INNOVATION Tropospheric Delay: Prediction for the WAAS User Paul Collins and Richard B. Langley University of New Brunswick The weather — it affects us all. Sometimes The ideal GPS measurement is the true range of the delay occurs within the troposphere, disastrously with vicious storms; sometimes or distance between the receiver’s antenna the whole delay is often referred to solely as pleasantly with sunshine and warm breezes. and the GPS satellite antenna. But as with the tropospheric delay. It also affects GPS. But, whereas bad most things in our imperfect world, we can- By assuming that the neutral atmosphere weather might disrupt our lives, causing not achieve the ideal. A number of error is both horizontally stratified and azimuthally us to curtail or postpone an activity, GPS sources bias GPS measurements, and pro- symmetric, we can model the tropospheric continues to perform — it’s an all-weather cessing software must account for these delay in two parts: the delay experienced in system. Rain, snow, fog, and clouds all errors to obtain accurate position, velocity, or the zenith direction and the scaling of that have a negligible effect on GPS. However, time information. One of these biases is the delay to the one experienced at the raypath’s unseen weather — temperature, pressure, tropospheric propagation delay, for which all zenith angle (referred to as either the map- and humidity variations throughout GPS receivers and postprocessing software ping function or obliquity factor). The com- the atmosphere — does affect GPS employ a delay algorithm of some kind that mon formulation of zenith delays and observations. These parameters determine attempts to model or predict, and thus mini- mapping functions seen in space geodetic the propagation speed of radio waves, an mize, its impact. Depending on the model’s and navigation literature derives from model- important factor that must be accounted sophistication, however, some error or resid- ing tropospheric delay in this way. It can be for when processing GPS or other ual delay will remain. described mathematically as radiometric observations. Because we Users often treat the residual tropospheric z z cannot predict their exact values ahead of delay in GPS position estimation in a very off- dtrop = dhyd · mhyd + dwet · mwet time, these invisible weather variables are hand manner — they assume that the effect is a source of error in GPS positioning and small or that a simple estimation technique in which total delay (dtrop) is a function of the navigation. In this month’s column, we will resolve the problem. But what is the true delays in the zenith direction caused by the examine the atmosphere’s effect on GPS impact? Just how much does the lower, electri- atmospheric gases in hydrostatic equilibrium z z and discuss how we’ve attempted to model cally neutral, atmosphere vary in terms of and those that are not (dhyd and dwet, respec- it for the users of the forthcoming Wide refractivity and its effect on GPS applications? tively) as well as their corresponding map- Area Augmentation System. The aim of this article is to provide answers to ping functions (mhyd and mwet), which project I am joined this month by Paul Collins. these questions and offer a quantification of the zenith delay into the line-of-sight delay. Paul graduated from the University of the neutral atmospheric effect for users of Gases not in hydrostatic equilibrium are pri- East London in 1993 with a B.Sc. (Honors) wide-area differential GPS systems, such as marily water vapor, and the mapping func- degree in surveying and mapping sciences. the Federal Aviation Administration’s (FAA’s) tions are usually described as functions of the He is currently enrolled in the M.Sc.E. Wide Area Augmentation System (WAAS), satellite elevation angle — the complement degree program in the Department of who seek meter-level accuracy or better and of the zenith angle. Geodesy and Geomatics Engineering at operate within a position critical environment. Because this customary formulation of the University of New Brunswick, where tropospheric delay assumes horizontal stratifi- he is investigating the tropospheric THE TROPOSPHERIC DELAY cation and azimuthal symmetry, it precludes effects on kinematic GPS positioning. Constituent gases affect an electromagnetic the existence of gradients in the atmosphere. “Innovation” is a regular column signal propagating through the neutral atmo- Researchers have derived more sophisticated featuring discussions about recent advances sphere. Their combined refractive index, models to try to account for atmospheric gradi- in GPS technology and its applications as slightly greater than unity (nominally 1.0003 ents caused by pressure slopes and passing well as the fundamentals of GPS positioning. at sea level), causes the signal’s velocity to be weather fronts, but the effects are typically at The column is coordinated by Richard lower than it would be in a vacuum and the centimeter level or less and are accordingly Langley of the Department of Geodesy and increases the time it takes a signal to reach a insignificant for most navigation applications. Geomatics Engineering at the University of GPS receiver’s antenna, thus extending the New Brunswick, who appreciates receiving equivalent path length. Both these effects are DELAY MODELS your comments as well as topic suggestions often referred to as delay. Refraction also Researchers have developed many different for future columns. To contact him, see the bends, and thereby lengthens, the raypath, algorithms over the years in an effort to “Columnists” section on page 4 of this issue. further increasing the delay. Because the bulk empirically model the tropospheric delay 52 GPS WORLD July 1999 www.gpsworld.com with varying degrees of accuracy. When pro- from the GPS data itself. This procedure, cessing GPS observations, a receiver or post- however, is typically only carried out for processing software program predicts a value such high-precision GPS applications as for the tropospheric delay from such a model deformation monitoring. using assumed or real-time values for the ambient temperature as well as total baromet- DEVELOPING A NEW MODEL ric and partial water-vapor pressures. Unfor- Although the geodetic community has been tunately, even with accurate real-time acutely aware of the propagation delay prob- measurements, models can rarely predict the lem and has striven over the years to improve true total delay with a degree of accuracy the accuracy of tropospheric delay models, much better than a few percent. the navigation community has overlooked, Although, we can determine the delay’s for the most part, these developments and hydrostatic component in the zenith direction continued to use simpler, less-accurate at the millimeter level, the highly variable models. The need for higher positioning nature of atmospheric water vapor degrades accuracies, however, concurrent with the the accuracy of the wet delay prediction to development of augmented GPS has necessi- the centimeter or even decimeter level. This tated a fresh look at tropospheric delay occurs because the hydrostatic delay in the models for navigation applications. WAAS in zenith direction is a function of the total sur- particular requires a model, as aircraft face pressure only, which, under conditions employing WAAS-augmented receivers need NovAtel of hydrostatic equilibrium, represents the the resulting increase in accuracy. total weight of the column of air above the At the University of New Brunswick 1/3 Page Vert user. Analogously, the zenith wet delay is a (UNB), we have developed a series of com- function of the total precipitable water — the posite or hybrid models for GPS navigation, amount of vapor present in the column of air culminating in UNB3, which the FAA and Ad Goes above the user. Nav Canada have adopted for the WAAS user Tropospheric delay models express these receiver. We based our original definition of Here two parameters in various ways. The most the model on the zenith delay algorithms of common method of describing the wet delay is Jouko Saastamoinen (whose work at the Keyline does through a combination of surface parameters National Research Council of Canada in the (water-vapor pressure, or relative humidity, early 1970s has withstood the test of time), not print and temperature) and some kind of water- the recent, high-accuracy mapping functions vapor lapse rate (commonly known as the of Haystack Observatory’s Arthur Niell, and page 53 lambda parameter). Not all models explicitly a table of atmospheric parameter values parameterize the wet delay as such, but they derived from the U.S. 1966 Standard Atmos- often do so implicitly. phere Supplements. The problem with modeling the wet delay In the interest of computational simplicity, in this way is that, unlike the hydrostatic a subsequent proposal was made to replace delay, no simple physical law governs the the Niell mapping functions with the com- distribution of water vapor in the lower bined function of Harold Black and Arie Eis- atmosphere; hence, a precise definition and ner, who both worked at the Johns Hopkins evaluation of the lambda parameter is not University Applied Physics Laboratory. This possible. As a consequence, the only way to change has a negligible impact on most of the accurately measure the lambda parameter is results presented in this article, because we to employ some technique that attempts to deal mainly with the zenith delay residual sample the whole atmospheric column, such error. (We did calculate our position error as a radiosonde or a radiometer. As these are simulations described later in this article impractical for real-time GPS users (and using the Black and Eisner mapping func- indeed for most other GPS users), the lambda tion; however, we do not expect the results to parameter can only be represented empiri- be significantly different when using the cally and will consequently always be associ- Niell functions.) ated with some error in the determination of UNB3.