Urban flooding triggered by intense rainfall is becoming increasingly frequent and widespread. While flood prediction and monitoring in high spatio-temporal resolution are desired, practical constraints in time, budget, and technology hinder its full implementation. How to monitor urban drainage networks and predict flow conditions under constrained resources is a major challenge. To address this, we introduced a data-driven sparse sensing (DSS) approach, demonstrated via a digital-twin of the Woodland catchment in Duluth, Minnesota. Specifically, we coupled EPA-SWMM with singular value decomposition and QR factorization-based sensor selection to optimize monitoring locations for system-level flow reconstruction. An ensemble of SWMM simulations, driven by diverse scenarios, provided the necessary hydraulic data to extract the reduced basis and identify informative sensor locations. Cross-event validation showed that three strategically placed sensors among 77 candidate nodes achieved a mean system-level Nash-Sutcliffe efficiency (NSE) of 0.949 across observed storm events. The QR-selected sensor sets were benchmarked against reference sensor configurations obtained from exhaustive searches and Monte Carlo random-placements. This comparison further showed that flow reconstruction based on QR-selected sensors closely tracked the exhaustive optimum while substantially outperforming random placements. We further evaluated the framework's robustness by introducing multiplicative Gaussian noise and simulating individual sensor failures. While the model is relatively resilient to noise, the impact of sensor dropouts depends heavily on the number of sensors allocated and their specific locations.