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- Author or Editor: Biao Wang x
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Abstract
A unified formulation of the general decomposition of radiance and the radiative transfer equation (RTE) of plane-parallel atmospheres and the general solutions of the generally decomposed RTE system (GD-RTES) are presented. It is shown that the eigenvalues of the coefficient matrix of the GD-RTES are real and the eigenvectors are independent of each other when the single-scattering albedo is less than unity; the general solution of the GD-RTES for a homogeneous layer can then be expressed in combinations of the exponential functions of the optical depth. The solution for nonhomogeneous atmosphere–surface systems can be obtained through either the matrix operator method or the linear system method. An outline of the general procedure is given, and a detailed example will be provided in Part II of this work. The formulation can serve as a meta-algorithm from which the prototypes of new algorithms can be developed and tested. Some of the conventional methods such as the discrete ordinate method and the spherical harmonic method can be considered as instances of the unified formulation. With the unified formulation, some interesting topics about the RTE and its solution can be discussed more generally, such as those about correction for energy conservation, treatment of boundary conditions, and transformation for numerical stability; some of the methods that have already proved useful to these issues in the well-established algorithms can be generalized to be available to the other methods that can be derived from the unified formulation.
Abstract
A unified formulation of the general decomposition of radiance and the radiative transfer equation (RTE) of plane-parallel atmospheres and the general solutions of the generally decomposed RTE system (GD-RTES) are presented. It is shown that the eigenvalues of the coefficient matrix of the GD-RTES are real and the eigenvectors are independent of each other when the single-scattering albedo is less than unity; the general solution of the GD-RTES for a homogeneous layer can then be expressed in combinations of the exponential functions of the optical depth. The solution for nonhomogeneous atmosphere–surface systems can be obtained through either the matrix operator method or the linear system method. An outline of the general procedure is given, and a detailed example will be provided in Part II of this work. The formulation can serve as a meta-algorithm from which the prototypes of new algorithms can be developed and tested. Some of the conventional methods such as the discrete ordinate method and the spherical harmonic method can be considered as instances of the unified formulation. With the unified formulation, some interesting topics about the RTE and its solution can be discussed more generally, such as those about correction for energy conservation, treatment of boundary conditions, and transformation for numerical stability; some of the methods that have already proved useful to these issues in the well-established algorithms can be generalized to be available to the other methods that can be derived from the unified formulation.
Abstract
Based on the unified formulation, the so-called hemispherical harmonics method with four components (HSHM4) is derived following the general procedure described in the first paper of this series. The numerical results of this method, including the flux reflections, transmissions, and absorptions for different optical depths, incident beam angles, and single-scattering albedos and the emissions for different optical depths and single-scattering albedos, are reported, in comparison with the results of DISORT with 128 streams as a benchmark. The application of the method to the radiation scheme for climate models is illustrated with the numerical results, including the heating-rate profiles for the shortwave and longwave radiation, radiative fluxes at the top and the bottom boundaries of the atmosphere, and the actinic flux profiles, for typical model atmospheres of Earth and different clear or cloudy conditions. The comparison of results with those of the discrete ordinate methods (DOMs) and the spherical harmonic method (SHM) with four components shows that the HSHM4 has comparable accuracy with the four-stream DOM with double-Gaussian quadrature and is more accurate than the four-stream SHM and the four-stream DOM with full-range Gaussian quadrature in general, especially in the cases of longwave radiation when the multiple-scattering effect should be accounted for. The HSHM4 can be deployed consistently to all of the bands without artificial division between the longwave and shortwave. The development and validation of the HSHM4 exhibit the usefulness of the unified formulation in the study of atmospheric radiative transfer.
Abstract
Based on the unified formulation, the so-called hemispherical harmonics method with four components (HSHM4) is derived following the general procedure described in the first paper of this series. The numerical results of this method, including the flux reflections, transmissions, and absorptions for different optical depths, incident beam angles, and single-scattering albedos and the emissions for different optical depths and single-scattering albedos, are reported, in comparison with the results of DISORT with 128 streams as a benchmark. The application of the method to the radiation scheme for climate models is illustrated with the numerical results, including the heating-rate profiles for the shortwave and longwave radiation, radiative fluxes at the top and the bottom boundaries of the atmosphere, and the actinic flux profiles, for typical model atmospheres of Earth and different clear or cloudy conditions. The comparison of results with those of the discrete ordinate methods (DOMs) and the spherical harmonic method (SHM) with four components shows that the HSHM4 has comparable accuracy with the four-stream DOM with double-Gaussian quadrature and is more accurate than the four-stream SHM and the four-stream DOM with full-range Gaussian quadrature in general, especially in the cases of longwave radiation when the multiple-scattering effect should be accounted for. The HSHM4 can be deployed consistently to all of the bands without artificial division between the longwave and shortwave. The development and validation of the HSHM4 exhibit the usefulness of the unified formulation in the study of atmospheric radiative transfer.
Abstract
A vertically one-dimensional model is developed with cloud fraction constrained by the maximum entropy production (MEP) principle. The model reasonably reproduces the global mean climate with its surface temperature, radiation and heat fluxes, cloud fraction, and lapse rate. The maximum convection hypothesis in Paltridge’s models is related to the MEP principle, and the MEP state of climate is approximately equivalent to that with the maximum lapse rate. The sensitivity investigation about the model assumptions and the prescribed parameters show that the model is considerably robust in simulating the global mean climate. With the MEP constraint, the feedbacks of cloud and water vapor to external forcings, such as changes of CO2 concentration, solar incidence, and surface albedo, are evaluated. While water vapor always behaves as a strong positive feedback, cloud feedbacks to the different forcings are different, in both magnitude and sign. The modeled feedback of cloud fraction to the forcing resulting from surface albedo variation seems in good agreement with the observed seasonal variation of the global cloud fraction.
Abstract
A vertically one-dimensional model is developed with cloud fraction constrained by the maximum entropy production (MEP) principle. The model reasonably reproduces the global mean climate with its surface temperature, radiation and heat fluxes, cloud fraction, and lapse rate. The maximum convection hypothesis in Paltridge’s models is related to the MEP principle, and the MEP state of climate is approximately equivalent to that with the maximum lapse rate. The sensitivity investigation about the model assumptions and the prescribed parameters show that the model is considerably robust in simulating the global mean climate. With the MEP constraint, the feedbacks of cloud and water vapor to external forcings, such as changes of CO2 concentration, solar incidence, and surface albedo, are evaluated. While water vapor always behaves as a strong positive feedback, cloud feedbacks to the different forcings are different, in both magnitude and sign. The modeled feedback of cloud fraction to the forcing resulting from surface albedo variation seems in good agreement with the observed seasonal variation of the global cloud fraction.
Abstract
This paper assesses the relative uncertainties from GCMs and from hydrological models in modeling climate change impact on runoff across southeast Australia. Five lumped conceptual daily rainfall–runoff models are used to model runoff using historical daily climate series and using future climate series obtained by empirically scaling the historical climate series informed by simulations from 15 GCMs. The majority of the GCMs project a drier future for this region, particularly in the southern parts, and this is amplified as a bigger reduction in the runoff. The results indicate that the uncertainty sourced from the GCMs is much larger than the uncertainty in the rainfall–runoff models. The variability in the climate change impact on runoff results for one rainfall–runoff model informed by 15 GCMs (an about 28%–35% difference between the minimum and maximum results for mean annual, mean seasonal, and high runoff) is considerably larger than the variability in the results between the five rainfall–runoff models informed by 1 GCM (a less than 7% difference between the minimum and maximum results). The difference between the rainfall–runoff modeling results is larger in the drier regions for scenarios of big declines in future rainfall and in the low-flow characteristics. The rainfall–runoff modeling here considers only the runoff sensitivity to changes in the input climate data (primarily daily rainfall), and the difference between the hydrological modeling results is likely to be greater if potential changes in the climate–runoff relationship in a warmer and higher CO2 environment are modeled.
Abstract
This paper assesses the relative uncertainties from GCMs and from hydrological models in modeling climate change impact on runoff across southeast Australia. Five lumped conceptual daily rainfall–runoff models are used to model runoff using historical daily climate series and using future climate series obtained by empirically scaling the historical climate series informed by simulations from 15 GCMs. The majority of the GCMs project a drier future for this region, particularly in the southern parts, and this is amplified as a bigger reduction in the runoff. The results indicate that the uncertainty sourced from the GCMs is much larger than the uncertainty in the rainfall–runoff models. The variability in the climate change impact on runoff results for one rainfall–runoff model informed by 15 GCMs (an about 28%–35% difference between the minimum and maximum results for mean annual, mean seasonal, and high runoff) is considerably larger than the variability in the results between the five rainfall–runoff models informed by 1 GCM (a less than 7% difference between the minimum and maximum results). The difference between the rainfall–runoff modeling results is larger in the drier regions for scenarios of big declines in future rainfall and in the low-flow characteristics. The rainfall–runoff modeling here considers only the runoff sensitivity to changes in the input climate data (primarily daily rainfall), and the difference between the hydrological modeling results is likely to be greater if potential changes in the climate–runoff relationship in a warmer and higher CO2 environment are modeled.
Abstract
Solar radiation is one of the most important factors affecting climate and the environment. Routine measurements of irradiance are valuable for climate change research because of long time series and areal coverage. In this study, a set of quality assessment (QA) algorithms is used to test the quality of daily solar global, direct, and diffuse radiation measurements taken at 122 observatories in China during 1957–2000. The QA algorithms include a physical threshold test (QA1), a global radiation sunshine duration test (QA2), and a standard deviation test applied to time series of annually averaged solar global radiation (QA3). The results show that the percentages of global, direct, and diffuse solar radiation data that fail to pass QA1 are 3.07%, 0.01%, and 2.52%, respectively; the percentages of global solar radiation data that fail to pass the QA2 and QA3 are 0.77% and 0.49%, respectively. The method implemented by the Global Energy Balance Archive is also applied to check the data quality of solar radiation in China. Of the 84 stations with a time series longer that 20 yr, suspect data at 35 of the sites were found. Based on data that passed the QA tests, trends in ground solar radiation and the effect of the data quality assessment on the trends are analyzed. There is a decrease in ground solar global and direct radiation in China over the years under study. Although the quality assessment process has significant effects on the data from individual stations and/or time periods, it does not affect the long-term trends in the data.
Abstract
Solar radiation is one of the most important factors affecting climate and the environment. Routine measurements of irradiance are valuable for climate change research because of long time series and areal coverage. In this study, a set of quality assessment (QA) algorithms is used to test the quality of daily solar global, direct, and diffuse radiation measurements taken at 122 observatories in China during 1957–2000. The QA algorithms include a physical threshold test (QA1), a global radiation sunshine duration test (QA2), and a standard deviation test applied to time series of annually averaged solar global radiation (QA3). The results show that the percentages of global, direct, and diffuse solar radiation data that fail to pass QA1 are 3.07%, 0.01%, and 2.52%, respectively; the percentages of global solar radiation data that fail to pass the QA2 and QA3 are 0.77% and 0.49%, respectively. The method implemented by the Global Energy Balance Archive is also applied to check the data quality of solar radiation in China. Of the 84 stations with a time series longer that 20 yr, suspect data at 35 of the sites were found. Based on data that passed the QA tests, trends in ground solar radiation and the effect of the data quality assessment on the trends are analyzed. There is a decrease in ground solar global and direct radiation in China over the years under study. Although the quality assessment process has significant effects on the data from individual stations and/or time periods, it does not affect the long-term trends in the data.
