In order to test the validity of the cluster ansatz approach as well as of the continuum model approach and to learn about the solvation shell, we carried out first-principles molecular dynamics simulations of the alanine hydration. Our calculations contained one alanine molecule dissolved in 60 water molecules. Dipole moments of individual molecules were derived by means of maximally localized Wannier functions. We observed an average dipole moment of about 16.0 D for alanine and of about 3.3 D for water. In particular, the average water dipole moment in proximity of alanine's COO- group decayed continously with increasing distance, while, surprisingly, close to the CH3 and NH3+ group, the dipole moment first rose before its value dropped. In a cluster ansatz approach, we considered snapshots of alanine surrounded by different water molecule shells. The dipole moments from the cluster approaches utilizing both maximally localized Wannier functions as well as natural population analysis served to approximate the dipole moments of the total trajectory. Sufficient convergence of the cluster ansatz approach is found for either of the two solvent shells around the polar groups and one solvent shell around the apolar groups or two solvent shells around the polar groups surrounded by a dieletric continuum.