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Abstract
The Arctic Stratus Experiment, conducted during June 1980 over the Beaufort Sea, produced an extensive set of simultaneous measurements of boundary layer structure, radiation fluxes, and cloud microphysical properties. In this paper these data are used to determine the interactions between mixing, radiative transfer, and cloud microphysics for four cloud decks. The thermodynamic structure and fluxes of the thermodynamic quantities in the cloudy boundary layer are examined, including liquid water fluxes. Net radiative heating profiles are also determined. A detailed analysis of the fine-scale structure of the cloud microphysics is presented, including correlations between the cloud microphysical parameters (droplet concentration, liquid water content, mean radius, spectral dispersion, and the 95% volume liquid water drop radius), which are used to infer the nature of the mixing processes and the local effects of radiative heating/cooling. A comparison is then made with other observations and existing model conceptions of the cloudy boundary layer and cloud microphysical processes.
Due to the large static stability and frequent occurrence of a humidity inversion, these clouds are not maintained by surface fluxes of moisture. The net radiative cooling at the cloud top is balanced differently for each of the cases examined, although in all four cases at least a portion of the radiative cooling was found to promote mixed-layer convection. The effects of turbulent entrainment do not penetrate beyond 50 m below mean cloud top, therefore not directly affecting the evolution of the drop spectra except for right near cloud top. Significant liquid water production due to radiative cooling is indicated by the profiles of buoyancy flux, entropy flux, water fluxes, and vertical velocity variance, and also by the large drop spectral dispersions and the correlations between the cloud microphysical parameters. Liquid water fluxes are determined to be nearly as large as the vapor fluxes. The liquid water flux divergences introduce significant structure into the profiles of liquid water content and drop spectra, and also enhance coalescence processes in the lower portion of the clouds.
Abstract
The Arctic Stratus Experiment, conducted during June 1980 over the Beaufort Sea, produced an extensive set of simultaneous measurements of boundary layer structure, radiation fluxes, and cloud microphysical properties. In this paper these data are used to determine the interactions between mixing, radiative transfer, and cloud microphysics for four cloud decks. The thermodynamic structure and fluxes of the thermodynamic quantities in the cloudy boundary layer are examined, including liquid water fluxes. Net radiative heating profiles are also determined. A detailed analysis of the fine-scale structure of the cloud microphysics is presented, including correlations between the cloud microphysical parameters (droplet concentration, liquid water content, mean radius, spectral dispersion, and the 95% volume liquid water drop radius), which are used to infer the nature of the mixing processes and the local effects of radiative heating/cooling. A comparison is then made with other observations and existing model conceptions of the cloudy boundary layer and cloud microphysical processes.
Due to the large static stability and frequent occurrence of a humidity inversion, these clouds are not maintained by surface fluxes of moisture. The net radiative cooling at the cloud top is balanced differently for each of the cases examined, although in all four cases at least a portion of the radiative cooling was found to promote mixed-layer convection. The effects of turbulent entrainment do not penetrate beyond 50 m below mean cloud top, therefore not directly affecting the evolution of the drop spectra except for right near cloud top. Significant liquid water production due to radiative cooling is indicated by the profiles of buoyancy flux, entropy flux, water fluxes, and vertical velocity variance, and also by the large drop spectral dispersions and the correlations between the cloud microphysical parameters. Liquid water fluxes are determined to be nearly as large as the vapor fluxes. The liquid water flux divergences introduce significant structure into the profiles of liquid water content and drop spectra, and also enhance coalescence processes in the lower portion of the clouds.
Abstract
The primary goal of this study is to examine the formation mechanisms for the intense North American anticyclone that developed in late January and early February 1989 and to assess the relative importance of adiabatic versus diabatic processes. The complete height tendency equation is used as the diagnostic tool in this study. Results of this analysis show that diabatic processes are relatively unimportant and that the principal forcing mechanisms in the anticyclogenesis are vorticity advection and differential thermal advection. The cold low-level air over Alaska enhances the anticyclogenesis by promoting a positive contribution from the differential thermal advection. The cold low-level temperatures preclude strong cold-air advection at low levels in the anticyclone; strong upper-level cold-air advection thus results in a large positive contribution from the differential thermal advection. The vertical advection of static stability opposes the other forcings, acting to slow the development. The ageostrophic vorticity tendency term makes a substantial contribution; during some portions of the anticyclogenesis, the ageostrophic vorticity tendency enhances the anticyclogenesis and at other times opposes the development. A comparison is made with the model results of a purely cold-core anticyclone forced solely by radiative cooling. It is determined that the forcing mechanisms are substantially different for the intense North American anticyclone when compared with the cold-core anticyclone driven by radiative cooling, even though the thermodynamic structures of the two anticyclones are similar.
Abstract
The primary goal of this study is to examine the formation mechanisms for the intense North American anticyclone that developed in late January and early February 1989 and to assess the relative importance of adiabatic versus diabatic processes. The complete height tendency equation is used as the diagnostic tool in this study. Results of this analysis show that diabatic processes are relatively unimportant and that the principal forcing mechanisms in the anticyclogenesis are vorticity advection and differential thermal advection. The cold low-level air over Alaska enhances the anticyclogenesis by promoting a positive contribution from the differential thermal advection. The cold low-level temperatures preclude strong cold-air advection at low levels in the anticyclone; strong upper-level cold-air advection thus results in a large positive contribution from the differential thermal advection. The vertical advection of static stability opposes the other forcings, acting to slow the development. The ageostrophic vorticity tendency term makes a substantial contribution; during some portions of the anticyclogenesis, the ageostrophic vorticity tendency enhances the anticyclogenesis and at other times opposes the development. A comparison is made with the model results of a purely cold-core anticyclone forced solely by radiative cooling. It is determined that the forcing mechanisms are substantially different for the intense North American anticyclone when compared with the cold-core anticyclone driven by radiative cooling, even though the thermodynamic structures of the two anticyclones are similar.
Abstract
An ice water path retrieval algorithm, using airborne Millimeter-Wave Imaging Radiometer brightness temperatures at 89, 150, and 220 GHz, is developed for tropical clouds. This algorithm is based on the results of radiative transfer model simulations, using in situ ice particle properties measured from aircraft as model inputs. The scattering signatures at the 150- and 220-GHz channels are the primary inputs into the algorithm, while 89-GHz data are used for determining the nonice background radiation. The ice water path is first calculated from each of the 150- and 220-GHz scattering signatures, and then a combination of the two channels is used for the final retrieval, based on the consideration of the different channel sensitivities to the magnitude of the ice water path. The algorithm is evaluated by comparing the retrieved with in situ measured ice water paths for seven cases observed during the Tropical Oceans Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE). Theoretical analysis shows that the uncertainty due to particle size could be the largest error in the retrievals and this error could be as large as plus or minus 50%. As an application of this algorithm, the ice water path characteristics during TOGA COARE are studied, including assessment of the mean of ice water path, its frequency distribution, and its relationships with cloud-top temperature and liquid water amount. Although tropical clouds are the target of this study, this algorithm could be modified and extended to other climatological regions.
Abstract
An ice water path retrieval algorithm, using airborne Millimeter-Wave Imaging Radiometer brightness temperatures at 89, 150, and 220 GHz, is developed for tropical clouds. This algorithm is based on the results of radiative transfer model simulations, using in situ ice particle properties measured from aircraft as model inputs. The scattering signatures at the 150- and 220-GHz channels are the primary inputs into the algorithm, while 89-GHz data are used for determining the nonice background radiation. The ice water path is first calculated from each of the 150- and 220-GHz scattering signatures, and then a combination of the two channels is used for the final retrieval, based on the consideration of the different channel sensitivities to the magnitude of the ice water path. The algorithm is evaluated by comparing the retrieved with in situ measured ice water paths for seven cases observed during the Tropical Oceans Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE). Theoretical analysis shows that the uncertainty due to particle size could be the largest error in the retrievals and this error could be as large as plus or minus 50%. As an application of this algorithm, the ice water path characteristics during TOGA COARE are studied, including assessment of the mean of ice water path, its frequency distribution, and its relationships with cloud-top temperature and liquid water amount. Although tropical clouds are the target of this study, this algorithm could be modified and extended to other climatological regions.
Abstract
The method of simultaneously retrieving ice water path and mass median diameter using microwave data at two frequencies is examined and implemented for tropical nonprecipitating clouds. To develop the retrieval algorithm, the authors first derived a bulk mass–size relation for ice particles in tropical clouds based on microphysical data collected during the Central Equatorial Pacific Experiment. This relation effectively allows ice particle density to decrease with particle size. In implementing the retrieval algorithm, 150- and 220-GHz Millimeter-Wave Imaging Radiometer data collected during the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment were used. Ice water path and mass median diameter are determined based on a lookup table generated by a radiative transfer model. The lookup table depends on cloud type, cloud liquid water path, and atmospheric temperature and humidity profiles. Only nonprecipitating clouds are studied in this paper. Error analyses were performed by a Monte Carlo procedure in which atmospheric profiles, ice cloud height, liquid water content, surface temperature, and instrument noise vary randomly within their uncertainty range through a Latin hypercube sampling scheme. The rms error in the retrievals is then assessed and presented in a two-dimensional diagram of ice water path and mass median diameter. It is shown that the simultaneous retrieval method using 150 and 220 GHz may be used for clouds with ice water path larger than 200 g m−2 and mass median diameter larger than 200 μm. To obtain meaningful retrievals for “thinner” clouds, higher microwave frequencies are needed. It is also shown that liquid water clouds that are at the same altitude as ice clouds interfere with the retrievals to a significant degree. To obtain reasonable ice water path and mass median size retrievals, it is necessary first to group clouds into several classes, then to apply separate algorithms to the different classes. The accuracy of the retrievals also depends on cloud type, with the best accuracy for cirrus and the worst for the midtop mixed-phase cloud among the clouds investigated in this study.
Abstract
The method of simultaneously retrieving ice water path and mass median diameter using microwave data at two frequencies is examined and implemented for tropical nonprecipitating clouds. To develop the retrieval algorithm, the authors first derived a bulk mass–size relation for ice particles in tropical clouds based on microphysical data collected during the Central Equatorial Pacific Experiment. This relation effectively allows ice particle density to decrease with particle size. In implementing the retrieval algorithm, 150- and 220-GHz Millimeter-Wave Imaging Radiometer data collected during the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment were used. Ice water path and mass median diameter are determined based on a lookup table generated by a radiative transfer model. The lookup table depends on cloud type, cloud liquid water path, and atmospheric temperature and humidity profiles. Only nonprecipitating clouds are studied in this paper. Error analyses were performed by a Monte Carlo procedure in which atmospheric profiles, ice cloud height, liquid water content, surface temperature, and instrument noise vary randomly within their uncertainty range through a Latin hypercube sampling scheme. The rms error in the retrievals is then assessed and presented in a two-dimensional diagram of ice water path and mass median diameter. It is shown that the simultaneous retrieval method using 150 and 220 GHz may be used for clouds with ice water path larger than 200 g m−2 and mass median diameter larger than 200 μm. To obtain meaningful retrievals for “thinner” clouds, higher microwave frequencies are needed. It is also shown that liquid water clouds that are at the same altitude as ice clouds interfere with the retrievals to a significant degree. To obtain reasonable ice water path and mass median size retrievals, it is necessary first to group clouds into several classes, then to apply separate algorithms to the different classes. The accuracy of the retrievals also depends on cloud type, with the best accuracy for cirrus and the worst for the midtop mixed-phase cloud among the clouds investigated in this study.
Abstract
In order to understand the mechanisms of formation of broad size spectra of cloud droplets and to develop a basis for the parameterization of cloud microphysical and optical properties, the authors derive a general kinetic equation of stochastic condensation that is applicable for various relationships between the supersaturation relaxation time τ f and the timescale of turbulence τ L . Supersaturation is considered as a nonconservative variable, and thus additional covariances and a turbulent diffusion coefficient tensor that is dependent on the supersaturation relaxation time, k ij (τ f ), are introduced into the kinetic equation. This equation can be used in cloud models with explicit microphysics or can serve as a basis for development of parameterizations for bulk cloud models and general circulation models.
Abstract
In order to understand the mechanisms of formation of broad size spectra of cloud droplets and to develop a basis for the parameterization of cloud microphysical and optical properties, the authors derive a general kinetic equation of stochastic condensation that is applicable for various relationships between the supersaturation relaxation time τ f and the timescale of turbulence τ L . Supersaturation is considered as a nonconservative variable, and thus additional covariances and a turbulent diffusion coefficient tensor that is dependent on the supersaturation relaxation time, k ij (τ f ), are introduced into the kinetic equation. This equation can be used in cloud models with explicit microphysics or can serve as a basis for development of parameterizations for bulk cloud models and general circulation models.
Abstract
The kinetic equation of stochastic condensation derived in Part I is solved analytically under some simplifications. Analytical solutions of the gamma-distribution type are found using an analogy and methodology from quantum mechanics. In particular, formulas are derived for the index of the gamma distribution p and the relative dispersion of the droplet size spectra, which determines the rate of precipitation formation and cloud optical properties. An important feature of these solutions is that, although the equation for p includes many parameters that vary by several orders of magnitude, the expression for p leads to a dimensionless quantity of the order 1–10 for a wide variety of cloud types, and the relative dispersion σ r is related directly to the meteorological factors (vertical velocity, turbulence coefficient, dry and moist adiabatic temperature lapse rates) and the properties of the cloud (droplet concentration and mean radius).
The following observed behavior of the cloud size spectra is explained quantitatively by the analytical solutions:narrowing of drop size spectra with increased cooling rate, and broadening of drop size spectra with increasing turbulence. The application of these solutions is illustrated using an example of a typical stratus cloud and possible applications for the convective clouds are discussed. The predictions of this solution are compared with some other models and with observations in stratus and convective clouds. These analytical solutions can serve as a basis for the parameterization of the cloud microphysical and optical properties for use in cloud models and general circulation models.
Abstract
The kinetic equation of stochastic condensation derived in Part I is solved analytically under some simplifications. Analytical solutions of the gamma-distribution type are found using an analogy and methodology from quantum mechanics. In particular, formulas are derived for the index of the gamma distribution p and the relative dispersion of the droplet size spectra, which determines the rate of precipitation formation and cloud optical properties. An important feature of these solutions is that, although the equation for p includes many parameters that vary by several orders of magnitude, the expression for p leads to a dimensionless quantity of the order 1–10 for a wide variety of cloud types, and the relative dispersion σ r is related directly to the meteorological factors (vertical velocity, turbulence coefficient, dry and moist adiabatic temperature lapse rates) and the properties of the cloud (droplet concentration and mean radius).
The following observed behavior of the cloud size spectra is explained quantitatively by the analytical solutions:narrowing of drop size spectra with increased cooling rate, and broadening of drop size spectra with increasing turbulence. The application of these solutions is illustrated using an example of a typical stratus cloud and possible applications for the convective clouds are discussed. The predictions of this solution are compared with some other models and with observations in stratus and convective clouds. These analytical solutions can serve as a basis for the parameterization of the cloud microphysical and optical properties for use in cloud models and general circulation models.
Abstract
To provide guidance for the development of satellite microwave rainfall-retrieval algorithms, the basic relationships between emission and scattering signals in natural clouds must be understood. In this study, the relationship between two parameters observed from microwave satellite data—the polarization difference at 19 GHz D and the polarization-corrected temperature PCT—is investigated over the global ocean on a monthly and 5° (lat) × 5° (long) mean basis. Using data from January and July 1993, the occurrence frequencies and latitudinal variation and horizontal distribution of the D–PCT relationships are investigated. The D–PCT slope is studied by dividing the entire weather range into three regimes: nonprecipitation, light precipitation, and heavy precipitation. The analysis shows that small variation of PCT in the nonprecipitation regime could be achieved by employing a variable coefficient in the PCT definition equation. The slopes in the light precipitation regime are latitude dependent. Although the interpretation is inconclusive, it is felt that the differences in the fractional coverage and the rain layer depth in different latitudes is responsible for the latitudinal dependence. No clear latitudinal dependence of slopes in the heavy precipitation regime is found.
The connection of the D–PCT relationship to the performances of an emission-based and a scattering-based rainfall algorithm are investigated using the Second WetNet Precipitation Intercomparison Project rainfall cases. The results of this study emphasize the necessity of incorporating the scattering signal in rainfall rate retrieval algorithms. Additionally, the D–PCT slope information can be used to help categorize precipitation types, which may be useful in determining the specific algorithm best used for a certain precipitation type and/or regime.
Abstract
To provide guidance for the development of satellite microwave rainfall-retrieval algorithms, the basic relationships between emission and scattering signals in natural clouds must be understood. In this study, the relationship between two parameters observed from microwave satellite data—the polarization difference at 19 GHz D and the polarization-corrected temperature PCT—is investigated over the global ocean on a monthly and 5° (lat) × 5° (long) mean basis. Using data from January and July 1993, the occurrence frequencies and latitudinal variation and horizontal distribution of the D–PCT relationships are investigated. The D–PCT slope is studied by dividing the entire weather range into three regimes: nonprecipitation, light precipitation, and heavy precipitation. The analysis shows that small variation of PCT in the nonprecipitation regime could be achieved by employing a variable coefficient in the PCT definition equation. The slopes in the light precipitation regime are latitude dependent. Although the interpretation is inconclusive, it is felt that the differences in the fractional coverage and the rain layer depth in different latitudes is responsible for the latitudinal dependence. No clear latitudinal dependence of slopes in the heavy precipitation regime is found.
The connection of the D–PCT relationship to the performances of an emission-based and a scattering-based rainfall algorithm are investigated using the Second WetNet Precipitation Intercomparison Project rainfall cases. The results of this study emphasize the necessity of incorporating the scattering signal in rainfall rate retrieval algorithms. Additionally, the D–PCT slope information can be used to help categorize precipitation types, which may be useful in determining the specific algorithm best used for a certain precipitation type and/or regime.
Abstract
This paper presents a unified treatment of cloud particle fall velocities for both liquid and crystalline cloud particles over the entire size range observed in the atmosphere. The fall velocity representation is formulated in terms of the Best (or Davies) number X, and the Reynolds number Re. For the power-law representations used in many applications, the coefficients are found as the continuous analytical functions of X (or diameter) over the entire hydrometeor size range. Analytical asymptotic solutions are obtained for these coefficients for the two regimes that represent large and small particles and correspond to potential and aerodynamical flows, respectively. The new formulation is compared with experimental data and previous formulations for small drops, large nonspherical drops, and various ice crystal habits. For ice crystals, published mass–dimension and area–dimension relationships are used. The advantage of the new representation of fall velocities over previous representations is that the continuous representation avoids inaccuracy at the points of discontinuity for different size regimes, allows easier parameterization of the hydrometeor size spectra, and allows for continuous integration over the size spectrum. The new fall velocity formulation may be applied to bin-resolving and bulk microphysical models, as well as to remote sensing.
Abstract
This paper presents a unified treatment of cloud particle fall velocities for both liquid and crystalline cloud particles over the entire size range observed in the atmosphere. The fall velocity representation is formulated in terms of the Best (or Davies) number X, and the Reynolds number Re. For the power-law representations used in many applications, the coefficients are found as the continuous analytical functions of X (or diameter) over the entire hydrometeor size range. Analytical asymptotic solutions are obtained for these coefficients for the two regimes that represent large and small particles and correspond to potential and aerodynamical flows, respectively. The new formulation is compared with experimental data and previous formulations for small drops, large nonspherical drops, and various ice crystal habits. For ice crystals, published mass–dimension and area–dimension relationships are used. The advantage of the new representation of fall velocities over previous representations is that the continuous representation avoids inaccuracy at the points of discontinuity for different size regimes, allows easier parameterization of the hydrometeor size spectra, and allows for continuous integration over the size spectrum. The new fall velocity formulation may be applied to bin-resolving and bulk microphysical models, as well as to remote sensing.
Abstract
This paper extends previous work on the theory of heterogenous ice nucleation. The goals of this analysis are to explain empirical observations of ice nucleation and to provide a suitable framework for modeling and parameterizing the ice nucleation process in cloud-scale and large-scale atmospheric models. Considered are the processes of heterogeneous freezing of deliquescent mixed cloud condensation nuclei that may serve as ice nuclei, and the properties of an ice germ critical radius, energy, and nucleation rate of ice crystals are examined as functions of temperature and supersaturation. Expressions for nucleation in a polydisperse aerosol for the deliquescence-freezing mode are developed. Equations are derived for the threshold and critical saturation ratios as functions of temperature and nucleation rate, and for the threshold and critical temperatures as functions of saturation ratio. Equivalence of the new formulation for the freezing point depression with traditional expressions is shown and the concepts of the effective temperature and supercooling are introduced. These new formulations are used in a companion paper for simulations of ice nucleation using a cloud parcel model.
Abstract
This paper extends previous work on the theory of heterogenous ice nucleation. The goals of this analysis are to explain empirical observations of ice nucleation and to provide a suitable framework for modeling and parameterizing the ice nucleation process in cloud-scale and large-scale atmospheric models. Considered are the processes of heterogeneous freezing of deliquescent mixed cloud condensation nuclei that may serve as ice nuclei, and the properties of an ice germ critical radius, energy, and nucleation rate of ice crystals are examined as functions of temperature and supersaturation. Expressions for nucleation in a polydisperse aerosol for the deliquescence-freezing mode are developed. Equations are derived for the threshold and critical saturation ratios as functions of temperature and nucleation rate, and for the threshold and critical temperatures as functions of saturation ratio. Equivalence of the new formulation for the freezing point depression with traditional expressions is shown and the concepts of the effective temperature and supercooling are introduced. These new formulations are used in a companion paper for simulations of ice nucleation using a cloud parcel model.
