Markovian transport processes in a heterogeneous, variably saturated watershed: A multi-domain spatial Markov model

Abstract

Transport processes in watersheds remain challenging to describe accurately with upscaled models because of their intricate complexities at multiple scales that can lead to multi-modal, non-Fickian breakthrough curves. One of the recent advances in solute transport modeling has been the Lagrangian spatial Markov model (SMM), which describes transport using velocity increments and models the correlated transitions between them. The approach has been applied previously to saturated porous media and fractured media, but these successful applications suggest it may be useful for describing watershed scale processes as well. An existing, 3-D, heterogeneous variably saturated model of a headwaters catchment and classical random walk particle tracking were used to generate a forward simulation and the resulting transport was analyzed with a spatial Markov framework. Existing SMM methods were used to analyze the transport paths through the complex, unconfined domain and we found that the vadose zone plays an important role in the correlation structure. As such, a new kind of SMM is proposed, termed a multi-domain SMM (MD-SMM), that uses separate correlation models for auto-transitions in the vadose zone and the saturated zone, and for the cross-transitions between them. The MD-SMM improves representation of transport relative to the single domain model and can naturally delineate times when a particle is in the vadose zone or the saturated zone, adding an additional degree of realism to the upscaled model. Finally, we show that the transition probability matrix for transport in the saturated portion of this unconfined system is approximately Markovian, which is an important validation of the proposed framework.