rdb_ocean_p_surf Module

Surface-pressure loading for the ocean C-grid dyn-core (PR-17). An atmospheric surface pressure p_surf(x,y) (Pa) adds a depth-uniform acceleration -(1/rho0) grad(p_surf) to the horizontal momentum (Wunsch & Stammer 1997). Because the term is depth-independent it is a purely BAROTROPIC forcing: it drives the free surface and, at rest, integrates to the equilibrium inverse-barometer response eta_ib = -p_surf/(rho0 g) + const (~1 cm depression per hPa of atmospheric high; Ponte 2006 for the closed-domain mean removal).

It lands on the SAME eta_forcing seam the equilibrium body tide and scalar SAL compose through: the barotropic substep drives -g grad(eta - eta_forcing), so folding eta_ib = -p_surf/(rho0 g_bt) into the seam gives the momentum an extra -g grad(eta) - (1/rho0) grad(p_surf) exactly. eta_ib and the combined seam field eta_seam = eta_ib [+ eta_tide] are cell-centred 2-D fields in metres, differenced on the identical two-point stencil the SSH uses, so the discrete inverse-barometer balance eta = eta_ib + const is an exact discrete steady state.

Sign: eta_ib = -p_surf/(rho0 g) — a high depresses the surface, a low bulges it. Gravity is bt_work%g_bt (what the barotropic substep that consumes the seam actually runs on), NOT rdb_constants:GRAVITY; the caller passes it in so eta_ib scales with the ocean’s own dynamics.

p_surf (the assembled total, Pa, >= 0) is consumed read-only from the surface-forcing type (ocean_surface_flux_t) — this module adds no forcing field of its own, and does not write p_surf (the dyn step holds sf intent(in)). With no ice mass-loading the assembly p_surf = p_surf_atm is a configure-time seed (set_p_surf_const fills both) since p_surf_atm is static; when sea-ice loading lands (PR-18) its ice_ocean_mass_load overwrites p_surf = p_surf_atm + g_load*mis via its own inout access earlier in the same outer step, and this module reads whatever p_surf then holds. Adcroft et al. (2019) levitating surface-load convention.