interp

Grid mapping — test_interp.x

What it tests

test_interp.x checks the maps in elsa_interp that carry the host model’s fields onto elsa’s grid. Every map is separable — the 2D weight is the outer product of a weight along x and a weight along y — and exact. Each is precomputed once at init and applied as a fixed stencil thereafter. The benchmark therefore asserts exactness properties, rather than tolerances.

Source: src/test_interp.f90. Run it with make run-interp.

The three maps

Field(s)	Source → target	Method
H_ice, smb, bmb	host cells → elsa cells	area-weighted (conservative)
ux	host velocity → elsa acx faces	bilinear
uy	host velocity → elsa acy faces	bilinear

Vertically, the host supplies velocity on nz sigma levels. elsa requires the thickness-average over each isochronal layer, which — since the profile is piecewise linear — is integrated exactly.

Results

 conservative remap
   grid_factor 1.0 -> 10 x 10   mass conserved (0),  identity to the source
   grid_factor 2.0 ->  5 x  5   mass conserved (0),  equals a 2x2 box mean
   grid_factor 2.5 ->  4 x  4   mass conserved (3.0e-16)

 bilinear velocity onto faces
   stagger = acx_acy   ux, uy reproduce a linear field exactly
   stagger = aa        ux, uy reproduce a linear field exactly

 layer-mean velocity
   constant profile exact
   linear profile -> layer midpoint value
   sum(u_k d_k) = exact integral   (err 1.7e-16)

Three things are established here:

• Non-integer coarsening conserves mass. At grid_factor = 2.5, elsa’s grid tiles the host’s without an integer ratio, and the total ice mass is preserved to \(3\times10^{-16}\). v2.0 required grid_factor to divide both nx and ny; it warned and continued otherwise, and silently lost mass.

• Staggering is a coordinate, rather than a code path. The bilinear map reproduces a linear field for both "acx_acy" and "aa", since stagger only shifts where the host’s velocity samples are taken from and nothing downstream branches on it. Any host grid — staggered or centred, at any resolution ratio — reaches elsa’s faces through the same code.

• The vertical average is exact and unbiased. For a linear profile the layer-mean equals the value at the layer midpoint, and the thickness-weighted sum equals the exact integral to \(2\times10^{-16}\). v2.0 instead sampled the layer’s upper interface, which biased every layer toward the faster ice above it — here by \(+1.13\) m yr\(^{-1}\) for the test profile.