feat: add harmonic resolution calculator (#44)

increase version number

Author: tsutterley

doc/source/index.rst

@@ -99,6 +99,7 @@ missions
     user_guide/aod1b_geocenter.md
     user_guide/aod1b_oblateness.md
     user_guide/calc_mascon.rst
+    user_guide/calc_harmonic_resolution.rst
     user_guide/calc_sensitivity_kernel.rst
     user_guide/combine_harmonics.rst
     user_guide/convert_harmonics.rst

doc/source/user_guide/calc_harmonic_resolution.rst

@@ -0,0 +1,33 @@
+===========================
+calc_harmonic_resolution.py
+===========================
+
+- Calculates the spatial resolution that can be resolved by the spherical harmonics of a certain degree [Barthelmes2013]_ [HofmannWellenhof2006]_
+- Default method uses the smallest half-wavelength that can be resolved
+- Secondary method calculates the smallest possible bump that can be resolved
+
+Calling Sequence
+################
+
+.. code-block:: bash
+
+     python calc_harmonic_resolution --lmax 60 --cap
+
+`Source code`__
+
+.. __: https://github.com/tsutterley/read-GRACE-harmonics/blob/main/scripts/calc_harmonic_resolution.py
+
+Command Line Options
+####################
+
+- ``--help``: list the command line options
+- ``-l X``, ``--lmax X``: maximum spherical harmonic degree
+- ``-R X``, ``--radius X``: Average radius of the Earth (km)
+- ``-C``, ``--cap``: Calculate the smallest possible bump that can be resolved
+
+References
+##########
+
+.. [Barthelmes2013] F. Barthelmes, "Definition of Functionals of the Geopotential and Their Calculation from Spherical Harmonic Models", GeoForschungsZentrum Scientific Technical Report, STR09/02, (2013). `doi: 10.2312/GFZ.b103-0902-26 <https://doi.org/10.2312/GFZ.b103-0902-26>`_
+
+.. [HofmannWellenhof2006] B. Hofmann-Wellenhof and H. Moritz, *Physical Geodesy*, 2nd Edition, 403 pp., (2006). `doi: 10.1007/978-3-211-33545-1 <https://doi.org/10.1007/978-3-211-33545-1>`_

scripts/calc_harmonic_resolution.py

@@ -0,0 +1,92 @@
+#!/usr/bin/env python
+u"""
+calc_harmonic_resolution.py
+Written by Tyler Sutterley (09/2020)
+
+Calculates the spatial resolution that can be resolved
+    by the spherical harmonics of a certain degree
+Default method uses the smallest half-wavelength that can be resolved
+    (is equal to approximately 20000/lmax km)
+Secondary method calculates the smallest possible bump that can be resolved
+    by dividing the area of a sphere by (lmax+1)^2
+
+CALLING SEQUENCE:
+    python calc_harmonic_resolution.py --lmax 60 --cap
+
+COMMAND LINE OPTIONS:
+    -l X, --lmax X: maximum degree of spherical harmonics
+    -R X, --radius X: average radius of the Earth in kilometers
+    -C, --cap: calculate the smallest possible bump that can be resolved
+
+PYTHON DEPENDENCIES:
+    numpy: Scientific Computing Tools For Python (https://numpy.org)
+
+REFERENCES:
+    Hofmann-Wellenhof and Moritz, "Physical Geodesy" (2005)
+        http://www.springerlink.com/content/978-3-211-33544-4
+    Barthelmes, "Definition of Functionals of the Geopotential and Their
+        Calculation from Spherical Harmonic Models", STR09/02 (2009)
+        http://icgem.gfz-potsdam.de/str-0902-revised.pdf
+
+UPDATE HISTORY:
+    Updated 09/2020: using argparse to set parameters
+    Updated 10/2019: changing Y/N flags to True/False
+    Updated 02/2014: minor update to if statement
+    Updated 08/2013: changed SPH_CAP option to (Y/N)
+    Written 01/2013
+"""
+import sys
+import argparse
+import numpy as np
+
+#-- PURPOSE: Calculates minimum spatial resolution that can be resolved
+#-- from spherical harmonics of a maximum degree
+def calc_harmonic_resolution(LMAX, RADIUS=6371.0008, SPH_CAP=False):
+    """
+    Calculates minimum spatial resolution that can be resolved from
+        spherical harmonics of a maximum degree
+        
+    Arguments
+    ---------
+    LMAX: maximum spherical harmonic degree
+
+    Keyword arguments
+    -----------------
+    RADIUS: average radius of the Earth in kilometers
+    SPH_CAP: calculate the smallest possible bump that can be resolved
+    """
+    if SPH_CAP:
+        # Smallest diameter of a spherical cap that can be resolved by the
+        # harmonics.  Size of the smallest bump, half-wavelength, which can
+        # be produced by the clm/slm
+        psi_min = 4.0*RADIUS*np.arcsin(1.0/(LMAX+1.0))
+    else:
+        # Shortest half-wavelength that can be resolved by the clm/slm
+        # This estimation is based on the number of possible zeros along
+        # the equator
+        psi_min = np.pi*RADIUS/LMAX
+    return psi_min
+
+# Main program that calls calc_harmonic_resolution()
+def main():
+    # Read the system arguments listed after the program
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--lmax','-l', metavar='LMAX',
+        type=int, nargs='+',
+        help='maximum degree of spherical harmonics')
+    parser.add_argument('--radius','-R',
+        type=float, default=6371.0008,
+        help='Average radius of the Earth in kilometers')
+    parser.add_argument('--cap','-C',
+        default=False, action='store_true',
+        help='Calculate smallest possible bump that can be resolved')
+    args,_ = parser.parse_known_args()
+    # for each entered spherical harmonic degree
+    for LMAX in args.lmax:
+        psi_min = calc_harmonic_resolution(LMAX,
+            RADIUS=args.radius, SPH_CAP=args.cap)
+        print('{0:5d}: {1:0.4f} km'.format(LMAX,psi_min))
+
+# run main program
+if __name__ == '__main__':
+    main()

version.txt

@@ -1 +1 @@
-1.0.1.23
+1.0.2.0