Azimuthal asymmetries in the atmospheric refractive index can lead to
errors in estimated vertical and horizontal station coordinates. Gener
ally these gradients are not modeled in standard very long baseline in
terferometry (VLBI) geodetic analysis. Daily average gradient effects
can be as large as 50 mm of delay at a 7 degrees elevation. To model g
radients, the constrained estimation of gradient parameters was added
to the standard VLBI solution procedure. Here the analysis of two sets
of data is summarized: the set of all geodetic VLBI experiments from
1990-1993 and a series of 12 state-of-the-art R&D experiments run on c
onsecutive days in January 1994. In both cases, when the gradient para
meters are estimated, the overall fit of the geodetic solution is impr
oved at greater than the 99% confidence level. Repeatabilities of base
line lengths ranging up to 11,000 km are improved by 1 to 8 mm in a ro
ot-sum-square sense. This varies from about 20% to 40% of the total ba
seline length scatter without gradient modeling for the 1990-1993 seri
es and 40% to 50% for the January series. Gradients estimated independ
ently for each day as a piecewise linear function are mostly continuou
s from day to day within their formal uncertainties.