Fred M. Snell

A Diffuse Thin Cloud Atmospheric Structure as a Feedback Mechanism in Global Climatic Modeling

Abstract This paper describes the first step in the development of another global climatic model in which the structure of the atmosphere and consequently its optical properties are dynamically coupled to the surface temperature. Rather than considering clouds as discrete entities, we structure the atmosphere as a diffuse thin cloud by utilizing the fundamental thermodynamics of the cooling of moist air of fixed surface relative humidity maintaining vertical mechanical equilibrium. Vertical convective thermal mixing is parameterized as is the amount of condensate that is “rained” out. The remaining condensate is distributed as spherical droplets by an assumed distribution function. The modified two-stream approximation employing a Gaussian quadrature is used to solve the radiative transfer equation. The reflectivity and transmissivity of the model atmosphere and a given amount of aerosol are then calculated. These quantities, together with a parameterization of surface reflectivity to surface temperature,...

Transfer function analysis of an oscillatory model chemical system

Abstract Oscillation occurring in the time course of a particular model reaction system is examined, utilizing the transfer function method of analysis developed in a previous paper. System properties predicted by the analytic technique correspond with those observed in analog computer solutions of the kinetic equations describing the system. The transfer function approach provides kinetic criteria for the existence of oscillation in terms of loop gain and phase shift, and elucidates the relation between oscillation and bistability, or flip-flop behavior. Although formulated to be biologically feasible, the model oscillating system is purely hypothetical, and is presented primarily as a basis for the development of general principles concerning periodicity and instability in complex reaction systems.

A MICROELECTRODE STUDY OF ELECTRICAL POTENTIALS IN FROG SKIN AND TOAD BLADDER.

Abstract The results of a microelectrode study of the electrical potential of frog skin and toad bladder are reported. Employing extremely fine tipped microelectrodes and exploiting a new technique for penetrating these tissue membranes, the results obtained indicate that on penetration from the external (mucosal) surface the electrical potential increases rather smoothly with distance once the presumed functioning cellular layer has been reached. This finding is at variance with the findings of others who have reported that the total transmembranal potential difference is distributed in two more or less equal steps. With the microelectrode at various positions within these tissue membranes, as determined by the fractional resistance, the K+ concentration in the solution bathing the internal (serosal) surface and the Na+ concentration in the solution bathing the external (mucosal) surface have been varied. The resultant potential change measured by the microelectrode is compared with the total transmembranal potential change. The results show that the K+ and Na+-sensitive functions previously envisaged to be located respectively at the internal and external bounding cell membranes of a single layer of cells are, in fact, more continuously and linearly distributed as a function of the fractional resistance. Furthermore, following a rapid change in the K+ concentration bathing the internal (serosal) surface the time course of potential change in the microelectrode always lagged the total transmembranal potential change. This time lag is a function of the position of the microelectrode, increasing the further it is from the internal (serosal) surface as measured in terms of the fractional resistance. All these results suggest that the Koefoed-Johnsen-Ussing model in its simplest form is untenable and that any model envisaged must take into account various cytoplasmic structures and/or intercellular spaces.

Statistical‐Mechanical Derivation of the Partial Molecular Stress Tensors in Isothermal Multicomponent Systems

Commencing with the general equations of molecular dynamics as used by Bearman and Kirkwood, the hydrodynamic equations of motion are derived for each component in an isothermal multicomponent system consisting of sensibly spherical nonreacting molecules. It was the primary purpose of the investigation of which this is a report to attempt to obtain a microscopic statistical basis for the macroscopic phenomenologic development of Snell and Spangler, especially in regard to their new formulation for the partial molecular stress tensors. An expansion of the number densities in pair space of perturbed nonequilibrium states alternate to that used by Bearman and Kirkwood is employed. Our expansion esplicitly recognizes the position vector arguments of both the number densities in singlet space and the local mean velocities of the individual components, as well as for the equilibrium pair correlation function. The quantities are then expanded about the central position vector in a Taylors series. The results ar...

Facilitated transport of oxygen through solutions of hemoglobin

Abstract A theoretical development is made to describe the facilitated diffusion of oxygen under steady state conditions through membranes containing concentrated solutions of hemoglobin. In contrast to the developments of other authors this development takes into consideration the kinetics of the chemical reactions of oxygen with hemoglobin. Equilibrium at the gas-liquid interfaces is assumed. The data of Scholander (1960), Hemmingsen & Scholander (1960), and Hemmingsen (1962) are quantitatively described by the resulting equations. For some of the data a reasonable semi-emperical chemical kinetic correction term, necessitated by the lack of experimental information, is utilized. The results indicate that for those data pertaining to the experiments in which a constant difference in oxygen partial pressure was maintained across the membrane at varying absolute partial pressures, the assumption of equilibrium among the chemical reactions is not justified and the kinetics of these reactions must be taken into consideration to obtain a quantitative description.

An Annual Zonally Averaged Hemispherical Climatic Model with Diffuse Cloudiness Feedback

Abstract An annual, zonally averaged, steady-state hemispherical climatic model is developed which incorporates the diffuse thin cloud tropospheric structure of Weare and Snell as a cloudiness feedback mechanism. The zones are 15° wide and the meridional energy transport is parameterized as that carried by the ocean and by tropospheric eddies, each using a single coefficient, and that carried by the mean annual circulation embodying four coefficients. The radiative transfer calculations through the atmosphere employ the Eddington approximation for the visible spectrum, using the appropriate annual averaged solar zenith angles and the Rodgers emissivity technique for the infrared. Ozone, above the troposphere, is assumed to act only as an absorber in the visible. In the infrared it is assumed to have a constant-hemispherical emissivity at the “tropopause” temperature (212 K). Surface reflectivities in terms of land and ocean are zonally set and land snow and ocean ice lines are calculated to occur at 273 a...

Aerosol and climate: some further considerations.

Approximate numerical radiative calculations show that whether added aerosol causes heating or cooling of the earth-atmosphere system is a function not only of its intrinsic absorption-backscatter characteristics but also of its particular location in the atmosphere with respect to the average cloud as well as of both the cloud reflectivity and the underlying surface reflectivity.

An Annual Zonally Averaged Global Climatic Model with Diffuse Cloudiness Feedback

Abstract An annual, zonally averaged, steady-state global climate model is developed which represents an extension of the hemispherical model reported by Temkin and Snell (1976). The model employs twelve 15° zones and incorporates the diffuse thin cloud tropospheric structure of Weare and Snell (1974) as a feedback mechanism calculated separately over land and ocean employing the appropriate mean land height temperatures and ocean level temperatures. Radiative calculations are also carried separately over land and ocean. Meridional energy transport is parameterized very similar to that of Temkin and Snell but also includes transport across the equator linearly related to the temperature difference. The response of the model to variations in various climatic determinants is studied, including global variations in carbon dioxide, aerosol and solar constant as well as additions of chlorofluorocarbons to the atmosphere. The model reveals that the Southern Hemisphere is more stable than the Northern Hemisphere...

Feedback Coupling of Absorbed Solar Radiation by Three Model Atmospheres with Clouds

Abstract A study of the amount of solar radiation absorbed by the earth-atmosphere system as a function of the surface temperature is made comparing three model atmospheres with clouds. The atmospheres are generated as previously reported by Weare and Snell. This involves a quasi-isentropic expansion of moist surface air of given relative humidity. “Rainout” of condensate and the lapse rate are parameterized. The three atmospheres to be compared are a horizontally homogeneous diffuse thin cloud structure, a half-cloud .half-clear structure, and a variable fractional cloud cover, each normalized to give the proper albedo at a reference point representative of global annual average conditions. Radiative transfer calculations are made using the modified two-stream approximation and/or the Eddington approximation. The results indicate that with the diffuse thin cloud the magnitude of the feedback coupling of solar radiation absorbed to surface temperature lies intermediate to that of the other structures, wit...

Transfer function analysis of chemical kinetic systems

Abstract A technique is developed for the analysis of complex coupled chemical reaction systems utilizing transfer functions to characterize the kinetic properties of each reaction process. The method of analysis involves linearization in the vicinity of some steady state of the system. A closed loop configuration of the reaction system imposes constraints upon the time course exhibited by the system, since the product of transfer functions around the loop must be unity. Instability of a particular steady state, and oscillatory behavior may be examined through this analytic approach.