The tropospheric propagation effect is one of several sources of error in radio science measurements. Systematically calibrated for the Earth troposphere disturbances, the ranging and Doppler data provided by the Martian landers have not been corrected so far for Mars troposphere effects. These effects were considered negligible because the Mars atmosphere is a hundred times less dense than that of the Earth. The constantly improving lander data accuracy and the challenging science objectives of the InSight-Rotation and Interior Structure Experiment (RISE) and ExoMars-2022-LaRa radio science experiments motivated this work. We propose here a simple model to compute the Mars troposphere errors affecting a radio wave transponded from the surface of Mars. The troposphere zenithal delay is first derived from the surface pressure at the lander location. We use a mapping function to infer the slant delay (range errors) induced by the troposphere of Mars. Being proportional to range rates, the contribution of Mars troposphere to the Doppler measurements is derived from the slant delays. Using our model, an elevation threshold of 15 degrees above the lander is identified, below which the Doppler data should be calibrated for Mars troposphere. When applied to the X-band Doppler data from Mars surface missions, the model predicts significant Mars troposphere contribution for less than 1% of RISE data, 2% of Opportunity data, and 2.5% of Pathfinder data. Among these tracking passes, some are strongly affected by the troposphere of Mars, with Doppler errors reaching sometimes more than 3 times the nominal noise level (10 mHz at 60 s integration time).
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