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∘, which ensured that the sun was always occluded. The maximum solar elevation at the time of the campaign was about 51∘. These measurements will be referred to as zenith radiance with a 60∘ field of view (FOV). Both instruments, in the following called DA1 and DA2, recorded synchronous spectra every 10 min. The instruments have been well characterized in the laboratory and during previous campaigns (Kreuter et al., 2014; Kreuter and Blumthaler, 2009).

The third diode array spectroradiometer was the Pandora-2s instrument (PAN). It has an input optics with 2.5∘ field of view mounted on a two-axis tracker to measure direct sun and sky radiances. It was specifically designed for the retrieval of trace gases and aerosols and has been well characterized (Herman et al., 2009). The spectral range of the Pandora covers the UV–VIS–NIR range 300–900 nm. For this campaign, it was programmed to measure the spectral radiance for a set of azimuth angles at 70∘ zenith angle, i.e. along an almucantar. The measurement duration for a complete scan was 4 min and the time stamp was assigned to the time at the middle of measurement. The order of the angles was reversed in the afternoon, so that the sequences were symmetric around solar noon. The scans were scheduled every 30 min. In between, we also performed direct sun measurements and radiance scans along the principal plane, which includes the zenith.

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 > 105 sampled photons, ensuring a statistical error of < 1 % standard deviation.

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∘ are considered, especially for ratios of radiances at identical SZA. Aerosol properties are specified according to the OPAC aerosol type continental average (Hess et al., 1998), with Ångström α and β parameters scaled to 1.4 and 0.05, respectively.

The 2-D surface is specified by a 400 km × 400 km grid with a 10 km resolution. The elevation at each grid point has been set constant to 100 m for land and 0 m for ocean. The coast is a straight line at an angle 20∘ (anticlockwise) from the north–south direction, depicted in Fig. 1. Each grid element also has a surface reflection property given by the BRDF. Here, we consider two BRDFs – that for water (ocean) and that for land.

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-1, estimated from the visual appearance of the ocean and local wind measurements. The land is modelled as a Lambertian surface with an albedo of 0.05, 0.18 and 0.3 for 450, 650 and 850 nm respectively. This is supported by the albedo products from the MODIS sensors on board Aqua and Terra satellites (Schaaf et al., 2011). The mean albedo retrieved from band 2 (841–876 nm) for the surrounding during September 2015 has been determined as 0.32 and 0.29 for the white-sky and black-sky albedo, respectively (referring to the albedo with and without scattering).

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.

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∘ viewing zenith angle, over the course of the day with varying SZA. The comparisons of the radiance in the morning and afternoon at the same SZA are shown in Fig. 2. SZAs of 78.2, 67.5, 57.4 and 41.9, corresponding to measurement times of 5.2, 4.2, 3.2 and 1.2 h from local noon, respectively, will be used as representative solar positions throughout this study.

Left and right panels show measured and modelled radiances, respectively. The viewing azimuth angle is defined relative to the sun at 0∘ and counted clockwise. The ocean–land distribution (blue–green patches), the position of the instrument at the coast (small black cross), the azimuth of the sun (dark circles) and the measured azimuth angles (small white ticks; 90, 180 and 270∘ are marked black) are indicated in the sketches on the right.

In general, the radiance increases towards the direction of the sun (viewing azimuth angle < 90∘ and > 270∘), which is mainly due to the forward scattering of aerosols. At 180∘, in viewing direction opposing the sun, the sky radiance has a local maximum which decreases with decreasing SZA. This maximum is associated with molecular backscattering. Furthermore, the sky radiance at angles around 180∘ shows the largest difference between morning (am) and evening (pm). As viewed from the coast in the morning, the sun is over the ocean, and at 180∘ azimuth angle, we are looking towards the horizon of the land, which has a higher albedo – which increases the radiance. The qualitative features are well reproduced in the model. Only at 78∘ SZA the difference between the modelled radiances of am and pm is notably smaller than observed.

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.

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∘ viewing zenith angle for the four selected SZA in the morning and afternoon are shown in Fig. 3. The viewing azimuth angles from 50 to 175∘ are relative to the principal plane. As above, the right panel of Fig. 3 shows the orientation of the radiance frame of reference with respect to the coastline.

As a first general observation, the ratios have a maximum between 90 and 135∘ viewing azimuth and increase with decreasing SZA. In the morning and afternoon, at high SZA, the ocean land distribution is almost symmetric with respect to the principal plane, resulting in ratios < 10 %. At 67.5∘ SZA in the afternoon, the principal plane is perpendicular to the coastline and the ratio is unity. With decreasing SZA towards noon, the relative frame of reference for the azimuth rotates and the right–left ratios increase. At 41.9∘ SZA in the morning, the principal plane is aligned with the coastline, maximizing the albedo asymmetry and hence the right–left ratio.

The maximum of the ratios is around 1.4 for 850 nm – i.e. at 70∘ zenith angle and 120∘ azimuth angle, the sky in the NIR is 40 % brighter over land than over the ocean. The ratios decreases with wavelength and vanish for a wavelength of 450 nm, where both land and ocean albedo are about 0.05. Considering the model simulations, we note that the characteristic features of the ratios with respect to azimuth angle, SZA and wavelength are well reproduced. Quantitatively, we generally have an agreement of measurements and model simulations of better than 5 %. In particular, the good agreement of the ratios at 850 nm at 41.9∘ SZA, which have the highest sensitivity to the albedo distribution, indicate that the Lambertian albedo model for the land with albedo 0.3 is appropriate.

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∘ viewing zenith angle at three wavelengths at the coastal site at four SZAs. The viewing azimuth angle is relative to the solar azimuth as in Fig. 2.

The ratios are close to unity for viewing azimuth angles towards the direction of the sun (azimuths < 50 and > 270∘) and maximal around 180∘ from the sun. For short wavelengths, the ratios are always close to 1, while the maxima increase with SZA and wavelength. The widths of the maxima decrease with decreasing SZA, which can be understood by looking at the difference of the albedo between am and pm for each viewing azimuth.

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.

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 (β= 0.05) with a remaining uncertainty from the standard deviation of about 0.005. Focusing on these factors individually, we set up three alternative model scenarios with modified model input parameters described in Table 1. All other parameters are the same as in the standard scenario.

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 (ρ0, k and Θ) to describe a generalized surface reflection function. Here we use the parameters which have been given for a pasture type surface, which could in principle apply to much of the surrounding of the measurement sites. The pasture land BRDF is close to a Lambertian albedo and differs essentially by an increased reflection in the backscatter direction. This so-called “hotspot” is often noticeable at high SZA when the sun is in the back of the observer, which is a result from geometric shading on structured surfaces. The effect is opposite to that of a specular reflection, albeit much weaker.

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-1 the ratios are (within noise) equal to the ratios modelled with a Lambertian albedo 0.05, which is shown here as the limiting, isotropic case. In the “aerosol” scenario, we change the AOD (the Ångström β parameter) by its uncertainty of 0.005. We model the radiances with a β of 0.055 in the morning and 0.045 in the afternoon and vice versa, keeping the Ångström exponent α constant (the standard deviation of α is 0.06, which would further increase the uncertainty of the AOD, predominantly at short wavelengths).

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∘ SZA and improves the agreement with the measurement, which is also the case for 41.9∘ SZA. At 67.5∘ SZA the am–pm ratio increases to 1.5, which then overestimates the measurement by almost 15 %.

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∘ SZA, compared to the standard scenario of the CM parameterization. The am–pm ratio is reduced by just over 10 % for all azimuth angles at 78.2∘ SZA. The amplitude of the angular dependence is not affected. The difference quantifies the contribution of the ocean's BRDF, the sun glint. This effect decreases with decreasing SZA to below 5 % at 42∘ SZA. This is plausible since the sun glint is most prominent at high SZA, as one can expect more specular reflection off a flat water surface at glancing angles of incident purely from Fresnel's law. The model–measurement agreement is reduced particularly at 78.2∘ SZA, except for 50∘ azimuth angle. We note that the Cox and Munk model for the ocean BRDF is not strictly suited for SZAs > 80∘, so its validity may already be limited for 78∘ SZA. Similarly, the validity of the land albedo, whether Lambertian or RPV BRDF, might not hold perfectly for higher SZAs.

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∘ SZA are mostly sensitive to the land albedo or BRDF because the sun glint effect is small and the ratio is not affected by the AOD uncertainty. A good agreement of the standard scenario indicates an appropriate albedo model especially for low SZAs, although the pasture land BRDF scenario improves the model agreement for high SZAs for the am–pm ratios. For high SZAs, the am–pm ratios are sensitive to the ocean BRDF and the “ocean” scenario shows that the CM model for the ocean BRDF with higher wind speeds reduces the agreement with the measurements.

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∘ FOV zenith measurements (DA1 and DA2) for the ratios investigated below.

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.

First, the ratios of instrument DA1 for a 60∘ FOV are in good agreement with those of the Pandora instrument for a 2.5∘ FOV zenith radiance (open circles) confirming the above argument. The measured am–pm ratios seem to be dominated by a large variation compared to the systematic increase with SZA of the ratios modelled with a constant AOD over the course of the day. Without any atmospheric disturbances, the modelled zenith radiance in the morning is 7 % higher than in the evening for large SZA above 70∘ for 650 nm and 4 % at 450 nm. This dependence is characteristic for the ocean's sun glint.

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 β between 0.045 and 0.055 (grey band). So the zenith radiance is highly sensitive to scattering by aerosols and even a small change of 0.01 in β, the range of the typical measurement uncertainty of well calibrated sun photometers, causes a change of the radiance of up to 15 % and would obscure the effect of ocean BRDF for one wavelength. However, the relative difference between the two wavelengths, increasing from about zero at 60∘ SZA up to 5 % at 75∘ SZA, remains as the characteristic signal of the sun glint.

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∘. Otherwise high clouds to the west of the inland site or convective clouds around noon spoiled the measurements. The am–pm ratios at the coast increase with SZA and wavelength, while little variation can be identified for the ratios measured 15 km inland.

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∘ SZA. The am–pm ratios are maximal directly at the coast and reduce to unity over the ocean and over the land about 30 km from the coast.