We calculate the absorption cross section of water dimer molecules in thermal equilibrium at temperatures typical of the lower atmosphere using quantum mechanical coupled nonlinear equations of motion. Empirical Morse-oscillator potentials are used to describe the local modes of water monomer, and the RWK2 potential is employed for the interaction between atoms of different water monomers. The strong anharmonicity is taken into account by an extension to molecular dimers of methods originally developed for the lattice dynamics of solid helium. Approximations based on exploiting the hierarchy of energy scales in the dynamics of the weakly hydrogen-bonded water dimer allow the determination of the absorption spectrum over the range of significant solar radiation, up to 20 000 cm(-1), including the important contributions of overtone and combination transitions. This approach can tackle the complicated task of mixing of vibrational fundamentals and overtones. We have found that the absorption by these vibrational overtones, within the solar energy range, is quite significant due to the anharmonicity of Morse-oscillator potentials and the large vibrational amplitude of hydrogen atoms. These overtones may play a role in the solar energy absorption of the atmosphere.