Fig. 4: Summary of simulation results for a non-stationary distribution using the observed 30-year moving window gamma parameters from 11 Global Historical Climatology Network (GHCN) sites.
From: Drought assessment has been outpaced by climate change: empirical arguments for a paradigm shift

The Standardized Precipitation Index (SPI) was estimated by fitting a gamma distribution to random samples of differing lengths, with each random sample being generated by the observed moving window generative gamma distribution for each site. The absolute SPI error was then computed using the known SPI value from the known (observed 30-year moving window) distribution for the most recent observation (e.g. 2020, consistent with operational SPI calculations). A Detailed simulation results for GHCN site USC00381770 located at Clemson University in South Carolina for the 30-day SPI for August 1st. Black lines and gray ribbons represent the median [interquartile] value of the 1000 simulations. B Results for 10 additional GHCN sites for various geographical locations and 30-, 60- and 90-day timescales for August 1st. Gray shading represents the interquartile range for simulations at all sites for each timescale.