设有界闭域$\Omega $由曲面${{x}^{2}}+{{y}^{2}}-3{{z}^{2}}=0$与$z=\sqrt{4-{{x}^{2}}-{{y}^{2}}}$围成，$\partial \Omega $为$\Omega $的边界面，外侧为正，则曲面积分$\iint\limits {\partial \Omega }{x(1+{{y}^{2}})\text{d}y\wedge \text{d}z+y(1+{{z}^{2}})\text{d}z\wedge \text{d}x+z(1+{{x}^{2}})\text{d}x\wedge \text{d}y}=$( ).