Exchange Grid

Exchange grid definition

The most computationally intensive component of conservative remapping is the exchange grid creation. The exchange grid consists of cells formed from the overlap between the input and output grid.

In the figure above where the black squares represent the output grid cells and the pink squares the input grid cells, the colored polygons formed by the overlapping input and output grid cells are the exchange grid cells. Fregrid_gpu, as with fregrid, supports exchange grid cells that have up to 8 vertices and can handle commonly used grids such at cubed-sphere, latxlon, and tripolar grids.

Remapping

For first order conservative methods, data is remapped to the output grid by

$$v_j = \sum_i w_{ij} v_i$$

where $$v_j$$ is the data value for output cell $$j$$, $$v_i$$ is the data value for input cell $$i$$, and $$w_{ij}$$ is the remapping weight between input cell $$i$$ and output cell $$j$$. Remapped data on the output grid is the weighted sum over all data values in input cells that overlap with cell $$j$$. The weights $$w_{ij}$$ represent the fractional contribution of $$v_i$$ to $$v_j$$ and is given by $$w_{ij} = A_{ij}/A_i$$, where $$A_{ij}$$ is the exchange grid cell area and $A_i$ is the input cell area. Weights for non-overlapping input and output cells will be zero.

The second order remapping scheme

$$v_j = \sum_i w_{ij}\space(v_i + \nabla v_i \dot dr_{ij})$$

takes into account the first order term in the data remapping series expansion where $$\nabla v_i$$ is the gradient of $$v_i$$ and $$dr_{ij}$$ is the difference betweeen centroid points for input cell $$i$$ and exchange cell $$ij$$. Second order remapping requires this additional centroid-related computations and will take longer.

Additional resources

• Jones, P.W.: First- and Second-Order Conservative Remapping Schemes for Grids in Spherical Coordinates, Mon. Wea. Rev., 127, 2204-2210

• Taylor, K. E.: Truly conserving with conservative remapping methods, Geosci. Model Dev., 17, 415–430