WeertmanSliding.cc

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/* Copyright (C) 2018, 2021, 2022, 2023 PISM Authors
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 * This file is part of PISM.
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 * FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more
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 * along with PISM; if not, write to the Free Software
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 */
 
#include "pism/stressbalance/WeertmanSliding.hh"
 
#include "pism/rheology/FlowLawFactory.hh"
#include "pism/geometry/Geometry.hh"
#include "pism/stressbalance/StressBalance.hh"
 
namespace pism {
namespace stressbalance {
 
WeertmanSliding::WeertmanSliding(std::shared_ptr<const Grid> grid)
  : ShallowStressBalance(grid) {
  // Use the SIA flow law.
  rheology::FlowLawFactory ice_factory("stress_balance.sia.", m_config, m_EC);
  m_flow_law = ice_factory.create();
}
 
void WeertmanSliding::init_impl() {
  m_log->message(2, "* Initializing Weertman-style basal sliding...\n");
}
 
 
/*!
 * Compute sliding velocity using a Weertman-style parameterization from [@ref Tomkin2007],
 * equation 5.
 *
 * @f[ u_s = \frac{2 A_s \beta_c (\rho g H)^{n}}{N - P} \cdot |\nabla h|^{n-1} \cdot \nabla h,
 * @f]
 *
 * where
 *
 * - @f$ A_s @f$ is the sliding parameter,
 * - @f$ \beta_c @f$ is a parameter capturing the effect of the presence of valley walls
 *   (set to 1 in this implementation),
 * - @f$ \rho @f$ is the ice density,
 * - @f$ H @f$ is the ice thickness,
 * - @f$ h @f$ is the ice surface elevation ,
 * - @f$ n @f$ is the flow law exponent (usually 3),
 * - @f$ g @f$ is the acceleration due to gravity,
 * - @f$ N @f$ is the ice overburden pressure,
 * - @f$ P @f$ is the basal water pressure.
 *
 * With these modifications and noting that @f$ N = \rho g H @f$, the formula above
 * becomes
 *
 * @f[ u_s = \frac{2 A_s}{1 - k} \cdot (N |\nabla h|)^{n-1} \cdot \nabla h,
 * @f]
 *
 * where
 * - @f$ N = \rho g H @f$,
 * - @f$ P = k N @f$ (we assume that basal water pressure is a given fraction of overburden)
 *
 * This parameterization is used for areas of grounded ice where the base of the ice is
 * temperate.
 */
void WeertmanSliding::update(const Inputs &inputs, bool full_update) {
 
  (void) full_update;
 
  const array::Scalar &H         = inputs.geometry->ice_thickness;
  const array::Scalar &h         = inputs.geometry->ice_surface_elevation;
  const auto          &cell_type = inputs.geometry->cell_type;
  const array::Array3D  &enthalpy  = *inputs.enthalpy;
 
  double n   = m_flow_law->exponent();
  double A_s = m_config->get_number("stress_balance.weertman_sliding.A", "Pa-3 s-1 m-2");
  double k   = m_config->get_number("stress_balance.weertman_sliding.k");
 
  array::AccessScope list{&m_velocity, &H, &h, &enthalpy, &cell_type};
 
  ParallelSection loop(m_grid->com);
  try {
    for (auto p = m_grid->points(); p; p.next()) {
      const int i = p.i(), j = p.j();
 
      double
        P_o    = m_EC->pressure(H(i, j)),
        E_base = enthalpy.get_column(i, j)[0];
 
      if (not m_EC->is_temperate(E_base, P_o) or cell_type.ocean(i, j)) {
        m_velocity(i, j) = 0.0;
        continue;
      }
 
      // Note: we may need to decide if we should use one-sided FD at ice margins.
      Vector2d grad_h = {diff_x_p(h, i, j), diff_y_p(h, i, j)};
 
      // Note: this could be optimized by computing this instead
      // 2 * A_s / (1 - k) * pow(P * P * (h_x * h_x + h_y * h_y), (n - 1) / 2) * grad_h;
      // ... but I'm not sure we need to and the current code is cleaner.
      m_velocity(i, j) = - 2.0 * A_s / (1.0 - k) * pow(P_o * grad_h.magnitude(), n - 1) * grad_h;
    }
  } catch (...) {
    loop.failed();
  }
  loop.check();
 
}
 
} // end of namespace stressbalance
} // end of namespace pism