Effects Of Multiscale Heterogeneity | MAGNET4WATER Curriculum

01 3 Scales of Heterogeneity

What does real-world heterogeneity look like when you keep zooming in?

What you’re watching The same aquifer at one, two, and three nested scales of heterogeneity: with one scale (top) only broad, smooth patches and a compact plume; with two scales (middle) intermediate patches embedded in the large ones and a more fingered plume; with three scales (bottom) fine texture nested inside the intermediate structure and a plume shredded into many channels.

The mechanism Real K fields are nested: large-scale structures contain intermediate-scale ones, which contain small-scale ones — heterogeneity within heterogeneity. A large plume samples all the scales at once, so each added scale carves the plume into finer fingers and spreads it further.

Key relationshipReal heterogeneity is nested — smaller-scale variability embedded within larger — and each scale a plume encounters adds another layer of fingering and spreading.

Why it matters This is the reality of field sites: with major effort you might characterize heterogeneity down to a scale of tens of meters — which still looks largely random — yet within each pocket, given enough data, there is another nested layer of finer structure. Characterizing one scale never tells the whole story, because finer and coarser structure are always also at work on the plume.

IGW-NET Adding scales one at a time and watching the plume go from compact to shredded makes nested heterogeneity — usually invisible — something you can see build up.

02 Macrodispersion w/ Multiscale Heterogeneity

Why does a plume seem to disperse faster the farther — and longer — it travels?

What you’re watching A plume spreading through multiscale heterogeneity, its apparent dispersion growing as it moves, because it progressively encounters ever-larger structures.

The mechanism With nested scales, a small plume first feels only the small-scale variability; as it grows it begins sampling the intermediate and then the large scales. So the apparent (macro)dispersivity keeps increasing with travel distance and time — the scale-dependent dispersivity seen in the field, here arising directly from nested structure.

Key relationshipNested scales produce scale-dependent dispersivity — apparent spreading grows as the plume samples progressively larger structures.

Why it matters It explains one of the field’s most persistent puzzles — why measured dispersivity grows with the scale of the experiment — and warns that a single dispersivity calibrated at one scale will not hold at another.

IGW-NET Watching the spreading rate climb as the plume reaches into larger structures turns scale-dependent dispersivity from a curve in a paper into a process you observe.

03 1 Scale vs 2 Scales

What does adding an intermediate scale actually change?

What you’re watching A direct comparison of transport with one scale of heterogeneity versus two; the two-scale plume is visibly more fingered and spread, even though the large-scale structure is the same.

The mechanism Adding an intermediate scale superimposes medium-sized high- and low-K patches on the large-scale pattern. These create new preferential paths and traps the single-scale field lacked, so the plume channels and spreads more.

Key relationshipAdding a scale adds structure — more channeling, more trapping, more spreading than the coarser field alone.

Why it matters It shows that resolving only the large scale systematically underpredicts spreading — the missing finer scale matters.

IGW-NET Running one- and two-scale fields side by side isolates exactly what the intermediate scale contributes.

04 2 Scales vs 3 Scales

Does the smallest scale behave the same on its own as it does nested inside the others?

What you’re watching A comparison of two-scale and three-scale fields; adding the third (smallest) scale does not just sprinkle in fine texture — it interacts with the intermediate structure, changing where the plume channels and traps in ways the small scale alone would not predict.

The mechanism The scales are not independent. The effect of small-scale heterogeneity depends on the intermediate structure it is embedded in — a small-scale feature inside a high-K intermediate zone routes the plume differently than the same feature in a low-K zone. The combined behavior is more than the sum of the scales taken separately.

Key relationshipScales interact — small-scale heterogeneity behaves differently embedded in an intermediate scale than it does alone.

Why it matters It means you cannot characterize each scale in isolation and simply add them; the nesting itself shapes transport, which is why partial characterization can still mislead.

IGW-NET Comparing the two- and three-scale runs reveals the interaction directly — the simulation shows that the three scales together do something none of them does alone, an insight very hard to reach any other way.