Calving schemes

Here is a summary of calving schemes.

Lipscomb et al. (2019)

c = k_\tau \tau_{\rm ec}

where k_\tau (m yr^{-1} Pa^{-1}) is an empirical constant and \tau_{\rm ec} (Pa) is the effective calving stress, which is defined by:

\tau_{\rm ec}^2 = \max(\tau_1,0)^2 + \omega_2 \max(\tau_2,0)^2

\tau_1 and \tau_2 are the eigenvalues of the 2D horizontal deviatoric stress tensor and \omega_2 is an empirical weighting constant. For partially ice-covered grid cells (with f_{\rm ice} < 1), these stresses are taken from the upstream neighbor.

The eigenvalues \tau_1 and \tau_2 are calculated from the depth-averaged (2D) stress tensor \tau_{\rm ij} as follows. Given the stress tensor components \tau_{\rm xx}, \tau_{\rm yy} and \tau_{\rm xy}, we can solve for the real roots \lambda of the tensor from the quadratic equation:

a \lambda^2 + b \lambda + c = 0

where

a = 1.0 \\ b = -(\tau_{\rm xx} + \tau_{\rm yy}) \\ c = \tau_{\rm xx}*\tau_{\rm yy} - \tau_{\rm xy}^2

glissade_velo_higher.F90:

tau_xz(k,i,j) = tau_xz(k,i,j) + efvs_qp * du_dz            ! 2 * efvs * eps_xz
tau_yz(k,i,j) = tau_yz(k,i,j) + efvs_qp * dv_dz            ! 2 * efvs * eps_yz
tau_xx(k,i,j) = tau_xx(k,i,j) + 2.d0 * efvs_qp * du_dx     ! 2 * efvs * eps_xx
tau_yy(k,i,j) = tau_yy(k,i,j) + 2.d0 * efvs_qp * dv_dy     ! 2 * efvs * eps_yy
tau_xy(k,i,j) = tau_xy(k,i,j) + efvs_qp * (dv_dx + du_dy)  ! 2 * efvs * eps_xy