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The five issues identified in the pre-migration (pre-20150901) toolchain and fixed by migration are:
1. ACME uses used flawed FV grids (rectangular and regular lat/lon grids with some funny business at the poles) that omit a small strip of longitude to the east of Greenwich. This problem was identified independently by Charles Doutriaux and myself. For FV 129x256, this amounts to 0.2% of global area. The maps 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. The solution is to generate grids with the proper interfaces, and to base maps on those 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 agree to double-precision. This problem was identified independently by Charles Doutriaux and myself. Together with the Gaussian grid problems described below, this shows that ACME (and CESM) should migrate to more accurate structured 2D grids.
2. SCRIP introduced, and CESM and ACME inherited, 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 eight digits. This goes all the way back to grand-daddy SCRIP. The solution is to base latitudes on quadrature points (i.e., Legendre solutions) computed to full double precision. NCO now generates SCRIP-format Gaussian grids accurate to sixteen digits, the best that double precision can reach.
3. The SCRIP/CESM/ACME Gaussian grids that I have examined (T42, T62, and T85) infer gridcell interfaces as midpoints between Gaussian quadrature points/angles. Software then infers the gridcell areas from gridcell interfaces. The single-precision quadrature weights are inconsistent with area determined by the the midpoint rule for interfacesproblem is that interfaces defined by the midpoint rule will always produce areas inconsistent with those implied by the quadrature weights. this causes a mismatch between "area"- and "gw"- weighted statistics. NCO now uses Newton-Raphson iteration (instead of the quadrature midpoints) to determine the gridcell interface location that exactly matches the area areas determined by the (now double-precision) Gaussian weights. With these grids, "area"- and "gw"-weighted statistics 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. Some if not all staggered FV regular lat/lon 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 (i.e., the difference of the sine of the latitudes bounding the zone). In fact the And some of these regular lat/lon grids are in fact used as staggered/offset FV grid used grids for dynamics variables (e.g., U, V). All regular lat/lon grids must have the same functional form for weights as the FV grid itself, as since they are simply offsets of eachother. Without this correction, statistics of variables computed on the dynamics grid may be misdiagnosed (fxm: last sentence not yet verified). Users of staggered FV grids/maps should ensure their grids/maps were produced with the correct weighting function.
5. For historical reasons, mapfiles generated by ESMF_RegridWeightGen using bilinear interpolation do not include complete output grid information. In particular, they lack gridcell area, probably perhaps because the presence of a diagnosed area could be misconstrued to imply a conservation property of the mapping which, by their nature, interpolative schemes lack. However, it is helpful to include area so long as users understand that interpolative maps are non-conservative. The new mapfiles include gridcell area for bilinear interpolation maps.
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