer to this method as the393

fill-in method. Only collocated RL and AERONET observations under clear-sky con-394

ditions (see the clear-sky threshold in Section 4) are considered. The collocated RL/AERONET395

observation along with the corresponding atmospheric profile which is closest to the time396

step within one week can be used. If the closest collocated RL/AERONET observation397

is beyond 1 week but the closest clear-sky RL observation is within one week, we use the398

closest RL observations (i.e., RL AOD scaled by the monthly mean scale factor between399

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the RL AOD and AERONET AOD, and aerosol vertical distribution and correspond-400

ing atmospheric profile) and the AERONET monthly mean spectral AOD, single-scattering401

albedo and asymmetry factor. For a time step that is not within 1 week of the closest402

RL clear-sky observation, we use monthly mean climatology aerosol optical properties403

from the RL and AERONET with the closest radiosonde observations. Each time step’s404

AOD is scaled such that the monthly mean AOD from the fill-in method matches the405

monthly mean AOD from observations.406

At SGP, there are 75169 time steps of daylight with 30-minute resolution for the407

time period considered (i.e., August 2008 to August 2016). Of the 75169 time steps, 12.0%408

are directly collocated RL/AERONET observations, 74.2% are within 1 week of a col-409

located RL/AERONET observation, 11.1% are within 1 week of a RL only clear-sky ob-410

servation, and only 2.7% are run using monthly mean climatology aerosol properties. When411

the closest collocated RL/AERONET observation is utilized, 69.4% of time steps are within412

∼1 day and 90% are within ∼3 days. When the closest RL only clear-sky observation413

is utilized, 50% of time steps are within 1.3 hours and 90% are within ∼1 day.414

The time series of the daily mean clear-sky aerosol DRE at the TOA and the sur-415

face are shown in Fig. 9. At the TOA, the daily mean aerosol DRE at SGP is generally416

negative with the largest negative forcing of -14.82 W m−2. The positive TOA aerosol417

DRE is also observed, which occurs on 39 days of the total 2953 days (1.3%) with a max-418

imum value of 2.04 W m−2. The positive TOA aerosol DRE is related to the aerosols419

with stronger absorption (i.e., lower single-scattering albedo) for given surface albedo420

(J. M. Haywood & Shine, 1995; J. Haywood & Boucher, 2000; Yu et al., 2006). At the421

surface, the daily mean aerosol DRE is always negative, ranging from -0.59 to -32.16 W422

m−2. The time series of the monthly mean aerosol DRE for the TOA and the surface423

are also shown in Fig. 9, which ranges from -0.66 to -7.02 W m−2 at the TOA and from424

-1.88 to -14.60 W m−2 at the surface. The aerosol DRE is typically more negative in the425

summer and less negative in the winter, which largely follows the seasonal cycle of AOD426

and daytime fraction (i.e., larger AODs and daytime fractions in the summer). The sea-427

sonal cycle of the aerosol DRE will be explored further in the next section.428

The sensitivity of the DREs to a time step of 30 minutes was tested against a time429

step of 10 minutes. The annual mean differed by 0.01 W m−2 at the TOA and the sur-430

face, which is ∼0.2% of the aerosol DREs. The slightly larger in magnitude aerosol DRE431

for 30 minutes compared to 10 minutes is the result of less resolution at sunrise and sun-432

set, which overestimates the aerosol DRE. However, the difference is very small.433

5.2 Seasonal cycle and annual mean climatology of clear-sky aerosol DRE434

at SGP and TWP435

We examine the seasonal cycle of aerosol DRE by presenting its monthly mean cli-436

matology. The seasonal cycle of the aerosol DRE at SGP is shown in Figs. 10a&c. Over-437

all, the seasonal cycle in the aerosol DRE largely follows the AOD seasonal cycle (see438

Fig. 6), which is further enhanced by the solar insolation seasonal cycle. The strongest439

aerosol DREs of -4.81 W m−2 at the TOA and -10.77 W m−2 at the surface occur in the440

summer, which coincide with the largest AODs. The weakest aerosol DREs are in November-441

January with -1.28 W m−2 at the TOA and -2.77 W m−2 at the surface. The weakest442

aerosol DREs corresponds to smaller AODs and lower single-scattering albedos (Fig. 6).443

The lower single-scattering albedo could be related to nearby agriculture and transporta-444

tion or atmospheric flow patterns (Sheridan et al., 2001). The annual mean clear-sky aerosol445

DRE climatology is -3.00 and -6.85 W m−2 at the TOA and surface, respectively, over446

the SGP site.447

Sherman and McComiskey (2018) determined the clear-sky aerosol DRE for a south-448

east United States site with aerosol and surface properties similar to those at SGP. They449

found a mean TOA aerosol DRE of -1 to -2 W m−2 in the winter and -5 to -6 W m−2450

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Figure 9. Time series of the clear-sky aerosol direct radiative effect (DRE) at (a) the top

of the atmosphere (TOA) and (b) surface (SFC) at the Southern Great Plains (SGP) site from

August 2008 to August 2016. Results are shown for the daily mean aerosol DRE (black) and the

monthly mean aerosol DRE (red).

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Figure 10. Seasonal cycle of aerosol direct radiative effect (DRE) at the (top) top of the

atmosphere (TOA) and (bottom) surface (SFC) at the (left) Southern Great Plains (SGP) site

from August 2008 to August 2016 and at the (right) Tropical Western Pacific (TWP) site from

December 2010 to January 2015. The mean and median are denoted as dots and open circles,

respectively. Shading corresponds to the 25th percentile through the 75th percentile of all avail-

able daily-mean values for a given month. The annual mean climatology values are given in the

bottom left.

in the summer with a mean surface aerosol DRE of -2 to -3 W m−2 in the winter and451

-10 W m−2 in the summer. Their seasonal cycle and magnitude of the aerosol DREs are452

comparable to those presented here (Figs. 10a&c).453

We also calculated the aerosol DRE using the ARM ground-based spectral surface454

albedo. The annual mean clear-sky aerosol DRE is -2.75 and -6.64 W m−2 at the TOA455

and surface, respectively. The weaker aerosol DRE from the ground-based spectral sur-456

face albedo is due to the typically larger surface albedo from the ground-based obser-457

vation compared to MODIS.458

In contrast to SGP, data availability is sparser at TWP. Therefore, the fill-in method459

utilized at SGP cannot be applied to create a daily mean aerosol DRE for each day of460

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the time period considered. Instead, we employ a different method to derive the monthly461

mean climatology of the aerosol DRE (i.e., the aerosol DRE seasonal cycle). In this method,462

a daily mean aerosol DRE is obtained for each RL clear-sky observation by running the463

radiative transfer model with a diurnal cycle of solar zenith angles representative of the464

observation’s month from sunrise to sunset at each 30-minute time step with the same465

aerosol and atmospheric state properties. When the RL is collocated with the AERONET,466

the RL extinction profiles scaled to the AERONET AOD and the spectral AERONET467

AOD, single scattering albedo and asymmetry factor observations are used. When the468

AERONET is not available, the RL extinction profile scaled by a monthly mean clima-469

tology scale factor based on AERONET AOD as well as the monthly mean climatology470

spectral AOD, single-scattering albedo and asymmetry factor are used.471

The representative diurnal cycle of the solar zenith angle for a given month is de-472

termined by first calculating the daily insolation for each day in that month, which is473

then averaged to yield a monthly mean daily insolation. The day in the month with a474

daily insolation closest to the monthly mean daily insolation is found. The diurnal cy-475

cle of the solar zenith angle for this day is used with the solar insolation scaled such that476

it equals the monthly mean daily insolation. We refer to this method as the monthly di-477

urnal integration method.478

To demonstrate this method, consider the example of July 2011 at TWP. The monthly479

mean daily insolation is 333.80 W m−2 and the day with the closest daily insolation is480

July 17th (332.43 W m−2). The solar flux at the TOA normal to the beam on July 17th481

is 1317.47 W m−2, which is scaled to 1318.93 W m−2 by a ratio of 333.80/332.43. For482

each available clear-sky observation at TWP in July 2011, the daily mean aerosol DRE483

is obtained for July 17th with slightly modified daily insolation.484

Results from the monthly diurnal integration method and the fill-in method agree485

well at SGP in the derived monthly and annual mean climatology of aerosol DRE. For486

example, the annual mean climatology of the aerosol DRE agrees within 0.04 W m−2487

(1.5%) at the TOA and 0.14 W m−2 (2.0%) at the surface over SGP. The agreement be-488

tween the two methods provides confidence that the monthly diurnal integration method489

can be employed to derive the annual mean climatology of the aerosol DRE at TWP where490

sparser data availability prohibits use of the fill-in method.491

The seasonal cycle of the aerosol DRE at TWP is shown in Figs. 10b&d. The aerosol492

DRE is strongest in November at the TOA (-5.95 W m−2), and in October at the sur-493

face (-22.20 W m−2). The strongest aerosol DRE at the TOA corresponds to a larger494

monthly mean AOD with higher single-scattering albedo compared to other months with495

larger monthly mean AODs (Fig. 6) (Bouya et al., 2010). The strongest aerosol DRE496

at the surface in October corresponds to the largest monthly mean AOD. The weakest497

aerosol DRE of -0.96 (-4.16) W m−2 is in March (April) at the TOA (surface) corresponds498

to the months with the smallest monthly mean AODs (Fig. 6).499

Luhar et al. (2008) investigated the TOA aerosol DRE in northern Australia where500

the TWP site is located for 1 dry season (April-November 2004). They found a seasonal501

mean of -1.8 W m−2 with a peak of -4 W m−2 in November. The mean and peak val-502

ues of the aerosol DRE are comparable to those presented here (Fig. 10b).503

In addition to the aerosol DRE at the TOA and the surface, we also examine the504

aerosol effect on the radiative heating profile, which is the difference in the daily mean505

radiative heating rate profiles with and without considering the aerosols. Figure 11 shows506

the monthly climatology of aerosol radiative heating rate profile over SGP and TWP.507

It is very similar to the aerosol extinction profile (Fig.1), as expected. The heating is pre-508

dominantly near the surface at SGP. The heating extends higher into the atmosphere509

from May to September at SGP and from September to January at TWP.510

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Figure 11. Monthly climatology of the aerosol radiative heating rate profiles for each month

at the (top) Southern Great Plains (SGP) site from August 2008 to August 2016 and at the (bot-

tom) Tropical Western Pacific (TWP) site from December 2010 to January 2015. The mean is

denoted as a line and the shading refers to the 25th to 75th percentiles.

6 Uncertainty Estimates511

Understanding the uncertainty in estimated aerosol DRF is essential to quantify-512

ing changes in Earth’s radiation budget due to aerosols (e.g., McComiskey et al., 2008).513

Here we quantify the uncertainty in the estimated clear-sky aerosol DRE as well as the514

simulated downwelling SW fluxes used in the radiative closure experiment. Both mea-515

surement and methodology uncertainties are considered.516

6.1 Uncertainty in estimated aerosol DRE517

For the uncertainty estimates, monthly mean climatology of the radiative trans-518

fer model inputs including aerosol optical properties, atmospheric profiles and surface519

albedo, were used to calculate the monthly mean aerosol DREs. The perturbation due520

to measurement and methodology uncertainties was then applied to assess how the cal-521

culated monthly mean and annual mean aerosol DREs changed as a result to quantify522

the aerosol DRE uncertainty. For simplicity, the monthly diurnal integration method is523

applied to one profile for each of the 12 months. The obtained annual mean aerosol DREs524

agree with those presented in Section 5 within 0.05 W m−2 (1.6%) for SGP and 0.03 W525

m−2 (1.2%) for TWP at the TOA, and within 0.01 W m−2 (0.1%) for SGP and 0.20 W526

m−2 (2.0%) for TWP at the surface. Note that the method described here is to quan-527

tify the aerosol DRE uncertainty instead of the aerosol DRE itself.528

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6.1.1 Measurement uncertainty529

The monthly and annual mean aerosol DRE uncertainties due to measurement un-530

certainty from the AOD, single-scattering albedo, asymmetry factor and surface albedo531

are quantified. The annual-mean results are summarized in Table 1.532

For AOD, the uncertainty used is ±0.01 for AOD at 500 nm and the same relative533

uncertainty is applied to the AOD at other wavelengths. This uncertainty is similar to534

AERONET’s AOD uncertainty (Giles et al., 2019). However, this uncertainty in the AOD535

may be an overestimate since the mean difference in the AOD at 355 nm between RL536

and AERONET is 0.01 or less (Fig. 3). The annual mean aerosol DRE uncertainty due537

to AOD is about ±6-8% at the TOA and the surface.538

For the single-scattering albedo and asymmetry factor, the AERONET Aerosol In-539

version Uncertainty for Level 2 Products is used. The data product uses the assumed540

one sigma biases for AOD, radiometric calibration, solar irradiance spectrum and sur-541

face reflectance to get the inversion results for each set of measurement. For all avail-542

able profiles, we derive the mean uncertainty estimate for each observational wavelength543

(440, 675, 870, and 1020 nm). The uncertainty estimate is then added and subtracted544

from each monthly mean climatology single-scattering albedo and asymmetry factor to545

determine the change in the aerosol DRE as a result. For wavelengths less than or greater546

than the observational range, the mean uncertainty estimate considering all observational547

wavelengths is considered. The largest uncertainty in derived aerosol DREs at both SGP548

and TWP at the TOA is due to the single-scattering albedo measurement uncertainty,549

which is consistent with McComiskey et al. (2008). In particular, the relative uncertainty550

in the annual mean aerosol DRE at the TOA at TWP is ±20.7%.551

For the surface albedo, the uncertainty considered is a relative uncertainty of ±10%552

(Mira et al., 2015; Berg et al., 2020). This results in a relative uncertainty in the annual553

mean aerosol DRE of 7-10% at the TOA and 2-3% at the surface. The differences in aerosol554

DRE between using the ARM and MODIS surface albedo at the SGP are similar to those555

due to the surface albedo uncertainties (Table 1).556

The total aerosol DRE uncertainty due to measurement uncertainties (∆DREmeasurement)557

is determined by adding the aerosol DRE measurement uncertainty due to the AOD (∆DREAOD),558

single-scattering albedo (∆DREω), asymmetry factor (∆DREg), and surface albedo (∆DREαs)559

in quadrature:560

561

∆DREmeasurement =√

(∆DREAOD)2 + (∆DREω)2 + (∆DREg)2 + (∆DREαs)2.562

(4)563

The monthly aerosol DRE ±∆DREmeasurement is shown in Fig. 11. The relative564

uncertainty is about 10-30% for each month. At SGP, the largest absolute aerosol DRE565

measurement uncertainty is in June for both the TOA and the surface, and the small-566

est is in January (December) for the TOA (surface). At TWP, the largest absolute aerosol567

DRE uncertainty is in October and the smallest at TWP is in April for both the TOA568

and the surface.569

6.1.2 Methodology uncertainty570

Observed aerosol spectral optical properties from the AERONET do not cover the571

entire solar spectra. Here we quantify the uncertainty due to the methodology used to572

extend the spectral aerosol optical properties outside the AERONET spectral range. The573

results are summarized in Table 2.574

For the AOD, the Angstrom exponent derived from AERONET observations is used575

to extend the AOD outside the AERONET spectra. We use three combinations of stan-576

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Figure 12. Seasonal cycle of aerosol direct radiative effect (DRE) along with the uncertainty

estimate (vertical line) due to aerosol optical properties and surface albedo measurement un-

certainty at the (left) Southern Great Plains (SGP) and the (right) Tropical Western Pacific

(TWP) sites for the (top) top of the atmosphere (TOA) and the (bottom) surface (SFC). The

monthly mean aerosol DRE is the same as those in Fig. 10. The annual mean values (calculated

as the average of monthly means) are given in the bottom with the range due to measurement

uncertainty in the parentheses.

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Table 1. The uncertainty (W m−2) in annual mean aerosol direct radiative effect (DRE) at the

top of atmosphere (TOA) and surface (SFC) over the (left) Southern Great Plains (SGP) and

the (right) Tropical Western Pacific (TWP) sites due to measurement uncertainty of the aerosol

optical depth (AOD), column-mean single-scattering albedo (ω), column-mean asymmetry factor

(g), surface albedo (αs), and all of them together. The relative difference is in the parentheses.

TOA DRE uncertainty [W m−2] SGP TWP

AOD ±0.24 (∓8.3%) ±0.17 (∓6.0%)ω ±0.45 (∓15.2%) ±0.58 (∓20.7%)g ±0.17 (∓5.9%) ±0.15 (∓5.6%)αs ±0.22 (∓7.4%) ±0.28 (∓10.0%)total ±0.58 (∓19.4%) ±0.68 (∓24.1%)

SFC DRE uncertainty [W m−2] SGP TWP

AOD ±0.57 (∓8.3%) ±0.65 (∓6.1%)ω ±0.78 (∓11.3%) ±1.13 (∓10.7%)g ±0.18 (∓2.7%) ±0.17 (∓1.6%)αs ±0.18 (∓2.6%) ±0.21 (∓2.0%)total ±1.00 (∓14.6%) ±1.33 (∓12.9%)

dard aerosol types (Appendix A) that provide the spectral AOD for the entire solar spec-577

tra to determine the uncertainty due to this extension method. Overall, the error in the578

annual mean aerosol DRE is less than 1% at the TOA and 5% at the surface, which is579

all related to the wavelengths greater than the AERONET spectral interval since the lower580

wavelengths are well constrained as the smallest wavelength of observed AODs is 340 nm.581

We conclude that the Angstrom exponent derived from the AERONET spectral range582

can be used to extend the AOD outside the range well to determine the aerosol DRE.583

For the single-scattering albedo, a combination of two standard aerosol types, which584

is found to best fit the AERONET-observed spectral single-scattering albedo over each585

site, is used to obtain the spectral single-scattering albedo outside the AERONET spec-586

tral range (Section 2.2, Appendix A). Two additional combinations over each site are587

found, which show similar fits to the AERONET observations (Appendix A). The an-588

nual mean aerosol DRE uncertainty due to the extension methodology is determined by589

comparing the aerosol DRE using the first fit with the second and third fits by keeping590

the spectral single-scattering albedo in the AERONET spectral range the same. The un-591

certainty in the annual mean aerosol DRE is less than 6% at the TOA, which is primar-592

ily related to longer wavelengths, and smaller than 2% at the surface with similar con-593

tributions from shorter and longer wavelengths (Table 2).594

The asymmetry factor spectral distribution uncertainty is determined in the same595

manner as the single-scattering albedo by comparing the aerosol DRE using the fit 1 asym-596

metry factor to those using the fit 2 and fit 3 asymmetry factors. The uncertainty in the597

annual mean aerosol DRE is less than 9% at the TOA and smaller than 4% at the sur-598

face (Table 2). In contrast to the AOD and single-scattering albedo, the annual mean599

aerosol DRE uncertainty due to the asymmetry factor for wavelengths less than the AERONET600

spectral range exceeds the uncertainty for the wavelengths greater. An additional asym-601

metry factor observation in this spectral range (i.e., λ < 440 nm) would improve aerosol602

DRE estimates, especially at the TOA. By comparing Tables 2 and 1, it is interesting603

to note that errors in aerosol DRE due to the methodology are smaller than those due604

to measurement uncertainties, except for the asymmetry factor.605

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In this study, we explicitly consider the solar zenith angle dependence of the sur-606

face albedo. We quantify the effect on the aerosol DRE of neglecting the solar zenith an-607

gle dependence of the black-sky surface albedo. When using the black-sky surface albedo608

at the solar zenith angle corresponding to local solar noon (as provided by MODIS), the609

TOA aerosol DRE difference is -0.16 W m−2 (5.5%) and -0.12 W m−2 (4.3%) for SGP610

and TWP, respectively. At the surface, the aerosol DRE difference is -0.14 W m−2 (2.1%)611

and -0.10 W m−2 (1.0%) for SGP and TWP, respectively. By neglecting the solar zenith612

angle dependence of the surface albedo, the aerosol DRE is overestimated as the black-613

sky surface albedo increases with increasing solar zenith angle. This highlights the im-614

portance of considering the solar zenith angle dependence for the surface albedo in es-615

timating the aerosol DRE.616

6.2 Uncertainty in simulated downwelling SW fluxes617

We quantify the uncertainty in the simulated downwelling SW fluxes including F↓total,618

F↓direct and F↓diffuse that were used in the radiative closure experiment (Section 4). The619

motivation is to examine how much difference between simulated and observed down-620

welling SW fluxes can be explained by the radiative transfer model input uncertainty621

related to both measurement and methodology used. A similar procedure as in Section622

6.1 is used except that the simulation was performed for all instantaneous profiles used623

in the radiative closure experiment. The uncertainty in simulated downwelling SW fluxes624

due to measurement uncertainty of aerosol optical depth, single-scattering albedo, asym-625

metry factor, and surface albedo is summarized in Table 3.626

Similar to aerosol DRE, the largest error in the F↓total is due to the single-scattering627

albedo measurement uncertainty. Note that the effect of the AOD uncertainty on sim-628

ulated F↓direct and F↓diffuse have opposite signs, leading to a small difference in F↓total.629

The uncertainties in single-scattering albedo, asymmetry factor, and surface albedo af-630

fect the simulated F↓total only through the F↓diffuse.631

At SGP, the differences between simulated and observed downwelling SW fluxes632

(Section 4) are within 1σ of the uncertainty associated with the aerosol optical proper-633

ties and surface albedo observations for the F↓total (1.18 vs. 2.49 W m−2), F↓direct (1.24634

vs. 4.98 W m−2) and F↓diffuse (-0.05 vs. 3.98 W m−2). At TWP, the measurement un-635

certainty due to aerosol optical properties and surface albedo can also explain the dif-636

ferences between simulations and observations in F↓total (2.38 vs. 2.92 W m−2), F↓direct637

(2.19 vs. 4.29 W m−2) and F↓diffuse (0.19 vs. 3.50 W m−2). The uncertainty in F↓direct638

(Table 3) as compared with the difference between simulated and observed F↓direct in-639

dicates that the uncertainties in the AOD might be overestimated by a factor of 2.640

The uncertainty in the simulated downwelling SW fluxes due to the methodology641

extending the spectral distributions of aerosol optical properties is also quantified, which642

is generally less than ∼0.7 W m−2 at SGP site and less than ∼0.3 W m−2 at TWP site643

(not shown). This indicates that the uncertainty in specifying the aerosol optical prop-644

erties at wavelengths outside the observational spectral range is small, despite the range645

of values (Figs. A1-A2).646

7 Conclusions647

The clear-sky aerosol DREs were estimated at the ARM SGP site for 8 years and648

at the TWP site for 4 years. The NASA Langley Fu-Liou radiative transfer model was649

used with observed inputs including aerosol vertical extinction profile from the Raman650

lidar; spectral aerosol optical depth (AOD), single-scattering albedo and asymmetry fac-651

tor from AERONET; temperature and water vapor profiles from radiosondes; and sur-652

face shortwave spectral albedo from radiometers. A clear-sky radiative closure experi-653

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Table

2.

The

unce

rtain

ty(W

m−2)

inth

eannual

mea

naer

oso

ldir

ect

radia

tive

effec

t(D

RE

)due

toth

em

ethodolo

gy

that

exte

nds

the

spec

tral

dis

trib

uti

on

of

aer

oso

lopti

cal

dep

th(A

OD

),co

lum

n-m

ean

single

-sca

tter

ing

alb

edo

(ω),

and

colu

mn-m

ean

asy

mm

etry

fact

or

(g),

toth

ew

avel

ength

souts

ide

the

AE

RO

NE

Tsp

ec-

tral

range,

over

the

(lef

t)South

ern

Gre

at

Pla

ins

(SG

P)

and

the

(rig

ht)

Tro

pic

al

Wes

tern

Paci

fic

(TW

P)

site

sat

the

top

of

the

atm

osp

her

e(T

OA

)and

surf

ace

(SF

C).

The

annual

mea

naer

oso

lD

RE

unce

rtain

tyis

furt

her

separa

ted

into

those

for

wav

elen

gth

sle

ssth

an

and

gre

ate

rth

an

the

AE

RO

NE

Tsp

ectr

al

range.

The

rela

tive

diff

eren

ces

are

inth

epare

nth

eses

.T

he

unce

rtain

tyquanti

fica

tion

isbase

don

the

thre

eco

mbin

ati

ons

of

standard

aer

oso

lty

pes

(i.e

.,fit

1,

fit

2,

and

fit

3),

whic

hb

est

fit

the

AE

RO

NE

T-o

bse

rved

spec

tral

single

-sca

tter

ing

alb

edo. S

GP

TW

PT

OA

DR

Eu

nce

rtai

nty

[Wm−

2]

tota

lλ<

ob

s.λ>

ob

s.to

tal

λ<

ob

s.λ>

ob

s.

AODλ(fi

t1)

-0.0

1(0

.4%

)0.0

0(0

.0%

)-0

.01

(0.4

%)

-0.0

1(0

.4%

)0.0

0(0

.0%

)-0

.01

(0.5

%)

AODλ(fi

t2)

0.02

(-0.6

%)

0.0

0(0

.0%

)0.0

1(-

0.4

%)

-0.0

1(0

.5%

)0.0

0(0

.0%

)-0

.01

(0.4

%)

AODλ(fi

t3)

-0.0

3(1

.1%

)0.0

0(0

.0%

)-0

.03

(1.1

%)

-0.0

1(0

.5%

)0.0

0(0

.0%

)-0

.01

(0.4

%)

ωλ(fi

t2)

-0.1

8(5

.9%

)0.0

6(-

2.1

%)

-0.2

4(7

.9%

)0.0

7(-

2.4

%)

0.0

2(-

0.9

%)

0.0

4(-

1.6

%)

ωλ(fi

t3)

-0.0

8(2

.8%

)-0

.03

(0.9

%)

-0.0

6(2

.0%

)0.0

9(-

3.1

%)

0.0

2(-

0.8

%)

0.0

6(-

2.3

%)

gλ(fi

t2)

0.25

(-8.4

%)

0.1

9(-

6.2

%)

0.0

7(-

2.2

%)

-0.0

8(2

.9%

)-0

.08

(2.9

%)

0.0

0(0

.0%

)gλ(fi

t3)

0.01

(-0.5

%)

0.0

4(-

1.2

%)

-0.0

2(0

.7%

)-0

.09

(3.0

%)

-0.0

8(2

.9%

)0.0

0(0

.1%

)

SG

PT

WP

SF

CD

RE

un

cert

ainty

[Wm−

2]

tota

lλ<

ob

s.λ>

ob

s.to

tal

λ<

ob

s.λ>

ob

s.

AODλ(fi

t1)

0.09

(-1.3

%)

0.0

0(0

.0%

)0.0

9(-

1.2

%)

0.2

2(-

2.2

%)

0.0

0(0

.0%

)0.2

2(-

2.1

%)

AODλ(fi

t2)

-0.1

9(2

.8%

)0.0

0(0

.0%

)-0

.20

(2.9

%)

0.1

8(-

1.7

%)

0.0

0(0

.0%

)0.1

7(-

1.6

%)

AODλ(fi

t3)

0.29

(-4.2

%)

0.0

0(0

.0%

)0.2

9(-

4.2

%)

0.1

8(-

1.7

%)

0.0

0(0

.0%

)0.1

7(-

1.6

%)

ωλ(fi

t2)

0.06

(-0.9

%)

-0.1

5(2

.2%

)0.2

1(-

3.1

%)

-0.1

6(1

.6%

)-0

.10

(0.9

%)

-0.0

6(0

.6%

)ωλ(fi

t3)

0.14

(-2.0

%)

0.0

7(-

1.1

%)

0.0

6(-

0.9

%)

-0.1

8(1

.8%

)-0

.10

(0.9

%)

-0.0

9(0

.8%

)

gλ(fi

t2)

0.26

(-3.7

%)

0.1

9(-

2.8

%)

0.0

6(-

0.9

%)

-0.0

9(0

.9%

)-0

.09

(0.9

%)

0.0

0(0

.0%

)gλ(fi

t3)

0.02

(-0.3

%)

0.0

4(-

0.6

%)

-0.0

2(0

.3%

)-0

.09

(0.9

%)

-0.0

9(0

.9%

)0.0

0(0

.0%

)

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Table 3. The uncertainty (in W m−2) in simulated downwelling SW surface (SFC) fluxes

including the total and direct and diffuse components due to measurement uncertainty of the

aerosol optical depth (AOD), column-mean single-scattering albedo (ω), column-mean asymme-

try factor (g), and surface albedo (αs), and all of them together, over the (left) Southern Great

Plains (SGP) and the (right) Tropical Western Pacific (TWP) sites. The ±(∓) sign before the

simulated downwelling SW fluxes refers to a positive (negative) change corresponding to the

positive change in aerosol optical properties.

SGP TWP

F↓SFC,simulated uncertainty [W m−2] total direct diffuse total direct diffuse

±AOD ∓1.52 ∓4.98 ±3.46 ∓1.71 ∓4.29 ±2.58±ω ±1.86 - ±1.86 ±2.31 - ±2.31±g ±0.44 - ±0.44 ±0.35 - ±0.35±αs ±0.47 - ±0.47 ±0.37 - ±0.37total ±2.49 ±4.98 ±3.98 ±2.92 ±4.29 ±3.50

ment was performed for clear-sky conditions by comparing simulated F ↓total, F↓direct, and654

F ↓diffuse with observations.655

At SGP, the mean differences between simulated and observed SW downwelling sur-656

face fluxes were 1.2 W m−2 (0.2%) for F ↓total, 1.2 W m−2 (0.3%) for F ↓direct, and -0.1 W657

m−2 (-0.1%) for F ↓diffuse. At TWP, the mean differences between simulated and observed658

SW downwelling surface fluxes were 2.4 W m−2 (0.5%) for F ↓total, 2.2 W m−2 (0.5%) for659

F ↓direct, and 0.2 W m−2 (0.2%) for F ↓diffuse. The correlation coefficients between the sim-660

ulated and observed fluxes were greater than 0.99 for F ↓total and F ↓direct, and ∼0.98 for661

the F ↓diffuse.662

At SGP, the daily mean aerosol DRE varied from 2.04 to -14.82 W m−2 at the TOA663

and from -0.59 to -32.16 W m−2 at the surface. The monthly mean aerosol DRE ranged664

from -0.66 to -7.02 W m−2 at the TOA and -1.88 to -14.60 W m−2 at the surface. The665

annual mean aerosol DRE was -3.00 W m−2 at the TOA and -6.85 W m−2 at the sur-666

face. The seasonal cycle of the aerosol DRE is influenced by the seasonal cycle of AOD667

as well as by the solar insolation seasonal cycle. The strongest aerosol DREs are in the668

summer (June-August) with -4.81 W m−2 at the TOA and -10.77 W m−2 at the sur-669

face, when the largest AODs are observed. The weakest aerosol DREs are in late fall into670

winter (November-January) with -1.28 W m−2 at the TOA and -2.77 W m−2 at the sur-671

face. The weakest aerosol DREs coincide with smaller AODs and lower single-scattering672

albedos, which both weaken the aerosol DRE. The lower single-scattering albedos could673

be due to the nearby agriculture and transportation or atmospheric flow patterns that674

transport more absorbing aerosols over the SGP site.675

At TWP, we did not derive the time series of the daily aerosol DRE due to sparse676

data availability. Instead we quantified the annual mean and seasonal cycle of the aerosol677

DRE there. The annual mean aerosol DRE was -2.82 W m−2 at the TOA and -10.34 W678

m−2 at the surface. The seasonal cycle of the aerosol DRE at TWP is influenced by the679

wet and dry season. The marine influences during the wet season lead to lower AODs680

and higher single-scattering albedos, as indicated by smaller aerosol DREs during December-681

April. The dry season is characterized by the biomass burning, which corresponds to larger682

AODs but also a range of lower single-scattering albedos depending on the intensity and683

the proximity of the wildfires. The aerosol DRE is strongest in November at the TOA684

(-5.95 W m−2) and in October at the surface (-22.20 W m−2). The strongest aerosol DRE685

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at TOA coincides with larger AODs and weakened absorption (i.e., higher single-scattering686

albedo) compared to other months with large AODs. At the surface, the strongest aerosol687

DRE corresponds to the largest monthly mean AOD when Australia’s biomass burning688

season is at its peak. The weakest aerosol DRE at the TOA (surface) of -0.96 (-4.16) W689

m−2 is in March (April) when the smallest AODs are observed.690

The uncertainty of estimated aerosol DREs is quantified. By considering the un-691

certainty in aerosol optical properties measurements as well as surface albedo measure-692

ments, the derived annual mean TOA aerosol DRE ranges from -2.42 to -3.58 (-2.14 to693

-3.50) W m−2 at SGP (TWP) while the annual mean aerosol DRE at the surface ranges694

from -5.85 to -7.84 (-9.00 to -11.67) W m−2 at SGP (TWP). The uncertainty of estimated695

aerosol DREs due to the methodology extending the spectral distribution of aerosol op-696

tical properties beyond the observed spectral range is also determined, which is 10% or697

less. The uncertainty in simulated downwelling surface fluxes is also quantified. It is shown698

that the difference between simulated and observed fluxes are within the 68% confidence699

interval (i.e., 1σ) of the uncertainty related to the observations of aerosol optical depth,700

single-scattering albedo, asymmetry factor, and surface albedo, for F ↓total, F↓direct, and701

F ↓diffuse at SGP and TWP.702

This study shows the regional aerosol direct radiative effect under clear-sky con-703

ditions at two locations by combining ground-based observations and RT modeling. The704

different aerosol properties observed at both sites led to absolute and seasonal contrasts705

in the clear-sky aerosol direct radiative effect. The range of the clear-sky aerosol direct706

radiative effect highlights the need to understand the global aerosol direct radiative ef-707

fect under a range of aerosol conditions as well as under cloudy-skies.708

Acknowledgments709

This study is supported by the U.S. Department of Energy Office of Science (BER) un-710

der Grant DE-SC0020135. The Raman lidar (RL-FEX), surface flux (QCRAD), surface711

spectral albedo (SURFSPECALB), radiosonde (sondewnpn) and microwave radiome-712

ter (mwrlos) data products can be downloaded from the ARM data archive (www.arm.gov/data).713

The AERONET datasets can be downloaded from the AERONET site (aeronet.gsfc.nasa.gov/new web/data.html).714

The MODIS spectral surface albedo data can be downloaded from NASA’s EARTHDATA715

website (earthdata.nasa.gov). The annual global mean trace gas concentrations can be716

downloaded from NOAA ESRL’s website717

(www.esrl.noaa.gov/gmd/aggi/aggi.html). The reanalysis data product (ERA-Interim)718

can be downloaded from the the ECMWF’s website (www.ecmwf.int/en/forecasts/datasets/reanalysis-719

datasets/era-interim). Solar zenith angle and Earth-Sun distance calculations were per-720

formed using code from GitHub721

(www.github.com/klapo/solargeo/blob/master/solargeo/sunae.pyx). We thank L. D. Rhi-722

imaki for useful discussions on surface radiometers observations. We also thank R. Wa-723

gener, L. Gregory and L. L. Ma for clarifying information on the AERONET data. X.724

Wu and K. A. Balmes are co-first authors of this paper.725

Appendix A Fitting observations to model single-scattering albedo and726

asymmetry factor727

For the spectral distribution of single-scattering albedo and asymmetry factor for728

model wavelengths outside the observational range (i.e., below 467.6 nm and above 960.9729

nm), a combination of two common aerosol types with known spectral aerosol optical730

properties is determined to best fit the observations. Five common aerosol types (D’Almeida731

et al., 1991; Hess et al., 1998) are utilized, which are continental, urban, water soluble,732

soot, and sulfate droplet aerosols. A combination of two aerosol types could be, e.g., con-733

tinental and soot.734

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The vertical profile of aerosol extinction from two aerosol types can be considered735

as:736

737

βλ(z) = βλ,1(z) + βλ,2(z),738

(A1)739

where βλ(z) is the total aerosol extinction profile at wavelength λ, βλ,1(z) are the aerosol740

extinction profile for aerosol types 1 and 2, respectively. The volume extinction coeffi-741

cient (βλ) is a product of the aerosol number concentration (N) and the extinction cross742

section (σ) (i.e., βλ=Nσ). If the fraction of the total number concentration for aerosol743

type 1 is f , the vertical profile of aerosol extinction due to two aerosol types can then744

be written as:745

746

βλ(z) = fN(z)σλ,1(z) + (1− f)N(z)σλ,2(z),747

(A2)748

where N(z) is the vertical profile of aerosol number concentration, and σλ,1(z) and σλ,2(z)749

are the vertical profiles of extinction cross section for aerosol types 1 and type 2, respec-750

tively.751

The single-scattering albedo profile, ωλ(z), is752

753

ωλ(z) =fN(z)σλ,1(z)ωλ,1(z)+(1−f)N(z)σλ,2(z)ωλ,2(z)

βλ(z) ,754

(A3)755

where ωλ,1(z) and ωλ,2(z) are the single-scattering albedo vertical profiles of aerosol types756

1 and 2, respectively. The column-mean single-scattering albedo, ωλ, which is what the757

AERONET observes, is758

759

ωλ =

∑fN(z)σλ,1(z)ωλ,1(z)∆z+(1−f)N(z)σλ,2(z)ωλ,2(z)∆z∑

βλ(z)∆z,760

(A4)761

where ∆z is the vertical interval.762

The aerosol vertical extinction profile from the RL, the column-mean single-scattering763

albedos at 440, 675, 870 and 1020 nm from AERONET, and relative humidity from ra-764

diosondes for all collocated RL and AERONET profiles are employed. The 10 combi-765

nations of 2 aerosol types from the 5 common aerosol types are used for the vertical pro-766

files of single-scattering albedo (i.e., ωλ,1 and ωλ,2) and extinction cross section (i.e., σλ,1767

and σλ,2) that are a function of relative humidity. The N(z) is constrained by the RL768

aerosol vertical extinction profile. The fraction of aerosol type 1, f , for each combina-769

tion is determined by the following. The spectral mean squared error in single-scattering770

albedo, weighted by the AOD at each wavelength is εi for a given profile, i, which is ex-771

pressed as:772

773

εi =

∑λ

(ωi,λ(f)−ωi,λ(AERONET ))2AODi,λ∑λAODi,λ

,774

(A5)775

where ωi,λ(f) is the column single-scattering albedo at wavelength λ for a given f , and776

ωi,λ(AERONET ) is the observed column single-scattering albedo. The εw, the average777

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of εi weighted by the RL AOD, AODi,355nm, is obtained by considering all profiles such778

that:779

780

εw =

∑iεiAODi,355nm∑iAODi,355nm

.781

(A6)782

The f is determined by minimizing εw for each of the 10 combinations.783

For SGP, the top aerosol type combination is the urban and sulfate droplets aerosols784

(f=0.99). For TWP, it is water soluble and soot (f=0.36). The top aerosol type com-785

bination can also be understood in terms of the percentage contributions to AOD from786

aerosol types 1 and 2, which can be calculated using Eqs. A1 and A2. We first obtain787

the percentage of AOD from aerosol type 1, e.g., for each profile, then the averaged per-788

centage of AOD for all profiles weighted by the RL AOD. In terms of the AOD contri-789

bution, the top aerosol type combinations at SGP is 84% urban and 16% sulfate droplets790

and at TWP is 87% water soluble and 13% soot. The best fits are applied to extend the791

spectral distribution of single-scattering albedo outside the observational spectral range792

for the radiative transfer model simulations.793

The asymmetry factor outside the observational spectral range is obtained from:794

795

gλ(z) =fN(z)σλ,1(z)ωλ,1(z)gλ,1(z)+(1−f)N(z)σλ,2(z)ωλ,2(z)gλ,2(z)

fN(z)σλ,1(z)ωλ,1(z)+(1−f)N(z)σλ,2(z)ωλ,2(z) ,796

(A7)797

where gλ(z) is the vertical profile of asymmetry factor at wavelength λ and gλ,1(z) and798

gλ,2(z) are the vertical profiles of asymmetry factor for aerosol types 1 and 2, respectively.799

We also consider the second and third best combinations at SGP and TWP to de-800

termine a range of possibility for the spectral distribution of single-scattering albedo and801

asymmetry factor outside the observational range. At SGP, the second and third aerosol802

type combinations are 89% sulfate droplets and 11% soot, and 97% water soluble and803

3% soot, respectively. At TWP, they are 88% continental and 12% soot, and 91% ur-804

ban and 9% soot. The second and third combinations are utilized for determining method-805

ology uncertainty for the aerosol DRE and the radiative closure experiment (Section 6).806

Figures A1 and A2 show the spectral distribution of the AOD, column-mean single-scattering807

albedo and column-mean asymmetry factor for the top three best fits at SGP and TWP.808

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X. Wu, K. A. Balmes , Q. Fu Article · 2021. 1. 25. · Corresponding author: K. A. Balmes, [email protected] {1{Accepted Article This article has been accepted for publication and undergone