INNOVATION of how atmospheric refraction maps into a The Effect of GPS positioning error. ATMOSPHERIC DELAY Weather Fronts As a GPS signal travels from the satellite to a receiver, it passes through the atmosphere, where different layers refract it in various on GPS ways. The first layer it encounters is the ionosphere, which is charged with a high Measurements number of free electrons that refract the sig- nal. The resulting delay depends on the signal frequency (because the ionosphere is a dis- Thierry Gregorius persive medium), which is why we can use Geoffrey Blewitt data from daul-frequency receivers to easily The University of Newcastle upon Tyne estimate and almost entirely eliminate the delay’s magnitude. The ionosphere actually accelerates the carrier phase (with a net phase advance) and slows down the pseudorandom Dr. Blewitt completed his Ph.D. research in noise codes and the navigation message (with high-energy physics in 1985 at the California a net modulation or group delay). Institute of Technology and then spent more The ionosphere’s electron content is tem- than eight years working at the National porally and spatially highly variable. Under Aeronautical and Space Administration’s Jet the influence of solar flares and coronal holes Propulsion Laboratory, where he coauthored and the resulting geomagnetic storms, these the GIPSY OASIS software for high-precision variations may become so rapid and unpre- On the southeast coast of England, not very far GPS applications. In 1994, he returned to the dictable that the higher-order terms of the from where the Battle of Hastings occurred, United Kingdom to join the University of delay not eliminated by the ionosphere-free lies Herstmonceux Castle — a fifteenth- Newcastle upon Tyne, where he is now linear combination of the L1 and L2 data century manor house that was, for many years, professor of space geodesy in the Department could cause a significant bias in the estimated the home of the Royal Greenwich Observatory of Geomatics. A governing board member of station position — the position of the geodetic (RGO). Although the skies above the castle are IGS, he is actively involved in IGS analysis. marker on which the receiver’s antenna rests. generally clearer than those above RGO’s “Innovation” is a regular column featuring Having passed through the ionosphere, the original home in the London borough of discussions about recent advances in GPS signal then undergoes a different kind of Greenwich, the frequently cloudy and rainy technology and its applications as well as the delay in the neutral atmosphere. Termed non- conditions are less than ideal for astronomy. fundamentals of GPS positioning. The column dispersive because it is not frequency-depen- RGO, therefore, built new telescopes on La is coordinated by Richard Langley of the dent and thus cannot be easily eliminated, Palma in the Canary Islands and moved most Department of Geodesy and Geomatics this neutral delay is caused by both the of its administrative and research facilities to Engineering at the University of New stratosphere and troposphere. Because the Cambridge in 1990. Brunswick, who appreciates receiving your bulk of the effect occurs in the troposphere, The same poor conditions dreaded by comments as well as topic suggestions for the geodetic community has taken to mis- astronomers, however, are ideal for studying future columns. To contact him, see the naming the neutral delay as the tropospheric weather fronts in relation to GPS. The grounds “Columnists”section on page 4 of this issue. delay, a convention that we shall follow here. of Herstmonceux Castle (now owned by We can adequately model the tropospheric Canada’s Queen’s University and operated as Weather fronts are an important meteorolog- delay’s dry part (more precisely, the part that an international study center) house an ical phenomenon that not only bring a change is in hydrostatic equilibrium, the bulk of International GPS Service (IGS) station. This in weather but can also significantly disturb which is accounted for by the dry gases) if we site has provided Drs. Thierry Gregorius and GPS observations. Because they occur in the know the surface pressure with high accu- Geoffrey Blewitt with a wealth of data for their troposphere, they leave their mark in the tro- racy, which is information a properly cali- studies of the effects of weather fronts on GPS pospheric propagation delay. brated barometer can provide. The tricky measurements, which they recount in this In the January 1993 issue of GPS World, aspect is the delay’s wet part, caused by month’s column. Fritz K. Brunner and Walter M. Welsch dis- water vapor in the tropo-sphere’s lower lay- Dr. Gregorius studied surveying at the cussed the troposphere’s effect on GPS mea- ers. Similar to the ionospheric electron con- Universities of Karlsruhe (Germany) and New surements. They correctly mentioned that (in tent, the water vapor’s spatial and temporal South Wales (Australia), where he graduated extreme cases) the wet part of the delay can distribution is largely unpredictable and can with a B.E. in geomatic engineering in 1995. vary by more than 3 centimeters per hour undergo rapid variations, especially in the He then went to the United Kingdom to work during the passage of a front. In this article, presence of a weather front. Surface humidity on geophysical and meteorological we will explain in more detail why fronts readings do not usually represent the tropos- applications of GPS at the University of cause such rapid variations in the delay, how phere’s moisture content very well. There- Newcastle upon Tyne. After obtaining his that affects GPS precision, and what we can fore, even with surface meteorological data, Ph.D. this year, he moved to The Netherlands, do to reduce or eliminate the problem. First, it is hard, if not impossible, to properly model where he now works for Shell International. however, we will provide a quick summary or predict the wet delay. 52 GPS WORLD May 1998 INNOVATION THE POSITIONING EFFECT For differential positioning (based on dou- matic-type surveys, however, this is more On top of GPS’s inherent geometric weak- ble differencing), Brunner and Welsch sug- difficult to determine. ness because a receiver cannot track satellites gested the following rule of thumb for the below the horizon, tropospheric delay is the propagation of tropospheric error into the WHAT IS A WEATHER FRONT? main additional ingredient to the heighting GPS estimates of height (for an elevation cut- Although most GPS users know about atmo- error budget. The accuracy of station height off angle of 15 degrees): height difference spheric delay and how it contributes to posi- determinations is less than that of the latitude error equals three times the differential tro- tioning error, they may be unfamiliar with the or longitude by a factor of two or so. pospheric delay error. In other words, an esti- concept of a weather front. Before we High-precision GPS software packages mated total tropospheric delay error of 1 describe how weather fronts affect GPS mea- account for the tropospheric delay by esti- centimeter will propagate into a heighting surements, we will briefly introduce the mating a zenith delay parameter that is linked bias of 3 centimeters. Achieving subcentime- physics of fronts. to arbitrary elevation angles through a map- ter heights, therefore, seems to require mod- Out in Front. A weather front is the boundary ping function. Traditionally, tropospheric eling and estimating the total delay with an between two air masses that display differ- variations over time have been accounted for overall accuracy better than 3 millimeters. ences, especially in temperature, wind direc- by stochastic estimation techniques, ranging One problem with estimating the residual tion, and humidity. Depending on the front’s in sophistication from Kalman filtering and tropospheric delay, though, is the high corre- direction of motion, it is denoted as either equivalent approaches to simply estimating a lation between the height and tropospheric cold or warm. For a stationary observer on new delay bias at regular intervals, for exam- parameters, which increases even further the earth’s surface, cold air replacing warm ple every hour. More recently, to account for with higher elevation cut-off angles. Mathe- air defines a cold front. Conversely, warm air spatial variations of tropospheric refraction, a matically, it is therefore unclear whether succeeding cold air denotes a warm front. number of scientists have attempted addition- observed, short-term changes in height are Often, a faster-moving cold front overtakes a ally to estimate tropospheric gradients in attributable to atmospheric variations or to warm front from behind, eventually resulting north and east directions to allow for any antenna motion. In static mode, one can rea- in a more complex, merged front called an azimuthal variation in the delay (as opposed sonably assume that the stationary antenna occlusion (or occluded front). Such a front to assuming that the delay varies with the (and the ground in which it is anchored) is then slowly dissolves as the differences vertical elevation angle only), apparently stable and, therefore, can attribute any short- between the bordering air masses gradually with some success. term changes to the atmosphere. In kine- disappear. 1/4 Page 1/4 Page Ad Goes Here Ad Goes Here Keyline Keyline does not print does not print page 53 page 53 Circle 36 Circle 37 May 1998 GPS WORLD 53 For some applications it is convenient to the passage, these properties usually do not causing a kink in the isobars. Such a trough, model a front as a two-dimensional boundary change much. however, may also be nonfrontal so that surface. In reality, however, it is a relatively This scenario is slightly different for a fronts cannot simply be inferred by such thin (40–200 kilometers thick), three-dimen- cold front, and any changes at the passage are anomalies in the pressure field.