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The map-checker reveals that the maximum frac_b, in grid B cell 27052765, is nearly two! This particular destination cell is nearly completely overlapped by two independent input gridcells. If this map were applied to the HYDRO1K elevation data (despite the WARNING message not to do so), and the input elevations are nearly equal in the two overlapping input gridcells, then then elevation in the output gridcell would be nearly twice as high as the input elevationelevations. We can learn more information about the self-overlapping problems by invoking the map-checker with a higher debugging level:
% ncks --dbg_lvl=2 --chk_map map_hydro1k_to_ne1024np4_nco.20200401.nc...WARNING consistency = 1.0555483035171453 = 1.0+5.6e-02 for grid B cell [17512046,+28.6551,+61.0204]WARNING consistency = 1.4909408462334364 = 1.0+4.9e-01 for grid B cell [22288166,-10.0243,+142.847]WARNING consistency = 1.5083400424248017 = 1.0+5.1e-01 for grid B cell [26813058,+24.7855,+141.304]WARNING consistency = 1.8095310966429947 = 1.0+8.1e-01 for grid B cell [26813059,+24.7929,+141.328]WARNING consistency = 1.1003605275652104 = 1.0+1.0e-01 for grid B cell [26813062,+24.8271,+141.328]WARNING consistency = 1.5691716370205997 = 1.0+5.7e-01 for grid B cell [27006682,+26.712,+142.119]WARNING consistency = 1.3010253856656488 = 1.0+3.0e-01 for grid B cell [27006683,+26.6633,+142.143]WARNING consistency = 1.5450145730783844 = 1.0+5.5e-01 for grid B cell [27006686,+26.6981,+142.143]WARNING consistency = 1.6607209155522704 = 1.0+6.6e-01 for grid B cell [27043555,+27.0515,+142.207]WARNING consistency = 1.3608697313423308 = 1.0+3.6e-01 for grid B cell [27052764,+27.0654,+142.183]WARNING consistency = 1.9322116675425409 = 1.0+9.3e-01 for grid B cell [27052765,+27.0731,+142.207]WARNING consistency = 1.1687177202454959 = 1.0+1.7e-01 for grid B cell [27052767,+27.1003,+142.183]WARNING consistency = 1.3914390175753097 = 1.0+3.9e-01 for grid B cell [27052768,+27.108,+142.207]WARNING consistency = 1.7110750268542088 = 1.0+7.1e-01 for grid B cell [27052771,+27.1296,+142.207]WARNING consistency = 1.0005420980107826 = 1.0+5.4e-04 for grid B cell [50257987,+61.086,+59.2809]WARNING consistency = 1.0004283863341064 = 1.0+4.3e-04 for grid B cell [50257997,+61.0767,+59.3492]WARNING consistency = 1.0004192624042263 = 1.0+4.2e-04 for grid B cell [50607727,+65.2985,+61.3002]WARNING non-consistent row-sums (error exceeds tolerance = 1.0e-08) for 17 of 56623106 grid B cells...
The map checker lists the 17 destination gridcells whose frac_b exceeds 1.0 by a pre-set tolerance of 1.0e-8. We can examine examined the input grid at these 17 latitudes and longitudes (the printed coordinates are formatted to be easily paste-able into Google Maps). For the HYDRO1K dataset, we found that there are self-overlapping gridcells at these locations, which include some islands (e.g., Iwo Jima) and continental regions. The resulting elevation biases in these gridcells range between factors of 1.10 -and 1.93. Considering that the other 56623089 destination gridcells trigger no warnings, the ESM simulations are probably not significantly degraded by faulty elevation elevations in only 17 gridcells. However, this remains to be tested.
The best solution to the self-overlapping issue is, of course, to pre-emptively adjust the input grid and input datasets to avoid self-overlap. However, this solution may be difficult or impractical where the original data, producer, or algorithm are unavailable or where it is unclear which of the overlapped input gridcells to retain. In such cases, NCO (versions 4.9.2 and later) provides a practical workaround. The ncks --frac_b_nrm flag invokes a corrective procedure that adjusts for the influence of self-overlapping gridcells.
The procedure first identifies destination gridcells as those with frac_b > 1.0+1.0e-8, as shown above.
Weights that contribute to any such gridcell are then normalized by the sum of the weights (i.e., by frac_b) that contribute to the gridcell. In the example above, the maximum frac_b is 1.93, so all weights contributing to that gridcell are divided by 1.93. The adjusted frac_b is then 1.0, which prevents "double counting" values regridded into that gridcell. The weights that were altered (to avoid double-counting values during regridding) will also alter the frac_a of ALL source gridcells involved. A shortcoming of this procedure is that it misses any self-overlapped input gridcells that contribute to destination gridcells with frac_b < 1, such as can occur along coastlines.
Invoking the corrective procedure is as simple as it is irreversible. Please understand that this procedure alters map-files in-place, so backup back-up the original file first:
% /bin/cp map_hydro1k_to_ne1024np4_nco.20200401.nc map_hydro1k_to_ne1024np4_nco_fix.20200401.nc% ncks --frac_b_nrm map_hydro1k_to_ne1024np4_nco_fix.20200401.nc
The map-checker will show that the "fixed" map-file no longer generates the above WARNINGs associated with frac_b. Instead, the WARNINGs are now associated with frac_a due to the weight-adjustment as described above:
% ncks --dbg_lvl=2 --chk_map map_hydro1k_to_ne1024np4_nco_fix.20200401.nc......
The new frac_a WARNINGs indicate that the intersection portion of each self-overlapped input gridcells gridcell will be weighted less than the portion of the gridcell that is not self-overlapped. This is expected and desired so these WARNINGs may be safely ignored.