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feat: add ECEF to ENU conversions (#326)
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refactor: use rotation matrix to convert from cartesian to spherical
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@tsutterley
tsutterley authored Aug 29, 2024
1 parent ee20348 commit a4a3254
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6 changes: 5 additions & 1 deletion doc/source/api_reference/spatial.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -79,7 +79,7 @@ General Methods

.. autofunction:: pyTMD.spatial.to_dms

.. autofunction:: pyTMD.spatial.to_degrees
.. autofunction:: pyTMD.spatial.from_dms

.. autofunction:: pyTMD.spatial.to_cartesian

Expand All @@ -93,4 +93,8 @@ General Methods

.. autofunction:: pyTMD.spatial._zhu_closed_form

.. autofunction:: pyTMD.spatial.to_ENU

.. autofunction:: pyTMD.spatial.from_ENU

.. autofunction:: pyTMD.spatial.scale_factors
130 changes: 73 additions & 57 deletions pyTMD/compute.py
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Original file line number Diff line number Diff line change
Expand Up @@ -61,6 +61,8 @@
UPDATE HISTORY:
Updated 08/2024: allow inferring only specific minor constituents
use prediction functions for pole tides in cartesian coordinates
use rotation matrix to convert from cartesian to spherical
Updated 07/2024: assert that data type is a known value
make number of days to convert JD to MJD a variable
added option to crop tide models to the domain of the input data
Expand Down Expand Up @@ -892,13 +894,26 @@ def LPT_displacements(
a_axis=units.a_axis, flat=units.flat)
# calculate geocentric latitude and convert to degrees
latitude_geocentric = np.arctan(Z / np.sqrt(X**2.0 + Y**2.0))/dtr
# geocentric colatitude in radians
npts = len(latitude_geocentric)
# geocentric colatitude and longitude in radians
theta = dtr*(90.0 - latitude_geocentric)
phi = dtr*lon.flatten()

# compute normal gravity at spatial location
# p. 80, Eqn.(2-199)
gamma_0 = units.gamma_0(theta)

# rotation matrix for converting from cartesian coordinates
R = np.zeros((npts, 3, 3))
R[:,0,0] = np.cos(phi)*np.cos(theta)
R[:,1,0] = -np.sin(phi)
R[:,2,0] = np.cos(phi)*np.sin(theta)
R[:,0,1] = np.sin(phi)*np.cos(theta)
R[:,1,1] = np.cos(phi)
R[:,2,1] = np.sin(phi)*np.sin(theta)
R[:,0,2] = -np.sin(theta)
R[:,2,2] = np.cos(theta)

# calculate radial displacement at time
if (TYPE == 'grid'):
ny,nx = np.shape(x)
Expand All @@ -915,12 +930,10 @@ def LPT_displacements(
l2=lb2,
convention=CONVENTION
)
# calculate radial component of load pole tides
dln,dlt,drad = pyTMD.spatial.to_geodetic(
X + dxi[:,0], Y + dxi[:,1], Z + dxi[:,2],
a_axis=units.a_axis, flat=units.flat)
# calculate components of load pole tides
S = np.einsum('ti...,tji...->tj...', dxi, R)
# reshape to output dimensions
Srad.data[:,:,i] = np.reshape(drad, (ny,nx))
Srad.data[:,:,i] = np.reshape(S[:,2], (ny,nx))
Srad.mask[:,:,i] = np.isnan(Srad.data[:,:,i])
elif (TYPE == 'drift'):
# calculate load pole tides in cartesian coordinates
Expand All @@ -933,13 +946,11 @@ def LPT_displacements(
l2=lb2,
convention=CONVENTION
)
# calculate radial component of load pole tides
dln,dlt,drad = pyTMD.spatial.to_geodetic(
X + dxi[:,0], Y + dxi[:,1], Z + dxi[:,2],
a_axis=units.a_axis, flat=units.flat)
# calculate components of load pole tides
S = np.einsum('ti...,tji...->tj...', dxi, R)
# reshape to output dimensions
Srad = np.ma.zeros((nt), fill_value=FILL_VALUE)
Srad.data[:] = drad.copy()
Srad.data[:] = S[:,2].copy()
Srad.mask = np.isnan(Srad.data)
elif (TYPE == 'time series'):
nstation = len(x)
Expand All @@ -957,12 +968,10 @@ def LPT_displacements(
l2=lb2,
convention=CONVENTION
)
# calculate radial component of load pole tides
dln,dlt,drad = pyTMD.spatial.to_geodetic(
X[s] + dxi[:,0], Y[s] + dxi[:,1], Z[s] + dxi[:,2],
a_axis=units.a_axis, flat=units.flat)
# calculate components of load pole tides
S = np.einsum('ti...,ji...->tj...', dxi, R[s,:,:])
# reshape to output dimensions
Srad.data[s,:] = drad.copy()
Srad.data[s,:] = S[:,2].copy()
Srad.mask[s,:] = np.isnan(Srad.data[s,:])

# replace invalid data with fill values
Expand Down Expand Up @@ -1111,20 +1120,21 @@ def OPT_displacements(
# read and interpolate ocean pole tide map from Desai (2002)
ur, un, ue = pyTMD.io.IERS.extract_coefficients(lon.flatten(),
latitude_geocentric, method=METHOD)
# convert to cartesian coordinates
R = np.zeros((3, 3, npts))
R[0,0,:] = np.cos(phi)*np.cos(theta)
R[0,1,:] = -np.sin(phi)
R[0,2,:] = np.cos(phi)*np.sin(theta)
R[1,0,:] = np.sin(phi)*np.cos(theta)
R[1,1,:] = np.cos(phi)
R[1,2,:] = np.sin(phi)*np.sin(theta)
R[2,0,:] = -np.sin(theta)
R[2,2,:] = np.cos(theta)
# rotation matrix for converting to/from cartesian coordinates
R = np.zeros((npts, 3, 3))
R[:,0,0] = np.cos(phi)*np.cos(theta)
R[:,0,1] = -np.sin(phi)
R[:,0,2] = np.cos(phi)*np.sin(theta)
R[:,1,0] = np.sin(phi)*np.cos(theta)
R[:,1,1] = np.cos(phi)
R[:,1,2] = np.sin(phi)*np.sin(theta)
R[:,2,0] = -np.sin(theta)
R[:,2,2] = np.cos(theta)
Rinv = np.linalg.inv(R)

# calculate pole tide displacements in Cartesian coordinates
# coefficients reordered to N, E, R to match IERS rotation matrix
UXYZ = np.einsum('ti...,jit...->tj...', np.c_[un, ue, ur], R)
UXYZ = np.einsum('ti...,tji...->tj...', np.c_[un, ue, ur], R)

# calculate radial displacement at time
if (TYPE == 'grid'):
Expand All @@ -1144,12 +1154,10 @@ def OPT_displacements(
g2=gamma,
convention=CONVENTION
)
# calculate radial component of ocean pole tides
dln,dlt,drad = pyTMD.spatial.to_geodetic(
X + dxi[:,0], Y + dxi[:,1], Z + dxi[:,2],
a_axis=units.a_axis, flat=units.flat)
# calculate components of ocean pole tides
U = np.einsum('ti...,tji...->tj...', dxi, Rinv)
# reshape to output dimensions
Urad.data[:,:,i] = np.reshape(drad, (ny,nx))
Urad.data[:,:,i] = np.reshape(U[:,2], (ny,nx))
Urad.mask[:,:,i] = np.isnan(Urad.data[:,:,i])
elif (TYPE == 'drift'):
# calculate ocean pole tides in cartesian coordinates
Expand All @@ -1164,13 +1172,11 @@ def OPT_displacements(
g2=gamma,
convention=CONVENTION
)
# calculate radial component of ocean pole tides
dln,dlt,drad = pyTMD.spatial.to_geodetic(
X + dxi[:,0], Y + dxi[:,1], Z + dxi[:,2],
a_axis=units.a_axis, flat=units.flat)
# calculate components of ocean pole tides
U = np.einsum('ti...,tji...->tj...', dxi, Rinv)
# convert to masked array
Urad = np.ma.zeros((nt), fill_value=FILL_VALUE)
Urad.data[:] = drad.copy()
Urad.data[:] = U[:,2].copy()
Urad.mask = np.isnan(Urad.data)
elif (TYPE == 'time series'):
nstation = len(x)
Expand All @@ -1191,12 +1197,10 @@ def OPT_displacements(
g2=gamma,
convention=CONVENTION
)
# calculate radial component of ocean pole tides
dln,dlt,drad = pyTMD.spatial.to_geodetic(
X[s] + dxi[:,0], Y[s] + dxi[:,1], Z[s] + dxi[:,2],
a_axis=units.a_axis, flat=units.flat)
# calculate components of ocean pole tides
U = np.einsum('ti...,ji...->tj...', dxi, Rinv[s,:,:])
# reshape to output dimensions
Urad.data[s,:] = drad.copy()
Urad.data[s,:] = U[:,2].copy()
Urad.mask[s,:] = np.isnan(Urad.data[s,:])

# replace invalid data with fill values
Expand Down Expand Up @@ -1316,6 +1320,24 @@ def SET_displacements(
SX, SY, SZ = pyTMD.astro.solar_ecef(ts.MJD, ephemerides=EPHEMERIDES)
LX, LY, LZ = pyTMD.astro.lunar_ecef(ts.MJD, ephemerides=EPHEMERIDES)

# geocentric latitude (radians)
latitude_geocentric = np.arctan(Z / np.sqrt(X**2.0 + Y**2.0))
npts = len(latitude_geocentric)
# geocentric colatitude (radians)
theta = (np.pi/2.0 - latitude_geocentric)
# calculate longitude (radians)
phi = np.arctan2(Y, X)
# rotation matrix for converting from cartesian coordinates
R = np.zeros((npts, 3, 3))
R[:,0,0] = np.cos(phi)*np.cos(theta)
R[:,1,0] = -np.sin(phi)
R[:,2,0] = np.cos(phi)*np.sin(theta)
R[:,0,1] = np.sin(phi)*np.cos(theta)
R[:,1,1] = np.cos(phi)
R[:,2,1] = np.sin(phi)*np.sin(theta)
R[:,0,2] = -np.sin(theta)
R[:,2,2] = np.cos(theta)

# calculate radial displacement at time
if (TYPE == 'grid'):
ny,nx = np.shape(x)
Expand All @@ -1332,12 +1354,10 @@ def SET_displacements(
dxi = pyTMD.predict.solid_earth_tide(t,
XYZ, SXYZ, LXYZ, a_axis=units.a_axis,
tide_system=TIDE_SYSTEM)
# calculate radial component of solid earth tides
dln,dlt,drad = pyTMD.spatial.to_geodetic(
X + dxi[:,0], Y + dxi[:,1], Z + dxi[:,2],
a_axis=units.a_axis, flat=units.flat)
# calculate components of solid earth tides
SE = np.einsum('ti...,tji...->tj...', dxi, R)
# reshape to output dimensions
tide_se[:,:,i] = np.reshape(drad, (ny,nx))
tide_se[:,:,i] = np.reshape(SE[:,2], (ny,nx))
elif (TYPE == 'drift'):
# convert coordinates to column arrays
XYZ = np.c_[X, Y, Z]
Expand All @@ -1347,12 +1367,10 @@ def SET_displacements(
dxi = pyTMD.predict.solid_earth_tide(tide_time,
XYZ, SXYZ, LXYZ, a_axis=units.a_axis,
tide_system=TIDE_SYSTEM)
# calculate radial component of solid earth tides
dln,dlt,drad = pyTMD.spatial.to_geodetic(
X + dxi[:,0], Y + dxi[:,1], Z + dxi[:,2],
a_axis=units.a_axis, flat=units.flat)
# calculate components of solid earth tides
SE = np.einsum('ti...,tji...->tj...', dxi, R)
# reshape to output dimensions
tide_se = np.copy(drad)
tide_se = SE[:,2].copy()
elif (TYPE == 'time series'):
nstation = len(x)
tide_se = np.zeros((nstation,nt))
Expand All @@ -1366,12 +1384,10 @@ def SET_displacements(
dxi = pyTMD.predict.solid_earth_tide(tide_time,
XYZ, SXYZ, LXYZ, a_axis=units.a_axis,
tide_system=TIDE_SYSTEM)
# calculate radial component of solid earth tides
dln,dlt,drad = pyTMD.spatial.to_geodetic(
X[s] + dxi[:,0], Y[s] + dxi[:,1], Z[s] + dxi[:,2],
a_axis=units.a_axis, flat=units.flat)
# calculate components of solid earth tides
SE = np.einsum('ti...,ji...->tj...', dxi, R[s,:,:])
# reshape to output dimensions
tide_se[s,:] = np.copy(drad)
tide_se[s,:] = SE[:,2].copy()

# return the solid earth tide displacements
return tide_se
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