  We extend the water retention model [C. L. Knecht et al., Phys. Rev. Lett.
108, 045703 (2012)] to correlated random surfaces. We find that the retention
capacity of discrete random landscapes is strongly affected by spatial
correlations among the heights. This phenomenon is related to the emergence of
power-law scaling in the lake volume distribution. We also solve the
uncorrelated case exactly for a small lattice and present bounds on the
retention of uncorrelated landscapes.
