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Remote Sensing of the Atmosphere



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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications 8 Remote Sensing of the Atmosphere

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications The Potential Role of GPS/MET Observations in Operational Numerical Weather Prediction Ronald McPherson, Eugenia Kalnay, Stephen Lord National Center for Environmental Prediction, National Weather Service INTRODUCTION Operational numerical weather prediction (NWP) applies the laws of physics, which govern the behavior of atmosphere, to the practical problem of weather prediction. In mathematical terms NWP is an initial value problem, in that the physical laws are used to calculate the temporal evolution of the physical state of the atmosphere, from an estimate of the initial atmospheric conditions. Determining this “initial state” of the atmosphere is one of the three central problems in operational NWP. It requires observations of wind, temperature, pressure and humidity through the depth of the atmosphere, plus observations of some characteristics of the earth's surface such as snow cover, wetness, vegetation, and sea-surface temperature. These observations are presently obtained by a mixture of observing techniques that have evolved in a largely unplanned manner over the last five or six decades. For forecast projections longer than three or four days the complete global atmosphere must be sampled, and this has led to a considerable emphasis on space-based remote sensing techniques. The second section of this essay describes briefly the current observing system. A second requirement for determining the initial state of the atmosphere is a system for assimilating disparate observations from this mixture of observing systems into a coherent, dynamically consistent, digital description of the atmosphere. Originally concerned merely with spatial interpolation of radiosonde data to grid of regularly-spaced points, modern four-dimensional data assimilation (4DDA) systems now seek to blend observations of many quantities from observing systems with widely differing error characteristics, with a highly accurate background (or “first guess”) estimate of the state of the atmosphere. Importantly, modern 4DDA systems are capable of ingesting observed quantities such as radiances or radar backscatter cross-sections rather than converting these quantities to more familiar meteorological variables such as temperature, wind, etc. The third section of this paper discusses characteristic of 4DDA systems that are relevant for the use of GPS/MET data. From time to time, new observing technologies appear, offering either new data (to fill gaps), or better data (more accurate), or cheaper data. Several such possibilities are now, or soon will be, available. Governments that operate the existing, composite observing system are under enormous financial pressure to reduce the costs of observing the atmosphere. Therefore, the U.S. has recently undertaken a systematic redesign of the North American Observing System (NAOS), with the intent of better observing at less cost. Several new technologies will be considered in this redesign effort, which will last for several years. One of those new technologies, using radio occultation techniques in connection with the Global Positioning System, is the subject of this essay. The last section of this paper addresses the potential usefulness of atmospheric refractivity inferred from these techniques in operational numerical weather prediction. THE CURRENT ATMOSPHERIC OBSERVING SYSTEM Vertical profile observations of the mass field (i.e., temperature) are obtained from two principal sources: balloon-borne radiosondes flown twice daily from about 600 stations world-wide, and from passive radiometric measurements from satellite platforms. The former are quite accurate, with standard errors of 0.5 - 0.8C, have excellent vertical resolution, and have for many years been the backbone of the global observing system. On the other hand, radiosonde stations are mostly located on northern hemisphere continents, which provides very uneven spatial coverage, and are expensive to operate. Satellite temperature observations are less accurate with standard errors of 2C, and have poorer vertical resolution, but offer excellent spatial coverage. Current satellite systems are also extremely expensive. Wind profiles are available from radiosondes, from ground-based radar wind profilers, Doppler weather-surveillance radars, and increasingly from wide-bodied jet aircraft on ascent and descent near airports. Single-level wind observations are obtained from aircraft, and by tracking cloud and moisture patterns in geostationary

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications satellite imagery. With the exception of the satellite-derived winds, these observations are accurate to within about 2m/s; satellite-derived wind are accurate to about 4-5 m/s. Importantly, essentially no wind profile information is available over the world's oceans. This is the greatest single deficiency in the present global observing system for operational NWP. Moisture profiles are available from radiosondes and vertically-integrated moisture measurements are available from satellite. New technology may soon make moisture profiles available from aircraft on ascent and descent but these profiles and radiosondes humidity are, again, restricted to land areas. Thus, the second most serious deficiency in the current observing system is the absence of moisture profiles over the oceans and over land with sufficient horizontal, vertical, and temporal resolution This is especially important, indeed crucial, for short-period precipitation forecasting. RECENT ADVANCES IN DATA ASSIMILATION SCIENCE Until October 1995, data assimilation systems in use at operational NWP centers around the world required that satellite measurements of atmospheric radiance be converted to temperature profiles before they could be ingested. This process, called a “retrieval”, introduces errors and uncertainties into the retrieval profile. These errors tend to be spatially correlated, which greatly reduces their utility in operational NWP. The U.S. National Centers for Environmental Prediction (NCEP) introduced a new data assimilation system in October 1995 that is based on a three-dimensional variational technique for satellite radiances. This new formulation permits radiance measurements to be ingested directly into the data assimilation, thereby by passing the retrieval process. Other operational centers are developing similar formulations. In previous assimilation methods, as in the present one, the analysis was obtained by minimizing its distance to both the first guess (background field) and to the observations. However, if the observations (e.g., satellite radiances) were different from the model variables (e.g., temperature and moisture), the observations were first converted into model variables through a “retrieval process”. Since satellite observations are not sufficient to determine a unique atmospheric profile, this is an ill-posed problem which requires additional information such as a background field (e.g. climatology). The accuracy of the retrievals is compromised by these additional assumptions, the error characteristic are less clearly defined, and quality control is less effective. Within the 3-D variational analysis, in which the observed radiances are compared with those that would be observed from a model atmosphere, we do not need to introduce any additional assumptions. It is a process similar to performing 3-D retrievals of all satellite data instead of the normal 1-D (column-wise) retrievals. Furthermore, it takes full advantage of the accurate model-generated first guess and all additional observations (e.g. radiosondes) simultaneously. The 3-D variational analysis with radiances produced improvements in five-day forecasts for the Northern Hemisphere equivalent to 40% of the total improvement of NCEP from 1984 to 1995. The improvement in Southern Hemisphere forecasts is even greater. The framework established by the three-dimensional variational data assimilation system is applicable to many geophysical measurements relevant to the atmosphere. This requires the development of a forward model to go from model variables (bending angles or index of refraction in the case of the radio-occultation GPS data). In addition, we need to create the linear tangent model for the forward model (i.e., a perturbation model that indicates how much the observed variables will change if a small change is introduced in the model variables), and the adjoint of the linear tangent model, which transforms observed perturbations to model perturbations. The forward model and its linear tangent and adjoint should be accurate, and if possible, computationally efficient. In the case of the radio-occultation technique using GPS, the measurements are actually of the signal delay due to the refraction of the atmosphere in the transmission of a radio signal from a GPS satellites to some point a known distance from the satellite. By geometric considerations, this delay can be transformed to a “bending angle”, which is proportional to the refractivity of the atmosphere. In turn, the refractivity is a function of temperature, humidity, and at a given altitude the pressure. Pressure can be determined hydrostatically, so given some external knowledge of the moisture distribution one can calculate temperature as a function of pressure; or, given some external knowledge of temperature, the moisture distribution can be determined from refractivity measurements. However, it is extremely important to note that in modern data assimilation systems, the refractivity may be used directly without decomposition into temperature and moisture distributions. A very suitable framework thus exists to use refractivity information from the radio occultation technique. Similarly, rather than assimilating precipitable water vapor estimates from delays observed in surface receiving stations, it would be preferable to assimilate the observed time delays themselves. This would make maximum use

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications of the GPS data by improving upon an already accurate model first guess of temperature and moisture. THOUGHTS ON THE MOST LIKELY NICHE FOR POTENTIAL GPS/MET (RADIO-OCCULTATION) DATA IN OPERATIONAL NWP The most important deficiency of the present observing system is most probably not the accuracy of the mass field, but rather the absence of wind profiles over the oceans. GPS/MET data will influence that only indirectly in the extra tropics, and not at all in the tropics. It does appear possible that GPS/MET observations based on radio occultation techniques can improve the description of the distribution of moisture. NCEP modelers are eager to acquire the “forward model ” to convert temperature and moisture profiles to refractivity from colleagues at NCAR, and to begin experimenting with the GPS/MET data in the operational data assimilation system. There is considerable evidence that the mass distribution in the atmosphere is fairly well measured and the recent advances in data assimilation noted above are making better use of that information. There is, therefore, limited room for GPS/MET observations to improve the current description of the atmospheric mass (temperature) field. GPS/MET observations may have precision, but experience clearly suggests that the addition of GPS/MET data is not likely to have a major impact on forecasting four or five days in advance. However, if GPS/MET can provide as good a description of the temperature distribution as current systems, but at a significantly lower cost, then this would be an extremely valuable contribution to the North American Observing System.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications GPS Sounding of the Atmosphere from Low Earth Orbit: Preliminary Results and Potential Impact on Numerical Weather Prediction Richard Anthes and William Schreiner University Corporation for Atmospheric Research Michael Exner, Douglas Hunt, Randolph Ware University NAVSTAR Consortium Ying-Hwa Kuo and Xiaolei Zou National Center for Atmospheric Research Sergey Sokolovskiy Russian Institute of Atmospheric Physics INTRODUCTION On 3 April 1995, a Pegasus rocket carried aloft by an aircraft from Vandenburg Air Force Base launched a small satellite (MicroLab 1) into a circular orbit of about 750-km altitude and 70° inclination. The disk-shaped satellite, which circles Earth every 100 minutes, carried a laptop-sized Global Positioning System (GPS) receiver to demonstrate sensing of the terrestrial atmosphere by the radio occultation, or limb-sounding technique. This proof-of concept experiment is called GPS/Meteorology (GPS/MET). Since the 3 April launch, many thousands of atmospheric soundings of refractivity, temperature, pressure and water vapor have been retrieved. Some of the early results of the GPS/MET experiment are described by Ware et al. (1996) and Kursinski et al. (1996). This paper summarizes recent progress toward obtaining accurate atmospheric soundings of temperature and water vapor and the potential uses of GPS/MET data in atmospheric and climate research and weather prediction. SCIENTIFIC BASIS FOR AND HISTORY OF THE RADIO OCCULTATION MEASUREMENT TECHNIQUE The radio occultation method used in GPS/MET was developed by scientists at the Jet Propulsion Laboratory (JPL) and used by scientists at Stanford University to measure the structure of planetary atmospheres (please see detailed references in Ware et al., 1996). In the GPS limb sounding method (Fig. 1), atmospheric soundings are retrieved from observations obtained when the radio path between a GPS satellite and a GPS receiver in low-Earth orbit (LEO) traverse's Earth's atmosphere. When the path of the GPS signal begins to transect the mesopause at about 85-km altitude, it is sufficiently FIGURE 1 Schematic of radio occultation technique (not to scale) retarded by the atmosphere that a detectable delay in the dual-frequency carrier phase is observed by the LEO GPS receiver. As the radio waves are slowed by the atmosphere, they bend by a small but observable angle, which reaches a maximum value of between 0.02 and 0.03 radians near the Earth's surface (Fig. 2). Vertical profiles of atmospheric refractivity can be computed from the bending angle. The atmospheric refractivity, N, depends on pressure (P), temperature (T) and water vapor pressure (e) according to (1)

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications Pressure is related hydrostatically to density, which is a function of temperature and water vapor. Thus refractivity is essentially a function of temperature and water vapor. Without knowing either temperature or water vapor, neither can be determined from refractivity alone in the general case. However, in regions of the atmosphere in which water vapor content is small and its contribution to refractivity negligible compared to that of temperature, accurate temperature profiles can be determined by assuming e=0 in (1). This approximation holds well in the upper troposphere, stratosphere, polar regions, and anywhere else where the temperatures are lower than 250 K. FIGURE 2 Bending angle and temperature profiles for GPS/MET retrieval at 17:24 UTC 21 October 1995. The location is 47°S 59°W. In the general case, if either temperature or water vapor is known from independent measurements or analyses (such as the global analyses prepared daily by the operational weather centers of the world), the other variable can be obtained from the refractivity. Thus, if water vapor pressure is known independently, temperature can be computed from (2) or, if temperature is known, water vapor pressure may be computed from (3) It is very important to note that for several important applications of GPS/MET, it is not necessary, or perhaps even desirable, to try to separate the temperature and water vapor effects. For example, trends of globally or regionally averaged atmospheric refractivity would be a good measure of global or regional climate change (Yuan et al. 1993). For operational numerical weather prediction, it is possible to assimilate directly refractivity measurements into the model. The assimilation of refractivity causes the model fields of temperature, pressure and winds to adjust in a dynamically and thermodynamically consistent way (Zou et al., 1995; Kuo et al., 1996). GPS/MET observations provide essentially global coverage with random spacing in the horizontal. A single GPS/MET satellite could theoretically produce approximately 500 soundings per day. Fig. 3 shows the soundings obtained on 21 October 1995 by the GPS/MET experiment; the number is significantly less than 500 because only setting occultations are obtained. With 12 (50) LEO satellites in orbit simultaneously, global atmospheric refractivity soundings at a horizontal resolution of approximately 400 km (200 km) can be expected every 12 hours. FIGURE 3 Distribution of GPS/MET sounding on 21 October 1995.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications SUMMARY OF ATMOSPHERIC RETRIEVALS Fig. 2 shows the retrieval of atmospheric bending angle and the temperature, derived with the assumption that water vapor is zero in (2). We call this the “dry temperature.” Because water vapor is a positive contribution to the computed temperature in (2), the “dry temperatures” generally show a significant cold bias in the lower troposphere. Fig. 2 indicates that the bending angle varies by more than three orders of magnitude from 60 km altitude to the surface. The temperature profile shows several interesting characteristics. The very sharp tropopause at around 12 km is characteristic of many GPS/MET temperature retrievals. It is in a region of the atmosphere where water vapor effects are negligible and the theoretical accuracy of the GPS/MET radio occultation methods is highest (better than 1 K). Thus the high vertical resolution and accuracy of the temperature in this regions suggests that GPS/MET observations will be very useful in upper-tropospheric and lower stratospheric research, including monitoring of climate change. Models predict a strong atmospheric response (cooling) in this region due to the enhanced greenhouse effect, and GPS/MET observations should be very useful in detecting any global or regional trends in this sensitive part of the atmosphere. The vertical wave structure in the temperature profile of Fig. 2 is present in most of the GPS/MET temperature retrievals. In the lower stratosphere the features are almost certainly real, and associated with gravity waves. In the upper stratosphere (above 40 km), both errors in the retrieval and real atmospheric variability likely contribute to the wave structure. It is very difficult to verify the waves shown in Fig. 2 because other remote sensing systems in the stratosphere, such as HALOE (Halogen Occultation Experiment) and MLS (Microwave Limb Sounder) have inherently much lower vertical resolution than the GPS/MET technique. However, we know from rocket soundings and the LIMS (Limb Infrared Monitor of the Stratosphere) experiment that wavelike features with characteristics similar to those shown in Fig. 2 are ubiquitous in the stratosphere. For example, Fetzer and Gille (1994) state “The LIMS data are characterized by high vertical resolution, and often contain small scale peak-to-peak amplitudes as large as 40 K. These signals have dominant vertical wavelengths of about 10 km and horizontal wavelengths of about 1000 km.” Fig. 4 shows a comparison of a GPS/MET temperature retrieval with a retrieval from the MLS and the global analysis of temperature from the National Centers from Environmental Prediction (NCEP). Both the MLS and NCEP soundings have much coarser vertical resolution in the upper troposphere and stratosphere so they do not show the sharp tropopause feature or the vertical waves that are observed in the GPS/MET sounding. However, the large-scale characteristics of the three soundings are similar, even in the upper part of the stratosphere (40-55 km). FIGURE 4 Same temperature sounding shown in Fig. 2 compared to MLS and NCEP temperature soundings. We have compared many GPS/MET temperature retrievals with nearby radiosondes. Fig. 5 shows a typical example of a dry temperature retrieval, from 5 May 1995. The high vertical resolution and the accuracy of the GPS/MET temperature profile in the layer from about 5 km to 35 km are confirmed by the nearby radiosonde measurements. The lower portion of the GPS/MET temperature sounding in Fig. 5, indicated by the dotted line beginning at about 6.5 km and extending toward higher temperatures to about 3.5 km is in error, and represents a typical behavior of the temperature

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications FIGURE 5 GPS/MET “dry” temperature sounding at 0502 UTC 5 May 1995 at 45.5°N 99.7°W compared to nearby balloon soundings. retrievals in the lower several kilometers of the atmosphere. Decreasing signal-to-noise ratio and the presence of increasing amounts of water vapor, and possible strong low-level temperature gradients cause multi-path effects and other errors. The manifestation of these errors is usually a sudden increase in the retrieved temperatures with decreasing elevation and is easily recognized as an erroneous result (a fact useful in quality control of the data). Fig. 6 shows a comparison of “dry” and “wet” GPS/MET temperature retrievals with the NCEP analyzed temperature for a complete set of 1138, and subsets of 1000, and 800 soundings respectively. The “wet” temperature retrievals refer to temperatures computed from (2) with water vapor pressure obtained from the NCEP analysis. The sets of soundings are determined as follows: The set containing 1138 soundings represents the total number of soundings processed during the period 10-25 October 1995. The 1000 and 800 sounding sets represent the subset of soundings which give the smallest mean and standard deviation differences from the NCEP data. In other words, the set of 1000 soundings was obtained by eliminating the “worst” 138 retrieved soundings out of the total set. The profiles in Fig. 6 demonstrate the ensemble effect of the “warm bias” errors in the lower troposphere that was seen in the single example of Fig. 5. Elimination of the “worst” retrievals removes those soundings which develop the warm bias error at the highest elevations. Thus the subset of the 800 “best” cases shows the ensemble warm bias beginning at a level around 5 km while the total set shows the bias beginning around 9 km. It is noteworthy that there is no significant difference between the three sets above 10 km, indicating that the retrieved soundings are very robust and stable in this region. Fig. 7 shows a comparison of 1000 “dry” and “wet” temperature retrievals with NCEP analyzed temperatures, categorized by polar, middle latitude and tropical regions. The “good” soundings reach closest to the surface in the polar regions (about 2-5 km), while the “good soundings in the tropics typically reach to only about 9 km, a reflection of the fact that the lower troposphere in the tropics contain much more moisture than in the middle latitudes or polar regions. Fig. 8 quantifies the number of retrieved “good” soundings which reach specified altitudes, again grouped into polar, middle latitude and tropical regions. The results from two retrieval algorithms are shown, the original algorithm and an improved algorithm. In tropical regions, the number of “good” soundings starts decreasing rapidly at the 9 km level, while for the middle latitude and polar regions the levels at which the number of “good” soundings begin to decrease rapidly are approximately 8 and 5 km respectively. The increase in the number of low-level “good” soundings due to the improved algorithm is apparent; for example, the number reaching the 5-km level approximately doubles from 100 to 200 in the tropical regions. This indicates that with adjustments in the instrumentation, antenna, and other aspects of the hardware, together with further improvement in the software, a significant improvement in the capability of GPS/MET to successfully sound the lower part of the atmosphere is possible. As will be shown later, it is very important in numerical weather prediction to obtain accurate refractivity profiles as close to the surface as possible.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications FIGURE 6 Mean and standard deviations of differences of “dry” and “wet” GPS/MET soundings compared to NCEP temperatures over period 10-25 October 1995. See text for details. FIGURE 7 Comparison by latitude regions of 1000 “dry” and “wet” GPS/MET temperatures with NCEP temperatures

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications FIGURE 8 Number of GPS/MET retrievals reading a given altitude using old (November 1995) and improved (February 1996) retrieval algorithms. Fig. 9 illustrates the ability to use the measured refractivity to compute temperature given an independent estimate of water vapor using (2) or, alternatively, to compute water vapor pressure given an independent estimate of temperature from (3). In this example the independent estimates of temperature and water vapor are obtained from the NCEP analyses. We note that because the analysis and short-term global forecasts of temperatures are much more accurate than those of water vapor, it is likely that it will be more useful to derive water vapor from refractivity and an independent estimate of temperature than vice versa. It is also noteworthy that water vapor retrievals of the accuracy shown in Fig. 9 on a global basis would be extremely useful for research and operational purposes. FIGURE 9 Example of temperature and water vapor retrieval using observed refractivity and either temperature or water vapor from the NCEP analysis as additional data. ASSIMILATION OF REFRACTIVITY DATA IN A NUMERICAL WEATHER FORECAST MODEL One of the greatest potential applications of GPS/MET data is in operational numerical weather prediction. Advantages of GPS/MET data for this purpose include global coverage in all weather (GPS/MET retrievals are not affected by clouds), high

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications accuracy and high vertical resolution. Because GPS/MET data will occur at different spatial locations and at different times over the Earth, the best way to use the data will be through four-dimensional variational data assimilation (4DVAR). The 4DVAR technique is described by Zou et al. (1995). In this section we present a brief summary of the potential impact of assimilating GPS/MET data in a numerical model (Kuo et al., 1996). In the 4DVAR technique, simulated atmospheric refractivity data are assimilated into the model during a six-hour period using an iterative process. The objective of the process is to minimize a “cost function ” defined by where x represents the model-predicted variables (in this case temperature, pressure and water vapor), N(x) is the model's value of refractivity and No is the observed value. Starting from an initial guess field xo(o), the minimization iteratively finds the better initial condition xo(k) which satisfies J(xo(k)) ≤ J (xo(k−1)), (5) where k is the interation number. During the interation process all variables in the model, including pressure and winds, adjust in response to the changing temperature and water vapor fields. The case selected for the 4DVAR study was one of intense cyclogenesis over the Northwestern Atlantic Ocean on 4-5 January 1989. This storm was the most intense storm ever observed in this region, with an estimated pressure of 936 mb at 0000 UTC 5 January. The storm started as a 996-mb low off Cape Hatteras, NC, embedded within a broad baroclinic zone with moderate thermal gradient. During the following 24 hours, with the approach of an intense upper-level trough, the storm intensified rapidly over the warm Gulf Stream. In order to simulate refractivity observations, we first conducted a control simulation with a version of the Penn State/NCAR mesoscale model version 5 (MM5). The horizontal resolution of this model was 90 km and there were 20 levels in the vertical. This simulation was initialized at 0000 UTC 3 January 1989 (defined as t = − 12 h) and was integrated for 60 hours. It covered the northern hemisphere with a mesh of 197x197x20. The initial conditions were obtained from conventional observations using the NCEP global analysis as the first guess. The lateral boundary conditions were obtained by linear interpolation of these analyses over 12-h intervals. The control simulation reproduced the observed storm quite well (Kuo et al., 1996). Fig. 10 shows the control model's simulation of sea-level pressure and surface temperature for four time periods beginning with 0600 UTC 4 January to 1200 UTC 5 January, which are 30-h, 36-h, 42-h and 60-h FIGURE 10 Sea-level pressure (4mb contour internal) and surface temperature (1°C contour internal) for control simulation forecasts respectively. During this time period the model storm deepened from a central pressure of 987 mb to an intense storm with central pressure of 938 mb, which compared very well with the observed minimum pressure of 936 mb. Other features of the simulation were realistic as well, and thus we felt confident in extracting model data from the control simulation and constructing simulated refractivity data from these model data for use in subsequent numerical experiments. To investigate the potential impact of refractivity data on subsequent model forecasts, we degraded the control model data at 1200 UTC 3 January 1989 (t=0) and then assimilated simulated refractivity data from the control simulation over a 6-h period from 1200 to 1800 UTC 3 January on the region shown in Fig. 11. We tested the impact of the simulated refractivity observations by running five 48-h simulations beginning at 1200 UTC 3 January and ending 1200 UTC 5 January 1989. To help avoid the “identical twin”

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications FIGURE 8 Observed TEC values from the dual-frequency altimeter on the TOPEX/Poseidon satellite.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications Another sensor that can be used to obtain ionospheric electron density profiles is a Low Earth Orbiting (LEO) dual frequency GPS receiver depicted in Figure 9. The occultation of the GPS satellites by the Earth allows the GPS/Met LEO dual frequency sensor to measure height profiles of TEC. These TEC profiles can be converted to electron density profiles if certain assumptions are made about the horizontal homogeneity of the ionosphere. Figure 10 and Figure 11 are electron density profiles obtained on May 4, 1995 from the GPS/MET satellite by George Hajj of JPL. These profiles are compared with the Parameterized Ionospheric Model (PIM) which is the theoretically-based model within PRISM. FIGURE 9 GPS occultation geometry. FIGURE 10 Electron density profiles.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications FIGURE 11 Electron density profiles. There are a number of global models of the neutral atmosphere and ionosphere being developed by Phillips Lab and the Ionospheric Effects Division. I will not describe all of the ones displayed in Figure 12 but will just mention a few. The Ionospheric Forecast Model (IFM) was delivered to HQ Air Weather Service (AWS) for transition to 50 WS. This will be operational in two years. It will provide 12 hour forecasts of global ionospheric ion and electron density profiles using PRISM values as the current (t=0) specification. The Thermospheric Forecast Model (TFM) currently being validated will be coupled with IFM to form the Coupled Ionosphere Thermosphere Forecast Model (CITFM) which will be a completely self-consistent, coupled model providing 12 hour forecasts of the neutral winds, temperature, densities and ion and electron density profiles. This will be especially important during geomagnetic storms. The advanced coupled models also include a Solar Prediction Model (SPM), an Advanced Coupled Magnetospheric Model (ACMM), a Global Forecast Model (GFM) and an executive model which carries out quality control and automatically determines which of the models should be run to satisfy specific 50 WS customer requirements. This overarching model is called the Integrated Space Environment Model (ISEM). Finally, a very important initiative called the National Space Weather Program (NSWP) is gaining momentum. From its inception, NSWP has done a remarkable job in bringing together various Government Departments and Agencies, at the highest levels, to define, implement and fund the four “pillars” of the program, Research, Observations, Models and Education. The Program Elements of NSWP are illustrated in Figure 13 from the NSWP Strategic Plan (August, 1995). The agencies actively involved in this effort include, Dept. of Commerce, Dept. of Defense, NSF, NASA, Dept. of Interior and Dept. of Energy. The Office of the Federal Coordinator for Meteorological Services and Supporting Research (OFCM) has responsibility for overall coordination. Both NOAA and Dept. of Defense, jointly, have taken on the responsibility of developing the global operational Space Weather models for NSWP. The models being developed by the Geophysics Directorate and briefly described here represent an integral part of the National Space Weather Program.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications FIGURE 12 Global models of the neutral atmosphere. FIGURE 13 Program elements of the National Space Weather Program.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications Ionospheric Modeling and FAA Wide Area Augmentation System Research at Stanford University Yi-Chung Chao, Per Enge, Bradford Parkinson Department of Aeronautics and Astronautics, Stanford University ABSTRACT The Wide Area Augmentation System is quickly being developed by the FAA. The goal is to use this satellite-ground network system as the primary navigation means. The National Satellite Test Bed is a prototype of WAAS and will be up and running by mid1997. Stanford University has participated in the FAA effort of the development of WAAS since 1992 and has demonstrated promising flight trial results using a threestation WAAS network on the West Coast. This paper describes the WAAS research at Stanford University with emphasis on the ionospheric modeling. INTRODUCTION Introduction to Wide Area Augmentation System (WAAS) The Global Positioning System (GPS) is a satellitebased navigation system invented and deployed by the U.S. Department of Defense. Local Area Code-phase Differential GPS (LADGPS) successfully demonstrated sub-10-meter navigation error performance. To further reduce the errors of LADGPS corrections, the Wide Area Differential GPS (WADGPS), originally, was invented at Stanford University. By estimating the satellite orbit errors and modeling the ionosphere, the time and spatial decorrelation of GPS errors can be minimized even over a large geographical region [Kee, 1992]. However, as the goal to use GPS as the primary navigation means for landing and en route flight, the system integrity, continuity and availability are all needed to be improved to reduce the sensitivity to the failure of individual system components. The concept of Wide Area Augmentation System (WAAS) was proposed. Presently, the real-time implementation of WAAS is being aggressively developed by Federal Aviation Administration (FAA) to serve the main goals. A pictorial outline of WAAS is presented in Figure 1. As fully deployed, WAAS will be composed of a nationwide reference stations for GPS data collection and a master station responsible for data crunching. Because of the widely distributed network, the GPS error components, mainly orbital and ionospheric error become observable and even the system integrity can be monitored at real time. Therefore, this system will not only provide the WAAS vector differential corrections to increase the user position accuracy to several meters, but also has built-in real time integrity. Finally, a ranging signal transmitted from the data link geosynchronous satellite will further improve the satellite geometry and therefore the service of navigation continuity and availability. FIGURE 1 The Wide Area Augmentation System. Satellite orbit and clock error, and L1 ionospheric delay will be transmitted to the single-frequency users from the geosynchronous satellite. For improving the position accuracy, WAAS is designed to use weighted navigation solutions. When calculating differential corrections, confidence numbers will be estimated at the same time. As received the corrections, the WAAS users will perform a weighted navigation solution. This weighting algorithm allows the system to be able to handle marginal situations better. For example, situations such as satellite has only been observed by one or two stations and/or low elevation noisy measurements.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications Introduction to the National Satellite Test Bed (NSTB) National Satellite Test Bed (NSTB) is one of the FAA efforts for WAAS development. It serves as a prototype of WAAS and is scheduled to be in service in mid-1997. Figure 2 gives the current Testbed Reference Station (TRS) layout in continental US (CONUS), and total of 25 TRS's will come on-line in the neat future. All the TRS's will be equipped with GPS dual-frequency Ashtech Z-12 receivers and meteorological stations. A DEC UNIX computer at each site will be employed for data collection and communication. Several Testbed Master Stations (TMS), including those at FAA Tech Center as well as Stanford University, have been set up. The data will be transmitted from TRS through T1 line and piped to different TMS' s to test independently developed WAAS algorithms. Except the data transmitting, the main capabilities of TMS will be: 1) the estimation of satellite orbit and clock errors to reduce DGPS errors, 2) ionospheric delay modeling for WAAS L1 single frequency users and 3) integrity monitoring and warning. FIGURE 2 The current NSTB 12-reference station locations as of March, 1996. WAAS RESEARCH AT STANFORD UNIVERSITY Stanford University has participated the FAA WAAS development since 1992. A three-station mini-network has been created and is shown in Figure 3. This real time system of WAAS has been supported by numerous flight trials conducted at Palo Alto, Livermore and Lake Tahoe area [Walter et al, 1994, Tsai et al, 1995, Lawrence et al, 1996]. As reported, the WAAS generated corrections can improve one-sigma ranging accuracy to less than 1 meter. The most challenging GPS vertical position error has been reduced to 1.25-meter one-sigma. In recent month, the WAAS user program has been integrated with the Stanford University developed Integrity Beacon Landing System (IBLS) [Cohen, 1995] and real-time flight guidance display system [Barrows, 1995]. This system integration greatly improves the capability of system testing and verification. (The IBLS is a carrier DGPS system with centimeter accuracy], and the display system is a cockpit based flight guidance system for the pilot). FIGURE 3 Stanford WAAS network and ionosphere pierce point locations. With the progress of NSTB, Stanford WAAS Laboratory has started to merge its research in many aspects of the development. There are several major research topics at the Stanford WAAS Laboratory: 1) the estimation of satellite orbit and clock errors to minimize the spatial and time decorrelation errors in Differential GPS (DGPS). Current development is through the use of the patented Common View Time Transfer and Single Difference method to separate the satellite slow (orbital) and fast (Selective Availability) errors. 2) Ionospheric delay modeling. Because WAAS is designed for L1 civilian frequency users for navigation purposes, the goal of this study is to derive an efficient and effective model for the ionospheric correction. 3) integrity study. This includes the development of Receiver Autonomous Integrity Monitoring (RAIM) algorithms as well as optimal scheduling of the WAAS messages to optimize the use of limited GEO data link and to broadcast the in-time system integrity warning. A flight test result is show in Fig 4.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications FIGURE 4 Stanford WAAS flight test vertical error from 18 touch-and-go sessions. The accuracy is shown by comparing the ground wheel position of the aircraft and the surface of the run way at level = 0. GOALS OF WAAS IONOSPHERE RESEARCH Along with the development of WAAS, it is important to keep in mind that WAAS is aimed to serve as a primary navigation tool. For this life-critical purpose, the federal certification process plays an important role. Therefore, WAAS is constrained to make use of the guaranteed L1-frequency GPS service only. Under this circumstance, the wide area L1 ionospheric delay model must be transmitted to the single frequency WAAS users who constitute the main service volume, in spite of the quick development of the dual frequency cross-correlation receiver technologies. The generation of ionospheric delay model and provision of real-time ionospheric correction integrity monitoring are therefore the main goal of this research. With the WAAS Minimum Operation Performance Standard (MOPS) [WAAS MOPS, 1995] specification created the RTCA-SC-159, Working Group 2, the users will be using a predefined ionosphere grid for their ionosphere corrections. Under this guideline, the research goals will naturally focus on the process of generation the ionosphere grid using different modeling methods and the grid ionosphere vertical error (GIVE). Moreover, the error analysis will be emphasized on the integrity study, i.e. the search for outliers. The progress of current research can be outlined as following: 1) real time dual-frequency carrier-phase smoothing, 2) GPS interfrequency bias calibration 3) development of different ionosphere modeling techniques and 4) ionosphere distance correlation function study. Each of these topics will be detailed in following sections. IONOSPHERE MEASUREMENTS The dual-frequency ionospheric delay measurements can be derived from the GPS dual-frequency code-phase and carrier-phase observables [ICD-GPS-200]: where IL1 is the ionospheric delay at L1 frequency, IL1,PR is the measurement of IL1 from code-phase, IL1,ϕ is the measurement of IL1 from carrier phase, PR is the GPS code-phase (pseudorange) ϕ is the GPS carrier-phase (integrated doppler). Amb represents the combination of ambiguities from L1 carrier and L2 carrier phases, and γ ≡ (L1 / L2)2 = (77 / 60)2 Note that the interfrequency biases in both GPS satellite transmitter and receivers are also included in the equations. is the actual (as opposed to the broadcast) transmitter inter-frequency bias in code-phase on L1 for the j-th satellite. is the respective bias on the carrier-phase. R1 is the receiver differential inter-frequency bias on L2 for the i-th receiver. Because of the timing of the GPS receivers is dependent on L1 C/A code, the inter-frequency bias on L1 is zero by definition. Figure 5 illustrates the situation of ionosphere measurements. In Eq (1) and (2), the sum of the satellite and receiver interfrequency biases clearly keep us from getting the real ionospheric delay on L1 frequency. Thus the first step of the data processing is to estimate the interfrequency biases. The following discussion will demonstrate that the calibration result is necessary for further error analysis.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications FIGURE 5 The ionosphere pierce point concept. Note that the interfrequency biases, Tgd and Ri are satellites and receivers dependent, respectively. Interfrequency Bias Calibration From the measurement equations, (1) and (2), the interfrequency biases has to be separated from the ionospheric delay. The separation is made possible by the variation of the obliquity factor (OF) with satellite line-of-sight elevation. The OF can be expressed as where Re is the radius of the Earth, h is the height of the ionosphere slab, el is the GPS elevation angle. There are several assumptions for this estimation process: 1) ionosphere is almost constant as expressed in solar magnetic frame [Knecht et al, 1985] 2) ionosphere remains at a constant height, usually at 350 km. 3) obliquity is elevation dependent only. 4) interfrequency biases are very slow time varying, possible with time constant of several weeks to months. 5) to make valid use of the obliquity factors, the large ionosphere gradient around day and night termination periods are avoided for data collection. [Chao, 1995]. The ionosphere is modeled by spherical harmonics expressed in solar-magnetic frame. The estimation state vector can be set up as x = [Sph Harm Coeff | IFB1 | IFBk − IFB1] (4) A sequential (recursive least square) algorithm with Householder reflection is employed for the measurement update [Bierman, 1977]. The estimated model has half meter accuracy across different satellites and receiver combinations when compared to real measurements and hence the total confidence of this estimation being declared The presented results of this calibration is from comparing of WAAS navigation solutions. Figure 6 and Figure 7 compare the vertical position error with and without the bias calibration. The comparison shows better mean value position error. The comparison also implies that the system integrity monitoring will be greatly improved by the fact of narrower error distribution after the calibration of this systematic error. FIGURE 6 Histogram of WAAS navigation solution errors before the estimated interfrequency biases (14-hour, 1 Hz data). FIGURE 7 Histogram of WAAS navigation solution errors after adjusting the estimated interfrequency biases. Notice the mean is closer to zeros, and much narrower error distribution (14 hour, 1 Hz data). This software approach also make the calibration easier once needed and provide a long-tern monitoring tool, such as change of satellite on-board transmitter and change of reference station receiver-antenna, etc.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications Dual Frequency Smoothing As required for the data processing, the carrier smoothing of ionospheric delay measurement must be accomplished with an estimate of the smoothing confidence. A Hatch filter [Hatch, 1982] has been used with some modification to take into account of the elevation related multipath effect. Figure 6 presents one of the smoothing result along with the estimation of confidence envelope. The dual-frequency smoothing technique has big advantage over the single-frequency smoothing because the ionosphere divergence between code-phase and carrier-phase measurements are completely avoided. As the filter smoothes with time, the multipath problem will be minimized. FIGURE 8 Dual-frequency carrier-smoothing of ionospheric delay. WAAS IONOSPHERIC GRID MODELING As mentioned above, the WAAS MOPS specifies the users' algorithm of reconstructing the ionospheric grid based correction. The master station is responsible for the generation of the grid-based vertical ionospheric delay corrections and estimated errors. The master station algorithm need to make optimal use of all the IPP measurements to calculate the ionosphere correction for each grid point. Two categories of modeling techniques are currently under studying: 1) use a weighting function to relate the grid point with the ionospheric delay measurement located at the ionosphere pierce point (IPP). An optimal weighting weighting is subject to study. 2) use a surface to directly model the ionosphere and then calculate the grid point delay from the fitted model. For both categories, the capability to model any local disturbances, i.e. the resolution of the model must be sufficient, is the most important consideration. In the meanwhile, computational complexity and time are also a factor of decision. Grid Model using Weighting Function A prototype of the grid generation function can be expressed as where Îgrid.V is the estimated vertical ionospheric delay at the grid, ÎNominal,V is a nominal ionospheric delay calculated from, Imeas,V,k is the measured ionospheric delay at the IPP. K is the total number of IPP's. The use of INominal is to take into account of the Geomagnetic longitudinal and latitudinal effect of the ionosphere variation. By using Inominal, the weighting function w is a function of distance from IPP to the desired grid point. The current implementation of the ionospheric delay model in Stanford WAAS conforms to the RTCA-SC-159 Working Group 2 (WG2) Grid algorithm [RTCA-SC-159, WG2, 1994]. The GPS Klobuchar ionosphere model is chosen to be nominal and wk = 1/dk is used as a weighting function, where dk is the distance from the kth IPP to the grid. The formula to generate each grid is therefore: A slightly modified weighting factor is used to incorporate the measurement confidence number σ as

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications Because of the singularity and lack of physical sense in the above weighting function, some other weighting schemes are also under investigation. One of the attractive function is exp.(−x2), with x defined as the normalized IPP-to-grid-point distance. This weighting with a good understanding of the physical ionosphere correlation function will be more desirable. Again, the confidence number can be used as wk = exp(−x2) / σ (8) Figure 9 shows a 3-D model generated by the above weighting function. The IPP-grid distance has been normalized by 10-degree arc length on the Earth surface great circle. This color coded 3-D ionosphere model facilitates the model development effort. FIGURE 9 3-D ionosphere model. The underlined generation model is by Eq (8). Another approach of the modeling is to fit with a functional surface. A natural choice of the function on a spherical surface will be the spherical harmonics. However, spherical harmonics are only orthogonal on the entire sphere, i.e. for latitude in [−90,+90] and longitude in [−180, +180]. The Spherical Cap Harmonics Analysis (SCHA) make it possible to work on a spherical cap which is the situation of the CONUS region. The downside of this function is that the model is quite complicated and the need of computational power for the surface fitting for the 1 Hz real time system increased significantly. Further investigation is needed. Ionosphere Distance Decorrelation Function For the modeling of ionosphere, it is important to understand its behavior. One of the important information is the distance correlation function of ionosphere. It will not only provide the background of how to choose the cut-off distance for choosing IPP's to create grid ionosphere correction, using figure 9, but also provide important messages about the study of ionosphere integrity monitoring. To attack this problem, the ionospheric variation from the IPP's geo-magnetic longitude and latitude has to be taken out or modeled first in order to reveal the correlation function associate with distance alone. Again, the single frequency Klobuchar model is used for the first order approximation of this effect. Figure 10 and Figure 11 presents the preliminary study of the ionosphere distance decorrelation function using the NSTB data. For up to 2000 KM, ionosphere is strongly correlated. Beyond that, the correlation coefficient becomes fluctuated, part of the reasons are that the available data samples become smaller and also the Klobuchar model may not be good enough in the longer range for correct modeling. Using this correlation information, a optimal linear estimator can be designed. Test result will be delivered in the ION National Meeting, Boston, MA, 1996. SUMMARY AND FUTURE WORK The real-time flight trials from Stanford University mini-WAAS network have demonstrated a very promising starting point for the Category I precision landing using WAAS. The ionospheric modeling is still one of the greatest challenge of WAAS in the aspects of accuracy and integrity monitoring. The interfrequency bias calibration and dual-frequency carrier-phase smoothing enable us to perform further error analysis such as correlation function. With the construction of NSTB, fascinating data bank are becoming available. Several studies need to be made for improvements toward ionospheric modeling. Among them are 1) validation of the nominal model used for generation of ionosphere grid, 2) best weighting function and 3) air and ground algorithm for ionosphere outliers detection. ACKNOWLEDGMENTS The authors would like to gratefully thank the support and assistance of the FAA AGS-100, the Satellite Program Office, FAA Technical Center and the FAA personnel at the reference stations. Would also want to thank Dr. Todd Walter, Y.J. Tsai, Jennifer Evans and Dave Lawrence for their numerous help.

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The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications FIGURE 10 Correlation coefficients of the ionospheric delay vs. IPP separation distance using daytime data (preliminary result). The day time data shows strong correlation up to 2000 ∼ 3000 km. FIGURE 11 Correlation coefficients of the ionospheric delay vs. IPP separation distance using nighttime data (preliminary result). The night time data shows much stronger correlation than the day time. REFERENCES Barrows, A., P.Enge, B.Parkinson, J.Powell, Flight Tests of a 3-D Perspective-View Glass-Cockpit Display for General Aviation Using GPS , Proceedings of ION-GPS-95, Palm Springs, CA, September, 1995, pp 1615-1622. Cohen, C., D.Lawrence, H.S. Cobb, B. Pervan, J.D.Powell, B. Parkinson, G.Aubrey, W. Loewe, D.Ormiston, B.D. McNally, D.Kaufmann, V.Wullschleger, and R Swider, “Preliminary Results of Category III Precision Landing With 110 Automatic Landings of United Boeing 737 Using GNSS Integrity Beacons,” Proceedings of the National Technical Meeting of the Institute of Navigation, Anaheim, pp. 157-166, January, 1995. Hatch, R.R., The Synergism of GPS Code and Carrier Measurements, Proceedings of the Third Geodetic Symposium on Satellite Doppler Positioning, Las Crues, NM, Feb, 1982, pp1213-1232. ICD-GPS-200 Revision B-PR, Rockwell International, July 1991. Kee C., B. Parkinson, P. Axlerad, Wide Area Differential GPS Navigation, Journal of the US Institute of Navigation, vol.38, no.2, Summer, 1991. Klobuchar, J.A Design and Characteristics of the GPS ionospheric Time Delay Algorithm for Single Frequency Users IEEE Position Location and Navigation Symposium, Las Vegas, NV, Nov. 1986. Knecht, D.J. Shuman, B.M. Handbook of Geophysics and the Space Environment, chapter of the geomagnetic field., 1985. Lawrence, D., J. Evans, Y.C. Chao, Y.J.Tsai, C.Cohen, T.Walter, P.Enge, J.D.Powell, B.Parkinson, Integration of Wide Area DGPS with Local Area Kinematic DGPS, IEEE PLANS 96, Atlantic City, GA, April, 1996. RTCA Special Committee 159 Working Group 2 Wide Area Augmentation System Signal Specification, March 1994. RTCA Special Committee 159, Minimum Operational Performance Standards (MOPS) for Airborne Supplemental Navigation Equipment Using GPS, RTCA 204-91/SC159-29, These MOPS are modified by Technical Standard Order TSO-C129, which was released December 10, 1992. Tsai, Y.J., P.Enge, Y.C. Chao, T. Walter, C.Kee, J.Evans, A.Barrows, D.Powell, B.Parkinson, Validation of the RTCA Message Format for WAAS, ION-GPS-95. Walter T., C. Kee, Y.C. Chao, Y.J. Tsai, U. Peled, J.Ceva, A. Barrows, E. Abbott, D. Powell, P. Enge and B. Parkinson Flight Trials of the Wide Area Augmentation System (WAAS), Proceeding of Institute of Navigation 1994 Annual Meeting of the Satellite Division (ION-GPS-94), Salt Lake City, Salt Lake City, Sept, 1994.