Inverse modeling is presented and applied to the computation of groundwater inflow in a shallow aquifer (the Alsace aquifer, west of the Rhine River, France) by separating pressure head variations into three components: recharge from rainfall, and exchanges with surface water in the Rhine River and in tributaries flowing out of the Vosges Mountains. The point estimates are interpolated for the whole aquifer to visualize the proportion of contribution and the response times. To represent the surface water/groundwater exchange, this method uses directly observed data of streamflow, precipitation, and pressure head without requiring either spatial description of the hydrosystem or knowledge of the boundary conditions on both sides of the Rhine (the border between France and Germany). Several zones of the aquifer are shown to be strongly influenced by the hydrographical network where response times are short. Although the direct influence of the Rhine is limited to its immediate surroundings, it contributes to maintaining the low level of the Alsace water table as a whole. The response time of recharge from rainfall closely reflects the thickness of the vadose zone south of Selestat and at the northern end of the Alsace plain whereas it discloses the contours and the thickness of the loess terraces nearby and south of Strasbourg to Selestat.