Characterizing Atmospheric Turbulence with Gps

The Global Positioning System (GPS), originally designed for navigation purposes, has shown its capabilities for use in atmospheric studies for over a decade now (e.g., Bevis et al. 1992). Atmospheric delays of the GPS signals, caused by the atmospheric refractivity along the ray path to a ground-based receiver, are used as tracers of atmospheric densities. The delay caused by the electrically neutral atmosphere consist of a wet and hydrostatic component and is often referred to as tropospheric delay, because the troposphere is responsible for most of this delay. Usually, Zenith Tropospheric Delays (ZTDs), are estimated by mapping slant delays (i.e., delays along the ray paths) to zenith-equivalent values by a zenith-angledependent mapping function. Mapping functions depend on (mean) atmospheric conditions and usually assume a horizontally layered (homogeneous) atmosphere. This way a single parameter, the ZTD, describes the mean atmospheric state. If we subtract the hydrostatic zenith delay, which is well predictable when accurate pressure values are known, the remaining part of the ZTD can be attributed to water vapor and is often used as observation for atmospheric studies. This single parameter does however not reflect any heterogeneous fluctuations in the atmosphere caused by turbulence. Although parameterization of all fluctuations is impossible since, even in a network of receivers, this would lead to an underdetermined set of equations, we can derive a stochastic model for the fluctuations if we assume Kolmogorov turbulence. In fact, we could estimate the fluctuations if we added extra zero-mean pseudoobservations (soft constraints) for these fluctuations with their corresponding covariance matrix (Kleijer 2004). If we knew the scaling of the covariance matrix, these soft constraints could improve the positioning precision for static applications, since atmospheric turbulence is believed to be a dominating error source. This scaling would represent the degree of heterogeneity, or turbulence, present in the atmosphere. This paper describes a method for estimating this turbulence variance scale factor with a single GPS receiver. The application we have in mind is that of an accurate, independent, continuous, all-weather, inexpensive, nearreal-time, passive remote-sensing technique for measuring atmospheric turbulence strength. Instantaneous measurements of refractive-index fluctuation variations are important for a variety of atmo-