Semi-analytical solutions for stream–aquifer interactions under triangular stream-stage variations and its application to study urbanization impacts in an ungaged watershed of south Texas

Simple yet physically based models to evaluate stream–aquifer interactions during a flooding event subject to triangular stream stage variation were developed in this study. The results from the developed models were compared with other analytical and numerical solutions and noted to be very accurate. The study fills an important gap with regard to available analytical and semi-analytical solutions for modeling stream–aquifer interactions, which can be used for evaluating numerical codes. In particular, the developed models are very useful to obtain preliminary insights with regard to bank storage in ungaged watersheds as required for watershed management and planning studies in rapidly urbanizing watersheds. The utility of the model is illustrated by applying it to study the effects of urbanization on stream–aquifer interactions in the Arroyo Colorado River Watershed along the US–Mexico border region. The results indicate that increased urbanization reduces the amount of influx into the banks. The reduction in flood passage time was noted to have a greater impact than the associated rise in stage. The presence of a semi-permeable barrier was seen to mask the effects of urbanization. The model results also implicitly highlight the importance of how water quality variations caused due to urbanization can affect stream–aquifer interactions.