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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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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, 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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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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Yongxiang Hu, David Winker, Mark Vaughan, Bing Lin, Ali Omar, Charles Trepte, David Flittner, Ping Yang, Shaima L. Nasiri, Bryan Baum, Robert Holz, Wenbo Sun, Zhaoyan Liu, Zhien Wang, Stuart Young, Knut Stamnes, Jianping Huang, and Ralph Kuehn

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 phase relationship, more constraints are necessary to uniquely determine cloud phase. Based on theoretical and modeling studies, an improved cloud phase determination algorithm has been developed. Instead of depending primarily on layer-integrated depolarization ratios, this algorithm differentiates cloud phases by using the spatial correlation of layer-integrated attenuated backscatter and layer-integrated particulate depolarization ratio. This approach includes a two-step process: 1) use of a simple two-dimensional threshold method to provide a preliminary identification of ice clouds containing randomly oriented particles, ice clouds with horizontally oriented particles, and possible water clouds and 2) application of a spatial coherence analysis technique to separate water clouds from ice clouds containing horizontally oriented ice particles. Other information, such as temperature, color ratio, and vertical variation of depolarization ratio, is also considered. The algorithm works well for both the 0.3° and 3° off-nadir lidar pointing geometry. When the lidar is pointed at 0.3° off nadir, half of the opaque ice clouds and about one-third of all ice clouds have a significant lidar backscatter contribution from specular reflections from horizontally oriented particles. At 3° off nadir, the lidar backscatter signals for roughly 30% of opaque ice clouds and 20% of all observed ice clouds are contaminated by horizontally oriented crystals.

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