Abstract
The reconstruction of hydro-stratigraphic units in subsoil (a general term indicating all the materials below ground level) plays an important role in the assessment of soil heterogeneity, which is a keystone in groundwater flow and transport modeling. A geostatistical approach appears to be a good way to reconstruct subsoil, and now other methods besides the classical indicator (co)kriging are available as alternative approximations of the conditional probabilities. Some of these techniques take specifically into account categorical variables as lithologies, but they are computationally prohibitive. Moreover, the stage before subsoil prediction/simulation can be very informative from a hydro-stratigraphic point of view, as the detailed transiogram analysis of this paper demonstrates. In this context, an application of the spMC package for the R software is presented by using a test site located within the Venetian alluvial plain (NE Italy). First, a detailed transiogram analysis was conducted, and then a maximum entropy approach, based on transition probabilities, named Markovian-type Categorical Prediction (MCP), was applied to approximate the posterior conditional probabilities. The study highlights some advantages of the presented approach in term of hydrogeological knowledge and computational efficiency. The spMC package couples transiogram analysis with a maximum entropy approach by taking advantage of High-Performance Computing (HPC) techniques. These characteristics make the spMC package useful for simulating hydro-stratigraphic units in subsoil, despite the use of a large number of lithologies (categories). The results obtained by spMC package suggest that this software should be considered a good candidate for simulating subsoil lithological distributions, especially of limited areas.
Highlights
How to approach predictions/simulations by geostatistical methods in hydrostatigraphy is a still open question [1,2,3,4,5,6,7,8], since the assessment of the subsoil heterogeneity is one of the keystones in groundwater flow and transport modeling
From the West to the East, we can observe the hydrographical system of Leogra Timonchio, Astico Bacchiglione, Brenta and Piave; these rivers have deposited a huge amount of loose materials, forming the subsoil of the Venetian Plain
Simulation Results by means of the Markovian-type Categorical Prediction (MCP) algorithm. This algorithm is implemented in the spMC package and uses a
Summary
How to approach predictions/simulations by geostatistical methods in hydrostatigraphy is a still open question [1,2,3,4,5,6,7,8], since the assessment of the subsoil heterogeneity is one of the keystones in groundwater flow and transport modeling. The most well-known lithological prediction/simulation in classical geostatistics is based on indicator kriging [14,15,16] This approach is very frequent in the literature, due to the availability of open-source programs, there are some intrinsic probabilistic inconsistencies typical of indicator. Hydrology 2020, 7, 15 kriging: the sum of occurrence is not exactly one, the probabilities are not guaranteed to be between zero and one and the cumulative distribution functions may not increase monotonically. These issues are well known in the literature as the “order relation problem” [1]. A post-processing of the conditional probabilities is frequently needed [17]
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