Continuous assessment of wind turbine performance is a key to maximising power generation at a very low cost. A wind turbine power curve is a non-linear function between power output and wind speed and is widely used to approach numerous problems linked to turbine operation. According to the current IEC standard, power curves are determined by a data reduction method, called binning, where hub height, wind speed and air density are considered as appropriate input parameters. However, as turbine rotors have grown in size over recent years, the impact of variations in wind speed, and thus of power output, can no longer be overlooked. Two environmental variables, namely wind shear and turbulence intensity, have the greatest impact on power output. Therefore, taking account of these factors may improve the accuracy as well as reduce the uncertainty of data-driven power curve models, which could be helpful in performance monitoring applications. This paper aims to quantify and analyse the impact of these two environmental factors on wind turbine power curves.Gaussian process (GP) is a data-driven, nonparametric based approach to power curve modelling that can incorporate these two additional environmental factors. The proposed technique's effectiveness is trained and validated using historical 10-minute average supervisory control and data acquisition (SCADA) datasets from variable speed, pitch control, and wind turbines rated at 2.5 MW. The results suggest that (i) the inclusion of the additional environmental parameters increases GP model accuracy and reduces uncertainty in estimating the power curve; (ii) a comparative study reveals that turbulence intensity has a relatively greater impact on GP model accuracy, together with uncertainty as compared to blade pitch angle. These conclusions are confirmed using performance error metrics and uncertainty calculations. The results have practical beneficial consequences for O&M related activities such as early failure detection.