A staggered ocean grid

The Arakawa C grid places scalar fields at cell centers and horizontal velocities on their corresponding cell faces. This gives a direct representation of the fluxes entering a cell's volume and tracer balances. NeuralPOM uses this arrangement in both physical cores. (Manuscript, Section 2.1, grid implementation)

Field locations

Location	Physical quantities	Code fields or geometry
Cell center	Temperature, salinity, density, surface elevation	t, s, rho, el; area art, mask fsm
Face normal to the first horizontal direction	Zonal velocity and its depth average	u, ua; area aru, mask dum
Face normal to the second horizontal direction	Meridional velocity and its depth average	v, va; area arv, mask dvm
Vertical interfaces	Transformed vertical transport	w; sigma interfaces z
Vertical layer centers	Tracers and horizontal velocity	sigma midpoints zz

The first two array axes are the horizontal indices i,j; the third is vertical index k. Boundary rows and columns carry the case's boundary treatment. Center and face masks have different locations, so a scalar wet mask cannot replace every velocity mask.

Sigma levels and physical volumes

Let ${\sigma }_k$ and ${\sigma }_{k+1}$ be successive vertical interfaces. The fractional layer thickness is $\mathrm{\Delta }{\sigma }_k={\sigma }_k-{\sigma }_{k+1}$. Let $A_{ij}$ be horizontal cell area, $D_{ij}$ total depth, and $m_{ij}$ the wet mask. The geometric volume of a cell is

$$V_{ijk}=A_{ij}{D}_{ij}\mathrm{\Delta }{\sigma }_k{m}_{ij}.$$

The model stores interfaces in z, midpoints in zz, interface differences in dz, and midpoint differences in dzz. The correction uses the volume weights defined by its physical-state convention in volume_weights.

Storage and active layers

The published setup has 16 vertical storage levels and 15 active layers. CorrectorNet reads all 16 storage levels for its six three-dimensional inputs, but predicts increments for 15 active layers. The inactive bottom storage level is left unchanged. See CorrectorNet for the full channel map.

The reference simulation uses a 354 × 322 horizontal grid, and the forecast model a 90 × 82 grid. The archived references are consistently restricted to the forecast grid, so target arrays and coarse states share the model's geometry. (Manuscript, Section 3.1 and Appendix B.1)

Practical consequence

Use each field's own mask, area, and vertical weights when calculating errors or budgets. Preserve staggering during data conversion. The dataset reader and evaluation code already encode these conventions; Data format and Reproduction describe the supported workflow.