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Prevent frontogenesis from returning nans #3696

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Prevent frontogenesis from returning nans #3696

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13 changes: 12 additions & 1 deletion src/metpy/calc/kinematics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -567,7 +567,18 @@ def frontogenesis(potential_temperature, u, v, dx=None, dy=None, x_dim=-1, y_dim

# Compute the angle (beta) between the wind field and the gradient of potential temperature
psi = 0.5 * np.arctan2(shrd, strd)
beta = np.arcsin((-ddx_theta * np.cos(psi) - ddy_theta * np.sin(psi)) / mag_theta)
arg = (-ddx_theta * np.cos(psi) - ddy_theta * np.sin(psi)) / mag_theta
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@DWesl DWesl Nov 19, 2024 •
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One option would be something like this:

Suggested change
arg = (-ddx_theta * np.cos(psi) - ddy_theta * np.sin(psi)) / mag_theta
arg = (-ddx_theta * np.cos(psi) - ddy_theta * np.sin(psi))
nonzero_denominator = mag_theta != 0
arg[nonzero_denominator] /= mag_theta[nonzero_denominator]

Given how mag_theta is calculated, arg should be already zero where mag_theta is zero.

While searching for the where argument to np.divide, I found a StackOverflow answer suggesting

Suggested change
arg = (-ddx_theta * np.cos(psi) - ddy_theta * np.sin(psi)) / mag_theta
arg = np.divide(-ddx_theta * np.cos(psi) - ddy_theta * np.sin(psi)), mag_theta, out=np.zeros_like(mag_theta), where=mag_theta!=0)

which is a single expresion and seems somewhat more explicit about what it is doing and why.


# A few problems may occur when calculating the argument to the arcsin function.
# First, we may have divided by zero, since a constant theta field would mean
# mag_theta is zero. To counter this, we set the argument to zero in this case.
# Second, due to round-off error, the argument may be slightly outside the domain
# of arcsin. To counter this, we use np.clip to force the argument to be an
# acceptable value. With these adjustments, we can make sure beta doesn't end up
# with nans somewhere.
arg[mag_theta == 0] = 0
arg = np.clip(arg, -1, 1)
beta = np.arcsin(arg)

return 0.5 * mag_theta * (tdef * np.cos(2 * beta) - div)
Comment on lines +581 to 583
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@DWesl DWesl Nov 19, 2024 •
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If I remember the cosine double-angle identities correctly, this should be equivalent:

Suggested change
beta = np.arcsin(arg)
return 0.5 * mag_theta * (tdef * np.cos(2 * beta) - div)
# cos(2*theta) = cos(theta)**2 - sin(theta)**2 = 1 - 2 * sin(theta)**2
# second equality uses cos(theta)**2 + sin(theta)**2 = 1
# sin(arcsin(arg)) == arg for all -1 <= arg <= 1
return 0.5 * mag_theta * (tdef * (1 - 2 * arg**2) - div)

The np.clip provides an opportunity to correct roundoff error, but we might be able to skip it and still get decent answers. (Fortunately the errors are near one rather than zero, so going a bit past doesn't introduce sign errors, so the relevant thing is whether this roundoff error is smaller than the discretization error in mag_theta and div).

If you want to declare the trigonometric identities out-of-scope for this PR, that is entirely understandable.


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53 changes: 53 additions & 0 deletions tests/calc/test_kinematics.py
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Expand Up @@ -307,6 +307,59 @@ def test_frontogenesis_asym():
assert_almost_equal(fronto, true_fronto)


def test_frontogenesis_nan():
"""Test that frontogenesis calculation does not result in nan."""
x = np.array([-4142340.8, -4061069.8, -3979798.8, -3898527.8, -3817256.8],
dtype=np.float32)
y = np.array([-832207.56, -750936.56, -669665.56, -588394.5, -507123.56],
dtype=np.float32)
lat = np.array([[12.38805122, 12.58268367, 12.77387305, 12.96159447, 13.14582354],
[13.07545967, 13.27159197, 13.46425116, 13.65341235, 13.83905111],
[13.76423766, 13.96186003, 14.15597929, 14.34657051, 14.53360928],
[14.45429168, 14.65339375, 14.84896275, 15.04097373, 15.22940228],
[15.14552468, 15.3460955, 15.54310332, 15.73652321, 15.92633074]])
lon = np.array([[-132.75696788, -132.05286812, -131.34671228, -130.63852983,
-129.92835084],
[-132.9590417, -132.25156385, -131.54199837, -130.83037505,
-130.11672431],
[-133.16323241, -132.45234731, -131.73934239, -131.02424779,
-130.30709426],
[-133.36957268, -132.65525085, -131.93877637, -131.22017972,
-130.49949199],
[-133.57809517, -132.86030681, -132.14033233, -131.41820252,
-130.69394884]])
uvals = np.array([[0.165024, 0.055023, -0.454977, -1.534977, -2.744976],
[0.155024, -0.434977, -2.114977, -3.474977, -4.034977],
[-1.554977, -2.714977, -2.084976, -5.274977, -3.334976],
[-3.424976, -7.644977, -7.654977, -5.384976, -3.224977],
[-9.564977, -9.934977, -7.454977, -6.004977, -4.144977]]) * units('m/s')
vvals = (np.array([[2.6594982, 1.9194984, 2.979498, 2.149498, 2.6394978],
[3.4994984, 4.0794983, 4.8494987, 5.2594986, 3.1694984],
[5.159498, 6.4594975, 6.559498, 5.9694977, 3.189499],
[6.5994987, 9.799498, 7.4594975, 4.2894993, 3.729498],
[11.3394985, 6.779499, 4.0994987, 4.819498, 4.9994984]])
* units('m/s'))
tvals = np.array([[290.2, 290.1, 290.2, 290.30002, 290.30002],
[290.5, 290.30002, 290.30002, 290.30002, 290.2],
[290.80002, 290.40002, 290.2, 290.40002, 289.90002],
[290.7, 290.90002, 290.7, 290.1, 289.7],
[290.90002, 290.40002, 289.7, 289.7, 289.30002]]) * units('degK')

x = xr.DataArray(data=x, coords={'x': x}, dims='x', attrs={'units': 'meters'})
y = xr.DataArray(data=y, coords={'y': y}, dims='y', attrs={'units': 'meters'})

dims = ['y', 'x']
coords = {'x': x, 'y': y, 'latitude': (dims, lat), 'longitude': (dims, lon)}

u = xr.DataArray(data=uvals, coords=coords, dims=dims)
v = xr.DataArray(data=vvals, coords=coords, dims=dims)
t = xr.DataArray(data=tvals, coords=coords, dims=dims)

th = potential_temperature(850 * units('hPa'), t)
f = frontogenesis(th, u, v)
assert not np.any(np.isnan(f))


def test_advection_uniform():
"""Test advection calculation for a uniform 1D field."""
u = np.ones((3,)) * units('m/s')
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