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<p>The retrieval algorithm for CO<span class="inline-formula">₂</span> column mixing ratio from measurements of a pulsed multi-wavelength integrated path differential absorption (IPDA) lidar is described. The lidar samples the shape of the 1572.33 nm CO<span class="inline-formula">₂</span> absorption line at multiple wavelengths. The algorithm uses a least-squares fit between the CO<span class="inline-formula">₂</span> line shape computed from a layered atmosphere model and that sampled by the lidar. In addition to the column-average CO<span class="inline-formula">₂</span> dry-air mole fraction (XCO<span class="inline-formula">₂</span>), several other parameters are also solved simultaneously from the fit. These include the Doppler shift at the received laser signal wavelength, the product of the surface reflectivity and atmospheric transmission, and a linear trend in the lidar receiver's spectral response. The algorithm can also be used to solve for the average water vapor mixing ratio, which produces a secondary absorption in the wings of the CO<span class="inline-formula">₂</span> absorption line under humid conditions. The least-squares fit is linearized about the expected XCO<span class="inline-formula">₂</span> value, which allows the use of a standard linear least-squares fitting method and software tools. The standard deviation of the retrieved XCO<span class="inline-formula">₂</span> is obtained from the covariance matrix of the fit. The averaging kernel is also provided similarly to that used for passive trace-gas column measurements. Examples are presented of using the algorithm to retrieve XCO<span class="inline-formula">₂</span> from measurements of the NASA Goddard airborne CO<span class="inline-formula">₂</span> Sounder lidar that were made at constant altitude and during spiral-down profile maneuvers.</p>