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R. M. Welch and B. A. Wielicki

Abstract

A parameterization scheme is presented which allows the calculation of radiative reflected fluxes from a stratocumulus cloud field. The scheme is based upon plane-parallel calculations, such as delta-Eddington, and a simple procedure is outlined by which the plane-parallel fluxes may be transformed to those of the broken cloud case. This parameterization scheme has been tested for optical thicknesses ranging from τ=3 to 49, solar zenith angles ranging from θ0 = 0° to 72.5°, and all values of cloud cover. Plane-parallel calculations become increasingly more accurate as optical depth decreases. This suggests that calculations including broken cloudiness effects such as shadowing are probably unnecessary in thin cirrus or aerosol layers over water.

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R. M. Welch and B. A. Wielicki

Abstract

Reflected fluxes are calculated for stratocumulus cloud fields as a function of sky cover, cloud aspect ratio, and cloud shape. Cloud liquid water volume is held invariant as cloud shape is varied so that the results can be utilized more effectively by general circulation models (GCM) and climate models.

The magnitude of the reflected flux differences between broken and plane-parallel cloudiness is of particular significance. On the basis of required accuracy in the Earth Radiation Budget Experiment (ERBE) program, an order of magnitude value of 10 W m−2 is used to estimate “significant differences” between plane-parallel and broken cloudiness. This limit is exceeded for cloud covers between 10% and 90%, indicating that plane-parallel calculations are not satisfactory at most values of cloud cover. The choice of cloud shape also leads to large differences in reflected fluxes. These differences may be traced to the anisotropic intensity pattern out the cloud sides, to the size and shape of the “holes” between clouds, and to variations in cloud area as viewed from the solar direction.

An empirical relationship for effective cloud cover is given at solar zenith angle of θ = 60°. This relationship allows for the relatively accurate (ΔF = 10–15 W m−2) computation of broken cloud field reflected fluxes from plane-parallel calculations. Although the present parameterization is limited to solar zenith angles near θ = 60°, this is an indication that further work may lead to reasonably accurate estimates of broken cloud field radiative properties using modified plane-parallel calculations, irrespective of assumed cloud shape.

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Yasushi Inomata, R. E. Feind, and R. M. Welch

Abstract

A new method based upon high-spatial-resolution imagery is presented that matches cloud and shadow regions to estimate cirrus and stratus cloud heights. The distance between the cloud and the matching shadow pattern is accomplished using the 2D cross-correlation function from which the cloud height is derived. The distance between the matching cloud-shadow patterns is verified manually. The derived heights also are validated through comparison with a temperature-based retrieval of cloud height. It is also demonstrated that an estimate of cloud thickness can be retrieved if both the sunside and antisunside of the cloud-shadow pair are apparent. The technique requires some intepretation to determine the cloud height level retrieved (i.e., the top, base, or mid-level). It is concluded that the method is accurate to within several pixels, equivalent to cloud height variations of about ±250 m. The results show that precise placement of the templates is unnecessary, so that the development of a semiautomated procedure is possible. Cloud templates of about 64 pixels on a side or larger produce consistent results. The procedure was repeated for imagery degraded to simulate lower spatial resolutions. The results suggest that spatial resolution of 150–200 m or better is necessary in order to obtain stable cloud height retrievals.

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R. M. Welch, M. G. Ravichandran, and S. K. Cox

Abstract

There is considerable controversy in the literature concerning fog formation. One set of observations suggests that fog forms during a lull in turbulence, white another set of observations suggests that increased turbulence leads to fog formation.

A number of first-order closure techniques are applied to numerical simulations. The results show that fog formation and development is directly correlated with the magnitude of the eddy mixing coefficients. Larger turbulence generation leads to more rapid fog development and to larger liquid water contents. The rate at which the fog top grows is directly related to the rate at which turbulence lifts the inversion.

During the mature fog stage, a series of fog dissipation and redevelopment episodes occur. Liquid water develops in the upper regions of the fog during the turbulently quiet periods. Subsequent destabilization of the atmosphere increases turbulence generation and mixes the upper-level liquid water to the surface, creating surface fog intensification. Quasi-periodic oscillations in fog parameters are largest in the upper regions of the fog and become progressively damped in the lower regions of a thick fog.

These results are in qualitative agreement with the observations reported by Jiusto and Lala and support the hypothesis that there are distinct stages of fog development.

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R. M. Welch, S. K. Sengupta, and K. S. Kuo

Abstract

Statistical measures of the spatial distributions of gray levels (cloud reflectivities) are determined for LANDSAT Multispectral Scanner digital data. Textural properties for twelve stratocumulus cloud fields, seven cumulus fields, and two cirrus fields are examined using the Spatial Gray Level Co-Occurrence Matrix method. The co-occurrence statistics are computed for pixel separations ranging from 57 m to 29 km and at angles of 0°, 45°, 90° and 135°. Nine different textual measures are used to define the cloud field spatial relationships. However, the measures of contrast and correlation appear to be most useful in distinguishing cloud structure.

Cloud field macrotexture describes general cloud field characteristics at distances greater than the size of typical cloud elements. It is determined from the spatial asymptotic values of the texture measures. The slope of the texture curves at small distances provides a measure of the microtexture of individual cloud cells. Cloud fields composed primarily of small cells have very steep slopes and reach their asymptotic values at short distances from the origin. As the cells composing the cloud field grow larger, the slope becomes more gradual and the asymptotic distance increases accordingly. Low asymptotic values of correlation show that stratocumulus cloud fields have no large scale organized structure.

Besides the ability to distinguish cloud field structure, texture appears to be a potentially valuable tool in cloud classification. Stratocumulus clouds are characterized by low values of angular second moment and large values of entropy. Cirrus clouds appear to have extremely low values of contrast, low values of entropy, and very large values of correlation.

Finally, we propose that sampled high spatial resolution satellite data be used in conjunction with coarser resolution operational satellite data to detect and identify cloud field structure and directionality and to locate regions of subresolution scale cloud contamination.

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W. J. Wiscombe, R. M. Welch, and W. D. Hall

Abstract

In an effort to bring more realism cloud-radiation calculations, arising-parcel model of cloud microphysics and a 191 waveband model of atmospheric radiation (ATRAD) have been brought to bear on the problem of cloud absorption of solar radiation, with emphasis on the effect of drops greater than 40–50 μm in radius. The earlier conclusions of Welch and others that such large drops can produce cloud absorptivities in excess of 30% have not been substantiated. Instead we find large-drop enhancements of only 0.02–0.04 in cloud and total atmospheric absorptivities. However, several other, more important influences were uncovered: 1) Large drops make it necessary to know the second and third moments of the drop distribution in order to parameterize the shortwave effect of clouds; parameterizations based only on the third moment (liquid water content) do not consider a wide enough range of variation of drop distribution. 2) Large drops cause a precipitous fall in both cloud and planetary albedo if the supply of liquid water is fixed. 3) Large drops enhance the solar greenhouse effect by distributing solar heating more deeply into the cloud. Plots of spectral heating rate reveal that the spectral regions 1.5–1.8 μm and 1.15–1.3 μm are most important for shortwave heating of clouds.

It is suggested that very large drops may also explain the looming “optical depth paradox,” whereby optical depths deduced from measurements of reflected radiation are much smaller than those calculated from measured liquid water profiles.

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Lindsay Parker, R. M. Welch, and D. J. Musil

Abstract

Aircraft observations and high resolution Landsat Multispectral Scanner digital data are used to determine the sizes of spatial inhomogeneities (“holes”) in cumulus clouds. The majority of holes are found near cloud edges, but the larger holes tend to be found in cloud interiors. Aircraft measurements show these cloud spatial inhomogeneities in the range of 100 to 500 m, while Landsat data show them in the range of 100 m to 3 km.

The number of holes per cloud decreases exponentially with increasing hole diameter. Small clouds not only have smaller holes, but also fewer holes than large clouds. Large clouds have large holes in them, as well as large numbers of the smaller holes. The total cloud area occupied by holes increases with increasing cloud size.

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K. S. Kuo, R. M. Welch, and S. K. Sengupta

Abstract

Twelve cirrus scenes are analyzed to determine textural and structural features using LANDSAT imagery. The main structural characteristics are: 1) cirrus cloud size distributions obey a power law, with larger cloud cells (D ⩾ 1.5 km) having smaller slopes than smaller cloud elements; 2) convective-type cirrus are fractal in nature with fractal dimensions of ≈ 1.4, while stratiform cirrus clouds show bifractal behavior, with larger clouds having smaller fractal dimensions (≈1.3); 3) stratiform cirrus cloud cells have significantly larger horizontal aspect ratio than do smaller cells; and 4) structural results are not sensitive to threshold selection.

The main textural characteristics are: 1) convective cirrus clouds have high contrast measures and a rapid decrease of correlation at short distances, while stratiform cirrus clouds have low contrast measures and more gradual slopes; 2) asymptotic values are good descriptors of general characteristics (macrotexture) of cloud fields, while the slopes of textural measure curves at small distances reveal information about cloud field microtexture; 3) contrast and correlation appear to be the best discriminators of cloud field structure, and their directional measures show preferred cloud field orientation; and 4) correlation measures are sensitive to threshold selection for cirrostratus cases.

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S. K. Sengupta, R. M. Welch, M. S. Navar, T. A. Berendes, and D. W. Chen

Abstract

Detailed observations of cumulus cloud scales and processes are an essential ingredient in models that deal with (i) high spatial resolution cumulus ensembles; and (ii) parameterization of cloud radiative processes. The present investigation focuses on three aspects of the morphology of cumulus clouds: 1) the inhomogeneity as represented by the size distribution of clouds and cloud “holes,” 2) the nearest-neighbor relationships regarding their sizes and mutual distances, and 3) the scales of their clustering.

Distributionwise, cloud size can best be represented by a mixture of two power laws. Clouds of diameter below 1 km have the slope parameter ranging from about 1.4 to 2.3, while larger clouds have slopes ranging from 2.1 to 4.75. Furthermore, these clouds are bifractal in nature. The break in power law and fractal dimension occurs at a size critical to the cloud-scale processes in the following sense. First, this is the cloud size that makes the largest contribution to the extent of cloud cover. Second, there are indications that this is the size at which clouds begin to modify their environment.

Cloud inhomogeneities have significant impact on radiative fluxes. The size distribution of holes in the cumulus clouds studied here have a single slope power law with estimated slopes close to 3; these holes have single fractal dimensions. Furthermore, the results suggest that as the cloud field matures, there is an increase in the number and size of the inhomogeneities along with increasing cloud size.

Nearest-neighbor relationships are studied from two different perspectives. First, the nearest-neighbor separation distance is modeled by four probability distributions: lognormal, gamma, extreme-value and Weibull. Lognormal appears to provide the best fit. Second, the nearest-neighbor pair sizes and the associated separation distance are studied using a co-occurrence frequency approach of spatial point processes using second-order statistics. The largest frequency of nearest-neighbor pairs occurs at a distance of 200–300 m, with the largest absolute differences in cloud size found at separations of about 500 m. At larger separations, there is a tendency for the larger clouds to be closer to other large clouds, apparently through the modification of the environment. Nonlinear dependence between the sizes of nearest-neighbor cloud pairs increases with increasing cloud size.

Cumulus cloud clustering scales are determined by using the classical Greig-Smith quadrat analysis technique. Clustering scales of about 15, 29, and 59 km are found for most of the ten cloud fields studied.

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R. M. Welch, S. K. Sengupta, A. K. Goroch, P. Rabindra, N. Rangaraj, and M. S. Navar

Abstract

Six Advanced Very High-Resolution Radiometer local area coverage (AVHPR LAC) arctic scenes are classified into ten classes. These include water, solid sea ice, broken sea ice, snow-covered mountains, snow-free land, and five cloud types. Three different classifiers are examined: 1) the traditional stepwise discriminant analysis (SDA) method; 2) the feed-forward back-propagation (FFBP) neural network; and 3) the probabilistic neural network (PNN).

More than 200 spectral and textural measures are computed. These are reduced to 20 features using sequential forward selection. Theoretical accuracy of the classifiers is determined using the bootstrap approach. Overall accuracy is 85.6%, 87.6%, and 87.0% for the SDA, FFBP, and PNN classifiers, respectively, with standard deviations of approximately 1%. Thin cloud/fog over ice is the class with the lowest accuracy (≈75%) for all of the classifiers. The snow-covered mountains, the cirrus over ice, and the land classes are classified with the highest accuracy (⩾90%) by all of the classifiers.

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