We present a unique case study of the spectral sky radiance distribution
above a coastline. Results are shown from a measurement campaign in Italy
involving three diode array spectroradiometers which are compared to 3-D
model simulations from the Monte Carlo model MYSTIC. On the coast, the
surrounding is split into two regions, a diffusely reflecting land surface
and a water surface which features a highly anisotropic reflectance function.
The reflectivities and hence the resulting radiances are a nontrivial
function of solar zenith and azimuth angle and wavelength. We show that for
low solar zenith angles (SZAs) around noon, the higher land albedo causes the
sky radiance at 20
In the absence of clouds, the solar radiation in the UV–near-infrared (UV–NIR) spectral region is scattered by air molecules and aerosols, which renders the radiant, blue sky. Part of the down-welling radiation is reflected back from the Earth's surface and contributes to the radiance (Kylling and Mayer, 2001). Gases may also absorb the light on its path through the atmosphere and characteristically modify the spectrum.
The spectral sky radiance thus carries information about the atmospheric composition, trace gases, aerosols and the underlying surface and is the basis for remote sensing of the atmosphere. For example, differential optical absorption spectroscopy (DOAS) (Platt and Stutz, 2008) utilizes the relative radiances of the spectrum to determine trace gas concentrations. The absolute radiance is analysed, for example, for the determination of the microphysical properties of aerosols (Dubovik and King, 2000).
Typically, as a simple approximation, land reflectance is assumed diffuse, i.e. isotropic and independent of viewing angle, which is described by Lambert's cosine law. Integration of the bidirectional reflectance function (BRDF) over all viewing angles is proportional to the albedo (Coakley, 2003). In the UV–visible (UV–VIS) spectral range, the Lambertian albedo for land surfaces ranges from almost 1 for fresh snow to around 0.2 for forest and 0.05 for water. In the NIR, vegetation has a higher reflectivity of about 0.4 (Coakley, 2003). The spectral albedo features are useful for satellite remote sensing of, for example, vegetation index and land cover (Hansen et al., 2000).
Compared to land, the ocean surface has a contrasting reflectivity property because it can be highly anisotropic and directional so the BRDF is strongly peaked at a certain reflection angle (Cox and Munk, 1954). The BRDF depends strongly on wind speed: a calm ocean shows a highly specular reflection, a phenomenon known as sun glint, which is best observed at high solar zenith angles (SZAs). At higher wind speeds the water surface is ruffled and the reflection becomes more isotropic and tends towards a Lambertian surface. Satellite observations of the sun glint allow a good estimate of the surface wind speed above the oceans (Wald and Monget, 1983).
Besides a weak wavelength dependence of the water's index of refraction which determines the reflectivity of a plane water surface by Fresnel's equation (e.g. Hecht, 2002), the wavelength dependence of the sun glint is more implicit. Specular reflection is only effective for a directional light source. The strong increase of Rayleigh scattering efficiency with shorter wavelengths causes a large diffuse component of the irradiance in the UV, i.e. a small direct to diffuse ratio. For VIS and NIR wavelengths, the direct component is much larger – hence the specular reflection. In addition, the direct-to-diffuse ratio of the global irradiance generally decreases with higher SZAs as the light path through the atmosphere lengthens. The resulting reflection property of the ocean has an intricate dependence on both wavelength and SZA.
Quantifying the effect of an inhomogeneous albedo distribution on the solar irradiance and sky radiance has been recognized as a challenging problem, since it requires the use of a 3-D radiative transfer model. As an extreme example, the Arctic regions are characterized by highly inhomogeneous albedo distributions due to the contrast of highly reflective snow (enhancing global irradiance by up to 50 %, e.g. Blumthaler, 2007) and dark ocean in the UV–VIS, which has been the subject of several experimental and model studies in the past (Kreuter et al., 2014; Ricchiazzi et al., 2002; Degünther et al., 1998).
In this paper, we report on spectral sky radiance measurements in the VIS–NIR range at a coastline which partitions the surface into two opposing segments: land and ocean. With detailed 3-D model simulations, we investigate this radiative transfer problem theoretically in pursuit of a deeper understanding of the components of the sky radiance above such a complex surface configuration. Following the conventional structure, we describe our methods before we present our measurement and model results and discuss relevant associated aspects.
A dedicated measurement campaign was performed for two weeks in September 2015 in Grottammare south of Ancona on the Adriatic coast in Italy. This site was chosen because it features a fairly straight coastline that runs close to the north–south direction. In this case, the course of the solar azimuth during the day is symmetric to the coast, which is ideal for studying the anisotropy of the ocean. We also favoured a location with low wind (wave) conditions and flat topography of the land. The beginning of autumn offered a high chance of cloud-free skies.
The measurement instruments included three diode array spectroradiometers
designed to measure global irradiances and radiances in the UV–VIS–NIR
spectral range. Two diode array spectroradiometers had global input optics
which were fitted with a shadow tube to measure diffuse irradiance from the
zenith (because surface reflectivities affect only the diffuse radiance and
hence the effect is decreased in the global irradiance by the direct sun
component). The shadow tube was a circular tube made of aluminium, coated
black on the inside and mounted on top of the global optics. The tube
shadowed the sky at elevation angles less than 60
The third diode array spectroradiometer was the Pandora-2s instrument (PAN).
It has an input optics with 2.5
Geographic locations of the measurement sites near Grottammare on the
Adriatic coast, Italy. Within 20 km from the coastal site, the landscape
consists of hills of less than 500 m elevation with patches of forest and
agricultural land. The measurements were made in September 2015.
The right panel shows the setup for the modelled radiances. The physical
scenario is approximated by a 400 km
We maintained two measurement sites, which are shown in Fig. 1: one directly on the coast, 100 m from the water line, and one 15 km inland. Two instruments (DA1 and PAN) were located at the coastal site, while the other instrument DA2 was set up at the inland site. The instruments were not calibrated in absolute radiometric units, since we will be considering relative ratios, where the absolute calibration is irrelevant. Only relative radiometric instrument stability has to be ensured, which is done by temperature stabilizing the instruments. Before the field measurements, DA1 and DA2 were operated together at the coastal site to check instrument stability. From this inter-comparison (and earlier campaigns; see Kreuter et al., 2014) we estimate the precision of these two instruments over the course of the day to about 1 %. The precision for the PAN instrument is expected to be of the same order. All instruments are fibre coupled to their respective input optics, with optical fibres that are not polarization maintaining, which ensures the instruments' insensitivity to the polarization of the sky radiance.
Two auxiliary instruments were deployed at the coastal site to complement the observations. First, a sun photometer (the precision filter radiometer (PFR-SPM) developed by the Physikalisch-Meteorologisches Observatorium (PMOD) in Davos, Switzerland, for the Global Atmospheric Watch Network) was used to measure the aerosol optical depth (AOD) at four wavelength channels, 368, 412, 501 and 862 nm. Second, we used an all-sky camera to monitor the sky and verify cloud-free conditions.
After 2 weeks of measurements, one full day (12 September 2015) and one half day (10 September 2015) were completely cloud-free, at least at the coastal site, and hence suitable for this investigation.
For modelling the sky radiances, we apply the 3-D Monte Carlo radiative transfer model MYSTIC within the libRadtran package (Mayer, 2009, 2010) in a cooperation agreement with the model developers. LibRadtran is a freely available, open source project. However, currently, only a 1-D version of MYSTIC is included in the public distribution (Mayer and Kylling, 2005).
In backward mode, MYSTIC randomly traces photons originating from the
detector through the atmosphere. At each scatter or surface reflection
event, a local estimate is performed, i.e. the probability that the photon
scatters/reflects toward the sun and reaches the sun without being extinct
is calculated. The sum over all local estimates, divided by the number of
simulated photons, gives the transmittance weighted by the cosine of the
SZA. The spectral radiances are computed for the two measurement locations
for the relevant day, in accordance with the solar geometry of the
measurement schedule. Each simulated radiance is a result of > 10
For the modelled standard scenario, the atmosphere is assumed cloud-free
with a standard midlatitude summer AFGL vertical profile (Anderson et al.,
1986). The atmosphere has a plane-parallel geometry since the spherical
atmosphere has not yet been implemented in MYSTIC in combination with a 2-D
surface. This approximation is usually well justified where only
SZAs < 80
The 2-D surface is specified by a 400 km
Water reflection is modelled applying the commonly used Cox and Munk (CM)
parameterized BRDF function of wind speed and direction (Cox and Munk,
1954). The wind speed has been set to 5 m s
Note that we explicitly model a simplified scenario in terms of geography here to illustrate the general features of the sky radiance at a coastline with respect to land and ocean reflectivities. In a model study on the global irradiances in Svalbard (Kreuter et al., 2014) we found that the effect of topography (which was comparable to the case here) could be neglected.
Measured and modelled radiances at 850 nm at 70
First, we look at the azimuthal scans of the sky radiance at 850 nm from the
Pandora instrument located at the coastal site and investigate its
dependence on the solar azimuth. The azimuthal scans were performed at
70
Left and right panels show measured and modelled radiances, respectively. The
viewing azimuth angle is defined relative to the sun at 0
In general, the radiance increases towards the direction of the sun (viewing
azimuth angle < 90
For NIR wavelengths, the coastline divides the surface around the observer at the coast into a high (land) and a low (ocean) albedo. Since the coastline is almost north–south, this breaks the symmetry in the sky radiance azimuthal scans in two ways: in an asymmetry between the left and the right hemisphere above the coastline and in an asymmetry with respect to the solar azimuth, i.e. between morning and afternoon. For shorter wavelengths towards the blue range of the spectrum, land and ocean reflectivities are similar and the anisotropy is expected to disappear. In the following, we will investigate the respective ratios which highlight this asymmetry of the radiance above the albedo distribution.
Asymmetry of the radiance with respect to the principal plane:
right–left ratios of the radiances at 70
Now we consider the ratios of the radiance in the right and left hemisphere,
i.e. the symmetry of the radiance with respect to the principal plane (the
plane through the observer, the zenith and the sun). The ratios at
70
As a first general observation, the ratios have a maximum between
90 and 135
The maximum of the ratios is around 1.4 for 850 nm – i.e. at 70
Asymmetry between morning and afternoon: measured and modelled am–pm
ratios of the radiances at 70
Next we will examine the asymmetry of the radiances between morning and
afternoon. In Fig. 4, we show measured and modelled ratios of the radiances
between morning (am) and afternoon (pm) at 70
The ratios are close to unity for viewing azimuth angles towards the
direction of the sun (azimuths < 50 and > 270
The general features of the ratios at each SZA are well reproduced by the model simulations. However, the magnitude of the modelled ratios is systematically smaller by about 10 %. As a next step, we revisit the model input parameters and assess a plausible uncertainty for each relevant parameter, and hence estimate the resulting model uncertainties.
The most relevant input parameters that affect our study are the land and ocean surface reflection properties as well as aerosol loading. In the following we will quantify the respective model sensitivities to these three parameters.
Model input parameter description for the three scenarios regarding land and ocean BRDF and aerosols.
First, we have assumed an idealized Lambertian model for the land
reflectivity, which may not be perfectly valid in reality. Second, the
ocean's BRDF model depends on wind speed, which was estimated from personal
observations and from the visual appearance of the sun glint. There is an
uncertainty from that as well as perhaps the parameterization of the model
itself. Third, the AOD measurements from the sun photometer indicate a
constant AOD (
The “land” scenario involves modelling the land reflectivity with a slightly
anisotropic BRDF, applying the semi-empirical parameterization by Rahman,
Pinty and Verstraete (RPV) (Rahman et al., 1993). The RPV model includes
three parameters (
In the “ocean” scenario, we modify the ocean BRDF, by increasing the wind
speed in the CM parameterization. This is expected to increase the isotropy
of the BRDF and we confirm that above 30 m s
Investigating the impact on the right–left ratios (am) and am–pm
ratios at 850 nm for three model scenarios: modified land and ocean surface
reflection models, and AOD uncertainty. The measurements are shown as dark circles for comparison. A difference of
For these scenarios, the resulting right–left ratios as well as the am–pm ratios for 850 nm at the four selected SZAs are shown in Fig. 5. This simultaneous comparison of both ratios with model and measurements at different SZA allows an intricate assessment of the model sensitivity to the various parameters.
Inspecting the first scenario with a modified land BRDF for pasture land, it
is noticeable that both right–left and am–pm ratios are generally increased.
Right–left ratios overestimate the measurements by up to 20 %. Since the
land and ocean are in opposite directions from the observer at the coast,
the hotspot has a similar effect on the radiance as the sun glint. The am–pm
ratio increases by 5 % at 78.2
When the ocean is modelled as a Lambertian reflector with albedo 0.05, the
right–left ratios are mainly unaffected, less than 5 % at 41.9
In the third scenario, we look at the sensitivity of the ratios to AOD changes during the day. The right–left ratios are not affected for this scenario because they are evaluated at one point in time (the measurement time is negligible here). For the am–pm ratios, small diurnal variations of 0.01 of the AOD result in an increase or decrease of the ratios of 10 %, depending on whether the AOD was 0.045 in the morning and 0.055 in the afternoon or vice versa. The corresponding uncertainty is depicted as the grey band in Fig. 5. The variation is slightly bigger for viewing azimuth angles towards the sun, which is caused by the prominent forwardly weighted scattering of aerosols. In simulations with other types of aerosols (OPAC type urban and marine aerosols with different properties like single-scattering albedo and phase function) we found a negligible effect on the ratios. In this context, additional uncertainties could also be caused by an inhomogeneous distribution of aerosols or even thin clouds far away from the observer.
Combining these observations, each scenario improves the model agreement at
least for some viewing angles or SZAs, but none of them constitutes a
convincing universal improvement in a way that improves the model for all
viewing azimuth angles and SZAs. However, the sensitivity of the ratios is
selective regarding model scenario, SZA and viewing angle. For example, the
right–left ratios at 41.9
Considering the uncertainty band due to the AOD uncertainty, the discrepancies of the modelled and measured ratios are well explained. A further refinement of the land and ocean reflectivity models, however, is not feasible within this study due to this uncertainty.
Finally, we investigate the zenith radiance measured with the shadow tubes in order to gain another perspective of the separate effects of BRDF anisotropy and Lambertian (or effective) albedo differences between land and ocean. The zenith radiance only depends on the effective albedo and not on the distribution. Above a Lambertian surface the zenith radiance is independent of the solar azimuth and independent on the albedo distribution. However, if part of the surface has a non-Lambertian reflection property, e.g. it shows a specular reflection like the ocean's sun glint at low solar elevation, then the zenith radiance would not be invariant to the solar position.
Both solar azimuth angle and SZA have an implicit importance here. On the
one hand, the ocean BRDF is strongly dependent on SZA, i.e. the higher the
SZA, the more pronounced the sun glint. On the other hand, from an
observer's point of view at the coast, it makes a difference whether the sun
is over the ocean or whether it is over the land, i.e. whether the specular
reflected photons are reflected towards the observer's zenith or not. This
effect concerns a wider range of angles around the zenith, which allows the
use of 60
Measured and modelled am–pm ratios at the coast for 450 and 650 nm
as a function of SZA. AOD variations during the day cause the measured
ratios to fluctuate. The grey band indicates the maximum variability of the
ratio due to an AOD difference of 0.01 (Ångström
To highlight this asymmetry of the zenith radiance with respect to the solar position, we consider the ratios of the radiance at identical SZA in the morning and afternoon, respectively. Measured and modelled am–pm zenith radiances for 450 and 650 nm at the coastal site are shown in Fig. 6. The NIR wavelength of 850 nm is not included in the analysis here because of a spatial stray-light problem. The tubular shadow band of instrument DA1 was covered with black felt on the inside, which is only absorptive for visible wavelengths while being reflective for the NIR part of the spectrum and may perturb the signal by a reflection of the direct sun.
Measured and modelled am–pm ratios of the zenith radiance at the two
locations over the day. Measured ratios are only available in the SZA range
65–75
First, the ratios of instrument DA1 for a 60
The SZA dependence of the sun glint has been explained before. However, the wavelength dependence is less trivial. A specular reflective surface is, of course, only relevant for the direct sun (or a directional light source in general). At longer wavelengths the ratio of the direct to diffuse irradiance is higher because of less scattering by air molecules and aerosols. On the other hand, a lower scattering probability also reduces the probability that the reflected light from the surface is scattered back towards the observer. So we have to consider two opposing effects, which are difficult to balance against each other from these basic arguments. The model has shown that the sun glint effect is indeed more pronounced at longer wavelengths.
The measured ratios are clearly dominated by AOD variation during the day
but are within the range of modelled ratios with a variation of
Furthermore, we want to investigate the translational dimension of the radiance above a non-uniform albedo distribution and we look at the zenith radiance with respect to the position of the observer relative to the coastline.
The dependence of the zenith radiance on the solar azimuth, i.e. the effect from the ocean BRDF discussed above, cannot be expected when the observer is in the midst of the ocean. Although the sky radiance distribution is strongly affected by the ocean specular reflection, the zenith radiance should be identical, morning and afternoon, since the geometry is rotationally invariant about the zenith. Of course, the same holds when the observer is surrounded by land surface. So the am–pm ratios should have a maximum at the coastline and decrease to unity after moving some distance either inland or towards the ocean. Assuming a Lambertian land albedo, this maximum is caused only by the ocean's strongly anisotropic BRDF.
In Fig. 7 we show the am–pm ratios of the zenith radiance measured
simultaneously at the two measurement sites, at the coast and 15 km inland,
respectively. Also shown are the modelled am–pm ratios of each site, as a
function of the SZA for two wavelengths, 450 and 650 nm. Measured
simultaneous ratios are only applicable for a single day in the SZA range
65–75
Although the measured values show a considerable variability (due to a AOD variability as discussed above), two small but important features are reproduced by the model: the am–pm ratios are higher at the coast and they increase with wavelength. Notably, the increasing difference of the ratios between the two wavelengths again demonstrates the effect of the ocean's sun glint.
The spatial extent of the sun glint effect is shown in the right panel of
Fig. 7: simulated am–pm ratios along a transect perpendicular to the coastline at 70
We have measured and modelled sky radiances at a coastline, where a near-Lambertian land albedo contrasts with the highly anisotropic ocean BRDF. At short wavelengths around 450 nm, the effective albedos of both surfaces are similar and low, while towards the NIR spectral range the albedo of the land is significantly higher. We have looked at various ratios between radiances at different solar azimuth angles for specific wavelengths and SZAs to investigate the effects of this albedo distribution.
First, we investigated the asymmetry of the sky radiance at the coastal site
by comparing the radiances in the right and the left viewing directions
(relative to the sun) at 70
The same is also apparent in the ratio between the radiances in the morning
and afternoon, especially towards noon for viewing directions opposing the
sun. The am–pm ratios decrease with increasing SZA and are about 1.3 for 850 nm at 78.2
A sensitivity study shows how the ratios are affected by model input
parameters regarding land and ocean BRDF and a diurnal variation of aerosol
loading. The right–left ratios, which are independent of AOD variations
during the day, indicate that a Lambertian land albedo of 0.3 in the NIR is
appropriate for low SZA although a slight anisotropy of the land BRDF
improves the model agreement at 78.2 and 41.9
In order to only focus on the anisotropic part of the reflectivity, mainly
the ocean BRDF, we investigate the zenith radiance. For a constant AOD
during the day, the modelled am–pm ratio of the zenith radiance has a maximum
of 7 % for 650 nm and 4 % at 450 nm for SZA > 70
While the zenith radiance is weakly affected by the inhomogeneous surface
reflectance distribution, the radiance at higher viewing zenith angles (as
shown here for 70
Our results are relevant for any ground-based remote sensing of radiances near the coast aiming to retrieve atmospheric components. For example, within AERONET, radiance measurements in the solar almucantar from sun photometers are used to retrieve aerosol microphysical properties, such as the size distribution and the index of refraction. Since the degree and angle of polarization may also be used in these retrievals, an interesting question for further studies in the future would be about the effect of inhomogeneous ground reflection on the radiance's polarization.
For data access please contact the corresponding author.
The authors declare that they have no conflict of interest.
The authors would like to thank Robert Buras, Claudia Emde and Bernhard Mayer for the help and support for 3-D modelling using MYSTIC. Edited by: Stelios Kazadzis Reviewed by: three anonymous referees