In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubi...In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.展开更多
This paper presents a comprehensive analysis of global human trafficking trends over a twenty-year period, leveraging a robust dataset from the Counter Trafficking Data Collaborative (CTDC). The study unfolds in a sys...This paper presents a comprehensive analysis of global human trafficking trends over a twenty-year period, leveraging a robust dataset from the Counter Trafficking Data Collaborative (CTDC). The study unfolds in a systematic manner, beginning with a detailed data collection phase, where ethical and legal standards for data usage and privacy are strictly observed. Following collection, the data undergoes a rigorous preprocessing stage, involving cleaning, integration, transformation, and normalization to ensure accuracy and consistency for analysis. The analytical phase employs time-series analysis to delineate historical trends and utilizes predictive modeling to forecast future trajectories of human trafficking using the advanced analytical capabilities of Power BI. A comparative analysis across regions—Africa, the Americas, Asia, and Europe—is conducted to identify and visualize the distribution of human trafficking, dissecting the data by victim demographics, types of exploitation, and duration of victimization. The findings of this study not only offer a descriptive and predictive outlook on trafficking patterns but also provide insights into the regional nuances that influence these trends. The article underscores the prevalence and persistence of human trafficking, identifies factors contributing to its evolution, and discusses the implications for policy and law enforcement. By integrating a methodological approach with quantitative analysis, this research contributes to the strategic planning and resource allocation for combating human trafficking. It highlights the necessity for continued research and international cooperation to effectively address and mitigate this global issue. The implications of this research are significant, offering actionable insights for policymakers, law enforcement, and advocates in the ongoing battle against human trafficking.展开更多
Rank Histograms are suitable tools to assess the quality of ensembles within an ensemble prediction system or framework. By counting the rank of a given variable in the ensemble, we are basically making a sample analy...Rank Histograms are suitable tools to assess the quality of ensembles within an ensemble prediction system or framework. By counting the rank of a given variable in the ensemble, we are basically making a sample analysis, which does not allow us to distinguish if the origin of its variability is external noise or comes from chaotic sources. The recently introduced Mean to Variance Logarithmic （MVL） Diagram accounts for the spatial variability, being very sensitive to the spatial localization produced by infinitesimal perturbations of spatiotemporal chaotic systems. By using as a benchmark a simple model subject to noise, we show the distinct information given by Rank Histograms and MVL Diagrams. Hence, the main effects of the external noise can be visualized in a graphic. From the MVL diagram we clearly observe a reduction of the amplitude growth rate and of the spatial localization （chaos suppression）, while from the Rank Histogram we observe changes in the reliability of the ensemble. We conclude that in a complex framework including spatiotemporal chaos and noise, both provide a more complete forecasting picture.展开更多
文摘In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.
文摘This paper presents a comprehensive analysis of global human trafficking trends over a twenty-year period, leveraging a robust dataset from the Counter Trafficking Data Collaborative (CTDC). The study unfolds in a systematic manner, beginning with a detailed data collection phase, where ethical and legal standards for data usage and privacy are strictly observed. Following collection, the data undergoes a rigorous preprocessing stage, involving cleaning, integration, transformation, and normalization to ensure accuracy and consistency for analysis. The analytical phase employs time-series analysis to delineate historical trends and utilizes predictive modeling to forecast future trajectories of human trafficking using the advanced analytical capabilities of Power BI. A comparative analysis across regions—Africa, the Americas, Asia, and Europe—is conducted to identify and visualize the distribution of human trafficking, dissecting the data by victim demographics, types of exploitation, and duration of victimization. The findings of this study not only offer a descriptive and predictive outlook on trafficking patterns but also provide insights into the regional nuances that influence these trends. The article underscores the prevalence and persistence of human trafficking, identifies factors contributing to its evolution, and discusses the implications for policy and law enforcement. By integrating a methodological approach with quantitative analysis, this research contributes to the strategic planning and resource allocation for combating human trafficking. It highlights the necessity for continued research and international cooperation to effectively address and mitigate this global issue. The implications of this research are significant, offering actionable insights for policymakers, law enforcement, and advocates in the ongoing battle against human trafficking.
基金support from MEC,Spain,through Grant No.CGL2007-64387/CLIthe AECID,Spain,for support through projects A/013666/07 and A/018685/08
文摘Rank Histograms are suitable tools to assess the quality of ensembles within an ensemble prediction system or framework. By counting the rank of a given variable in the ensemble, we are basically making a sample analysis, which does not allow us to distinguish if the origin of its variability is external noise or comes from chaotic sources. The recently introduced Mean to Variance Logarithmic （MVL） Diagram accounts for the spatial variability, being very sensitive to the spatial localization produced by infinitesimal perturbations of spatiotemporal chaotic systems. By using as a benchmark a simple model subject to noise, we show the distinct information given by Rank Histograms and MVL Diagrams. Hence, the main effects of the external noise can be visualized in a graphic. From the MVL diagram we clearly observe a reduction of the amplitude growth rate and of the spatial localization （chaos suppression）, while from the Rank Histogram we observe changes in the reliability of the ensemble. We conclude that in a complex framework including spatiotemporal chaos and noise, both provide a more complete forecasting picture.
