ForceThickness.cc

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// Copyright (C) 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2022, 2023 PISM Authors
//
// This file is part of PISM.
//
// PISM is free software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the Free Software
// Foundation; either version 3 of the License, or (at your option) any later
// version.
//
// PISM is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more
// details.
//
// You should have received a copy of the GNU General Public License
// along with PISM; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 
#include "pism/coupler/surface/ForceThickness.hh"
#include "pism/util/Grid.hh"
 
#include "pism/util/ConfigInterface.hh"
#include "pism/util/error_handling.hh"
#include "pism/util/array/CellType.hh"
#include "pism/util/MaxTimestep.hh"
#include "pism/util/io/File.hh"
#include "pism/geometry/Geometry.hh"
#include "pism/util/interpolation.hh"
 
namespace pism {
namespace surface {
 
///// "Force-to-thickness" mechanism
ForceThickness::ForceThickness(std::shared_ptr<const Grid> g, std::shared_ptr<SurfaceModel> input)
  : SurfaceModel(g, input),
    m_target_thickness(m_grid, "thk"),
    m_ftt_mask(m_grid, "ftt_mask")
{
 
  m_ftt_mask.set_interpolation_type(NEAREST);
 
  m_alpha                        = m_config->get_number("surface.force_to_thickness.alpha", "s-1");
  m_alpha_ice_free_factor        = m_config->get_number("surface.force_to_thickness.ice_free_alpha_factor");
  m_ice_free_thickness_threshold = m_config->get_number("surface.force_to_thickness.ice_free_thickness_threshold");
  m_start_time                   = m_config->get_number("surface.force_to_thickness.start_time", "seconds");
 
  m_ftt_mask.metadata(0)
      .long_name("mask specifying where to apply the force-to-thickness mechanism")
      .set_output_type(io::PISM_INT)
      .set_time_independent(true);
 
  m_ftt_mask.set(1.0); // default: applied in whole domain
 
  m_mass_flux = allocate_mass_flux(g);
 
  m_accumulation = allocate_accumulation(g);
  m_melt         = allocate_melt(g);
  m_runoff       = allocate_runoff(g);
}
 
void ForceThickness::init_impl(const Geometry &geometry) {
 
  m_input_model->init(geometry);
 
  m_log->message(2, "* Initializing force-to-thickness mass-balance modifier...\n");
 
  std::string input_file = m_config->get_string("surface.force_to_thickness.file");
 
  if (input_file.empty()) {
    throw RuntimeError(PISM_ERROR_LOCATION, "surface.force_to_thickness.file cannot be empty");
  }
 
  m_log->message(
      2,
      "    alpha = %.6f year-1 for -force_to_thickness mechanism\n"
      "    alpha = %.6f year-1 in areas with target ice thickness of less than %.3f meters\n",
      units::convert(m_sys, m_alpha, "s-1", "year-1"),
      m_alpha_ice_free_factor * units::convert(m_sys, m_alpha, "s-1", "year-1"),
      m_ice_free_thickness_threshold);
 
  // check of the input file is really there and regrid the target thickness
  File file(m_grid->com, input_file, io::PISM_GUESS, io::PISM_READONLY);
 
  m_log->message(2,
                 "    reading target thickness 'thk' from %s ...\n"
                 "    (this field will appear in output file as 'ftt_target_thk')\n",
                 input_file.c_str());
  {
    m_target_thickness.metadata(0).set_name("thk"); // name to read by
    // set attributes for the read stage; see below for reset
    m_target_thickness.metadata(0)
        .long_name("target thickness for force-to-thickness mechanism (hit this at end of run)")
        .units("m")
        .standard_name("land_ice_thickness"); // standard_name *to read by*
 
    m_target_thickness.regrid(input_file, io::Default::Nil());
 
    // reset name to avoid confusion; set attributes again to overwrite "read by" choices above
    m_target_thickness.metadata(0).set_name("ftt_target_thk");
    m_target_thickness.metadata(0).standard_name(""); // no CF standard_name, to put it mildly
  }
 
  {
    m_log->message(2,
                   "    reading force-to-thickness mask 'ftt_mask' from %s ...\n",
                   input_file.c_str());
    m_ftt_mask.regrid(input_file, io::Default::Nil());
  }
}
 
/*!
If `-force_to_thickness_file` `foo.nc` is in use then vthktarget will have a target ice thickness
map.  Let \f$H_{\text{tar}}\f$ be this target thickness,
and let \f$H\f$ be the current model thickness.  Recall that the mass continuity
equation solved by GeometryEvolution is
  \f[ \frac{\partial H}{\partial t} = M - S - \nabla\cdot \mathbf{q} \f]
and that this procedure is supposed to produce \f$M\f$.
In this context, the semantics of `-force_to_thickness` are that \f$M\f$ is modified
by a multiple of the difference between the target thickness and the current thickness.
In particular, the \f$\Delta M\f$ that is produced here is
  \f[\Delta M = \alpha (H_{\text{tar}} - H)\f]
where \f$\alpha>0\f$ is determined below.  Note \f$\Delta M\f$ is positive in
areas where \f$H_{\text{tar}} > H\f$, so we are adding mass there, and we are ablating
in the other case.
 
Let \f$t_s\f$ be the start time and \f$t_e\f$ the end time for the run.
Without flow or basal mass balance, or any surface mass balance other than the
\f$\Delta M\f$ computed here, we are solving
  \f[ \frac{\partial H}{\partial t} = \alpha (H_{\text{tar}} - H) \f]
Let's assume \f$H(t_s)=H_0\f$.  This initial value problem has solution
\f$H(t) = H_{\text{tar}} + (H_0 - H_{\text{tar}}) e^{-\alpha (t-t_s)}\f$
and so
  \f[ H(t_e) = H_{\text{tar}} + (H_0 - H_{\text{tar}}) e^{-\alpha (t_e-t_s)} \f]
 
The constant \f$\alpha\f$ has a default value `pism_config:surface.force_to_thickness.alpha`.
 
The next example uses files generated from the EISMINT-Greenland experiment;
see the corresponding chapter of the User's Manual.
 
Suppose we regard the SSL2 run as a spin-up to reach a better temperature field.
It is a spinup in which the surface was allowed to evolve.  Assume the
early file `green20km_y1.nc` has the target thickness, because it essentially
has the input thickness.  This script adds a 500 a run, to finalize the spinup,
in which the ice sheet geometry goes from the the thickness values in
`green_ssl2_110ka.nc` to values very close to those in `green20km_y1.nc`:
\code
#!/bin/bash
 
NN=8  # default number of processors
if [ $# -gt 0 ] ; then  # if user says "test_ftt.sh 8" then NN = 8
  NN="$1"
fi
 
# set MPIDO if using different MPI execution command, for example:
#  $ export PISM_MPIDO="aprun -n "
if [ -n "${PISM_MPIDO:+1}" ] ; then  # check if env var is already set
  echo "$SCRIPTNAME      PISM_MPIDO = $PISM_MPIDO  (already set)"
else
  PISM_MPIDO="mpiexec -n "
  echo "$SCRIPTNAME      PISM_MPIDO = $PISM_MPIDO"
fi
 
# check if env var PISM_DO was set (i.e. PISM_DO=echo for a 'dry' run)
if [ -n "${PISM_DO:+1}" ] ; then  # check if env var DO is already set
  echo "$SCRIPTNAME         PISM_DO = $PISM_DO  (already set)"
else
  PISM_DO=""
fi
 
# prefix to pism (not to executables)
if [ -n "${PISM_PREFIX:+1}" ] ; then  # check if env var is already set
  echo "$SCRIPTNAME     PISM_PREFIX = $PISM_PREFIX  (already set)"
else
  PISM_PREFIX=""    # just a guess
  echo "$SCRIPTNAME     PISM_PREFIX = $PISM_PREFIX"
fi
 
# set PISM_EXEC if using different executables, for example:
#  $ export PISM_EXEC="pismr -energy cold"
if [ -n "${PISM_EXEC:+1}" ] ; then  # check if env var is already set
  echo "$SCRIPTNAME       PISM_EXEC = $PISM_EXEC  (already set)"
else
  PISM_EXEC="pismr"
  echo "$SCRIPTNAME       PISM_EXEC = $PISM_EXEC"
fi
 
 
PISM="${PISM_PREFIX}${PISM_EXEC}"
 
cmd="$PISM_MPIDO $NN $PISM -ys -1000.0 -ye 0 -skip 5 -i green_ssl2_110ka.nc -atmosphere searise_greenland \
    -surface pdd -pdd_fausto \
    -o no_force.nc -ts_file ts_no_force.nc -ts_times -1000:yearly:0"
$PISM_DO $cmd
 
echo
 
cmd="$PISM_MPIDO $NN $PISM -ys -1000.0 -ye 0 -skip 5 -i green_ssl2_110ka.nc -atmosphere searise_greenland \
  -surface pdd,forcing -pdd_fausto -force_to_thickness_file green20km_y1.nc \
  -o default_force.nc -ts_file ts_default_force.nc -ts_times -1000:yearly:0"
$PISM_DO $cmd
 
echo
 
cmd="$PISM_MPIDO $NN $PISM -ys -1000.0 -ye 0 -skip 5 -i green_ssl2_110ka.nc -atmosphere searise_greenland \
    -surface pdd,forcing -pdd_fausto -force_to_thickness_file green20km_y1.nc -force_to_thickness_alpha 0.005 \
    -o weak_force.nc -ts_file ts_weak_force.nc -ts_times -1000:yearly:0"
$PISM_DO $cmd
 
 
cmd="$PISM_MPIDO $NN $PISM -ys -1000.0 -ye 0 -skip 5 -i green_ssl2_110ka.nc -atmosphere searise_greenland \
    -surface pdd,forcing -pdd_fausto -force_to_thickness_file green20km_y1.nc -force_to_thickness_alpha 0.05 \
    -o strong_force.nc -ts_file ts_strong_force.nc -ts_times -1000:yearly:0"
$PISM_DO $cmd
 
\endcode
The script also has a run with no forcing, one with forcing at a lower alpha value,
a factor of five smaller than the default, and one with a forcing at a higher alpha value, a factor of five higher.
 */
void ForceThickness::adjust_mass_flux(double time,
                                      const array::Scalar &ice_thickness,
                                      const array::CellType &cell_type,
                                      array::Scalar &result) const {
 
  if (time < m_start_time) {
    return;
  }
 
  m_log->message(5,
                 "    updating surface mass balance using -force_to_thickness mechanism ...");
 
  double ice_density = m_config->get_number("constants.ice.density");
 
  array::AccessScope list{&cell_type, &ice_thickness,
      &m_target_thickness, &m_ftt_mask, &result};
 
  for (auto p = m_grid->points(); p; p.next()) {
    const int i = p.i(), j = p.j();
 
    if (m_ftt_mask(i,j) > 0.5 and cell_type.grounded(i, j)) {
      if (m_target_thickness(i,j) >= m_ice_free_thickness_threshold) {
        result(i,j) += ice_density * m_alpha * (m_target_thickness(i,j) - ice_thickness(i,j));
      } else {
        result(i,j) += ice_density * m_alpha * m_alpha_ice_free_factor * (m_target_thickness(i,j) - ice_thickness(i,j));
      }
    }
  }
  // no communication needed
}
 
void ForceThickness::update_impl(const Geometry &geometry, double t, double dt) {
  m_input_model->update(geometry, t, dt);
 
  m_mass_flux->copy_from(m_input_model->mass_flux());
 
  adjust_mass_flux(t,
                   geometry.ice_thickness,
                   geometry.cell_type,
                   *m_mass_flux);
  
  dummy_accumulation(*m_mass_flux, *m_accumulation);
  dummy_melt(*m_mass_flux, *m_melt);
  dummy_runoff(*m_mass_flux, *m_runoff);
}
 
const array::Scalar &ForceThickness::mass_flux_impl() const {
  return *m_mass_flux;
}
 
const array::Scalar &ForceThickness::accumulation_impl() const {
  return *m_accumulation;
}
 
const array::Scalar &ForceThickness::melt_impl() const {
  return *m_melt;
}
 
const array::Scalar &ForceThickness::runoff_impl() const {
  return *m_runoff;
}
 
/*!
The timestep restriction is, by direct analogy, the same as for
   \f[\frac{dy}{dt} = - \alpha y\f]
with explicit (forward) Euler.  If \f$\Delta t\f$ is the time step then Euler is
\f$y_{n+1} = (1-\alpha \Delta t) y_n\f$.  We require for stability that
\f$|y_{n+1}|\le |y_n|\f$, which is to say \f$|1-\alpha \Delta t|\le 1\f$.
Equivalently (since \f$\alpha \Delta t>0\f$),
   \f[\alpha \Delta t\le 2\f]
Therefore we set here
   \f[\Delta t = \frac{2}{\alpha}.\f]
 */
MaxTimestep ForceThickness::max_timestep_impl(double my_t) const {
  double max_dt = 2.0 / m_alpha;
  MaxTimestep input_max_dt = m_input_model->max_timestep(my_t);
 
  return std::min(input_max_dt, MaxTimestep(max_dt, "surface forcing"));
}
 
void ForceThickness::define_model_state_impl(const File &output) const {
  m_ftt_mask.define(output, io::PISM_DOUBLE);
  m_target_thickness.define(output, io::PISM_DOUBLE);
 
  if (m_input_model != NULL) {
    m_input_model->define_model_state(output);
  }
}
 
void ForceThickness::write_model_state_impl(const File &output) const {
  m_ftt_mask.write(output);
  m_target_thickness.write(output);
 
  if (m_input_model != NULL) {
    m_input_model->write_model_state(output);
  }
}
 
} // end of namespace surface
} // end of namespace pism