Eyvind Aas

Two-stream irradiance model for deep waters.

The two-stream model expresses the vertical attenuation coefficient K and the irradiance ratio R as functions of the absorption coefficient a, the backward scattering coefficient b(b), the downward and upward average cosines micro (d) and micro (u), and the normalized reflectance coefficients of downward and upward scalar irradiance, r(d) and r(u). While K/a and R are almost linear functions of b(b)/a when b(b)/a is small, they will approach asymptotic values, which only depend on r(d), r(u), micro (d), and micro (u) when b(b)/a becomes large. The results agree well with oceanic observations of K and R. They also agree with theoretical results derived by other methods. Still proper testing of the model in turbid waters remains.

Analysis of underwater radiance observations: Apparent optical properties and analytic functions describing the angular radiance distribution

A primary data set consisting of 70 series of angular radiance distributions observed in clear blue western Mediterranean water and a secondary set of 12 series from the more green and turbid Lake Pend Oreille, Idaho, have been analyzed. The results demonstrate that the main variation of the shape of the downward radiance distribution occurs within the Snell cone. Outside the cone the variation of the shape decreases with increasing zenith angle. The most important shape changes of the upward radiance appear within the zenith angle range 90°–130°. The variation in shape reaches its minimum around nadir, where an almost constant upward radiance distribution implies that a flat sea surface acts like a Lambert emitter within ±8% in the zenith angle interval 140°–180° in air. The ratio Q of upward irradiance and nadir radiance, as well as the average cosines μd and μu for downward and upward radiance, respectively, have rather small standard deviations, ≤10%, within the local water type. In contrast, the irradiance reflectance R has been observed to change up to 400% with depth in the western Mediterranean, while the maximum observed change of Q with depth is only 40%. The dependence of Q on the solar elevation for blue light at 5 m depth in the Mediterranean coincides with observations from the central Atlantic as well as with model computations. The corresponding dependence of μd shows that diffuse light may have a significant influence on its value. Two simple functions describing the observed angular radiance distributions are proposed, and both functions can be determined by two field observations as input parameters. The e function approximates the azimuthal means of downward radiance with an average error ≤7% and of upward radiance with an error of ∼1%. The α function describes the zenith angle dependence of the azimuthal means of upward radiance with an average error ≤7% in clear ocean water, increasing to ≤20% in turbid lake water. The a function suggests that the range of variation for μu falls between 0 and 1/2, and for Q it is between π and 2π. The limits of both ranges are confirmed by observations. By combining the e and α functions, a complete angular description of the upward radiance field is achieved.

Validation of MERIS water products and bio-optical relationships in the Skagerrak

The MERIS Level 2 Reduced Resolution products for Case 2 water available in September 2003, and conversion functions used in the reference model, have been validated against in situ data from the Skagerrak, collected during the summers of 2002 and 2003. The MERIS water‐leaving reflectance deviated less than 20% from the measured reflectances in the blue‐green part of the spectrum, but it had a tendency of being overestimated by up to 40% in the blue part of the spectrum and underestimated by up to 20% in the red part. The average relative deviation between the MERIS product for total suspended material (dry weight) and the in situ values was 30%. The MERIS values for chlorophyll a were on an average a factor 2 higher than the in situ values, and a new conversion factor should be used for the Skagerrak area. The absorption coefficients for the sum of yellow substance and bleached particles at 442 nm were underestimated by a factor of up to 10 by the MERIS product. The mean values of the spectral slopes of particle scattering and bleached particle absorption were close to the values of the reference model, while the observed slope of yellow substance was slightly lower than the model slope.

Comparison of radiance and polarization values observed in the Mediterranean Sea and simulated in a Monte Carlo model

Measurements of the radiance and degree of polarization made in 1971 in the Mediterranean Sea are presented along with the simulation of all observed quantities by a Monte Carlo technique. It is shown that our independent scattering treatment utilizing a Stokes vector formalism to describe the polarization state of the light field produces remarkably good agreement with those values measured in situ.

A RELATIONSHIP FOR THE PENETRATION OF ULTRAVIOLET B RADIATION INTO THE NORWEGIAN SEA

A linear relation between the vertical attenuation coefficients of UV-B and blue irradiances is obtained for the Norwegian Sea. The Atlantic waters in this region are on average characterized by a deeper 1% depth of UV-B irradiance than the surrounding waters, the depth being situated between 23 and 33 m.

Spectral backscattering coefficient in coastal waters

Based on 186 field observations in the Oslo Fjord of irradiance and radiance and 105 laboratory measurements of beam attenuation, this analysis demonstrates that the ratio between the backscattering coefficient b pb and the scattering coefficient b p of the particles is wavelength dependent and not a constant value. The mean values of b pb/b p at the different wavelengths are close to Petzolds 0.017–0.019 from the San Diego Harbor at 515 nm. For all wavelengths and stations (630 observations) the mean value of b pb/b p is 0.020, the standard deviation of the dataset is 0.015, half of the ratios are greater than 0.020, more than 10% are greater 0.030 and about 5% greater than 0.040. The numerical magnitude of these ratios indicates that small particles are the cause of the latter deviations from the ‘Petzold case’. An example from the northern border of the Skagerrak shows a spectral shape of b pb that can be approximated by λ−1.54, λ being the wavelength, while b p is roughly proportional to λ−0.41. The spectral shape of b pb/b p becomes ∼λ−1.12. During a dinoflagellate bloom in the inner part of the Oslo Fjord direct measurements of b pb have revealed a slope of b pb∼λ−1.59. The spectral shape of the mean values of b p(λ) in the Oslo Fjord, based on the 105 observations, can be approximated by the function ∼λ−0.67, while the spectral shapes of b pb(λ) and b pb(λ)/b p(λ) display a greater variety of forms.

Reflection of Spectral Sky Irradiance on the Surface of the Sea and Related Properties

Abstract Observed angular distributions of spectral sky radiance clearly demonstrate the anisotropic nature of the radiance and lead to significant deviations from the isotropic case when the optical quantities resulting from these distributions are calculated. The ratio of diffuse downward irradiance and zenith radiance is determined at seven wavelengths from 370 nm to 650 nm, varying between 1.8 and 5.1 at 370 nm for the solar zenith angle range θs=17°–67°, and between 1.2 and 8.5 at 650 nm for the range θs=16°–76°. A consequence of these observations is that the frequently applied assumption of isotropic sky radiance may lead to errors of up to 170% for the contribution to nadir radiance from zenith radiance reflected on the surface of the sea. The surface reflectance of diffuse irradiance obtains values between 0.053 and 0.088 at 370 nm θ s =12°–67° and between 0.048 and 0.124 at 650 nm θ s =13°–76° . The assumption of isotropic sky radiance may in this case lead to errors of up to 85% for the reflectance. The values for the average cosine of downward sky radiance lie in the range 0.43–0.60 at 370 nm θ s =12°–67° and in 0.31–0.62 at 650 nm θ s =13°–76° , which again are significant deviations from the value 0.50 for the average cosine of the isotropic radiance distribution. Beneath the surface of the sea the transmitted sky radiance produces an average cosine that only varies between 0.82 and 0.89 at 370 nm θ s =12°–67° and between 0.78 and 0.89 at 650 nm θ s =13°–76° . Linear relations approximating the ratio of diffuse irradiance and zenith radiance, the diffuse reflectance, and the average cosines as functions of the solar zenith angle are presented. The determining factors in predictions of the mentioned optical quantities become the diffuse downward irradiance, the ratio of diffuse and total irradiance, and the solar zenith angle.

Spectral Properties and UV-Attenuation in Arctic Marine Waters

The Arctic can be delimited by the Arctic Circle at 66 ° 32 ‘N, which is the southern boundary of the midnight sun. For many purposes, however, it will be more meaningful to base the limits of the Arctic on climate, vegetation, or seawater characteristics (Murray 1998). In this chapter, we have chosen to define Arctic marine waters as the sea within the region delineated by the Arctic Monitoring and Assessment Programme (AMAP). The boundaries of this region are a compromise between major oceanographic features, permafrost limits, vegetation boundaries, and political boundaries (Murray 1998). The Arctic marine waters will then include the Pacific Ocean north of the Aleutian Islands, Hudson Bay, and parts of the North Atlantic Ocean including the Labrador Sea, South-Icelandic waters and the Faroe Islands. The boundary follows the Norwegian coast northward from 62°N (Fig2.1). Within this area all solar elevations will be less than 60 °.

Conversion of sub-surface reflectances to above-surface MERIS reflectance

Factors for converting sub-surface reflectances to above-surface MERIS reflectances have been determined both as analytic functions and average numbers for solar zenith angles in the range 30°–75°, wind speeds up to 10 m s−1, and the spectral domain 400–700 nm. The conversion factors have been obtained by numerical and statistical computations based on field observations of spectral radiance and irradiance, above and below the surface of the sea. The estimated maximum errors of the different algorithms range from ≤0.1% up to 10%, depending on the chosen method and the types of optical quantities that are available. The errors are smallest for solar zenith angles between 30° and 60° and increase when the solar zenith angle approaches 75°. The influence of the wind on the conversion factors is practically negligible. The algorithms, which have been derived for conditions representative of the Skagerrak and the adjacent seas, are assumed to be valid for both Case 1 and 2 waters.

Horizontal convection in water heated by infrared radiation and cooled by evaporation: scaling analysis and experimental results

Abstract An experimental study of horizontal convection with a free surface has been conducted. Fresh water was heated from above by an infrared lamp placed at one end of a tank, and cooled by evaporation as the water moved away from the heat source. The heat radiated from the lamp was absorbed in a thin (less than 1 mm) layer next to the surface, and then advected and diffused away from the lamp region. Latent heat loss dominated the surface cooling processes and accounted for at least 80% of the energy loss. The velocity and temperature fields were recorded with PIV technology, thermometers and an infrared camera. In similarity with previous horizontal convection experiments the measurements showed a closed circulation with a gradually cooling surface current moving away from the lamp. Below the surface current the water was stably stratified with a comparatively thick and slow return current. The thickness and speed, and hence the mass transport, of the surface-and the return current increased with distance from the lamp. The latent cooling at the free surface gives a heat flux which increases with the temperature difference between the surface water and the air above it. Hence the surface temperature relaxes towards an equilibrium value, for which the heat flux is zero. The main new result is a scaling law, taking into account this relaxation boundary condition for the surface temperature. The new scaling includes a (relaxation) length scale for the surface temperature, equivalent to the distance the surface current travels before it has lost the heat that was gained underneath the lamp. The length scale increases with the forcing strength and the (molecular) thermal diffusivity but decreases with the strength of the relaxation. Numerical simulations of this problem for a shallow tank have also been performed. The velocity and temperature in the laboratory and numerical experiments agree with the scaling laws in the upper part of the tank, but not in the lower.