ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-13791-2016The spectral signature of cloud spatial structure in shortwave irradianceSongShiSchmidtK. Sebastiansebastian.schmidt@lasp.colorado.eduhttps://orcid.org/0000-0003-3899-228XPilewskiePeterKingMichael D.https://orcid.org/0000-0003-2645-7298HeidingerAndrew K.WaltherAndiIwabuchiHironobuhttps://orcid.org/0000-0002-9311-8598WindGalaCoddingtonOdele M.https://orcid.org/0000-0002-4338-7028Department of Atmospheric and Oceanic Sciences, University of Colorado,
Boulder, CO, USALaboratory for Atmospheric and Space Physics, University of Colorado,
Boulder, CO, USANOAA Center for Satellite Applications and Research, Madison, WI, USACenter for Atmospheric and Oceanic Studies, Tohoku University, Sendai, JapanSpace Systems and Applications, INC., Greenbelt, MD, USAK. Sebastian Schmidt (sebastian.schmidt@lasp.colorado.edu)8November20161621137911380611November201514March20169September201628September2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/16/13791/2016/acp-16-13791-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/13791/2016/acp-16-13791-2016.pdf
In this paper, we used cloud imagery from a NASA field experiment in
conjunction with three-dimensional radiative transfer calculations to show
that cloud spatial structure manifests itself as a spectral signature in
shortwave irradiance fields – specifically in transmittance and net
horizontal photon transport in the visible and near-ultraviolet wavelength
range. We found a robust correlation between the magnitude of net horizontal
photon transport (H) and its spectral dependence (slope), which is
scale-invariant and holds for the entire pixel population of a domain. This
was surprising at first given the large degree of spatial inhomogeneity. We
prove that the underlying physical mechanism for this phenomenon is molecular
scattering in conjunction with cloud spatial structure. On this basis, we
developed a simple parameterization through a single parameter ε,
which quantifies the characteristic spectral signature of spatial
inhomogeneities. In the case we studied, neglecting net horizontal photon
transport leads to a local transmittance bias of ±12–19 %, even at
the relatively coarse spatial resolution of 20 km. Since three-dimensional
effects depend on the spatial context of a given pixel in a nontrivial way,
the spectral dimension of this problem may emerge as the starting point for
future bias corrections.
Introduction
Determining cloud radiative effects for scenes with a high degree of spatial
complexity remains one of the most persistent problems in atmospheric
radiation, especially at the surface where satellite observations can only
be used indirectly to infer energy budget terms. In the shortwave (solar)
spectral range, it is especially challenging to derive consistent albedo,
absorption, and transmittance from spaceborne, aircraft, and ground-based
observations for inhomogeneous cloud conditions (Kato et al., 2013; Ham et
al., 2014). This problem is closely related to the long-debated discrepancy
between observed and modeled cloud absorption (Stephens et al., 1990) since
energy conservation for a three-dimensional (3-D) atmosphere (Marshak and
Davis, 2005, Eq. 12.13),
R+T= 1-(A+H),
connects reflectance R, transmittance T, and absorptance A of a layer.
The term H accounts for lateral net radiative flux from pixel to pixel (which
we will call net horizontal photon transport). Out of necessity, most
algorithms for deriving R, T, and A from passive imagery inherently presume
isolated pixels by relying on 1-D radiative transfer
(independent pixel approximation), which does not reproduce H. Net horizontal
photon transport has therefore long been a common explanation not only for
inconsistencies between measured and calculated broadband cloud absorption
(Fritz and MacDonald, 1951; Ackerman and Cox, 1981) but also for remote
sensing artifacts (Platnick, 2001).
Observational evidence for this explanation emerged with the availability of
spectrally resolved aircraft measurements of shortwave irradiance (Solar
Spectral Flux Radiometer, SSFR: Pilewskie et al., 2003). Schmidt et
al. (2010) derived apparent absorption, the sum of A and H, from
irradiance measurements aboard the NASA ER-2 and DC-8 aircraft that flew
along a collocated path above and below a heterogeneous anvil cloud during
the Tropical Composition, Cloud and Climate Coupling Experiment (TC4)
(Toon et al., 2010). The results of this study showed that, in absolute
terms, H at visible wavelengths (where cloud and gas absorption are
negligible) can attain a similar magnitude as the absorbed irradiance A at
near-infrared wavelengths. Horizontal photon transport thus has the potential
to mimic substantially enhanced absorption. Three-dimensional
calculations confirmed the measurements, and radiative closure was achieved
within measurement and model uncertainties without invoking proposed enhanced
gas absorption (Arking, 1999) or
big cloud droplets (Wiscombe et al., 1984). The results also suggested that
the overestimation of absorption would persist even when averaging over long
distances as proposed by Titov (1998). This is simply because radiation
flight legs are often preferentially targeted at cloudy regions
(H > 0) and do not adequately
sample clear-sky areas where photons are depleted (H < 0), which is interpreted as apparent emission in
measurements.
Perhaps the most significant finding by Schmidt et al. (2010) was the
distinct spectral shape of H from the near-ultraviolet well into the visible
wavelength range, leading to the notion of “colored” net horizontal photon
transport (Schmidt et al., 2014). A previous study addressing horizontal
photon transport from an energy budget point of view (Kassianov and Kogan,
2002) had focused on the wavelength range of 0.7–2.7 µm, specifically
to avoid molecular scattering at shorter wavelengths. Strategies for
mitigating the overestimation of cloud absorption (Ackerman and Cox, 1981;
Marshak et al., 1999) require that H be more or less constant in the visible
wavelength range (Welch et al., 1980), and so the discovery of the spectral
dependence of H suggested that they should be applied with caution. For example, Marshak et al. (1999) in their conditional sampling technique
required that H= 0 for at least two different wavelengths. Kindel et al. (2011)
applied such a modified scheme for boundary layer clouds.
Further analysis of the relationship between cloud structure and its
spectral signature, presented here, revealed a surprisingly robust
correlation between the magnitude of H and its spectral slope, dH/ dλ. In the course of this
paper, we provide evidence for molecular scattering as the physical
mechanism behind this correlation, and develop a simple parameterization
based on this knowledge. We also examined at which spatial aggregation scale
H can be ignored and whether the correlation between H and
dH/ dλ is scale-invariant. Finally, we considered the ramifications of
our findings on the shortwave surface energy budget.
Following this introduction, we provide definitions of relevant terms and
explain how H relates to top-of-atmosphere (TOA) and surface cloud radiative
effects (CREs). We then discuss the data and model calculations that lay the
basis for our study (Sects. 3 and 4). In Sect. 5, we discuss the
correlations between H and dH/ dλ, followed by the underlying physical
mechanism and parameterization presented in Sect. 6. The discovered
relationship is then examined as a function of spatial scale (Sect. 7) and
interpreted in terms of the surface CREs (Sect. 8). In the conclusions, we
discuss the significance of our findings and propose multispectral or
spectral techniques for deriving first-order correction factors in CRE
estimates from space, aircraft, and from the surface that may render 3-D
calculations unnecessary.
Net horizontal photon transport and cloud radiative effect
The instantaneous radiative effect of any atmospheric constituent is the
difference of net irradiance (flux density) in its presence (all-sky) and
absence (clear-sky). For clouds, we define
CREλ=Fλ↓-Fλ↑all-skyFλ↓,TOA-Fλ↓-Fλ↑clear-skyFλ↓,TOA×100%,
where Fλ↓ and Fλ↑ are
downwelling and upwelling irradiance, and their difference is net irradiance.
For this paper, we normalize the absolute radiative effect by the TOA downwelling
irradiance Fλ↓,TOA, and consider
the relative radiative effect as percentage of the incident irradiance. We use
spectrally resolved rather than broadband quantities, indicated by subscript
λ.
The TOA shortwave CRE is always negative (cooling effect) because the reflected
irradiance Fλ↑,TOA in the presence of clouds is
larger than for clear-sky conditions. The surface shortwave CRE is also
negative because clouds decrease the transmitted irradiance Fλ↓,SUR, at least for homogeneous conditions; broken clouds
can locally increase surface insolation. In contrast to the shortwave CRE at
TOA and at the surface, clouds have a warming effect on the layer in
which they reside. For homogeneous conditions (H= 0), this can be quantified
in terms of the layer property absorptance
Aλ=Fλ↓,top-Fλ↑,topFλ↓,top-Fλ↓,base-Fλ↑,baseFλ↓,top×100%,
for a cloud located between htop and hbase with the same
normalization as used above for the relative CRE. It can be determined from
aircraft measurements by collocated legs above and below the cloud (Schmidt
et al., 2010). The warming within the layer arises from absorption (A > 0) primarily in
the near-infrared wavelength range (1 µm < λ < 4 µm). Similarly, layer transmittance
and reflectance are defined as
Tλ=Fλ↓,baseFλ↓,top×100%andRλ=Fλ↑,top-Fλ↑,baseFλ↓,top×100%.
Related to layer reflectance is the albedo αλ=Fλ↑/Fλ↓. The sum of layer absorptance, transmittance, and
reflectance defined in this way is 100 %, and thus satisfies energy
conservation for horizontally homogeneous layers. For individual pixel
sub-volumes within an inhomogeneous layer (voxels), Aλ in Eq. ()
can be replaced with Aλ+Hλ≡Vλ, where Vλ stands for the vertical flux
divergence (the net irradiance difference above and below a layer). In this
way, energy conservation including horizontal transport (Eq. 1) is
retained.
The difference of the CRE at TOA and at the surface from Eq. () can be
related to Eq. () as follows:
CRETOA-CREsurface=Fλnet, cloud-Fλnet, clearTOAFλ↓,TOA-Fλnet, cloud-Fλnet, clearsurfaceFλ↓,TOA×100%=Fλnet, TOA-Fλnet, surfacecloudFλ↓,TOA-Fλnet, TOA-Fλnet, surfaceclearFλ↓,TOA×100%.
The first term inside the brackets of Eq. () is identical to Aλ
from Eq. () if the boundaries of the layer htop and hbase are
extended to the TOA and surface, respectively. We denote this
by A^λ and distinguish full-column properties using a
caret (A^, H^, R^, T^) from the layer
properties that bracket only the cloud itself (A, H, R, T). The second term in
Eq. () stems from clear-sky absorption by atmospheric constituents
other than clouds (gases and aerosols). Equation () can then be rewritten as
A^λ=CRETOA-CREsurface+Fλnet, TOA-Fλnet, surfaceclearFλ↓,TOA×100%,
which simply means that the total atmospheric column absorption comprises
contributions from the cloud itself as well as from clear-sky absorption. In
the presence of horizontal inhomogeneities, the left and right side of Eq. ()
may be inconsistent unless A^λ is replaced with
V^λ=A^λ+H^λ as
above.
Presented in this way, the central role of absorptance and horizontal
transport in linking the net irradiances above and below a cloud (Eq. ),
as well as the TOA and surface CRE (Eq. ), becomes clear. While the
global TOA CRE can directly be derived from reflected radiances (Loeb et
al., 2005), for example from the Clouds and the Earth's Radiant Energy
System (CERES) on the Aqua and Terra satellites (Wielicki et al., 1996), the
derivation of the surface CRE also requires the knowledge of atmospheric
absorptance or transmittance. In the case of CERES, the required cloud
properties are obtained from retrievals of the accompanying imager, the
Moderate Resolution Imaging Spectroradiometer (MODIS) (Minnis et al., 2011).
As stated in the previous section, this is accomplished through lookup
tables which are based on 1-D calculations and therefore do not provide H.
Recognizing the crucial significance of horizontal photon transport for
obtaining an accurate surface CRE, Barker et al. (2012) and Illingworth et
al. (2015) described the ambitious goal of using 3-D radiative transport
operationally in the European radiative budget experiment Earth Clouds,
Aerosols and Radiation Explorer (EarthCARE). They tested their algorithm
with A-Train data. As a metric for 3-D effects, they employed the commonly
used difference between 3-D and IPA calculations (e.g., Scheirer and Macke,
2003). In a similar manner, Ham et al. (2014) calculated the effect of
horizontal photon transport on cloud absorption, transmission, and reflected
radiance. They found these three quantities to be correlated when
stratifying their results by cloud type after spatial aggregation to at
least 5 km.
Since the studies cited above pertained to EarthCARE and CERES, they only
considered broadband effects. This does not allow the separation
of Aλ and Hλ by means of their distinct spectral
characteristics. Our approach, first presented by Schmidt et al. (2014),
bridges this gap. In this paper, we focus exclusively on the
near-ultraviolet and visible wavelength range, and explore the spectral
fingerprint from cloud inhomogeneities in conjunction with molecular
scattering in Hλ, which also imprints itself on reflected
radiances (Song, 2016; Song et al., 2016). We chose not to include aerosols
in either study, primarily to isolate the spectral signature of
heterogeneous clouds before considering the more general case of clouds and
aerosols in combination.
Cloud optical thickness from MAS along an ER-2 leg from 17
July 2007 (length: 192 km, swath: 17.5 km), re-gridded to a horizontal
resolution of 500 mm. The red dashed line indicates the ER-2 flight track in
the center of the MAS swath. Results of net horizontal photon transport for
the eight highlighted pixels are shown in Table 1 and Fig. 3a.
Cloud data
Our study builds upon the results by Schmidt et al. (2010), and therefore
uses the same cloud case, a tropical convective core with anvil outflow,
observed during the TC4 experiment on 17 July 2007 (from 15:19 to 15:35 UTC) by the NASA ER-2 aircraft about 300 km south of Panama. Two
realizations of the observed cloud field were used as input to 3-D radiative
transfer calculations, one based on airborne imagery only (as in the earlier
study, Sect. 3.1), and one based on merged airborne and geostationary
imagery (Sect. 3.2) to study large-scale effects.
Sub-scene from ER-2 passive and active remote sensors
Level-2 cloud retrievals of the Moderate Resolution Imaging Spectrometer (MODIS)
Airborne Simulator (MAS: King et al., 1996, 2010) were
combined with reflectivity profiles from the Cloud Radar System (CRS: Li et
al., 2004) as described in detail by Schmidt et al. (2010). The primary
information originates from MAS optical thickness, thermodynamic phase,
effective radius, and cloud top height retrievals for each pixel (x,y)
within the imager's swath (roughly 20 km for a cloud top height of 10 km).
The imagery-derived information was extended into the vertical dimension z
by simple approximations as follows.
The effective radius from MAS, re(x,y), was used throughout the vertical
dimension z although only representative of the topmost layer. Since the
study is limited to the near-ultraviolet and visible wavelength range where
cloud absorption is negligible, this simplification only affects the
scattering phase function. Approximating it with that at cloud top is
acceptable because to first approximation, 3-D radiative transfer is
determined by the distribution of cloud extinction.
The MAS-retrieved optical thickness τ(x,y) for each pixel was vertically
distributed by using the water content (WC) profile from CRS:
WC(z)=0.137×Z0.64 (Liu and Illingworth, 2000), where Z is the radar
reflectivity from CRS in dBZ. Since WC(z) is only available along the flight
track, nadir-only CRS profiles were also used across the entire MAS swath
(shifted vertically by z0 to match the MAS cloud top height at off-nadir
pixels). Cloud extinction β for each voxel (x,y,z) was thus obtained as
β(x,y,z)=τMAS (x,y) ×WC(z+z0)/∑zWC(z).
Along the flight track, the mismatch between MAS- and CRS-retrieved cloud
top height is ≤ 0.5 km. The CRS-derived average cloud top height is
10.8 km, and the mean geometrical thickness is 3.3 km.
The resulting cloud field was gridded to a resolution of 0.5 km horizontally
(similar to the MODIS pixel size of some channels) and 1.0 km vertically
(chosen larger than the mismatch between CRS and MAS in cloud top height).
Figure 1 shows the cloud optical thickness field from MAS after regridding,
with the nadir track highlighted as a dashed line. The length of this scene
is 192 km (384 pixels in x), and the width is 17.5 km (35 pixels in y).
Large-scale field from ER-2 data merged with geostationary imagery
To generalize our findings to larger scales than 17.5 km, we embedded the
sub-scene from the ER-2 remote sensors in the context of the large-scale
cloud field as retrieved from the Geostationary Operational Environmental
Satellite East (GOES-12). The imager on board GOES-12 has five channels
centered at 0.65, 3.9, 6.7, 10.7, and 12.0 µm. In the sampling region,
cloud property retrievals were produced at 15:15 and 15:45 UTC (Walther and
Heidinger, 2012; Heidinger et al., 2013). We chose the earlier time because it was more consistent
with the MAS retrieval in terms of the optical thickness along the ER-2
track. There are small discrepancies between the GOES and MAS cloud top
height retrievals, which are due to a combination of the different spatial
resolutions, and channels that are used for the respective retrievals
(Walther and Heidinger, 2012; Platnick et al., 2003; King et al., 2010). For
the purpose of this study, these differences are not significant.
Optical thickness of the large-scale cloud field. The green
rectangle marks the embedded MAS swath (Fig. 1); the red squares mark 20 km
“super-pixels” within the scene. Radiative transfer model output outside
the dashed green square is discarded (see Sect. 7).
Figure 2 shows the extended cloud scene (240 km × 240 km). Outside
the MAS swath, GOES-12 retrievals were used instead of those from MAS.
Similarly, as for the sub-scene cloud, the effective radius retrieval was
extended throughout the vertical dimension. The optical thickness was
distributed vertically using the CRS profile with the closest match in
column-integrated water path (as compared to the retrieved value from GOES)
and adjusted in altitude to match the cloud top height retrievals from
GOES-12. This approach for distributing profile information from active
instrumentation across the swath of a passive imager is more simplistic than
that developed by Barker et al. (2011) who used multispectral radiances
from MODIS. Transferring radar information to off-nadir pixels as far away
as 120 km is not necessarily justified due to spatial decorrelation of
cloud systems (Miller et al., 2014). However, in the absence of any other
information, it was considered the best alternative to estimating the cloud
vertical structure without any a priori knowledge.
Model calculations
The calculations in this study were performed with the 3-D Monte Carlo
Atmospheric Radiative Transfer Simulator (MCARaTS: Iwabuchi, 2006). MCARaTS
is an open-source code written in FORTRAN-90, which can be obtained at
www.sites.google.com/site/mcarats/. It calculates shortwave and
longwave spectral or broadband radiances and irradiances based on a forward
propagating photon transport algorithm. It is optimized to run efficiently
on parallel computers.
In addition to the two 3-D cloud fields described in Sect. 3, the standard
tropical summer atmosphere as distributed within the libRadtran radiative
transfer package (www.libradtran.org: Mayer and Kylling, 2005)
was used to prescribe the vertical profile of temperature, pressure, water
vapor, and other atmospheric gases. For gas molecular scattering, we
calculated the optical thickness for each layer using the approximation by
Bodhaine et al. (1999), and used the built-in Rayleigh scattering phase
function from MCARaTS. For gas molecular absorption, we adopted the
correlated k-distribution method described by Coddington et al. (2008). It
was originally based on Mlawer and Clough (1997), modified for the shortwave
by Bergstrom et al. (2003), and was specifically developed for the Solar
Spectral Flux Radiometer (SSFR: Pilewskie et al., 2003). The SSFR instrument
line shape (6–8 nm full-width half-maximum) defines the width of the
channels in this study (narrower than MODIS or MAS channels). The spectrum
by Kurucz (1992) served as the extraterrestrial solar spectrum.
Calculations were performed at 11 wavelengths ranging from the near
ultraviolet to the very-near infrared (350, 400, 450, 500, 550, 600, 650,
700, 750, 800, 1000 nm) to capture the spectral dependence of horizontal
photon transport over a wide range of molecular scattering. At 1000 nm,
molecular scattering is negligible and water vapor absorption is small;
cloud absorption is negligible for all wavelengths. For pixels dominated by
ice clouds, the scattering phase function and single scattering albedo were
used from the general habit mixture of the ice cloud bulk models developed
by Baum et al. (2011) (parameterized by the effective radius). For liquid
water clouds (minority of cloud pixels), single scattering albedo and
asymmetry parameter from Mie calculations were used in conjunction with a
Henyey–Greenstein phase function (which generally simplifies irradiance
calculations). In this study, all calculations were performed for an ocean
surface albedo (Coddington et al., 2010) and for a solar zenith angle of
35∘ for consistency with the earlier publication by Schmidt et al. (2010). The solar azimuth angle was 60∘ (northeast). The scene
parameters (solar geometry, surface albedo, cloud properties) will be
generalized in future work. For each wavelength, 1011
(1012) photons were used for the sub-scene (large-scale) cloud field,
which corresponds to 7 × 106 (4 × 106) per pixel, respectively.
MCARaTS was run in the forward irradiance mode with periodic boundary
conditions. For each 3-D model run, calculations were also performed using
the independent pixel approximation (IPA) where horizontal photon transport
is deactivated.
Relationship between cloud spatial structure, net horizontal photon
transport, and its spectral dependence
This section discusses the relationship between spatial structure and
spectrally dependent horizontal photon transport based on the small
sub-scene. Since true absorption, Aλ, is negligible,
Hλ is equal to Vλ, the vertical flux divergence of an
inhomogeneous cloud layer as defined in Sect. 2, with htop≈ 13 km and hbase≈ 8 km.
Cloud optical thickness τ, effective radius
re, and values of H0 and S0 for the eight pixels
highlighted in Fig. 1 (sorted by H0). For pixels 5, 6, 7, and 8, Fig. 3a shows the spectral shape of Hλ.
Table 1 shows the optical thickness and effective radius for the eight
highlighted pixels from Fig. 1 along with H0, the horizontal photon
transport at λ= 500 nm, expressed in percent of the incident
irradiance. Positive values of H0 are related to net photon loss to
other pixels (“radiation donors”), negative values to net photon gain
(“radiation recipient” pixels). In the small domain, values as high as
50 % and as low as -125 % were attained. When H0 falls below
-100 %, the radiation received through the sides of a column or voxel
exceeds that from the top of the domain. Table 1 is sorted by H0 rather
than by optical thickness. It shows immediately that there is no
relationship between the optical thickness (or cloud reflectance) and
horizontal photon transport. For example, pixel no. 6 is a net radiation
donor, whereas pixel no. 4 with roughly the same optical thickness is a net
recipient. For the extreme case of zero cloud optical thickness, the effect
of horizontal photon transport had previously been observed as clear-sky
radiance enhancement in the vicinity of clouds (Wen et al., 2007; Kassianov
and Ovtchinnikov, 2008; Várnai and Marshak, 2009; Marshak et al., 2014).
Statistically, this enhancement is a function of the distance of a pixel to
the nearest cloud. However, the horizontal scale of this dependence varies
with the spatial context. Consequently, the distance to a certain cloud
element cannot generally be used to parameterize 3-D cloud effects for
individual pixels, whether cloud-free or cloud-covered. This is illustrated
when considering pixels no. 4–8 in the anvil outflow, which have low
optical thickness (around 10) compared to the convective core (optical
thickness ≥ 40) overflown from 15:45–15:48 UTC. The small contrasts in
optical thickness (reflectance) between the pixels in close proximity tend
to drive the sign of H0 to a greater extent than the exchange of
radiation with the (bright) core (for example, no. 6 → 7, no. 5 → 4, no. 7 → 8, but not no. 5 → 6). On the other hand,
pixels no. 2 and 3 have relatively low values of H0 although they
have the largest optical thickness of all eight pixels. While still donors,
the magnitude of net horizontal flux to other pixels seems to be diminished
by the vicinity to the convective core. Overall, the direction, let alone
the magnitude of net horizontal flux, is difficult to predict from the
distribution of optical thickness, emphasizing 3-D effects as a non-local
phenomenon.
For the highlighted pixels in Table 1 (no. 5–8), Fig. 3a shows the
spectral shape of Hλ. The absolute value Hλ increases
with wavelength until it reaches an asymptotic value towards near-infrared
wavelengths, which we denote H∞. Donor pixels
(Hλ > 0) are associated with a positive spectral
slope, Sλ≡ dHλ/ dλ > 0;
recipient pixels have a negative spectral slope. Remote sensing studies
(e.g., Marshak et al., 2008; Várnai and Marshak, 2009) had previously
established that the above-mentioned radiance enhancement for clear-sky pixels near clouds was
associated with “apparent bluing,” and proposed molecular scattering as
the underlying cause for this spectral dependence. To demonstrate that the
same effect is at work here, molecular scattering was deactivated in
MCARaTS, keeping everything else the same in the calculations. In the
resulting spectra (* symbols in Fig. 3a), the wavelength dependence in the
near-ultraviolet and visible range disappears almost entirely, suggesting
molecular scattering as the primary cause for the spectral shape not only
for clear-sky, but also for cloudy pixels. This begs the question (addressed
in the next section) of how it is possible to observe such a significant
spectral effect for cloudy pixels, given that cloud scattering outweighs
molecular scattering by far. After turning molecular scattering off, the
remaining variability in Hλ is due to the weak dependence of
cloud scattering properties on wavelength and droplet or crystal effective
radius, as well as minor gas absorption features. Note that the earlier
study by Schmidt et al. (2010) remained inconclusive as to the mechanism of
the spectral dependence they observed.
To first order, the spectral shape over the range of 350 to 650 nm can be
characterized by a single number – the spectral slope at λ= 500 nm, S0 (obtained from a linear fit to Hλ= 350–600 nm,
included in Fig. 3a). Table 1 lists the value of S0 for the eight pixels
from Fig. 1, whereas Fig. 3b depicts the relationship between H0 and
S0 for every pixel. It shows that not only the sign, but also the magnitude
of the net horizontal photon transport, is surprisingly well correlated with
its slope at 500 nm (in % (100 nm)-1). This suggests that the phenomenon
observed by Schmidt et al. (2010) for a few isolated data points is a
general occurrence throughout a heterogeneous cloud field. The close
relationship between the magnitude and spectral shape of net horizontal
photon transport is the basis for the spectral parameterization of
Hλ, developed in the next section.
(a) TheHλ spectra of pixels {5, 6, 7, 8} from Fig. 1 and Table 1 with (•) and
without (∗) molecular scattering in the 3-D calculations, as well as a
fit based on Eq. () from Sect. 6 (dashed lines) and the simplified
linear fit for obtaining S0 (solid lines). (b) Spectral slope
(S0) vs. net horizontal photon transport (H0) from
(a) (both at 500 nm) for all the pixels from Fig. 1. Only 3-D calculations with
molecular scattering (black dots) show the systematic correlation between
H0 and S0. Disabling molecular scattering (gray dots)
incorrectly predicts a spectrally neutral (flat) Hλ (S0≈ 0 for all pixels). By definition, 1-D calculations (IPA, red
dots) do not reproduce net horizontal photon transport at all (H0= 0 for all pixels).
Profiles of (a) downwelling, (b) net, and (c) upwelling
irradiance at 1000 nm for the cloud field from Fig. 1. The location of the
cloud layer is marked in gray. Both IPA (dashed line, hollow symbols) and 3-D
calculations (solid line, full symbols) are shown, averaged over the full
domain (black), over all columns with τ < 1 (blue), and over
columns with τ > 120 (red).
In H0–S0 space, all IPA calculations (red dots in Fig. 3b) are
reduced to the origin because they do not allow horizontal pixel-to-pixel
radiation exchange by definition. Owing to periodic boundary conditions, the
domain average of H0 is zero. The calculations without molecular
scattering (gray dots) confirm that molecular scattering dominates the
spectral shape throughout the domain. The vertical spread of the gray data
points is due to the other factors mentioned above (e.g., variability in
cloud microphysics). To some extent, it is also apparent in the IPA
calculations.
Conceptual visualization of the mechanism of horizontal
photon transport.
(a) An example of the linear regression between logδ(λ)H∞ and logλλ0, from which the values of x and ε can be
derived. (b) The scatter plot of x vs. ε for all pixels,
joint PDFs p(x,ε) (contours) as well as the marginal PDFs
p(x) and p(ε) (histograms). The peak of p(x,ε), and
thus the most likely {x,ε} values
for the cloud field, is located at {3.85, 0.065}, and the domain-averaged values are {3.91,
0.070}.
PDF of ε for all pixels with Δ(ε) < 5 %, median (purple dashed line), and
domain-wide effective ε derived from regression of S0 vs.
H0 (blue dashed line).
Physical mechanism and parameterization
Our interpretation of Fig. 3 is that Hλ can be understood as the
combination of two terms:
Hλ=H∞+δ(λ).
The constant offset H∞ is caused by
column-to-column radiation exchange between cloud elements. This is
illustrated by Fig. 4, which shows the vertical profile of (a) downwelling,
(b) net, and (c) upwelling irradiance at 1000 nm wavelength for the cloud
field from Fig. 1. A change of net irradiance between altitudes z0 and
z1 corresponds to net radiation loss or gain within that layer. In this
case, the domain-averaged profile of net irradiance (black line in Fig. 4b)
decreases slightly near the surface, due to small absorption in the wing of
the 936 nm water vapor band. When subsampling over columns with a cloud
optical thickness τ < 1, or τ > 120, the 3-D
calculations differ from the IPA calculations because column-to-column
radiation transfer is enabled. Above the cloud field, columns with high
cloud optical thickness have higher reflectance than the domain average
(Fig. 4c), and collectively lose radiation to those with lower optical
thickness; the opposite is true below the cloud where columns with high
optical thickness have lower transmittance (Fig. 4a). The magnitude of the
net horizontal photon transport (the difference of net irradiances at the
bottom and top altitude of a layer) increases with the geometrical layer
thickness. Fig. 5 conceptually depicts the processes at work. Above clouds,
net horizontal photon transport (reflected radiance, projected into a
horizontal plane) occurs from the high- to low-reflectance column. Below
clouds, the direction is reversed because the transmittance of thin clouds
is larger than that of thicker clouds. Note that below τ≈ 4,
directly transmitted radiation dominates the downwelling irradiance, and the
cloud may not act as a “diffuser” as shown in Fig. 5. The direction of the
green arrows is then along the direct beam. This simplified figure should
not be interpreted to suggest that the net horizontal transport generally
occurs along gradients of cloud optical thickness. As stated above, its
direction and magnitude depend not only on directly adjacent columns, but
also on the large-scale context, which is why a parameterization of 3-D cloud
effects in clear-sky areas in terms of the distance to the nearest cloud is
only possible in a statistical way, but not on an individual pixel basis
(Wen et al., 2007). The value of H∞ can be obtained from
Hλ for wavelengths where molecular scattering becomes negligible
and where cloud and gas absorption are small compared to Hλ:
Aλ≪Hλ. For the purpose of this study, we
chose λ= 1000 nm: H∞≈Hλ= 1000 nm.
The spectral perturbation δλ,
superimposed on H∞, introduces the wavelength dependence of
Hλ. It is perhaps not immediately intuitive why molecular
scattering would reduce the magnitude of Hλ as indicated by the
symbolic blue arrows in Fig. 5. Molecular scattering essentially reduces the
directionality of horizontal photon transport by redistributing radiation,
part of which can then be detected as enhanced clear-sky reflectance of
clouds (Marshak et al., 2008). A different, secondary process occurs when
radiation is scattered out of the direct beam in clear-sky areas into cloud
shadows (dashed blue arrow in Fig. 5). It is spectrally dependent as
δλ but, unlike δλ, independent of H∞
and its direction – thus increasing the net radiation under both optically
thick and thin clouds. Below 550 nm wavelengths (not shown in
Fig. 4), the net irradiance does indeed increase towards the surface, both
for τ > 120 and for τ < 1. This secondary
effect is not explicitly captured by the first-order parameterization given
below.
We express the proportionality of δλ to H∞ as
δ(λ)=-ελλ0-xH∞(ε≥0,λ0= 500nm),
where (λ/λ0)-x describes the wavelength
dependence, and ε is the constant of proportionality. The layer
thickness for which Hλ is derived affects both H∞ and
δλ, but only marginally changes the correlation
between them. Therefore, ε is a general parameter that can be
used for relating spatial inhomogeneities and spectral signature of a cloud
scene as a whole. It depends on scene parameters such as surface albedo,
solar zenith angle, and cloud micro- and macrophysics (including vertical
structure). This dependence is explored in a separate publication (Song,
2016). Using Eq. (8), the spectral slope S0 can be derived as
S0=dHλdλλ=λ0=dδ(λ)dλλ=λ0=xεH∞λ0.
By combining Eqs. (7) and (8), one obtains H0=Hλ= 500nm=H∞(1-ε), and Eq. () can be rewritten as
S0=xε1-εH0λ0,
where xε/(1-ε)λ0 is the slope of
the linear regression derived using all pixels in the cloud domain (for
example, in Fig. 3b). Alternatively, one can derive both ε and
x for each individual pixel from the regression of
log-δ(λ)H∞=logε-xlogλλ0,
with log ε as intercept and x as slope, as shown in Fig. 6a. In
this example, the fit parameter x is about 4 as would be expected for
molecular scattering as the underlying physical mechanism. The
2-D probability distribution function (PDF) p(x,ε) for the population of pixels in the
domain peaks at {x,ε}≈ {3.85, 0.065} but has a considerable spread in
both parameters, which is caused by pixels with negligible horizontal photon
transport (and consequently large uncertainties in the fit parameters). The
dashed lines in Fig. 3a show the fitted spectra (labeled “theoretical”)
from this approach. For practical purposes, we fix x≡ 4 for the
remainder of this paper. This allows
Hλ=H∞1-ελλ0-4
to be used instead of Eq. () and ε and H∞ to be derived for each
pixel from a linear regression of Hλ vs. (λ/λ0)-4 (i.e., H∞ is no longer a required
input parameter as for the logarithmic regression). With ε known,
S0 can be calculated from Eq. (). This is more accurate than the
derivation of the slope from a linear fit to the spectrum as used for Fig. 3, which, due to the nonlinearity of the spectral dependence, differs from
that of the tangent if finite wavelength intervals are used. The domain-wide
“effective” ε can then be derived from the slope of the
regression line of S0 vs. H0 for all pixels (Eq. () with x= 4).
Fig. 7 shows the distribution of ε as derived from () for all
those pixels with an uncertainty of Δ(ε) < 5 %. The median of
this distribution (0.069) is almost identical to the effective value of
ε (0.067). The standard deviation of the distribution is about
0.01. This means that the parameterized correlation between net horizontal
transport and its spectral dependence can be applied to the domain as a
whole as well as for individual pixels; if the spectral shape of
Hλ is known, one can infer its magnitude throughout the
near-ultraviolet and visible wavelength range. The correlation is robust
regardless of the cloud context of a pixel, which is remarkable given the
considerable variability in distance-based measures of 3-D cloud effects
(Várnai and Marshak, 2009).
Scatter plot of S0 vs. H0 as
obtained from linear regression of Eq. () for (a) the small domain from
Fig. 1 and (b) the large-scale domain from Fig. 2, spatially aggregated to
different scales, including the 20 km super-pixels as highlighted in
Fig. 2 (red squares). The dashed lines indicate the range for 15 km pixels.
(c) Spatial distribution of S0 from (b). Red (blue) indicates net
photon donor (recipient) pixels, and green “neutral zones”
(Hλ≈S0≈ 0). (d) Dependence of
max(H) and min(H) on spatial aggregation scale (km). The color is the same as
in (b).
(a) Transmittance biases (IPA-3-D transmittance) for the
eight super-pixels from Fig. 2. (b) Correlation between net horizontal
photon transport from Fig. 8b and transmittance bias for multiple spatial
aggregation scales. The dashed lines indicate the range of variability for
20 km super-pixel size. (c) Correlation of the slopes of the quantities from (b).
(d) Same as (c), but for a bracket from the surface to cloud top, rather
than the cloud layer only.
Although our study was instigated by aircraft measurements, its findings are
also relevant for satellite-based derivations of cloud radiative effects
since the spectral perturbations δλ propagate into
observed radiances (Song et al., 2016). This may be exploited in future
applications for deriving correction terms for 3-D radiative effects via
their spectral signature.
The mean albedo of an inhomogeneous cloud field derived from CERES
observations should be fairly insensitive to 3-D effects because they are
statistically folded into anisotropy models of such scene types (if these
empirical models adequately accomplish the radiance-to-irradiance conversion
for a range of sun-sensor geometries). By contrast, surface cloud radiative
effects are much less constrained by direct CERES observations because cloud
transmittance has to be derived from concomitant imagery. This is where
biases introduced by Hλ are most significant. For the remainder
of this paper, we therefore analyze the significance of H for varying degrees
of spatial aggregation (Sect. 7), and make the connection to cloud
transmittance (Sect. 8).
Scale dependence and spatial aggregation
The results presented so far (e.g., in Fig. 3b) are based on calculations at
a resolution of 0.5 km. The question is whether the correlation between the
magnitude and spectral shape of H is scale-invariant, and to what extent the
effect of horizontal photon transport can be mitigated by spatial
aggregation. To answer this question, we successively coarsened the pixel
resolution to 15 km, the largest “super-pixel” contained within the MAS swath
(Fig. 1). Figure 8a shows that the correlation is indeed independent of the
spatial aggregation scale and thus pixel size. The magnitude of H0
decreases with pixel size: it ranges from +6 to -5 % at 15 km
resolution (close to CERES for nadir viewing), compared to about ±50 % at 1–5 km (resolution of various MODIS level-2 products). Here, we
use the large cloud scene (Fig. 2) to estimate for which aggregation scale
beyond 15 km the magnitude of H0 drops below the radiometric
uncertainty of typical space- or ground-based radiometers (3–5 %), at
which point 3-D cloud effects become insignificant from a practical
point of view.
The results for the large scene, shown in Fig. 8b, confirm that the
correlation is preserved for scales up to 70 km. However, H0 at
15 km resolution varies from +17 to -13 % throughout the
large-scene domain, much more than in the MAS-only domain (+6 to
-5 %). One explanation for this larger range is the greater complexity of
the large domain, providing a more extensive sample of cloud variability
than the smaller sub-scene. This becomes quite clear when looking at the
spatial distribution of horizontal photon transport (Fig. 8c). We chose to
plot S0 (y axis in Fig. 8b) rather than H0; they are
practically interchangeable thanks to the correlation between the two. The
distribution of effective donor, recipient, and “neutral” regions (red, blue,
green, respectively) bears almost no resemblance to the optical thickness
field from Fig. 2. This demonstrates once again that horizontal photon
transport cannot be derived from the spatial distribution of clouds in any
simple way; strong contrasts between negative and positive H0 (or
S0) can arise in optically thin boundary layer clouds (southwest
corner of Fig. 2 and 8c) as well as in optically thick areas (deep
convection, northeast corner of cloud scene). Considering the GOES-MAS
large-scene results within the boundaries of the MAS swath only (marked by
the rectangle in Fig. 8c) allows the net exchange of
radiation between the MAS domain and its large-scene context to be estimated. The average
value of H0 within the small-scene subset is +7.9 %, which
means that the small scene effectively loses photons to its surroundings.
This would not be detectable for such a large aggregation scale (where the
entire MAS domain represents a single super-pixel). This net energy
export is not reproduced by the calculations based on the MAS-only domain
where the mean value of H0 is zero, in keeping with energy
conservation that is satisfied by periodic boundary conditions in the
radiative transfer model. The range of H0 in the MAS-only
sub-scene of the GOES-MAS scene is +17 to -6 % at 15 km aggregation
scale. This is still a larger range than obtained from the MAS-only
calculations (+6 to -5 %), even after subsetting the results from
the large scene to the boundaries of the small ones. The reason is simply
that the 15 km super-pixel size is already half the width of the MAS-only
domain. Boundary conditions enforce the convergence of H0 to zero as
the area ratio of pixel to domain size approaches 1, which causes an
underestimation of the variability of H0 for large aggregation scales.
By contrast, photons can also travel outside the confines of the domain in
the real world as represented by the larger GOES-MAS cloud scene in our
study.
This is illustrated in Fig. 8d, which shows the range of H0 for both
the large and the small cloud scene as a function of aggregation scale. At
small scales, the range is comparable for the small and large scene. At 15
km aggregation scale, the range obtained from the small scene has decreased
to about half that of the large one. At 50 km pixel resolution, H0 ranges from +7 to -3 % (+5 to -1 % at 70 km). It is
likely that the boundary conditions imposed on the large domain also cause
an underestimation of the H0 variability at these large scales.
Nevertheless, these results suggest that above 60 km super-pixel size (about
3 × 3 CERES nadir footprints), horizontal photon transport can be
neglected for this cloud scene, based on a 3 % uncertainty threshold. This
is only true when aggregating all native-resolution pixels, regardless of
whether they are flagged as clear sky or as cloud-covered. However, sampling
cloudy and clear pixels separately would result in much larger biases than 3 %
because high optical thickness pixels are more likely to be effective photon
donors than low-optical thickness or clear pixels, causing an asymmetry in
the distribution of H0 (Song et al., 2016).
Significance for cloud radiative effects
In this section, we evaluate the ramifications of net horizontal photon
transport on estimates of cloud radiative effects. For any atmospheric
column, H is connected to R and T through Eq. (1) and manifests itself in a
transmittance and reflectance bias (λ index omitted):
ΔT=TIPA-T3-DΔR=RIPA-R3-D.
Juxtaposing energy conservation for a horizontally homogeneous atmosphere
(TIPA+RIPA= 1) with Eq. (1) for conservative scattering
(A= 0, therefore T3-D+R3-D=1-H) yields the plausible
relationship
H=ΔT+ΔR,
which means that the error introduced by horizontal photon transport is
partitioned into transmittance and reflectance bias. Since the bias ΔR is folded into the empirical radiance-to-irradiance conversion employed by
CERES, we focus on ΔT in this study.
H0 is only weakly correlated with reflectance
biases ΔR0 (IPA-3-D reflectance) at scales below 15 km,
which means that, statistically, biases introduced by horizontal photon
transport propagate primarily into transmittance, not albedo. This changes
for larger scales.
For the eight super-pixels no. 11–18 from Fig. 2, Fig. 9a shows the IPA
bias ΔT, ranging from +2 to +14 % in the mid-visible spectrum. Its
spectral dependence is more complicated than the one shown for H in Fig. 3a,
with a less obvious correlation between magnitude and spectral shape.
Nevertheless, Fig. 9b shows a remarkable correlation between H0 and
ΔT0 (TIPA-T3-D at 500 nm) for the same aggregation
scales as in Fig. 8b. For example, the H0 range of +15 to -10 %
translates into +19 to -12 % in ΔT0 for a horizontal
resolution of 20 km. Linear regression between H0 and ΔT0 suggests that in this case, H0 propagates mainly into ΔT0, whereas it is uncorrelated with ΔR0 for scales below 20 km (Fig. 10).
For simplicity, the spectral dependence of ΔT as shown in Fig. 9a is
approximated by
ΔTλ=TλIPA-Tλ3-D=ξ0350-600nm×(λ-λ0)+(T0IPA-T03-D);λ0= 500nm,
where ξ0 is the spectral slope of TλIPA-Tλ3-D calculated from the spectrum between 350 and 600 nm. Fig. 9c shows
that the spectral slopes of H and ΔT, S0 and ξ0, are
correlated despite the more complicated spectral dependence of T compared to
that of H (Fig. 9a). However, there is clearly no 1:1 relationship as found
between H0 and ΔT0 above. For example, S0=-10 % (100 nm)-1 corresponds to only ξ0=-6 % (100 nm)-1. This
changes when extending the vertical layer boundaries (8–13 km so far,
bracketing only the cloud layer itself) to the atmosphere reaching from the
ground to cloud top (Fig. 9d). This distinction is indicated by carets above all
quantities. This is slightly different from the definition of T^ in
Sect. 2 where the upper boundary is the top of atmosphere, not the top of
the cloud. The spectral dependencies of H^ and ΔT^ have
similar magnitudes (Fig. 9d), as opposed to the equivalent quantities shown in Fig. 9c. However, the relationship between S^0 and ξ^0 is not scale-invariant
above 15 km. This means that the vertical bracket for deriving T, R, and H has to
be chosen with consideration of the vertical location of the cloud layer. By
contrast, the correlation between H and S as discussed in Sect. 6 is fairly
independent of the layer boundaries and scale.
For future studies of IPA-3-D biases in satellite-derived estimates of
surface cloud radiative effects, Fig. 4b suggests the center of a cloud as
upper boundary of the bracket where dFnet/dz reaches a domain-wide minimum because 3-D effects can be vertically
separated into a transmittance and reflectance part below and above this
level, respectively. Moreover, the correlation between ΔT and its
spectral dependence ξ0 (not shown) can be exploited to detect
IPA-3-D biases in ground-based irradiance measurements below cloud fields
(Song, 2016). While our study suggests that horizontal photon transport
mainly propagates into transmittance biases, there is some indication (Fig. 10) that at scales above 20 km, nonzero values of H0 translate into
albedo (reflected irradiance) biases as well. This increasing correlation
with scale is probably associated with the gradual decorrelation between
S^0 and ξ^0 observed in Fig. 9d. In order to
improve satellite-based estimates of cloud radiative effects, it is
important to understand how H0 is partitioned into ΔTand ΔR (Eq. 14) at different aggregation scales. A detailed study would need to
be conducted for different cloud morphologies, sun angles, and surface
albedos, and is left for the future.
Summary and conclusions
Deriving the radiative effects of inhomogeneous cloud scenes from
observations by satellite, aircraft, or at the surface is often portrayed as
an intractable problem because it cannot be accomplished by isolating a
pixel from its spatial context. At the core of the issue is pixel-to-pixel
exchange of radiation, or net horizontal photon transport, which occurs over
a range of scales. The original motivation for this study was to gain a
physical understanding of this phenomenon's spectral dependence in the
near-ultraviolet and visible wavelength range, which had been found in
aircraft irradiance observations (Schmidt et al., 2010). We were able to
identify molecular scattering as the underlying mechanism for the spectral
dependence using 3-D radiative transfer calculations with
cloud imagery and radar observations as input. When deactivating molecular
scattering in the radiative transfer model, the wavelength dependence
disappeared almost entirely in the vertical flux divergence V, which comprises
net horizontal flux density H as well as true layer absorption A. To simplify
the analysis, we limited our study to conservative scattering by choosing
wavelengths with negligible gas or cloud absorption (A≈ 0), and by
excluding aerosols. When activated in the model, molecular scattering
manifested itself as a spectral perturbation (more accurately: modulation)
δλ to an otherwise spectrally neutral horizontal flux density
H∞, which in turn could be traced back to horizontal exchange of
radiation due to spatial inhomogeneity of cloud elements within the domain.
Beyond the original scope of this study, we made a few surprising
discoveries:
The spectral perturbation δλ is not independent of the
spectrally neutral part H∞ caused by the clouds themselves.
Instead, the mid-visible spectral slope of Hλ is correlated with
H itself (i.e., with the magnitude of the spectrally neutral part
H∞), which led to the simple parameterizationδλ=-ελλ0-xH∞.
We were able to show that the exponent x is close to 4, which further
confirmed molecular scattering as the dominating physical mechanism behind
the spectral perturbation. The constant of proportionality, ε,
can be regarded as universally valid for all pixels within the cloud domain,
independently of the vertical or horizontal spatial distribution of clouds.
This means that the spectrally dependent horizontal photon transport can be
represented asHλ=H∞+δλ=H∞1-ελλ0-4for each pixel within the domain with ε= 0.07 ± 0.01 for the scene
we studied. It seems remarkable that one single value of ε
should suffice to describe the relationship between the magnitude of H
(caused by clouds) and its spectral dependence (imprinted on H by a
completely different physical process, molecular scattering) – especially
considering the range of different clouds within the domain. The correlation
holds for each pixel, no matter what its spatial context may be. Once
ε is established for a given cloud scene, the spectral
perturbations associated with horizontal photon transport can be derived for
each pixel if the value of H0 is known. Conversely, if the spectral
shape of Hλ is known at one wavelength, its magnitude can easily
be inferred for the whole spectrum. This may be especially significant
considering that H cannot be directly observed from space. It is likely that
the spectral perturbations will propagate into the observed radiances.
Indeed, Song et al. (2016) found evidence of this connection in aircraft
data, which had previously been reported by Várnai and Marshak (2009) in
clear-sky satellite observations near clouds. The close correlation that we
found in our study may be a future pathway to inferring the magnitude of H
from its spectral manifestation in the observed radiances.
The correlation and parameterization hold for a range of spatial aggregation
scales, and are fairly independent of the location of the bracketing
altitudes that define the layer. This scale invariance only breaks down when
extending a layer very close to the surface where a secondary spectral
effect has to be factored in (see Sect. 6 and dashed arrow in Fig. 5).
The observed correlation between H and its spectral shape can also be found
between transmitted irradiance T and its spectral shape, although it is not
scale-invariant beyond 20 km.
H is correlated with ΔT, the IPA transmittance bias for each pixel,
but not with ΔR (at least at small scales). This means that 3-D cloud
effects in the form of horizontal photon transport translate almost
exclusively into a transmittance bias. At scales above 20 km, a correlation
between H and ΔR does emerge, which requires further study. The
correlation between H and ΔT can potentially be exploited for
ground-based spectral irradiance observations (Song, 2016).
Few of these findings could be expected at the outset of our research, and
they evoke a number of new questions:
How does the discovered correlation and the constant of proportionality in
its parameterization, ε, depend on scene parameters such as
solar zenith and azimuth angle, surface albedo (magnitude and spectral
dependence), and cloud morphology and microphysics? What “drives” the
parameter ε?
Can the spectral perturbations associated with H indeed be detected in
reflected radiances, and can they be used to infer the magnitude of H
indirectly?
Can the findings for the near-ultraviolet and visible wavelength range be
generalized to the near-infrared wavelength range where clouds and
atmospheric gases do absorb?
What are the implications of our findings for estimating aerosol radiative
effects (such as heating rates) in the presence of inhomogeneous cloud fields?
Can the method by Ackerman and Cox (1981) to correct for horizontal photon
transport in aircraft measurements of atmospheric absorption by using a
visible channel as basis for the correction of near-infrared absorption be
upheld for future measurements, even in the modified form proposed by
Kassianov and Kogan (2002)?
Can H and ΔT be derived from spectral perturbations in transmitted
irradiance observations by ground-based spectrometers?
Question 2 will be partially addressed by Song et al. (2016); questions 1,
3, 5, and 6 are discussed by Song (2016), and will be further investigated in
future publications. Furthermore, questions 3 and 4 are the subjects of
active research in the framework of ongoing or planned field missions
(NASA ORACLES and CAMP2Ex). This publication constitutes a further
contribution to the emerging field of cloud-aerosol spectroscopy (Schmidt
and Pilewskie, 2012), which is expected to improve the estimation of
cloud-aerosol parameters and their radiative effects through spectrally
resolved observations from the ground, aircraft, and, ultimately, space.
Data availability
The MAS (King et al., 2007) and GOES (Heidinger et al., 2007; Walther et al.,
2010) level-2 data (the input for the cloud fields) can be obtained at
http://lasp.colorado.edu/lisird/resources/lasp/nnx14ap72g/MASL2_07919_09_20070717_1519_1534_V03.hdf
and
http://lasp.colorado.edu/lisird/resources/lasp/nnx14ap72g/goes12_2007_198_1515.level2.hdf,
respectively. More recent versions of the MAS data can be downloaded from
https://ladsweb.nascom.nasa.gov/archive/MAS_eMAS/TC4/ (flight 07_919).
All other data, the derived 3-D cloud fields, and the irradiance calculations
can be requested from the corresponding author.
Acknowledgements
The research presented in this paper was supported by grants NNX14AP72G (Shi
Song and Sebastian Schmidt) and NNX12AC41G (Michael King) within the NASA
radiation sciences program. The calculations were performed on the
supercomputer “Janus”, which is supported by the US National Science
Foundation (award number CNS-0821794) and the University of Colorado
Boulder. It is a joint effort of the University of Colorado Boulder, the
University of Colorado Denver, and the National Center for Atmospheric
Research. Janus is operated by the University of Colorado Boulder. We
appreciate the effort of Thomas Arnold (NASA Goddard Space Flight Center) in
supporting the MAS calibrations and retrievals.
Edited by: J.-Y. C. Chiu
Reviewed by: two anonymous referees
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