This study evaluates the performance of physically-based and deep learning models in simulating runoff and estimating terrestrial water storage (TWS) in the Hablehroud River Basin, a semi-arid watershed in northern Iran with increasing irrigation demands. Two semi-distributed and physically-based models, including SWAT (Soil and Water Assessment Tool), VIC (Variable Infiltration Capacity), and lumped and semi-distributed configurations of Bidirectional Long Short-Term Memory (BLSTM-L and BLSTM-S), were applied using daily meteorological and hydrometric data. The GLEAM v4.2 (Global Land Evaporation Amsterdam Model) dataset was used to estimate evapotranspiration, and a water balance method was used to determine monthly TWS. The monthly TWS results from each model varied considerably, especially during the growing season, but the annual storage estimates from each model exhibited a similar bias. The BLSTM-S model showed excellent consistency in monthly TWS estimation and the highest accuracy in streamflow simulation (NSE = 0.87, KGE = 0.91). According to observational analysis, BLSTM-S best represented the seasonal pattern of water being withdrawn during the agricultural months and primarily stored in the winter and early spring (often as snow in mountainous regions). These results suggest that in areas affected by irrigation, monthly TWS is a more sensitive indicator of model performance. Although physically-based models offer process transparency, their higher monthly biases can reduce their reliability in short-term water allocation. The study highlights the added value of deep learning, particularly semi-distributed BLSTM, in improving both runoff simulation and seasonal water storage representation for operational water management.