The Budyko, Bouchet, and Penman hypotheses together describe, using different formulae, the tight connections and feedbacks between water–energy balances and the landscape. The discrepancy between the Penman and Bouchet hypotheses is usually highlighted in non-humid regions. In this paper, using Fu's equation for annual water-energy balances at the catchment scale, which was derived phenomenologically and mathematically on the basis of the Budyko hypothesis, consistency among the three hypotheses is explained. In non-humid regions, change of actual evaporation is dominated by change in precipitation rather than potential evaporation, and the Bouchet complementary relationship between actual evaporation and potential evaporation comes about because actual evaporation and potential evaporation are correlated via precipitation. The annual water balances in 108 non-humid catchments of China have been examined as part of this study, and the results supported the complementary relationship. In humid regions, change in actual evaporation is controlled by change in potential evaporation rather than precipitation, and this is identical to the Penman hypothesis.