Complex groundwater flow systems as traveling agent models

TL;DR

This paper demonstrates that complex groundwater flow systems exhibit 1/f power spectrum behavior, which can be modeled using traveling agent models that account for medium complexity and require non-Kolmogorovian probability frameworks.

Contribution

It introduces a novel agent-based model to explain complex groundwater flow dynamics and derives new PDEs, highlighting the role of medium complexity and non-classical probabilities.

Findings

Groundwater flow exhibits 1/f power spectrum.

Traveling agent model reproduces complex dynamics.

Non-Kolmogorovian probability is necessary for analysis.

Abstract

Analyzing field data from pumping tests, we show that as with many other natural phenomena, groundwater flow exhibits a complex dynamics described by 1/f power spectrum. This result is theoretically studied within an agent perspective. Using a traveling agent model, we prove that this statistical behavior emerges when the medium is complex. Some heuristic reasoning is provided to justify both spatial and dynamic complexity, as the result of the superposition of an infinite number of stochastic processes. Even more, we show that this implies that non-Kolmogorovian probability is needed for its study, and provide a set of new partial differential equations for groundwater flow.