Negative rate factors with reasonable temperatures

[icepack]

Negative rate factors with reasonable temperatures

[dlilien]

To update, A = max_value(small_number, A) is not sufficient to fix this--it seems like it will put a floor on nodal values, but the function overall can take negative values at intermediate points (although maybe that is less of an issue depending on the function space of the velocity).

MWE follows--in this one, the problem is solved for vertical degree greater than 4, but that is not true in the general case.

import numpy as np
import icepack
from scipy.interpolate import RegularGridInterpolator
from matplotlib import pyplot as plt


res = 250
Lx = 1000
nx = Lx // res
mesh1d = firedrake.IntervalMesh(nx, Lx)
mesh = firedrake.ExtrudedMesh(mesh1d, layers=1)

x, ζ = firedrake.SpatialCoordinate(mesh)

QT = firedrake.FunctionSpace(mesh, "CG", 2, vfamily="CG", vdegree=4)

meshT = QT.mesh()
element = QT.ufl_element()
MV = firedrake.VectorFunctionSpace(meshT, element)
coordsT = firedrake.interpolate(meshT.coordinates, MV).dat.data_ro[:]

T = firedrake.Function(QT)

z_T = np.linspace(0, 1, 101)
x_T = np.array([-1, Lx + 1])
T_z = 240.0 + (z_T - 0.66) ** 2.0 * 74.0

T_arr = np.repeat(T_z, 2).reshape((101, 2))
T.dat.data[:] = RegularGridInterpolator((x_T, z_T), T_arr.T)(coordsT)

cmT = firedrake.tripcolor(T, num_sample_points=100)
plt.colorbar(cmT, label='T')

A = firedrake.project(firedrake.max_value(icepack.rate_factor(T), 1.0e-8), QT)
cmA = firedrake.tripcolor(A, num_sample_points=100, vmin=-5, vmax=5, cmap='bwr')
plt.colorbar(cmA, label='A')

plt.show()

[danshapero]

Thanks for catching this! I suspect the problem is happening because the temperature crosses the slope break at -10C. That could certainly cause the interpolated or projected fluidity field to do something wrong. We might be able to work around this by interpolating with Bernstein polynomials. I'll see what I can figure out and get back to you.

I've run into similar (but not as severe) problems before and it has me wondering if I should implement a 2- or multi-layer model. Clearly using a single layer and high-degree polynomials can cause problems like what you're seeing or other ringing artifacts.