tupdate README, add LICENSE and remove old and unused files - granular-channel-hydro - subglacial hydrology model for sedimentary channels
(HTM) git clone git://src.adamsgaard.dk/granular-channel-hydro
(DIR) Log
(DIR) Files
(DIR) Refs
(DIR) README
(DIR) LICENSE
---
(DIR) commit f93ba7d18a7e1c4571d858a6281ae493558a630f
(DIR) parent 46dfffde617f0688622073bd949a6d64311f8368
(HTM) Author: Anders Damsgaard <andersd@riseup.net>
Date: Tue, 17 Oct 2017 13:08:00 -0400
update README, add LICENSE and remove old and unused files
Diffstat:
D 1d-channel-flux.py | 292 -------------------------------
D 1d-channel-wilcock-two-phase.py | 431 -------------------------------
M 1d-channel.py | 49 +++++++++++++++----------------
A LICENSE.md | 636 +++++++++++++++++++++++++++++++
M README.md | 13 +++++++++++++
D granular_channel_drainage/__init__… | 5 -----
D granular_channel_drainage/model.py | 137 -------------------------------
M requirements.txt | 1 -
8 files changed, 673 insertions(+), 891 deletions(-)
---
(DIR) diff --git a/1d-channel-flux.py b/1d-channel-flux.py
t@@ -1,292 +0,0 @@
-#!/usr/bin/env python
-
-# # ABOUT THIS FILE
-# The following script uses basic Python and Numpy functionality to solve the
-# coupled systems of equations describing subglacial channel development in
-# soft beds as presented in `Damsgaard et al. "Sediment plasticity controls
-# channelization of subglacial meltwater in soft beds"`, submitted to Journal
-# of Glaciology.
-#
-# High performance is not the goal for this implementation, which is instead
-# intended as a heavily annotated example on the solution procedure without
-# relying on solver libraries, suitable for low-level languages like C, Fortran
-# or CUDA.
-#
-# License: Gnu Public License v3
-# Author: Anders Damsgaard, adamsgaard@ucsd.edu, https://adamsgaard.dk
-
-import numpy
-import matplotlib.pyplot as plt
-import sys
-
-
-# # Model parameters
-Ns = 25 # Number of nodes [-]
-Ls = 100e3 # Model length [m]
-t_end = 24.*60.*60.*120. # Total simulation time [s]
-tol_Q = 1e-3 # Tolerance criteria for the normalized max. residual for Q
-tol_P_c = 1e-3 # Tolerance criteria for the normalized max residual for P_c
-max_iter = 1e2*Ns # Maximum number of solver iterations before failure
-output_convergence = False # Display convergence statistics during run
-safety = 0.1 # Safety factor ]0;1] for adaptive timestepping
-
-# Physical parameters
-rho_w = 1000. # Water density [kg/m^3]
-rho_i = 910. # Ice density [kg/m^3]
-rho_s = 2600. # Sediment density [kg/m^3]
-g = 9.8 # Gravitational acceleration [m/s^2]
-theta = 30. # Angle of internal friction in sediment [deg]
-
-# Water source term [m/s]
-# m_dot = 7.93e-11
-m_dot = 4.5e-8
-# m_dot = 5.79e-5
-
-# Hewitt 2011 channel flux parameters
-manning = 0.1 # Manning roughness coefficient [m^{-1/3} s]
-F = rho_w*g*manning*(2.*(numpy.pi + 2.)**2./numpy.pi)**(2./3.)
-
-# Channel growth-limit parameters
-c_1 = -0.118 # [m/kPa]
-c_2 = 4.60 # [m]
-
-# Minimum channel size [m^2], must be bigger than 0
-# S_min = 1e-1
-S_min = 1.5e-2
-
-
-# # Initialize model arrays
-# Node positions, terminus at Ls
-s = numpy.linspace(0., Ls, Ns)
-ds = s[1:] - s[:-1]
-
-# Ice thickness and bed topography
-H = 6.*(numpy.sqrt(Ls - s + 5e3) - numpy.sqrt(5e3)) + 1.0 # max: 1.5 km
-# H = 1.*(numpy.sqrt(Ls - s + 5e3) - numpy.sqrt(5e3)) + 1.0 # max: 255 m
-# H = 0.6*(numpy.sqrt(Ls - s + 5e3) - numpy.sqrt(5e3)) + 1.0
-b = numpy.zeros_like(H)
-
-N = H*0.1*rho_i*g # Initial effective stress [Pa]
-p_w = rho_i*g*H - N # Initial guess of water pressure [Pa]
-hydro_pot = rho_w*g*b + p_w # Initial guess of hydraulic potential [Pa]
-
-# Initialize arrays for channel segments between nodes
-S = numpy.ones(len(s) - 1)*S_min # Cross-sect. area of channel segments [m^2]
-S_max = numpy.zeros_like(S) # Max. channel size [m^2]
-dSdt = numpy.zeros_like(S) # Transient in channel cross-sect. area [m^2/s]
-W = S/numpy.tan(numpy.deg2rad(theta)) # Assuming no channel floor wedge
-Q = numpy.zeros_like(S) # Water flux in channel segments [m^3/s]
-Q_s = numpy.zeros_like(S) # Sediment flux in channel segments [m^3/s]
-dQ_s_ds = numpy.empty_like(S) # Transient in channel cross-sect. area [m^2/s]
-N_c = numpy.zeros_like(S) # Effective pressure in channel segments [Pa]
-P_c = numpy.zeros_like(S) # Water pressure in channel segments [Pa]
-res = numpy.zeros_like(S) # Solution residual during solver iterations
-
-
-# # Helper functions
-def gradient(arr, arr_x):
- # Central difference gradient of an array ``arr`` with node positions at
- # ``arr_x``.
- return (arr[:-1] - arr[1:])/(arr_x[:-1] - arr_x[1:])
-
-def avg_midpoint(arr):
- # Averaged value of neighboring array elements
- return (arr[:-1] + arr[1:])/2.
-
-def channel_water_flux(S, hydro_pot_grad):
- # Hewitt 2011
- return numpy.sqrt(1./F*S**(8./3.)*-hydro_pot_grad)
-
-def update_channel_size_with_limit(S, dSdt, dt, N):
- # Damsgaard et al, in prep
- S_max = ((c_1*N.clip(min=0.)/1000. + c_2)*\
- numpy.tan(numpy.deg2rad(theta))).clip(min=S_min)
- S = numpy.minimum(S + dSdt*dt, S_max).clip(min=S_min)
- W = S/numpy.tan(numpy.deg2rad(theta)) # Assume no channel floor wedge
- return S, W, S_max
-
-def flux_solver(m_dot, ds):
- # Iteratively find new fluxes
- it = 0
- max_res = 1e9 # arbitrary large value
-
- # Iteratively find solution, do not settle for less iterations than the
- # number of nodes
- while max_res > tol_Q or it < Ns:
-
- Q_old = Q.copy()
- # dQ/ds = m_dot -> Q_out = m*delta(s) + Q_in
- # Upwind information propagation (upwind)
- Q[0] = 1e-2 # Ng 2000
- Q[1:] = m_dot*ds[1:] + Q[:-1]
- max_res = numpy.max(numpy.abs((Q - Q_old)/(Q + 1e-16)))
-
- if output_convergence:
- print('it = {}: max_res = {}'.format(it, max_res))
-
- #import ipdb; ipdb.set_trace()
- if it >= max_iter:
- raise Exception('t = {}, step = {}:'.format(time, step) +
- 'Iterative solution not found for Q')
- it += 1
-
- return Q
-
-def sediment_flux(Q):
- #return Q**(3./2.)
- return Q/2.
-
-def sediment_flux_divergence(Q_s, ds):
- # Damsgaard et al, in prep
- return (Q_s[1:] - Q_s[:-1])/ds[1:]
-
-def pressure_solver(psi, F, Q, S):
- # Iteratively find new water pressures
- # dP_c/ds = psi - FQ^2/S^{8/3}
-
- it = 0
- max_res = 1e9 # arbitrary large value
- while max_res > tol_P_c or it < Ns*40:
-
- P_c_old = P_c.copy()
-
- # Upwind finite differences
- P_c[:-1] = -psi[:-1]*ds[:-1] \
- + F*Q[:-1]**2./(S[:-1]**(8./3.))*ds[:-1] \
- + P_c[1:] # Upstream
-
- # Dirichlet BC (fixed pressure) at terminus
- P_c[-1] = 0.
-
- # von Neumann BC (no gradient = no flux) at s=0
- P_c[0] = P_c[1]
-
- max_res = numpy.max(numpy.abs((P_c - P_c_old)/(P_c + 1e-16)))
-
- if output_convergence:
- print('it = {}: max_res = {}'.format(it, max_res))
-
- if it >= max_iter:
- raise Exception('t = {}, step = {}:'.format(time, step) +
- 'Iterative solution not found for P_c')
- it += 1
-
- return P_c
-
-def plot_state(step, time):
- # Plot parameters along profile
- fig = plt.gcf()
- fig.set_size_inches(3.3, 3.3)
-
- ax_Pa = plt.subplot(2, 1, 1) # axis with Pascals as y-axis unit
- ax_Pa.plot(s_c/1000., P_c/1000., '--r', label='$P_c$')
-
- ax_m3s = ax_Pa.twinx() # axis with m3/s as y-axis unit
- ax_m3s.plot(s_c/1000., Q, '-b', label='$Q$')
- ax_m3s.plot(s_c/1000., Q_s, ':b', label='$Q_s$')
-
- plt.title('Day: {:.3}'.format(time/(60.*60.*24.)))
- ax_Pa.legend(loc=2)
- ax_m3s.legend(loc=1)
- ax_Pa.set_ylabel('[kPa]')
- ax_m3s.set_ylabel('[m$^3$/s]')
-
- ax_m2 = plt.subplot(2, 1, 2, sharex=ax_Pa)
- ax_m2.plot(s_c/1000., S, '-k', label='$S$')
- ax_m2.plot(s_c/1000., S_max, '--k', label='$S_{max}$')
- #ax_m.semilogy(s_c/1000., S, '-k', label='$S$')
- #ax_m.semilogy(s_c/1000., S_max, '--k', label='$S_{max}$')
-
- ax_m2s = ax_m2.twinx()
- ax_m2s.plot(s_c/1000., dSdt, ':b', label='$dS/dt$')
-
- ax_m2.legend(loc=2)
- ax_m2s.legend(loc=1)
- ax_m2.set_xlabel('$s$ [km]')
- ax_m2.set_ylabel('[m$^2$]')
- ax_m2s.set_ylabel('[m$^2$/s]')
-
- plt.setp(ax_Pa.get_xticklabels(), visible=False)
- plt.tight_layout()
- if step == -1:
- plt.savefig('chan-0.init.pdf')
- else:
- plt.savefig('chan-' + str(step) + '.pdf')
- plt.clf()
-
-def find_new_timestep(ds, Q, S):
- # Determine the timestep using the Courant-Friedrichs-Lewy condition
- dt = safety*numpy.minimum(60.*60.*24., numpy.min(numpy.abs(ds/(Q*S))))
-
- if dt < 1.0:
- raise Exception('Error: Time step less than 1 second at step '
- + '{}, time '.format(step)
- + '{:.3} s/{:.3} d'.format(time, time/(60.*60.*24.)))
-
- return dt
-
-def print_status_to_stdout(time, dt):
- sys.stdout.write('\rt = {:.2} s or {:.4} d, dt = {:.2} s '\
- .format(time, time/(60.*60.*24.), dt))
- sys.stdout.flush()
-
-s_c = avg_midpoint(s) # Channel section midpoint coordinates [m]
-
-# Find gradient in hydraulic potential between the nodes
-hydro_pot_grad = gradient(hydro_pot, s)
-
-# Find field values at the middle of channel segments
-N_c = avg_midpoint(N)
-H_c = avg_midpoint(N)
-
-# Find fluxes in channel segments [m^3/s]
-Q = channel_water_flux(S, hydro_pot_grad)
-
-# Water-pressure gradient from geometry [Pa/m]
-psi = -rho_i*g*gradient(H, s) - (rho_w - rho_i)*g*gradient(b, s)
-
-# Prepare figure object for plotting during the simulation
-fig = plt.figure('channel')
-plot_state(-1, 0.0)
-
-
-# # Time loop
-time = 0.; step = 0
-while time <= t_end:
-
- #print('@ @ @ step ' + str(step))
-
- dt = find_new_timestep(ds, Q, S)
-
- print_status_to_stdout(time, dt)
-
- # Find the sediment flux
- Q_s = sediment_flux(Q)
-
- # Find sediment flux divergence which determines channel growth, no growth
- # in first segment
- dSdt[1:] = sediment_flux_divergence(Q_s, ds)
-
- # Update channel cross-sectional area and width according to growth rate
- # and size limit for each channel segment
- S, W, S_max = update_channel_size_with_limit(S, dSdt, dt, N_c)
-
- # Find new water fluxes consistent with mass conservation and local
- # meltwater production (m_dot)
- Q = flux_solver(m_dot, ds)
-
- # Find new water pressures consistent with the flow law
- P_c = pressure_solver(psi, F, Q, S)
-
- # Find new effective pressure in channel segments
- N_c = rho_i*g*H_c - P_c
-
- plot_state(step, time)
-
- #import ipdb; ipdb.set_trace()
- #if step > 0:
- #break
-
- # Update time
- time += dt
- step += 1
(DIR) diff --git a/1d-channel-wilcock-two-phase.py b/1d-channel-wilcock-two-phase.py
t@@ -1,431 +0,0 @@
-#!/usr/bin/env python
-
-# # ABOUT THIS FILE
-# The following script uses basic Python and Numpy functionality to solve the
-# coupled systems of equations describing subglacial channel development in
-# soft beds as presented in `Damsgaard et al. "Sediment plasticity controls
-# channelization of subglacial meltwater in soft beds"`, submitted to Journal
-# of Glaciology.
-#
-# High performance is not the goal for this implementation, which is instead
-# intended as a heavily annotated example on the solution procedure without
-# relying on solver libraries, suitable for low-level languages like C, Fortran
-# or CUDA.
-#
-# License: Gnu Public License v3
-# Author: Anders Damsgaard, adamsgaard@ucsd.edu, https://adamsgaard.dk
-
-import numpy
-import matplotlib.pyplot as plt
-import sys
-
-
-# # Model parameters
-Ns = 25 # Number of nodes [-]
-Ls = 1e3 # Model length [m]
-total_days = 60. # Total simulation time [d]
-t_end = 24.*60.*60.*total_days # Total simulation time [s]
-tol_S = 1e-3 # Tolerance criteria for the norm. max. residual for Q
-tol_Q = 1e-3 # Tolerance criteria for the norm. max. residual for Q
-tol_N_c = 1e-3 # Tolerance criteria for the norm. max. residual for N_c
-max_iter = 1e2*Ns # Maximum number of solver iterations before failure
-print_output_convergence = False # Display convergence in nested loops
-print_output_convergence_main = True # Display convergence in main loop
-safety = 0.01 # Safety factor ]0;1] for adaptive timestepping
-plot_interval = 20 # Time steps between plots
-plot_during_iterations = False # Generate plots for intermediate results
-#plot_during_iterations = True # Generate plots for intermediate results
-speedup_factor = 1. # Speed up channel growth to reach steady state faster
-#relax_dSdt = 0.3 # Relaxation parameter for channel growth rate ]0;1]
-relax = 0.05 # Relaxation parameter for effective pressure ]0;1]
-
-# Physical parameters
-rho_w = 1000. # Water density [kg/m^3]
-rho_i = 910. # Ice density [kg/m^3]
-rho_s = 2600. # Sediment density [kg/m^3]
-g = 9.8 # Gravitational acceleration [m/s^2]
-theta = 30. # Angle of internal friction in sediment [deg]
-sand_fraction = 0.5 # Initial volumetric fraction of sand relative to gravel
-D_g = 5e-3 # Mean grain size in gravel fraction (> 2 mm) [m]
-D_s = 5e-4 # Mean grain size in sand fraction (<= 2 mm) [m]
-#D_g = 1
-#D_g = 0.1
-
-# Boundary conditions
-P_terminus = 0. # Water pressure at terminus [Pa]
-#m_dot = 3.5e-6
-m_dot = numpy.linspace(0., 3.5e-6, Ns-1) # Water source term [m/s]
-Q_upstream = 1e-5 # Water influx upstream (must be larger than 0) [m^3/s]
-
-# Channel hydraulic properties
-manning = 0.1 # Manning roughness coefficient [m^{-1/3} s]
-friction_factor = 0.1 # Darcy-Weisbach friction factor [-]
-
-# Channel growth-limit parameters
-c_1 = -0.118 # [m/kPa]
-c_2 = 4.60 # [m]
-
-# Minimum channel size [m^2], must be bigger than 0
-S_min = 1e-2
-# S_min = 1e-1
-# S_min = 1.
-
-
-# # Initialize model arrays
-# Node positions, terminus at Ls
-s = numpy.linspace(0., Ls, Ns)
-ds = s[1:] - s[:-1]
-
-# Ice thickness [m]
-H = 6.*(numpy.sqrt(Ls - s + 5e3) - numpy.sqrt(5e3)) + 1.0
-# slope = 0.1 # Surface slope [%]
-# H = 1000. + -slope/100.*s
-
-# Bed topography [m]
-b = numpy.zeros_like(H)
-
-N = H*0.1*rho_i*g # Initial effective stress [Pa]
-
-# Initialize arrays for channel segments between nodes
-S = numpy.ones(len(s) - 1)*S_min # Cross-sect. area of channel segments[m^2]
-S_max = numpy.zeros_like(S) # Max. channel size [m^2]
-dSdt = numpy.zeros_like(S) # Transient in channel cross-sect. area [m^2/s]
-W = S/numpy.tan(numpy.deg2rad(theta)) # Assuming no channel floor wedge
-Q = numpy.zeros_like(S) # Water flux in channel segments [m^3/s]
-Q_s = numpy.zeros_like(S) # Sediment flux in channel segments [m^3/s]
-N_c = numpy.zeros_like(S) # Effective pressure in channel segments [Pa]
-P_c = numpy.zeros_like(S) # Water pressure in channel segments [Pa]
-tau = numpy.zeros_like(S) # Avg. shear stress from current [Pa]
-porosity = numpy.ones_like(S)*0.3 # Sediment porosity [-]
-res = numpy.zeros_like(S) # Solution residual during solver iterations
-Q_t = numpy.zeros_like(S) # Total sediment flux [m3/s]
-Q_s = numpy.zeros_like(S) # Sediment flux where D <= 2 mm [m3/s]
-Q_g = numpy.zeros_like(S) # Sediment flux where D > 2 mm [m3/s]
-f_s = numpy.ones_like(S)*sand_fraction # Initial sediment fraction of sand [-]
-
-
-# # Helper functions
-def gradient(arr, arr_x):
- # Central difference gradient of an array ``arr`` with node positions at
- # ``arr_x``.
- return (arr[1:] - arr[:-1])/(arr_x[1:] - arr_x[:-1])
-
-
-def avg_midpoint(arr):
- # Averaged value of neighboring array elements
- return (arr[:-1] + arr[1:])/2.
-
-
-def channel_hydraulic_roughness(manning, S, W, theta):
- # Determine hydraulic roughness assuming that the channel has no channel
- # floor wedge.
- l = W + W/numpy.cos(numpy.deg2rad(theta)) # wetted perimeter
- return manning**2.*(l**2./S)**(2./3.)
-
-
-def channel_shear_stress(Q, S):
- # Determine mean wall shear stress from Darcy-Weisbach friction loss
- u_bar = Q/S
- return 1./8.*friction_factor*rho_w*u_bar**2.
-
-
-def channel_sediment_flux_sand(tau, W, f_s, D_s):
- # Parker 1979, Wilcock 1997, 2001, Egholm 2013
- # tau: Shear stress by water flow
- # W: Channel width
- # f_s: Sand volume fraction
- # D_s: Mean sand fraction grain size
-
- # Piecewise linear functions for nondimensional critical shear stresses
- # dependent on sand fraction from Gasparini et al 1999 of Wilcock 1997
- # data.
- ref_shear_stress = numpy.ones_like(f_s)*0.04
- ref_shear_stress[numpy.nonzero(f_s <= 0.1)] = 0.88
- I = numpy.nonzero((0.1 < f_s) & (f_s <= 0.4))
- ref_shear_stress[I] = 0.88 - 2.8*(f_s[I] - 0.1)
-
- # Non-dimensionalize shear stress
- shields_stress = tau/((rho_s - rho_w)*g*D_s)
-
- # import ipdb; ipdb.set_trace()
- Q_c = 11.2*f_s*W/((rho_s - rho_w)/rho_w*g) \
- * (tau/rho_w)**1.5 \
- * numpy.maximum(0.0,
- (1.0 - 0.846*numpy.sqrt(ref_shear_stress/shields_stress))
- )**4.5
-
- return Q_c
-
-
-def channel_sediment_flux_gravel(tau, W, f_g, D_g):
- # Parker 1979, Wilcock 1997, 2001, Egholm 2013
- # tau: Shear stress by water flow
- # W: Channel width
- # f_g: Gravel volume fraction
- # D_g: Mean gravel fraction grain size
-
- # Piecewise linear functions for nondimensional critical shear stresses
- # dependent on sand fraction from Gasparini et al 1999 of Wilcock 1997
- # data.
- ref_shear_stress = numpy.ones_like(f_g)*0.01
- ref_shear_stress[numpy.nonzero(f_g <= 0.1)] = 0.04
- I = numpy.nonzero((0.1 < f_g) & (f_g <= 0.4))
- ref_shear_stress[I] = 0.04 - 0.1*(f_g[I] - 0.1)
-
- # Non-dimensionalize shear stress
- shields_stress = tau/((rho_s - rho_w)*g*D_g)
-
- # From Wilcock 2001, eq. 3
- Q_g = 11.2*f_g*W/((rho_s - rho_w)/rho_w*g) \
- * (tau/rho_w)**1.5 \
- * numpy.maximum(0.0,
- (1.0 - 0.846*ref_shear_stress/shields_stress))**4.5
-
- # From Wilcock 2001, eq. 4
- I = numpy.nonzero(ref_shear_stress/shields_stress < 1.)
- Q_g[I] = f_g[I]*W[I]/((rho_s - rho_w)/rho_w*g) \
- * (tau[I]/rho_w)**1.5 \
- * 0.0025*(shields_stress[I]/ref_shear_stress[I])**14.2
-
- return Q_g
-
-
-def channel_growth_rate_sedflux(Q_t, porosity, s_c):
- # Damsgaard et al, in prep
- return 1./porosity[1:] * gradient(Q_t, s_c)
-
-
-def update_channel_size_with_limit(S, S_old, dSdt, dt, N_c):
- # Damsgaard et al, in prep
- S_max = numpy.maximum(
- numpy.maximum(
- 1./4.*(c_1*numpy.maximum(N_c, 0.)/1000. + c_2), 0.)**2. *
- numpy.tan(numpy.deg2rad(theta)), S_min)
- S = numpy.maximum(numpy.minimum(S_old + dSdt*dt, S_max), S_min)
- W = S/numpy.tan(numpy.deg2rad(theta)) # Assume no channel floor wedge
- dSdt = S - S_old # adjust dSdt for clipping due to channel size limits
- return S, W, S_max, dSdt
-
-
-def flux_solver(m_dot, ds):
- # Iteratively find new water fluxes
- it = 0
- max_res = 1e9 # arbitrary large value
-
- # Iteratively find solution, do not settle for less iterations than the
- # number of nodes
- while max_res > tol_Q:
-
- Q_old = Q.copy()
- # dQ/ds = m_dot -> Q_out = m*delta(s) + Q_in
- # Upwind information propagation (upwind)
- Q[0] = Q_upstream
- Q[1:] = m_dot[1:]*ds[1:] + Q[:-1]
- max_res = numpy.max(numpy.abs((Q - Q_old)/(Q + 1e-16)))
-
- if print_output_convergence:
- print('it = {}: max_res = {}'.format(it, max_res))
-
- # import ipdb; ipdb.set_trace()
- if it >= max_iter:
- raise Exception('t = {}, step = {}: '.format(time, step) +
- 'Iterative solution not found for Q')
- it += 1
-
- return Q
-
-
-def pressure_solver(psi, f, Q, S):
- # Iteratively find new water pressures
- # dN_c/ds = f*rho_w*g*Q^2/S^{8/3} - psi (Kingslake and Ng 2013)
-
- it = 0
- max_res = 1e9 # arbitrary large value
- while max_res > tol_N_c:
-
- N_c_old = N_c.copy()
-
- # Dirichlet BC (fixed pressure) at terminus
- N_c[-1] = rho_i*g*H_c[-1] - P_terminus
-
- N_c[:-1] = N_c[1:] \
- + psi[:-1]*ds[:-1] \
- - f[:-1]*rho_w*g*Q[:-1]*numpy.abs(Q[:-1]) \
- /(S[:-1]**(8./3.))*ds[:-1]
-
- max_res = numpy.max(numpy.abs((N_c - N_c_old)/(N_c + 1e-16)))
-
- if print_output_convergence:
- print('it = {}: max_res = {}'.format(it, max_res))
-
- if it >= max_iter:
- raise Exception('t = {}, step = {}:'.format(time, step) +
- 'Iterative solution not found for N_c')
- it += 1
-
- return N_c
- #return N_c_old*(1 - relax_N_c) + N_c*relax_N_c
-
-
-def plot_state(step, time, S_, S_max_, title=True):
- # Plot parameters along profile
- fig = plt.gcf()
- fig.set_size_inches(3.3*1.1, 3.3*1.1*1.5)
-
- ax_Pa = plt.subplot(3, 1, 1) # axis with Pascals as y-axis unit
- ax_Pa.plot(s_c/1000., N_c/1e6, '-k', label='$N$')
- ax_Pa.plot(s_c/1000., H_c*rho_i*g/1e6, '--r', label='$P_i$')
- ax_Pa.plot(s_c/1000., P_c/1e6, ':y', label='$P_c$')
-
- ax_m3s = ax_Pa.twinx() # axis with m3/s as y-axis unit
- ax_m3s.plot(s_c/1000., Q, '.-b', label='$Q$')
-
- if title:
- plt.title('Day: {:.3}'.format(time/(60.*60.*24.)))
- ax_Pa.legend(loc=2)
- ax_m3s.legend(loc=4)
- ax_Pa.set_ylabel('[MPa]')
- ax_m3s.set_ylabel('[m$^3$/s]')
-
- ax_m3s_sed = plt.subplot(3, 1, 2, sharex=ax_Pa)
- ax_m3s_sed.plot(s_c/1000., Q_t, '-', label='$Q_{total}$')
- ax_m3s_sed.plot(s_c/1000., Q_s, ':', label='$Q_{sand}$')
- ax_m3s_sed.plot(s_c/1000., Q_g, '--', label='$Q_{gravel}$')
- ax_m3s_sed.set_ylabel('[m$^3$/s]')
- ax_m3s_sed.legend(loc=2)
-
- ax_m2 = plt.subplot(3, 1, 3, sharex=ax_Pa)
- ax_m2.plot(s_c/1000., S_, '-k', label='$S$')
- ax_m2.plot(s_c/1000., S_max_, '--', color='#666666', label='$S_{max}$')
-
- ax_m2s = ax_m2.twinx()
- ax_m2s.plot(s_c/1000., dSdt, ':', label='$dS/dt$')
-
- ax_m2.legend(loc=2)
- ax_m2s.legend(loc=3)
- ax_m2.set_xlabel('$s$ [km]')
- ax_m2.set_ylabel('[m$^2$]')
- ax_m2s.set_ylabel('[m$^2$/s]')
-
- ax_Pa.set_xlim([s.min()/1000., s.max()/1000.])
-
- plt.setp(ax_Pa.get_xticklabels(), visible=False)
- plt.tight_layout()
- if step == -1:
- plt.savefig('chan-0.init.pdf')
- else:
- plt.savefig('chan-' + str(step) + '.pdf')
- plt.clf()
- plt.close()
-
-
-def find_new_timestep(ds, Q, Q_t, S):
- # Determine the timestep using the Courant-Friedrichs-Lewy condition
- dt = safety*numpy.minimum(60.*60.*24.,
- numpy.min(numpy.abs(ds/(Q*S),\
- ds/(Q_t*S)+1e-16)))
-
- if dt < 1.0:
- raise Exception('Error: Time step less than 1 second at step '
- + '{}, time '.format(step)
- + '{:.3} s/{:.3} d'.format(time, time/(60.*60.*24.)))
-
- return dt
-
-
-def print_status_to_stdout(step, time, dt):
- sys.stdout.write('\rstep = {}, '.format(step) +
- 't = {:.2} s or {:.4} d, dt = {:.2} s '
- .format(time, time/(60.*60.*24.), dt))
- sys.stdout.flush()
-
-s_c = avg_midpoint(s) # Channel section midpoint coordinates [m]
-H_c = avg_midpoint(H)
-
-# Water-pressure gradient from geometry [Pa/m]
-psi = -rho_i*g*gradient(H, s) - (rho_w - rho_i)*g*gradient(b, s)
-
-# Prepare figure object for plotting during the simulation
-fig = plt.figure('channel')
-plot_state(-1, 0.0, S, S_max)
-
-
-# # Time loop
-time = 0.
-step = 0
-while time <= t_end:
-
- # Determine time step length from water flux
- dt = find_new_timestep(ds, Q, Q_t, S)
-
- # Display current simulation status
- print_status_to_stdout(step, time, dt)
-
- it = 0
-
- # Initialize the maximum normalized residual for S to an arbitrary large
- # value
- max_res = 1e9
-
- S_old = S.copy()
- # Iteratively find solution with the Jacobi relaxation method
- while max_res > tol_S:
-
- S_prev_it = S.copy()
-
- # Find new water fluxes consistent with mass conservation and local
- # meltwater production (m_dot)
- Q = flux_solver(m_dot, ds)
-
- # Find average shear stress from water flux for each channel segment
- tau = channel_shear_stress(Q, S)
-
- # Determine sediment fluxes for each size fraction
- f_g = 1./f_s # gravel volume fraction is reciprocal to sand
- Q_s = channel_sediment_flux_sand(tau, W, f_s, D_s)
- Q_g = channel_sediment_flux_gravel(tau, W, f_g, D_g)
- Q_t = Q_s + Q_g
-
- # Determine change in channel size for each channel segment.
- # Use backward differences and assume dS/dt=0 in first segment.
- dSdt[1:] = channel_growth_rate_sedflux(Q_t, porosity, s_c)
- #dSdt *= speedup_factor * relax
-
- # Update channel cross-sectional area and width according to growth
- # rate and size limit for each channel segment
- #S_prev = S.copy()
- S, W, S_max, dSdt = \
- update_channel_size_with_limit(S, S_old, dSdt, dt, N_c)
- #S = S_prev*(1.0 - relax) + S*relax
-
-
- # Find hydraulic roughness
- f = channel_hydraulic_roughness(manning, S, W, theta)
-
- # Find new water pressures consistent with the flow law
- N_c = pressure_solver(psi, f, Q, S)
-
- # Find new effective pressure in channel segments
- P_c = rho_i*g*H_c - N_c
-
- if plot_during_iterations:
- plot_state(step + it/1e4, time, S, S_max)
-
- # Find new maximum normalized residual value
- max_res = numpy.max(numpy.abs((S - S_prev_it)/(S + 1e-16)))
- if print_output_convergence_main:
- print('it = {}: max_res = {}'.format(it, max_res))
-
- #import ipdb; ipdb.set_trace()
- if it >= max_iter:
- raise Exception('t = {}, step = {}: '.format(time, step) +
- 'Iterative solution not found')
- it += 1
-
- # Generate an output figure for every n time steps
- if step % plot_interval == 0:
- plot_state(step, time, S, S_max)
-
- # Update time
- time += dt
- step += 1
(DIR) diff --git a/1d-channel.py b/1d-channel.py
t@@ -3,16 +3,16 @@
# # ABOUT THIS FILE
# The following script uses basic Python and Numpy functionality to solve the
# coupled systems of equations describing subglacial channel development in
-# soft beds as presented in `Damsgaard et al. "Sediment plasticity controls
-# channelization of subglacial meltwater in soft beds"`, submitted to Journal
-# of Glaciology.
+# soft beds as presented in `Damsgaard et al. "Sediment behavior controls
+# equilibrium width of subglacial channels"`, accepted for publicaiton in
+# Journal of Glaciology.
#
# High performance is not the goal for this implementation, which is instead
# intended as a heavily annotated example on the solution procedure without
# relying on solver libraries, suitable for low-level languages like C, Fortran
# or CUDA.
#
-# License: Gnu Public License v3
+# License: GNU Public License v3
# Author: Anders Damsgaard, andersd@princeton.edu, https://adamsgaard.dk
import numpy
t@@ -27,7 +27,7 @@ total_days = 2. # Total simulation time [d]
t_end = 24.*60.*60.*total_days # Total simulation time [s]
tol_S = 1e-2 # Tolerance criteria for the norm. max. residual for S
tol_Q = 1e-2 # Tolerance criteria for the norm. max. residual for Q
-tol_N_c = 1e-2 # Tolerance criteria for the norm. max. residual for N_c
+tol_P_c = 1e-2 # Tolerance criteria for the norm. max. residual for P_c
max_iter = 1e2*Ns # Maximum number of solver iterations before failure
print_output_convergence = False # Display convergence in nested loops
print_output_convergence_main = True # Display convergence in main loop
t@@ -81,8 +81,8 @@ dSdt = numpy.zeros_like(S) # Transient in channel cross-sect. area [m^2/s]
W = S/numpy.tan(numpy.deg2rad(theta)) # Assuming no channel floor wedge
Q = numpy.zeros_like(S) # Water flux in channel segments [m^3/s]
Q_s = numpy.zeros_like(S) # Sediment flux in channel segments [m^3/s]
-N_c = numpy.zeros_like(S) # Effective pressure in channel segments [Pa]
-P_c = numpy.zeros_like(S) # Water pressure in channel segments [Pa]
+P_c = numpy.zeros_like(S) # Effective pressure in channel segments [Pa]
+P_w = numpy.zeros_like(S) # Effective pressure in channel segments [Pa]
tau = numpy.zeros_like(S) # Avg. shear stress from current [Pa]
porosity = numpy.ones_like(S)*0.3 # Sediment porosity [-]
res = numpy.zeros_like(S) # Solution residual during solver iterations
t@@ -132,11 +132,11 @@ def channel_growth_rate_sedflux(Q_s, porosity, s_c):
return 1./porosity[1:] * gradient(Q_s, s_c)
-def update_channel_size_with_limit(S, S_old, dSdt, dt, N_c):
+def update_channel_size_with_limit(S, S_old, dSdt, dt, P_c):
# Damsgaard et al, in prep
S_max = numpy.maximum(
numpy.maximum(
- 1./4.*(c_1*numpy.maximum(N_c, 0.)/1000. + c_2), 0.)**2. *
+ 1./4.*(c_1*numpy.maximum(P_c, 0.)/1000. + c_2), 0.)**2. *
numpy.tan(numpy.deg2rad(theta)), S_min)
S = numpy.maximum(numpy.minimum(S_old + dSdt*dt, S_max), S_min)
W = S/numpy.tan(numpy.deg2rad(theta)) # Assume no channel floor wedge
t@@ -174,33 +174,33 @@ def flux_solver(m_dot, ds):
def pressure_solver(psi, f, Q, S):
# Iteratively find new water pressures
- # dN_c/ds = f*rho_w*g*Q^2/S^{8/3} - psi (Kingslake and Ng 2013)
+ # dP_c/ds = f*rho_w*g*Q^2/S^{8/3} - psi (Kingslake and Ng 2013)
it = 0
max_res = 1e9 # arbitrary large value
- while max_res > tol_N_c:
+ while max_res > tol_P_c:
- N_c_old = N_c.copy()
+ P_c_old = P_c.copy()
# Dirichlet BC (fixed pressure) at terminus
- N_c[-1] = rho_i*g*H_c[-1] - P_terminus
+ P_c[-1] = rho_i*g*H_c[-1] - P_terminus
- N_c[:-1] = N_c[1:] \
+ P_c[:-1] = P_c[1:] \
+ psi[:-1]*ds[:-1] \
- f[:-1]*rho_w*g*Q[:-1]*numpy.abs(Q[:-1]) \
/ (S[:-1]**(8./3.))*ds[:-1]
- max_res = numpy.max(numpy.abs((N_c - N_c_old)/(N_c + 1e-16)))
+ max_res = numpy.max(numpy.abs((P_c - P_c_old)/(P_c + 1e-16)))
if print_output_convergence:
print('it = {}: max_res = {}'.format(it, max_res))
if it >= max_iter:
raise Exception('t = {}, step = {}:'.format(time, step) +
- 'Iterative solution not found for N_c')
+ 'Iterative solution not found for P_c')
it += 1
- return N_c
+ return P_c
def plot_state(step, time, S_, S_max_, title=False):
t@@ -209,9 +209,9 @@ def plot_state(step, time, S_, S_max_, title=False):
fig.set_size_inches(3.3*1.1, 3.3*1.1*1.5)
ax_Pa = plt.subplot(3, 1, 1) # axis with Pascals as y-axis unit
- ax_Pa.plot(s_c/1000., N_c/1e6, '-k', label='$N$')
+ ax_Pa.plot(s_c/1000., P_c/1e6, '-k', label='$P_c$')
ax_Pa.plot(s_c/1000., H_c*rho_i*g/1e6, '--r', label='$P_i$')
- ax_Pa.plot(s_c/1000., P_c/1e6, ':y', label='$P_c$')
+ ax_Pa.plot(s_c/1000., P_w/1e6, ':y', label='$P_w$')
ax_m3s = ax_Pa.twinx() # axis with m3/s as y-axis unit
ax_m3s.plot(s_c/1000., Q, '.-b', label='$Q$')
t@@ -339,15 +339,14 @@ while time <= t_end:
# Update channel cross-sectional area and width according to growth
# rate and size limit for each channel segment
S, W, S_max, dSdt = \
- update_channel_size_with_limit(S, S_old, dSdt, dt, N_c)
+ update_channel_size_with_limit(S, S_old, dSdt, dt, P_c)
f = channel_hydraulic_roughness(manning, S, W, theta)
- # Find new water pressures consistent with the flow law
- N_c = pressure_solver(psi, f, Q, S)
-
- # Find new effective pressure in channel segments
- P_c = rho_i*g*H_c - N_c
+ # Find new effective pressures consistent with the flow law and water
+ # pressures in channel segments
+ P_c = pressure_solver(psi, f, Q, S)
+ P_w = rho_i*g*H_c - P_c
if plot_during_iterations:
plot_state(step + it/1e4, time, S, S_max)
(DIR) diff --git a/LICENSE.md b/LICENSE.md
t@@ -0,0 +1,636 @@
+The SeaIce.jl package is licensed under the GNU Public License, Version 3.0+:
+
+> Copyright (c) 2017: Anders Damsgaard.
+> This program 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.
+>
+> This program 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.
+>
+>
+> GNU GENERAL PUBLIC LICENSE
+> Version 3, 29 June 2007
+>
+> Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+> Everyone is permitted to copy and distribute verbatim copies
+> of this license document, but changing it is not allowed.
+>
+> Preamble
+>
+> The GNU General Public License is a free, copyleft license for
+> software and other kinds of works.
+>
+> The licenses for most software and other practical works are designed
+> to take away your freedom to share and change the works. By contrast,
+> the GNU General Public License is intended to guarantee your freedom to
+> share and change all versions of a program--to make sure it remains free
+> software for all its users. We, the Free Software Foundation, use the
+> GNU General Public License for most of our software; it applies also to
+> any other work released this way by its authors. You can apply it to
+> your programs, too.
+>
+> When we speak of free software, we are referring to freedom, not
+> price. Our General Public Licenses are designed to make sure that you
+> have the freedom to distribute copies of free software (and charge for
+> them if you wish), that you receive source code or can get it if you
+> want it, that you can change the software or use pieces of it in new
+> free programs, and that you know you can do these things.
+>
+> To protect your rights, we need to prevent others from denying you
+> these rights or asking you to surrender the rights. Therefore, you have
+> certain responsibilities if you distribute copies of the software, or if
+> you modify it: responsibilities to respect the freedom of others.
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+>
+> Developers that use the GNU GPL protect your rights with two steps:
+> (1) assert copyright on the software, and (2) offer you this License
+> giving you legal permission to copy, distribute and/or modify it.
+>
+> For the developers' and authors' protection, the GPL clearly explains
+> that there is no warranty for this free software. For both users' and
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(DIR) diff --git a/README.md b/README.md
t@@ -1,2 +1,15 @@
# README
+Supplementary code for *Sediment behavior controls equilibrium width of
+subglacial channels* (A. Damsgaard, J. Suckale, J.A. Piotrowski, M. Houssais,
+M.R. Siegfried, H.A. Fricker) accepted for publication in Journal of
+Glaciology.
+This finite-difference example implementation will simulate the dynamics of a
+1d channel segment along a square-root ice geometry, with constant water
+pressure at the terminus.
+
+## License
+GNU Public License v3, see `LICENSE.md` for details.
+
+## Author
+Anders Damsgaard, https://adamsgaard.dk
(DIR) diff --git a/granular_channel_drainage/__init__.py b/granular_channel_drainage/__init__.py
t@@ -1,5 +0,0 @@
-#!/usr/bin/env python
-__all__ = ['model']
-__version__ = '0.01'
-
-from model import model
(DIR) diff --git a/granular_channel_drainage/model.py b/granular_channel_drainage/model.py
t@@ -1,137 +0,0 @@
-#!/usr/bin/env python
-import numpy
-import matplotlib.pyplot as plt
-import landlab
-
-class model:
- def __init__(self, name='unnamed'):
- '''
- Initialize a blank hydrology model object and optionally assign a
- simulation name to it.
-
- :param name: A uniquely identifying simulation name
- :type name: str
- '''
- self.name = name
-
- def genreateRegularGrid(self, Lx, Ly, Nx, Ny):
- '''
- Generate a uniform, regular and orthogonal grid using Landlab.
-
- :param Lx: A tuple containing the length along x of the model
- domain.
- :type Lx: float
- :param Ly: A tuple containing the length along y of the model
- domain.
- :type Ly: float
- :param Nx: The number of random model nodes along ``x`` in the model.
- :type Nx: int
- :param Ny: The number of random model nodes along ``y`` in the model.
- :type Ny: int
- '''
- self.grid_type = 'Regular'
- self.grid = landlab.grid.RasterModelGrid(shape=(Nx, Ny), spacing=Lx/Nx)
-
- def generateVoronoiDelaunayGrid(self, Lx, Ly, Nx, Ny,
- structure='pseudorandom',
- distribution='uniform'):
- '''
- Generate a Voronoi Delaunay grid with randomly positioned nodes using
- Landlab.
-
- :param Lx: A tuple containing the length along x of the model
- domain.
- :type Lx: float
- :param Ly: A tuple containing the length along y of the model
- domain.
- :type Ly: float
- :param Nx: The number of random model nodes along ``x`` in the model.
- :type Nx: int
- :param Ny: The number of random model nodes along ``y`` in the model.
- :type Ny: int
- :param structure: The type of numeric distribution used to seed the
- grid. A ``random`` grid will produce uniformly random-distributed
- grid points, while ``pseudorandom`` (default) will add random noise
- to a regular grid.
- :type structure: str
- :name distribution: Type of random numeric distribution adding noise to
- the pseudorandom structured grid. Accepted values are 'uniform'
- (default) or 'normal'.
- :type distribution: str
- '''
- self.grid_type = 'VoronoiDelaunay'
-
- if structure == 'random':
- x = numpy.random.rand(Nx*Ny)*Lx
- y = numpy.random.rand(Nx*Ny)*Ly
-
- elif structure == 'pseudorandom':
- dx = Lx/Nx
- dy = Ly/Ny
- xPoints = numpy.linspace(dx*.5, Lx - dx*.5, Nx)
- yPoints = numpy.linspace(dy*.5, Ly - dy*.5, Ny)
- gridPoints = numpy.array([[x,y] for y in yPoints for x in xPoints])
- N = len(gridPoints[:, 0])
-
- if distribution == 'normal':
- gridPoints[::2, 1] = gridPoints[::2, 1] + dy*0.5
- x = gridPoints[:, 0] + numpy.random.normal(0., dx*0.10, N)
- y = gridPoints[:, 1] + numpy.random.normal(0., dy*0.10, N)
-
- elif distribution == 'uniform':
- x = gridPoints[:, 0] + numpy.random.uniform(-dx*.4, dx*.4, N)
- y = gridPoints[:, 1] + numpy.random.uniform(-dy*.4, dy*.4, N)
-
- else:
- raise Exception('generateVoronoiDelaunayGrid: ' +
- 'distribution type "' + distribution +
- '" not understood.')
-
- self.grid = landlab.grid.VoronoiDelaunayGrid(x, y)
-
- def plotGrid(self, field='nodes',
- save=False, saveformat='pdf'):
- '''
- Plot the grid nodes or one of the fields associated with the grid.
-
- :param field: Field to plot (e.g., 'bed_elevation')
- :type field: str
- :param save: Save figure to file (default) or show in interactive
- window?
- :type save: bool
- :param saveformat: File format to save the plot as if ``save=True``.
- :type saveformat: str
- '''
-
- fig = plt.figure()
- if field == 'nodes':
- plt.plot(self.grid.node_x, self.grid.node_y, '.')
- plt.axis('equal')
- else:
- landlab.plot.imshow_grid(self.grid, field)
- #plt.tight_layout()
- if save:
- plt.savefig(self.name + '-' + field + '.' + saveformat)
- else:
- plt.show()
- plt.clf()
- plt.close()
-
- def gridCoordinates(self):
- '''
- Returns the grid coordinates.
- '''
- return self.grid.node_x, self.grid.node_y
-
- def addScalarField(self, name, values, units):
- '''
- Add scalar field to the model grid.
-
- :param name: A uniquely identifying name for the scalar field.
- :type name: str
- :param values: The values to be inserted to the scalar field.
- :type name: ndarray
- :param units: The unit associated with the values, e.g. 's' or 'm'
- :type units: str
- '''
- self.grid.add_field('node', name, values, units=units, copy=True)
(DIR) diff --git a/requirements.txt b/requirements.txt
t@@ -1,4 +1,3 @@
scipy>=0.14
numpy
-landlab
matplotlib