The RUSLE is a purely deterministic model in which the product of physical measures is used to derive the amount of soil loss, a rigorous assessment of uncertainties is not feasible, especially for a large-scale estimation. In the article “An assessment of the global impact of 21st century land use change on soil erosion” published on “Nature Communication” in 2017, the authors proposed a method based on the Markov Chain Monte Carlo (MCMC) algorithm in the “Supplementary Note 4 Uncertainty analysis”, but I need more understandings about this process.

As mentioned, “each of the input layers was treated as a spatial random field defined in terms of expectation and covariance”, and “different simulation is created in the random field based on Gibbs sampling”. Here, how to understand “a spatial random field”? Does it mean that each input layer has one expectation and one covariance, or each pixel has one expectation and one covariance, or other meanings? Is the Gibbs sampling applied in spatial fields to get a series of samples to determine the prior distribution of the input layer in some spatial ranges? We saw that the uncertainty (that is, SD) is spatially explicit in “Supplementary Fig. 8”, what determines the uncertainty of each pixel? Is there any relationship between the realization of the input layers and the uncertainty of RUSLE model in each pixel? To which resolution and by which means can we determine the prior distribution of each input layer?