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transient_budd.m
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%% This is just so changes to combined (in case i revisit things) don't disrupt these experiments
close all
clear all
clc
%% Physical parameters
params.A = 0.9e-25;
params.n = 3;
params.rho_i = 917;
params.rho_w = 1028;
params.g = 9.81;
params.C = 7.624; % base 0.2
params.As = 2.26e-21; % Calculated
params.f = 0.07; % From Kingslake thesis
params.K0 = 10^-24; % From Kingslake thesis
params.L = 3.3e5; % Kingslake thesis
params.year = 3600*24*365;
%% Scaling params (coupled model equations solved in non-dim form)
params.x0 = 100*10^3;
params.h0 = 1000;
params.Q0 = 1;
params.psi0 = params.rho_w*params.g*params.h0/params.x0;
params.M0 = params.Q0/params.x0;
params.m0 = params.Q0*params.psi0/params.L;
params.eps_r = params.m0*params.x0/(params.rho_i*params.Q0);
params.S0 = (params.f*params.rho_w*params.g*params.Q0^2/params.psi0)^(3/8);
params.th0 = params.rho_i*params.S0/params.m0;
params.N0 = (params.K0*params.th0)^(-1/3);
params.delta = params.N0/(params.x0*params.psi0);
params.u0 = (params.rho_i*params.g*params.h0^2/(params.x0*params.N0*params.C))^params.n;
params.t0 = params.x0/params.u0;
params.a0 = params.h0/params.t0;
params.alpha = 2*params.u0^(1/params.n)/(params.rho_i*params.g*params.h0*(params.x0*params.A)^(1/params.n));
params.beta = params.th0/params.t0;
params.r = params.rho_i/params.rho_w;
params.transient = 0;
%% Grid parameters - ice sheet
params.Nx = 700; %number of grid points - 200
params.N1 = 100; %number of grid points in coarse domain - 100
params.Nh = 1000;
params.sigGZ = 0.95; %extent of coarse grid (where GL is at sigma=1) - 0.97
sigma1=linspace(params.sigGZ/(params.N1+0.5), params.sigGZ, params.N1);
sigma2=linspace(params.sigGZ, 1, params.Nx-params.N1+1);
params.sigma = [sigma1, sigma2(2:end)]'; %grid points on velocity (includes GL, not ice divide)
params.dsigma = diff(params.sigma); %grid spacing
params.sigma_elem = [0;(params.sigma(1:params.Nx-1) + params.sigma(2:params.Nx))./2 ]; %grid points on thickness (includes divide, not GL)
%% Grid parameters - hydro
params.sigma_h = linspace(0,1,params.Nh)';
params.dsigma_h = diff(params.sigma_h); %grid spacing
%% Establish timings
params.year = 3600*24*365; %number of seconds in a year
params.Nt =1000; %number of time steps - normally 150
params.end_year = 50; % either 5 or 5000 years
params.dt = params.end_year*params.year/params.Nt;
%% Determine at what points there is coupling
% 1 - coupling on, 0 - coupling off
params.hydro_u_from_ice_u = 1;
params.hydro_psi_from_ice_h = 1;
params.ice_N_from_hydro = 1;
%% Initial "steady state" conditions
params.shear_scale = 1;
Q = ones(params.Nh,1);
N = ones(params.Nh,1);
S = ones(params.Nh,1);
params.S_old = S;
params.M = 1e-6/params.M0; % zero when using schoof bed
params.N_terminus = 0;
params.accum = 1./params.year;
xg = 1500e3/params.x0; % Set high past sill for retreat
hf = (-bed_schoof(xg.*params.x0,params)/params.h0)/params.r;
h = 1 - (1-hf).*params.sigma;
u = 0.1*(params.sigma_elem.^(1/3)) + 1e-3; % 0.1 for C = 0.5, 0.3 for C = 0.1-0.4
params.Q_in = 1/params.Q0;
params.h_old = h;
params.xg_old = xg;
params.ice_start = 3*params.Nh;
sig_old = params.sigma;
sige_old = params.sigma_elem;
QNShuxg0 = [Q;N;S;h;u;xg];
options = optimoptions('fsolve','Display','iter','SpecifyObjectiveGradient',false,'MaxFunctionEvaluations',1e6,'MaxIterations',1e3);
flf = @(QNShuxg) budd_schoofbed_transient(QNShuxg,params);
[QNShuxg_init,F,exitflag,output,JAC] = fsolve(flf,QNShuxg0,options);
Q = QNShuxg_init(1:params.Nh);
N = QNShuxg_init(params.Nh+1:2*params.Nh);
S = QNShuxg_init(2*params.Nh+1:3*params.Nh);
h = QNShuxg_init(params.ice_start+1:params.ice_start+ params.Nx);
u = QNShuxg_init(params.ice_start + params.Nx+1:params.ice_start+2*params.Nx);
xg = QNShuxg_init(params.ice_start+2*params.Nx+1);
hf = (-bed_schoof(xg.*params.x0,params)/params.h0)/(params.r);
%% Final steady state solution
% params.accum = 1./params.year;
% params.Q_in = 10/params.Q0;
params.A_old = params.A;
params.A = 2.9e-25;
params.alpha = 2*params.u0^(1/params.n)/(params.rho_i*params.g*params.h0*(params.x0*params.A)^(1/params.n));
% flf = @(QNShuxg) schoof_combined_hydro_ice_eqns(QNShuxg,params);
% [QNShuxg_final,F,exitflag,output,JAC] = fsolve(flf,QNShuxg_init,options);
% xg_f = QNShuxg_final(params.ice_start+2*params.Nx+1);
%% Now for evolution
Qs = nan.*ones(params.Nt,params.Nh);
Ns = nan.*ones(params.Nt,params.Nh);
Ss = nan.*ones(params.Nt,params.Nh);
hs = nan.*ones(params.Nt,params.Nx);
us = nan.*ones(params.Nt,params.Nx);
xgs = nan.*ones(1,params.Nt);
QNShuxg_t = QNShuxg_init;
Qs(1,:) = QNShuxg_t(1:params.Nh);
Ns(1,:) = QNShuxg_t(params.Nh+1:2*params.Nh);
Ss(1,:) = QNShuxg_t(2*params.Nh+1:3*params.Nh);
hs(1,:) = QNShuxg_t(params.ice_start+1:params.ice_start+ params.Nx);
us(1,:) = QNShuxg_t(params.ice_start+params.Nx+1:params.ice_start+2*params.Nx);
xgs(1) = QNShuxg_t(params.ice_start+2*params.Nx+1);
params.h_old = h;
params.xg_old =xg;
params.S_old = S;
params.transient = 1;
time_to_ss = 0; % to 99 percent
for t=2:params.Nt
% if t == 50
% params.A = 0.9e-25;
% params.alpha = 2*params.u0^(1/params.n)/(params.rho_i*params.g*params.h0*(params.x0*params.A)^(1/params.n));
%
% end
flf = @(QNShuxg) budd_schoofbed_transient(QNShuxg,params);
[QNShuxg_t,F,exitflag,output,JAC] = fsolve(flf,QNShuxg_t,options);
t
Qs(t,:) = QNShuxg_t(1:params.Nh);
Ns(t,:) = QNShuxg_t(params.Nh+1:2*params.Nh);
Ss(t,:) = QNShuxg_t(2*params.Nh+1:3*params.Nh);
hs(t,:) = QNShuxg_t(params.ice_start+1:params.ice_start+ params.Nx);
us(t,:) = QNShuxg_t(params.ice_start+params.Nx+1:params.ice_start+2*params.Nx);
xgs(t) = QNShuxg_t(params.ice_start+2*params.Nx+1);
params.h_old = QNShuxg_t(params.ice_start+1:params.ice_start+ params.Nx);
params.xg_old = xgs(t);
params.S_old = QNShuxg_t(2*params.Nh+1:3*params.Nh);
%if abs(xg_f - xgs(t)) < 0.001*xg_f && time_to_ss == 0
% time_to_ss = (t-1)*params.dt/params.year;
%end
end
%% Plotting
ts = linspace(0,params.end_year,params.Nt);
figure();
subplot(3,1,1);plot(ts,xgs.*params.x0./1e3,'linewidth',3);xlabel('time (yr)');ylabel('x_g');
subplot(3,1,2);contourf(ts,params.sigma_elem,hs'.*params.h0);colorbar;xlabel('time (yr)');ylabel('sigma');title('thickness (m)');set(gca,'Ydir','Reverse');
subplot(3,1,3);contourf(ts,params.sigma,us'.*params.u0.*params.year);colorbar;xlabel('time (yr)');ylabel('sigma');title('velocity (m/yr)');set(gca,'Ydir','Reverse');
figure();
Q_dim = Qs.*params.Q0;
N_dim = Ns.*params.N0;
S_dim = Ss.*params.S0;
subplot(3,1,1);surface(ts,params.sigma_h,Q_dim',EdgeColor='None');colorbar;xlabel('time (yr)');ylabel('distance');title('Flow (m^3/s)');set(gca,'Ydir','Reverse')
subplot(3,1,2);surface(ts,params.sigma_h,N_dim',EdgeColor='None');colorbar;xlabel('time (yr)');ylabel('distance');title('Effective Pressure (Pa)');set(gca,'Ydir','Reverse')
subplot(3,1,3);surface(ts,params.sigma_h,S_dim',EdgeColor='None');colorbar;xlabel('time (yr)');ylabel('distance');title('Surface Area (m^2)');set(gca,'Ydir','Reverse')
%% Saving values
results.params = params;
results.init_cond = QNShuxg_init;
%results.steady_state = QNShuxg_final;
results.xgs = xgs;
results.ts = ts;
results.hs = hs';
results.us = us';
results.Qs = Qs';
results.Ns = Ns';
results.Ss = Ss';
%results.time_to_ss = time_to_ss;
%fname = strcat('base_run',num2str(params.A*1e25),'_c.mat');
fname = 'budd_retreat_50yr.mat';
%fname = strcat('Nh_',num2str(params.Nh),'_coarse_',num2str(params.N1),'_fine_',num2str(params.Nx-params.N1),'.mat');
save(fname,'results');