Preprints
https://doi.org/10.31223/X5ND5B
https://doi.org/10.31223/X5ND5B
17 Jun 2024
 | 17 Jun 2024
Status: this preprint is open for discussion.

Ensemble modeling of the two-dimensional stochastic confined groundwater flow through the evolution of the hydraulic head's probability density function

Joaquin Meza and M. Levent Kavvas

Abstract. Groundwater storage in aquifers has become a vital water source due to water scarcity in recent years. However, aquifer systems are full of uncertainties, which inevitably propagate throughout the modeling computations, mainly reducing the reliability of the model output. This study develops a novel two-dimensional stochastic confined groundwater flow model. The proposed model is developed by linking the stochastic governing partial differential equations by means of their one-to- one correspondence to the nonlocal Lagrangian-Eulerian extension to the Fokker-Planck equation (LEFPE). In the form of the LEFPE, the resulting deterministic governing equation describes the spatio-temporal evolution of the probability density function of the state variables in the confined groundwater flow process by one single numerical realization instead of requiring thousands of simulations in the Monte Carlo approach. Consequently, the ensemble groundwater flow process's mean and standard deviation behavior can be modeled under uncertainty in the transmissivity field and recharge and/or pumping conditions. In addition, an appropriate numerical method for LEFPE's solution is subsequently devised. Then, its solution is presented, discussed, and illustrated through a numerical example, which is compared against the results obtained by means of the Monte Carlo simulations. Results suggest that the proposed model appropriately characterizes the ensemble behavior in confined groundwater systems under uncertainty in the transmissivity field.

Joaquin Meza and M. Levent Kavvas

Status: open (until 22 Aug 2024)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
Joaquin Meza and M. Levent Kavvas
Joaquin Meza and M. Levent Kavvas

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Short summary
Our study develops a new model to study groundwater flow under uncertainty, using mathematical techniques to improve accuracy and efficiency. This approach allows for better management of water resources, particularly in drought-prone areas, by providing more reliable groundwater availability and movement estimations. This research combines traditional techniques with innovative methods to address water scarcity and support sustainable water use.