Stephen K. Cox

Scattering of Visible Radiation by Finite Clouds

Abstract A theoretical model of the scattering of shortwave radiation is applied to clouds finite in horizontal extent. The resulting irradiance patterns are then compared with calculations for horizontally semi-infinite clouds. This analysis shows, that the irradiance fields are dramatically dependent upon energy passing through the vertical sides of the finite sized clouds. Directional reflectance of individual cubic clouds is shown to be approximately 25% less than for semi-infinite clouds of optical depths ranging from 20 to 80. Directional reflectance from the top of cubic clouds for small solar zenith angle continues to increase at large optical depths (∼70) while the infinite cloud becomes nearly asymptotic at this point. It is shown that for a solar zenith angle of 60°, the directional reflectance for a 2/10 sky cover of cubic clouds is 0.29 while for 2/10 coverage of semi-infinite cloud the directional reflectance is 0.185. Implications of differences between the cubic cloud results and the semi-...

Cirrus Clouds. Part I: A Cirrus Cloud Model

Abstract A two-dimensional (x, z), time-dependent, numerical cloud model is developed for the purpose of investigating the role of various physical processes involved in the maintenance of cirriform clouds. In addition to accounting for dynamic and thermodynamic processes including phase changes of water, effects due to microphysical composition and radiative processes are also explicitly incorporated into the model. Diagnostic parameterizations for the local radiative properties of cloudy volumes and the gravity induced relative fall speed of the contained ice water are presented. Results of a simulation of a thin cirrostratus cloud are given. Features of the simulated cloud structure are quite realistic. Quantitative agreement is found between the simulated ice water contents and vertical motions and comparable observations. It is shown that radiative effect may be very significant in the maintenance of cirrus. The effects of the gravity-induced relative fall speed of ice crystals are found to be of cri...

Cirrus Clouds. Part II: Numerical Experiments on the Formation and Maintenance of Cirrus

Abstract The numerical cirrus cloud model of Starr and Cox is used to investigate the role of various physical processes in the formation and maintenance of cirrus. Effects due to microphysical composition, i.e., crystal habit and size distribution, are found to be quite important in determining the overall cloud water budget. Radiative processes are also shown to affect the organization and bulk properties of the cloud. Substantial differences between simulations of thin cirrus under midday and nighttime conditions are found with the cloud being less dense overall (∼20%) but more persistently cellular during the day with all other environmental factors being the same. Cloud-scale interactions and feedbacks between dynamic, thermodynamic and radiative processes and the microphysical composition are significant and strongly modulate the properties of the simulated clouds. A comparison is made between simulations of weakly forced cirrostratus and nonprecipitating altostratus (liquid phase) under comparable ...

Marine Stratocumulus Convection. Part I: Governing Equations and Horizontally Homogeneous Solutions

Abstract A coupled, convective-radiative, boundary-layer model of marine stratocumulus clouds is presented. The model, which is a slight generalization of the cloud-topped, mixed-layer model of Lilly (1968), has as dependent variables the cloud-top height, cloud-base height, mixed-layer moist static energy and total water content, the turbulent fluxes of moist static energy and total water, the cloud-top jumps of moist static energy and total water, the cloud-top temperature, and the net radiative flux divergence at cloud top and in the mixed layer. Under horizontally homogeneous steady-state conditions the governing equations reduce to a system of algebraic equations which is easily solved. This system has been solved for sea surface temperatures between 13 and 18°C and large-scale divergences between 1×10−6 and 6×10−6 s−1. These calculations have been performed for the case when all the radiative cooling is confined to the cloud-top jump condition and for the case when some of the cooling is allowed to ...

Model of the Thermodynamic Structure of the Trade-Wind Boundary Layer: Part I. Theoretical Formulation and Sensitivity Tests

Abstract A numerical model which predicts the time variation of the thermodynamic structure of the trade-wind boundary layer is developed. Horizontally homogeneous conditions are assumed and the large-scale divergence, sea surface temperature and surface wind speed are specified externally. The model predicts the average value of mixing ratio and moist static energy in the subcloud and cloud layer and the slopes of these quantities in the cloud layer; the model also predicts the height of the transition layer (the layer which defines the boundary between the cloud and subcloud layer) and the height of the trade inversion. Subcloud layer convective fluxes are specified by using the bulk aerodynamic method for specifying the surface fluxes and a mixed-layer parameterization of the fluxes at the top of the subcloud layer. The moist convective processes are parameterized in terms of a mass flux which varies linearly with height and a cloud-environment difference in thermodynamic quantities which also varies l...

FIRE—The First ISCCP Regional Experiment

The First International Satellite Cloud Climatology Project Regional Experiment (FIRE) designed to study the roles of clouds, in particular marine stratocumulus and cirrus-cloud systems, in the global climate is discussed. The objectives of FIRE are: (1) to develop a cloud-classification scheme; (2) to validate and improve satellite cloud-retrieval techniques; (3) to improve cloud radiation models; (4) to collect cloud space/time statistics; (5) to improve cloud dynamics models; and (6) to validate and improve GCM cloud parameterizations. The methods used to acquire extended time data and intensive field observations are described. The extended time and intensive field data collected during the FIRE are to be archived in the NASA Pilot Climate Data System at Goddard Space Flight Center.

Marine Stratocumulus Convection. part II: Horizontally Inhomogeneous Solutions

Abstract Solutions of the horizontally inhomogeneous version of the coupled, convective-radiative, cloud-topped mixed-layer model described in Part I of this study are presented. Both numerical and approximate analytical methods are used to investigate the downstream variations which occur as boundary-layer air flows through regions of varying sea surface temperature and large-scale divergence. Six numerical experiments are performed. In the first two experiments boundary-layer air flows through regions of constant large-scale divergence but of increasing or decreasing sea surface temperature. In the cold advection case the boundary layer warms, moistens and deepens in time, while the turbulent fluxes increase. In the warm advection case the boundary layer cools, drys and becomes shallower, while the turbulent fluxes decrease. In addition the cloud base descends and there is a tendency to form a surface fog. In the third and fourth experiments boundary-layer air flows through regions of constant sea surfa...

Infrared radiative properties of tropical cirrus clouds inferred with aircraft measurements

Abstract Longwave emissivities and the vertical profile of cooling rates of tropical cirrus clouds are determined using broadband hemispheric irradiance data. Additionally, a broadband mass absorption coefficient is defined and used to relate emissivity to water content. The data used were collected by the National Center for Atmospheric Research (NCAR) Sabreliner during the GARP Atlantic Tropical Experiment (GATE) in the summer of 1974. Three case studies are analyzed showing that these tropical cirrus clouds approached an emissivity of 1.0 within a vertical distance of 1.0 km. Broadband mass absorption coefficients ranging from 0.076 to 0.096 m2 g−1 are derived. A comparison of these results with other work suggests that tropical cirrus cloud emissivities may be significantly larger than heretofore believed. Ice water content of the clouds was deduced from data collected by a one-dimensional particle spectrometer. Analyses of the ice water content and the observed particle size distributions are presented.

Aircraft Observations of the Shortwave Fractional Absorptance of Non-Homogeneous Clouds

Abstract Techniques for normalizing aircraft measurements of solar irradiance to a horizontal surface and a constant solar zenith angle are outlined. The effects of these normalization procedures are a minimum when the data are collected at small solar zenith angles. A method of analysis is discussed which takes into account the effects of the heterogeneous structure of clouds on observations of cloud fractional absorptance in the 0.3–2.8 μm spectral interval. Application of the technique to the observed absorptance, results in a corrected fractional absorptance value which is in better agreement with theoretical calculations than previously reported. In addition, the technique significantly reduces the sampling time required to obtain a representative cloud fractional absorptance.

Estimates of Radiative Divergence during Phase III of the GARP Atlantic Tropical Experiment: Part II. Analysis of Phase III Results

Abstract The GATE Phase III radiative divergence profiles generally show less upper tropospheric radiative divergence and more middle level divergence than previous cilimatological estimates suggest. These differences are due primarily to the extensive middle and upper tropospheric cloudiness in the GATE area, the large mean values of total precipitable water vapor (∼5.1 cm), and the inclusion in the present study of the effects of the water vapor pressure broadened continuum. Averages for the 6 h local time periods 0000–0600, 0600–1200, 120–1800 and 1800–2400 show all layers of the GATE Phase III B-scale atmosphere experience a net radiative loss of energy. However, actual radiative heating of some layers is evident near midday. For a convectively suppressed composite case all levels above 700 mb show heating for the 1000–1400 LST period. The total troposphere shows a net radiative gain for the same 6 h interval (0900–1500 LST). For the enhanced convection case absolute warming is generally confined to t...