Reliable wind energy assessment is often limited by reliance on single-point wind measurements at nacelle height, as commonly used in international standards. Here, we present a closed-form analytical rotor-averaging model for turbine power that integrates the vertical variation of horizontal wind speed – the changes in wind with height – using a Taylor expansion of the inflow velocity over the rotor disk. We assess idealised wind profiles to understand the isolated effects of typical shear, veer profiles, and turbulence on the power production of the turbine. This analytical model is then validated against power measurements from five Enercon E92 turbines on the Gotthard Pass, a complex-terrain wind park in the Swiss Alps, across 10 distinct wind events. The analytical model consistently outperforms both OpenFAST simulations and the International Electrotechnical Commission (IEC) standards, providing smoother and more accurate power estimates, reducing RMSE by 8.8% and bias by 25.4% relative to IEC-standard single-point extrapolations. This equates to an annual energy production estimate that is 23.7 MWh closer to reality, for a 2.35 MW turbine at this specific site. Additionally, it enables effective filtering of wake-affected LiDAR measurements, demonstrating flexibility, robustness, and applicability for pre-construction assessment and wind park expansion in complex terrain.