Implementation of a Conservative Two-step Shape-Preserving Advection Scheme on a Spherical Icosahedral Hexagonal Geodesic Grid

An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid） to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes （a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity） to calculate the fluxes at the cell walls （one scheme corresponds to one cell wall）. The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport （FCT） approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.

Ocean surface currents estimated from satellite remote sensing data based on a global hexagonal grid

Global ocean surface currents estimated from satellite derived data based on a regular global grid are affected by the grid’s shape and placement.Due to different neighbourhood relationships,the rectangular lat/lon grids lose accuracy when interpolating andfitting elevation data.Hexagonal grids have shown to be advantageous due to their isotropic,uniform neighbourhood.Considering these merits,this paper aims to estimate global ocean surface current using a global isotropic hexagonal grid from satellite remote sensing data.First,gridded satellite altimeter data and wind data with different resolutions are interpolated into the centre of the global isotropic hexagonal grid.Then,geostrophic and Ekman currents components are estimated according to the Lagerlof Ocean currents theory.Finally,the inversion results are verified.By analyzing the results,we conclude that the ocean surface currents estimated based on the global isotropic hexagonal grid have considerable accuracy,with improvement over rectangular lat/lon grids.

Extraction of ocean tidal information based on global equal-area grid and satellite altimeter data

Harmonic analysis of satellite altimetry data based on a global regular grid is affected by the grid spatial tessellation and placement of the grids.With the increase of latitude,the traditional lat/lon grid deforms greatly,resulting in uneven distribution of satellite altimeter data with latitude,which affects the extraction of tidal information.Alternatively,Hexagonal grids have been proved to be advantageous due to their isotropic,uniform neighbourhood,equal-area and more.Considering the merits above,the purpose of this paper is to use the global equal-area hexagonal grid to conduct a harmonic analysis of satellite altimeter data.First,the Icosahedron Snyder Equal Area projection method is used to construct a global equal-area hexagonal grid,Then the time series data of 19.8 years of Jason series satellite altimeter data are obtained.Finally,the harmonic constants of eight constituents(the M2,S2,N2,K2,K1,O1,P1,Q1)are extracted by harmonic analysis.By analysing the results,we conclude that the harmonic constants extracted from the global equal-area hexagonal grid have considerable accuracy and are consistent with the tidal characteristics of the eight components.Meanwhile,the accuracy of harmonic constants extracted from equal-area hexagonal grids is better than that of lat/lon grids.