Thiel-Sen trend analysis for geospatial data fields

Thiel-Sen slope estimator and Mann-Kendall statistics for geospatial data fields

The non-parametric trend analysis estimates monotonic trends for each pixel in a three-dimensional input field (x,y,time) using the Theil–Sen median slope estimator (Theil, 1950; Sen, 1968) and provides complementary Mann–Kendall statistics (Mann, 1945; Kendall, 1975; Gilbert, 1987). Missing values (NaNs) are handled, but there must be at least two valid time points per pixel. Value ties (identical y-values at different times) are handled using the standard Mann–Kendall tie-adjustment for S, but duplicate time stamps are not supported.

Note: tsmk3D does not support irregular time intervals, such cases will produce incorrect slopes.

Author info and references:

The tsmk3D function was written by F. Werner, adapted from C. A. Greene's mann_kendall function (https://de.mathworks.com/matlabcentral/fileexchange/70338-climate-data-toolbox-for-matlab)

Theil, H. (1950). A rank-invariant method of linear and polynomial regression analysis. Indagationes mathematicae, 12(85), 173.

Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall's tau. Journal of the American statistical association, 63(324), 1379-1389.

Mann, H. B. (1945). Nonparametric tests against trend. Econometrica: Journal of the econometric society, 245-259.

Kendall, M. G. (1948). Rank correlation methods.

Gilbert, R. O. (1987). Statistical methods for environmental pollution monitoring. John Wiley & Sons.