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This paper establishes the relationship between the signal of a lidar system corrected for the incomplete overlap effect and the signal of another lidar system or a ceilometer for which the overlap function is unknown. Simple mathematical relationships permit the estimation of the overlap function of the second system as well as the associated error. Several overlap functions have been retrieved with this method over a period of 1.5 years with two lidar systems of the Universitat Politècnica de Catalunya, Barcelona, Spain. The error when the overlap function reaches 1 is usually less than 7%. The temporal variability estimated over a period of 1.5 years is less than 11% in the first 1.5 km from the surface and peaks at 18% at heights between 1.7 and 2.4 km. The use of a non-appropriate overlap function in the retrieval of the backscatter coefficient yield errors up to 60% in the first 0.5 km and up to 20% above.

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Calculation of the Overlap Function and Associated Error of an Elastic Lidar or a Ceilometer: Cross-Comparison with a Cooperative Overlap-Corrected System