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Knut Stamnes and Henri Dale

Abstract

The recently developed matrix method to solve the discrete ordinate approximation to the radiative transfer equation in plane parallel geometry (Stamnes and Swanson, 1981) is extended to compute the full azimuthal dependence of the intensity, Comparing computed intensifies with those obtained by other established methods, we find that for phase functions typical of atmospheric haze 32 streams are sufficient for better than 1% agreement, while 16 streams yield an accuracy of about 1–5% except for angles close to the forward and backward directions for which the error is about 10–15%. The results of the intensity computations are summarized by presenting three-dimensional “stack plots” of the intensity as a function of polar and azimuthal angles. We also show that for flux calculations four streams suffice to obtain 1% accuracy, while eight streams yield an accuracy better than 0.1%.

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Knut Stamnes and Roy A. Swanson

Abstract

The difficulties inherent in the conventional numerical implementation of the discrete ordinate method (following Chandrasekhar's 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 realistic planetary atmospheres.

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Xiaozhen Xiong, Knut Stamnes, and Dan Lubin

Abstract

A method is presented for retrieving the broadband albedo over the Arctic Ocean using advanced very high resolution radiometer (AVHRR) data obtained from NOAA polar-orbiting satellites. Visible and near-infrared albedos over snow and ice surfaces are retrieved from AVHRR channels 1 and 2, respectively, and the broadband shortwave albedo is derived through narrow-to-broadband conversion (NTBC). It is found that field measurements taken under different conditions yield different NTBC coefficients. Model simulations over snow and ice surfaces based on rigorous radiative transfer theory support this finding. The lack of a universal set of NTBC coefficients implies a 5%–10% error in the retrieved broadband albedo. An empirical formula is derived for converting albedo values from AVHRR channels 1 and 2 into a broadband albedo under different snow and ice surface conditions. Uncertain calibration of AVHRR channels 1 and 2 is the largest source of uncertainty, and an error of 5% in satellite-measured radiance leads to an error of 5%–10% in the retrieved albedo. NOAA-14 AVHRR data obtained over the Surface Heat Budget of the Arctic Ocean (SHEBA) ice camp are used to derive the seasonal variation of the surface albedo over the Arctic Ocean between April and August of 1998. Comparison with surface measurements of albedo by Perovich and others near the SHEBA ice camp shows very good agreement. On average, the retrieval error of albedo from AVHRR is 5%–10%.

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Si-Chee Tsay, Knut Stamnes, and Kolf Jayaweera

Abstract

A radiation model is constructed that includes radiative interactions with atmospheric gases as well as parameterized treatments of scattering and absorption/emission by cloud droplets and haze particles. A unified treatment of solar and terrestrial radiation is obtained by using identical cloud and haze parameterization procedure for the shortwave and longwave region. The influence of the relative humidity of the haze particles is also considered. Snow conditions of the arctic region are simulated in terms of snow grain sizes and soot contamination in the surface layers. Data from the Arctic Stratus Cloud Experiment collected in 1980 are used for model comparisons and sensitivity studies under cloudy and hazy sky conditions.

During the arctic summer, stratus clouds are a persistent feature and decrease the downward flux at the surface by about 130–200 W m−2. Arctic haze in the summertime is important if it is above the cloud layer or in air with low relative humidity, and it decreases the downward flux at the surface by about 10–12 W m−2. By comparison the greenhouse effect of doubling the carbon dioxide amount increases the downward flux at the surface by about 4–7 W m−2 and can be offset by the background haze or by an increase in cloudiness of about 4%.

Assuming steady microstructures of stratus clouds, we find that in late June a clear sky condition results in more available downward flux for snow melt (yielding a melting rate of 9.3 em day−1) than does a cloudy sky condition (6 cm day−1). This is because the increase of infrared radiation diffused back to the surface by the cloud can not compensate for the reduction of solar radiation. When the snow starts to melt, the decreasing snow albedo further accelerates the melting process.

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Xiaozhen Xiong, Dan Lubin, Wei Li, and Knut Stamnes

Abstract

This study examines the validity and limitations associated with retrieval of cloud optical depth τ and effective droplet size r e in the Arctic from Advanced Very High Resolution Radiometer (AVHRR) channels 2 (0.725–1.10 μm), 3 (3.55–3.93 μm), and 4 (10.3–11.3 μm). The error in r e is found to be normally less than 10%, but the uncertainty in τ can be more than 50% for a 10% uncertainty in the satellite-measured radiance. Model simulations show that the satellite-retrieved cloud optical depth τ sat is overestimated by up to 20% if the vertical cloud inhomogeneity is ignored and is underestimated by more than 50% if overlap of cirrus and liquid water clouds is ignored. Under partially cloudy conditions, τ sat is larger than that derived from surface-measured downward solar irradiance (τ surf) by 40%–130%, depending on cloud-cover fraction. Here, τ sat derived from NOAA-14 AVHRR data agrees well with τ surf derived from surface measurements of solar irradiance at the Surface Heat Budget of the Arctic Ocean (SHEBA) ice camp in summer, but τ sat is about 2.3 times τ surf before the onset of snowmelt. This overestimate of τ sat is mainly due to the high reflectivity in AVHRR channel 2 over snow/ice surfaces, the presence of partial cloud cover, and inaccurate representation of the scattering phase function for mixed-phase clouds.

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Zhenyi Lin, Nan Chen, Yongzhen Fan, Wei Li, Knut Stamnes, and Snorre Stamnes

Abstract

The treatment of strongly anisotropic scattering phase functions is still a challenge for accurate radiance computations. The new delta-M+ method resolves this problem by introducing a reliable, fast, accurate, and easy-to-use Legendre expansion of the scattering phase function with modified moments. Delta-M+ is an upgrade of the widely used delta-M method that truncates the forward scattering peak with a Dirac delta function, where the “+” symbol indicates that it essentially matches moments beyond the first M terms. Compared with the original delta-M method, delta-M+ has the same computational efficiency, but for radiance computations, the accuracy and stability have been increased dramatically.

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R. Paul Lawson, Knut Stamnes, Jakob Stamnes, Pat Zmarzly, Jeff Koskuliks, Chris Roden, Qixu Mo, Michael Carrithers, and Geoffrey L. Bland

Abstract

A tethered-balloon system capable of making microphysical and radiative measurements in clouds is described and examples of measurements in boundary layer stratus clouds in the Arctic and at the South Pole are presented. A 43-m3 helium-filled balloon lofts an instrument package that is powered by two copper conductors in the tether. The instrument package can support several instruments, including, but not limited to, a cloud particle imager; a forward-scattering spectrometer probe; temperature, pressure, humidity, and wind sensors; ice nuclei filters; and a 4-π radiometer that measures actinic flux at 500 and 800 nm. The balloon can stay aloft for an extended period of time (in excess of 24 h) and conduct vertical profiles up to about 1–2 km, contingent upon payload weight, wind speed, and surface elevation. Examples of measurements in mixed-phase clouds at Ny-Ålesund, Svalbard (79°N), and at the South Pole are discussed. The stratus clouds at Ny-Ålesund ranged in temperature from 0° to −10°C and were mostly mixed phase with heavily rimed ice particles, even when cloud-top temperatures were warmer than −5°C. Conversely, mixed-phase clouds at the South Pole contained regions with only water drops at temperatures as cold as −32°C and were often composed of pristine ice crystals. The radiative properties of mixed-phase clouds are a critical component of radiative transfer in polar regions, which, in turn, is a lynch pin for climate change on a global scale.

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Jeffrey Koskulics, Steven Englehardt, Steven Long, Yongxiang Hu, Matteo Ottaviani, and Knut Stamnes

Abstract

Submerged objects viewed through wavy water surfaces appear distorted by refraction. An imaging system exploiting this effect is implemented using a submerged planar light source designed so that color images reveal features of small-amplitude waves in a wind-wave tank. The system is described by a nonlinear model of image formation based on the geometry of refraction, spectral emission from the light source, radiative transfer through the water and surface, and camera spectral response. Surface normal vector components are retrieved from the color image data using an iterative solution to the nonlinear model. The surface topography is then retrieved using a linear model that combines surface normal data with a priori constraints on elevation and curvature. The high-resolution topographic data reveal small-amplitude waves spanning wavelength scales from capillary through short gravity wave regimes. The system capabilities are demonstrated in the retrieval of test surfaces, and of a case of wind-driven waves, using data collected at high spatial and temporal resolution in a wave tank. The approach of using a physical model of image formation with inverse solution methods provides an example of how surface topography can be retrieved and may be applicable to data from other similar instruments.

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Matteo Ottaviani, Knut Stamnes, Jeff Koskulics, Hans Eide, Steven R. Long, Wenying Su, and Warren Wiscombe

Abstract

The reflection of sunlight from a wavy water surface, often referred to as sun glint, is a well-known phenomenon that presents challenges but also hitherto untapped opportunities in remote sensing based on satellite imagery. Despite being extensively investigated in the open ocean, sun glint lacks a fundamental characterization obtained under controlled laboratory conditions. A novel apparatus is presented, which is suitable for highly time-resolved measurements of light reflection from different computer-controlled wave states, with special emphasis on the detection of the polarization components. Such a system can help establish a link between the evanescent “atomic glints” from a single wave facet and the familiar sunglint pattern obtained by time averaging over a surface area containing many facets.

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Taneil Uttal, Judith A. Curry, Miles G. McPhee, Donald K. Perovich, Richard E. Moritz, James A. Maslanik, Peter S. Guest, Harry L. Stern, James A. Moore, Rene Turenne, Andreas Heiberg, Mark. C. Serreze, Donald P. Wylie, Ola G. Persson, Clayton A. Paulson, Christopher Halle, James H. Morison, Patricia A. Wheeler, Alexander Makshtas, Harold Welch, Matthew D. Shupe, Janet M. Intrieri, Knut Stamnes, Ronald W. Lindsey, Robert Pinkel, W. Scott Pegau, Timothy P. Stanton, and Thomas C. Grenfeld

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 goals, experimental design, instrumentation, and the resulting datasets. Examples of various data products available from the SHEBA project are presented.

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