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The four issues identified and fixed are:
1. ACME uses flawed FV grids that omit a small strip of longitude to the east of Greenwich. For FV 129x256, this amounts to 0.2% of global area. The maps based on the flawed grids somehow reapportion area so that total area is conserved (4*pi sr), yet this necessarily redistributes weights from their true positions. This may cause the behavior you noticed (if you are looking at FV grids). Fixed FV grids and maps (with suffix .20150724.nc) are in
/lustre/atlas/proj-shared/cli115/zender/[grids,maps] on rhea
With these grids, "area"- and "gw"-weighted statistics should agree to double-precision. This problem was identified independently by Charles Doutriaux and myself. Together with the Gaussian grid problems described below, it this shows that ACME (and CESM) should migrate to more accurate structured 2D grids.
2. SCRIP introduced, and CESM and ACME inherited, a format of storing all coordinates coordinate storage in double precision (yay!). Unfortunately, every Gaussian grid I have examined has grid center latitudes (= sine of the Gaussian quadrature points) accurate to no greater than ~8 eight digits. This goes all the way back to grandaddy SCRIP. NCO now generates SCRIP-format Gaussian grids accurate to 16 digitssixteen digits, the best that double precision can reach.
3. The Gaussian grids employed by SCRIP/CESM/ACME Gaussian grids that I have examined (T42, T62, and T85) infer gridcell interfaces as midpoints between the Gaussian quadrature points/angles. Gridcell areas are inferred from the area between Software then infers the gridcell areas from gridcell interfaces. The ~singlesingle-precision quadrature weights are inconsistent with area determined by the the midpoint rule for interfaces. This may be the problem you noticed (if you are working on your own with Gaussian grids). NCO now uses Newton-Raphson iteration (instead of the quadrature midpoints) to determine the gridcell interface location that exactly matches the area determined by the (now double-precision) Gaussian weights. With these grids, "area"- and "gw"-weighted statistics do agree to double-precision. This procedure moves interfaces by, typically, a few tenths of a degree (for moderate resolution spectral grids) from their previous locations as quadrature midpoints.
4. It is thought that the staggered FV grids historically produced by NCL and fed to ESMF_RegridWeightGen utilize the continuous form of the weighting function (i.e., cosine(lat)) evaluated on the discretized grid, rather than the exact discretized weight function (which depends on i.e., the difference of the sine of the latitudes bounding the zone). This leads to a problem similar to the problem with the interface location on the Gaussian gridIn fact the staggered/offset FV grid used for dynamics variables should have the same functional form for weights as the FV grid itself.
The new grids and mapfiles address these problems, which have always existed in ACME and its predecessors (CESM, CCSM, CCM)...