  An important class of observables for gravitational waves consists of the
fluxes of energy, momentum and angular momentum carried away by them and are
well understood for weak gravitational waves in Minkowski background. In de
Sitter background, the future null infinity, $\mathcal{J}^+$, is space-like
which makes the meaning of these observables subtle. A spatially compact source
in de Sitter background also provides a distinguished null hypersurface, its
{\em cosmological horizon}, $\mathcal{H}^+$. For sources supporting the short
wavelength approximation, we adopt the Isaacson prescription to define an
effective gravitational stress tensor. We show that the fluxes computed using
this effective stress tensor can be evaluated at $\mathcal{H}^+$, match with
those computed at $\mathcal{J}^+$ and also match with those given by Ashtekar
et al at $\mathcal{J}^+$ {{\em at a coarse grained level}}.
