feat: add calculation of zenith angle

doc/source/api_reference/spatial.rst

@@ -99,4 +99,6 @@ General Methods
 
 .. autofunction:: pyTMD.spatial.to_horizontal
 
+.. autofunction:: pyTMD.spatial.to_zenith
+
 .. autofunction:: pyTMD.spatial.scale_factors

pyTMD/math.py

@@ -26,7 +26,10 @@
 ]
 
 # PURPOSE: calculate the sum of a polynomial function of time
-def polynomial_sum(coefficients: list | np.ndarray, t: np.ndarray):
+def polynomial_sum(
+        coefficients: list | np.ndarray,
+        t: np.ndarray
+    ):
     """
     Calculates the sum of a polynomial function using Horner's method [1]_
 
@@ -48,7 +51,10 @@ def polynomial_sum(coefficients: list | np.ndarray, t: np.ndarray):
     t = np.atleast_1d(t)
     return np.sum([c * (t ** i) for i, c in enumerate(coefficients)], axis=0)
 
-def normalize_angle(theta: float | np.ndarray, circle: float = 360.0):
+def normalize_angle(
+        theta: float | np.ndarray,
+        circle: float = 360.0
+    ):
     """
     Normalize an angle to a single rotation
 
@@ -61,15 +67,18 @@ def normalize_angle(theta: float | np.ndarray, circle: float = 360.0):
     """
     return np.mod(theta, circle)
 
-def rotate(theta: float | np.ndarray, axis: str = 'x'):
+def rotate(
+        theta: float | np.ndarray,
+        axis: str = 'x'
+    ):
     """
     Rotate a 3-dimensional matrix about a given axis
 
     Parameters
     ----------
     theta: float or np.ndarray
         Angle of rotation in radians
-    axis: str
+    axis: str, default 'x'
         Axis of rotation (``'x'``, ``'y'``, or ``'z'``)
     """
     # allocate for output rotation matrix
@@ -112,13 +121,13 @@ def legendre(
     Parameters
     ----------
     l: int
-        degree of Legrendre polynomials (0 to 3)
+        degree of the Legrendre polynomials (0 to 3)
     x: np.ndarray
         elements ranging from -1 to 1
 
         Typically ``cos(theta)``, where ``theta`` is the colatitude in radians
-    m: int, default = 0
-        order of the Legendre polynomial
+    m: int, default 0
+        order of the Legendre polynomials (0 to ``l``)
 
     Returns
     -------
@@ -183,13 +192,13 @@ def sph_harm(
     Parameters
     ----------
     l: int
-        degree of spherical harmonics (0 to 3)
+        degree of the spherical harmonics (0 to 3)
     theta: np.ndarray
         colatitude in radians
     phi: np.ndarray
         longitude in radians
     m: int, default 0
-        order of the spherical harmonics (0 to l)
+        order of the spherical harmonics (0 to ``l``)
 
     Returns
     -------

pyTMD/spatial.py

@@ -157,6 +157,7 @@
     "to_ENU",
     "from_ENU",
     "to_horizontal",
+    "to_zenith",
     "scale_areas",
     "scale_factors",
 ]
@@ -2193,6 +2194,54 @@ def to_horizontal(
     phi = np.mod(np.arctan2(E/D, N/D)*180.0/np.pi, 360.0)
     return (alpha, phi, D)
 
+def to_zenith(
+        x: np.ndarray,
+        y: np.ndarray,
+        z: np.ndarray,
+        lon0: float | np.ndarray = 0.0,
+        lat0: float | np.ndarray = 0.0,
+        h0: float | np.ndarray = 0.0,
+        a_axis: float = _wgs84.a_axis,
+        flat: float = _wgs84.flat,
+    ):
+    """
+    Calculate zenith angle of an object from Earth-Centered
+    Earth-Fixed (ECEF) cartesian coordinates
+
+    Parameters
+    ----------
+    x, np.ndarray
+        cartesian x-coordinates
+    y, np.ndarray
+        cartesian y-coordinates
+    z, np.ndarray
+        cartesian z-coordinates
+    lon0: float or np.ndarray, default 0.0
+        reference longitude (degrees east)
+    lat0: float or np.ndarray, default 0.0
+        reference latitude (degrees north)
+    h0: float or np.ndarray, default 0.0
+        reference height (meters)
+    a_axis: float, default 6378137.0
+        semimajor axis of the ellipsoid
+    flat: float, default 1.0/298.257223563
+        ellipsoidal flattening
+
+    Returns
+    -------
+    zenith: np.ndarray
+        zenith angle of object in degrees
+    """
+    # convert from ECEF to ENU
+    E, N, U = to_ENU(x, y, z, lon0=lon0, lat0=lat0, h0=h0,
+        a_axis=a_axis, flat=flat)
+    # convert from ENU to horizontal coordinates
+    alpha, phi, D = to_horizontal(E, N, U)
+    # calculate zenith angle in degrees
+    zenith = 90.0 - alpha
+    # return zenith angle
+    return zenith
+
 def scale_areas(*args, **kwargs):
     warnings.warn("Deprecated. Please use pyTMD.spatial.scale_factors instead",
         DeprecationWarning)

test/test_spatial.py

@@ -478,9 +478,20 @@ def test_ECEF_to_horizontal():
     # convert from ENU to horizontal coordinates
     salt, saz, sdist = pyTMD.spatial.to_horizontal(SE, SN, SU)
     lalt, laz, ldist = pyTMD.spatial.to_horizontal(LE, LN, LU)
+    # calculate zenith angle from ECEF coordinates
+    solar_zenith = pyTMD.spatial.to_zenith(SX, SY, SZ,
+        lon0=lon0, lat0=lat0, h0=h0)
+    lunar_zenith = pyTMD.spatial.to_zenith(LX, LY, LZ,
+        lon0=lon0, lat0=lat0, h0=h0)
     # check solar azimuth and elevation
     assert np.isclose(salt, -5.486, atol=0.001)
     assert np.isclose(saz, 115.320, atol=0.001)
     # check lunar azimuth and elevation
     assert np.isclose(lalt, 36.381, atol=0.001)
     assert np.isclose(laz, 156.297, atol=0.001)
+    # check solar and lunar zenith angles
+    assert np.isclose(solar_zenith, 95.486, atol=0.001)
+    assert np.isclose(lunar_zenith, 53.619, atol=0.001)
+    # verify relation between altitudes and zenith angles
+    assert solar_zenith == (90.0 - salt)
+    assert lunar_zenith == (90.0 - lalt)