[JanStreffing]

Draft. Adds ocp_tool/subgrid_oro_lott_miller.py and tools/validate_subgrid_orography.py, and nothing else. Not wired into a pipeline yet; nothing here writes an ICMGG.

Replaces #63, which is the same work on a branch that picked up unrelated files by accident.

Two methods, not two use cases

paleo_subgrid_oro.py        calnoro, for ECHAM
subgrid_oro_lott_miller.py  Lott and Miller, for OpenIFS

calnoro implements a different definition and cannot serve OpenIFS. Fed ECMWF's own TCO1279 orography it returns a global mean sdor of 43.3 against ECMWF's 60.4, with a point-by-point RMS difference of 74.8 against a field mean of 60.4. The gap is definitional, not resolution: moving its input from ECHAM5 T511 (26 km, 2007) to TCO1279 (9 km) closed about 9% of it. The calnoro path is correct for ECHAM and is untouched.

What this does

Lott and Miller (1997) statistics onto the reduced Gaussian grid, following the IFS orographic drag documentation and Elvidge et al. (ECMWF Tech Memo 893):

1. average the source to 2'30", about 5 km, since scales below that belong to TOFD and the effective roughness scheme;
2. subtract the large scales, leaving a residual carrying only 5 km to grid length;
3. accumulate the gradient correlation tensor from that residual.

A global ETOPO1 pass takes about 15 seconds.

Validation

tools/validate_subgrid_orography.py compares against what ECMWF ship beside the model, climate.v020/<res>/{stdgwd,isogwd,slogwd}. Against 95_4 over ice-free land, with ETOPO1:

	ratio	corr	ECMWF's own lag-1 coherence
sdor	0.767	0.847	0.819
slor	0.844	0.913	0.807
isor	0.967	0.576	0.416

The last column is the point. ECMWF's isor barely agrees with itself one grid box away, because anisotropy is a ratio of the tensor's eigenvalues and is genuinely noisy. All three fields here track ECMWF more closely than ECMWF tracks its own neighbour, so 0.576 is at the field's noise floor rather than short of a target.

Box-mean orography against 95_4/orog is the control, correlation 0.967, which is what says the grid mapping is right.

Worth a reviewer's attention

• The high-pass cutoff is derived, not fitted. It is the grid length. Held fixed at 150 km the slor ratio drifts 0.910 at TCO79 to 0.955 at TCO319; scaled as 1.5 times the equatorial spacing it stays inside 0.911 to 0.927.
• The 5 km prefilter is physical, not a free parameter. At TCO319, refining it from 3' to 1' takes the slope ratio from 0.93 to 1.73.
• Polar convergence had to be removed explicitly. A 3 arcmin cell is 5.5 km square at the equator and 5.5 km by 1 km at 80S, which biased the anisotropy into radial spokes about the pole, visible on a south polar map. The zonal prefilter width and the zonal gradient span are now per-row, and box means are area weighted.
• The fields are zeroed below 0.5 land fraction, as ECMWF ship them. Without it, a cell holding an island carries a full-scale anisotropy on a sub-metre standard deviation: 4446 such sea cells on ETOPO1, half with sdor under a metre.

Open

• sdor sits about 20% low at every resolution and setting tried. Stable enough that a single factor would be defensible, but not understood.
• isor degrades with target resolution, 0.52 at TCO79 and TCO95 down to 0.39 at TCO319, and it is not sample starvation: nine times the fine points per box moves it 0.394, 0.410, 0.375.
• ETOPO1 Bed is what is available here, so Greenland and Antarctica are bedrock and are excluded from validation. Production wants the Ice version.

[JanStreffing]