“Albedo dome”: a method for measuring spectral
flux-reflectance in a laboratory for media
with long optical paths
BONNIE LIGHT,
1,2,* REGINA C. CARNS,
3 AND STEPHEN G. WARREN2,3
1
Polar Science Center, Applied Physics Laboratory, University of Washington, Seattle, Washington 98105, USA
2
Department of Atmospheric Sciences, University of Washington, Seattle, Washington 98195, USA
3
Department of Earth and Space Sciences, University of Washington, Seattle, Washington 98195, USA
*Corresponding author: bonnie@apl.washington.edu
Received 7 January 2015; revised 23 April 2015; accepted 24 April 2015; posted 4 May 2015 (Doc. ID 232083); published 2 June 2015
A method is presented for accurate measurement of spectral flux-reflectance (albedo) in a laboratory, for media
with long optical path lengths, such as snow and ice. The approach uses an acrylic hemispheric dome, which,
when placed over the surface being studied, serves two functions: (i) it creates an overcast “sky” to illuminate the
target surface from all directions within a hemisphere, and (ii) serves as a platform for measuring incident and
backscattered spectral radiances, which can be integrated to obtain fluxes. The fluxes are relative measurements
and because their ratio is used to determine flux-reflectance, no absolute radiometric calibrations are required.
The dome and surface must meet minimum size requirements based on the scattering properties of the surface.
This technique is suited for media with long photon path lengths since the backscattered illumination is collected
over a large enough area to include photons that reemerge from the domain far from their point of entry because
of multiple scattering and small absorption. Comparison between field and laboratory albedo of a portable test
surface demonstrates the viability of this method. © 2015 Optical Society of America
OCIS codes: (120.0120) Instrumentation, measurement, and metrology; (280.0280) Remote sensing and sensors; (120.3150)
Integrating spheres; (120.5630) Radiometry; (120.5820) Scattering measurements; (160.4760) Optical properties.
http://dx.doi.org/10.1364/AO.54.005260
1. INTRODUCTION
The flux-reflectance, or “albedo,” is the fraction of incident
solar radiation backscattered by a planetary surface, cloud, or
the Earth–atmosphere system. The surface albedo is a major
determinant of the surface heat budget. Quantitative information
about the surface heat budget is essential for an understanding
of climate. Regions of the planet with high surface
albedo (e.g., snow, ice) respond differently to solar heating than
regions with low surface albedo (e.g., water, wet soil, tundra,
forest). Such contrasts in surface albedo can lead to climatically
sensitive feedback. One example of this contrast occurs in the
polar oceans, where the open ocean has broadband (visible
and near-infrared) albedo of typically less than 0.1 [1] and
the frozen sea surface has broadband albedo of typically
0.4–0.9, depending on the state of the ice surface [2]. This contrast
drives a positive feedback [3,4] capable of amplifying ice
retreat or expansion. Our present understanding of Earth’s
climate indicates that this sensitive positive feedback has been
contributing to the anomalously large temperature increases
seen at high latitudes in response to increased greenhouse gases
in Earth’s atmosphere [5–8]. While gross features of Earth’s
climate can be understood with knowledge of the spatially averaged
planetary albedo, the most informative climate models require
detailed information about the spatial and temporal
distribution of albedo of different surface types and states.
Ground-based measurement of surface albedo in a field
setting is typically straightforward (for example, see work by
Levinson et al. [9]). If a relatively small area (approximately
12 m2) of the surface can be considered representative, and
the measurement site is accessible during sunlit hours, then
albedo measurement requires little more than a single radiometer
outfitted with an appropriate cosine collector (for example,
see Grenfell et al. [10]). The radiometer is turned upward
to measure the downwelling irradiance (flux), then turned
downward to measure the backscattered irradiance. The ratio
of the two irradiances is the albedo for that surface type.
Measurements of homogeneous and planar surfaces are the
most generally applicable. The plane of the radiometer should
be parallel to the surface. If the surface is horizontal, a leveling
device on the radiometer ensures that the respective fields
of view capture only the surface and only the sky. Spectral
data provide the most broadly applicable estimates; broadband
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measurements are inherently dependent on the spectral distribution
of incident radiation. Measurements made under cloud
cover, where incident light is notably more diffuse, are most
accurate, because errors caused by surface slope and tilt of the
radiometer are then minimized. Measurements made while the
ambient illumination is constant over the measurement interval
provide the highest quality data. If the radiometer and accompanying
support are properly configured, then the need for
shadowing corrections is minimized to typically a few percent.
Figure 1 shows a “field” albedo being measured over the test
surface used in this study. In this example, approximately 90%
of the backscattered irradiance originates from within a 2 m
radius, centered directly beneath the radiometer. For the purpose
of building predictive tools, the most useful measurements
are made over uniform surface type under either complete overcast
skies or beneath clear skies with documented sun angle.
While measurements of naturally occurring surfaces under
naturally occurring illumination are essential, there is also
need for techniques to make albedo measurements in the laboratory.
The ability to study surfaces that can be controlled,
manipulated, or altered is necessary when such surfaces form
only under unique conditions, are inaccessible in the field,
or are useful proxies for past or future climates. Techniques
for making laboratory albedo measurements exist, but they
generally require more specialized corrections than their field
albedo counterparts. Finite surface extent, artificial illumination,
multiple light reflections in a confined space, instrument
shadows on the surface, and unnatural variations in the angular
distribution of the incident illumination can be difficult to
characterize and control in the laboratory. Since field albedo
measurements are relatively simple, experiments carried out
in the laboratory sometimes extend that simplicity indoors,
in which a radiometer is used over the surface to look up
and look down, and the resulting ratio is assumed to be an accurate
estimate of the field albedo (for example, see Perovich
and Grenfell [11]). Such measurements ignore the possibility of
the instrumentation shadowing the surface, and there may be
no attempt to characterize the geometry of the incident light
field. More sophisticated techniques have been employed,
where an integrating sphere is used to measure the albedo of
a small sample volume [12]. In this case, however, only small
samples were measured and it was necessary to ensure that the
snow samples were densely packed to maximize the optical
depth and reduce the distance that radiation traveled in the
sample holder. To overcome this, corrections were necessary
for extending this finite sample size measurement to a measurement
appropriate for snow of infinite depth.
In some instances, where laboratory characterization of the
apparent optical properties of a material are needed, the albedo
is not quantified directly, but instead the angular reflectance
[13–15] or bidirectional-reflectance distributions (BRDF)
[16–20] are measured. While such measurements may contain
considerably more information about the optical response of a
surface than a simple albedo, and albedos may be calculated
from these reflectance measurements, they also require more
complex instrumentation and a more complicated measurement
protocol. Furthermore, calculation of albedo from a
BRDF measurement requires measurement of a standard of
known BRDF, and is limited to opaque surfaces and the albedo
resulting from direct illumination. While these various techniques
have merits, we desired a technique that would be useful
for characterizing the spectral albedo of laboratory-grown sea
ice under a variety of conditions, temperatures, and histories,
and where the need for corrections is minimized and the illuminated
area and viewing area are large enough to directly
capture the effects of multiple scattering radiative transport.
In particular, media with long optical paths require samples
and viewing geometries large enough to include photons that
travel significant horizontal distances within the domain before
reemerging to contribute to the backscattered light field. If the
domain is small, then transport of such photons may be interrupted
by the boundaries. If the viewing area is small, then photons
that emerge far from their entry point will not be sampled.
This paper describes an approach for making spectral albedo
measurements on media with long optical paths, grown and
maintained in a laboratory setting.
2. MOTIVATION FOR ALBEDO STUDIES OF
LABORATORY-GROWN SEA ICE
If the albedo of a specific surface type on Earth is needed, the
best approach is to travel to that surface and measure it directly.
However, surfaces in remote regions may be inaccessible and
some surfaces hypothesized to be prevalent in Earth’s past history
or in the future may not exist naturally on modern Earth.
Surrogates formed in the laboratory may be the only practical
way to study such surfaces.
Fig. 1. (a) Photograph of measurement of “field albedo” for the
white tarp test surface on a parking lot under overcast sky and schematic
of apparatus used to make the albedo measurement. The end of
the arm is equipped with a fiber optic cable that views a flat diffusely
reflecting plate. The cable is coupled to a spectroradiometer. The apparatus
in the schematic (b) is shown viewing the upward propagating
backscattered light field. The arm would then be rotated to measure
the downwelling incident light field. Photograph by B. Light.
Engineering and Laboratory Note Vol. 54, No. 17 / June 10 2015 / Applied Optics 5261
One such surface that has gained attention in our laboratory
is low-temperature sea ice. Paleoclimate records suggest periods
in Earth’s history known as “Snowball Earth” events, when
surface temperatures and moisture budgets would likely have
promoted the existence of bare, snow-free sea ice with temperature
below −23°C on the tropical oceans [21–23]. Ice such as
this is not seen on modern Earth, where the frozen sea surface is
typically covered by a layer of snow, which acts both to insulate
the surface thermally, such that the ice rarely becomes colder
than −23°C, and conceal it optically, so that the optical properties
of the ice itself rarely govern the surface albedo.
A distinguishing feature of ice grown on the ocean is the
incorporation of numerous inclusions of liquid seawater
throughout the ice matrix. For sea ice at moderate temperatures,
these inclusions remain at least partially liquid, but as
the ice is cooled, dissolved salts begin to precipitate [24]. In
particular, as the temperature drops below −23°C, crystals of
sodium chloride dihydrate (hydrohalite) begin to crystallize.
Light scattering from these crystals dramatically increases the
surface albedo of cold sea ice. While this surface type is presently
rare in nature [25], it is easily grown in the laboratory.
Sublimation of this cold sea ice at consistently low temperatures
would (after several years) result in a surface crust of hydrohalite
salt formed as a lag deposit. Such a crust does not exist on sea
ice anywhere on modern Earth, so it can be studied only in the
laboratory. Speculation that the albedo of this surface type
could be important for understanding the climate dynamics
of Snowball Earth has motivated the development of a technique
for reliably measuring the albedo of proxy surfaces grown
and maintained in a walk-in freezer laboratory and not accessible
using traditional field techniques.
3. APPROACH FOR LABORATORY ALBEDO
MEASUREMENT
The design of this tool for laboratory albedo measurement
was inspired by the concept of an integrating sphere, or in this
case, half-sphere. The hemisphere, or “albedo dome,” is large
enough to fit over the surface of our laboratory ice tank
(1.22 m × 1.12 m in horizontal extent) and serves two essential
functions: (i) the interior of the dome serves as a reflecting surface
for providing diffuse downwelling illumination of the ice
surface, and (ii) the dome itself serves as a platform for making
measurements to estimate both downwelling irradiance incident
on the surface and the upwelling irradiance backscattered
by the surface. Figure 2 shows a schematic of the basic elements
of the dome. The radius (R) of the dome is 61 cm, the location
of the reflecting plate is at the dome origin (R 0), and the
location of the footprint on the surface is at R∕2. A chimney for
light entry was cut in the top of the dome. A collimated light
source mounted exterior to the dome is directed into the dome,
through the chimney, and onto a diffusely reflecting plate
positioned on the ice surface. Light reflected from the plate
illuminates the diffusely reflecting dome interior, which in turn
illuminates the entire ice surface in the tank. The incident
illumination reaching the surface is designed to simulate an
idealized overcast sky. Estimates of the incident and backscattered
light fields at the surface are made using a single fiber
optic probe coupled to a spectroradiometer by viewing the
dome interior wall and the target surface through port holes
in the dome. The target surface is assumed to be approximately
uniform, but the albedo of only a small area, or “footprint,” is
actually measured. Details of each component of the design
follow.
A. Physical Layout
The maximum physical extent of the target surface and the
albedo dome are limited only by space and cost. The minimum
physical extent of the target surface and size of the dome are
limited by the optical properties of the surface being measured.
Media with relatively short optical path length can be measured
with a relatively small dome. Media with longer optical path
lengths require a larger dome for accurate measurement. If
the finite extent of the dome affects the albedo at the footprint
due to light leakage, either photons entering the study surface
from outside the dome or photons escaping the study surface
without detection, then the dome is not large enough. For example,
in a weakly absorbing medium such as snow or ice at
visible wavelengths, some of the light entering the surface from
above will travel horizontally to the wall and be absorbed there,
resulting in a low bias to the albedo estimate at wavelengths
where the albedo is high. The minimum size of the tank holding
the target surface requires that the measurement footprint
be sufficiently far from tank edges to minimize the measurement
of photons that have interacted with the walls of the
enclosure. Such an effect would be difficult to correct for in
this approach.
In the case of our cold sea ice, it was desired to measure the
albedo evolution for ice growth and demise, so surface types
with a wide variety of optical path lengths were studied.
We thus chose to create a surface and use a dome as large
as practical. The horizontal dimensions of the tank used for
growing the ice were 1.22 m × 1.12 m (height 1.24 m;
www.bonarplastics.com/Products/BagintheBox.aspx). We used
Fig. 2. Schematic of albedo dome over target surface. The dome
has radius R. The center of the measurement footprint is positioned
at R∕2. The illumination source is indicated with yellow lines. Wedges
indicate approximate fields of view, for example, measurement of
incident radiance profile (I k) and backscattered radiance profile at
0 deg (I up). I k and I up are measured with the fiber optic probe positioned
in the viewing ports on the dome. The height of the I up port is ffiffi
3 p
2 R above the ice surface. The dome used in this prototype has
R 61 cm.
5262 Vol. 54, No. 17 / June 10 2015 / Applied Optics Engineering and Laboratory Note
an acrylic prefabricated dome with 1.22 m diameter (http://
plastic-domes-spheres.com/plastic-domes/).
An acrylic dome was chosen because it was commercially
available, lightweight, rigid, and capable of being painted.
As purchased, the dome was transparent so it was necessary
to prepare both the interior and exterior surfaces. To maximize
the spectral reflectivity of the interior surface, it was painted
with six coats of white latex paint followed by eight coats of
white latex paint mixed with barium sulfate powder. When suspended
in paint, barium sulfate is known to have diffuse reflectivity
[26]. Tests were carried out to determine the maximum
concentration of barium sulfate that left the paint still applicable
(not too clumped) and with adequate bonding properties.
A mass concentration of 30% barium sulfate was used. The
goal for the surface preparation was to ensure that reflections
off the dome interior would be as isotropic as possible with as
high reflectivity as possible across the visible and near-infrared
spectrum (wavelengths 350–2500 nm).
The exterior surface was treated to prevent leakage of
ambient room light through the walls of the dome. To accomplish
this, a single layer of black landscaping plastic was affixed
to the exterior of the dome. Insulation was applied on top of the
black plastic to prevent the plastic from overheating, as it was
proximal to the light source, which occasionally became hot
(>60°C) when in use, even within the freezer laboratory.
Figure 3 shows a photograph of the dome positioned on top
of the tank. Locations on the dome (both interior and exterior)
are referenced using latitude (specified by elevation angle, θ)
and longitude (specified by azimuthal angle, ϕ). Three viewing
ports were cut in the dome for access by the fiber optic probe.
The longitude corresponding to the line of viewing ports is
arbitrarily assigned ϕ 0 and the three ports are at θ 60,
34.4, and 10.3 deg, corresponding to zenith viewing angles
of 0, 30, and 70 deg relative to the footprint. Each port opening
was about 1 cm in diameter and the θ 60° and 34.4° ports
were equipped with fiber holders with fixed viewing angle. The
θ 10.3° port was left open so that the fiber could scan
through the full range of angles to view the entire wall profile
on the opposite side of the dome interior.
B. Surface Illumination
The albedo dome was designed to illuminate the study surface
with diffuse light. We first attempted to accomplish this by
mounting a point light source at the origin of the dome, but
we were not successful at producing isotropic illumination.
Furthermore, the source generated excessive heat inside the
dome, which warmed the ice surface too much. A redesign of
the apparatus moved the lamp outside of the dome. A
tungsten–halogen bulb was positioned in a collimator (Oriel
66013 Lamp Housing with F∕0.7 fused silica condenser),
and the collimated beam output was aimed at a mirror with
broad spectral reflectivity (50-mm-diameter 1/10 wave mirror
with UV enhanced aluminum coating, Edmund Optics part
no. NT68-319) positioned on top of the dome. The mirror
was set at a 45 deg angle; it reflected the horizontal beam
downward through a 2 cm diameter entrance port cut in
the top of the dome. The addition of a mirror in the optical
path was necessary because of space limitations between the top
of the dome and the ceiling of the cold room (approximately
10 cm). Due to this constraint, it was not possible to mount a
light source with high intensity immediately above the dome.
The light-entry port was fitted with a 10 cm long pipe to baffle
the interior of the dome from stray light emanating directly
from the lamp and grazing the port. The downwelling beam
was aimed directly at a reflecting plate (20 cm in diameter) constructed
from 6.35 mm thick Spectralon material (Labsphere,
Inc.), which has approximate Lambertian reflectance. The plate
rested on a small aluminum frame positioned on the measurement
surface directly beneath the entrance port. Light reflected
from the plate then illuminated the entire dome interior. As in
an integrating sphere, multiple reflections between the highreflectivity
interior dome surface and the measurement surface
enhanced the diffuseness of the light field on the dome walls.
A 750 W tungsten–halogen bulb with broad spectral output
was chosen for the source. Since an albedo measurement is
made at each wavelength, and since this technique makes use
only of relative measurements, there was no need to simulate
the spectral composition of natural sunlight. The spectroradiometer
used for this study (FieldSpec Pro, manufactured by
Analytical Spectral Devices) has sensitivity between 350 and
2500 nm wavelength, so there was no advantage in supplying
illumination outside this wavelength range.
C. Estimation of Downwelling Irradiance
The downwelling irradiance (F↓) at the ice surface was estimated
by integrating measurements of the wall-leaving radiance
field [Iθ; ϕ ] on the dome interior. To compute F↓, values of
[Iθ; ϕ ] are weighted by the cosine of their respective elevation
angles and integrated over their respective solid angles:
F↓
Z 2π
0
Z π∕2
0
Iθ; ϕ cos θ sin θdθ dϕ: (1)
While the light leaving the dome wall was consistently diffuse,
it was never isotropic. The radiance leaving any one point was
assumed to be the same in all viewing directions, but radiances
leaving the upper parts of the dome were generally larger than
radiances leaving the lower parts. While Iθ; ϕ was known to
vary in θ, it was assumed to be invariant in ϕ. As a result, it was
desired to measure the radiance profile with as much resolution
Fig. 3. Dome, mounted inside the freezer laboratory. Annotations
show latitude (θ) and longitude (ϕ) reference frame and locations of
viewing ports (yellow stars). The lights seen in this photograph are the
room lights, which would normally be turned off during measurement.
The experimental light source is not shown in this image.
Engineering and Laboratory Note Vol. 54, No. 17 / June 10 2015 / Applied Optics 5263
in θ as practical. All Iθ were measured with the probe positioned
just inside the 10.3 deg viewing port. A positioning
guide was constructed from a piece of rigid acrylic to ensure
that the hand-held fiber cable could be reliably repositioned
at each viewing angle. Radiances were recorded at approximately
10 deg increments in θ, with the probe aimed at positions
on the dome interior corresponding to θ 0 to 90 along
ϕ 180 deg (directly opposite the port longitude). For the
convenience of summing discrete measurements, the Iθ
are denoted I k (where k 0 to 9 and θ 10k deg deg).
Two examples of measured I k profiles are shown in Fig. 4.
The profile with larger raw instrument counts was measured
above a fully developed hydrohalite crust with strong multiple
scattering. The profile with lower counts was measured over a
dissolving, wetted crust with weaker scattering. Clearly, the
magnitude, and to some degree the shape, of these profiles
depends on the character of the measurement surface. In fact,
if the surface were black (completely absorbing), the only
radiance reaching the dome walls would come directly from
the Lambertian reflecting plate and there would be no multiple
reflections within the dome. When viewed from any direction,
the radiance leaving the plate should be isotropic. The intensity
observed on the interior surface of the dome would not be
uniform, but would vary as sinθ. Figure 4 includes this curve,
although, since it was never measured, it is of arbitrary magnitude,
and should be used only for comparing its shape with the
other curves. If the measurement surface were also Lambertian,
the radiance profile on the dome wall would be uniform, as
would be found in a full integrating sphere.
Typically, measurements of the wall-leaving radiance were
made only at k 9, 8, 7, 6, 5, 4, and 3. Measurements at
k 2, 1, and 0 were impossible to make accurately because
the reflecting plate either partially or fully obscured the field
of view at these positions, contaminating the radiance measurement
with directly reflected light. A linear extrapolation from
the k 3, 4, and 5 measurements was used to estimate I k for
k 2, 1, and 0.
Equation (1) gives the downwelling irradiance at the dome
origin (R 0), and can be approximated as a sum over the
individual contributions from a discrete set of measured radiances,
I k. For this experimental setup, however, it is necessary
to compute the downwelling irradiance at the location of the
footprint (R∕2), not R 0. A coordinate transformation was
thus necessary for assigning an appropriate weight for each
measured radiance in the sum. Figure 5 illustrates the transformation,
where the green hemisphere indicates the albedo dome
on top of the ice surface. Green lines indicate constant θ and
constant ϕ. The red interior dome represents a virtual hemisphere
of arbitrary size centered on the target footprint
(R∕2, ϕ 0). Red lines on the virtual dome indicate lines
of constant elevation (θf ) for all azimuth angles (ϕf ) as referenced
to the transformed coordinate system of the footprint.
Red X’s indicate k 0 to 9 positions where the radiance
[Iθ ] is sampled on the dome wall and blue symbols show
latitudinal bands from the virtual footprint hemisphere (constant
θf ) projected onto the albedo dome. The integration
of downwelling irradiance at the footprint location (F↓
f ) is carried
out by summing the radiance penetrating through each red
band of constant θf onto the footprint location. Equation (1),
as applied to the target footprint, can be expressed as a sum of
the discrete measurements I k, weighted by coefficients Ck:
F↓
f X
k
CkI k: (2)
The derivation of the Ck values is documented in
Appendix A. For a footprint located at R∕2 and the height
of the ice surface aligned with the base of the dome, the values
of Ck (z 0) are given in the first row of Table 1 (z 0).
Equation (2) is computed using raw spectroradiometer counts
for I k values, a convenience made possible by the fact that this
albedo is a ratio of two radiometric quantities measured with
Fig. 4. Sample of typical downward radiance profiles incident on
the more strongly scattering high albedo surface of a salt crust on ice
and the lesser scattering surface of a low albedo melting ice surface.
Fig. 5. Illustration showing geometry of coordinate transformation
for calculation of downwelling incident irradiance at the location of
the footprint (center of small red dome). Green mesh indicates lines
of constant θ, ϕ on the albedo dome, the red dome is a virtual dome
centered on footprint, with lines of constant θf , red X’s indicate
locations where dome-leaving radiance is measured on the dome
interior, and blue circles are red circles projected on to the albedo
dome.
5264 Vol. 54, No. 17 / June 10 2015 / Applied Optics Engineering and Laboratory Note
the same instrument. To within round-off error, the sum of the
Ck coefficients is π.
These coefficients are valid when the ice surface is flush with
the base of the dome (z 0). When the ice surface is depressed
below the level of the dome base, the coefficients need to
be recalculated. This was frequently the case, as the height
of the ice surface was rarely predictable as the ice grew and sublimated.
For an ice surface 6.3 cm below the dome floor, the Ck
values are given in the second row of Table 1 (z −0.063 m).
This positioning necessitates an additional measurement of
radiance 10 deg below the base of the dome (k −1), which
falls on the inside wall of the ice tank, as the radiance leaving
the wall of the tank contributes to the total illumination on the
ice surface. The sum of Ck (z −0.063 m) is also approximately
π, as both integrations (z 0 and z −0.063 m) occur
only over the transformed coordinate system θf 0 to 90.
D. Estimation of Surface-Leaving Backscattered
Irradiance at the Footprint
The total backscattered irradiance leaving the footprint was
estimated by measuring the radiance field at the footprint location
and integrating [as in Eq. (1)] to estimate the upwelling
irradiance (F↑
f ). Radiance measurements were made using the
same bare fiber optic probe as the dome-leaving radiances, but
through the 60 and 34.4 deg viewing ports. Use of a bare fiber
viewed through the ports eliminates shadows that would appear
if a detector were physically placed inside the dome.
Since the incident radiance field was diffuse and the surface
approximately Lambertian, we assumed the surface-leaving radiance
distribution to be isotropic. Two measurements of the
surface-leaving radiance were recorded, one at 0 deg zenith
(looking straight down from the 60 deg port), and the other
at 30 deg zenith (viewed from the 34.4 deg port). We initially
attempted to collect radiance data also at 70 deg zenith angle
(viewed through the 10.3 deg port), but that measurement
proved to be unreliable since the finite acceptance cone of
the bare fiber made it difficult to avoid contamination by incident
light backscattered directly from the reflecting plate.
This made integration by standard quadrature methods impossible.
The integration of irradiance was carried out by assuming
isotropy of the upwelling radiance field, and so the two radiances
were simply averaged:
F↑
f π × avgI 0; I 30 :
I 0 and I 30 were typically within 10% of each other at all wavelengths.
Unlike the incident irradiance, integration of the backscattered
irradiance is independent of the height of the ice
surface relative to the dome floor.
4. VALIDATION
A validation test for the albedo dome was carried out by
comparing the field albedo of a white tarp surface measured
outdoors with the albedo dome technique applied to a sample
of the same tarp cut to fit and laid on top of the ice surface in
the laboratory ice tank. The two spectral albedos of the same
material, measured using the two different techniques, were
compared directly.
The albedo of a large (approximately 6 m × 9 m) white plastic
tarp was measured outdoors in a flat parking lot (see Fig. 1).
The field albedo measurements were made under uniform overcast
sky with relatively steady illumination. Ten albedo measurements
were made in succession and averaged to ensure
that the effects of small variations in illumination or spectroradiometer
leveling were minimized. The same spectroradiometer
that was used in the laboratory measurements was used to
measure the field albedo. For the field albedo measurements,
the spectroradiometer was outfitted with a cosine collector
for collecting upwelling and downwelling irradiances (as in
Fig. 1). The white tarp itself was not opaque, so a sheet of optically
thick black landscape plastic was laid down on the pavement
first. This served to protect the white tarp from getting
soiled, but the combination of plastic and tarp also served as an
optically thick, reproducible surface. Figure 6 shows the spectral
albedos of the tarp measured in the field using a cosine
collector and in the laboratory using the albedo dome.
5. DISCUSSION
A. Albedo Comparison
The field albedo measurement is an established technique, so
we treat it as “ground truth” for this comparison. Several tests,
however, were applied to the field albedo to verify its accuracy.
The effects of the finite size of the tarp were estimated by making
albedo measurements at a variety of locations proximal to
Table 1. Weighting Coefficients (Ck ) for the Computation of Downwelling Incident Irradiance at a Footprint Located
at R∕2
k −10 1 2 3 4 5 6 7 8 9
Ck z 0 m — 0.0555 0.3039 0.4972 0.5599 0.5321 0.4554 0.3544 0.2412 0.1219 0.0204
Ck z −0.063 m 0.0250 0.1732 0.4058 0.5050 0.5141 0.4712 0.3993 0.3107 0.2120 0.1074 0.0180
Fig. 6. Field and laboratory spectral albedo for white tarp test surface.
Individual gray lines indicate the 10 individual laboratory albedo
measurements made, and error bars indicate their standard deviation.
Engineering and Laboratory Note Vol. 54, No. 17 / June 10 2015 / Applied Optics 5265
the center of the tarp, but offset from it. No variation was observed,
so we conclude that no horizontal boundary effects were
observed in the field albedo measurement. However, a shadowing
correction was applied to the field albedo. Brandt et al. [27]
estimated a correction for the shadows of the instrument and
the operator using geometric analysis to be 1.7% for this particular
setup for diffuse incidence. We applied this correction
by multiplying the albedo at each wavelength by 1.017.
The field albedo could not be measured between 1350 and
1550 nm due to absorption of almost all natural insolation at
these wavelengths by atmospheric water vapor. Likewise, light
at wavelengths longer than 1800 nm is also strongly attenuated
by the atmosphere, so albedos tend to be noisy at these wavelengths,
as well. In contrast, the laboratory measurements have
no spectral dropout, as the continuous output of the halogen
bulb provides ample light at these wavelengths. However,
wavelengths shorter than 500 nm and longer than 1800 nm
do not produce reliable measurement in the laboratory, where
reduced instrument sensitivity and lower bulb output combine
to produce radiance estimates too noisy to be reliable. This
limitation was largely caused by the extreme space constraints
of our freezer laboratory. Headspace above the dome was
limited to about 10 cm, so it was difficult to position a light
source with higher output, which could have delivered significantly
more light to the Spectralon plate. We anticipate that
had there been more space, the removal of the mirror and
replacement with a downwelling light source in its place would
have produced adequate light for acceptable signal-to-noise ratio
at wavelengths shorter than 500 nm, as well as longer than
1800 nm.
The variability of the albedo dome measurements is
significantly larger than the variability of the field albedo
measurements. The standard deviation of the laboratory measurements
is indicated in Fig. 6 and is generally <2% at wavelengths
shorter than about 1000 nm and typically closer to
3.5% at longer wavelengths. For the field albedo, the observed
variability was less than the line width on Fig. 6. The variability
of the field albedo is tightly tied to the constancy of the incident
illumination, and the incident light was notably steady over the
time the 10 measurements were made (duration about 10 min
near local solar noon). For the laboratory measurements, variability
is tied to the repeatability of the radiance measurements
for both incident and backscattered fields. Relative to the field
albedo, the average of the laboratory measurements (blue curve
in Fig. 6) is biased slightly low (about 2%) at all wavelengths
shorter than about 1600 nm, but the agreement is generally
favorable.
B. Limitations and Uncertainties
The albedo dome technique is limited to estimation of the
albedo under diffuse illumination conditions. It is ideally suited
for estimating the spectral albedo of multiply scattering media
with approximately isotropic backscattering. Surfaces with large
specular reflectance or highly anisotropic BRDF would be difficult
to characterize using this method, although estimation of
a diffuse albedo should still be possible because the incident
light is diffuse. Surfaces with high albedo generate a more uniform
incident light field due to multiple reflections between
surface and dome interior, likely reducing the measurement
error. The difference in albedo for diffuse illumination and
direct illumination depends on the nature of the surface
being measured. In the case of snow, the largest differences
occur at wavelengths with moderate absorption (Fig. 11(a) of
Wiscombe and Warren [28]). Wavelengths with little absorption
display enough multiple scattering that the albedo does not
depend on the relative fraction of direct-to-total radiation and it
is generally very high, and wavelengths with large absorption
display little scattering and the albedo is low, again making
the character of the incident illumination of little importance.
The albedo for a direct beam at the global-average solar zenith
angle of 60° is approximately the same as the albedo for diffuse
incidence.
Because the footprint size on the measurement surface
is finite, it must be assumed to be representative of the entire
surface. A surface that is not horizontally homogeneous is problematic
beyond mere violation of the assumption of representativeness,
as the radiance field reflected from the dome interior
could have significant azimuthal variation if the surface were
highly inhomogeneous. This would make the integration of
downwelling irradiance from estimated radiances at a single
longitude difficult. Another significant limitation of the albedo
dome is the intensity of the source. Even with a 750 W tungsten–halogen
bulb, most of the measured radiance fields were
close to the limit of detection at some wavelengths, forcing us
to rely heavily on the automatic accounting of variable dark
level within the spectroradiometer. A single dark-level correction
taken at the beginning of a set of albedo scans was applied
to each scan. Precautions were taken to keep the instrument
well insulated in the cold environment, but it is possible that
dark levels did drift during individual experiments.
A number of potential biases inherent in the albedo-dome
technique have been identified. Concerted effort was made to
track down light leakage into the dome, specifically light that
enters the entry port at directions that miss the reflecting plate
on the ice surface. During the course of development, numerous
bright spots on the dome interior were spotted, and efforts
to baffle these spots were made. Any light entering the dome
that causes a less azimuthally isotropic dome interior radiance
field will bias the measurements.
An additional bias is due to the finite field of view of the bare
fiber-optic cable. The numerical aperture of this fiber yields an
acceptance cone of 12.5° half angle. The processing algorithm
for integrating both downwelling and backscattered irradiances
assumes that the measured radiances had zero angular divergence.
Such idealized radiances are not practical to measure,
but this assumption greatly simplified the processing. A bias
results from the imprecision of these radiance estimates, where
neighboring radiances essentially overlap. Perhaps the most
problematic case is that of the measurement of backscattered
radiance at 30°, where the large field of view likely included
some of the ice that was partially shaded by the reflecting plate.
This would impose a low bias on the albedo. Unfortunately,
this is a difficult bias to quantify. Attempts to narrow the fiber’s
field of view were made with a collimating lens, but this reduced
the signal recorded by the spectroradiometer.
Another bias results from the inability to accurately measure
wall-leaving radiances at low elevation angles on the dome
5266 Vol. 54, No. 17 / June 10 2015 / Applied Optics Engineering and Laboratory Note
interior. Measurements at k 2, 1, 0, and −1 were consistently
contaminated with direct light from the reflecting plate. Linear
extrapolation of radiances measured at higher elevation angles is
probably reasonable for the angles that actually fall on the dome
wall (k 2, 1). Extrapolation of these radiances that fall at the
base of or below the dome wall (k 0, −1) should bias the
albedo low, as it will consistently overestimate the incident
irradiance owing to the relatively dark tank walls that were
not measured. If the tank walls are brighter than the dome,
then this would mean the incident irradiance is underestimated
and the albedo is biased high, but this was generally not the
case. The walls of the tank are gray plastic, and the top edge
of the translucent plastic liner could also be seen in front of the
tank wall. The reflectivity of this surface was not measured, but
it is generally smaller than that of the highly reflecting dome
interior. A sensitivity analysis was carried out to estimate a correction
for the albedo-dome data due to this effect. Figure 7
shows the calculated albedo-dome result for the white tarp measurement
with no contribution from the tank walls, I k −1 0
(cyan line), and for I k −1 0 and I k 0 reduced by 50% (green
line). A 50% reduction of I k 0 would account for the fact that.
at θ 0. Only half of the field of view sampled by the fiber
optic is occupied by the dome wall; the rest is the relatively dark
tank wall. This adjustment caused the dome albedo to agree
with the field albedo (Fig. 7). We have used this simple correction
in the processing of incident irradiance for our studies
of artificial sea ice and the development of the salt crust [29].
6. CONCLUSIONS
We have described a technique for estimating the spectral
albedo of cold, laboratory-grown saline ice in a freezer laboratory.
The development of this method was motivated by the
need to measure the flux-reflectance (albedo) of a laboratory
proxy for cold, sublimating sea ice not currently found in
nature. The technique requires a simple list of equipment:
hemispherical dome prepared with reflecting interior surface
and light-blocking exterior surface, collimated broadband light
source, mirror, Lambertian reflecting plate, and spectroradiometer
with a fiber optic probe. This albedo-dome technique was
validated by comparison of field and laboratory albedos applied
to samples of a white tarp material. The validation experiment
yielded agreement at wavelengths between 500 and 1800 nm
that was generally within 2%.
We expect this technique to be applicable to a variety of
surfaces that can be created in the laboratory. The principal
requirement for a surface is horizontal homogeneity over the
area beneath the dome. Materials with significant specular reflection
or non-Lambertian BRDF can be used in the albedo
dome to estimate diffuse albedo, but no information about the
specular reflection or BRDF can be learned from this technique.
Techniques that do measure the full BRDF provide a
more comprehensive characterization of the surface, but this
method has been implemented in a cold (T < −25°C) environment
and uses only simple materials and a simple measurement
protocol to describe the reflectance properties of media with
long optical path lengths, such as snow and ice.
Both biases and random errors have been investigated for
this technique. The most significant bias appears to stem from
the inability to make direct dome-leaving radiance measurements
at low latitudes on the dome. Having such measurements
would increase the accuracy of the estimated incident
irradiance. Without such measurements, we suspect the albedo
is biased low. Additional bias may result from uncertainty of
the backscattered radiance measurement at 30 deg, where it
is possible that parts of the surface within the fiber optic field
of view have been shadowed by the reflecting plate.
The most significant random errors appear to be a result of
lack of repeatability in the measurements using the handheld
fiber optic cable. Efforts were continually made to improve this
repeatability, but clearly more improvement can be made.
Additionally, there was concerted effort to track down light
leakage into the dome from stray light emanating from the
source. While baffles were constructed to eliminate this stray
light, it is likely that not all leakage was prevented. Despite
the bright appearance of the 750 W bulb, individual radiance
measurements were often at the limit of detection for our spectroradiometer.
The system would be improved with better
beam collimation and other ways for increasing the intensity
of light inside the dome. In this implementation, space constraints
prevented alternative paths for the incident light that
Fig. 7. Albedo sensitivities for quantifying the effects of overestimating
the incident radiance profile at low dome latitudes.
Fig. 8. Schematic drawing of the implementation of Eq. (A2). The
blue band illustrates one term in the series, as detailed in Eq. (A3).
Engineering and Laboratory Note Vol. 54, No. 17 / June 10 2015 / Applied Optics 5267
would have yielded higher light intensities delivered to the
interior reflecting plate. Development of a more portable
version of this laboratory tool would also be advantageous, such
that albedo dome measurements could be made in a larger
variety of settings and locations.
APPENDIX A
Following Eq. (1), the downwelling irradiance incident at the
location of the footprint can be written as the integral
F↓
f
Z π∕2
0
Z 2π
0
Iθf ; ϕf dϕf cos θf sin θf dθf ; (A1)
where subscript f pertains to the virtual hemisphere centered
on the footprint (red dome in Fig. 5). The integral of radiance
for a particular θf over all azimuth angles ϕf can be expressed
as a weighted series calculated from the dome-leaving radiances
I k measured on the dome interior:
Z 2π
0
Iθf ; ϕf dϕf X
k
mkθf I k; (A2)
where the mk are weightings. Subscript k indicates the discrete
locations where surface-leaving radiance is measured on the
albedo dome. In our treatment, k varies from −1 to 9, but more
measurements could be made and k could have a larger range.
Figure 8 illustrates the integration of Eq. (A2) for one such blue
band. In this purely illustrative example,
Z 2π
0
Iθf Θ dϕf X
k
mkΘ I k
2·m5I 5 2·m6I 6 2·m7I 7; (A3)
where the mk correspond to the length of the arc in radians that
passes through each k band. The m6I 6 term is indicated by the
darker portion of the blue band in Fig 8. The sum of all mk
must equal 2π.
The list of I k values included for each θf is known from a
list of dome intersect points that maps each θf ; ϕf pair with
its corresponding θ; ϕ pair on the albedo dome. This relationship
is compiled by taking a unit vector through each θf ; ϕf
pair and calculating the θ; ϕ pair where it intersects with the
outer dome.
Substituting Eq. (A2) into Eq. (A1),
F↓
f
Z π∕2
0
1
2
sin2θf
X
k
mkθf I k
dθf ; (A4)
and rewriting as a sum,
F↓
f Xπ∕2
0
1
2
sin2θf
X
k
mkθf I k
Δθf ; (A5)
we can then assign
Ck Xπ∕2
0
1
2
sin2θf Δθf mkθf (A6)
such that
F↓
f X
k
CkI k; (A7)
which is Eq. (2) in the main text.
United States National Science Foundation Office of Polar
Programs (OPP) (ANT-0739779, ANT-1142963).
The capable laboratory assistance of Ruzica Dadic, Alan Wright,
and Taryn Black is gratefully acknowledged. Thanks also to
Matt Wyant for sage technical advice and production of
Figure 5, and to Richard E. Brandt for fruitful discussion and
loan of the Oriel collimator. An anonymous reviewer provided
helpful comments.
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