Compute \(\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}\) for the given oriented surface or parametrized surface.

\(\mathbf{F}(x, y, z)=\left\langle 0,0, x^{2}+y^{2}ightangle, \quad x^{2}+y^{2}+z^{2}=4, \quad z \geq 0\), outward-pointing normal