Using computer simulations we examine the ranges of validity of the first Born and first Rytov approximations employed in diffraction tomography. To that end we apply the filtered backpropagation(FBP) algorithm in conjunction with the first Born approximation and the hybrid FBP algorithm in conjunction with the first Rytov approximation. We find that the range of validity of the first Born approximation is approximately 3 times smaller than that of the first Rytov approximation and that the range of validity of each approximation can be expressed in terms of the product of the refractive-index difference between the object and the background and the size of the object. Also, we establish precise criteria for the validity of diffraction tomography within each of these two approximations. For the first Rytov approximation the validity of the hybrid FBP algorithm is found to be limited by phase-unwrapping problems.

[1] On the basis of input from in situ measurements of key parameters determining optical properties (i.e., snow grain size, density, ice salinity, ice temperature, etc.) we calculate the transmittance of shortwave radiation (280 nm < l < 800 nm) through first-year sea ice with and without snow cover. We use a multistream radiative transfer code that takes into account the coupling between two strata with different indices of refraction (i.e., the atmosphere-snow stratum and the ice-ocean stratum). Also, we give a detailed description of the parameterization used to calculate the optical properties for shortwave radiation in the atmosphere, snow, ice, and ocean. Through comparisons between calculated and in situ measured transmittances we tune the model to obtain consistency. We find that for the type of snow and ice considered in this study a 2.5-cm-thick layer of snow is less transparent than a 61-cm-thick layer of ice. Also, the diffuse attenuation coefficient for snow K d varies considerably with the snow thickness, emphasizing the need for accurate radiative transfer modeling. Our model not only provides accurate transmittances but also gives accurate values for ultraviolet and visible light versus depth in the atmosphere, snow, ice, and ocean. This makes it a suitable tool for both calculating energy deposition in icy polar waters and predicting effects on polar aquatic ecology due to changes in the light conditions.

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[1] We present measurements of solar UV radiation performed with multichannel moderate-bandwidth NILU-UV filter instruments during winter and summer in 2003 in the altitude region from 3000 m to 5000 m at 29N in the Lhasa region in Tibet. During summer the UV index was found frequently to exceed 15 on clear days and occasionally to exceed 20 on partially cloudy days. High altitudes, low ozone column amounts, clean atmospheres, and relatively low latitudes are factors that contribute to the high UV levels on the Tibetan plateau. UV index values of 12 were measured in late winter for a solar zenith angle of 40 at a snow-covered 5000 m altitude site. This is a 35% increase compared to a corresponding snow-free surface. Our measurements show that the solar UV radiation increases with altitude. For clear-sky and snow-free conditions the altitude increase is 7-8% per km for erythemal UV dose rates and 3% per km at a wavelength of 340 nm. Results from clear-sky calculations using a multiple-scattering radiative transfer model were found to agree within 5% with clear-sky UV measurements. Radiative transfer calculations combined with measurements were used to estimate the influence of clouds on the UV radiation at the surface. On the average the variable cloud cover in Lhasa reduced the daily integrated erythemal UV dose by 25%. The NILU-UV instruments also provide total ozone column amounts. The mean difference between daily total ozone column amounts derived from NILU-UV measurements and from Earth Probe TOMS data was À1.4% ± 3.2% (1s).

This new and completely updated edition gives a detailed description of radiative transfer processes at a level accessible to advanced students. The volume gives the reader a basic understanding of global warming and enhanced levels of harmful ultraviolet radiation caused by ozone depletion. It teaches the basic physics of absorption, scattering and emission processes in turbid media, such as the atmosphere and ocean, using simple semi-classical models. The radiative transfer equation, including multiple scattering, is formulated and solved for several prototype problems, using both simple approximate and accurate numerical methods. In addition, the reader has access to a powerful, state-of-the-art computational code for simulating radiative transfer processes in coupled atmosphere-water systems including snow and ice. This computational code can be regarded as a powerful educational aid, but also as a research tool that can be applied to solve a variety of research problems in environmental sciences.

[1] The particulate backscattering coefficient b bp is an inherent optical property that plays a central role in studies of ocean color remote sensing. Because of practical difficulties associated with measurements of the volume scattering function (VSF) over the whole backward hemisphere, b bp is currently derived using fixed-angle backscattering sensors and applying a conversion factor for particulate backscattering, referred to as c p . The underlying assumptions of the fixed-angle approach are as follows: (1) in the green band, c p is fairly constant in the angular range 100°-150°and (2) for a fixed scattering angle, c p is wavelength-independent. In this study we investigated the variability of c p based on spectral measurements of the full VSF, both in situ and for algal culture in the laboratory. The in situ data used in our study were acquired in a coastal environment outside of phytoplankton blooms, whereas the laboratory data were representative for phytoplankton bloom conditions in oceanic waters. At 555 nm, c p was found to vary significantly in the angular range 100°-130°, and at 140°, c p was found to be weakly variable in nonblooming waters only. The spectral variability of c p was studied for the first time, and the spectral slopes of c p , measured in situ, were found to vary within ±6%. Under the assumption that c p (140°) is wavelength-independent, the induced error in the estimates of b bp was found to be lower than 10%. The algal culture showed a much higher spectral variability in c p (±20%), which induced an error in the estimates of b bp up to ±25.8%.Citation: Chami, M., E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev (2006), Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,

Frette Ø, Erga SR, Hamre B, Aure J, Stamnes JJ. 2004. Seasonal variability in inherent optical properties in a western Norwegian fjord. Sarsia 89:276-291. SARSIAWe present measured seasonal variations in the inherent optical properties (the absorption and scattering coefficients) of water in a deep silled fjord (Samnangerfjorden) in western Norway. These were based on measurements taken at monthly intervals during an annual cycle. The measurements also include concentrations of chlorophyll a and yellow substance, which were assumed to dominate the behaviour of the absorption and scattering coefficients. The stations were at three fixed locations, one being placed in the innermost part of the fjord where there is little mixing of fjord water with water from the coastal current. The other two stations were placed at different distances from the mouth of the fjord, so that the water masses are characterized by different amounts of mixing between fjord water and coastal current water. Our data set shows how the absorption and scattering coefficients vary in a Norwegian fjord during an annual cycle, and how they depend on the concentrations of chlorophyll a and yellow substance. Values of the absorption coefficient at 412 nm varied between 0.1 and 2.0 m À1 , and scattering coefficients were also found to vary within this range. Little variation over the spectral range was found for the scattering coefficients, but the absorption coefficient had larger spectral variations. The chlorophyll a concentrations varied from 0.01 to 6.3 mg m À3 , and the concentration of yellow substance, as expressed by its absorption coefficient at 310 nm, was within the range 0.7-7.8 m À1 .