Virtual Library of Simulation Experiments:

Test Functions and Datasets

MARTHE Dataset


Input dimensions: 20

Output dimensions: 10

Observations: 300

The MARTHE dataset consists of realizations of the MARTHE code (developed by BRGM, the French Geological Survey), which provides a numerical simulation of Strontium-90 transport in the upper aquifer of the RRC "Kurchatov Institute" radwaste disposal site in Moscow, Russia (Volkova et al., 2008). The computer code is no longer accessible.

The dataset can be used for testing methods of uncertainty propagation and global sensitivity analysis. There are 20 uncertain input parameters in the model, and the outputs of interest are restricted to the contaminant concentrations at 10 observation wells, labelled:
p102K, p104, p106, p2.76, p29K, p31K, p35K, p37K, p38, and p4b.

The data has been obtained from the webpage "Benchmark Proposals of GdR MASCOT-NUM" (retrieved April 2014).

Input Distributions:

The input random variables and their distributions are:

per1 ~ Uniform[1, 15] hydraulic conductivity layer 1
per2 ~ Uniform[5, 20] hydraulic conductivity layer 2
per3 ~ Uniform[1, 15] hydraulic conductivity layer 3
perz1 ~ Uniform[1, 15] hydraulic conductivity zone 1
perz2 ~ Uniform[1, 15] hydraulic conductivity zone 2
perz3 ~ Uniform[1, 15] hydraulic conductivity zone 3
perz4 ~ Uniform[1, 15] hydraulic conductivity zone 4
d1 ~ Uniform[0.05, 2] longitudinal dispersivity layer 1
d2 ~ Uniform[0.05, 2] longitudinal dispersivity layer 2
d3 ~ Uniform[0.05, 2] longitudinal dispersivity layer 3
dt1 ~ Uniform[0.01*d1, 0.1*d1] transversal dispersivity layer 1
dt2 ~ Uniform[0.01*d2, 0.1*d2] transversal dispersivity layer 2
dt3 ~ Uniform[0.01*d3, 0.1*d3] transversal dispersivity layer 3
kd1 ~ Weibull(α=1.1597, β=19.9875) volumetric distribution coefficient 1.1
kd2 ~ Weibull(α=0.891597, β=24.4455)    volumetric distribution coefficient 1.2
kd3 ~ Weibull(α=1.27363, β=22.4986) volumetric distribution coefficient 1.3
poros ~ Uniform[0.3, 0.37] porosity
i1 ~ Uniform[0, 0.0001] infiltration type 1
i2 ~ Uniform[i1, 0.01] infiltration type 2
i3 ~ Uniform[i2, 0.1] infiltration type 3

Above, the Weibull law used is:
where α is the shape parameter, and β is the scale parameter.

Data File Description:

The first 20 columns of the dataset below consist of the input values, and the last 10 columns are the corresponding output values.



Benchmark Proposals of GdR MASCOT-NUM. Retrieved April 2014, from

Marrel, A., Iooss, B., Van Dorpe, F., & Volkova, E. (2008). An efficient methodology for modeling complex computer codes with Gaussian processes. Computational Statistics and Data Analysis, 52, 4731-4744.

Volkova, E., Iooss, B., & Van Dorpe, F. (2008). Global sensitivity analysis for a numerical model of radionuclide migration from the "RRC" Kurchatov Institute radwaste disposal site. Stochastic Environmental Research and Risk Assessment, 22, 17-31.

For questions or comments, please email Derek Bingham at: