Corrections to zenith atmospheric delays (including hydrostatic components) are estimated in geodetic analyses using partial derivatives that relate wet delays to the phase observations. At low-elevation angles, partial derivatives of the hydrostatic and wet delays are sufficiently different as to cause errors in the estimates of station heights and zenith total delays unless accurate surface pressure values are used to model the hydrostatic delay. The associated errors are latitude dependent because sites at high latitudes have a higher percentage of low-elevation observations. A priori zenith hydrostatic delay errors project into GPS height estimates with typical sensitivities of up to -0.2 mm/hPa, depending on the elevation angle cutoff and elevation angle dependent data weighting used in the analysis. This generates height errors of up to 10 mm and seasonal variations of up to 2 mm amplitude. The errors in zenith delay estimates are about half the magnitude of the height errors.