Please cite the publication and code DOI when you use this code
- Gilpin, S., Matsuo, T., Cohn, S.E. (2023). A generalized, compactly-supported correlation function for data assimilation applications. Q. J. Roy. Meteor. Soc., https://doi.org/10.1002/qj.4490
- Gilpin, S. _A Generalized Gaspari-Cohn (GenGC) Correlation Function.
The GenGC correlation function is a generalization of the compactly-supported, piecewise rational correlation function introduced by Gaspari and Cohn (1999) and the subsequent extension by Gaspari et al. (2016). The GenGC correlation function allows both parameters a and c to vary, as continous functions, over the domain to generate inhomogeneous and anisoptric correlation functions that remain compactly-supported.
This repository contains the Python code that implements the GenGC correlation function introduced in Gilpin et al. (2023). Two implementations of the GenGC correlation function are included: gengc.py that can be adapted to other languages such as Fortran, and gengc1d.py, an object-oriented version specific to constructing 1D correlations in Python. In addition, this repo contains the scripts to reproduce 1D examples in Sections 3 and 4 of Gilpin et al. (2023).
See requirements.txt for the additional Python packages and their versions needed to run these scripts.
Note: all Python scripts include comments that further detail their use.
gengc.py Standard implementation of the GenGC correlation function. This GenGC Python function as a matrix-vector operator that outputs the GenGC correlation matrix acting on an input vector z, which is a vector of scalars of the normed distance between grid cells. This version is not object-oriented is and can be adapted to other coding languages such as Fortran with minimal modifications.
gengc1d.py Object-oriented construction of the GenGC correlation function. This script is written specifically for Python to output the GenGC correlation function as a 2D numpy array. To optimize construction, two methods are implemented:
- Continuous form of GenGC, in which a and c are specified as continuous functions over the domain
- Piecewise constant form, in which at least one subdomain is larger than one grid cell and a and c are defined as piecewise constant functions. This script calls gengc_conv.py to evaluate the GenGC correlation function.
gengc_conv.py Explicit implementation of the GenGC correlation function that is used to construct correlation matrices in gengc1d.py. The coefficient tables in Tables 1-19 in Appendix C of Gilpin et al. (2023) are implemented here in a slightly different form than done in gengc.py.
run_examples.py Generates Figures 2, 4-6 from Gilpin et al. (2023) by running this script. Gives several examples of how to construct the GenGC correlation function using the gengc1d.py script.
Please see comments of the specific scripts to see how to use this function.