Abstract
We present a method for estimating water vapor maps using signal delay time series measurementsfrom a sparse network of GPS receivers. We use these maps to correct phase errors in an example Interferometric Synthetic Aperture Radar (InSAR) interferogram showing mainly atmospheric phase signatures. Our method separately estimates spatial variations caused by vertical-stratification of moisture and horizontal turbulent mixing of water vapor. By measuring the altitude-dependence of GPS delay acquired at the radar observation times, we estimate a topography-dependent integrated water vapor map which reduces phase distortions in the interferogram by 46%. We use the same GPS measurements to spatially interpolate another map which then reduces the turbulence-induced residual phase errors by an additional 7%. We find that the amount of correction is limited by the spatially sparse GPS observations in the imaged area.

We have developed two techniques to further reduce phase distortions by incorporating additional GPS measurements prior to and after the radar observation times. The first method is based on the "frozen-flow" hypothesis which posits a flow-driven, advecting slab of atmosphere with homogeneous spatial statistics. We estimate mean flow from covariance analysis of the GPS delay time series. We use these estimates to infer dense networks of virtual control points. Interpolating these networks and filtering out the short-scale variations not reproducible by the GPS data, we obtain a map of water vapor that reduces the residual phase errors by an additional 31%.

In the second method, we model the advection and diffusion of delay fields using a conservation law for humidity parameterized by a spatially-variable flow field. We develop a numerical scheme for least-squares estimation of the flow field which we then used in an algorithm to generate a water vapor map from the GPS time series data. This map reduces the phase errors by an additional 17% compared to using data only at the imaging times.