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- Author or Editor: Rudolph W. Preisendorfer 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
A nine year record (December 1973 to February 1983) of seasonal temperature and precipitation anomaly forecasts is examined. The four independent forecasters were J. Namias, the National Weather Service (D. Gilman and colleagues), the Analoger (T. Barnett and R. Preisendorfer), and A. Douglas. The skills of these human forecasters are compared to three benchmark forecasters, climatology, persistence and random chance, and to several simple objective forecasters.
It was found that the human forecasters are all of comparable skill, and that they are generally better than climatology or random chance. However, the humans are often no better than persistence or some of the objective forecasters. In general, temperature was predicted better than precipitation. For both temperature and precipitation, winters were most-well predicted and falls were least-well predicted. Temperature was best predicted in the Southwest Desert, Pacific Coast and Northern Plains, and worst predicted on the Gulf Coast, Atlantic Coast and Southern Plains. Precipitation was best predicted in the Southwest Desert, Great Lakes, and Northern Great Basin and worst predicted along the Gulf, Atlantic and Pacific Coasts.
Abstract
A nine year record (December 1973 to February 1983) of seasonal temperature and precipitation anomaly forecasts is examined. The four independent forecasters were J. Namias, the National Weather Service (D. Gilman and colleagues), the Analoger (T. Barnett and R. Preisendorfer), and A. Douglas. The skills of these human forecasters are compared to three benchmark forecasters, climatology, persistence and random chance, and to several simple objective forecasters.
It was found that the human forecasters are all of comparable skill, and that they are generally better than climatology or random chance. However, the humans are often no better than persistence or some of the objective forecasters. In general, temperature was predicted better than precipitation. For both temperature and precipitation, winters were most-well predicted and falls were least-well predicted. Temperature was best predicted in the Southwest Desert, Pacific Coast and Northern Plains, and worst predicted on the Gulf Coast, Atlantic Coast and Southern Plains. Precipitation was best predicted in the Southwest Desert, Great Lakes, and Northern Great Basin and worst predicted along the Gulf, Atlantic and Pacific Coasts.
Abstract
The problem of determining confidence intervals for climatic signals using data sets with spatial and temporal sampling inhomogeneities is solved by a four-step process. First, the actual data set is analysed to determine autoregressive models which are consistent with the actual data at daily, monthly and annual time scales. Second, these models are used to generate artificial, but realistic, data sets which reproduce selected statistical properties of the actual data. Third, these artificial data sets are sampled by Monte Carlo techniques to determine certain confidence interval coefficients appropriate to different fields, geographical regions, and averaging periods. Fourth, these confidence interval coefficients are used to place error bars on climatic signals derived from the actual data set. The technique is illustrated by the analysis of historical sea surface temperature and sea level pressure data in the eastern tropical Pacific Ocean.
Abstract
The problem of determining confidence intervals for climatic signals using data sets with spatial and temporal sampling inhomogeneities is solved by a four-step process. First, the actual data set is analysed to determine autoregressive models which are consistent with the actual data at daily, monthly and annual time scales. Second, these models are used to generate artificial, but realistic, data sets which reproduce selected statistical properties of the actual data. Third, these artificial data sets are sampled by Monte Carlo techniques to determine certain confidence interval coefficients appropriate to different fields, geographical regions, and averaging periods. Fourth, these confidence interval coefficients are used to place error bars on climatic signals derived from the actual data set. The technique is illustrated by the analysis of historical sea surface temperature and sea level pressure data in the eastern tropical Pacific Ocean.
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
The downward albedo (irradiance reflectance) r − and the upward albedo r + of a random air–water surface, formed by capillary waves, are computed as a function of lighting conditions and wind speed by Monte Carlo means for incident unpolarized radiant flux. The possibility of multiple scattering of light rays and of ray-shielding of waves by other waves is included in the calculations. The effects on r ± of multiple scattering and wave shielding are found to be important for higher speeds (≳10 m s−1) and nearly horizontal light ray angles of incidence (≳70°). The Monte Carlo procedure is used to generate reflected and transmitted glitter patterns as functions of wind speed and sun position. These results are used to check the procedure's patterns against observed patterns. A simple analytic first-order model of glitter patterns and irradiance reflectance, which assumes a binormal distribution of water facet slopes, is tested against the relatively exact Monte Carlo results. Regions are defined in wind-speed and incident-angle space over which the first-order model is acceptable. Plots of the Monte Carlo r ± are drawn as functions of wind speed and angle of incidence of light rays. The albedos r ± are also found for various continuous radiance distribution simulating overcast skies and upwelling submarine light fields just below the air–water surface. Good agreement is found, were comparison can be made, between the computed albedos and albedos measured over the ocean surface.
Abstract
The downward albedo (irradiance reflectance) r − and the upward albedo r + of a random air–water surface, formed by capillary waves, are computed as a function of lighting conditions and wind speed by Monte Carlo means for incident unpolarized radiant flux. The possibility of multiple scattering of light rays and of ray-shielding of waves by other waves is included in the calculations. The effects on r ± of multiple scattering and wave shielding are found to be important for higher speeds (≳10 m s−1) and nearly horizontal light ray angles of incidence (≳70°). The Monte Carlo procedure is used to generate reflected and transmitted glitter patterns as functions of wind speed and sun position. These results are used to check the procedure's patterns against observed patterns. A simple analytic first-order model of glitter patterns and irradiance reflectance, which assumes a binormal distribution of water facet slopes, is tested against the relatively exact Monte Carlo results. Regions are defined in wind-speed and incident-angle space over which the first-order model is acceptable. Plots of the Monte Carlo r ± are drawn as functions of wind speed and angle of incidence of light rays. The albedos r ± are also found for various continuous radiance distribution simulating overcast skies and upwelling submarine light fields just below the air–water surface. Good agreement is found, were comparison can be made, between the computed albedos and albedos measured over the ocean surface.
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.
