Exchange Grid - NOAA-GFDL/FRE-NCtools GitHub Wiki
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.
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.