The Earth's magnetic field,which has been extensively observed from ground to satellite altitudes over several decades,originates from multiple sources,such as the core dynamo,the conductive mantle,the magnetized ...The Earth's magnetic field,which has been extensively observed from ground to satellite altitudes over several decades,originates from multiple sources,such as the core dynamo,the conductive mantle,the magnetized lithosphere,and the space current systems.Modeling of the lithospheric contribution plays an important role in the geophysical studies and industrial applications.In this paper,we propose a new method for global and regional modeling of the lithospheric magnetic field based on the cubed-sphere.An equivalent dipole source method on a quasi-uniform cubed-sphere grid is employed in the forward modeling.The dipole directions are fixed according to a priori magnetization and the relative intensities are estimated by an inversion procedure of least-squares fitting with minimum model regularization.Several numerical tests are performed to validate the accuracy and efficiency of both forward modeling and inversion procedure.The proposed method is applied to the global and regional modeling based on the latest magnetic data from Swarm Alpha satellite and MSS-1 mission.The model results indicate that the proposed method works quite well for realistic satellite data and MSS-1 data is consistent with the Swarm data in terms of lithospheric field modeling.展开更多
A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid.Two kinds of moments(i.e.,point values(PV moment) at cell interface...A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid.Two kinds of moments(i.e.,point values(PV moment) at cell interfaces and volume integrated average(VIA moment) value) are defined within a single cell.The PV moment is updated by a conventional semi-Lagrangian method,while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation.Different from the spatial approximation used in the CSL2(conservative semi-Lagrangian scheme with second order polynomial function) scheme,a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment.To achieve exactly positive-definite preserving,two kinds of corrections are made on the original conservative semi-Lagrangian with rational function(CSLR)scheme.The resulting scheme is inherently conservative,non-negative,and allows a Courant number larger than one.Moreover,the spatial reconstruction can be performed within a single cell,which is very efficient and economical for practical implementation.In addition,a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry,which benefitsthe implementation of the 1 D CSLR solver with large Courant number.The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry.Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical nonnegativity,and it has the potential to transport the tracers accurately in a real atmospheric model.展开更多
In this study,the adaption of a novel three-point multi-moment constrained finite-volume transport scheme for uniform points with center constraints(MCV3_UPCC)to cubed sphere geometry is implemented and described.For ...In this study,the adaption of a novel three-point multi-moment constrained finite-volume transport scheme for uniform points with center constraints(MCV3_UPCC)to cubed sphere geometry is implemented and described.For the MCV3_UPCC scheme,the three equidistant solution points are located within a single cell and a polynomial of 4th degree can be built by imposing the multi-moment center constraints.The resultant scheme has third-order accuracy and guarantees the exact numerical conservation.The Fourier analysis of MCV3_UPCC scheme demonstrates that the novel MCV3_UPCC has better numerical dissipation and dispersion than the original 3rd order Multi-moment Constrained finite Volume(MCV3)scheme.Then it is applied to quasi-uniform cubed-sphere grid,which is designed to avoid the polar problem on the traditional latitude–longitude grid.To suppress the non-physical numerical oscillations,a bound-preserving(BP)algorithm to constrain the conserved advected tracer to within the initial maximum and minimum values is also implemented.The scheme is validated with several widely used benchmarks involving prescribed non-divergent two-dimensional flow on the sphere and different initial tracer distributions.The resulting conservative transport model with high-order accuracy and positive preserving property is comparable to other high-order schemes and has the potential for the numerical simulation of various traces in the atmosphere.展开更多
基金supported by the National Natural Science Foundation of China(42250101,42250102,42250103,12250013)the Macao Foundation。
文摘The Earth's magnetic field,which has been extensively observed from ground to satellite altitudes over several decades,originates from multiple sources,such as the core dynamo,the conductive mantle,the magnetized lithosphere,and the space current systems.Modeling of the lithospheric contribution plays an important role in the geophysical studies and industrial applications.In this paper,we propose a new method for global and regional modeling of the lithospheric magnetic field based on the cubed-sphere.An equivalent dipole source method on a quasi-uniform cubed-sphere grid is employed in the forward modeling.The dipole directions are fixed according to a priori magnetization and the relative intensities are estimated by an inversion procedure of least-squares fitting with minimum model regularization.Several numerical tests are performed to validate the accuracy and efficiency of both forward modeling and inversion procedure.The proposed method is applied to the global and regional modeling based on the latest magnetic data from Swarm Alpha satellite and MSS-1 mission.The model results indicate that the proposed method works quite well for realistic satellite data and MSS-1 data is consistent with the Swarm data in terms of lithospheric field modeling.
基金supported by the National Key Research and Development Program of China (Grant Nos.2017YFC1501901 and 2017YFA0603901)the Beijing Natural Science Foundation (Grant No.JQ18001)。
文摘A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid.Two kinds of moments(i.e.,point values(PV moment) at cell interfaces and volume integrated average(VIA moment) value) are defined within a single cell.The PV moment is updated by a conventional semi-Lagrangian method,while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation.Different from the spatial approximation used in the CSL2(conservative semi-Lagrangian scheme with second order polynomial function) scheme,a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment.To achieve exactly positive-definite preserving,two kinds of corrections are made on the original conservative semi-Lagrangian with rational function(CSLR)scheme.The resulting scheme is inherently conservative,non-negative,and allows a Courant number larger than one.Moreover,the spatial reconstruction can be performed within a single cell,which is very efficient and economical for practical implementation.In addition,a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry,which benefitsthe implementation of the 1 D CSLR solver with large Courant number.The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry.Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical nonnegativity,and it has the potential to transport the tracers accurately in a real atmospheric model.
基金Supported by the National Natural Science Foundation of China(42275168 and 42105002)。
文摘In this study,the adaption of a novel three-point multi-moment constrained finite-volume transport scheme for uniform points with center constraints(MCV3_UPCC)to cubed sphere geometry is implemented and described.For the MCV3_UPCC scheme,the three equidistant solution points are located within a single cell and a polynomial of 4th degree can be built by imposing the multi-moment center constraints.The resultant scheme has third-order accuracy and guarantees the exact numerical conservation.The Fourier analysis of MCV3_UPCC scheme demonstrates that the novel MCV3_UPCC has better numerical dissipation and dispersion than the original 3rd order Multi-moment Constrained finite Volume(MCV3)scheme.Then it is applied to quasi-uniform cubed-sphere grid,which is designed to avoid the polar problem on the traditional latitude–longitude grid.To suppress the non-physical numerical oscillations,a bound-preserving(BP)algorithm to constrain the conserved advected tracer to within the initial maximum and minimum values is also implemented.The scheme is validated with several widely used benchmarks involving prescribed non-divergent two-dimensional flow on the sphere and different initial tracer distributions.The resulting conservative transport model with high-order accuracy and positive preserving property is comparable to other high-order schemes and has the potential for the numerical simulation of various traces in the atmosphere.
