Several studies have used the temperature dependence of gas solubilities in water to derive paleotemperatures from noble gases in groundwaters. We present a general method to infer environmental parameters from concentrations of dissolved atmospheric noble gases in water. Our approach incorporates statistical methods to quantify uncertainties of the deduced parameter values. The equilibration temperatures of water equilibrated with the atmosphere under controlled conditions could be inferred with a precision and accuracy of ±0.2°C. The equilibration temperatures of lake and river samples were determined with a similar precision. Most of these samples were in agreement with atmospheric equilibrium at the water temperature. In groundwaters either recharge temperature or altitude could be determined with high precision (±0.3°C and ±60 m, respectively) despite the presence of excess air. However, typical errors increase to ±3°C and ±700 m if both temperature and altitude are determined at the same time, because the two parameters are correlated. In some groundwater samples the composition of the excess air deviated significantly from atmospheric air, which was modeled by partial reequilibration. In this case the achievable precision of noble gas temperatures was significantly diminished (typical errors of ±1°C).