Residual instrument tilt can introduce systematic errors in Doppler-lidar wind retrievals when instrument-reported pitch and roll are not incorporated in post-processing. We derive practical retrieval equations that map line-of-sight (LOS) velocities to Earth-fixed wind components (u, v, w) by explicitly accounting for the reported tilt. The system is closed by stacking LOS measurements from one or more scanning strategies under the standard assumption that the wind field is horizontally homogeneous and statistically stationary over the scan footprint and acquisition period. We show that the proposed matrix equations reduce to the conventional LOS measurement relation for lidar and radar retrievals in the zero-tilt limit. For conical velocity–azimuth display (VAD) scans, we further derive a compact closed-form least-squares solution for the wind components expressed in a Cartesian coordinate system. For an idealized uniform wind of \(10~\mathrm {m\,s^{-1}}\) aligned with the x axis, neglecting rotations of \(2^\circ \) about x and \(1^\circ \) about y produces a spurious vertical velocity of \(0.17~\mathrm {m\,s^{-1}}\) . The resulting measurement bias scales as \(\text {bias}\propto (\text {tilt})\times (\text {speed})\) . The framework is illustrated using Doppler-lidar measurements in the urban boundary layer over downtown Montréal, Canada. Over a one-year period, daily mean tilts are typically sub-degree (pitch \(\approx 0.25^\circ \) , roll \(\approx -0.57^\circ \) ) yet are sufficient to induce measurable retrieval differences. At \(z\approx 1.2~\textrm{km}\) , a tilt of \(\sim 4.4^\circ \) shifts the inferred range-gate center height by \(\sim 24~\textrm{m}\) , comparable to the instrument range increment; across case studies spanning distinct wind regimes, accounting for tilt removes biases in time-averaged vertical velocity of order \(0.1~\mathrm {m\,s^{-1}}\) ; in a wind-energy diagnostic at \(z=107~\textrm{m}\) above ground level, the sector-wise wind power density for northeasterly flow differs by up to \(4.7\%\) when tilt is included. The formalism developed herein provides a practical means to reduce tilt-induced bias in lidar, radar, and sodar wind retrievals, thereby improving measurement accuracy in atmospheric boundary-layer studies and in wind-energy applications.
