Table 4 Empirical mean \(\widehat{\mu }\), standard deviation \(\widehat{\sigma }\), skewness \(\widehat{s}\), kurtosis \(\widehat{k}\) and coefficient of variation \(\widehat{c_\mathrm{v}}\) estimated with \(10^6\) realizations of the surrogate models.
From: Uncertainty propagation in pore water chemical composition calculation using surrogate models
QoI | Small range case | Large range case | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
\(\widehat{\mu }\) | \(\widehat{\sigma }\) | \(\widehat{s}\) | \(\widehat{k}\) | \(\widehat{c_\mathrm{v}}\ [\%]\) | \(\widehat{\mu }\) | \(\widehat{\sigma }\) | \(\widehat{s}\) | \(\widehat{k}\) | \(\widehat{c_\mathrm{v}}\ [\%]\) | |
\(\mathrm{pH}\) | 7.17 | 0.20 | \(-0.004\) | 2.66 | 3 | 7.19 | 0.39 | \(-0.03\) | 2.68 | 5 |
\(\mathrm{pe}+\mathrm{pH}\) | 4.20 | \(6.13\cdot 10^{-2}\) | 0.043 | 2.79 | 1.5 | 4.20 | \(1.26\cdot 10^{-1}\) | 0.17 | 2.97 | 3 |
\({\mathrm{Na}}^{+}\) | \(4.29\cdot 10^{-2}\) | \(3.05\cdot 10^{-3}\) | 0.2 | 2.93 | 7 | \(4.43\cdot 10^{-2}\) | \(7.07\cdot 10^{-3}\) | 0.94 | 5.85 | 16 |
\({\mathrm{K}}^{+}\) | \(1.04\cdot 10^{-3}\) | \(2.50\cdot 10^{-4}\) | 0.38 | 2.27 | 24 | \(1.17\cdot 10^{-3}\) | \(5.75\cdot 10^{-4}\) | 0.92 | 3.85 | 49 |
\({\mathrm{Ca}}^{2+}\) | \(8.46\cdot 10^{-3}\) | \(2.21\cdot 10^{-3}\) | 0.52 | 3.16 | 26 | \(9.33\cdot 10^{-3}\) | \(4.80\cdot 10^{-3}\) | 1.48 | 7.89 | 51 |
\({\mathrm{Mg}}^{2+}\) | \(5.91\cdot 10^{-3}\) | \(2.14\cdot 10^{-3}\) | 0.62 | 3.13 | 36 | \(6.68\cdot 10^{-3}\) | \(5.06\cdot 10^{-3}\) | 2.61 | 21.0 | 76 |
\({\mathrm{Sr}}^{2+}\) | \(2.10\cdot 10^{-4}\) | \(2.87\cdot 10^{-5}\) | 0.45 | 3.08 | 14 | \(2.17\cdot 10^{-4}\) | \(6.42\cdot 10^{-5}\) | 1.05 | 4.95 | 30 |
\(\mathrm{Fe}\) | \(4.59\cdot 10^{-5}\) | \(5.48\cdot 10^{-5}\) | 3.33 | 20.0 | 119 | \(1.85\cdot 10^{-4}\) | \(6.99\cdot 10^{-4}\) | 13.1 | 319.0 | 378 |
\(\mathrm{Si}\) | \(1.83\cdot 10^{-4}\) | \(2.11\cdot 10^{-5}\) | 0.14 | 1.83 | 12 | \(1.87\cdot 10^{-4}\) | \(4.29\cdot 10^{-5}\) | 0.28 | 1.89 | 23 |
\(\mathrm{Al}\) | \(9.34\cdot 10^{-8}\) | \(5.25\cdot 10^{-8}\) | 1.05 | 3.83 | 56 | \(1.55\cdot 10^{-7}\) | \(1.83\cdot 10^{-7}\) | 2.38 | 10.9 | 117 |
\(\mathrm{S(VI)}\) | \(1.46\cdot 10^{-2}\) | \(3.00\cdot 10^{-3}\) | 0.32 | 2.84 | 21 | \(1.66\cdot 10^{-2}\) | \(8.63\cdot 10^{-3}\) | 2.43 | 18.3 | 52 |
\(\mathrm{S(-II)}\) | \(7.50\cdot 10^{-10}\) | \(3.93\cdot 10^{-10}\) | 1.80 | 8.15 | 52 | \(1.31\cdot 10^{-9}\) | \(1.84\cdot 10^{-9}\) | 5.65 | 62.2 | 141 |
\({\mathrm{log}}_{10}\,{\mathrm{p}}_{{\mathrm{CO}}_2}\) | \(-2.07\) | 0.41 | \(-0.014\) | 2.66 | \(-20\) | \(-2.11\) | 0.79 | \(-0.058\) | 2.62 | \(-38\) |
