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For each realization, particle transport is performed by resorting to the Monte Carlo simulation.
We randomly sample each PDF 5000 times at each time slice and scale each realization by its associated fingerprint.
Each realization undergoes large stretching up to failure, where force displacement curves and fracture surface energies are recorded.
The simulation procedure involves repeated realizations, where each realization in turn consists of the nucleation and growth of cells.
The total CO2 release is computed for each realization by summing the products of the simulated CO2 flux value at each grid cell by the cell surface.
Each realization of the time series was then interpolated to a regular 0.5 Myr spacing and LOESS curves were fitted to each interpolated realization using the programme R81.
Each realization was then interpolated to a regular 0.5 Myr spacing and a LOESS fit was performed with the degree of smoothing optimized by generalized cross-validation30.
Inset plots show frequency distributions of the slope and r2 derived from linear regressions carried out for each realization, indicating consistency in the relationship across the uncertainty range.
Daily rainfall time series are converted into streamflows by routing each realization of the synthetic ensemble through a conceptual hydrologic model, the Rio Grande rainfall-runoff model.
Furthermore, only 46,592 active computational elements are utilized in each realization to achieve these results for 12 decades of scaling behavior.
We jointly determine a first-order decay coefficient in each realization, leading to conditional statistical distributions of all estimated parameters and the total mass discharge.
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