Gradients in the atmospheric refractive index can lead to errors in estimated vertical and horizontal station coordinates. These errors produce systematic errors in the terrestrial and celestial reference frames determined from our very long baseline interferometry (VLBI) measurements. Estimation of gradients for our global VLBI data set changes the terrestrial reference frame length scale by -0.7 ppb and produces station position adjustments that vary approximately monotonically with latitude. Estimating gradients reduces the radio source declinations by an amount that peaks at about 0.5 mas near the equator and decreases toward the poles. VLBI gradient estimates are consistent with gradients derived from a global three-dimensional model of assimilated meteorological data. Both indicate that mean atmospheric delay gradients point toward the equator in both the northern and southern hemispheres. The correlation coefficient between VLBI and meteorological model gradients for VLBI sessions for the VLBI antenna at Westford, Massachusetts was 0.56.¿ 1997 American Geophysical Union