Is there a general methodology to replicate the local spatial correlation structure of a spatial (2-D) field? If the results can be clearly got, how to describe the spatial variation of such field?
Can you explain what you mean by replicate? Do you want to simulate data with set amount of spatial autocorrelation?
Is this what you are after
https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html
https://www.researchgate.net/post/How_to_simulate_a_raster_with_clustered_spatial_autocorrelation
https://rpubs.com/jguelat/autocorr
Perhaps our work on the use of the short space Fourier transform to replicate the local correlation structure of precipitation fields might be relevant:
https://www.hydrol-earth-syst-sci.net/21/2777/2017/
There are also ways to achieve this using wavelet analysis and "autocorrelation wavelets", e.g.:
Eckley, I.A., Nason, G.P. and Treloar, R.L., 2010. Locally stationary wavelet fields with application to the modelling and analysis of image texture. Journal of the Royal Statistical Society: Series C (Applied Statistics), 59(4), pp.595-616.
I recently published some examples where a similar approach was applied to precipitation fields, here:
Scovell, R.W. (2020), Applications of Directional Wavelets, Universal Multifractals and Anisotropic Scaling in Ensemble Nowcasting; A Review of Methods with Case Studies. Q J R Meteorol Soc. Accepted Author Manuscript. doi:10.1002/qj.3780
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