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- Author or Editor: Rudolph W. Preisendorfer x
- Journal of the Atmospheric Sciences x
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Abstract
In this paper we develop a new method for solving the transfer of radiation within a laterally finite optical medium. A new radiative transfer equation, based on a multimode approach, is developed which includes the explicit effects of the sides of the medium. This equation, derived for a box shaped medium, is exactly analogous to the plane parallel radiative transfer equation with a source term. Accordingly, the new equation is solved using the familiar plane-parallel techniques based on invariant imbedding relationships in the form of doubling and adding. The additional terms in the newly derived radiative transfer equation can be interpreted as apparent source and sink terms which arise from the lateral finiteness of the medium. The geometric and physical aspects of these source-sink terms and their influence on the solutions are discussed. Results also show that the multimode solutions compare well with the Monte Carlo simulations.
Abstract
In this paper we develop a new method for solving the transfer of radiation within a laterally finite optical medium. A new radiative transfer equation, based on a multimode approach, is developed which includes the explicit effects of the sides of the medium. This equation, derived for a box shaped medium, is exactly analogous to the plane parallel radiative transfer equation with a source term. Accordingly, the new equation is solved using the familiar plane-parallel techniques based on invariant imbedding relationships in the form of doubling and adding. The additional terms in the newly derived radiative transfer equation can be interpreted as apparent source and sink terms which arise from the lateral finiteness of the medium. The geometric and physical aspects of these source-sink terms and their influence on the solutions are discussed. Results also show that the multimode solutions compare well with the Monte Carlo simulations.
Abstract
When a numerical model's representation of a physical field is to be compared with a corresponding real observed field, it is usually the case that the numbers of realizations of model and observed field are relatively small, so that the natural procedure of producing histograms of pertinent statistics of the fields (e.g., means, variances) from the data sets themselves cannot be usually carried out. Also, it is not always safe to adopt assumptions of normality and independence of the data values. This prevents the confident use of classical statistical methods to make significance statements about the success or failure of the model's replication of the data. Here we suggest two techniques of determinable statistical power, in which small samples of spatially extensive physical fields can be made to blossom into workably large samples on which significance decisions can be based. We also introduce some new measures of location, spread and shape of multivariate data sets which may be used in conjunction with the two techniques. The result is a pair of new data intercomparison procedures which we illustrate using GCM simulations of the January sea-level pressure field and regional ocean model simulations of the new-shore velocity field of South America. We include with these procedures a method of determining the spatial and temporal locations of non-random errors between the model and data fields so that models can be improved accordingly.
Abstract
When a numerical model's representation of a physical field is to be compared with a corresponding real observed field, it is usually the case that the numbers of realizations of model and observed field are relatively small, so that the natural procedure of producing histograms of pertinent statistics of the fields (e.g., means, variances) from the data sets themselves cannot be usually carried out. Also, it is not always safe to adopt assumptions of normality and independence of the data values. This prevents the confident use of classical statistical methods to make significance statements about the success or failure of the model's replication of the data. Here we suggest two techniques of determinable statistical power, in which small samples of spatially extensive physical fields can be made to blossom into workably large samples on which significance decisions can be based. We also introduce some new measures of location, spread and shape of multivariate data sets which may be used in conjunction with the two techniques. The result is a pair of new data intercomparison procedures which we illustrate using GCM simulations of the January sea-level pressure field and regional ocean model simulations of the new-shore velocity field of South America. We include with these procedures a method of determining the spatial and temporal locations of non-random errors between the model and data fields so that models can be improved accordingly.
Abstract
This paper extends the theoretical developments of Part I to illustrate the power of the method in solving multiple scattering problems with sources that result from i) the single scatter of a collimated beam of solar radiation that is directly transmitted to a given point in the medium and ii) thermal emission. These source terms are derived in the multimode context and solutions are presented to illustrate the effects of sun angle and infrared emission on the radiance and irradiance fields that emerge from hypothetical box shaped clouds. The results reiterate the earlier findings that the sides of clouds play an important role in the exchange of radiative energy between the cloud and its environment. The total infrared emission by cuboidal clouds, for example, is shown to be substantially larger than the emission from plane parallel clouds as a result of this additional exchange of radiant energy.
The results presented in the paper, including the comparisons with available Monte Carlo calculations show the multimode approach to be a viable, accurate and computationally efficient method of solving the general problem of anisotropic scattering in horizontally finite optical media.
Abstract
This paper extends the theoretical developments of Part I to illustrate the power of the method in solving multiple scattering problems with sources that result from i) the single scatter of a collimated beam of solar radiation that is directly transmitted to a given point in the medium and ii) thermal emission. These source terms are derived in the multimode context and solutions are presented to illustrate the effects of sun angle and infrared emission on the radiance and irradiance fields that emerge from hypothetical box shaped clouds. The results reiterate the earlier findings that the sides of clouds play an important role in the exchange of radiative energy between the cloud and its environment. The total infrared emission by cuboidal clouds, for example, is shown to be substantially larger than the emission from plane parallel clouds as a result of this additional exchange of radiant energy.
The results presented in the paper, including the comparisons with available Monte Carlo calculations show the multimode approach to be a viable, accurate and computationally efficient method of solving the general problem of anisotropic scattering in horizontally finite optical media.
