Knut Stamnes

Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media

We summarize an advanced, thoroughly documented, and quite general purpose discrete ordinate algorithm for time-independent transfer calculations in vertically inhomogeneous, nonisothermal, plane-parallel media. Atmospheric applications ranging from the UV to the radar region of the electromagnetic spectrum are possible. The physical processes included are thermal emission, scattering, absorption, and bidirectional reflection and emission at the lower boundary. The medium may be forced at the top boundary by parallel or diffuse radiation and by internal and boundary thermal sources as well. We provide a brief account of the theoretical basis as well as a discussion of the numerical implementation of the theory. The recent advances made by ourselves and our collaborators-advances in both formulation and numerical solution-are all incorporated in the algorithm. Prominent among these advances are the complete conquest of two illconditioning problems which afflicted all previous discrete ordinate implementations: (1) the computation of eigenvalues and eigenvectors and (2) the inversion of the matrix determining the constants of integration. Copies of the FORTRAN program on microcomputer diskettes are available for interested users.

Surface Heat Budget of the Arctic Ocean

A summary is presented of the Surface Heat Budget of the Arctic Ocean (SHEBA) project, with a focus on the field experiment that was conducted from October 1997 to October 1998. The primary objective of the field work was to collect ocean, ice, and atmospheric datasets over a full annual cycle that could be used to understand the processes controlling surface heat exchanges—in particular, the ice–albedo feedback and cloud–radiation feedback. This information is being used to improve formulations of arctic ice–ocean–atmosphere processes in climate models and thereby improve simulations of present and future arctic climate. The experiment was deployed from an ice breaker that was frozen into the ice pack and allowed to drift for the duration of the experiment. This research platform allowed the use of an extensive suite of instruments that directly measured ocean, atmosphere, and ice properties from both the ship and the ice pack in the immediate vicinity of the ship. This summary describes the project goal...

Comparison of Numerical Models for Computing Underwater Light Fields

Seven models for computing underwater radiances and irradiances by numerical solution of the radiative transfer equation are compared. The models are applied to the solution of several problems drawn from optical oceanography. The problems include highly absorbing and highly scattering waters, scattering by molecules and by particulates, stratified water, atmospheric effects, surface-wave effects, bottom effects, and Raman scattering. The models provide consistent output, with errors (resulting from Monte Carlo statistical fluctuations) in computed irradiances that are seldom larger, and are usually smaller, than the experimental errors made in measuring irradiances when using current oceanographic instrumentation. Computed radiances display somewhat larger errors.

An Accurate Parameterization of the Radiative Properties of Water Clouds Suitable for Use in Climate Models

Abstract A new parameterization of the radiative properties of water clouds is presented. Cloud optical properties for both solar and terrestrial spectra and for cloud equivalent radii in the range 2.5–60 µm are calculated from Mie theory. It is found that cloud optical properties depend mainly on equivalent radius throughout the solar and terrestrial spectrum and are insensitive to the details of the droplet size distribution, such as shape, skewness, width, and modality (single or bimodal). This suggests that in cloud models, aimed at predicting the evolution of cloud microphysics with climate change, it is sufficient to determine the third and the second moments of the size distribution (the ratio of which determines the equivalent radius). It also implies that measurements of the cloud liquid water content and the extinction coefficient are sufficient to determine cloud optical properties experimentally (i.e., measuring the complete droplet size distribution is not required). Based on the detailed cal...

A new spherical model for computing the radiation field available for photolysis and heating at twilight

Abstract Accurate computation of atmospheric photodissociation and heating rates is needed in photo-chemical models. These quantities are proportional to the mean intensity of the solar radiation penetrating to various levels in the atmosphere. For large solar zenith angles a solution of the radiative transfer equation valid for a spherical atmosphere is required in order to obtain accurate values of the mean intensity. Such a solution based on a perturbation technique combined with the discrete Ordinate method is presented. Mean intensity calculations are carried out for various solar zenith angles. We compare these results with calculations from a plane parallel radiative transfer model in order to assess the importance of using correct geometry around sunrise and sunset. This comparison shows, in agreement with previous investigations, that for solar zenith angles less than 90° adequate solutions are obtained for plane parallel geometry as long as spherical geometry is used to compute the direct beam attenuation; but for solar zenith angles greater than 90° this “pseudo-spherical” plane parallel approximation overestimates the mean intensity. At 400 nm this overestimation is as much as 30% between 10 and 30 km for a solar zenith angle of 98°, while at 300 nm it is about 20% between 40 and 60 km for a solar zenith angle of 96°. The assumption of isotropic rather than Rayleigh (molecular) scattering may lead to an incorrect assessment of the radiation field available for photolysis and heating. Thus, at 450 nm isotroplc scattering leads to an underestimation of the mean intensity of a few percent when the Sun is above the horizon increasing to as much as 15% when the Sun is below the horizon. Model computations of zenith sky intensities agree well with twilight observations of Umkehr curves including the location of the minimum point (second Umkehr).

CALIPSO/CALIOP Cloud Phase Discrimination Algorithm

Abstract The current cloud thermodynamic phase discrimination by Cloud-Aerosol Lidar Pathfinder Satellite Observations (CALIPSO) is based on the depolarization of backscattered light measured by its lidar [Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP)]. It assumes that backscattered light from ice crystals is depolarizing, whereas water clouds, being spherical, result in minimal depolarization. However, because of the relationship between the CALIOP field of view (FOV) and the large distance between the satellite and clouds and because of the frequent presence of oriented ice crystals, there is often a weak correlation between measured depolarization and phase, which thereby creates significant uncertainties in the current CALIOP phase retrieval. For water clouds, the CALIOP-measured depolarization can be large because of multiple scattering, whereas horizontally oriented ice particles depolarize only weakly and behave similarly to water clouds. Because of the nonunique depolarization–cloud ph...

Radiative transfer in nonuniformly refracting layered media: atmosphere--ocean system

We have applied the discrete-ordinate method to solve the radiative-transfer problem pertaining to a system consisting of two strata with different indices of refraction. The refraction and reflection at the interface are taken into account. The relevant changes (as compared with the standard problem with a constant index of refraction throughout the medium) in formulation and solution of the radiative-transfer equation, including the proper application of interface and boundary conditions, are described. Appropriate quadrature points (streams) and weights are chosen for the interface-continuity relations. Examples of radiative transfer in the coupled atmosphere-ocean system are provided. To take into account the region of total reflection in the ocean, additional angular quadrature points are required, compared with those used in the atmosphere and in the refractive region of the ocean that communicates directly with the atmosphere. To verify the model we have tested for energy conservation. We also discuss the effect of the number of streams assigned to the refractive region and the total reflecting region on the convergence. Our results show that the change in the index of refraction between the two strata significantly affects the radiation field. The radiative-transfer model we present is designed for application to the atmosphere-ocean system, but it can be applied to other systems that need to consider the change in the index of refraction between two strata.

A New Look at the Discrete Ordinate Method for Radiative Transfer Calculations in Anisotropically Scattering Atmospheres

Abstract The difficulties inherent in the conventional numerical implementation of the discrete ordinate method (following Chandrasekhars prescription) for solving the radiative transfer equation are discussed. A matrix formulation is developed to overcome these difficulties, and it is specifically shown that the order of the algebraic eigenvalue problem can be reduced by a factor of 2. An expression for the source function is derived and used to obtain angular distributions. By appealing to the reciprocity principle, it is shown that substantial computational shortcuts are possible if only integrated quantities such as albedo and transmissivity are required. Comparison of fluxes calculated by the present approach with those obtained by other methods shows that low-order discrete ordinate approximations yield very accurate results. Thus, the present approach offers an efficient and reliable computational scheme that lends itself readily to the solution of a variety of radiative transfer problems in reali...

Effects of Climate on the Active Layer and Permafrost on the North Slope of Alaska, U.S.A.

Thermal regimes of the active layer and permafrost and their relations to the present-day climatic conditions on the north slope of Alaska, U.S.A. were investigated by using data collected over six years and by numerical modelling. The thickness of the active layer increases from the Arctic coast to the foothills of the Brooks Range and is directly proportional to summer air temperatures and thawing index. Within about 120 km from the Arctic coast, mean annual air temperature for the period from 1987 through 1992 was nearly constant at about −12.4±0.4°C, while the mean annual ground surface and permafrost surface temperatures increased more than 4°C. Variations in the length of thaw season and thawing index are the major factors which influence permafrost temperatures during the summer. Interactions of wind, microrelief, vegetation and seasonal snow cover and variations of physical (such as density and structure) and thermal properties of snow are the major factors affecting permafrost temperatures during the winter. The insulating effect of the seasonal snow cover could be either positive or negative on a daily basis depending upon the synoptic weather processes and on a monthly basis depending upon the time of year. On an annual basis, seasonal snow cover could increase the mean annual ground surface temperature by 2 to 7°C. Over a decade, snow cover also shows a strong effect on permafrost temperatures. Modelling results show that the depth hoar fraction of the seasonal snow cover varies from about 0.31 along the coast to about 0.57 inland. Higher permafrost temperatures along the foothills of the Brooks Range are the results of warm winters due to the impact of less strong atmospheric temperature inversion.

A reliable and efficient two-stream algorithm for spherical radiative transfer : documentation of accuracy in realistic layered media

We present a fast and well documented two-stream algorithm for radiative transfer and particle transport in vertically inhomogeneous, layered media. The physical processes considered are internal production (emission), scattering, absorption, and Lambertian reflection at the lower boundary. The medium may be forced by internal sources as well as by parallel or uniform incidence at the top boundary. This two-stream algorithm is based on a general purpose multi-stream discrete ordinate algorithm released previously. It incorporates all the advanced features of this well-tested and unconditionally stable algorithm, and includes two new features: (i) corrections for spherical geometry, and (ii) an efficient treatment of internal sources that vary rapidly with depth. It may be used to compute fluxes, flux divergences and mean intensities (actinic fluxes) at any depth in the medium. We have used the numerical code to investigate the accuracy of the two-stream approximation in vertically inhomogeneous media. In particular, computations of photodissociation and warming/cooling rates and surface fluxes of ultraviolet and visible radiation for clear, cloudy and aerosol-loaded atmospheres are presented and compared with results from multi-stream computations. The O3 +hv → O(1D) + O2 and O3 +hv → O(3P) + O2 photodissociation rates were considered for solar zenith angles between 0.0–70.0° and surface albedos in the range 0.0–1.0. For small and moderate values of the solar zenith angle and the surface albedo the error made by the two-stream approximation is generally smaller, <10%, than the combined uncertainty in cross sections and quantum yields. Surface ultraviolet and visible fluxes were calculated for the same range of solar zenith angles and surface albedos as the photodissociation rates. It was found that surface ultraviolet and visible fluxes may be calculated by the two-stream approximation with 10% error or less for solar zenith angles less than 60.0° and surface albedos less than 0.5. For large solar zenith angles and/or large surface albedos, conditions typical at high latitudes, the error made by the two-stream approximation may become appreciable, i.e. 20% or more for the photodissociation rates in the lower stratosphere and for ultraviolet and visible surface fluxes for large surface albedos. The two-stream approximation agrees well with multi-stream results for computation of warming/cooling rates except for layers containing cloud and aerosol particles where errors up to 10% may occur. The numerical code provides a fast, well-tested and robust two-stream radiative transfer program that can be used as a ‘software tool’ by aeronomers, atmospheric physicists and chemists, climate modellers, meteorologists, photobiologists and others concerned with radiation or particle transport problems. Copies of the FORTRAN77 program are available to interested users.