Nudging to climatology

REMORA supports nudging to climatology both on the boundaries and in an interior sponge region. Nudging at the boundaries is discussed in Boundary Conditions.

The climatology history and nudging coefficients are read from NetCDF files. The nudging coefficients are expected to be in units of 1/day, as in ROMS.

Nudging for Tracers

Tracers \(S\) are nudged towards solution by:

\[S = S + C_{\mathrm{tracer}} \Delta t \left(S_{\mathrm{clim}} - S\right)\]

where \(S_{mathrm{clim}}\) is the value given in the climatology and \(C_{\mathrm{tracer}}\) is the nudging coefficient for the relevant tracer.

Nudging for 2D velocity

The 2D velocity components are updated in the right-hand side term rhs_ubar according to:

\[\mathrm{RHS}_{\overline{u}} = \mathrm{RHS}_{\overline{u}} + C_{\mathrm{M2}} \frac{D}{mn} \left(\overline{u}_{\mathrm{clim}} - \overline{u}_{\mathrm{krhs}}\right)\]

or similar for v. \(C_{\mathrm{M2}}\) is the nudging coefficient, \(D\) is the water column depth, and \(\overline{u}_{\mathrm{clim}}\) is the climatology value read from file. \(\mathrm{RHS}_{\overline{u}}\) is the variable rhs_ubar and \(\overline{u}_{\mathrm{krhs}}\) is the value of \(\overline{u}\) at the time index krhs.

Nudging for 3D velocity

The 3D velocity components are updated in the right-hand side term ru according to:

\[\mathrm{RHS}_{u} = \mathrm{RHS}_{u} + C_{\mathrm{M3}} \frac{H_{z}}{mn} \left(u_{\mathrm{clim}} - u_{\mathrm{old}}\right)\]

or similar for v. \(C_{\mathrm{M3}}\) is the nudging coefficient and \(u_{\mathrm{clim}}\) is the climatology value read from file. \(\mathrm{RHS}_{u}\) is the variable ru and \(u_{\mathrm{old}}\) is the value of \(u\) at the prior time step.