Modelling spatial uncertainty of soil erodibility factor using joint stochastic simulation

Soil erosion varies greatly over space and is commonly estimated using the revised universal soil loss equation (RUSLE).
Neglecting information about estimation uncertainty, however, may lead to improper decision-making. One geostatistical
approach to spatial analysis is joint stochastic simulation, which draws alternative, equally probable, joint realizations of a
regionalized variable. Differences between the realizations provide a measure of spatial uncertainty and allow us to carry out an
error propagation analysis.
The objective of this paper was to assess spatial uncertainty of a soil erodibility factor (K) model resulting from the
uncertainties in the input parameters (texture and organic matter). The 500 km2 study area was located in central-eastern Sardinia
(Italy) and 152 samples were collected. A Monte Carlo analysis was performed where spatial cross-correlation information
through joint turning bands simulation was incorporated. A linear coregionalization model was fitted to all direct and
cross-variograms of the input variables, which included three different structures: a nugget effect, a spherical structure with
a shorter range (3500 m) and a spherical structure with a longer range (10 000 m). The K factor was then estimated for each set of
the 500 joint realizations of the input variables, and the ensemble of the model outputs was used to infer the soil erodibility
probability distribution function. This approach permitted delineation of the areas characterized by greater uncertainty, to
improve supplementary sampling strategies and K value predictions.