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
