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Groundwater supports streamflow and ecosystems in semi-arid, montane catchments, which are environments considered particularly sensitive to climate change. Despite its importance, the relationship between groundwater and streamflow is not well understood. To remedy this, we seek to model groundwater-surface water interactions to assess how groundwater discharge to surface water varies temporally and spatially. Our study area, Gordon Gulch, is a semi-arid, montane, forested, 2.6 km2 catchment with prominent north-south aspects within the Colorado Front Range, ranging in elevation from 2450 to 2750 meters. Gordon Gulch is located within the Boulder Creek Critical Zone Observatory (BcCZO) and has been actively monitored and studied for over a decade. We use the wealth of available data from the BcCZO including groundwater levels, precipitation, snow depth, streamflow, and soil moisture, and shallow seismic refraction surveys to develop a numerical model using MODFLOW. The model simulates groundwater-surface water interactions and computes the hydrologic heads within the catchment. We observe biannual maxima in groundwater elevation and streamflow occur in spring and late summer and find evidence of a correlated system response triggered by a recharge threshold composed of precipitation and spring snowmelt. Model results show that over a typical water year, the system is relatively flashy with groundwater elevation and stream discharge rapidly responding to recharge events (on the scale of days). Over a longer record, extreme recharge events result in a sustained system response with a prolonged period (on the scale of years) of elevated groundwater level. Spatially, we observe that groundwater level and its interaction with surface water is strongly influenced by topography. Our model offers a framework for constraining the mechanisms driving groundwater-surface water exchanges and characterizing the relationships between hydrologic system inputs (precipitation and snowmelt) and system responses (stream discharge and groundwater elevation).