ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-17-2359-2017Directional, horizontal inhomogeneities of cloud optical thickness
fields retrieved from ground-based and airbornespectral
imagingSchäferMichaelmichael.schaefer@uni-leipzig.deBierwirthEikeEhrlichAndréhttps://orcid.org/0000-0003-0860-8216JäkelEvelynWernerFrankWendischManfredhttps://orcid.org/0000-0002-4652-5561Leipzig Institute for Meteorology, University of Leipzig, Leipzig, GermanyJoint Center for Earth Systems Technology, University of Maryland, 5523 Research Park Drive 320, Baltimore, MD 21228, USAnow at: PIER-ELECTRONIC GmbH, Nassaustr. 33–35, 65719 Hofheim-Wallau, GermanyMichael Schäfer (michael.schaefer@uni-leipzig.de)15February20171732359237216August201626August201615December201628December2016This 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/17/2359/2017/acp-17-2359-2017.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/17/2359/2017/acp-17-2359-2017.pdf
Clouds exhibit distinct horizontal inhomogeneities of their optical and
microphysical properties, which complicate their realistic representation in
weather and climate models. In order to investigate the horizontal structure
of cloud inhomogeneities, 2-D horizontal fields of optical thickness (τ)
of subtropical cirrus and Arctic stratus are investigated with a spatial
resolution of less than 10 m. The 2-D τ-fields are derived from
(a) downward (transmitted) solar spectral radiance measurements from the
ground beneath four subtropical cirrus and (b) upward (reflected) radiances
measured from aircraft above 10 Arctic stratus. The data were collected
during two field campaigns: (a) Clouds, Aerosol, Radiation, and tuRbulence in
the trade wind regime over BArbados (CARRIBA) and (b) VERtical Distribution
of Ice in Arctic clouds (VERDI). One-dimensional and 2-D autocorrelation
functions, as well as power spectral densities, are derived from the
retrieved τ-fields. The typical spatial scale of cloud inhomogeneities
is quantified for each cloud case. Similarly, the scales at which 3-D
radiative effects influence the radiance field are identified. In most of the
investigated cloud cases considerable cloud inhomogeneities with a prevailing
directional structure are found. In these cases, the cloud inhomogeneities
favour a specific horizontal direction, while across this direction the cloud
is of homogeneous character. The investigations reveal that it is not
sufficient to quantify horizontal cloud inhomogeneities using 1-D
inhomogeneity parameters; 2-D parameters are necessary.
Introduction
The globally and annually averaged cloud cover is in the range of about
70 % . Because of this high percentage, and the
important effect of cloud cover on Earth's radiation budget, clouds need to
be considered as an important regulator of Earth's climate
. Clouds scatter and absorb solar radiation
in the wavelength range from 0.2 to 5 µm; they emit and absorb
terrestrial radiation from 5 to 50 µm. Although clouds have been
studied for several decades, they are still poorly represented in weather and
climate models . The latest report of the Intergovernmental
Panel on Climate Change (IPCC) classifies cloud effects as one of the largest
uncertainties in climate simulations, significantly contributing to problems
in the determination of Earth's energy budget . These
issues partly arise from an unrealistic representation of complex horizontal
cloud structures and from cloud-radiation feedback processes that control the
cloud evolution . Therefore, the
representation of cloud inhomogeneities needs to be more realistic
. This is particularly important because changes of cloud
properties may have serious consequences for the interaction of clouds with
radiation .
Several independent studies investigated the influence of the plane-parallel
assumption on cloud retrievals e.g.. They found that the magnitudes of
model biases are related to the degree of horizontal photon transport. In
1-D
radiative transfer simulations, clouds are divided into separate vertical
columns with horizontal homogeneous optical and microphysical properties
(independent pixel approximation, IPA). However, horizontal photon transport
cannot be neglected in case of inhomogeneous clouds. Additionally, multiple
cases of scattering due to 3-D microphysical cloud structures smooth the horizontal
radiation field. On small scales, this limits the accuracy of IPA. For
example, and revealed discrepancies
for individual pixel radiances exceeding 50 % due to a plan-parallel
bias.
High ice clouds (cirrus) and Arctic stratus exhibit horizontal
inhomogeneities at different horizontal scales. Both cloud types can either
warm or cool Earth's climate system, depending on their optical and
microphysical properties and the meteorological conditions. For example,
reported for tropical regions a positive (warming) net
radiative effect of cirrus for a cirrus optical thickness (τci)
of less than 10, but a cooling effect for τci>10. For Arctic
stratus, showed that for low surface albedo
(αs) and low solar zenith angle (θ0), the cloud cools
the sub-cloud layer. With increasing αs and increasing
θ0, the cooling effect of the low-level cloud turns into a warming.
Both clouds and surface reflection properties can vary significantly on
different horizontal scales.
In many remote-sensing applications clouds are assumed to be plane-parallel
, which may introduce biases
into the modelled radiation budget . For example, in the
case of cirrus, found a plane-parallel cirrus albedo
bias of up to 25 % due to spatial cirrus inhomogeneity. For Arctic
stratus over variable sea-ice surfaces, reported
a plane-parallel albedo bias of less than 2 %, but an absolute value of
the transmittance bias that could exceed 10 %.
Three-dimensional Monte Carlo radiative transfer simulations account for horizontal photon
transport . However, they are costly in terms of
computational time and memory . This renders Monte Carlo
radiative transfer simulations inappropriate for application in
operational or global models. Other approaches introduce Monte Carlo
integration of independent column approximation (McICA), as proposed by
. McICA is a computational efficient technique for
computing domain-averaged broadband radiative flux densities in vertically
and horizontally variable cloud fields . Improvements
compared to the plane-parallel assumption are achieved with this approach,
but results are still not as accurate as those from 3-D Monte Carlo models. To
reduce uncertainties associated with the 1-D plane-parallel assumption,
applied spatial autocorrelation functions of cloud
extinction coefficients to capture the net effects of sub-grid cloud
interactions with radiation. With several orders less of computation time, this
approach reproduces 3-D Monte Carlo radiative transfer simulations with an
accuracy within 1 %. However, assumed perfect
knowledge about the spatial correlation functions of cloud extinction
coefficients, which underlines the need for measurements of comparable
resolved inhomogeneity measures.
General circulation or numerical weather forecast models require sub-grid
scale parameterization of cloud structures, liquid water content
(LWC), and/or ice water content (IWC), for example . In reality, cloud
structures reveal spatial features down to distances below the metre scale
. Therefore, measurements with appropriate spatial and
temporal resolution have to be conducted in order to derive the needed
parameterizations. The required measurements include cloud altitude
(temperature), its geometry (vertical and horizontal extent), and cloud
microphysical properties (e.g., LWC, IWC, droplet size, ice crystal size, and
shape distributions).
Cloud inhomogeneities often exhibit a typical directional structure (e.g.,
induced by the prevailing wind). In such a case, 1-D observations with lidar
(light detecting and ranging) or point spectrometers can lead to an
underestimation or overestimation of the degree of cloud inhomogeneity of the
whole cloud scene. For example, a cloud with a rather inhomogeneous character
may be classified as horizontally homogeneous (underestimation of
inhomogeneity) if the dominating cloud structure has the same orientation as
the cloud observational path. Conversely, the cloud inhomogeneity would be
overestimated if the cloud were scanned perpendicular to the major directional
structure. Therefore, 2-D observations are a useful tool for avoiding such
misinterpretations of cloud inhomogeneity.
In this paper, horizontal τ fields retrieved from solar spectral
radiance measurements are analysed to quantify horizontal inhomogeneities of
two cloud types: subtropical cirrus and Arctic stratus. The information
content of 1-D and 2-D approaches to cloud inhomogeneity analysis is compared
to identify their scientific value and limits. In Sect. ,
a statistical evaluation of the horizontal inhomogeneity of the fields of
τ is presented using common 1-D inhomogeneity parameters from the
literature. Those bulk properties are valid to quantify the overall cloud
inhomogeneity but cannot reproduce spatial inhomogeneities of the cloud
field. In Sect. , the derived bulk properties from the 1-D
inhomogeneity parameters are compared to 1-D and 2-D autocorrelation functions.
Finally, in Sect. , 1-D and 2-D Fourier analysis is used to
investigate the effect of horizontal cloud inhomogeneities on radiative
transfer.
Data set: 2-D fields of cloud optical thickness
Data from two international field campaigns were analysed: the Clouds,
Aerosol, Radiation, and Turbulence in the Trade Wind Regime over Barbados
CARRIBA, campaign performed on
Barbados in April 2011 and the Vertical Distribution of Ice in Arctic Clouds
VERDI, observations carried out in Inuvik, Canada,
in May 2012. Two-dimensional fields of downward and upward solar
spectral radiances (Iλ↓, Iλ↑)
were measured from the ground (CARRIBA) and from an aircraft (VERDI). The
imaging spectrometer AisaEAGLE manufactured by Specim Ltd., Finland;
was used for the measurements.
It is a single-line sensor with a field of view (FOV) of 37∘ and
1024 spatial pixels detecting radiation in the wavelength range from 400
to 970 nm with a spectral resolution of 1.25 nm full width at half maximum
(FWHM). The 2-D scans of the cloud scenes are generated from sequential (4
to 30 Hz frame rate) measurements of the single sensor-line, while the
target (cloud) moves with the wind (ground-based) or the flying aircraft
across this sensor line. Adding up all measured lines behind each other, the
2-D scan evolves as an image with a spatial (number of sensor pixels) and
temporal (number of recorded frames) axis. Applying the known geometry,
integration time, and cloud and aircraft velocities, the axis dimensions can be
transferred into distances. The 2-D images evolved either from the heading of
the clouds above the sensor line (ground-based) or by the movement of the
sensor line itself above the clouds (airborne). The imaging spectrometer was
characterized and calibrated in the laboratory to transform the AisaEAGLE's
raw data (12-bit digital numbers) into radiance. The procedure of data
evaluation (calibrations, corrections) follows the methods described by
and .
As proposed by , , or
, horizontal cloud inhomogeneities are studied by scale
analysis of cloud-top reflectances. However, radiance measurements include
the information of the scattering phase function (e.g., forward–backward
scattering peak, halo features) in the measured fields of radiance
. To avoid artefacts in the scale analysis resulting
from such features, parameters that are independent of the directional
scattering of the cloud particles have to be analysed. The cloud optical
thickness τ does not include the fingerprint of the scattering phase
function. Therefore, the ground-based and airborne measured fields of
Iλ↓ (CARRIBA) and Iλ↑ (VERDI)
were used to retrieve horizontal fields of τ with a spatial resolution
of less than 10 m. The retrieved fields of τ were then applied to
investigate horizontal cloud inhomogeneities of subtropical cirrus (index ci)
and Arctic stratus (index st).
Label, measurement period (day and time of day in UTC), cloud top
altitude, pixel size (width, length), domain size (swath, length), and
average and standard deviation (τ‾±στ) of
the retrieved fields of τci and τst from
ground-based measured CARRIBA (Ci-01 to Ci-04) and airborne measured VERDI
(St-01 to St-10) cases. The flight altitude for each VERDI case was at
2920 m. The right three columns include calculated 1-D inhomogeneity
parameters (ρτ, Sτ, χτ) of the retrieved fields
of τ. They are discussed in Sect. .
Simulations were performed with the radiative transfer solver DISORT 2
(Discrete Ordinate Radiative Transfer). Input parameters such as cloud
optical properties, aerosol content, and spectral surface albedo are provided
by the library for radiative transfer calculations libRadtran,
. The required profiles of thermodynamic parameters are
derived from measurements from radiosondes and/or dropsondes. Despite
assuming plane-parallel clouds in the simulations, the investigation of 3-D
radiative effects is still possible using the retrieved fields of τ, but
directional features related to the scattering phase function are avoided.
Iλ↓ and Iλ↑ were simulated as
a function of values of τci and τst, respectively.
The simulations were performed for all scattering angles within the FOV of
AisaEAGLE. Thus, simulated grids of possible Iλ↓ and
Iλ↑ and corresponding τci and
τst are available for each time step of the measurements and
each spatial pixel. The retrieved τci and τst are
derived by interpolating the simulated Iλ↓ and
Iλ↑ to the measured value for each spatial pixel using
a linear interpolation. More detailed descriptions and sensitivity tests of
the applied retrieval procedures are reported by for
subtropical cirrus and by and
for Arctic stratus. Fields of cloud optical thickness
are derived for four subtropical cirrus cases (τci) and 10
Arctic stratus cases (τst). Subsequently, those fields of
τci and τst are used to investigate and quantify
horizontal cloud inhomogeneities.
Table summarizes the statistical parameters of the four
retrieved fields of τci (Ci-01 to Ci-04) and the 10 retrieved
fields of τst (St-01 to St-10). Figure illustrates
example cutouts for cases St-04 and St-07, both characterized by
a measurement duration of 60 s. Table further provides
information on the measurement time, cloud altitude (hcld), field
size (swath, length), and average and standard deviation of
τci (τ‾ci±στ,ci) and
τst (τ‾st±στ,st). The
sampled subtropical cirrus fields of about 13–44 km length and 7–8 km width
are determined by the time of observation and the swath covered by AisaEAGLE.
For the Arctic stratus cases the average swath of the covered cloud fields
has a size close to 1.3 km. The length varies from 4 to up to 26 km.
Thus, for CARRIBA and VERDI sufficiently large areas of the clouds are
covered to provide a statistically firm analysis of τci and
τst and to investigate their horizontal inhomogeneities.
(a) Georeferenced field of τst. Cutout from
measurement case St-04 with 60 s measurement duration. The dark blue, red,
and light blue lines illustrate the nadir viewing direction in a range of
±1∘. (b) Same as panel (a) for case St-07.
One-dimensional inhomogeneity parameters
The standard deviation στ of the cloud optical thickness does
not allow a comparison between cases with different average cloud optical
thickness τ‾. A cloud with higher τ‾ can exhibit a higher
standard deviation. Therefore, similar to the studies by
, who used ratios between mean τ and the variance of
τ, and utilized the normalized
inhomogeneity measure ρτ to quantify the horizontal inhomogeneity
of τ. It is defined by the ratio of στ and the average
value τ‾ of the corresponding sample:
ρτ=σττ‾.
A homogeneous cloud is characterized by ρτ=0.
Increasing values of ρτ indicate rising cloud inhomogeneity.
However, ρτ has no predefined upper limit, which might lead to
misinterpretations in a variability analysis. This renders ρτ not
as a quantitative but qualitative measure only. Therefore,
and convert the relative variability
ρτ into the inhomogeneity parameter Sτ as follows:
Sτ=lnρτ2+1ln10.
In case of a log-normal frequency distribution of τ,
Sτ is proportional to ρτ. This is because the
reflected or transmitted radiance is approximately linear to log τ for
moderate τ (for logτ= 0.5–1.5 with τ≈ 3–30).
Without net horizontal photon transport, moments of reflected or transmitted
radiance are closely linked with moments of logτ rather than moments
of τ. Therefore, Sτ quantifies the degree
of cloud inhomogeneity.
investigated the inhomogeneity parameter
χτ, first introduced by . χτ is
defined as the ratio of the logarithmic and linear average of a distribution
of τ‾:
χτ=explnτ‾τ‾.
The 1-D inhomogeneity parameter χτ ranges between 0 and 1, with
values close to unity indicating horizontal homogeneity and values
approaching zero characterizing high horizontal inhomogeneity.
state that the reflected solar flux is approximately
a linear function of the logarithm of τ for a wide range of τ
(≈ 3 to ≈ 30, depending on θ0). Thus, the
logarithmically averaged τ provides a way to account for cloud
inhomogeneity effects in plane-parallel radiative transfer calculations using
χτ as a scaling factor with which τ needs to be multiplied to
approximate the IPA albedo.
The three 1-D inhomogeneity parameters ρτ, Sτ, and
χτ are calculated for each retrieved field of τci and
τst from the CARRIBA and VERDI campaigns. The results are listed
in the right three columns of Table . When comparing them to
literature values, one has to keep in mind that cloud inhomogeneities appear
on different spatial scales. For example, cloud fields may change on synoptic scales
(≈ 100 km) or dynamic scales (10–100 m) depending on the cloud
type. Therefore, inhomogeneity parameters depend on the pixel and domain size
of the analysed cloud fields. The larger the domain size or the smaller the
pixel size is, the broader the probably density function of the cloud
parameter may become. Therefore, a comparison of different cloud cases is
only valid when pixel size and cloud domain are in the same range.
The subtropical cirrus cases observed during CARRIBA show ρτ in
the range of 0.17–0.91, while Sτ is in the range of 0.08–0.48. The
largest values of ρτ and Sτ are found for Ci-04, the
lowest for Ci-03. The values for ρτ and Sτ show that the
subtropical cirrus of Ci-02 and Ci-03 were quite homogeneous, whereas those of
Ci-01 and Ci-04 were rather inhomogeneous. For the 10 Arctic stratus cases,
ρτ and Sτ are in the range of 0.15–0.34 and 0.07–0.20,
respectively. For stratocumulus days (6.9 km domain with 15 m horizontal
resolution), quantified the inhomogeneity of τ with
Sτ= 0.1–0.3. and
investigated the inhomogeneity of τ for overcast boundary layer clouds
using a visible-wavelength moderate-resolution (about 1 km) sensor and found
values of Sτ= 0.03–0.3, which lead to ρτ= 0.07–0.78. Thus, considering the different pixel and domain
sizes, the derived values from CARRIBA and VERDI compare well with those
reported by , , and
. Among all 10 cases, ρτ and Sτ
indicate cases St-03 and St-08 to be more inhomogeneous.
For CARRIBA, the values of χτ range from 0.63 to 0.99, indicating
rather inhomogeneous cirrus for Ci-04 and quite homogeneous cirrus during
the other days. In contrast to the results for ρτ, Sτ
and χτ indicate that the subtropical cirrus of Ci-01 are less
inhomogeneous. The calculated values of χτ for the retrieved
fields of τst from the VERDI campaign yield values larger than
0.9 in each case, with the lowest values for cases St-03 and St-08, which were
already indicated by ρτ and Sτ to be more inhomogeneous.
Using the Moderate Resolution Imaging Spectroradiometer (MODIS), depending on
cloud type, cloud phase, surface type, season, and time of day,
estimated the range of χτ to be from
≈ 0.65 to 0.8 at spatial scales of 1∘× 1∘.
The 1-D inhomogeneity parameters ρτ, Sτ, and χτ
are easy to calculate and suitable for being implemented in simulations that
assume horizontally homogeneous clouds to achieve more realistic results.
They do not provide a measure of the directional variability of the
inhomogeneities. However, different clouds exhibit preferred horizontal
inhomogeneity patterns and typical features. For example, the clouds observed
during CARRIBA and VERDI are different in terms of cloud altitude, structure,
phase, particle size, and shape, although ρτ, Sτ, and
χτ yield comparable values (compare Fig. and
Table ). Therefore, not only the horizontal inhomogeneity but
also the spatial coherence of cloud inhomogeneity parameters and their
directional dependence need to be investigated .
Spatial 1-D and 2-D autocorrelation functions and decorrelation length
The 2-D autocorrelation function Pτ(Lx,Ly) is
calculated in two horizontal dimensions at fixed distances (pixel lags)
Lx and Ly, which are derived as integer multiples of the
equidistant sample intervals xj and yk of the 2-D fields
of τ. The maximum pixel lags Lx and
Ly are given by the number of pixels n and m of the 2-D fields.
Here, with n and m equidistant, measurement intervals xj and
yk, Pτ(Lx,Ly) for 2-D fields of τ are
calculated by
PτLx,Ly=∑j,k+1n,mτxj+Lx,yk+Ly-τ‾×τxj,yk-τ‾∑j,k+1n,mτxj,yk-τ‾2.
Here, τ(xj,yk) is the cloud optical thickness
observed at the reference position, and τ(xj+Lx,yk+Ly) is the cloud optical thickness
at pixel lags Lx and Ly. The autocorrelation function
Pτ(Lx,Ly) yields values between -1 and 1, with
1 representing a perfect positive correlation (e.g., for a spatial shift
equal to zero); a value of -1 is a perfect negative correlation and
0 indicates no correlation. Thus, spatial autocorrelation functions quantify
the degree of similarity between spatially distributed neighbouring samples.
Usually, τ values in close horizontal distance reveal similar values,
while cloud pixels at larger distances may show significantly different
values of τ, depending on the cloud heterogeneity. Here, only the degree
of correlation matters; the positive or negative sign of the autocorrelation
result is of less importance. To avoid misinterpretations with the sign, the
squared autocorrelation function Pτ2(Lx,Ly) is used
here.
Figure b and d show examples of Pτ2(Lx,Ly) in
a 2-D plot for Lx=-250 to Lx= 250 and
Ly=-250 to Ly= 250, calculated for a selected area
(500 by 500 pixels, Fig. a and b) of the cirrus fields from cases
Ci-01 and Ci-03 with Lx=250 and Ly=250. The positive and negative
signs of Lx and Ly in Fig. b and d illustrate the
direction into which the particular image is shifted against itself to derive
the depicted autocorrelation coefficients. Both cases show a different
pattern of Pτ2(Lx,Ly) with increasing absolute values of
Lx and Ly. While Ci-01 shows a circular spot indicating a symmetry
independent of direction, Ci-03 displays high correlation factors for all
considered Ly values within a range from Lx=-50 to Lx=50. This pattern
indicates a homogeneous cloud structure along the y axis, while the τ
field along the x axis is heterogeneous. The magnitude of decrease of
Pτ2(Lx,Ly) with increasing Lx and Ly depends on the
horizontal structure of the cloud inhomogeneities. The Pτ2(Lx,Ly) calculated from Ci-01 (Fig. b) show a decrease
independent of the direction. In contrast, the Pτ2(Lx,Ly)
calculated from Ci-03 (Fig. d) show a directional dependence.
(a) Selected cloud scene (3.5 km by 3.5 km) for field of
τci from case Ci-01. (b) Colour-coded 2-D field of
Pτ2(Lx,Ly), calculated for field of τci from
panel (a). The blue and red lines illustrate the pixel lags selected
for the illustration in Fig. a. The white line illustrates
ξτ at Pτ2(Lx,Ly)= 1/e2. (c) Same
as panel (a) for case Ci-03. (d) Same as panel (b)
for selected τci field shown in panel (c).
The squared spatial autocorrelation functions Pτ2(Lx,Ly) are
used to calculate the decorrelation length
ξτ=Lx2+Ly2 implicitly defined by
Pτ2ξτ=1e2.
Here, ξτ quantifies the length scale (in metres) where
individual cloud parcels are decorrelated; it provides a measure of the
horizontal extent of cloud inhomogeneities. Strong inhomogeneities correspond
to small ξτ. In Fig. b and d, ξτ is
indicated by a white line. For Ci-01, ξτ forms a circular shape,
indicating a similar magnitude of cloud inhomogeneities in all directions of
the cloud field. Conversely, for Ci-03, ξτ along pixel lag
Lx is significantly smaller than ξτ along pixel lag
Ly. This directional dependence is related to the structure of the
cloud with regular filaments in the swath direction of the image in
Fig. c. For case Ci-01, the symmetry in Pτ2(Lx,Ly) means that the cloud inhomogeneity can be characterized by
a single value ξτ, independent of direction. For regularly structured
clouds such as Ci-03, however, the 2-D decorrelation can be split into
a component of the largest variability and another one along the smallest
variability of τ. In the cloud fields presented here, both major axes
align with the x and y directions. One-dimensional autocorrelation functions along the
axes of strongest (↔, red line in Fig. b and
d) and weakest (↕, blue line in Fig. b
and d) variability are provided in Fig. a and
b. To derive quantitative values for ξτ↔
and ξτ↕ in SI units of metre, the pixel lag is
transformed into horizontal distances by multiplying the number of pixels by
their pixel size.
(a) Average of squared 1-D autocorrelation functions
Pτ2(Lx,Ly) (solid lines) calculated for pixels, which are
orientated into the direction of the blue (Lx) and red lines (Ly)
illustrated in Fig. b. The dashed lines mark the derived distance
of the decorrelation length ξτ, where Pτ2(Lx) and
Pτ2(Ly) are decreased to 1/e2. (b) Same as
panel (a) for Pτ2(Lx,Ly) shown in
Fig. d.
For case Ci-01 (Figs. a, b, and a), the
derived Pτ2(Lx,Ly) along and across the prevailing
directional structure are similar and
ξ‾τ↕=1.14 km compares well with
ξ‾τ↔=1.02 km within the range of standard
deviation given in Table . For case Ci-03 (Figs. c,
d, and b), the Pτ2(Lx,Ly)
along and across the prevailing directional structure differ significantly
from each other and ξ‾τ↕=5.03 km is about
6 times larger than ξ‾τ↔=0.91 km. Thus, for
clouds with a prevailing directional structure it is advisable to give
variable ξτ as a function of observational direction, e.g., by two
parameters, ξτ↕ along and ξτ↔
across the prevailing cloud structure.
Decorrelation length calculated for the retrieved fields of τ
from the CARRIBA (Ci-01–Ci-04) and VERDI (St-01–St-10) campaigns. Vertical
arrows (↕) indicate the calculation of Pτ2(Lx,Ly) and subsequent derivation of ξτ along Ly, horizontal
arrows (↔) along Lx. Furthermore,
ξ‾τ is the average of all pixels,
ξ‾τ-σξ is the average minus standard deviation,
and ξ‾τ+σξ is the average plus standard
deviation.
The decorrelation lengths are calculated for each measurement case along
(ξ‾τ↕) and across
(ξ‾τ↔) the prevailing directional structure of
the cloud inhomogeneities, which is identified by the 2-D autocorrelation
analysis. Table summarizes and Fig. illustrates the
resulting ξ‾τ↕ (blue bars) and
ξ‾τ↔ (red bars). Additionally,
ξ‾τ±σξ are included
(ξ‾τ↕±σξ, ξ‾τ↔±σξ)
in Table . Those values illustrate the pixel-by-pixel variability
for the calculated Pτ2(Lx,Ly) along one direction.
Due to the exponential behaviour of Pτ2(Lx,Ly), they
are asymmetric with respect to ξ‾τ↕ and
ξ‾τ↔.
The results show that the observed subtropical cirrus cases yield larger
decorrelation lengths ξ‾τ than the Arctic stratus cases. Thus,
the subtropical cirrus cases are more homogeneous than the Arctic stratus
cases. Furthermore, the results indicate that for most of the measurement
cases a distinct directional structure of cloud inhomogeneities is observed.
The results for ξ‾τ↕ are more than twice as large as for
ξ‾τ↔ in 9 of the 14 investigated cases.
Decorrelation length calculated for the retrieved fields of τ
from the (a) CARRIBA (Ci-01–Ci-04) and (b) VERDI
(St-01–St-10) campaigns. Vertical arrows (↕) indicate the
calculation of Pτ2(Lx,Ly) and subsequent derivation of
ξτ along Ly, horizontal arrows (↔) along
Lx.
For the subtropical cirrus cases, ξτ varies from 0.82 to 5.03 km,
depending on the cloud structure and inhomogeneity. The rather inhomogeneous
cases Ci-01 and Ci-04, with highly variable τci on small scales,
yield rapidly decreasing Pτ2(Lx,Ly) with low
ξ‾τ. In contrast, the quite homogeneous cases Ci-02 and
Ci-03 yield slowly decreasing Pτ2(Lx,Ly) and larger
ξτ‾. The differences between
ξ‾τ↕ and
ξτ‾↔ reach up to
82 %.
For the Arctic stratus fields observed during VERDI,
ξ‾τ↕ and ξ‾τ↔ range
between 0.09 and 1.12 km. Similar to the CARRIBA cirrus cases, the
differences between ξ‾τ↕ and
ξ‾τ↔ are significant, reaching values of up to
84 %.
However, the absolute values of ξ‾τ↕ and
ξ‾τ↔ for the Arctic stratus cases are smaller (more
inhomogeneous) than those for the subtropical cirrus cases, although the 1-D
inhomogeneity parameters from Table yield similar values. This
reveals that the 1-D inhomogeneity parameters ρτ, Sτ, and
χτ just provide incomplete information for a comparison of
different types of clouds since they are not able to consider the horizontal
structure of cloud inhomogeneities. Differences can only be observed by an
evaluation of the horizontal pattern of the cloud inhomogeneities.
(a–c) AisaEAGLE image (3.5 km by 3.5 km),
(d–f) 2-D power spectral density E(kx,ky), and
(g–i) 1-D power spectral density E(kx,ky) across (red
arrows, Ea) and along (black arrows, Eb) the prevailing direction
of scale-invariant areas for (a, d, g) inhomogeneous cloud without
directional structure, (b, e, h) homogeneous cloud with slight
directional structure, and (c, f, i) inhomogeneous cloud with
distinct directional structure. The ξτ,s are marked by
dashed coloured lines.
Power spectral density analysis
Multiple scattering in inhomogeneous 1-D cloud structures causes a smoothing
of the reflected radiances Iλ above clouds
. This effect generates uncertainties in
the retrieved fields of τ if homogeneous plane-parallel clouds are
assumed in the retrieval. Therefore, in this paper the smoothing effect is
analysed using the Fourier transform of the retrieved fields of τ. The
application of Fourier transforms for the investigation of cloud
inhomogeneities is widely used in the existing literature
e.g.,. However, in most
of these studies, the 1-D Fourier transformation is adopted to narrow pixel
lines of radiative quantities such as Iλ or the reflectivity
γλ. Here, a 2-D Fourier transformation is applied to spatial
2-D cloud scenes. showed that angular features of the
scattering phase functions are imprinted in the Iλ measurements of
AisaEAGLE. To avoid artefacts in the Fourier transform arising from those
features, fields of τ are used for the analysis.
The Fourier transformation decomposes a periodic function into a sum of
sinusoidal base functions. For a given measurement, here τ(x,y), the 2-D
Fourier transform Fτ(kx,ky) is defined by
Fτkx,ky=∫-∞∞∫-∞∞τ(x,y)×e-2πi×kxx+kyydxdy.
The base functions are described by a complex exponential of
different frequency. The fields of τ are given as a function of
horizontal distances x and y. Therefore, wave numbers kx=1/x
and ky=1/y are used in the base functions.
The Fourier coefficients Fτ(kx,ky) are calculated
using a discrete Fourier transform (DFT). With n and m discrete elements
in the xj and yk dimension of the τ field, the 2-D DFT is
derived by
Figures and present the Fourier transform
in the form of power spectral densities E(kx) and E(ky),
in the following called E(kx,ky), calculated from the
complex Fourier coefficients by
E(kx,ky)=DFT2kx,ky.
One-dimensional power spectral density E(ky) (gray dots) for each spatial
pixel on the swath axis of the τ field from (a) case Ci-01 and
(b) case St-07. Scale-invariant slopes β are marked with
solid coloured lines. The E(krn) derived from the octave binning are
included as dark green diamonds. Scale breaks ξτ,L and
ξτ,s are indicated by dashed lines.
Figure a–c show τci fields of three
selected cloud areas of 3.5 km by 3.5 km size extracted from the cases
Ci-01, Ci-02, and Ci-03. Ci-01 represents an inhomogeneous subtropical cirrus
case without a preferred direction in the cloud structure (Fig. a). In
Ci-02 a homogeneous subtropical cirrus case with a moderate directional structure
(Fig. b) is selected, while in Ci-03 an inhomogeneous subtropical
cirrus case with a distinct directional structure (Fig. c) is
presented. Figure d–f show the corresponding
logarithm of the 2-D power spectral densities E(kx,ky).
The largest values of E(kx,ky) are found at the smallest wave
numbers kx and ky, which are located in the centre of the
image. In general the values of E(kx,ky) decrease with
increasing kx and ky. Inhomogeneous clouds
(Fig. d and f) show higher values of E(kx,ky) over a wide range of wave numbers kx and ky,
whereas the dominating E(kx,ky) for homogeneous clouds
(Fig. e) are only located close to the smallest wave numbers
kx and ky. Similar to the autocorrelation functions, the
decrease of E(kx,ky) is rotationally symmetric for clouds
with no preferred directional structure (Fig. d), but
asymmetrical for clouds with a prevailing directional structure
(Fig. e, f).
To quantify the 2-D nature of the symmetry, Fig. g–f show the E(kx,ky) along (black,
Eb) and across (red, Ea) the direction of the strongest
symmetry axis. For the inhomogeneous case without a prevailing directional
structure (Ci-01), both components Ea and Eb are almost
identical. For the homogeneous case with a moderate directional structure
(Ci-02), both Ea and Eb are similar over most of the
covered range of kx and ky, except for the smallest wave
numbers kx<3 km-1 and ky<3 km-1. For
the inhomogeneous case with a distinct directional structure (Ci-03), both
Ea and Eb are of similar magnitude only at
kx>7 km-1 and ky>7 km-1. The
differences in Ea and Eb of clouds with a prevailing
directional structure result from the different kx and
ky, at which the signal turns into white noise (constant
E(kx,ky), independent of kx and ky).
This transition is used to characterize the small-scale break
ξτ,s, which determines the lower size range of the detected
cloud inhomogeneities and identifies the scale at which the measurements turn
into white noise. To derive ξτ,s, fits are applied to the
two scale-invariant regimes of E(kx,ky) (shown for
Eb in Fig. i). Subsequently, the small-scale break
ξτ,s is determined as the intersection of those fits. The
small-scale break ξτ,s is connected to the pixel size, which
depends on the distance between cloud and sensor. The corresponding
kx and ky give ξτ,s. The small-scale
breaks ξτ,s(Ea) and
ξτ,s(Eb) for case Ci-01 are at about 0.03 km
(log2kx,y≈5). For Case Ci-02,
ξτ,s(Ea) and ξτ,s(Eb) are
in the length range of 0.09 km (log2kx,y≈3.5) and
0.03 km (log2kx,y≈5), respectively. The small-scale
break ξτ,s(Ea) from case Ci-03 is at about 0.03 km
(log2kx,y≈5), while ξτ,s(Eb) is
at about 0.01 km (log2kx,y≈6.5), which is already close
to the pixel size, which corresponds to the lower detection limit that leads
to white noise. Thus, ξτ,s yields quantitatively larger
values along the prevailing cloud structure than across. Furthermore, the
ranges of the derived small-scale breaks ξτ,s are found to
be close to the ranges of the small-scale breaks reported in literature.
derived small-scale breaks for
a broken-stratocumulus–towering cumulus cloud complex from LWC measurements
with a particulate volume monitor probe (4 cm resolution) at ranges of about
2–5 m. They proposed that those small-scale breaks are related to extreme
values in the detected LWC, which appear on small horizontal scales. Aside
from Poissonian fluctuations of the cloud optical thickness τ and the white
noise related to power spectral signals at scales below the pixel size, this
might be a further explanation for the derived small-scale breaks in the
current study and needs to be investigated in further studies.
discussed cloud inhomogeneity and horizontal photon
transport being scale-dependent processes. The E(kx,ky) of
cloud optical and microphysical properties are proportional to
kxβ and kyβ, where β is the slope of
the power spectral density. On large scales, the E(kx,ky)
of Iλ, τ, LWC, or IWC, for example, follow Kolmogorov's β=-5/3
law of energy distribution in a turbulent fluid . On
these scales, the variability in the radiation field follows the variability
in LWC. Increasing cloud inhomogeneity causes a decrease of β of
optical properties on smaller scales, but not in β of microphysical
properties. On scales influenced by horizontal photon transport, β may
differ from -5/3 depending on the cloud inhomogeneity that changes the
magnitude of horizontal photon transport. Typically, this affects horizontal
scales smaller than 1000 m. The higher the cloud inhomogeneity, the larger
the deviation from -5/3. Thus, the slope β at scales below 1000 m
provides a measure of cloud inhomogeneity. Usually, the scale break ξ is
used to quantify the deviation from -5/3. In the following, the horizontal
scale at which the power spectrum starts to deviate from the -5/3 law defines
the large-scale break ξτ,L. The position of the large-scale
break depends on the size of the horizontal cloud structures; more
inhomogeneous clouds with larger variability on smaller scales yield smaller
ξτ,L. For scales smaller than ξτ,L, the
radiative smoothing leads to uncertainties in 1-D cloud retrievals, where the
horizontal photon transport is automatically neglected .
A comparison of the E(kx,ky) to the -5/3 law in
Fig. g to h shows that the analysed scenes are too
small to cover the larger scales, which are necessary to identify
ξτ,L. The range of kx and ky is lower
than ξτ,L, and E(kx,ky) already exhibit
a steeper slope than β=-5/3. Therefore, the size of the selected
areas was extended. Unfortunately, this is only possible for calculations of
the DFT along Ly (across swath). Calculations along Lx
(swath) do not cover a sufficiently large distance to derive quantitative
values for ξτ,L. Therefore, the following analysis is
performed using 1-D DFT along Ly only. Furthermore, both cloud
cases, subtropical cirrus and Arctic stratus, exhibit a similar pixel length
along Ly (5 ± 2 m), which results from the chosen frame rate
(subtropical cirrus: 4 Hz, Arctic stratus: 30 Hz) and given cloud
(≈ 20 m s-1) and aircraft (≈ 70 m s-1)
velocity. This allows a direct comparison between these two different cloud
types with different observation geometry.
Figure a and b show the 1-D DFT calculated across the
swath for two typical cases of subtropical cirrus (CARRIBA case Ci-01) and
Arctic stratus (VERDI case St-07). The two cases are selected because they
exhibit a similar length Ly. For each line of the τ field
(each swath pixel) E(ky) is calculated and the individual power
spectra are overlaid as grey dots in Fig. . To evaluate the
resulting 1-D Fourier spectra with reduced noise (rn) characteristics, the
Ern(k)∼kβ are calculated with the use of octave
binning, following the method proposed by ,
, and . Logarithmically spaced bins
kn are calculated by
kn=12n∑i=2n2n+1-1ki,n=1,2,…,log2(N-2),
for the number of data points N. E(krn) is then
obtained by
Ekrn=12n∑i=2n2n+1-1E(ki),n=1,2,…,log2(N-2).
Within each bin 2n data points are averaged. In addition to the
reduced noise of E(krn) compared to E(ky) the binning
provides a uniform contribution of all scales to the average values.
The E(krn) derived from the octave binning are included as green
diamonds in Fig. . The data of the octave binning were used to fit
the spectra for different slopes in the different scale ranges. A green line
indicates the β=-5/3 law. For large scales, the
Ern(ky) (blue fit) approximately follow the -5/3 relation
in both cases. The large-scale break (ξτ,L) is evident at
the intersection between the blue and the red line. Here, the slope in the
Ern(ky) becomes steeper. For the CARRIBA case,
ξτ,L= 0.31 km and the middle-scale slope βm decreases to -2.2. For the VERDI case
ξτ,L=0.06 km and βm decreases to -2.2. The
middle-scale slope βm is a function of the inhomogeneity in
the measured signals. With increasing inhomogeneity of the optical thickness
τ, βm decreases. Together with the smaller
ξτ,L, this indicates that the selected Arctic stratus case
is more inhomogeneous compared to the selected subtropical cirrus case. As
discussed above, ξτ,s is observed at the intersection
between the fits for the middle (red, βm) and small scales
(orange, βs). Due to the analysis of a significantly larger
distance compared to Fig. , it is highly uncertain to give
quantitative numbers for ξτ,s. Therefore, it is indicated
only qualitatively. However, ξτ,s identifies at which scales
the measurements turn into noise. The scale depends on the distance between
sensor and cloud. For the sensor, noise dominated at scales 2 times the pixel
range, which corresponds to about 15 m for the subtropical cirrus
observations (≈ 12 km cloud base altitude) and 3.5 m for the
Arctic stratus observations where the aircraft was closer to cloud top
(≈ 2 km distance).
Figure illustrates ξτ,L for all available cloud
cases from CARRIBA and VERDI. Especially the values for the Arctic stratus
are in the size range that was also reported by , who
found scale breaks for fractal clouds in the range of 200–500 m.
Furthermore, the values compare well with the derived decorrelation length
ξτ derived in Sect. . Although the exact values of
ξτ,L are not equal to ξτ, both are in the same size
range for each individual case. Similar to ξτ given in
Table , ξτ,L confirms that Ci-02 and Ci-03 are
more homogeneous than Ci-01 and Ci-04. Furthermore, the resulting large-scale
breaks ξτ,L confirm the results from the derived
decorrelation lengths ξτ that the subtropical cirrus observed
during CARRIBA are more homogeneous (larger ξτ and
ξτ,L) than the Arctic stratus from VERDI (smaller
ξτ and ξτ,L). This is related to the fact that
ξτ,L, which is the radiative smoothing scale, is a function
of the cloud geometrical thickness and the transport mean free path. For
Arctic stratus both parameters are significantly smaller than for subtropical
cirrus.
Across swath-derived large-scale breaks, ξτ,L for
the retrieved fields of τ from the (a) CARRIBA (Ci-01 to Ci-04,
red) and (b) VERDI (St-01 to St-10, blue) campaigns. The values were
derived using the method presented in Fig. .
An estimation of the uncertainty in the derived ξτ,L can be
obtained from a comparison to investigations performed by
. Amongst others, investigated
scale breaks as a function of wavelengths and absorption bands. Their results
show uncertainties in a range of 3 to 8 %.
derived those uncertainty values by subsetting the points of the power
spectrum that are used for the slope fit. Using this method, they obtained
a set of different slopes and scale breaks. The particular standard
deviations of those sets are used as an uncertainty for the octave binning
method. Applied to the VERDI cases, the 3 to 8 % result in
a maximum uncertainty of ±5 m (St-07) to ±15 m (St-03, St-09)
in the derived ξτ,L. For the CARRIBA cases the maximum
uncertainty is in the range of 16 (Ci-04) to 226 m (Ci-03). However,
case Ci-03 is especially characterized as rather homogeneous.
Therefore, much lower uncertainty values are to be expected.
Summary and conclusions
During the two field campaigns CARRIBA and VERDI, downward (ground-based) and
upward (measured from aircraft) fields of solar spectral radiance
(Iλ↓, Iλ↑) were measured with
high spatial resolution (less than 10 m), using the imaging spectrometer
AisaEAGLE. The measured radiance fields were used to retrieve fields of
τ, which were subsequently analysed to quantify horizontal cloud
inhomogeneities. Furthermore, due to the observation of 2-D fields, the
prevailing directional structure of the cloud inhomogeneities was
investigated.
Four subtropical cirrus cases collected during CARRIBA and 10 Arctic stratus
cases sampled during VERDI were studied in detail. The cloud inhomogeneity
was quantified by three 1-D inhomogeneity parameters
ρτ, Sτ, and χτ, 1-D and
2-D autocorrelation functions, and Fourier analysis.
Considering the pixel and domain size of the analysed measurements, the
results from the calculated 1-D inhomogeneity parameters ρτ and Sτ are in agreement with values given in the literature for similar
cloud types. The calculated ρτ are in the range of 0.17–0.91 for
the subtropical cirrus observed during CARRIBA and 0.15–0.34 for the Arctic
stratus measured during VERDI. The literature values are in the range of
0.07–0.78. The inhomogeneity parameter Sτ exhibits values of 0.08
to 0.48 for CARRIBA and 0.07 to 0.20 for VERDI, which agrees with values of
0.03 to 0.3 given in literature. For χτ, the literature estimates
values between ≈ 0.65 and 0.8, while the results from CARRIBA and
VERDI are significantly larger. This is probably related to the different
pixel and domain sizes. All values except for Ci-04 (χτ= 0.63)
are in the range between 0.92 and 0.99. A further comparison between the
results for the clouds encountered during CARRIBA and VERDI showed that all
three 1-D inhomogeneity parameters exhibit values of similar magnitude for
both cloud types; subtropical cirrus and Arctic stratus. This might lead to
the conclusion that the inhomogeneity of both cloud types could be treated by
the same 1-D inhomogeneity parameters.
However, the comparison of the 2-D analysis of squared autocorrelation
functions Pτ2(Lx,Ly) with the 1-D inhomogeneity
parameters ρτ, Sτ, and χτ showed that it is
important to consider the full horizontal structure of clouds using 2-D
analysis rather than 1-D analysis when determining cloud inhomogeneity. For
both cloud cases (subtropical cirrus, Arctic stratus) the 1-D inhomogeneity
parameters yield similar values, but significant differences result from
the analysis of Pτ2(Lx,Ly), which additionally
contain information about the horizontal structure of cloud inhomogeneities.
The 1-D inhomogeneity parameters are not capable of differentiating the
directional structure of clouds and may lead to misinterpretations of cloud
inhomogeneity. From the squared autocorrelation functions
Pτ2(Lx,Ly) the decorrelation length ξτ
was derived, which is a measure of the size range of the cloud
inhomogeneities. The 2-D analysis of Pτ2(Lx,Ly)
revealed that ξτ is a function of the directional structure of the
cloud inhomogeneities. Without knowledge of the directional structure of
cloud inhomogeneities, no universally valid value for ξτ can be
derived from the retrieved fields of τ. The differences in ξτ
as derived from a 1-D autocorrelation analysis along and across the prevailing
structure of cloud inhomogeneities reached up to 82 and 84 % for
CARRIBA and VERDI, respectively. It is concluded that the directional cloud
structure has to be taken into account for a quantification of cloud
inhomogeneities. The absolute values of ξτ were in the range of
0.82 to 5.03 km for CARRIBA and 0.09 to 1.12 km for VERDI.
Furthermore, the results from the 2-D analysis showed that for the observed
cloud cases the subtropical cirrus was more homogeneous than the Arctic
stratus. This result was not available from the investigation of the commonly
used 1-D inhomogeneity parameters. Therefore, using 2-D methods in future
studies for the characterization of cloud inhomogeneities is advisable since
their information content exceeds the information content of the commonly
used 2-D inhomogeneity parameters. Today, 2-D images of cloud fields are
widespread by measurements of all-sky cameras or satellite observation
with high spatial resolution, for example. Applying the presented methods to such
continuous measurements would provide detailed views into the climatology of
cloud inhomogeneities.
Three-dimensional radiative effects are quantified by applying 2-D Fourier transformation to
the retrieved fields of τ. The power spectral densities
E(kx,y) calculated from the Fourier transform of
Iλ↓ and Iλ↑ show evidence that
3-D
radiative effects did affect the radiation field of both cloud types,
subtropical cirrus and Arctic stratus. For larger scales (> 1000 m), no
horizontal photon transport was observed because the E(kx,y) followed
Kolmogorov's -5/3 law. Approaching smaller scales (< 1000 m), the derived
slopes become steeper, indicating radiative smoothing by cloud inhomogeneities
and horizontal photon transport. From the intersection of fits of the three
slope regimes, the small-scale break ξτ,s (between small-
and middle-scale slopes) and the large-scale break ξτ,L
(between middle- and large-scale slopes) were derived. Similar to the
analysis using autocorrelation functions, ξτ,s depends on
the directional structure of the cloud inhomogeneities. Due to a too-small
swath width, a similar analysis for ξτ,L could not be
performed. However, the calculated ξτ,L along the image are
comparable to the results derived from the analysis of Pτ(Lx,Ly). The large-scale break ξτ,L for CARRIBA was in
the range of 0.20 to 2.83 km. For VERDI a range of 0.06 to 0.19 km
was covered by ξτ,L.
In early studies, by or for example, the
scale dependence of cloud radiation measurements was analysed along one
direction (narrow pixel lines) using 1-D DFT. However, the resulting E(k)
are valid for the particular observation direction along the given path only.
Due to prevailing wind directions, clouds tend to evolve directional
structures. In such cases, the calculated E(k), β,
ξτ,s, and ξτ,L will only be valid for the
whole cloud if the cloud structure exhibits a nondirectional character
(compare Figs. b and a). In all other cases,
significant differences can be expected (compare Figs. d and
b). We found such differences for more than half of the
observed cloud scenes. Therefore, the directional structure of cloud
inhomogeneities should be taken into account when cloud inhomogeneities are
characterized. It is expected that the information content derived from the
directional analysis of cloud inhomogeneities can clearly improve sub-grid
scale parametrizations in weather and climate models. For this, depending on
the application, the decorrelation length (size and structure of cloud
inhomogeneities) or the scale breaks (horizontal photon transport, 3-D
radiative effects) may provide better proxies compared to commonly used 1-D
inhomogeneity parameters.
However, so far only two cloud types were investigated. To build up a better
idea on cloud inhomogeneity of different cloud types, more high definition
observations of cloud fields are needed. Aside from dedicated field campaigns,
continuous observations by all-sky cameras or satellites with high spatial
resolution such as Landsat (15–90 m resolution) or ASTER (Advanced
Spaceborne Thermal Emission and Reflection Radiometer, 15–90 m resolution)
may provide the required data.
The 1-D and 2-D autocorrelation functions and Fourier analysis in conjunction
with the derived decorrelation length and scale break are helpful tools to
verify cloud-resolving models in terms of typical horizontal cloud
geometries.
Data availability
The data used in this study are available upon request from the corresponding
author (michael.schaefer@uni-leipzig.de).
Acknowledgements
This study was supported by the German Research Foundation (Deutsche
Forschungsgemeinschaft, DFG) as part of the CARRIBA project (WE 1900/18-1 and
SI 1534/3-1). We gratefully acknowledge the support by the SFB/TR 172
“ArctiC Amplification: Climate Relevant Atmospheric and SurfaCe Processes,
and Feedback Mechanisms (AC)3” in Project B03 funded by the DFG. We thank
the Max Planck Institute for Meteorology, Hamburg, for supporting the
ground-based radiation measurements with the infrastructure of the Barbados
Cloud Observatory at Deebles Point on Barbados. We are grateful to the Alfred
Wegener Institute Helmholtz Centre for Polar and Marine Research,
Bremerhaven, Germany, for supporting the VERDI campaign with the aircraft and
manpower. In addition we would like to thank Kenn Borek Air Ltd., Calgary,
Canada, for the great pilots who made the complicated measurements possible.
For excellent ground support with offices and accommodations during the
campaign we are grateful to the Aurora Research Institute, Inuvik,
Canada. Edited by: M. Shupe
Reviewed by: three anonymous referees
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