Three river basins in central Rhode Island-the Hunt River, the Annaquatucket River, and the Pettaquamscutt River-contain 15 production wells clustered in 4 pumping centers from which drinking water is withdrawn. These high-capacity production wells, operated by three water suppliers, are screened in coarse-grained deposits of glacial origin. The risk of contaminating water withdrawn by these well centers may be reduced if the areas contributing recharge to the well centers are delineated and these areas protected from land uses that may affect the water quality. The U.S. Geological Survey, in cooperation with the Rhode Island Department of Health, began an investigation in 2009 to improve the understanding of groundwater flow and delineate areas contributing recharge to the well centers as part of an effort to protect the source of water to these well centers. A groundwater-flow model was calibrated by inverse modeling using nonlinear regression to obtain the optimal set of parameter values, which provide a single, best representation of the area contributing recharge to a well center. Summary statistics from the calibrated model were used to evaluate the uncertainty associated with the predicted areas contributing recharge to the well centers. This uncertainty analysis was done so that the contributing areas to the well centers would not be underestimated, thereby leaving the well centers inadequately protected. The analysis led to contributing areas expressed as a probability distribution (probabilistic contributing areas) that differ from a single or deterministic contributing area. Groundwater flow was simulated in the surficial deposits and the underlying bedrock in the 47-square-mile study area. Observations (165 groundwater levels and 7 base flows) provided sufficient information to estimate parameters representing recharge and horizontal hydraulic conductivity of the glacial deposits and hydraulic conductance of streambeds. The calibrated value for recharge to valley-fill deposits was 27.3 inches per year (in/yr) and to upland till deposits was 18.7 in/yr. Calibrated values for horizontal hydraulic conductivity of the valley-fill deposits ranged from 20 to 480 feet per day (ft/d) and of the upland till deposits was 16.2 ft/d. Calibrated values of streambed hydraulic conductance ranged from 10,000 to 52,000 feet squared per day. Values of recharge and horizontal hydraulic conductivity of the valley-fill deposits were the most precisely estimated, whereas the horizontal hydraulic conductivity of till deposits was the least precisely estimated. Simulated areas contributing recharge to the well centers on the basis of the calibrated model ranged from 0.19 to 1.12 square miles (mi2) and covered a total area of 2.79 mi2 for average well center withdrawal rates during 2004-08 (235 to 1,858 gallons per minute (gal/min)). Simulated areas contributing recharge for the maximum well center pumping capacities (800 to 8,500 gal/min) ranged from 0.37 to 3.53 mi2 and covered a total area of 7.99 mi2 in the modeled area. Simulated areas contributing recharge extend upgradient of the well centers to upland till and to groundwater divides. Some areas contributing recharge include small, isolated areas remote from the well centers. Relatively short groundwater traveltimes from recharging locations to discharging wells indicated the wells are vulnerable to contamination from land-surface activities: median traveltimes ranged from 2.9 to 5.0 years for the well centers, and 78 to 93 percent of the traveltimes were 10 years or less for the well centers. Land cover in the areas contributing recharge includes a substantial amount of urban land use for the two well centers in the Hunt River Basin, agriculture and sand and gravel mining uses for the well center in the Annaquatucket River Basin, and, for the well center in the Pettaquamscutt River Basin, land use is primarily undeveloped. Model-prediction uncertainty was evaluated using a Monte Carlo analysis. The parameter variance-covariance matrix from nonlinear regression was used to create parameter sets that reflect the uncertainty of the parameter estimates and the correlation among parameters. The remaining parameters representing the glacial deposits (vertical anisotropy of valley-fill deposits and of till deposits, maximum groundwater evapotranspiration, and hydraulic conductance for headdependent cells representing a groundwater divide) that could not be estimated with nonlinear regression were incorporated into the variance-covariance matrix using prior information on parameters. Thus the uncertainty analysis was an outcome of calibrating the parameters to available observations and to information that the modeler provided. A water budget and model-fit statistical criteria were used to assess parameter sets so that prediction uncertainty was not overestimated. Because of the effects of parameter uncertainty, the size of the probabilistic contributing areas for each well center for both average and maximum pumping rates was larger than the size of the deterministic contributing areas for the well center. Thus, some areas not in the deterministic contributing area may actually be in the contributing area, including additional areas of urban and agricultural land use. Generally, areas closest to the well centers with short groundwater traveltimes are associated with higher probabilities, whereas areas distant from the well centers with long groundwater traveltimes are associated with lower probabilities. The deterministic contributing areas generally corresponded to areas associated with high probabilities (greater than 50 percent). Areas associated with low probabilities extended long distances along groundwater divides in the uplands remote from the well centers.