def errors(plot_results=True, T_final_years=1000.0, dt_years=100, Mz=101):
"""Test the bedrock temperature solver with Neumann B.C. at the base and
Dirichlet B.C. at the top surface.
"""
T_final = convert(T_final_years, "years", "seconds")
dt = convert(dt_years, "years", "seconds")
Lz = 1000.0
dz = Lz / (Mz - 1.0)
column = PISM.BedrockColumn("btu", ctx.config, dz, int(Mz))
z = np.linspace(-Lz, 0, Mz)
T_base = 240.0 # Kelvin
T_surface = 260.0 # Kelvin
dT_base = (T_surface - T_base) / Lz
T_steady = T_base + dT_base * (z - (-Lz))
Q_base = -K * dT_base
T_exact = exact(Lz, dT_base, T_surface)
t = 0.0
# initial condition
x = T_exact(z, t)
while t < T_final:
x = column.solve(dt, Q_base, T_surface, x)
t += dt
T_exact_final = T_exact(z, t)
if plot_results:
t_years = convert(t, "seconds", "years")
plt.figure()
plt.xlabel("z, meters")
plt.ylabel("T, K")
plt.step(z, T_exact(z, 0), color="blue", label="initial condition")
plt.step(z, T_exact_final, color="green", label="exact solution")
plt.step(z,
T_steady,
"--",
color="black",
label="steady state profile")
plt.grid(True)
plt.step(z, x, label="T={} years".format(t_years), color="red")
plt.legend(loc="best")
errors = T_exact(z, t) - x
max_error = np.max(np.fabs(errors))
avg_error = np.average(np.fabs(errors))
return max_error, avg_error
def setUp(self):
self.grid = shallow_grid()
self.geometry = PISM.Geometry(self.grid)
self.model = surface_simple(self.grid)
self.filename = "surface_force_to_thickness_input.nc"
self.output_filename = "surface_force_to_thickness_output.nc"
self.H = 1000.0
self.dH = 1000.0
self.geometry.ice_thickness.set(self.H)
# save ice thickness to a file to use as the target thickness
PISM.util.prepare_output(self.filename)
self.geometry.ice_thickness.write(self.filename)
ftt_mask = PISM.IceModelVec2S(self.grid, "ftt_mask",
PISM.WITHOUT_GHOSTS)
ftt_mask.set(1.0)
ftt_mask.write(self.filename)
alpha = 10.0
ice_density = config.get_number("constants.ice.density")
self.dSMB = -ice_density * alpha * self.dH
config.set_string("surface.force_to_thickness_file", self.filename)
config.set_number("surface.force_to_thickness.alpha",
convert(alpha, "1/s", "1/year"))
def write(self, filename):
"""Saves all of :attr:`modeldata`'s vecs (and the solution) to an
output file."""
grid = self.grid
vecs = self.modeldata.vecs
pio = util.prepare_output(filename)
pio.close()
# Save time & command line
util.writeProvenance(filename)
vel_ssa = self.ssa.velocity()
vecs.add(vel_ssa)
velbar_mag = model.createCBarVec(self.grid)
velbar_mag.set_to_magnitude(vel_ssa)
velbar_mag.mask_by(vecs.thk, util.convert(-0.01, "m/year", "m/second"))
vecs.add(velbar_mag)
taud = PISM.SSA_taud(self.ssa).compute()
vecs.add(taud)
try:
nuH = PISM.SSAFD_nuH(self.ssa).compute()
vecs.add(nuH)
except:
pass
taud_mag = PISM.SSA_taud_mag(self.ssa).compute()
vecs.add(taud_mag)
vecs.writeall(filename)
def write(self, filename):
"""Saves all of :attr:`modeldata`'s vecs (and the solution) to an
output file."""
grid = self.grid
vecs = self.modeldata.vecs
pio = util.prepare_output(filename)
pio.close()
# Save time & command line
util.writeProvenance(filename)
vel_ssa = self.ssa.velocity()
vecs.add(vel_ssa)
velbar_mag = model.createCBarVec(self.grid)
velbar_mag.set_to_magnitude(vel_ssa)
velbar_mag.mask_by(vecs.thk, util.convert(-0.01, "m/year", "m/second"))
vecs.add(velbar_mag)
taud = PISM.SSA_taud(self.ssa).compute()
vecs.add(taud)
try:
nuH = PISM.SSAFD_nuH(self.ssa).compute()
vecs.add(nuH)
except:
pass
taud_mag = PISM.SSA_taud_mag(self.ssa).compute()
vecs.add(taud_mag)
vecs.writeall(filename)
def exactSolution(self, i, j, x, y):
tauc_threshold_velocity = self.config.get_double("basal_resistance.pseudo_plastic.u_threshold",
"m/second")
v0 = convert(100, "m/year", "m/second")
alpha = math.sqrt((tauc0 / tauc_threshold_velocity) / (4 * nu0 * H0))
return [v0 * math.exp(-alpha * (x - L)), 0]
def create2dVelocityVec(grid, name="", desc="", intent="", ghost_type=PISM.WITH_GHOSTS, stencil_width=None):
"""Returns an :cpp:class:`IceModelVec2V` with attributes setup for horizontal velocity data.
:param grid: The grid to associate with the vector.
:param name: The intrinsic name to give the vector.
:param ghost_type: One of ``PISM.WITH_GHOSTS`` or
``PISM.WITHOUT_GHOSTS`` indicating if the vector
is ghosted.
:param stencil_width: The size of the ghost stencil. Ignored if
``ghost_type`` is ``PISM.WITHOUT_GHOSTS``. If
``stencil_width`` is ``None`` and the vector
is ghosted, the grid's maximum stencil width
is used.
"""
stencil_width = _stencil_width(grid, ghost_type, stencil_width)
vel = PISM.IceModelVec2V()
vel.create(grid, name, ghost_type, stencil_width)
vel.set_attrs(intent, "%s%s" % ("X-component of the ", desc), "m s-1", "", 0)
vel.set_attrs(intent, "%s%s" % ("Y-component of the ", desc), "m s-1", "", 1)
vel.metadata(0).set_string("glaciological_units", "m year-1")
vel.metadata(1).set_string("glaciological_units", "m year-1")
huge_vel = convert(1e10, "m/year", "m/second")
attrs = [("valid_min", -huge_vel), ("valid_max", huge_vel), ("_FillValue", 2 * huge_vel)]
for a in attrs:
for component in [0, 1]:
vel.metadata(component).set_double(a[0], a[1])
vel.set(2 * huge_vel)
return vel
def test_elevation_change_shift(self):
"Modifier elevation_change: shift"
config.set_string("surface.elevation_change.smb.method", "shift")
model = surface_simple(self.grid)
modifier = PISM.SurfaceElevationChange(self.grid, model)
modifier.init(self.geometry)
# change surface elevation
self.geometry.ice_surface_elevation.shift(self.dz)
# check changes in outputs
modifier.update(self.geometry, 0, 1)
ice_density = config.get_number("constants.ice.density")
dSMB = self.dz * ice_density * convert(
-self.dSMBdz, "kg m-2 year-1 / km", "kg m-2 s-1 / m")
# shifting SMB by dSMB reduced accumulation to zero
dA = 0.0 - sample(model.accumulation())
dM = dA - dSMB
dR = dM
check_modifier(model,
modifier,
T=self.dT,
SMB=dSMB,
accumulation=dA,
melt=dM,
runoff=dR)
write_state(modifier, self.output_filename)
probe_interface(modifier)
def initialize_uplift(uplift):
"Initialize the uplift field."
grid = uplift.grid()
peak_uplift = convert(10, "mm/year", "m/second")
with PISM.vec.Access(nocomm=[uplift]):
for (i, j) in grid.points():
r = PISM.radius(grid, i, j)
if r < 1.5 * R0:
uplift[i, j] = peak_uplift * (cos(pi * (r / (1.5 * R0))) + 1.0) / 2.0
else:
uplift[i, j] = 0.0
def _initSSA(self):
# Test J has a viscosity that is independent of velocity. So we force a
# constant viscosity by settting the strength_extension
# thickness larger than the given ice thickness. (max = 770m).
nu0 = convert(30.0, "MPa year", "Pa s")
H0 = 500.0 # 500 m typical thickness
ssa = self.ssa
ssa.strength_extension.set_notional_strength(nu0 * H0)
ssa.strength_extension.set_min_thickness(800.)
def _initSSA(self):
# Test J has a viscosity that is independent of velocity. So we force a
# constant viscosity by settting the strength_extension
# thickness larger than the given ice thickness. (max = 770m).
nu0 = convert(30.0, "MPa year", "Pa s")
H0 = 500.0 # 500 m typical thickness
ssa = self.ssa
ssa.strength_extension.set_notional_strength(nu0 * H0)
ssa.strength_extension.set_min_thickness(800.)
def set_constants(config):
# Set up the sliding law so that tauc == beta**2:
config.set_flag("basal_resistance.pseudo_plastic.enabled", True)
config.set_number("basal_resistance.pseudo_plastic.q", 1.0)
config.set_number("basal_resistance.pseudo_plastic.u_threshold",
convert(1.0, "m / s", "m / year"))
# Set flow law parameters
config.set_string("stress_balance.blatter.flow_law", "isothermal_glen")
config.set_number("stress_balance.blatter.Glen_exponent", 3.0)
config.set_number("flow_law.isothermal_Glen.ice_softness",
convert(1e-16, "Pa-3 year-1", "Pa-3 s-1"))
# Set constants:
config.set_number("constants.ice.density", 910.0)
config.set_number("constants.standard_gravity", 9.81)
# Support compression
config.set_string("output.format", "netcdf4_serial")
def setUp(self):
self.filename = "surface_reference_surface.nc"
self.output_filename = "surface_lapse_rates_output.nc"
self.grid = shallow_grid()
self.dTdz = 1.0 # 1 Kelvin per km
self.dSMBdz = 2.0 # m year-1 per km
self.dz = 1500.0 # m
self.geometry = PISM.Geometry(self.grid)
# save current surface elevation to use it as a "reference" surface elevation
self.geometry.ice_surface_elevation.dump(self.filename)
config.set_string("surface.elevation_change.file", self.filename)
config.set_number("surface.elevation_change.temperature_lapse_rate",
self.dTdz)
config.set_number("surface.elevation_change.smb.lapse_rate",
self.dSMBdz)
self.dT = self.dz * convert(-self.dTdz, "Kelvin / km", "Kelvin / m")
def create2dVelocityVec(grid,
name="",
desc="",
intent="",
ghost_type=PISM.WITH_GHOSTS,
stencil_width=None):
"""Returns an :cpp:class:`IceModelVec2V` with attributes setup for horizontal velocity data.
:param grid: The grid to associate with the vector.
:param name: The intrinsic name to give the vector.
:param ghost_type: One of ``PISM.WITH_GHOSTS`` or
``PISM.WITHOUT_GHOSTS`` indicating if the vector
is ghosted.
:param stencil_width: The size of the ghost stencil. Ignored if
``ghost_type`` is ``PISM.WITHOUT_GHOSTS``. If
``stencil_width`` is ``None`` and the vector
is ghosted, the grid's maximum stencil width
is used.
"""
stencil_width = _stencil_width(grid, ghost_type, stencil_width)
vel = PISM.IceModelVec2V()
vel.create(grid, name, ghost_type, stencil_width)
vel.set_attrs(intent, "%s%s" % ("X-component of the ", desc), "m s-1", "",
0)
vel.set_attrs(intent, "%s%s" % ("Y-component of the ", desc), "m s-1", "",
1)
vel.metadata(0).set_string("glaciological_units", "m year-1")
vel.metadata(1).set_string("glaciological_units", "m year-1")
huge_vel = convert(1e10, "m/year", "m/second")
attrs = [("valid_min", -huge_vel), ("valid_max", huge_vel),
("_FillValue", 2 * huge_vel)]
for a in attrs:
for component in [0, 1]:
vel.metadata(component).set_double(a[0], a[1])
vel.set(2 * huge_vel)
return vel
def rangeVector(self):
"""Constructs a brand new vector from the range (i.e. state) vector space"""
v = PISM.IceModelVec2V()
v.create(self.grid, "", True, WIDE_STENCIL)
# Add appropriate meta data.
intent = "?inverse?" # FIXME
desc = "SSA velocity computed by inversion"
v.set_attrs(intent, "%s%s" % ("X-component of the ", desc), "m s-1",
"m year-1", "", 0)
v.set_attrs(intent, "%s%s" % ("Y-component of the ", desc), "m s-1",
"m year-1", "", 1)
huge_vel = convert(1e6, "m/year", "m/second")
attrs = [("valid_min", -huge_vel), ("valid_max", huge_vel),
("_FillValue", 2 * huge_vel)]
for a in attrs:
for component in range(2):
v.metadata(component).set_number(a[0], a[1])
return PISMLocalVector(v)
def setup():
global grid
# "inputs" does not own its elements, so we need to make sure
# these don't expire when setup() returns
global basal_melt_rate, ice_thickness, inputs, surface_temp
global climatic_mass_balance, basal_heat_flux, shelf_base_temp, cell_type
global u, v, w, strain_heating3
grid = create_dummy_grid()
zero = PISM.IceModelVec2S()
zero.create(grid, "zero", PISM.WITHOUT_GHOSTS)
zero.set(0.0)
cell_type = PISM.IceModelVec2CellType()
cell_type.create(grid, "mask", PISM.WITHOUT_GHOSTS)
cell_type.set(PISM.MASK_GROUNDED)
basal_heat_flux = PISM.IceModelVec2S()
basal_heat_flux.create(grid, "bheatflx", PISM.WITHOUT_GHOSTS)
basal_heat_flux.set(convert(10, "mW m-2", "W m-2"))
ice_thickness = PISM.model.createIceThicknessVec(grid)
ice_thickness.set(4000.0)
# TemperatureModel needs ice_thickness to set enthalpy in restart(...)
grid.variables().add(ice_thickness)
shelf_base_temp = PISM.IceModelVec2S()
shelf_base_temp.create(grid, "shelfbtemp", PISM.WITHOUT_GHOSTS)
shelf_base_temp.set(260.0)
surface_temp = PISM.IceModelVec2S()
surface_temp.create(grid, "surface_temp", PISM.WITHOUT_GHOSTS)
surface_temp.set(260.0)
strain_heating3 = PISM.IceModelVec3()
strain_heating3.create(grid, "sigma", PISM.WITHOUT_GHOSTS)
u = PISM.IceModelVec3()
u.create(grid, "u", PISM.WITHOUT_GHOSTS)
v = PISM.IceModelVec3()
v.create(grid, "v", PISM.WITHOUT_GHOSTS)
w = PISM.IceModelVec3()
w.create(grid, "w", PISM.WITHOUT_GHOSTS)
ice_thickness.set(4000.0)
u.set(0.0)
v.set(0.0)
w.set(0.0)
basal_melt_rate = zero
climatic_mass_balance = zero
inputs = PISM.EnergyModelInputs()
inputs.cell_type = cell_type
inputs.basal_frictional_heating = zero
inputs.basal_heat_flux = basal_heat_flux
inputs.ice_thickness = ice_thickness
inputs.surface_liquid_fraction = zero
inputs.shelf_base_temp = shelf_base_temp
inputs.surface_temp = surface_temp
inputs.till_water_thickness = zero
inputs.strain_heating3 = strain_heating3
inputs.u3 = u
inputs.v3 = v
inputs.w3 = w
inputs = PISM.EnergyModelInputs()
inputs.cell_type = cell_type
inputs.basal_frictional_heating = zero
inputs.basal_heat_flux = basal_heat_flux
inputs.ice_thickness = ice_thickness
inputs.surface_liquid_fraction = zero
inputs.shelf_base_temp = shelf_base_temp
inputs.surface_temp = surface_temp
inputs.till_water_thickness = zero
inputs.strain_heating3 = strain_heating3
inputs.u3 = u
inputs.v3 = v
inputs.w3 = w
dt = convert(1, "years", "seconds")
def use_model(model):
print("* Performing a time step...")
model.update(0, dt, inputs)
try:
model.update(0, dt)
raise Exception("this should fail")
except RuntimeError:
pass
try:
model.max_timestep(0)
raise Exception("this should fail")
except RuntimeError:
def __call__(self, inverse_solver, count, data):
if not self.l2_weight_init:
vecs = inverse_solver.ssarun.modeldata.vecs
if vecs.has('vel_misfit_weight'):
self.l2_weight = self.toproczero(vecs.vel_misfit_weight)
self.l2_weight_init = True
method = inverse_solver.method
r = self.toproczero(data.residual)
Td = None
if 'T_zeta_step' in data:
Td = self.toproczero(data.T_zeta_step)
TStarR = None
if 'TStar_residual' in data:
TStarR = self.toproczero(data.TStar_residual)
d = None
if 'zeta_step' in data:
d = self.toproczero(data.zeta_step)
zeta = self.toproczero(data.zeta)
secpera = convert(1.0, "year", "second")
if self.grid.rank() == 0:
import matplotlib.pyplot as pp
pp.figure(self.figure())
l2_weight = self.l2_weight
pp.clf()
V = self.Vmax
pp.subplot(2, 3, 1)
if l2_weight is not None:
rx = l2_weight * r[0, :, :] * secpera
else:
rx = r[0, :, :] * secpera
rx = np.maximum(rx, -V)
rx = np.minimum(rx, V)
pp.imshow(rx, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('r_x')
pp.jet()
pp.subplot(2, 3, 4)
if l2_weight is not None:
ry = l2_weight * r[1, :, :] * secpera
else:
ry = r[1, :, :] * secpera
ry = np.maximum(ry, -V)
ry = np.minimum(ry, V)
pp.imshow(ry, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('r_y')
pp.jet()
if method == 'ign':
pp.subplot(2, 3, 2)
Tdx = Td[0, :, :] * secpera
pp.imshow(Tdx, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('Td_x')
pp.jet()
pp.subplot(2, 3, 5)
Tdy = Td[1, :, :] * secpera
pp.imshow(Tdy, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('Td_y')
pp.jet()
elif method == 'sd' or method == 'nlcg':
pp.subplot(2, 3, 2)
pp.imshow(TStarR, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('TStarR')
pp.jet()
if d is not None:
d *= -1
pp.subplot(2, 3, 3)
pp.imshow(d, origin='lower', interpolation='nearest')
# colorbar does a divide by zero if 'd' is all zero,
# as it will be at the start of iteration zero.
# The warning message is a distraction, so we suppress it.
import warnings
with warnings.catch_warnings():
warnings.simplefilter("ignore")
pp.colorbar()
pp.jet()
pp.title('-zeta_step')
pp.subplot(2, 3, 6)
pp.imshow(zeta, origin='lower', interpolation='nearest')
pp.colorbar()
pp.jet()
pp.title('zeta')
pp.ion()
pp.draw()
pp.show()
#
# 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
import PISM
from PISM.util import convert
import math
context = PISM.Context()
L = 50.e3 # // 50km half-width
H0 = 500 # // m
dhdx = 0.005 # // pure number, slope of surface & bed
nu0 = convert(30.0, "MPa year", "Pa s")
tauc0 = 1.e4 # // 1kPa
class test_linear(PISM.ssa.SSAExactTestCase):
def _initGrid(self):
self.grid = PISM.IceGrid.Shallow(PISM.Context().ctx, L, L, 0, 0,
self.Mx, self.My,
PISM.CELL_CORNER,
PISM.NOT_PERIODIC)
def _initPhysics(self):
config = self.config
config.set_boolean("basal_resistance.pseudo_plastic.enabled", True)
config.set_double("basal_resistance.pseudo_plastic.q", 1.0)
def setup():
global grid
# "inputs" does not own its elements, so we need to make sure
# these don't expire when setup() returns
global basal_melt_rate, ice_thickness, inputs, surface_temp
global climatic_mass_balance, basal_heat_flux, shelf_base_temp, cell_type
global u, v, w, strain_heating3
grid = create_dummy_grid()
zero = PISM.IceModelVec2S(grid, "zero", PISM.WITHOUT_GHOSTS)
zero.set(0.0)
cell_type = PISM.IceModelVec2CellType(grid, "mask", PISM.WITHOUT_GHOSTS)
cell_type.set(PISM.MASK_GROUNDED)
basal_heat_flux = PISM.IceModelVec2S(grid, "bheatflx", PISM.WITHOUT_GHOSTS)
basal_heat_flux.set(convert(10, "mW m-2", "W m-2"))
ice_thickness = PISM.model.createIceThicknessVec(grid)
ice_thickness.set(4000.0)
# TemperatureModel needs ice_thickness to set enthalpy in restart(...)
grid.variables().add(ice_thickness)
shelf_base_temp = PISM.IceModelVec2S(grid, "shelfbtemp", PISM.WITHOUT_GHOSTS)
shelf_base_temp.set(260.0)
surface_temp = PISM.IceModelVec2S(grid, "surface_temp", PISM.WITHOUT_GHOSTS)
surface_temp.set(260.0)
strain_heating3 = PISM.IceModelVec3(grid, "sigma", PISM.WITHOUT_GHOSTS)
u = PISM.IceModelVec3(grid, "u", PISM.WITHOUT_GHOSTS)
v = PISM.IceModelVec3(grid, "v", PISM.WITHOUT_GHOSTS)
w = PISM.IceModelVec3(grid, "w", PISM.WITHOUT_GHOSTS)
ice_thickness.set(4000.0)
u.set(0.0)
v.set(0.0)
w.set(0.0)
basal_melt_rate = zero
climatic_mass_balance = zero
inputs = PISM.EnergyModelInputs()
inputs.cell_type = cell_type
inputs.basal_frictional_heating = zero
inputs.basal_heat_flux = basal_heat_flux
inputs.ice_thickness = ice_thickness
inputs.surface_liquid_fraction = zero
inputs.shelf_base_temp = shelf_base_temp
inputs.surface_temp = surface_temp
inputs.till_water_thickness = zero
inputs.volumetric_heating_rate = strain_heating3
inputs.u3 = u
inputs.v3 = v
inputs.w3 = w
vel_sia_observed.metadata(1).set_name('v_sia_observed')
vel_sia_observed.metadata(1).set_string('long_name', "y-component of the 'observed' SIA velocities")
vel_surface_observed = PISM.model.create2dVelocityVec(grid, "_surface_observed",
"observed surface velocities",
stencil_width=1)
vel_surface_observed.copy_from(vel_sia_observed)
vel_surface_observed.add(1., vel_ssa_observed)
vecs.markForWriting(vel_surface_observed)
final_velocity = vel_surface_observed
# Add the misfit weight.
if misfit_weight_type == "fast":
misfit_weight = fastIceMisfitWeight(modeldata, vel_ssa,
convert(fast_ice_speed, "m/year", "m/second"))
else:
misfit_weight = groundedIceMisfitWeight(modeldata)
modeldata.vecs.add(misfit_weight, writing=True)
if not noise is None:
u_noise = PISM.vec.randVectorV(grid, noise / math.sqrt(2), final_velocity.stencil_width())
final_velocity.add(convert(1.0, "m/year", "m/second"),
u_noise)
pio = PISM.util.prepare_output(output_file_name)
pio.close()
vecs.write(output_file_name)
# Save time & command line
-snes_monitor \
-ksp_monitor
This command uses "aggressive" coarsening (factor of 4) and 2 multigrid levels (5 and 2
nodes in the vertical direction).
To use AMG on the coarse level, add "-mg_coarse_pc_type gamg".
"""
import numpy as np
import PISM
import PISM.testing
from PISM.util import convert
seconds_per_year = convert(1.0, "year", "second")
ctx = PISM.Context()
config = ctx.config
tests = {"A": PISM.HOM_A, "B": PISM.HOM_B, "C": PISM.HOM_C, "D": PISM.HOM_D}
def surface_AB(x, y, L):
alpha = 0.5 * (np.pi / 180.0) # 0.5 degrees
return -x * np.tan(alpha)
def surface_C(x, y, L):
alpha = 0.1 * (np.pi / 180.0) # 0.1 degrees
return -x * np.tan(alpha)
def run(T_final_years=10.0, dt_days=1, Lz=1000, Mz=101, R=20, omega=0.005):
"""Run the one-column cryohydrologic warming setup"""
T_final = convert(T_final_years, "years", "seconds")
dt = convert(dt_days, "days", "seconds")
ice = EnthalpyColumn("energy.enthalpy", Mz, dt, Lz=Lz)
ch = EnthalpyColumn("energy.ch_warming", Mz, dt, Lz=Lz)
H = ice.Lz
z = np.array(ice.sys.z())
P = pressure(H - z)
z_coarse = np.array(ice.grid.z())
P_coarse = pressure(H - z_coarse)
T_mean_annual = 268.15 # mean annual temperature, Kelvin
T_amplitude = 6 # surface temperature aplitude, Kelvin
summer_peak_day = 365/2
G = 0.0 # geothermal flux, W/m^2
E_initial = E_steady_state(H, z_coarse, T_mean_annual, G, k)
with PISM.vec.Access(nocomm=[ice.enthalpy, ice.strain_heating, ice.u, ice.v, ice.w,
ch.enthalpy, ch.strain_heating, ch.u, ch.v, ch.w]):
# set initial state for the ice enthalpy
ice.enthalpy.set_column(1, 1, E_initial)
# set initial state for the CH system enthalpy
ch.enthalpy.set_column(1, 1, E_initial)
times = []
T_ice = []
T_ch = []
W_ice = []
W_ch = []
t = 0.0
while t < T_final:
times.append(t)
# compute the heat flux from the CH system into the ice
T_s = T_surface(t, T_mean_annual, T_amplitude, summer_peak_day)
T_column_ice = temperature(ice.enthalpy.get_column_vector(1, 1), P_coarse)
T_column_ch = temperature(ch.enthalpy.get_column_vector(1, 1), P_coarse)
if R > 0:
Q = ch_heat_flux(T_column_ice, T_column_ch, k, R)
else:
Q = np.zeros_like(P_coarse)
# add it to the strain heating term
ice.strain_heating.set_column(1, 1, Q)
ch.strain_heating.set_column(1, 1, -Q)
if T_s > T_melting:
E_s = EC.enthalpy(T_melting, 0.0, 0.0)
else:
E_s = EC.enthalpy(T_s, 0.0, 0.0)
# set boundary conditions and update the ice column
ice.init()
ice.sys.set_surface_dirichlet_bc(E_s)
ice.sys.set_basal_heat_flux(G)
x = ice.sys.solve()
T_ice.append(temperature(x, P))
W_ice.append(water_fraction(x, P))
ice.sys.fine_to_coarse(x, 1, 1, ice.enthalpy)
if T_s > T_melting:
E_s = EC.enthalpy(T_melting, omega, 0.0)
# Re-set enthalpy in the CH system during the melt season
ch.enthalpy.set_column(1, 1, enthalpy(melting_temperature(P), omega, P))
else:
E_s = EC.enthalpy(T_s, 0.0, 0.0)
# set boundary conditions and update the CH column
ch.init()
ch.sys.set_surface_dirichlet_bc(E_s)
ch.sys.set_basal_heat_flux(G)
x = ch.sys.solve()
T_ch.append(temperature(x, P))
W_ch.append(water_fraction(x, P))
ch.sys.fine_to_coarse(x, 1, 1, ch.enthalpy)
t += dt
return z, np.array(times), np.array(T_ice), np.array(W_ice), np.array(T_ch), np.array(W_ch)
'long_name', "y-component of the 'observed' SIA velocities")
vel_surface_observed = PISM.model.create2dVelocityVec(
grid,
"_surface_observed",
"observed surface velocities",
stencil_width=1)
vel_surface_observed.copy_from(vel_sia_observed)
vel_surface_observed.add(1., vel_ssa_observed)
vecs.markForWriting(vel_surface_observed)
final_velocity = vel_surface_observed
# Add the misfit weight.
if misfit_weight_type == "fast":
misfit_weight = fastIceMisfitWeight(
modeldata, vel_ssa, convert(fast_ice_speed, "m/year", "m/second"))
else:
misfit_weight = groundedIceMisfitWeight(modeldata)
modeldata.vecs.add(misfit_weight, writing=True)
if not noise is None:
u_noise = PISM.vec.randVectorV(grid, noise / math.sqrt(2),
final_velocity.stencil_width())
final_velocity.add(convert(1.0, "m/year", "m/second"), u_noise)
pio = PISM.util.prepare_output(output_file_name)
pio.close()
vecs.write(output_file_name)
# Save time & command line
* re-initializing
* one more 1000 year step
Used as a regression test for PISM.LingleClark.
"""
import PISM
from PISM.util import convert
import pylab as plt
import numpy as np
import os
ctx = PISM.Context()
# disc load parameters
disc_radius = convert(1000, "km", "m")
disc_thickness = 1000.0 # meters
# domain size
Lx = 2 * disc_radius
Ly = Lx
N = 101
dt = convert(1000.0, "years", "seconds")
def allocate_storage(grid):
ice_thickness = PISM.IceModelVec2S(grid, "thk", PISM.WITHOUT_GHOSTS)
ice_thickness.metadata().set_string("standard_name", "land_ice_thickness")
bed = PISM.IceModelVec2S(grid, "topg", PISM.WITHOUT_GHOSTS)
bed_uplift = PISM.IceModelVec2S(grid, "uplift", PISM.WITHOUT_GHOSTS)
sea_level = PISM.IceModelVec2S(grid, "sea_level", PISM.WITHOUT_GHOSTS)
Testing program for PISM's implementations of the SSA.
Does a time-independent calculation. Does not run IceModel or a derived
class thereof. Uses the van der Veen flow-line shelf geometry. Also may be
used in a PISM software (regression) test.
"""
usage = \
"""
usage of SSA_TEST_CFBC:
run ssa_test_cfbc -Mx <number> -My <number>
"""
context = PISM.Context()
H0 = 600. # meters
V0 = convert(300, "m/year", "m/second")
C = 2.45e-18 # "typical constant ice parameter"
T = 400 # time used to compute the calving front location
Q0 = V0 * H0
Hc1 = 4. * C / Q0
Hc2 = 1. / (H0**4)
def H_exact(x):
return (Hc1 * x + Hc2)**(-1 / 4.)
def u_exact(x):
return Q0 / H_exact(x)
vel_sia_observed.metadata(1).set_name('v_sia_observed')
vel_sia_observed.metadata(1).set_string('long_name', "y-component of the 'observed' SIA velocities")
vel_surface_observed = PISM.model.create2dVelocityVec(grid, "_surface_observed",
"observed surface velocities",
stencil_width=1)
vel_surface_observed.copy_from(vel_sia_observed)
vel_surface_observed.add(1., vel_ssa_observed)
vecs.markForWriting(vel_surface_observed)
final_velocity = vel_surface_observed
# Add the misfit weight.
if misfit_weight_type == "fast":
misfit_weight = fastIceMisfitWeight(modeldata, vel_ssa,
convert(fast_ice_speed, "m/year", "m/second"))
else:
misfit_weight = groundedIceMisfitWeight(modeldata)
modeldata.vecs.add(misfit_weight, writing=True)
if not noise is None:
u_noise = PISM.vec.randVectorV(grid, noise / math.sqrt(2), final_velocity.stencil_width())
final_velocity.add(convert(1.0, "m/year", "m/second"),
u_noise)
pio = PISM.util.prepare_output(output_file_name)
pio.close()
vecs.write(output_file_name)
# Save time & command line
def run():
context = PISM.Context()
config = context.config
com = context.com
PISM.set_abort_on_sigint(True)
WIDE_STENCIL = int(config.get_double("grid.max_stencil_width"))
usage = \
""" pismi.py [-i IN.nc [-o OUT.nc]]/[-a INOUT.nc] [-inv_data inv_data.nc] [-inv_forward model]
[-inv_design design_var] [-inv_method meth]
where:
-i IN.nc is input file in NetCDF format: contains PISM-written model state
-o OUT.nc is output file in NetCDF format to be overwritten
-a INOUT.nc is input/output file in NetCDF format to be appended to
-inv_data inv_data.nc is data file containing extra inversion data (e.g. observed surface velocities)
-inv_forward model forward model: only 'ssa' supported
-inv_design design_var design variable name; one of 'tauc'/'hardav' for SSA inversions
-inv_method meth algorithm for inversion [sd,nlcg,ign,tikhonov_lmvm]
notes:
* only one of -i/-a is allowed; both specify the input file
* only one of -o/-a is allowed; both specify the output file
* if -o is used, only the variables involved in inversion are written to the output file.
* if -a is used, the varaibles involved in inversion are appended to the given file. No
original variables in the file are changed.
"""
append_mode = False
input_filename = config.get_string("input.file")
if len(input_filename) == 0:
input_filename = None
append = PISM.OptionString("-a", "append file")
append_filename = append.value() if append.is_set() else None
output_filename = config.get_string("output.file_name")
if len(output_filename) == 0:
output_filename = None
if (input_filename is None) and (append_filename is None):
PISM.verbPrintf(1, com, "\nError: No input file specified. Use one of -i [file.nc] or -a [file.nc].\n")
sys.exit(0)
if (input_filename is not None) and (append_filename is not None):
PISM.verbPrintf(1, com, "\nError: Only one of -i/-a is allowed.\n")
sys.exit(0)
if (output_filename is not None) and (append_filename is not None):
PISM.verbPrintf(1, com, "\nError: Only one of -a/-o is allowed.\n")
sys.edit(0)
if append_filename is not None:
input_filename = append_filename
output_filename = append_filename
append_mode = True
inv_data_filename = PISM.OptionString("-inv_data", "inverse data file", input_filename).value()
do_plotting = PISM.OptionBool("-inv_plot", "perform visualization during the computation")
do_final_plot = PISM.OptionBool("-inv_final_plot",
"perform visualization at the end of the computation")
Vmax = PISM.OptionReal("-inv_plot_vmax", "maximum velocity for plotting residuals", 30)
design_var = PISM.OptionKeyword("-inv_ssa",
"design variable for inversion",
"tauc,hardav", "tauc").value()
do_pause = PISM.OptionBool("-inv_pause", "pause each iteration")
do_restart = PISM.OptionBool("-inv_restart", "Restart a stopped computation.")
use_design_prior = config.get_boolean("inverse.use_design_prior")
prep_module = PISM.OptionString("-inv_prep_module",
"Python module used to do final setup of inverse solver")
prep_module = prep_module.value() if prep_module.is_set() else None
is_regional = PISM.OptionBool("-regional", "Compute SIA/SSA using regional model semantics")
using_zeta_fixed_mask = config.get_boolean("inverse.use_zeta_fixed_mask")
inv_method = config.get_string("inverse.ssa.method")
if output_filename is None:
output_filename = "pismi_" + os.path.basename(input_filename)
saving_inv_data = (inv_data_filename != output_filename)
forward_run = SSAForwardRun(input_filename, inv_data_filename, design_var)
forward_run.setup()
design_param = forward_run.designVariableParameterization()
solver = PISM.invert.ssa.createInvSSASolver(forward_run)
modeldata = forward_run.modeldata
vecs = modeldata.vecs
grid = modeldata.grid
# Determine the prior guess for tauc/hardav. This can be one of
# a) tauc/hardav from the input file (default)
# b) tauc/hardav_prior from the inv_datafile if -inv_use_design_prior is set
design_prior = createDesignVec(grid, design_var, '%s_prior' % design_var)
long_name = design_prior.metadata().get_string("long_name")
units = design_prior.metadata().get_string("units")
design_prior.set_attrs("", "best prior estimate for %s (used for inversion)" % long_name, units, "")
if PISM.util.fileHasVariable(inv_data_filename, "%s_prior" % design_var) and use_design_prior:
PISM.logging.logMessage(" Reading '%s_prior' from inverse data file %s.\n" % (design_var, inv_data_filename))
design_prior.regrid(inv_data_filename, critical=True)
vecs.add(design_prior, writing=saving_inv_data)
else:
if not PISM.util.fileHasVariable(input_filename, design_var):
PISM.verbPrintf(1, com, "Initial guess for design variable is not available as '%s' in %s.\nYou can provide an initial guess in the inverse data file.\n" % (
design_var, input_filename))
exit(1)
PISM.logging.logMessage("Reading '%s_prior' from '%s' in input file.\n" % (design_var, design_var))
design = createDesignVec(grid, design_var)
design.regrid(input_filename, True)
design_prior.copy_from(design)
vecs.add(design_prior, writing=True)
if using_zeta_fixed_mask:
if PISM.util.fileHasVariable(inv_data_filename, "zeta_fixed_mask"):
zeta_fixed_mask = PISM.model.createZetaFixedMaskVec(grid)
zeta_fixed_mask.regrid(inv_data_filename)
vecs.add(zeta_fixed_mask)
else:
if design_var == 'tauc':
logMessage(
" Computing 'zeta_fixed_mask' (i.e. locations where design variable '%s' has a fixed value).\n" % design_var)
zeta_fixed_mask = PISM.model.createZetaFixedMaskVec(grid)
zeta_fixed_mask.set(1)
mask = vecs.mask
with PISM.vec.Access(comm=zeta_fixed_mask, nocomm=mask):
for (i, j) in grid.points():
if mask.grounded_ice(i, j):
zeta_fixed_mask[i, j] = 0
vecs.add(zeta_fixed_mask)
adjustTauc(vecs.mask, design_prior)
elif design_var == 'hardav':
PISM.logging.logPrattle(
"Skipping 'zeta_fixed_mask' for design variable 'hardav'; no natural locations to fix its value.")
pass
else:
raise NotImplementedError("Unable to build 'zeta_fixed_mask' for design variable %s.", design_var)
# Convert design_prior -> zeta_prior
zeta_prior = PISM.IceModelVec2S()
zeta_prior.create(grid, "zeta_prior", PISM.WITH_GHOSTS, WIDE_STENCIL)
design_param.convertFromDesignVariable(design_prior, zeta_prior)
vecs.add(zeta_prior, writing=True)
# Determine the initial guess for zeta. If we are restarting, load it from
# the output file. Otherwise, if 'zeta_inv' is in the inverse data file, use it.
# If none of the above, copy from 'zeta_prior'.
zeta = PISM.IceModelVec2S()
zeta.create(grid, "zeta_inv", PISM.WITH_GHOSTS, WIDE_STENCIL)
zeta.set_attrs("diagnostic", "zeta_inv", "1", "zeta_inv")
if do_restart:
# Just to be sure, verify that we have a 'zeta_inv' in the output file.
if not PISM.util.fileHasVariable(output_filename, 'zeta_inv'):
PISM.verbPrintf(
1, com, "Unable to restart computation: file %s is missing variable 'zeta_inv'", output_filename)
exit(1)
PISM.logging.logMessage(" Inversion starting from 'zeta_inv' found in %s\n" % output_filename)
zeta.regrid(output_filename, True)
elif PISM.util.fileHasVariable(inv_data_filename, 'zeta_inv'):
PISM.logging.logMessage(" Inversion starting from 'zeta_inv' found in %s\n" % inv_data_filename)
zeta.regrid(inv_data_filename, True)
else:
zeta.copy_from(zeta_prior)
vel_ssa_observed = None
vel_ssa_observed = PISM.model.create2dVelocityVec(grid, '_ssa_observed', stencil_width=2)
if PISM.util.fileHasVariable(inv_data_filename, "u_ssa_observed"):
vel_ssa_observed.regrid(inv_data_filename, True)
vecs.add(vel_ssa_observed, writing=saving_inv_data)
else:
if not PISM.util.fileHasVariable(inv_data_filename, "u_surface_observed"):
PISM.verbPrintf(
1, context.com, "Neither u/v_ssa_observed nor u/v_surface_observed is available in %s.\nAt least one must be specified.\n" % inv_data_filename)
exit(1)
vel_surface_observed = PISM.model.create2dVelocityVec(grid, '_surface_observed', stencil_width=2)
vel_surface_observed.regrid(inv_data_filename, True)
vecs.add(vel_surface_observed, writing=saving_inv_data)
sia_solver = PISM.SIAFD
if is_regional:
sia_solver = PISM.SIAFD_Regional
vel_sia_observed = PISM.sia.computeSIASurfaceVelocities(modeldata, sia_solver)
vel_sia_observed.metadata(0).set_name('u_sia_observed')
vel_sia_observed.metadata(0).set_string('long_name', "x-component of the 'observed' SIA velocities")
vel_sia_observed.metadata(1).set_name('v_sia_observed')
vel_sia_observed.metadata(1).set_string('long_name', "y-component of the 'observed' SIA velocities")
vel_ssa_observed.copy_from(vel_surface_observed)
vel_ssa_observed.add(-1, vel_sia_observed)
vecs.add(vel_ssa_observed, writing=True)
# If the inverse data file has a variable tauc/hardav_true, this is probably
# a synthetic inversion. We'll load it now so that it will get written
# out, if needed, at the end of the computation in the output file.
if PISM.util.fileHasVariable(inv_data_filename, "%s_true" % design_var):
design_true = createDesignVec(grid, design_var, '%s_true' % design_var)
design_true.regrid(inv_data_filename, True)
design_true.read_attributes(inv_data_filename)
vecs.add(design_true, writing=saving_inv_data)
# Establish a logger which will save logging messages to the output file.
message_logger = PISM.logging.CaptureLogger(output_filename, 'pismi_log')
PISM.logging.add_logger(message_logger)
if append_mode or do_restart:
message_logger.readOldLog()
# Prep the output file from the grid so that we can save zeta to it during the runs.
if not append_mode:
pio = PISM.util.prepare_output(output_filename)
pio.close()
zeta.write(output_filename)
# Log the command line to the output file now so that we have a record of
# what was attempted
PISM.util.writeProvenance(output_filename)
# Attach various iteration listeners to the solver as needed for:
# Iteration report.
solver.addIterationListener(PISM.invert.ssa.printIteration)
# Misfit reporting/logging.
misfit_logger = PISM.invert.ssa.MisfitLogger()
solver.addIterationListener(misfit_logger)
if inv_method.startswith('tikhonov'):
solver.addIterationListener(PISM.invert.ssa.printTikhonovProgress)
# Saving the current iteration
solver.addDesignUpdateListener(PISM.invert.ssa.ZetaSaver(output_filename))
# Plotting
if do_plotting:
solver.addIterationListener(InvSSAPlotListener(grid, Vmax))
if solver.method == 'ign':
solver.addLinearIterationListener(InvSSALinPlotListener(grid, Vmax))
# Solver is set up. Give the user's prep module a chance to do any final
# setup.
if prep_module is not None:
if prep_module.endswith(".py"):
prep_module = prep_module[0:-2]
exec("import %s as user_prep_module" % prep_module)
user_prep_module.prep_solver(solver)
# Pausing (add this after the user's listeners)
if do_pause:
solver.addIterationListener(PISM.invert.listener.pauseListener)
# Run the inverse solver!
if do_restart:
PISM.logging.logMessage('************** Restarting inversion. ****************\n')
else:
PISM.logging.logMessage('============== Starting inversion. ==================\n')
# Try solving
reason = solver.solveInverse(zeta_prior, vel_ssa_observed, zeta)
if reason.failed():
PISM.logging.logError("Inverse solve FAILURE:\n%s\n" % reason.nested_description(1))
quit()
PISM.logging.logMessage("Inverse solve success (%s)!\n" % reason.description())
(zeta, u) = solver.inverseSolution()
# It may be that a 'tauc'/'hardav' was read in earlier. We replace it with
# our newly generated one.
if vecs.has(design_var):
design = vecs.get(design_var)
design_param.convertToDesignVariable(zeta, design)
else:
# Convert back from zeta to tauc or hardav
design = createDesignVec(grid, design_var)
design_param.convertToDesignVariable(zeta, design)
vecs.add(design, writing=True)
vecs.add(zeta, writing=True)
u.metadata(0).set_name("u_ssa_inv")
u.metadata(0).set_string("long_name", "x-component of SSA velocity computed by inversion")
u.metadata(1).set_name("v_ssa_inv")
u.metadata(1).set_string("long_name", "y-component of SSA velocity computed by inversion")
vecs.add(u, writing=True)
residual = PISM.model.create2dVelocityVec(grid, name='_inv_ssa_residual')
residual.copy_from(u)
residual.add(-1, vel_ssa_observed)
r_mag = PISM.IceModelVec2S()
r_mag.create(grid, "inv_ssa_residual", PISM.WITHOUT_GHOSTS, 0)
r_mag.set_attrs("diagnostic", "magnitude of mismatch between observed surface velocities and their reconstrution by inversion",
"m s-1", "inv_ssa_residual", 0)
r_mag.metadata().set_double("_FillValue", convert(-0.01, 'm/year', 'm/s'))
r_mag.metadata().set_double("valid_min", 0.0)
r_mag.metadata().set_string("glaciological_units", "m year-1")
r_mag.set_to_magnitude(residual)
r_mag.mask_by(vecs.land_ice_thickness)
vecs.add(residual, writing=True)
vecs.add(r_mag, writing=True)
# Write solution out to netcdf file
forward_run.write(output_filename, append=append_mode)
# If we're not in append mode, the previous command just nuked
# the output file. So we rewrite the siple log.
if not append_mode:
message_logger.write(output_filename)
# Save the misfit history
misfit_logger.write(output_filename)
def __call__(self, inverse_solver, count, data):
if not self.l2_weight_init:
vecs = inverse_solver.ssarun.modeldata.vecs
if vecs.has('vel_misfit_weight'):
self.l2_weight = self.toproczero(vecs.vel_misfit_weight)
self.l2_weight_init = True
method = inverse_solver.method
r = self.toproczero(data.residual)
Td = None
if 'T_zeta_step' in data:
Td = self.toproczero(data.T_zeta_step)
TStarR = None
if 'TStar_residual' in data:
TStarR = self.toproczero(data.TStar_residual)
d = None
if 'zeta_step' in data:
d = self.toproczero(data.zeta_step)
zeta = self.toproczero(data.zeta)
secpera = convert(1.0, "year", "second")
if self.grid.rank() == 0:
import matplotlib.pyplot as pp
pp.figure(self.figure())
l2_weight = self.l2_weight
pp.clf()
V = self.Vmax
pp.subplot(2, 3, 1)
if l2_weight is not None:
rx = l2_weight * r[0, :, :] * secpera
else:
rx = r[0, :, :] * secpera
rx = np.maximum(rx, -V)
rx = np.minimum(rx, V)
pp.imshow(rx, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('r_x')
pp.jet()
pp.subplot(2, 3, 4)
if l2_weight is not None:
ry = l2_weight * r[1, :, :] * secpera
else:
ry = r[1, :, :] * secpera
ry = np.maximum(ry, -V)
ry = np.minimum(ry, V)
pp.imshow(ry, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('r_y')
pp.jet()
if method == 'ign':
pp.subplot(2, 3, 2)
Tdx = Td[0, :, :] * secpera
pp.imshow(Tdx, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('Td_x')
pp.jet()
pp.subplot(2, 3, 5)
Tdy = Td[1, :, :] * secpera
pp.imshow(Tdy, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('Td_y')
pp.jet()
elif method == 'sd' or method == 'nlcg':
pp.subplot(2, 3, 2)
pp.imshow(TStarR, origin='lower', interpolation='nearest')
pp.colorbar()
pp.title('TStarR')
pp.jet()
if d is not None:
d *= -1
pp.subplot(2, 3, 3)
pp.imshow(d, origin='lower', interpolation='nearest')
# colorbar does a divide by zero if 'd' is all zero,
# as it will be at the start of iteration zero.
# The warning message is a distraction, so we suppress it.
import warnings
with warnings.catch_warnings():
warnings.simplefilter("ignore")
pp.colorbar()
pp.jet()
pp.title('-zeta_step')
pp.subplot(2, 3, 6)
pp.imshow(zeta, origin='lower', interpolation='nearest')
pp.colorbar()
pp.jet()
pp.title('zeta')
pp.ion()
pp.draw()
pp.show()
import numpy as np
from PISM.util import convert
config = PISM.Context().config
log = PISM.Context().log
# constants
standard_gravity = config.get_double("constants.standard_gravity")
ice_density = config.get_double("constants.ice.density")
mantle_density = config.get_double("bed_deformation.mantle_density")
mantle_viscosity = config.get_double("bed_deformation.mantle_viscosity")
lithosphere_flexural_rigidity = config.get_double(
"bed_deformation.lithosphere_flexural_rigidity")
# disc load parameters
disc_radius = convert(1000, "km", "m")
disc_thickness = 1000.0 # meters
# domain size
Lx = 2 * disc_radius
# time to use for the comparison
T = convert(1e6, "years", "second")
t_final = convert(20000, "years", "second")
dt = convert(500, "years", "second")
def deflection(time, radius, disc_thickness, disc_radius):
"""Compute the viscous plate deflection. See formula (17) in 'Fast
computation of a viscoelastic deformable Earth model for ice-sheet
simulations' by Bueler, Lingle, and Brown, 2007.
"""
return PISM.viscDisc(time, disc_thickness, disc_radius, radius,
def errors_ND(plot_results=True, T_final_years=1000.0, dt_years=100, Mz=101):
"""Test the enthalpy solver with Neumann B.C. at the base and
Dirichlet B.C. at the top surface.
"""
T_final = convert(T_final_years, "years", "seconds")
dt = convert(dt_years, "years", "seconds")
column = EnthalpyColumn(Mz, dt)
Lz = column.Lz
z = np.array(column.sys.z())
E_base = EC.enthalpy(240.0, 0.0, EC.pressure(Lz))
E_surface = EC.enthalpy(260.0, 0.0, 0.0)
dE_base = (E_surface - E_base) / Lz
E_steady = E_surface + dE_base * (z - Lz)
Q_base = -K * dE_base
E_exact = exact_ND(Lz, dE_base, E_surface)
with PISM.vec.Access(nocomm=[
column.enthalpy, column.u, column.v, column.w,
column.strain_heating
]):
column.sys.fine_to_coarse(E_exact(z, 0), 1, 1, column.enthalpy)
column.reset_flow()
column.reset_strain_heating()
t = 0.0
while t < T_final:
column.init_column()
column.sys.set_basal_heat_flux(Q_base)
column.sys.set_surface_dirichlet_bc(E_surface)
x = column.sys.solve()
column.sys.fine_to_coarse(x, 1, 1, column.enthalpy)
t += dt
E_exact_final = E_exact(z, t)
if plot_results:
t_years = convert(t, "seconds", "years")
plt.figure()
plt.xlabel("z, meters")
plt.ylabel("E, J/kg")
plt.step(z, E_exact(z, 0), color="blue", label="initial condition")
plt.step(z, E_exact_final, color="green", label="exact solution")
plt.step(z, cts(pressure(Lz - z)), "--", color="black", label="CTS")
plt.step(z,
E_steady,
"--",
color="green",
label="steady state profile")
plt.grid(True)
plt.step(z, x, label="T={} years".format(t_years), color="red")
plt.legend(loc="best")
errors = E_exact(z, t) - x
max_error = np.max(np.fabs(errors))
avg_error = np.average(np.fabs(errors))
return max_error, avg_error
inputs = PISM.EnergyModelInputs()
inputs.cell_type = cell_type
inputs.basal_frictional_heating = zero
inputs.basal_heat_flux = basal_heat_flux
inputs.ice_thickness = ice_thickness
inputs.surface_liquid_fraction = zero
inputs.shelf_base_temp = shelf_base_temp
inputs.surface_temp = surface_temp
inputs.till_water_thickness = zero
inputs.volumetric_heating_rate = strain_heating3
inputs.u3 = u
inputs.v3 = v
inputs.w3 = w
dt = convert(1, "years", "seconds")
def use_model(model):
print("* Performing a time step...")
model.update(0, dt, inputs)
try:
model.update(0, dt)
raise Exception("this should fail")
except TypeError:
pass
print(model.stdout_flags())
stats = model.stats()
enthalpy = model.enthalpy()
bmr = model.basal_melt_rate()
Testing program for PISM's implementations of the SSA.
Does a time-independent calculation. Does not run IceModel or a derived
class thereof. Uses the van der Veen flow-line shelf geometry. Also may be
used in a PISM software (regression) test.
"""
usage = \
"""
usage of SSA_TEST_CFBC:
run ssa_test_cfbc -Mx <number> -My <number>
"""
context = PISM.Context()
H0 = 600. # meters
V0 = convert(300, "m/year", "m/second")
C = 2.45e-18 # "typical constant ice parameter"
T = 400 # time used to compute the calving front location
Q0 = V0 * H0
Hc1 = 4. * C / Q0
Hc2 = 1. / (H0 ** 4)
def H_exact(x):
return (Hc1 * x + Hc2) ** (-1 / 4.)
def u_exact(x):
return Q0 / H_exact(x)
def run(scenario, plot, pause, save):
# set grid defaults
config.set_number("grid.Mx", 193)
config.set_number("grid.My", 129)
config.set_number("grid.Lx", 3000e3)
config.set_number("grid.Ly", 2000e3)
config.set_number("grid.Mz", 2)
config.set_number("grid.Lz", 1000)
scenarios = {
"1": (False, False, 1000.0),
"2": (True, False, 1000.0),
"3": (False, True, 0.0),
"4": (True, True, 1000.0)
}
elastic, use_uplift, H0 = scenarios[scenario]
print("Using scenario %s: elastic model = %s, use uplift = %s, H0 = %f m" %
(scenario, elastic, use_uplift, H0))
config.set_flag("bed_deformation.lc.elastic_model", elastic)
grid = create_grid()
thickness, bed, uplift, sea_level = allocate(grid)
# set initial geometry and uplift
bed.set(0.0)
thickness.set(0.0)
sea_level.set(0.0)
if use_uplift:
initialize_uplift(uplift)
time = ctx.ctx.time()
time.init(ctx.ctx.log())
model = PISM.LingleClark(grid)
model.bootstrap(bed, uplift, thickness, sea_level)
# now add the disc load
initialize_thickness(thickness, H0)
dt = convert(100, "365 day", "seconds")
# the time-stepping loop
while time.current() < time.end():
# don't go past the end of the run
dt_current = min(dt, time.end() - time.current())
model.update(thickness, sea_level, time.current(), dt_current)
if plot:
model.bed_elevation().view(400)
model.uplift().view(400)
print("t = %s years, dt = %s years" %
(time.date(), time.convert_time_interval(dt_current, "years")))
time.step(dt_current)
print("Reached t = %s years" % time.date())
if pause:
print("Pausing for 5 seconds...")
PISM.PETSc.Sys.sleep(5)
if save:
model.bed_elevation().dump("bed_elevation.nc")
model.uplift().dump("bed_uplift.nc")
def run():
context = PISM.Context()
config = context.config
com = context.com
PISM.set_abort_on_sigint(True)
WIDE_STENCIL = int(config.get_number("grid.max_stencil_width"))
usage = \
""" pismi.py [-i IN.nc [-o OUT.nc]]/[-a INOUT.nc] [-inv_data inv_data.nc] [-inv_forward model]
[-inv_design design_var] [-inv_method meth]
where:
-i IN.nc is input file in NetCDF format: contains PISM-written model state
-o OUT.nc is output file in NetCDF format to be overwritten
-a INOUT.nc is input/output file in NetCDF format to be appended to
-inv_data inv_data.nc is data file containing extra inversion data (e.g. observed surface velocities)
-inv_forward model forward model: only 'ssa' supported
-inv_design design_var design variable name; one of 'tauc'/'hardav' for SSA inversions
-inv_method meth algorithm for inversion [sd,nlcg,ign,tikhonov_lmvm]
notes:
* only one of -i/-a is allowed; both specify the input file
* only one of -o/-a is allowed; both specify the output file
* if -o is used, only the variables involved in inversion are written to the output file.
* if -a is used, the varaibles involved in inversion are appended to the given file. No
original variables in the file are changed.
"""
append_mode = False
input_filename = config.get_string("input.file")
if len(input_filename) == 0:
input_filename = None
append = PISM.OptionString("-a", "append file")
append_filename = append.value() if append.is_set() else None
output_filename = config.get_string("output.file_name")
if len(output_filename) == 0:
output_filename = None
if (input_filename is None) and (append_filename is None):
PISM.verbPrintf(
1, com,
"\nError: No input file specified. Use one of -i [file.nc] or -a [file.nc].\n"
)
sys.exit(0)
if (input_filename is not None) and (append_filename is not None):
PISM.verbPrintf(1, com, "\nError: Only one of -i/-a is allowed.\n")
sys.exit(0)
if (output_filename is not None) and (append_filename is not None):
PISM.verbPrintf(1, com, "\nError: Only one of -a/-o is allowed.\n")
sys.edit(0)
if append_filename is not None:
input_filename = append_filename
output_filename = append_filename
append_mode = True
inv_data_filename = PISM.OptionString("-inv_data", "inverse data file",
input_filename).value()
do_plotting = PISM.OptionBool(
"-inv_plot", "perform visualization during the computation")
do_final_plot = PISM.OptionBool(
"-inv_final_plot",
"perform visualization at the end of the computation")
Vmax = PISM.OptionReal(context.unit_system, "-inv_plot_vmax",
"maximum velocity for plotting residuals",
"m / year", 30)
design_var = PISM.OptionKeyword("-inv_ssa",
"design variable for inversion",
"tauc,hardav", "tauc").value()
do_pause = PISM.OptionBool("-inv_pause", "pause each iteration")
do_restart = PISM.OptionBool("-inv_restart",
"Restart a stopped computation.")
use_design_prior = config.get_flag("inverse.use_design_prior")
prep_module = PISM.OptionString(
"-inv_prep_module",
"Python module used to do final setup of inverse solver")
prep_module = prep_module.value() if prep_module.is_set() else None
is_regional = PISM.OptionBool(
"-regional", "Compute SIA/SSA using regional model semantics")
using_zeta_fixed_mask = config.get_flag("inverse.use_zeta_fixed_mask")
inv_method = config.get_string("inverse.ssa.method")
if output_filename is None:
output_filename = "pismi_" + os.path.basename(input_filename)
saving_inv_data = (inv_data_filename != output_filename)
forward_run = SSAForwardRun(input_filename, inv_data_filename, design_var)
forward_run.setup()
design_param = forward_run.designVariableParameterization()
solver = PISM.invert.ssa.createInvSSASolver(forward_run)
modeldata = forward_run.modeldata
vecs = modeldata.vecs
grid = modeldata.grid
# Determine the prior guess for tauc/hardav. This can be one of
# a) tauc/hardav from the input file (default)
# b) tauc/hardav_prior from the inv_datafile if -inv_use_design_prior is set
design_prior = createDesignVec(grid, design_var, '%s_prior' % design_var)
long_name = design_prior.metadata().get_string("long_name")
units = design_prior.metadata().get_string("units")
design_prior.set_attrs(
"", "best prior estimate for %s (used for inversion)" % long_name,
units, units, "", 0)
if PISM.util.fileHasVariable(inv_data_filename,
"%s_prior" % design_var) and use_design_prior:
PISM.logging.logMessage(
" Reading '%s_prior' from inverse data file %s.\n" %
(design_var, inv_data_filename))
design_prior.regrid(inv_data_filename, critical=True)
vecs.add(design_prior, writing=saving_inv_data)
else:
if not PISM.util.fileHasVariable(input_filename, design_var):
PISM.verbPrintf(
1, com,
"Initial guess for design variable is not available as '%s' in %s.\nYou can provide an initial guess in the inverse data file.\n"
% (design_var, input_filename))
exit(1)
PISM.logging.logMessage(
"Reading '%s_prior' from '%s' in input file.\n" %
(design_var, design_var))
design = createDesignVec(grid, design_var)
design.regrid(input_filename, True)
design_prior.copy_from(design)
vecs.add(design_prior, writing=True)
if using_zeta_fixed_mask:
if PISM.util.fileHasVariable(inv_data_filename, "zeta_fixed_mask"):
zeta_fixed_mask = PISM.model.createZetaFixedMaskVec(grid)
zeta_fixed_mask.regrid(inv_data_filename)
vecs.add(zeta_fixed_mask)
else:
if design_var == 'tauc':
logMessage(
" Computing 'zeta_fixed_mask' (i.e. locations where design variable '%s' has a fixed value).\n"
% design_var)
zeta_fixed_mask = PISM.model.createZetaFixedMaskVec(grid)
zeta_fixed_mask.set(1)
mask = vecs.mask
with PISM.vec.Access(comm=zeta_fixed_mask, nocomm=mask):
for (i, j) in grid.points():
if mask.grounded_ice(i, j):
zeta_fixed_mask[i, j] = 0
vecs.add(zeta_fixed_mask)
adjustTauc(vecs.mask, design_prior)
elif design_var == 'hardav':
PISM.logging.logPrattle(
"Skipping 'zeta_fixed_mask' for design variable 'hardav'; no natural locations to fix its value."
)
pass
else:
raise NotImplementedError(
"Unable to build 'zeta_fixed_mask' for design variable %s.",
design_var)
# Convert design_prior -> zeta_prior
zeta_prior = PISM.IceModelVec2S(grid, "zeta_prior", PISM.WITH_GHOSTS,
WIDE_STENCIL)
design_param.convertFromDesignVariable(design_prior, zeta_prior)
vecs.add(zeta_prior, writing=True)
# Determine the initial guess for zeta. If we are restarting, load it from
# the output file. Otherwise, if 'zeta_inv' is in the inverse data file, use it.
# If none of the above, copy from 'zeta_prior'.
zeta = PISM.IceModelVec2S(grid, "zeta_inv", PISM.WITH_GHOSTS, WIDE_STENCIL)
zeta.set_attrs("diagnostic", "zeta_inv", "1", "1", "zeta_inv", 0)
if do_restart:
# Just to be sure, verify that we have a 'zeta_inv' in the output file.
if not PISM.util.fileHasVariable(output_filename, 'zeta_inv'):
PISM.verbPrintf(
1, com,
"Unable to restart computation: file %s is missing variable 'zeta_inv'",
output_filename)
exit(1)
PISM.logging.logMessage(
" Inversion starting from 'zeta_inv' found in %s\n" %
output_filename)
zeta.regrid(output_filename, True)
elif PISM.util.fileHasVariable(inv_data_filename, 'zeta_inv'):
PISM.logging.logMessage(
" Inversion starting from 'zeta_inv' found in %s\n" %
inv_data_filename)
zeta.regrid(inv_data_filename, True)
else:
zeta.copy_from(zeta_prior)
vel_ssa_observed = None
vel_ssa_observed = PISM.model.create2dVelocityVec(grid,
'_ssa_observed',
stencil_width=2)
if PISM.util.fileHasVariable(inv_data_filename, "u_ssa_observed"):
vel_ssa_observed.regrid(inv_data_filename, True)
vecs.add(vel_ssa_observed, writing=saving_inv_data)
else:
if not PISM.util.fileHasVariable(inv_data_filename,
"u_surface_observed"):
PISM.verbPrintf(
1, context.com,
"Neither u/v_ssa_observed nor u/v_surface_observed is available in %s.\nAt least one must be specified.\n"
% inv_data_filename)
exit(1)
vel_surface_observed = PISM.model.create2dVelocityVec(
grid, '_surface_observed', stencil_width=2)
vel_surface_observed.regrid(inv_data_filename, True)
vecs.add(vel_surface_observed, writing=saving_inv_data)
sia_solver = PISM.SIAFD
if is_regional:
sia_solver = PISM.SIAFD_Regional
vel_sia_observed = PISM.sia.computeSIASurfaceVelocities(
modeldata, sia_solver)
vel_sia_observed.metadata(0).set_name('u_sia_observed')
vel_sia_observed.metadata(0).set_string(
'long_name', "x-component of the 'observed' SIA velocities")
vel_sia_observed.metadata(1).set_name('v_sia_observed')
vel_sia_observed.metadata(1).set_string(
'long_name', "y-component of the 'observed' SIA velocities")
vel_ssa_observed.copy_from(vel_surface_observed)
vel_ssa_observed.add(-1, vel_sia_observed)
vecs.add(vel_ssa_observed, writing=True)
# If the inverse data file has a variable tauc/hardav_true, this is probably
# a synthetic inversion. We'll load it now so that it will get written
# out, if needed, at the end of the computation in the output file.
if PISM.util.fileHasVariable(inv_data_filename, "%s_true" % design_var):
design_true = createDesignVec(grid, design_var, '%s_true' % design_var)
design_true.regrid(inv_data_filename, True)
try:
f = PISM.File(com, inv_data_filename, PISM.PISM_NETCDF3,
PISM.PISM_READONLY)
PISM.read_attributes(f, design_true.get_name(),
design_true.metadata())
finally:
f.close()
vecs.add(design_true, writing=saving_inv_data)
# Establish a logger which will save logging messages to the output file.
message_logger = PISM.logging.CaptureLogger(output_filename, 'pismi_log')
PISM.logging.add_logger(message_logger)
if append_mode or do_restart:
message_logger.readOldLog()
# Prep the output file from the grid so that we can save zeta to it during the runs.
if not append_mode:
pio = PISM.util.prepare_output(output_filename)
pio.close()
zeta.write(output_filename)
# Log the command line to the output file now so that we have a record of
# what was attempted
PISM.util.writeProvenance(output_filename)
# Attach various iteration listeners to the solver as needed for:
# Iteration report.
solver.addIterationListener(PISM.invert.ssa.printIteration)
# Misfit reporting/logging.
misfit_logger = PISM.invert.ssa.MisfitLogger()
solver.addIterationListener(misfit_logger)
if inv_method.startswith('tikhonov'):
solver.addIterationListener(PISM.invert.ssa.printTikhonovProgress)
# Saving the current iteration
solver.addDesignUpdateListener(PISM.invert.ssa.ZetaSaver(output_filename))
# Plotting
if do_plotting:
solver.addIterationListener(InvSSAPlotListener(grid, Vmax))
if solver.method == 'ign':
solver.addLinearIterationListener(InvSSALinPlotListener(
grid, Vmax))
# Solver is set up. Give the user's prep module a chance to do any final
# setup.
if prep_module is not None:
if prep_module.endswith(".py"):
prep_module = prep_module[0:-2]
exec("import %s as user_prep_module" % prep_module)
user_prep_module.prep_solver(solver)
# Pausing (add this after the user's listeners)
if do_pause:
solver.addIterationListener(PISM.invert.listener.pauseListener)
# Run the inverse solver!
if do_restart:
PISM.logging.logMessage(
'************** Restarting inversion. ****************\n')
else:
PISM.logging.logMessage(
'============== Starting inversion. ==================\n')
# Try solving
reason = solver.solveInverse(zeta_prior, vel_ssa_observed, zeta)
if reason.failed():
PISM.logging.logError("Inverse solve FAILURE:\n%s\n" %
reason.nested_description(1))
quit()
PISM.logging.logMessage("Inverse solve success (%s)!\n" %
reason.description())
(zeta, u) = solver.inverseSolution()
# It may be that a 'tauc'/'hardav' was read in earlier. We replace it with
# our newly generated one.
if vecs.has(design_var):
design = vecs.get(design_var)
design_param.convertToDesignVariable(zeta, design)
else:
# Convert back from zeta to tauc or hardav
design = createDesignVec(grid, design_var)
design_param.convertToDesignVariable(zeta, design)
vecs.add(design, writing=True)
vecs.add(zeta, writing=True)
u.metadata(0).set_name("u_ssa_inv")
u.metadata(0).set_string(
"long_name", "x-component of SSA velocity computed by inversion")
u.metadata(1).set_name("v_ssa_inv")
u.metadata(1).set_string(
"long_name", "y-component of SSA velocity computed by inversion")
vecs.add(u, writing=True)
residual = PISM.model.create2dVelocityVec(grid, name='_inv_ssa_residual')
residual.copy_from(u)
residual.add(-1, vel_ssa_observed)
r_mag = PISM.IceModelVec2S(grid, "inv_ssa_residual", PISM.WITHOUT_GHOSTS,
0)
r_mag.set_attrs(
"diagnostic",
"magnitude of mismatch between observed surface velocities and their reconstrution by inversion",
"m s-1", "m year-1", "inv_ssa_residual", 0)
r_mag.metadata().set_number("_FillValue", convert(-0.01, 'm/year', 'm/s'))
r_mag.metadata().set_number("valid_min", 0.0)
PISM.compute_magnitude(residual, r_mag)
PISM.apply_mask(vecs.land_ice_thickness, 0.0, r_mag)
vecs.add(residual, writing=True)
vecs.add(r_mag, writing=True)
# Write solution out to netcdf file (always append because the file was created already)
forward_run.write(output_filename, append=True)
# If we're not in append mode, the previous command just nuked
# the output file. So we rewrite the siple log.
if not append_mode:
message_logger.write(output_filename)
# Save the misfit history
misfit_logger.write(output_filename)
* re-initializing
* one more 1000 year step
Used as a regression test for PISM.LingleClark.
"""
import PISM
from PISM.util import convert
import pylab as plt
import numpy as np
import os
ctx = PISM.Context()
# disc load parameters
disc_radius = convert(1000, "km", "m")
disc_thickness = 1000.0 # meters
# domain size
Lx = 2 * disc_radius
Ly = Lx
N = 101
dt = convert(1000.0, "years", "seconds")
def allocate_storage(grid):
ice_thickness = PISM.IceModelVec2S(grid, "thk", PISM.WITHOUT_GHOSTS)
ice_thickness.metadata().set_string("standard_name", "land_ice_thickness")
bed = PISM.IceModelVec2S(grid, "topg", PISM.WITHOUT_GHOSTS)
bed_uplift = PISM.IceModelVec2S(grid, "uplift", PISM.WITHOUT_GHOSTS)
sea_level = PISM.IceModelVec2S(grid, "sea_level", PISM.WITHOUT_GHOSTS)
def errors_ND(plot_results=True, T_final_years=1000.0, dt_years=100, Mz=101):
"""Test the enthalpy solver with Neumann B.C. at the base and
Dirichlet B.C. at the top surface.
"""
T_final = convert(T_final_years, "years", "seconds")
dt = convert(dt_years, "years", "seconds")
column = EnthalpyColumn(Mz, dt)
Lz = column.Lz
z = np.array(column.sys.z())
E_base = EC.enthalpy(240.0, 0.0, EC.pressure(Lz))
E_surface = EC.enthalpy(260.0, 0.0, 0.0)
dE_base = (E_surface - E_base) / Lz
E_steady = E_surface + dE_base * (z - Lz)
Q_base = - K * dE_base
E_exact = exact_ND(Lz, dE_base, E_surface)
with PISM.vec.Access(nocomm=[column.enthalpy,
column.u, column.v, column.w,
column.strain_heating]):
column.sys.fine_to_coarse(E_exact(z, 0), 1, 1, column.enthalpy)
column.reset_flow()
column.reset_strain_heating()
t = 0.0
while t < T_final:
column.init_column()
column.sys.set_basal_heat_flux(Q_base)
column.sys.set_surface_dirichlet_bc(E_surface)
x = column.sys.solve()
column.sys.fine_to_coarse(x, 1, 1, column.enthalpy)
t += dt
E_exact_final = E_exact(z, t)
if plot_results:
t_years = convert(t, "seconds", "years")
plt.figure()
plt.xlabel("z, meters")
plt.ylabel("E, J/kg")
plt.step(z, E_exact(z, 0), color="blue", label="initial condition")
plt.step(z, E_exact_final, color="green", label="exact solution")
plt.step(z, cts(pressure(Lz - z)), "--", color="black", label="CTS")
plt.step(z, E_steady, "--", color="green", label="steady state profile")
plt.grid(True)
plt.step(z, x, label="T={} years".format(t_years), color="red")
plt.legend(loc="best")
errors = E_exact(z, t) - x
max_error = np.max(np.fabs(errors))
avg_error = np.average(np.fabs(errors))
return max_error, avg_error