  We study surface modes in semi-infinite chirped two-dimensional photonic
lattices in the frame- work of an effective discrete nonlinear model. We
demonstrate that the lattice chirp can change dramatically the conditions for
the mode localization near the surface, and we find numerically the families of
surface modes, in linear lattices, and discrete surface solitons, in nonlinear
lattices. We demonstrate that, in a sharp contrast to one-dimensional discrete
surface solitons, in two-dimensional lattices the mode threshold power is
lowered by the action of both the surface and lattice chirp. By manipulating
with the lattice chirp, we can control the mode position and its localization.
