Atmospheric turbulence characterisation in the upper atmospheric boundary layer (ABL) remains a challenge, as conventional measurement techniques, such as masts and lidars, have fundamental limitations at those altitudes. Airborne Wind Energy Systems (AWES), which operate tethered kites at altitudes beyond the surface-layer, show great promise as turbulence sensing platforms. This paper describes a methodology to characterise atmospheric turbulence from quantities that are available from standard onboard sensors. The methodology has been developed in UniSimAWE, Kitemill's in-house simulator framework, where the Mann model has been employed to generate atmospheric turbulence. The two operational phases of ground generation AWES, production and return phase, have been exploited as complementary sampling strategies. During the return phase, the kite follows a near-streamwise trajectory, enabling measurement of the turbulence intensity and integral time and length scales for the three velocity components. Moreover, Taylor's frozen turbulence hypothesis has been shown to hold for this sampling strategy, both through the integral length-to-time scale ratio, and the wavenumber-to-frequency power spectral density ratio. In the production phase, the kite flies in crosswind manoeuvres, following a helical path; the dominant crosswind component allows measurement of the integral time and length scales in the crosswind direction which are unavailable from conventional fixed-point sensors. In addition, the helical path enables the measurement of streamwise integral time scale. A novel time scale is introduced to characterise the interaction between the atmospheric turbulent structures and the AWES trajectory, with relevance for turbulence-adaptive control. The results demonstrate the potential of AWES to measure relevant atmospheric turbulence quantities throughout its operation, with advantages over conventional measurement techniques.