The quantification of recharge and trans-valley underflow is needed in arid regions to estimate the impacts of new water withdrawals on the water table. However, for mountainous desert areas, such estimates are highly challenging, due to data scarcity, heterogeneous soils, and long residence times. Conventional assessment employs isolated groundwater models configured with simplified uniform estimates of recharge. Here, we employed a data-constrained surface-subsurface process model to provide an ensemble of spatially distributed recharge and underflow estimates using perturbed parameters. Then, the Model-Independent Parameter Estimation and Uncertainty Quantification (PEST) package was used to calibrate the aquifer hydraulic conductivity field in MODFLOW for this ensemble and reject implausible recharge values. This novel dual-model approach, broadly applicable to mountainous arid regions, was designed to maximally exploit available data sources. It can assimilate groundwater head observations, reject unrealistic parameters, and narrow the range of estimated drawdowns due to pumping. We applied this approach to the Chuckwalla basin in California, USA to determine natural recharge. Simulated recharge concentrates along alluvial fans at the mountain fronts and ephemeral washes where run-off water infiltrates. If an evenly distributed recharge was employed as in conventional studies, it would result in regional biases in estimated drawdown and larger uncertainty bounds. We also note that the speed of groundwater recovery does not guarantee sustainability: heavy pumping induces large hydraulic gradients that initially recover quickly when pumping is halted, but the system may not ultimately recover to pre-pumping levels.