Abstract: In this work, we incorporate local smoothness indicators, apply their q-th root to design two high-order global smoothness indicators, and rigorously prove the convergence order of these indicators. Additionally, an adaptive function is introduced to optimize the calculation of weights, ultimately leading to the development of a novel high-order accuracy method known as WENO-ZH. Theoretical analysis reveals that the new scheme achieves fifth-order accuracy at first-order critical point and fourth-order accuracy at second-order point. Numerical experiments indicate that, the WENO-ZH scheme exhibits superior shock-capturing capabilities, numerical robustness, and low numerical dissipation.