GPS ' of Atmospheric Using the Global Positioning System


We present a new approach to remote sensingof water vapor based on the global positioning system (GPS). Geodesistsand geophysicistshave devised methods for estimating the extent to which signals propagating from GPS to ground-based GPS receivers are delayed by atmospheric water vapor. This delay is parameterized in terms of a time-varying zenith wet delay (ZWD) which is retrieved by stochasticfiltering of the GPS data. Given surface and readings at the GPS receiver, the retrieved ZWD can be transformed with very little additional uncertainty into an estimate of the integrated water vapor (IWV) overlying that receiver. Networks of continuously operating GPS receivers are being constructedby geodesists,geophysicists, government and military agencies, and others in order to implement a wide range of positioning capabilities. These emerging GPS networks offer the possibility of observing the horizontal distribution of IWV or, equivalently, precipitable water with unprecedented coverage and a temporal resolution of the order of 10 min. These measurementscould be utilized in operational and in fundamental research into atmospheric storm systems, the hydrologic cycle, , and global change. Specially designed, dense GPS networks could be used to the vertical distribution of water vapor in their immediate vicinity. Data from ground-basedGPS networks could be analyzed in concert with observations of GPS occultations by GPS receivers in low orbit to characterize the at planetary scale.

INTRODUCTION accuracies of--•0.2øC and --•3.5%, respectively, with dimin- ishing performance in cold, dry regions [Elliot and Gaffen, Water vapor plays a crucial role in atmospheric processes 1991]. Although the advantages of measurements that that act over a wide range of temporal and spatial scales, provide good vertical resolution are clear, mea- from global climate to micrometeorology. Water vapor is the surements have some serious disadvantages too. - most variable of the major constituents of the atmosphere. It sondes are expendable, and the cost of these devices re- contributes more than any other component of the atmo- stricts the number of launches to twice daily (0000 and 1200 sphere to the . The distribution of water UTC) at a limited number of stations. Because of these vapor is intimately coupled to the distribution of and restrictions, radiosonde measurements inadequately resolve rainfall. Because of the unusually large associated the temporal and spatial variability of water vapor, which with water' s changeof , the distribution of water vapor occurs at scales much finer than the spatial and temporal plays a critical role in the vertical stability of the atmosphere variability of temperature or [Anthes, 1983]. In fact, and in the structure and evolution of atmospheric storm limitations in the analysis of water vapor are the major systems.The of water vapor and its latent heat by source of error in short-term (0-24 hours) forecasts of the general circulation of the atmosphere is an important . Efforts to modernize the National Weather component of the Earth's meridional energy balance. In Service and fiscal austerity recently have conspired to addition, water plays a critical role in many chemical reac- degrade the network [Bosart, 1990]. Curtailment of National tions that occur in the atmosphere. Oceanic and Atmospheric Administration support for the Atmospheric scientistshave developed a variety of means Mexican radiosonde program has resulted in the loss of the to measure the vertical and horizontal distribution of water 0000 UTC Mexican soundings, which are often crucial in vapor. The radiosonde, a balloon-borne instrument package resolving upstream features in the atmosphere that are that sends temperature, , and pressure data to the precursors to over the southern United ground by radio signal, is the cornerstoneof the operational States. analysis and prediction system at the National Meteorolog- Ground-based, upward-looking water vapor radiometers ical Center in this country and at similar operational weather (WVRs) are instruments that measure the background mi- forecast centers worldwide. Contemporary radiosonde in- crowave radiation produced by atmospheric water vapor and struments measure temperature and relative humidity with can estimate the integrated water vapor (IWV) content along a given line of sight. They can simultaneously measure 1Departmentof Marine,Earth and Atmospheric Sciences, North integrated water (ILW) along the same line of sight. Carolina State University, Raleigh. 2Departmentof Earth, Atmosphericand PlanetarySciences, WVRs actually measure the sky brightness temperature at MassachusettsInstitute of Technology, Cambridge. two or more frequencies. It is the frequency dependence of 3UniversityNavstar Consortium, Boulder, Colorado. the brightness temperature that enables the simultaneous 4UniversityCorporation for AtmosphericResearch, Boulder, estimation of IWV and ILW [Resch, 1984]. The algorithm Colorado. that is used to retrieve IWV from observation of sky Copyright 1992 by the American Geophysical Union. brightness temperature contains parameters which show Paper number 92JD01517. seasonal and site variations. Thus the retrieval algorithm 0148-0227/92/92JD-01517505.00 usually must be "tuned" to local conditions using indepen-


sensingof atmospheric water vapor. The global positioning system (GPS) consists of a constellation of satellites that transmit L band (1.2 and 1.6 GHz) radio signals to large 140 ø W numbers of users equipped with GPS receivers who use the system for navigation, time transfer, and relative position- ing. When the constellation is completed in the next few years it will incorporate 21 active satellites and 3 spares orbiting the earth at an altitude of 20,000 km in six orbital planes. During the last few years the practitioners of GPS , and those of a related geodetic technique known as 20 very long baseline (VLBI), have devised 36 procedures for estimating the extent to which the atmo- sphere in general, and water vapor in particular, are slowing the propagation speed of GPS radio () signals. More specifically, it is possible to determine the "zenith wet IWV (kg delay" caused by the overlying each GPS (or VLBI) receiver in a network. Since this delay is nearly proportional to the amount of precipitable water above the GPS site [Hogg et al., 1981; Resch, 1984], the possibility 16 arises that GPS networks might be used by meteorologists for remote sensing of the atmosphere. (The quantity of atmospheric water vapor overlying a given point on (or above) the Earth's surface usually is stated as the vertically integrated mass of water vapor per unit area (e.g., in per square meter) or as the height of an equivalent PW (mm) / •50ø w 3• column of liquid water. Since these measures have different dimensionsit is convenient to give them separate names. We Fig. 1. Nimbus image of vertically integrated water vapor use the term integrated water vapor when we state the mass (IWV) within a storm system, redrawn from McMurdie et al. [1987]. of vapor per unit area, and precipitable water (PW) if we The units of IWV are in kilograms per square meter. The numbers in the key can be interpreted equivalently as millimeters of precipitable refer to the height of an equivalent column of water. Clearly, water (PW). PW = IWV/p, where p is the density of liquid water. A useful rule of thumb is that the zenith wet delay stated in units of length is roughly 6.4 times the PW.) dently obtained meteorological data (usually radiosonde The prospect of using GPS networks for operational data). Most meteorologists are more familiar with space- weather forecasting and research is made interesting by the based, downward-looking WVRs. While upward-looking fact that continuously operating GPS networks are now WVRs measure water vapor emission lines against the cold being constructed around the world by geophysicists, geod- background of space, downward-looking WVRs measurethe esists, surveyors and others implementing various classes of corresponding absorption lines in the radiation from the hot positioning capabilities. As new applications, such as real- background provided by the Earth. Figure 1 shows an image time differentialpositioning of aircraft and shipping,are imple- of IWV for a typical mid-latitude obtained over the mented, the number of continuouslyoperating GPS stationsis Pacific by a scanning multichannel microwave radi- likely to increasevery rapidly, particularly in the United States ometer aboard the Nimbus 7 satellite. The recovery of IWV and Europe. By the turn of the century it is likely that at least by space-based WVRs is greatly complicated over by a few and sometimesmany continuously operating GPS sta- the fact that the temperature of the hot background is quite tions will be located in every state in the United States. It is variable and difficult to determine. A similar problem occurs probable that every major airport in the United States eventu- in the presence of , because the background tempera- ally will incorporate a continuously operating GPS station. ture may change from ---290 K (Earth's surface) to ---220 K These GPS networksmight be usedto estimatethe precipitable (cloud top). These changes are large and important but are water overlying each GPS station every 10 min or so, with an not easily specified. It is possiblein principle to model these accuracy not yet well determined but probably better than effects, but in most cases it would be a difficult and time- ___5%in nonarid environments.This application involves me- consuming task. For this reason, satellite-based WVRs tend teorologistsutilizing data from networks establishedand main- to be more useful over the than over land, and their tained by nonmeteorologists.At the other end of the potential utility is degraded in the presence of clouds. Ground-based applicationspectrum, specially designed, dense meteorological WVRs are not affected by light or moderate cloud cover, GPS arrays could be used to sense the distribution of water though their performance may be degraded in the presence vapor in both space and time, that is, to engagein water vapor of heavy cloud, and few if any of these instruments provide tomography. useful data when it is raining. Ground and space-based WVRs are complementary rather than competing systems. ATMOSPHERIC PROPAGATION DELAYS: GEODETIC NOISE Ground-based units provide good temporal but poor spatial OR METEOROLOGICAL SIGNALS. 9 coverage, whereas space-based WVRs have the opposite characteristics. GPS was originally designed as a navigational and time In this article we present a novel approach to the remote transfer system, but since its implementation it has revolu- BEVIS ET AL,: GLOBAL POSITIONING SYSTEM METEOROLOGY 15,789 tionized the of geodetic positioning (very precise sur- always much smaller than the hydrostatic delay, it is usually veying) and in this context it is now widely employed by far more variable and more difficult to remove. In temperate geodesists, geophysicists, and surveyors [Leick, 1990; areas the daily variability of the wet delay usually exceeds Dixon, 1991]. In GPS geodesy the distances between GPS that of the hydrostatic delay by an order of magnitude satellites and GPS receivers are determined either by mea- [Elgered et al., 1991]. Becauseit is not possibleto accurately suring the time of flight of the time-taggedradio signalsthat predict the wet delay from surface meteorologicalmeasure- propagatefrom satellitesto receivers ("pseudoranging") or, ments [Resch, 1984; Tralli et al., 1988], geodesists predict over a more extended period of time, by finding the associ- the hydrostatic delay from surface measurements and at- ated path lengths by an interferometric technique ("phase tempt to measurethe wet delay. One approachto measuring measurement"). Both of these approaches are complicated the wet delay uses ground-based water vapor radiometer by the presence of the Earth's atmosphere, which increases observations [Resch, 1984; Ware et al., 1986; Elgered et al., the optical path length between satelliteand receiver and the 1991]. However, in an alternative approach, GPS and VLBI correspondingtime of flight of the GPS radio signal. One of geodesistshave developedestimation techniquesthat deter- the key tasks of geodetic GPS processing software is to mine the time-varying zenith wet delay (and any unmodeled "correct" the ranges between receivers and satellites so as or residual zenith hydrostatic delay) from the GPS or VLBI to remove the effects of the Earth's atmosphere, thereby data themselves [Tralli et al., 1988; Herring et al., 1990]. reducingall optical path lengthsto straight-linepath lengths. These estimation techniques usually assume azimuthal sym- These corrections can be formulated in terms of excess path metry of the atmosphere, and they exploit the form of the lengths, signal delays, or phase advances. elevation dependence of the delay (i.e., the mapping func- Both the and the neutral atmosphereintroduce tion) and the fact that the delay changes little over short propagation delays into the GPS signal. The ionosphere periods of time. These analyses typically constrain the introduces a delay that can be determined and removed by variations in the zenith wet delay to between 1 and 20 mm recording both of the frequencies(L 1 and L2) transmitted by per hour, dependingon location and time of year. The zenith GPS satellites and exploiting the known dispersionrelations wet delay can be recovered from GPS and VLBI data with for the ionosphere (Spilker [1980] and Brunner and Gu an accuracy between 5 and 20 mm (as discussedbelow). [1991]; see the appendix for a brief review of ionospheric GPS geodesists estimate ionospheric and tropospheric effects). The delay associatedwith the neutral atmosphere is delays only to eliminate them. But ionospheric physicists are effectively nondispersive at GPS frequencies and so cannot beginning to use GPS as a tool to study the ionosphere be corrected in this way. The neutral atmosphere is a [Coco, 1991]. We believe that in a similar manner meteorol- mixture of dry gasesand water vapor. Water vapor is unique in this mixture because it is the only constituent which ogistsmay be able to exploit GPS as a means of studyingthe possessesa dipole moment contribution to its refractivity. In refractivity of the atmosphere and tropospheric water vapor fact, for , its reftactivity is dominated by the distribution in particular. This may require further innova- dipole component. Throughout most of the tropospherethe tion in the modeling of the wet and hydrostatic tropospheric dipole component of the reftactivity is about 20 times larger delays. Existing models employed by geophysicists and than the nondipole component. For this reason it has be- geodesistsare somewhat idealized, for example, they nor- come common to treat the dipole component of the water mally assume azimuthal symmetry of the atmosphere in the vapor reftactivity separatelyfrom the nondipole components vicinity of a given GPS receiver, whereas azimuthal varia- of the reftactivities of the water vapor and other constituents tions of 20% are quite commonly observed in humid areas in the atmosphere. These two componentsare referred to as [Rocken et al., 1991]. Recent VLBI studies have started to the "wet" and "hydrostatic" delays. (The hydrostatic delay incorporate azimuthal asymmetry models, although these is often erroneously referred to as the "dry" delay.) Both types of solutions are not yet routinely used [e.g., Herring, delays are smallest for paths oriented along the zenith 1992]. Furthermore, the techniques used to estimate hydro- direction and increase approximately inversely with the sine static and wet delays are focused on correcting the signals of the elevation angle. That is, either delay will tend to recorded at an isolated receiver and not on studying the increase by about a factor of 4 from zenith to an elevation of atmospherefor its own sake, nor on exploiting the power of about 15ø. Most expressionsfor the delay along a path of an array of GPS receivers to study the spatial structure of the arbitrary elevation consistof the zenith delay multiplied by a propagation delay. Meteorologists and GPS specialists mapping function. The mapping function describes the de- working together should be able to design procedures that pendence on elevation angle [e.g., Davis et al., 1985]. can be used to characterize the troposphere in more detail. Geodesists and geophysicistshave spent a great deal of For example, one can conceive of using arrays of GPS effort learning how to model these delays in order to be able receivers to perform tomographic inversions of the space- to remove them from GPS and VLBI observations [e.g., time structure of the overlying water vapor distribution (we Tralli and Lichten, 1990; Herring et al., 1990]. The hydro- discussthis below). GPS geodesistsare motivated to assist static delay reaches about 2.3 m in the zenith direction. in such an effort because this may lead to better ways of Given surface pressure measurements,it is usually possible correcting for propagation delays. It is widely appreciated to model and remove the hydrostatic delay with an accuracy that improved modeling of tropospheric delay is necessaryto of a few millimeters or better. If the atmosphere is in improve the vertical accuracy of GPS geodesy. Improved hydrostatic equilibrium and the barometer is well calibrated vertical accuracy is of great interest to geophysicists and (error <0.3 mbar), then the hydrostatic zenith delay will be others who study , land, and level changes in the determined to better than 1 mm. The zenith wet delay can be context of global [National Research Coun- as small as a few centimeters or less in arid regions and as cil, 1990; Bilham, 1991]. It is also attractive to geophysicists large as 35 cm in humid regions. Although the wet delay is performing research on the crustal motion and deformation 15,790 BEVIS ET AL.: GLOBALPOSITIONING SYSTEM METEOROLOGY associated with , volcanic activity, and plate only on surface pressure, called the "hydrostatic delay," tectonics [Hager et al., 1991; Dixon 1991]. and a smaller quantity which is a function of water vapor distribution and is called the "wet delay" (see Davis et al. [1985], for details). Many authors refer to the hydrostatic PHYSICS OF THE ATMOSPHERIC PROPAGATION DELAY delay as the "dry delay," but we avoid this usage. The The atmosphere affects microwave transmissions from largest contribution to the hydrostatic delay is that of the dry space in two ways. First, the waves travel slower than they air. Nevertheless, the hydrostatic delay usually includes a would in a vacuum. Second, they travel in a curved path significantcontribution from water vapor (due to the nondi- instead of in a straight line. Both of these effects are due to pole componentof water vapor refractivity), and so the term a variable index of along the ray path. The delay in dry delay is misleading. Wet delay is a more appropriate signal arrival time can be stated in terms of an equivalent term in that it is produced solely by atmosphericwater vapor increase in travel path length. This excess path length is (due to the dipole component of its refractivity), though it given by shouldbe kept in mind that it is not the only delay produced by water vapor. Elgered et al. [1991] adopted a model in which the zenith (1) AL=f r n(s) ds- G hydrostatic delay (ZHD), in millimeters, is given by where n(s) is the refractive index as a function of position s AL• = ZHD = (2.2779_+ O.0024)Ps/f(A, H) (5) along the curved ray path L, and G is the straight-line geometrical path length through the atmosphere (the path where P s is the total pressure(in millibars) at the Earth's that would occur if the atmosphere was replaced by a surface, and vacuum). Equivalently, f(A, H)= (1 -0.00266 cos 2A -0.00028H) (6)

accounts for the variation in gravitational acceleration with AL=f/• [n(s) - 1]ds +[S - G] (2)latitude A and the height H of the surface above the ellipsoid (in kilometers). The troposphere accountsfor about 75% of where S is the path length alongL. The first term on the right the total hydrostatic delay. is due to the slowing effect, and the second term is due to The second component of total delay is known as the wet bending. The bending term [S - G] is much the smaller, delay ALw. The zenith wet delay (ZWD) is given by about 1 cm or less, for paths with elevations greater than about 15ø . For rays oriented along the zenith, and in the absenceof horizontal gradients in n, the ray path is a straight line and the bending term vanishes. Equation (2) is often formulated in terms of atmospheric refractivity N, defined (7) by N = 106(n - 1), ratherthan the indexof refraction. The refractivity of the atmosphere is a function of its temperature, pressure, and water . Smith and wherek• = (17 - 10) K mbar-1, the integralis alongthe Weintraub [1953] suggestedthe relationship zenith path, and the delay is given in the units of z [Davis et al., 1985]. It is usually adequate to approximate this expres- N = 77.6(P/T)+ 3.73 x 105(Pv/T2) (3) sion by where P is the total (in millibars), T is the atmospheric temperature (in degrees ), and Pv is (8) the of water vapor (in millibars). This ALøw=(0.382 - 0.004)K 2mbar -1• (Pv/T 2)dz expression is considered accurate to about 0.5% under These expressionscan be evaluated from profiles of P v and normal atmospheric conditions [Resch, 1984]. In most con- T provided by , if such data are available. texts the first term in (3) is considerably larger than the Almost all of the wet delay occurs in the troposphere, and second. A more accurate formula for refractivity is provided most of it occurs in the lower troposphere. by Thayer [1974]: Although some effort has been made to develop models N = kl(Pd/r)z•-1 q- k2(Pv/T)Z• -1+ k3(Pv/T2)Z•-1 (4) that can be used to predict the zenith wet delay from surface measurements,their predictive value is very poor compared wherek 1 = (77.604 -+ 0.014) K mbar-1, k2 = (64.79 -+ to the surface model given above for the zenith hydrostatic 0.08)mbar -1, k3 = (3.776-+ 0.004) x 105K 2 mbar-1, Pa delay [Resch, 1984; Tralli et al., 1988, Baby et al., 1988]. In is thepartial pressure of dry air (in millibars),and Z• 1 and practice, the wet delay must be measured using radiosonde Z•-1 are the inversecompressibility factors for dry air and launchesor WVRs or derived by stochasticor other forms of water vapor, respectively. Both of these factors, which are parametric modeling of the GPS or VLBI data themselves. corrections for nonideal behavior, have nearly constant We must use one or more mapping functions to relate values that differ from unity by a few parts per thousand zenith path delays to delays along paths with arbitrary [Owens, 1967]. The uncertainties in the constants of (4) limit elevation angles.The total delay for a path with an elevation the accuracy with which the refractivity can be computed to angle 0 can be computedfrom the hydrostatic and wet zenith about 0.02% [Davis et al., 1985]. delays via Saastamoinen [1972] showed that the total atmospheric 0 delay can be partitioned into a large quantity which depends Am= AZ•mh(O) + AZwmw(O) (9) BEVISET AL.' GLOBALPOSITIONING SYSTEM METEOROLOGY 15,791 where Mh(O ) is the hydrostatic mapping function and In order to achieve the best possible retrieval of IWV or Mw(O) is the wet mapping function. Various forms have PW from an observed zenith wet delay, via equation (11) or been proposed for the wet and hydrostatic (or "dry") (13), the constantg shouldbe estimatedusing a value for T m mapping functions [e.g., Chao, 1972; Black and Eisner, that is "tuned" to the specific area and season. This can be 1984; Lanyi, 1984;Davis et al., 1985]. These functions differ done, for example, by statistical analysis of a large number in the number of meteorological parameters that are incor- of radiosondeprofiles. If we choosea singlevalue of T m for porated. For example, Chao's [ 1972] mappingfunctions, one all areas and seasons,say T m = 260 +_ 20 K, then (11) is each for M n and Mw, make no reference to meteorological accurate only to about 15%. A more powerful approach conditions, whereas the hydrostatic mapping function de- would be to use operationalmeteorological models to predict rived by Davis et al. [1985] incorporates surface tempera- the actual value of T m. In the event that operational model ture, pressure and relative humidity, the height of the output is not available, an alternative approach is to estimate , and the tropospheric temperature . T m solely on the basis of the observed surfacetemperature. Because the mapping functions Mh and Mw are similar If the Earth's atmospherewere isothermal, then T m would above elevation angles of 10ø-15ø, and GPS observations at be constant and equal to surface temperature. However, lower elevations are rarely used, it is possible to lump the since the atmosphere usually has a negative temperature two delays together and estimate them jointly [Tralli and gradient up to the tropopause, T m will be the average Lichten, 1990]. Nearly all of the mappingfunctions that have temperature of atmosphereweighted by the pressureof water been suggestedin the literature assume no azimuthal varia- vapor, as indicated by (10). Therefore we should expect that tion in path delay. Recent VLBI studies indicate that azi- T m will depend on surface temperature, and tropospheric muthal asymmetry effects at 15ø elevation typically produce temperature profile, and on the vertical distribution of water a root-mean-square (rms) variation of 7 ram, ouLaL times u,• •at.,m ,h• •u•a• temperature effect can be as much as 5 times larger. The assumption of comparison of T m computed from (10) using radiosonde azimuthal symmetry may cause significant errors when the profilesof P• and T and the values of surfacetemperature local tropospherehas large lateral temperature, pressure, or reported at the time of launch. In Figure 2 the ratio ZWD/PW humidity gradients [Gardner, 1976; Davidson and Trask, and Ts are shown as a function of time, based on 748 1985], as usually accompany strongfrontal weather systems radiosondeprofiles from Albany, New York. Inverting these (Figure 1). results for the dependenceof T m on T s yields T m • 55.8 + 0.77 Ts, with an rms scatter about this regressionof 4.4 K. The rms scatter about this simple regressionindicates that ESTIMATING INTEGRATED WATER VAPOR FROM can be recovered at this site with an rms error of less than AN OBSERVED WET DELAY 2% from just knowledge of the surface temperature. An It is possible to derive an approximate relationship be- analysis of 8718 radiosonde profiles spanningapproximately tween the vertically integrated water vapor (IWV) and an a two-year interval from sites in the United States with a observed zenith wet delay [Askne and Nordius, 1987]. latitude range of 27ø to 65ø and a height range of 0 to 1.6 km Following Davis et al. [1985], we introduce the weighted yields a linear regressionT m • 70.2 + 0.72 T•, with an rms "mean temperature" of the atmosphere, Tm, defined by deviation from this regression of 4.74 K (Figure 3), which is a relative error of less than 2%. Less than 3% of the data points deviate from the regression by more than 10 K, and we suspectthat many of these points reflect unusual levels of Tm = f (Pv/T)dz (10) error in the corresponding radiosonde data. We conclude that •

ESTIMATING ATMOSPHERIC DELAY IWV=f Pv dz= •(AL wø (11) FROM GPS AND VLBI DATA Virtually all high-accuracy GPS data processing software whereAL w 0 is the zenithwet delay,and the "constant"•< is given by packages in use today include among their functions the estimation of tropospheric delay parameters. In most cases 1/K= 10-6(k3/Tm+ k•)Rv (12) these parameters are estimated at the same time as the station and satellite coordinates are being estimated. While where R• is the specificgas constant for water vapor. The most software packageseliminate clock errors through dou- water vapor content of the atmosphere is sometimes stated ble differencing, a technique in which one combines observ- as the height of an equivalent column of liquid water, which ables in such a way that clock errors are canceled out [Leick, we refer to as the precipitable water (PW). Numerically, the 1990], other software packages process the undifferenced IWV is just the product of p and PW, where p is the density data by introducing an explicit model for clock drift. Several of water. Since PW and ZWD both have units of length, their packages are capable of modeling tropospheric delays in ratio more than one way. For example, one may chooseto predict PW/ZWD=PW/ALøw= K/p (13) the zenith hydrostatic delay (ZHD) from surface meteoro- logical measurements and model only the zenith wet delay is a dimensionlessquantity. (ZWD). In this case the ZWD model will tend to absorb 15,792 BEVIS ET AL.: GLOBAL POSITIONINGSYSTEM METEOROLOGY

7.5 i i i i i i ! i

4- _


i i i i i i i •. Jan Apr Jul OcL Jan Apr Jul OcL 1990 1991 Fig. 2. Values of (1) the dimensionlessratio of zenith wet delay (ZWD) to precipitable water (PW) and (2) surface temperature (T$) from an analysisof 2 years of radiosondedata from Albany, New York. Note that the ZWD is given in units of equivalent excess path length and that PW is the vertically integrated quantity of water vapor stated as the height of an equivalent column of liquid water. (IWV = PW multiplied by the density of water).

errors in the modeling of the ZHD. Another approach is to necessaryto choose a specific class of stochasticprocess to measure the wet delay, using a WVR, and to model only the represent fluctuations in this tropospheric parameter. Ide- residual wet delay due to the instrumental and calibration ally, this choice would be based on insight into the underly- errors of the WVR. In some situations it is reasonable to ing physical processes. In practice, the class of stochastic model the total zenith delay as a single entity. The following process is usually selected on the basis of the observed discussionassumes that the ZWD is being modeled, but keep power spectrum of the system being modeled. Most practi- in mind that further generalization is possible. tioners assume that the ZWD can be modeled as a random The simplest estimation approach is to assume that the walk process or as a first-order Gauss-Markov process ZWD is constant for a given time interval and to estimate its [Treuhaft and Lanyi, 1987; Lichten and Border, 1987; Tralli value as part of the overall least squares inversion. Typi- et al., 1988; Herring et al., 1990]. The stochastic process cally, practitioners of this approach assumethat the ZWD is noise typically is chosen so as to constrain the variation of constant for an interval ranging from 1 hour to 1 day. the ZWD to between 1 and 20 mm per hour depending on Depending on the length of the survey, this may mean that location and time of year. only one troposphericparameter is estimated at each station Retrieval of the ZWD by stochastic filtering has been or perhaps as many as 24 per GPS day. This standard least tested more extensively in the context of VLBI rather than squares approach (the "deterministic" approach) usually GPS geodesy because of the very long continuous observa- involves placing some constraintson the value of the ZWD, tion periods that are available to VLBI geodesists and and perhaps on its rate of change, to keep it within reason- because VLBI geodesistshave routinely monitored atmo- able bounds. spheric water vapor using WVRs at many of their sites, A more sophisticated approach utilizes the fact that tem- which provides some basis for comparison. The VLBI poral variation of the ZWD has exploitable statistical prop- technique is similar to GPS in that it involves recording and erties. The ZWD is not likely to change by a large amount correlating radio signals from extraterrestrial radio sources over a short period of time (such as 10 min). In fact, the (quasars), and it observes at two frequencies in order to ZWD can be viewed as a stochasticprocess, and the process determine the ionospheric delay. It has some significant parameters can be estimated using a Kalman filter or a differences too. The VLBI measurement is similar to that related class of optimal filters based on the state-space,time used to implement time-of-flight determinations in GPS domain formulation [Gelb, 1974]. Some VLBI and GPS geodesy("pseudoranging"), but it does not utilize the phase processing packages model clock errors as a stochastic of the carrier wave as does GPS geodesy ("phase measure- process whose parameters are estimated along with the ment"). VLBI and GPS have relative strengths and weak- tropospheric processparameters [Herring et al., 1990; Lich- nessesin inverting for the atmospheric delay. For example, ten and Border, 1987]. In order to estimate the ZWD or an VLBI enjoys a stronger geometry of sourcesin the sky, and alternative tropospheric quantity via a stochasticfilter it is its directional antennas track down to lower elevation an- BEVISET AL.: GLOBALPOSITIONING SYSTEM METEOROLOGY 15,793

1000 , residuald!stribution ,

800 n= 8718 -


300 400 - , ,

290 ;..:..: •, ;?;, •. :" ß.•.:,.....g, .. oo_0 -2o•._•,,,,,,,,,,,,,,,,•,,r•-• 211111111111 o 20, - '. ß:.'. ,•,, • .•..,,' .... ß ... • ß,I"• "4;." ' 280 ßo '., {•;-_i;:*,'•'". •..• •.;i'it,:i'.'.-;".•:" 270 ß .. ß ...."' -

..., '.: . ...: .','.?.,.'- ,.•.•.,?i.•:.;-.' ...... 260 '." ß .... :', i'..'";?:' s-•%.7::''. ß . '..-" ".. ß .... ß. :., .: . . 250 ß L'."::".'"'.'.'"%': ":' ß '

240 rms dev = 4.74 K

230 I I i I I i I 2. 240 250 260 270 280 290 300 310

SurfaceTemperature, Ts (K) Fig. 3. Relationshipbetween T m and T$ determinedfrom the analysisof 8718 radiosondeprofiles acquired between fall 1989 and fall 1991. The solid line shows the linear regression through all of the data. The profiles used are from 13 stations in the United States, whose latitude ranges from that of Fairbanks, Alaska, to that of West Palm Beach, Florida. The stations used have WBAN numbers 70200, 70261, 72203, 72270, 72291,72366, 72381, 72387, 72391, 72393, 72618, 72606, and 74494. The histogram depicts the distribution of residuals (observed minus predicted) about the linear fit.

gles, but GPS is capable of totally eliminating clock errors of the research groups using them have made systematic (which can trade off with tropospheric parameter estimates) comparisons of the ZWD estimated from the GPS data and via the double-differencing technique. The recovery of the the ZWD determined using WVRs or radiosonde data. One zenith wet delay from VLBI data by Kalman filtering has notable exception is the research group at Jet Propulsion been discussedby Herring et al. [1990]. Elgered et al. [1991] Laboratory (JPL) that has developed and applied a GPS have discussed the results of an extensive intercomparison processing package called GIPSY [Lichten and Border, of the ZWD, as estimated by stochastic filtering of VLBI 1987] and has made several interesting intercomparisons of data, and the ZWD, as estimated from WVR observations. geodetic and tropospheric parameter estimation for cases The two plots in Figure 4 show typical intercomparisons for where the ZWD was recovered from GPS data alone via sites at the Haystack , Massachusetts, and stochastic filtering and where the recovery of the ZWD was Mojave, California. Note that the two sets of estimates track achieved or calibrated using WVRs [Tralli et al., 1988; Dixon each other very well, but in the case of the Haystack data and Kornreich Wolf, 1990]. Figure 5 shows an intercompar- there is an offset or bias of about 17 mm. The source of these ison of stochastic and WVR-based estimates for the ZWD long-term biases is not well understood. If long-term biases based on observations from Central America in January are removed, then the rms discrepancy between WVR and 1988. It is worth noting that the GPS satellite constellation Kalman estimates of the ZWD are usually ---10 mm or less. early in 1988 was considerably weaker (geometrically) than The typical level of bias is ---10 mm. Because the offset that available today. There has also been some comparison between the stochastic and WVR estimates almost certainly of GPS- and VLBI-estimated wet delays, discussedby Tralli derives from errors in both techniques, it is likely that the et al. [1992]. The rms agreement in this study was below 10 bias between the stochastic estimate of the ZWD and the mm in all but one case. The recovery of the ZWD by true ZWD is typically less than 10 mm. stochastic modeling of GPS data is comparable to that Given the massively overdetermined of GPS inver- achieved by VLBI geodesists. sions, and the similar approaches that GPS and VLBI The JPL group was the first to adopt a stochastic estima- geodesistshave taken to tropospheric modeling, we would tion module for atmospheric modeling within a GPS process- expect that stochastic estimation routines in GPS processing ing package. Most of the other major GPS processing software would perform at similar levels to those employed packages took the deterministic rather than stochastic ap- in VLBI processing software. Although many GPS process- proach to estimating atmospheric delays. At the time of this ing packages include tropospheric parameter estimation, few writing, however, most groups producing high-accuracy 15,794 BEVIS ET AL..' GLOBAL POSITIONINGSYSTEM METEOROLOGY

lOO analysisduring a secondpass through the data, thereby focusingmore resolvingpower on the inversionfor the ZWD history. Second, the number of GPS satellites is still increas- ing, so the numberof observationsper unit time that can be usedin the inversionfor the ZWD is goingto increaseuntil the GPS satellite constellationis complete. Third, the num- ber and quality of global tracking stationsin networks such as the CooperativeInternational GPS Network and the Deep ß Kalman filter estimate Space Network is steadily increasing, and as a result, the _ o WVR data GPS satellite orbits are becoming better controlled. Since MOJAVE the orbital parameters are among the unknowns estimated

• I • I • I • I • I • I during GPS data analysis, and there exist trade-offsbetween Mean 1 mm orbital and troposphericparameters, strengthening the con- R_MS about mean 5 mm trol on the orbits will strengthenthe inversion for the ZWD. Finally, we may be able to improve the algorithmsused to invert for troposphericdelays. Even if we exclude this last -lO factor, we expect to be able to retrieve the ZWD on a more or less routine basiswith less than 10 mm of long-term bias

-30 ] i , i • i ! i • i , i and less than 10 mm of random noise. 18:00 0:00 6:00 12:00 18:00 0:00 6:00 15May, 1986 16May, 1986 TOTAL ERROR BUDGET ON INTEGRATED WATER VAPOR RETRIEVAL lOO , i . i . [ oo OOo ß Kalmanfilter estimate The error budgetfor the recovery of IWV from geodetic % c• o o• o WVRdata Ooøcb o measurements comprises several distinct error sources, some of which are independent of the total IWV and others which are proportionalto the IWV. The resultspresented here suggestthat in nonarid environments the inversion from path delay to IWV will introduce errors of less than 5% under nearly all conditions.The remainingerror sourcesare related to the accuracywith which the path delay can be • 20 recovered from the geodetic measurements (GPS in the cases consideredhere). Noise in the GPS carrier phase

0 , I , I' • I measurements,as propagated through the Kalman filtering Mean - 17 mm techniques, typically introduces rms errors of less than 10 RMS about mean 6 mm mm in the path delay. In the limited comparisonsbetween o zenith path delays estimatedfrom VLBI and GPS data, the rms difference between estimates varied between 3 and 29 mm, with a typical value of 10 mm [Tralli et al., 1992]. The I -20 case with 29 mm rms difference is considered anomalous and may have been affected by some of the additional error 2:00 8:00 14:00 20:00 sourcesdiscussed below. Errors in the ZWD arisingfrom the 6 May, 1983 standarddual-frequency range correction are of the order of Fig. 4. Estimatesof the zenithwet delay obtainedby stochastic 3 rnm under normal ionosphericconditions (see the appen- filteringof VLBI data and from collocatedwater vapor radiometer dix). The effectsof atmosphericdynamics on the hydrostatic (WVR) measurements[after Elgered et al., 1991].The intercompar- delay are likely to introduceerrors of considerablyless than isonsshown are for VLBI sitesat (a) Mojave, California,where a 1% (23 mm) of the hydrostaticdelay and typically would be new R-seriesWVR was used, and (b) the HaystackObservatory, Massachusetts, where an old R-series WVR was used. The stochas- only a few millimeters. If station barometers are calibrated tic estimatesat eachsite differ from thosereported by Elgeredet al. to better than 0.3 mbar, then the effects of this noise source [1991] because new atmosphericmapping functions have been on the hydrostatic delay will be less than 1 mm. The effects employed. of multipathsignals (i.e., reflectedrather than direct signals received at the antenna)on the GPS phase measurementsis difficultto quantify sinceit dependson the type of antenna GPS processingsoftware have incorporatedor are incorpo- and the environmentin which the antenna is positioned. rating both stochasticand deterministicalgorithms in the Multipath signalsgrow with decreasingelevation angle and latest versions of their codes. therefore can alias into zenith delay estimates. Previous There is goodreason to supposethat we can significantly experience with GPS multipath signals suggeststhat this improve the performance of ZWD retrieval from GPS data. error source is likely to be less than 100 mm on the carrier First, GPS meteorologywould focuson networksthat oper- phasemeasurements made at 15ø elevation angle, and there- ated continuously,or at least for periodsof severalmonths. fore it perturbs the zenith delay measurementsby less than This would enable massiveaveraging of the daily solutions 20 mm. Multipath signalstypically have periods of less than for the network geometry, so that the correspondinggeo- 20 min and therefore should average out rapidly. Fortu- metrical parameters could be removed from the statistical nately, recent developmentsin antennadesign and process- BEVIS ET AL.' GLOBAL POSITIONINGSYSTEM METEOROLOGY 15,795




a• c• 14


12 w

10 z 6 8 10 12 14 16



3: 23

O O 21

• 19

m 17 N 6 8 10 1 1 16 TIME (UTC HRS) Fig. 5. Estimates of the zenith wet delay obtainedfrom WVR measurements,and from stochasticfiltering of GPS data, for a site in Central America in January, 1988 [from Dixon and Kornreich Wolf, 1990]. The solid curves indicate approximatelythe + 1-•rformal error rangefor the GPS-derivedestimates. Crosses at 1515UTC show solar measurementsmade near local sunrise. The dots in the lower plot indicate the formal errors in the WVR measurements.

ing are reducing the multipath problem. The effects of Mapping of Integrated Water Vapor Using Existing incorrect modeling of the elevation angle dependenceof the Geodetic GPS Networks hydrostatic delay have been under intensive study by the GPS is one of most important innovations of the last VLBI community in recent years because of their use of century in the fields of surveying and navigation, and the very low elevation angle data (as low as 5ø ) [e.g., Herring, number of GPS receivers in use has been increasing expo- 1992]. These studies indicate that at elevation angles of 20ø nentially with a double time of less than one year, and the or more the rms errors from this source are typically less space-basedportion of the system is not yet fully opera- than 1 mm. tional! There is no doubt that continuously operating G PS Ultimately, our estimates on the accuracy of IWV recov- systemswill be deployed worldwide in very large numbers in ery are based on the comparisonson VLBI, GPS, and WVR the coming decade. GPS networks are likely to be particu- results. The comparison of these data types has typically larly dense in North America and Europe. We have noted shown rms differences of the path delay estimates of less above that stochastic filters and other statistical techniques than 10 mm about mean differencesof typically less than 10 can be used to recover the zenith wet delay from GPS data mm. We therefore conclude that the precipitable water and that it is possible to estimate the IWV from an observed typically should be recoverable with an rms error of less than zenith wet delay (via equation (11)). The IWV recovered in 2 mm + 2% of the PW and biases of less than 2 mm. this way from data recorded by a given GPS receiver would apply to the immediate vicinity of that GPS station. Given a SOME POTENTIAL CLASSES OF GPS METEOROLOGY sufficientlydense network of receivers, it would be possible to map the distribution of IWV in some detail. A key point is A great number of meteorological applications can be that the data sets required for the regional monitoring of envisionedfor the GPS-derived water vapor data, involving IWV would be available at little cost to the meteorological topics as diverse as storm and frontal systems,global climate community. change, and atmospheric chemistry. We visualize three One can get some idea of the rapid spatial and temporal separate classes of "GPS meteorology," which we discuss changes in the ZWD that are associated with weather below, beginningwith the least complex application. systems from Figure 1. This figure shows an image of IWV 15,796 BEVIS ET AL.: GLOBAL POSITIONINGSYSTEM METEOROLOGY for a typical mid-latitude cyclone obtained over the Pacific process.We coin the term "stochastictomography" to refer Ocean by a scanning multichannel to this generalization of conventional tomographic analysis. (SMMR) aboard the Nimbus 7 satellite. Data from the (A more "deterministic" approach to the problem would be SMMR and the special sensormicrowave imager have been to assume that the water vapor distribution could be repre- used to diagnose the distribution of IWV associated with sented as a quadruple series of orthogonal polynomials in both hemispheres [Katsaros et al., 1989]. The defined over the space-time aperture of the network.) units for IWV in Figure 1 are kilograms per square meter. If such a network was operated for many months, its Here, 1 kg m-2 of IWV is roughlyequivalent to 6.4 mmof geometrycould be found with great accuracy by averaginga path delay. One can see that the IWV "signal" can vary by large number of daily geodetic solutions. By 1993, satellite more than a factor of 3 from just behind the front to just ephemerides(orbital paths) will be known to great accuracy ahead of it. The correspondingchange in the value of the in nearly real time by virtue of automatic processingof data zenith wet delay is from ---8 to ---28 cm. As the front passes from a global tracking network (indeed, such a system is over a stationary observer, this change could occur in as already under construction at Scripps Institute of Oceanog- little as 1 hour or as long as 12 or more hours, dependingon raphy). The point is that the geometry of the situation, both the speed of the front. Since it is possible to recover the on the ground and in space, will be exactly known, and so ZWD from GPS data with an accuracy of 1 or 2 cm, changes estimating this geometry need not complicate the recovery of this magnitude should be easily resolved. of the signal delay observed along a given receiver satellite vector. (Additionally, it may be advantageous in some contexts to minimize receiver clock noise by employing Tropospheric Water Vapor Tomography Using external atomic clocks.) It should be possible in such a Meteorological GPS Networks context to determine a good estimate of the signal delay One can conceive of GPS networks designed specifically along each receiver satellite vector. Because these vectors to optimize their value for remote sensingof the atmosphere. denselysample the troposphereabove the network, it should This class of network would be constructed and maintained be possibleto determine the spatial structure of this delay as by and for meteorologists. When the GPS satellite constel- a function of time. Given a means either to estimate or lation is completed in 1993 it will consist of 21 satelliteswith measurethe vertical temperature profile above the network, orbital periods of 12 hours. At least four satellites will be the space-timedistribution of the propagation delay can be visible at any time anywhere on Earth, and five or six transformedinto the space-timedistribution of water vapor. satellites will be visible much of the time. A satellite that (We assume that the hydrostatic delay can be recovered passes directly above a receiver will take about 6 hours to adequately using surface measurements.) In areas such as cross the sky. Most satellites do not pass directly overhead the United States and Europe, which enjoy well-developed a given ground station but traverse the sky at low to meteorologicalobservation networks, operational models of moderate elevation angles, sometimes rising and setting the atmospheremay well provide sufficient control of the twice within a given 24-hour period. If one imaginesthe set temperature profile so that local sensingof the temperature of vectors passing from a single receiver to each visible distribution may not be necessaryto support GPS tomogra- satellite, realized every 10 min throughout the day, these phy of water vapor distribution. vectors clearly pass through the atmosphere with a wide Of course, the geometry of the network would be designed range of elevations and azimuths. Now conceive of a 5 x 5 accordingto the particular needsof its users. Presumably,it grid of such receivers, spaced say 1 km apart. The total set would always contain a subnet whose spacing was smaller of vectors criss-crossingthe troposphere above the network than or comparable to the vertical extent of the lower constitutes a sampling geometry somewhat reminiscent of troposphere.But it need not be set up as a squaregrid. Other that employed in CAT scan tomography. geometries, such as a logarithmic spiral, have been used to Actually, the situation is fundamentally different from study the ionosphere [Gourevitch et al., 1989]. Although a CAT scan tomography in that a CAT scan target is not meteorological network designed for water vapor tomogra- changing during the period in which the observations are phy would be much smaller and denser than the regional collected, and therefore the fact that observations along GPS networks described in the previous section, it would different vectors through the target were collected at differ- probably be necessaryto incorporate some data from outly- ent times is irrelevant. In contrast, the atmosphere does ing sites. Most GPS-processing software uses a double- change over periods long enough for receiver satellite vec- differencingscheme to eliminate the influenceof satelliteand tors to sweep across the sky, and so we must take into receiver clock errors on parameter estimation. Because of account that most of the vectors realized in a given day do this differencing the GPS data may be more sensitive to not cross instantaneously. We may exploit the fact that the relative than to absolute tropospheric changes. The tropo- atmosphere changes only slowly and modify existing meth- spheric delay at one station is called the absolute delay, ods of tomographic analysis accordingly. For example, we while the relative delay is the differential tropospheric delay might divide the atmosphere above the network into a suite between two stations. Absolute tropospheric delays can be of boxes (a three-dimensional grid) and estimate the water estimated for stations that are widely separated (> 100 km) vapor content in each box, subject to the condition that this because the elevation angles of the various satellites are quantity is a stochastic process whose process variance is significantly different. Closely spaced stations are better constrained according to height, site, and season. Alterna- suited to the recovery of relative delays, and the tropo- tively, we might parameterize the water vapor distribution in spheric parameters recovered at these stationswill usually terms of a triple series of orthogonal polynomials defined be highly correlated. It should be possible to resolve this over the spatial coordinates and require that each unknown problem by augmenting the observations obtained from a coefficient in this series evolves in time as a stochastic dense meteorological array with observations collected at a BEVIS ET AL.: GLOBAL POSITIONING SYSTEM METEOROLOGY 15,797


/ /


! !


Fig. 6. A schematicdiagram of the GPS occultationconcept [after Hardy et al., 1992]. A (LEO) satellitereceives signals from GPS satellitesorbiting at heightsof about 20,000 km. The expandedview illustratesthat in the 60 s or so prior to the occultationof a GPS satelliteby the Earth the signalspropagating from the GPS satellite to the LEO satellite are refracted by the Earth's atmosphere. small number of distant GPS stations. Indeed, should the Where significant tropospheric moisture is present, temper- meteorological community embrace the concept of GPS ature can be measured by GPS occultation if humidity is meteorology, it might prove advantageousto run a small modeled, or vice-versa. In cold and dry conditions such as number of "fiducial" sites across the nation at locations those found during polar night, temperature soundingsmay where frequent sounding of the atmosphere occurs on a be obtained down to altitudes of 1 km or so. In the tropics, regular basis, allowing prior constraintsto be introducedinto operational models predict temperature distribution more the analysis of any network which incorporates GPS data reliably than humidity, and so the emphasis would be on from these sites. humidity soundings. Although the data gathering and processing requirements Early opportunities may exist to test the GPS occultation of this technique are of necessity demanding, the potential concept. Several hundred new private communication satel- benefits are exciting indeed. The structure and evolution of lites have been announced for launch in the next several storms rangingfrom thunderstormsto mid-latitude cyclones years (see Table 1). Many of these satellites will carry GPS and hurricanes are strongly affected by the release of latent receivers for tracking and attitude measurements. In addi- heat and therefore are extremely sensitive to the distribution tion, satellites such as TOPEX/POSEIDON, Gravity Probe of water vapor. The prospect of determining the full three- dimensional distribution of water vapor, for example, in a developing mid-latitude frontal system, through GPS tomog- TABLE 1. Communication Satellites Proposed for Launch in raphy may provide an important data source to document the Next Several Years Which May Carry GPS Receivers the evolution of precipitation structures within these storm [Ware et al. , 1992] systems. Number Satellite of Company Name Satellites GPS Occultations Observed From Space The technique was developed and re- Constellation Communication Aries 48 fined in order to study the atmospheresof , , and Corporation Ellipsat Incorporated Ellipso 24 several outer planets and their moons [Fjeldbo and Eshel- Inmarsat System 21 21 man, 1968; Eshleman et al., 1977; Lindal et al., 1981]. This Leosat Incorporated Leosat 18 well-established technique could now be applied much Motorola Iridium 77 closer to home. Phase measurements of GPS signals as they Orbital Sciences Corporation Orbcomm 24 Qualcomm/Loral Globalstar 48 are occludedby Earth's atmosphere(Figure 6) could provide Smolsat Smolsat 36 atmosphericrefractivity soundingsand so yield information Starsys Starnet 24 on global atmospheric temperature, humidity, and iono- TRW/Defense Systems Odyssey 12 spheric structures [Yunck et al., 1988; Gurvich and Krasil- Incorporated Total 332 'nikova, 1990; Chiu et al., 1991; Hardy et al., 1992]. A GPS receiver in low Earth orbit (LEO) can observe Ellipso planscall for a Molniya orbit and the othersfor low Earth roughly 600 GPS occultations per day. A typical GPS orbit. The number of possible occultation observations and their occultation measurement effectively samplesover a horizon- vertical resolution decreases as the altitude of the orbit increases. tal path of roughly 200 km with a vertical resolution of 1 km For example, GPS receivers in geostationary orbit can observe roughly 50 occultationsper day with a vertical resolutionof 10 km. (Figure 6). Results from the Voyager missions suggestthat In low Earth orbit roughly 600 occultationscan be observedper day temperature soundingsof Earth's , from 8 to 45 with a vertical resolution of 1 km. Plans for Iridium do not include km altitude, could achieve accuracies of 1 K or better. GPS receivers at this time. 15,798 BEVIS ET AL.: GLOBAL POSITIONINGSYSTEM METEOROLOGY

B, ARISTOTELES, and EOS B will carry GPS receivers, tion by the spacingof the radiosondenetwork) with which to and other U.S. and foreign government satellites may be initialize regional fine-mesh models. During the past decade similarly equipped. there has been considerable effort to develop regional fine- In order to explore the potential of the GPS occultation mesh primitive-equation models of the atmosphere and technique, simulations should be conducted with two- apply them to operational, short-range weather forecasting dimensional models that include climatology, ionospheric and mesoscale research problems in the mid-latitudes. An conditions, and distributions of temperature, humidity, essential ingredient for the initialization and testing of the cloud liquid water, and . In addition, appropriate GPS new regional models are sets of observational data that span receiver hardware, software, and antennas must be speci- both the synoptic scales and mesoscales. Recent modeling fied, developed, and tested in orbit. Overall, GPS occulta- studies [Kuo et al., 1992] indicate that assimilating precipi- tion measurements promise to provide valuable data for table water observations into mesoscale numerical weather weather, climatology, and global change research. models would significantly improve precipitation forecasts. If the early excitement about the GPS occultation tech- Continuouslyoperating networks of GPS receivers could be nique survives an expanded analysis, then it would be of used to help document the presence of mesoscale moisture interest to consider how the ground-based GPS approach gradients in the atmosphere such as dry lines [Schaefer, advocated here could be coupled with its more exotic 1974; McCarthy and Koch, 1982; Parsons et al., 1991]. Dry cousin. Consider, for example, the lateral extent of the lines are commonly observed over Texas and Oklahoma atmosphere sampled during occultation (Figure 6). Clearly, from May through July, as warm, dry air descending from if several ground-based GPS receivers were embedded in the and/or the Rocky Mountains meets this region and could provide estimatesof lateral gradientsin extremely humid air from the Gulf of Mexico. In the absence the IWV, it would be possible to devise increasingly sophis- of strong flow across the mountains, the pressure signal ticated retrieval algorithms with which to processthe occul- associated with dry lines is overwhelmed by the moisture tation data. Given that both ground-based and space-based signal, making GPS data especially appropriate. Similarly, GPS techniques for are in their in- GPS data may also have special application to sensingcold fancy, it would be premature to spendmuch time speculating fronts aloft (CFA). This term was recently used by Hobbs et on their possible synergy. We provided this sectionjust to al. [1990] to denote cold frontal zones whose bases are above indicate the enormous potential of GPS meteorology. the surface in the lower or middle troposphere. The CFA is marked by a zone of moisture as well as temperature contrast [Businger et al., 1991; Locattelli et al., 1989] and DISCUSSION has been associated with enhanced precipitation and the Water vapor plays an essential role in the dynamics and triggering of squall lines. of many atmospheric storm systems and In discussingthe possibilities of GPS meteorology, one of the hydrologic cycle on local, regional, and global scales. the first questionsthat arises is its advantagesand disadvan- Because water vapor shows great spatial and temporal tages relative to the now well-establishedtechnique of water variability, its distribution is difficult to resolve by conven- vapor radiometry. Under good operating conditions, ground- tional means. Errors in the initial conditions of water vapor based WVRs may constitute a better means of sensingIWV in operational numerical models contribute greatly to the than does recovering the wet delay from GPS observations. errors in the short-term (0-24 hours) precipitation forecasts. Furthermore, WVRs can measure ILW as well as IWV, and Emerging networks of continuously operating GPS receivers ILW contributes very little to the wet delay (nor is it offer the possibility of observing the horizontal distribution measured by radiosondes). However, WVRs have some of integrated water vapor or, equivalently, precipitable wa- shortcomings too. Unlike GPS receivers, WVRs are not ter with unprecedented coverage. These measurements "all-weather" instruments. Nearly all WVRs produced to could prove extremely useful in operational weather fore- date do not generate useful data when it is raining heavily, casting and in fundamental research into atmospheric storm and their performance may be degradedin the presence of systems, atmospheric chemistry, and the hydrologic cycle. heavy cloud or light rain. GPS receivers have advantages Long-term, global measurement of IWV could provide vital over WVRs in that they are more rugged instruments, are information on regional and global climate change [Randall being produced in large numbers, and are far less costly and Tjemkes, 1991]. Most theorists believe that global warm- (their price has been dropping25-50% every year). Perhaps ing will cause systematic changes in the total water vapor the most important potential advantageof GPS over ground- content of the atmosphere. These changes in atmospheric based WVRs is that GPS receivers are going to exist in huge water vapor may be easier to detect than the associated numbers over wide areas in just a few years, and the use of changes in atmospheric temperature. this resource for meteorological purposes could occur at A significant practical motivation for mesoscalefield pro- little incremental cost. It is possible that many of the such as the Genesis of Atlantic Lows Experiment applications discussedherein could be implemented using (GALE) [Dirks et al., 1988] and STORM-FEST [STORM GLONASS (a system similar to the GPS constructed by the Project Office, 1991] has been the limited successof opera- former Soviet Union) and future space-basedradio naviga- tional models to predict precipitation patterns and severe tion systems. weather, despite significant gains in the skill of predicting Another concern that often arises in the context of GPS synoptic-scale circulations. The disparity in the prognostic technology is the effect of "selective availability" (SA). The skill for precipitation and synoptic-scalepatterns is a conse- Department of Defense implemented SA in March 1990 in quence of the formation of precipitation on scalesessentially order to deny most civilian users of the system the maximum smaller than those resolved by present-day global models achievable accuracy in single-pointpositioning (navigation) and the lack of mesoscale data (currently limited in resolu- applications.Although this policy has angered many civilian BEVIS ET AL.: GLOBAL POSITIONINGSYSTEM METEOROLOGY 15,799 users of GPS, it has not had a significantimpact on geodetic bances(TIDs), and more rapid ionosphericscintillations, the (relative positioning) applications [e.g., Rocken and Earth's magnetic field, season, location, and direction. A Meertens, 1991]. Provided that all receivers sample the GPS typical daily average zenith delay due to the ionosphereis 10 signal close to simultaneously, the effects of SA can be m. The delay can change by an order of magnitude between eliminated after the fact. Consequently, SA is not a signifi- day and night. TIDs, which are thought to be related to cant problem for ground-basedGPS meteorology. weather patterns, have spatial wavelengths between several Meteorological studies of water vapor using geodetic hundred and several thousand kilometers and temporal methods should bring benefits to the geodetic community as periods between 10 rain and several hours. They typically well as to atmosphericscience. These studiesshould provide cause --•10% fluctuations in the total ionospheric delay. better stochastic models of the wet delay, particularly with A dual-frequency GPS receiver records the differential respect to its spatial variability. GPS specialistshave not yet group delay between the L1 and L2 frequencies, and the exploited the fact that the ZWD is coherent in space as well total delay at either frequency can be estimated from this as in time. Meteorologists can help geodesiststo make better observation using a model for ionospheric dispersion. The use of operational weather models and to tune assigned standard dual-frequency correction described by Spilker parameters (such as stochasticprocess noise) accordingto a [1980] ignores third- and higher-order terms in the refractive priori information on the meteorological context of a given index of the ionosphere. Nevertheless, it achieves (for station. At the very least it should be possible to develop elevation angles -> 15ø) a residual range error (RRE) of less indicators of conditions in which the existing classes of than 30 mm in all but unusual circumstances [Brunner and stochastic models will not represent the water vapor vari- Gu, 1991]. The RREs generated by the standard model tend ability well, thereby enabling analysts to flag geodetic solu- to decrease with increasing elevation angles; at zenith the tions that should be considered suspect due to unfavorable RRE is almost always less than 10 mm. Because the ZWD atmospheric conditions. normally is estimated at each epoch using observationsfrom four or more satellites, the residual range errors may par- tially cancel during the computation of the ZWD. More APPENDIX: IONOSPHERIC EFFECTS ON GPS SIGNALS importantly the mappingfunction used in the computationof We did not discuss above the nature of the ionospheric the ZWD tends to reduce the influence of large RREs contribution to the overall error budget for the ZWD, but the obtained at low elevations. Thus one would expect the magnitude of this contribution is implicit in our discussionof ionosphere PREs under normal conditions to induce ZWD total system performance. Empirical comparisons between errors of less than 10 mm and usually of the order of a few results obtained using VLBI, WVR, and GPS observations millimeters. Recent improvements in the dual-frequency establish a total error budget (including ionospheric and range correction algorithm, which involve approximate ex- other effects) for the estimated ZWD of---10-mm rms ran- pressionsfor the higher-order effects, can reduce the resid- dom error and ---10-mm long-term bias using present tech- ual range error to less than 2 mm at any elevation angle niques. Implicitly, the ionospheric contribution is typically [Brunner and Gu, 1991]. The suggestionis that when these at or below this level. We include this section to provide new algorithms are introduced into GPS processing soft- additional information on the phenomenologyof ionosphere- ware, ionosphericerror sourcescontaminating GPS-derived induced errors. estimates of the ZWD should be reduced by an order of The free electrons of the ionosphere, which extends from magnitude to ---1 mm or less, except under extraordinary about 50 to about 1000 km above the Earth's surface, affect circumstances such as a major magnetic storm. the propagation of radio waves. At frequencies above about 30 MHz, radio waves pass through the ionospherebut suffer Acknowledgments. This work was supportedin part by grants to dispersion. The phase velocities of carrier waves are in- M.G.B. from NSF (EAR-8721013) and NASA (NAGW-2616) and to creased, but the group velocities of modulationssuperposed T.A.H. from NASA (NAS5-3-3017) and NOAA (NA-90AA-D- on the carrier waves are reduced. The magnitude of phase AC481). We thank C. Counselman III and T. Dixon for useful advanceand group delay are similar, the effectsdiffer only in discussionsand J. Davis for a copy of his Ph.D. thesis. We thank the reviewers for their constructive remarks and criticisms. sign. The magnitude of the group delay is, to a good approximation, proportional to the total electron content (TEC) along the path between satellite and receiver and REFERENCES inversely proportional to the squareof the carrier frequency. Anthes, R. A., Regional models of the atmosphere in middle By making measurementsat two sufficiently widely spaced latitudes, Mort. Weather Rev., 111, 1306-1335, 1983. frequencies the ionospheric effect can be modeled and Askne, J., and H. Nordius, Estimation of tropospheric delay for microwaves from surface weather data, Radio Sci., 22, 379-386, largely removed from the observations. It is for this reason 1987. that GPS satellites transmit signals on two carrier frequen- Baby, H. B., P. Gole, and J. 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