Monte Carlo Simulations

How does not knowing the aquifer turn into not knowing where the contamination goes?

What you’re watching A set of equally-likely conductivity realizations, each producing its own flow field and its own plume — same statistics, very different outcomes.

The mechanism Uncertainty propagates along a chain. Uncertainty in K creates uncertainty in the flow velocity field, which in turn creates uncertainty in the concentration. Each realization carries one plausible aquifer all the way through to one plausible plume.

Why it matters It is why a single deterministic plume prediction is misleading: the input (K) is uncertain, so the output (where the contamination is) must be uncertain too.

IGW-NET Generating realizations and running flow and transport through each, live, shows the propagation chain happen — the same uncertainty flowing from aquifer to velocity to plume in front of you.

How wide is the spread of possible plumes?

What you’re watching More realizations of the same problem; the plume’s position, shape, and reach vary dramatically from one equally-likely aquifer to the next.

The mechanism Because each realization routes the plume differently, the collection spans the range of what could happen. The wider that spread, the more the prediction depends on data we do not have.

Why it matters Seeing the full spread, rather than one plume, is what keeps a prediction honest about what is not known.

IGW-NET Watching realization after realization, each plausible and each different, builds the intuition that no single run is ‘the answer.’

How do we summarize hundreds of different plumes into one prediction — without drowning in data?

What you’re watching Top: the ensemble-mean plume, accumulated over hundreds of realizations — smooth and spread. Bottom: a single realization (here #340) — a concentrated, fingered channel. The average looks nothing like any individual plume.

The mechanism Monte Carlo runs many realizations and compiles their statistics — mean, variance, covariance. Crucially, IGW-NET computes these recursively: each new realization updates the running statistics on the fly, so it never has to store every plume at every time. This ‘scalable Monte Carlo’ makes thousands of runs feasible.

Why it matters Recursive accumulation is what makes large Monte Carlo studies practical — but note the catch: the statistics converge fast at first, then the last refinement is very slow, so ‘enough realizations’ takes more than intuition suggests.

IGW-NET Watching the running mean stabilize as realizations stream in — quickly at first, then crawling — shows scalable Monte Carlo working, and why patience is needed for the tail of the convergence.

Is the average plus a standard deviation enough to describe the risk?

What you’re watching Probability distributions sampled across many realizations: ln K and head are roughly bell-shaped, but the concentration PDFs at the monitoring wells are wildly skewed — a tall spike near zero with a long tail, and at one well two peaks (bimodal). The breakthrough curves fan out enormously, the mean curve resembling none of them.

The mechanism Uncertainty changes character as it propagates. ln K is nearly Gaussian and head often is too, but velocity, flux, and especially concentration are strongly skewed — sometimes to the left, sometimes to the right, sometimes bimodal. For such distributions the variance is a poor summary: mean ± standard deviation can describe a shape the variable never actually takes.

Why it matters Decisions hinge on the right question: not ‘what is the average concentration’ but ‘what is the probability concentration exceeds the MCL’ or ‘what is the probability the plume hits the well.’ Those come only from the full PDF — the variance-as-uncertainty habit can badly misstate the risk.

IGW-NET IGW-NET accumulates these full distributions recursively as realizations stream in, building probability-of-exceedance and capture-probability maps directly. The stable part of the distribution emerges fast; pinning down the tail — exactly the part that governs rare, high-consequence exceedance — is the slow last stretch.