  We study how much water can be retained without leaking through boundaries
when each unit square of a two-dimensional lattice is randomly assigned a block
of unit bottom area but with different heights from zero to $n-1$. As more
blocks are put into the system, there exists a phase transition beyond which
the system retains a macroscopic volume of water. We locate the critical points
and verify that the criticality belongs to the two-dimensional percolation
universality class. If the height distribution can be approximated as
continuous for large $n$, the system is always close to a critical point and
the fraction of the area below the resulting water level is given by the
percolation threshold. This provides a universal upper bound of areas that can
be covered by water in a random landscape.
