GivenTH init_impl m_salinity_ocean m_theta_ocean max_timestep_impl pointwise_update subshelf_salinity subshelf_salinity_diffusion_only subshelf_salinity_freeze_on subshelf_salinity_melt update_impl ~GivenTH

subshelf_salinity_melt() void pism::ocean::GivenTH::subshelf_salinity_melt ( const Constants &  c, double  sea_water_salinity, double  sea_water_potential_temperature, double  thickness, double *  shelf_base_salinity  ) private Compute basal salinity in the basal melt case. We use the parameterization of the temperature gradient from [Hellmeretal1998], equation 13: \[ T_{\text{grad}} = -\Delta T\, \frac{\frac{\partial h}{\partial t}}{\kappa}, \] where \( \Delta T \) is the difference between the ice temperature at the top of the ice column and its bottom: \( \Delta T = T^S - T^B. \) With this parameterization, we have \[ Q_T^I = \rho_I\, c_{pI}\, {\frac{\partial h}{\partial t}}\, (T^S - T^B). \] Then the coefficients of the quadratic equation for basal salinity (see pointwise_update()) are \begin{align*} A &= a_{0}\,\gamma_S\,c_{pI}-b_{0}\,\gamma_T\,c_{pW}\\ B &= \gamma_S\,\left(L-c_{pI}\,\left(T^S+a_{0}\,S^W-a_{2}\,h-a_{1}\right)\right)+ \gamma_T\,c_{pW}\,\left(\Theta^W-b_{2}\,h-b_{1}\right)\\ C &= -\gamma_S\,S^W\,\left(L-c_{pI}\,\left(T^S-a_{2}\,h-a_{1}\right)\right) \end{align*} Parameters [in] c physical constants, stored here to avoid looking them up in a double for loop [in] sea_water_salinity salinity of the ocean immediately adjacent to the shelf, [g/kg] [in] sea_water_potential_temperature potential temperature of the sea water, [degrees Celsius] [in] thickness thickness of the ice shelf, [meters] [out] shelf_base_salinity resulting shelf base salinity Returns 0 on success Definition at line 370 of file GivenTH.cc. References pism::ocean::GivenTH::Constants::a, pism::ocean::GivenTH::Constants::b, C, pism::ocean::GivenTH::Constants::gamma_S, pism::ocean::GivenTH::Constants::gamma_T, pism::ocean::GivenTH::Constants::ice_specific_heat_capacity, L, pism::ocean::GivenTH::Constants::sea_water_specific_heat_capacity, pism::ocean::GivenTH::Constants::shelf_top_surface_temperature, and pism::ocean::GivenTH::Constants::water_latent_heat_fusion. Referenced by subshelf_salinity().