Mathematical Modelling of Surface-Groundwater Interactions under Varying Hydrological Conditions: Review of Past Works

Surface-groundwater interaction is a research area of significant importance for its central role in wastewater treatment, irrigation, drainage, flood control, erosion and sediment control. Mathematical models are often used for the estimation of surface-groundwater interactions under the variety of hydrological conditions. Due to cost effectiveness and ability to accommodate variations in aquifer parameters, mathematical models have gained immense importance in the past few decades. The objective of this review paper is to portray the contribution of the hydrologist towards the growing area of surface-ground water interaction from all over the world who proposed, analyzed, executed and validated the developed Mathematical models. To begin with, we briefly introduce the main mathematical equations that govern the flow of groundwater in unconfined and confined aquifer systems. The development of stream-aquifer models is presented in a chronological order to provide a clear understanding of the contributions of past works. The methodology used in the past work is adequately discussed without going into mathematical details. Furthermore, we also summarize recent developments concerning groundwater flow in presence of vertical streambed, partial penetration, stream-stage variations and multiple recharge/discharge basins.