An adaptive force matching (AFM) scheme using the nonlinear optimization to reparametrize the three-site, flexible, and polarizable single-point-charge (SPC) water model is reported. We compare the radial distribution functions of the intermolecular oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen distances with the recent scattering experiments, the previous AFM-fitting water model (MP2f), and the atomic multipole expanded AMOEBA model. Our nonpolarizable SPC-3f(0) model captures the feature of the first solvation shell of bulk water. With the ad hoc inclusion of the isotropic polarizability, the polarizable SPC-3f(0.6) water model recovers the many-body effect of the second solvation shell. In the n-body decomposition analysis, the SPC-3f(0) model predicts the best agreement with MP2/aug-cc-pVTZ calculations with the use of the low-dimensional (H2O)(4)-ring and (H2O)(6)-ring clusters. For the comparison using the three-dimensional (H2O)(6)-prism and (H2O)(16)-4444a clusters, SPC-3f(0.6) predicts the results consistent with those of AMOEBA and MP2 levels. For simulating a water-cluster-dominant system such as supercritical water, SPC-3f(0) well characterizes the combination mode of bending and stretching at 5300 cm(-1).