The Measurement of Precipitable Water Vapor Over Texas. Using the Global Positioning System. David Owen Whitlock. March 2000

Transcription

1 The Measurement of Precipitable Water Vapor Over Texas Using the Global Positioning System by David Owen Whitlock March 2000 Center for Space Research The University of Texas at Austin CSR-TM-00-03

2 This work was supported by the Texas Higher Education Board Advanced Technology Program Center for Space Research The University of Texas at Austin Austin, Texas Supervised by: Robert S. Nerem

3 The Measurement of Precipitable Water Vapor Over Texas Using the Global Positioning System The goal of this experiment was to demonstrate that the Global Positioning System (GPS) can be a fast, accurate, and inexpensive method to measure atmospheric precipitable water vapor (PWV). Data from a network of up to 20 GPS receivers were processed to measure PWV in near real time (approximately one hour) over the state of Texas. 16 permanent GPS antennas from the Continuously Operating Reference Stations network (which encompasses sites operated by the Forecast Systems Laboratory, United States Coast Guard, Federal Aviation Administration/National Travel Safety Board, and the International GPS Service) as well as four new GPS antennas and receivers (set up by the Center for Space Research within the state of Texas) were utilized to gather the data. The four Trimble antennas and receivers were installed as part of this investigation in Austin, Brownwood, Laredo, and Wichita Falls, Texas. Paroscientific MET3 meteorological sensors were installed with the GPS equipment to measure surface pressure and temperature, both of which are necessary to extract PWV from GPS data. GPS data were gathered hourly from all available sites, then processed using the Jet Propulsion Laboratory's GIPSY-OASIS II software to estimate the total atmospheric delay of the GPS signal in the zenith direction. This signal can be converted to PWV with knowledge of the aforementioned surface atmospheric conditions. The output from this processing were near real time maps showing PWV over Texas and its surrounding states and time series of PWV, pressure, and temperature at each individual GPS site.

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5 Table of Contents CHAPTER 1 - INTRODUCTION... 1 THE GLOBAL POSITIONING SYSTEM...1 Signals...2 Observables...3 DEFINITION OF PRECIPITABLE WATER VAPOR...4 HISTORICAL TECHNIQUES FOR MEASURING WATER VAPOR...5 Radiosonde...5 Water Vapor Radiometer...7 The Global Positioning System...9 MOTIVATION FOR PWV MEASUREMENT...9 Utility in Weather Forecasting Utility in Climate Monitoring PREVIOUS EXPERIMENTATION UNAVCO Colorado Campaign Westford Water Vapor Experiment (WWAVE) Gradient and Line of Sight Measurements HOW THE ATMOSPHERE AFFECTS THE GPS SIGNAL The Atmosphere The Effect on the GPS Signal CHAPTER 2 THEORY OF ATMOSPHERIC DELAY...19 THE PHYSICAL EFFECTS OF THE TROPOSPHERE ON THE GPS SIGNAL Excess Path Length Refractivity HOW GPS CAN BE USED TO MEASURE WATER VAPOR Basics of the Signal Delay Separation of Wet Delay from the Hydrostatic Delay Mapping the Delay to the Zenith Calculation of PWV from Zenith Delay ERRORS IN MEASURING WATER VAPOR GPS Orbits Multipath Errors WVR Errors Pressure Sensor Errors Total Errors CHAPTER 3 THE GPS NETWORK AND COMPUTATIONAL PROCEDURE...32 THE GPS NETWORK GPS SITE INSTALLATION Site Requirements Hardware for Each CSR Installed Site Antenna Installation Receiver and PC Set Up Firmware Configuration... 39

6 COMPUTATIONAL PROCEDURE Downloading GPS Data Daily Station Position Runs Estimation Background Tropospheric Delay Estimation Post-GIPSY-OASIS Processing CHAPTER 4 - WATER VAPOR RESULTS...50 NEAR REAL TIME RESULTS Time Series of Maps Time Series of PWV, Temperature, and Pressure Discussion of Near Real Time Results EFFECT OF ORBIT ACCURACY ON PWV Orbit and Polar Motion Data Orbit Comparison Results Orbit Data Comparison One Day Predicted Orbits vs. Precise Orbits Two Day Predicted Orbits vs. Precise Orbits Discussion of Orbit Comparison Results COMPARISON TO RADIOSONDE MEASURED PWV Radiosonde Comparison Results Radiosonde Data Comparison Discussion of Radiosonde Comparison Results PROBLEMS AND DELAYS IN PROCESSING CORS Downloading Orbit Download CSR Machine Delays Summary of Near Real Time Application CATASTROPHIC ERRORS Station Position File Errors Orbit Errors Computation Load and Network Errors CHAPTER 5 - CONCLUSIONS...84 ACCURACY AND WEATHER MODELING FUTURE WORK Azimuth and Gradient Water Vapor Calculation Increase the Network Dual Frequency APPENDIX A...87 BIBLIOGRAPHY...89

7 List of Tables TABLE COEFFICIENTS OF THE HYDROSTATIC MAPPING FUNCTION [NIELL, 1996] TABLE COEFFICIENTS OF THE WET MAPPING FUNCTIONS [NIELL, 1996] TABLE ERROR BUDGET FOR PWV CALCULATIONS TABLE ANTENNA SITE LOCATIONS AND RESPONSIBLE AGENCIES TABLE PWV DATA COMPARISON USING DIFFERENT ORBIT FILES TABLE UNAVCO AND CSR NRT COMPARISON TO RADIOSONDE... 76

8 List of Figures FIGURE 1.1 ALTITUDE RANGE FOR VARIOUS LAYERS OF THE ATMOSPHERE FIGURE 1.2 INCREASED SIGNAL DELAY FOR LOWER ELEVATION SATELLITES FIGURE 2.1 MULTIPATH COHERENCE FOR FIVE SEPARATE DAYS [ROCKEN ET AL., 1993] FIGURE MAP OF GPS RECEIVER LOCATIONS [WHITLOCK ET AL., 1999] FIGURE LEVELING PLATE (BRWD) FIGURE COMPLETE ANTENNA WITH RAYDOME (BRWD) FIGURE HARDWARE CONFIGURATION FIGURE PROCESSING FLOW DIAGRAM FOR ANY HOUR OF DAY 1 (GMT) FIGURE DATA FLOW DIAGRAM FOR CSR SITES FIGURE NEAR REAL TIME MAPS FIGURE NEAR REAL TIME MAPS (CONTINUED) FIGURE NEAR REAL TIME MAPS (CONTINUED) FIGURE NEAR REAL TIME MAPS (CONTINUED) FIGURE NEAR REAL TIME MAPS (CONTINUED) FIGURE NEAR REAL TIME MAPS (CONTINUED) FIGURE NEAR REAL TIME MAPS (CONTINUED) FIGURE NEAR REAL TIME MAPS (CONTINUED) FIGURE DAY 2/26/00 TIME SERIES (ARP3) FIGURE DAY 2/26/00 TIME SERIES (CSR1) FIGURE DAY 2/26/00 TIME SERIES (PATT) FIGURE DAY 2/26/00 TIME SERIES (WTFL) FIGURE ORBIT COMPARISON FOR FIVE SITES - 2/26/ FIGURE ORBIT COMPARISON FOR FIVE SITES - 2/26/00 (CONTINUED) FIGURE ORBIT COMPARISON FOR FIVE SITES - 2/26/00 (CONTINUED) FIGURE RAPIDLY CHANGING PWV; NRT VS. RADIOSONDE COMPARISON FIGURE STEADY PWV; NRT VS. RADIOSONDE COMPARISON... 75

9 Chapter 1 - Introduction The Global Positioning System The Global Positioning System (GPS) was initially designed by the Department of Defense (DoD) as a ranging/timing system from satellites with known orbits to unknown positions on Earth, in the air, or in space [Hofmann-Wellenhof et al., 1997]. The satellite constellation consists of 24 satellites inclined at 55. The satellites are separated into 6 orbital planes with 4 satellites in each plane, with the ascending node of each plane separated by 60. The satellites orbit at about half of geosynchronous orbit, at near 20,200 km altitude above Earth, giving them a period of about 12 hours. Each of the satellites carries several highly accurate atomic clocks and transmits a coded signal to receivers that decipher the signal to determine the time it left the satellite and the orbital position of the satellite at that time. Because there are at least 24 GPS satellites operating around Earth, no less than six are visible at any given time over the Continental United States (and with the right conditions, up to 11 can be visible at one time) [Bar-Sever et al., 1998; Coster et al., 1996]. In addition to positioning a receiver, many more applications using GPS have been investigated because of the high position accuracy now obtainable. Because of the increasing amount of GPS applications, the entire system has transformed into a valuable remote 1

10 sensing system in addition to its original use as a navigation tool [Bar-Sever et al., 1998]. Signals Each satellite transmits coded data on two frequencies, L1 ( MHz) and L2 ( MHz) [Chen and Herring, 1997; Coster et al., 1996; Hofmann-Wellenhof et al., 1997; Juan et al., 1997; Ruffini et al., 1998; Ware et al., 1997]. Two distinct codes, Course-Acquisition (C/A) code and Precision (P) code, are superimposed on the carrier frequencies, along with satellite ephemerides, system time, satellite clock corrections, ionospheric modeling coefficients, and satellite status (health) information. The C/A code (also known as the Standard Positioning Service) is a pseudorandom noise (PRN) code that is broadcast on the L1 carrier only. During initial experimentation, the C/A code produced point-positioning accuracies much better than expected, so the DoD introduced Selective Availability (SA) to deny this high accuracy to unauthorized users. SA dithers the clock and satellite position information to limit accuracy to approximately 100 m in the horizontal direction, and 150 m in the vertical direction. The P code (also known as the Precise Positioning Service) is a PRN code transmitted on both the L1 and L2 carrier frequencies, which allows for first order removal of ionospheric errors. To reserve precise positioning for DoD use, the P code 2

11 is almost always encrypted to what is referred to as Y code. The Y code is a combination of the P code and an encryption code called the W code. This protection of the P code is called Anti-Spoofing, or A-S. A-S is either on or off; there is no variable effect. Observables A pseudorange, or measured range from satellite to receiver, is derived from the broadcast signal. If four or more satellite signals are received simultaneously, an approximate three-dimensional position and correction to the less accurate receiver clock are calculated by the receiver in real time. Because the transmit time and receive time are different, true range cannot be measured. The pseudorange is derived from the equation ( ) ρ = ρ + c δ δ (1.1) true r t where ρ is the observed pseudorange calculated from the light-time equation, ρ true is the difference of position of the receiver at the true receive time and the satellite at the true transmit time, and δ t and δ r represent the bias created by clock errors in the satellite and receiver. Another observable is the carrier phase of the signal, which does not look at the actual information on the signal, but only the phase of the signal. The carrier phase is defined by 3

12 ρ = ρ + ( φ δ δ )+ true c r t N λ (1.2) where ρ = λ R φ φ = λ Φ S (1.3) where the fractional beat phase of the signal is converted into a pseudorange by scaling with the wavelength, λ. ρ true and the clock corrections remain the same as for the code pseudorange definition. The integer number of cycles, N, is unique for each receiver-satellite combination and is typically not known. Once a receiver has locked onto a satellite signal, only the fractional beat phase changes while N remains constant. N, known as the integer ambiguity, can be solved for using the code pseudoranges, or estimated. If a receiver loses signal lock on a satellite, a new integer ambiguity must be solved for once the lock is re-established. The use of carrier phase data can improve the accuracy of positioning to sub-centimeter precision [Blewitt, 1990; Dong and Bock, 1989] Definition of Precipitable Water Vapor Precipitable water vapor is defined as the height of liquid water that would result from condensing all the water vapor in a column from the surface of Earth to the top of the atmosphere [Bevis et al., 1992; Coster et al., 1996]. PWV is typically calculated in centimeters or millimeters and is a measure of the amount of water vapor 4

13 that can be found in the lower atmosphere over a given location. PWV is highly varying in both space and time. Historical Techniques for Measuring Water Vapor Atmospheric precipitable water vapor is not easy to measure in near real time, primarily because of the difficulty in placing instrumentation where knowledge of PWV is desired. Outside of GPS, radiosondes and water vapor radiometers are the industry standard in measuring PWV, although both show many weaknesses, especially in spatial and temporal resolution. Radiosonde A radiosonde is a balloon-launched instrument package that measures atmospheric conditions above the surface of Earth [Bevis et al., 1996; Bevis et al., 1992]. They are implemented in a geographical location for which meteorological characteristics of the troposphere are desired to be known. Radiosondes ascend through the atmosphere slowly, while communicating atmospheric conditions back to the ground through a radio communications link. There are several advantages to using radiosondes to measure water vapor in the atmosphere. First, the radiosonde measurements can be gathered nearly anywhere. True humidity, temperature, and pressure values can be obtained without tedious processing of the data. Finally, since radiosondes have been utilized for many 5

14 years, they are proven to be reliable and their data are known to be dependable and accurate. Unfortunately, there are several drawbacks to the use of radiosondes. Because of the fundamental nature of balloon-borne instrumentation, the equipment can only be used once. This makes the use of radiosondes very cost inefficient [Bevis et al., 1992; Coster et al., 1996]. In fact, most current geographical locations with regular radiosonde launches are considering a reduction in launch frequency due to excessive cost [Coster et al., 1996]. Also, in near real time applications, radiosondes are not as useful as other methods. They take approximately one hour to reach the tropopause (the upper boundary of the lowest layer of the atmosphere), thus providing little data on a rapid time scale [Coster et al., 1996]. If data are needed for prediction of inclement or rapidly changing weather, radiosonde measurements are essentially useless. There is a severe limit on the two-dimensional geographical space that can be measured using a radiosonde [Bevis et al., 1992; Coster et al., 1996; Rocken et al., 1993]. Because water vapor varies on a much finer scale than temperature and wind, radiosonde measurement of water vapor cannot be accurately modeled in two dimensions [Anthes, 1983]. Once released, data are abundant for the space in which the radiosonde travels, but not for other locations surrounding that area [Coster et al., 1996]. 6

15 Water Vapor Radiometer A water vapor radiometer (WVR) is a radio telescope, either land-borne or space-borne, that can determine atmospheric conditions by measuring the background temperature along a given line of sight [Bevis et al., 1992; Hogg et al., 1981; Rocken et al., 1993; Ware et al., 1993]. Land-based WVRs measure the background radiation in deep space to measure calculate the water vapor between the ground and space along the bore site [Bevis et al., 1992]. Space-based WVRs are installed on satellites and pointed towards Earth. They measure the background temperature of the Earth s surface and estimate the atmospheric conditions between the satellite and Earth in that manner [Bevis et al., 1992]. Space-based WVRs cannot accurately measure atmospheric conditions over land or cloud cover, because the background temperature can vary significantly depending on the surface that the radio waves strike. Spacebased WVRs can be quite useful over oceans and large bodies of water, because the background temperature is nearly uniform on the surface of the water [Bevis et al., 1996; Bevis et al., 1992; Coster et al., 1996; Rao et al., 1990; Rocken et al., 1993]. For uses in which WVR data are compared to GPS data, the WVR will be programmed to point toward visible GPS satellites. For a five satellite array, it takes about eight minutes to look in each satellite direction and gather data [Rocken et al., 1993; Ware et al., 1997]. 7

16 The advantages of WVRs are that they are mobile and can be placed nearly anywhere. Some initialization time is needed to calculate calibration coefficients, but scientists can place WVRs almost anywhere on the surface of Earth and get measurements with relative ease [Bevis et al., 1992]. Also, they have near real time capability. Unlike radiosondes, there is no instrument travel time required to make meteorological measurements. Once calibrated, the WVR can be pointed, line-of-sight measurements made, and data accumulated very swiftly. Also, as in the use of radiosondes, WVRs have been utilized for many years and have proven to be a reliable method for accurate atmospheric data measurement. WVRs suffer from similar limitations as the radiosonde, including instrument cost. A single WVR can cost hundreds of thousands of dollars, so any kind of array of WVRs for use in mapping or data gathering over a significant two-dimensional space becomes cost-prohibitive [Coster et al., 1996]. This tends to limit the spatial resolution of atmospheric data, as most research organizations cannot afford one WVR, let alone several, to provide accurate atmospheric modeling in a twodimensional sense [Rocken et al., 1993]. A major disadvantage unique to the WVR is that no data can be gathered when the weather is extremely overcast or raining [Bevis et al., 1992; Niell et al., 1996; Ware et al., 1997]. 8

17 The Global Positioning System In addition to the more obvious uses, such as high-precision geodesy, an increasing number of applications for GPS are being developed, especially in the fields of climatology and meteorology [Bar-Sever et al., 1998]. Because the GPS signal travels through the entire atmosphere, the signal can be processed on the ground and atmospheric water vapor extracted. The current technologies used to measure atmospheric water vapor discussed above can be expensive and may provide little meaningful data, especially in near real time. Because there are many GPS antennas continuously operating, a significant quantity of water vapor data can be gathered in near real time using GPS. Chapter 2 will discuss in detail how GPS can be used to measure PWV. Motivation for PWV Measurement Atmospheric water vapor plays a critical role in atmospheric processes that act on a variety of temporal and spatial scales [Bevis et al., 1992]. Because water vapor is the most variable major constituent in our atmosphere, near real time measurement of PWV can help meteorologists better understand how local weather and climate are changing over time [Bevis et al., 1992]. 9

18 Utility in Weather Forecasting Limitations in the quantity and accuracy of water vapor data are a major source of error in daily forecasts of precipitation and inclement weather. Accurate information regarding the horizontal and vertical distribution of PWV can lead to significant improvement in daily weather forecasting. GPS receivers distributed over small spatial scales (less than 500 km) can provide water vapor data that could be assimilated into numerical weather forecasts [Rocken et al., 1993]. The distribution of water vapor is closely coupled to the formation of clouds and subsequent rainfall, as there is an unusually large latent heat associated with water s change of phase, which can play a critical role in the evolution of storm systems and severe weather [Bevis et al., 1993; Bevis et al., 1992]. Due to the high temporal and spatial variance of PWV, mathematical modeling of water vapor to the accuracy needed for weather prediction is not feasible. Direct measurement remains the only way to gather accurate water vapor values useful for weather forecasting. Utility in Climate Monitoring Water vapor contributes more than any other atmospheric component to the greenhouse effect [Bevis et al., 1992; Coster et al., 1996]. In order to understand and predict changes in Earth s climate on a large time scale, long-term measurement of PWV on a global scale must be carried out. The increasing number of GPS antennas throughout the United States and the world can provide atmospheric scientists with 10

19 an abundance of long term data over land for climate studies to compliment existing WVR and radiosonde measurements, which are more useful over the oceans [Bevis et al., 1993; Bevis et al., 1992; Yuan et al., 1993]. Previous Experimentation Several GPS campaigns have been performed to verify the utility and accuracy of GPS water vapor measurements. Initial experimentation attempted to verify the accuracy of GPS measured PWV when compared to WVR or radiosonde measurements. PWV accuracy of 1 mm has been verified during various experiments and campaigns [Coster et al., 1996; Nam et al., 1996; Niell et al., 1996; Rocken et al., 1993; Ware et al., 1993]. Recently, more detailed experimentation and analysis has been done to investigate the feasibility of measuring delays in the individual directions of the GPS satellites, whereas initial experimentation only estimated water vapor in the zenith direction. UNAVCO Colorado Campaign The University Navstar Consortium (UNAVCO) performed a two-antenna GPS campaign to determine the accuracy of PWV measurement with GPS from September 17, 1992 to November 28, 1992 [Rocken et al., 1993; Ware et al., 1993]. Antennas were placed 50 kilometers apart in Boulder and Platteville, Colorado, with a meteorological sensor and WVR at each receiver location. No radiosonde balloons 11

20 were used, and PWV data obtained from GPS were compared to the WVR measured PWV. Because a relatively short baseline was used, PWV was only estimated and compared to WVR results at Boulder. When using precise GPS orbits, the experiment showed sub-millimeter accuracy of PWV values obtained with GPS as compared to PWV values obtained with a WVR. When broadcast orbits were used for satellite positions, the accuracy decreased by 30% to an accuracy of about 1 mm of PWV. This level of accuracy using broadcast orbits demonstrated the near real time capability of PWV measurement with GPS. Westford Water Vapor Experiment (WWAVE) 11 GPS antennas were placed within a very short baseline of about 25 kilometers to measure the temporal and spatial variability of PWV over the area surrounding Westford, Massachusetts [Coster et al., 1996; Niell et al. 1996]. The data were collected from August 15, 1995 to August 30, Three of the antennas were placed within a kilometer radius near the center of the network and meteorological sensors were placed at eight of the sites. The zenith PWV data gathered were compared to zenith WVR and radiosonde PWV measurements gathered at the central location. Accuracy of 1-2 mm of PWV was obtained when comparing the PWV results estimated with GPS with PWV results obtained by WVR and radiosondes. From GPS site to GPS site, agreement in PWV of less than 1 mm was obtained, although this high degree of accuracy can be attributed to some identical 12

21 error sources (such as orbit errors) seen by each of the receivers. Because of the limit in radiosonde launches, and the lack of utility of WVRs during rain (it rained twice during the campaign), the quantity of alternatively measured data for comparison was limited during the WWAVE experiment. Gradient and Line of Sight Measurements When calculating zenith delay, which is converted to PWV, symmetry in the azimuthal direction is a common assumption. This assumption can be far from valid, especially during the time when weather systems may be approaching an antenna from a distinct azimuth direction. This asymmetry can be especially important in atmospheric correction for horizontal and vertical precise-positioning [Bar-Sever et al., 1998]. Gradient effects can be as high as 5 cm difference in delay at 7 elevation [MacMillan, 1995]. By modeling this gradient, a horizontal and vertical position repeatability increase of nearly 20% is obtainable [Bar-Sever et al., 1998]. GPS can help model azimuth gradients by analyzing the slant-path water vapor along GPS signal paths. During a three day campaign in May, 1996, 1.3 mm rms agreement was found when comparing GPS line of sight delays with WVR measurements [Ware et al., 1997]. During an experiment in Madrid, Spain, gradient estimates obtained with GPS and a WVR compared favorably, leading to the belief that GPS slant delay estimation capability is a strong possibility in the near future [Ruffini et al., 1999]. This capability was also demonstrated in Onsala, Sweden during a similar gradient 13

22 estimate campaign [Bar-Sever et al., 1998]. By removing the assumption of atmospheric symmetry in the azimuth direction, an improvement positioning and atmospheric measurement accuracy can be obtained using GPS. How the Atmosphere Affects the GPS Signal The Atmosphere The atmosphere (Figure 1.1) is made up of several layers. Scientists define these layers by their atmospheric characteristics, such as temperature, pressure, and humidity [Brunner and Welsch, 1993]. The closest layer to Earth is the troposphere, which begins at Earth s surface and extends to between 9 and 16 kilometers above the surface. The approximately 7 kilometer region between the troposphere and the next layer, the stratosphere, is called the tropopause. The tropopause has characteristics of both the troposphere and stratosphere. From 16 kilometers to 50 kilometers above Earth s surface is the stratosphere. The troposphere, tropopause, and stratosphere compose what is referred to as the neutral atmosphere, as it is electrically neutral. Above the stratosphere, the atmosphere is electrically charged and called the ionosphere. From about 50 kilometers to about 80 kilometers is the mesosphere, which is the lower ionosphere. Outside the mesosphere is the remainder of the ionosphere, which extends from about 80 kilometers above the surface to the upper reaches of the atmosphere (extending even beyond 1000 km). Each of these 14

23 atmospheric regions adversely affects the GPS signal by delaying its arrival at Earth s surface by a finite amount of time. 80 Kilometers Ionosphere Ionosphere/Mesosphere 50 Kilometers Stratosphere 16 Kilometers 9 Kilometers Tropopause 0 Kilometers Troposphere Figure 1.1 Altitude Range for Various Layers of the Atmosphere 15

24 The Effect on the GPS Signal The delay of the atmosphere can cause significant errors for precisepositioning applications. The ionospheric signal delay is dispersive in nature in that the delay is dependent upon the frequency of the signal [Hofmann-Wellenhof et al., 1997]. Because GPS broadcasts on two separate frequencies, this error can be eliminated by the mathematical combination of the two separate frequency signals. The focus of the research discussed here will be the delay caused by the troposphere, or neutral atmosphere. Unlike the ionosphere, the delay caused by the troposphere is non-dispersive, or completely independent of the signal frequency. However, with accurate knowledge of GPS antenna location and GPS satellite location, the signal delay errors caused by the troposphere can be measured. Atmospheric delay caused by the troposphere is typically computed in length. For example, a standard zenith tropospheric delay would be about 2.3 meters, meaning that the troposphere caused a GPS receiver to read an extra 2.3 meters distance between itself and a fictitious satellite at zenith [Bevis et al. 1996; Chen and Herring, 1997]. The delay caused by the troposphere can be categorized into two components, the hydrostatic delay and the wet delay [Bar-Sever et al., 1998; Bevis et al., 1996; Bevis et al., 1992; Coster et al., 1996; Gregorius and Blewitt, 1998; Hofmann- Wellenhof et al., 1997; Rocken et al., 1993; Ware et al., 1997; Yuan et al., 1993]. The hydrostatic delay is caused by dry gases in the troposphere and the non-dipole 16

25 component of water refractivity while the wet delay is caused solely by the dipole component of water refractivity, which we refer to as water vapor [Bar-Sever et al., 1998]. The hydrostatic delay makes up almost 95% of the total tropospheric delay and typically does not vary more than 0.5% over the course of a day [Bevis et al., 1996]. This delay is dependent on the atmospheric pressure and can be estimated by utilizing the surface pressure on Earth. If surface pressure is known to 0.4 mbar, then the hydrostatic delay can be estimated within the accuracy of 1 millimeter using well known models, such as the Saastamoinen model [Bevis et al., 1996; Nam et al., 1996; Rocken et al., 1993]. The wet delay, however, cannot be estimated using surface atmospheric measurements. By estimating the total zenith delay, then calculating the hydrostatic delay from surface pressure, the remaining delay is caused by water vapor in the atmosphere. As discussed in the previous section, initial experimentation is being done to estimate line-of-sight delays in the individual directions to the GPS satellites. However, in general, mapping functions are used to take signal delays from each individual GPS satellite and map them to the zenith direction to estimate only one zenith signal delay, or the delay in signal transmission (measured in length) a GPS satellite would experience were it at zenith over the GPS antenna. Mapping functions used for this purpose will be discussed in the next chapter. Of the 2.3 m approximate zenith delay, about 2.2 m is caused by hydrostatic atmospheric characteristics and 17

26 approximately 10 cm of range error is caused by water vapor [Bevis et al., 1996; Bevis et al., 1992; Chen and Herring, 1997]. As satellites decrease in elevation toward the horizon, the atmospheric delay can increase significantly because the signal must transmit through more of the lower atmosphere. For a satellite at about 5 degrees elevation, the delay can be up to 25 m. Figure 1.2 shows how decreased elevation leads to the signal going through more of the atmosphere, which leads to increased signal delay. Once the delay is mapped to zenith, that value can be converted to precipitable water vapor through a constant, k, which will also be discussed in Chapter 2. Zenith Satellite Lower Elevation Satellite Neutral Atmosphere Boundary GroundAntenna Note: not to scale Figure 1.2 Increased Signal Delay for Lower Elevation Satellites 18

27 Chapter 2 Theory of Atmospheric Delay The Physical Effects of the Troposphere on the GPS Signal The neutral, lower atmosphere has two effects on a GPS signal. The first effect is the delay of the signal due to the troposphere. The second effect is to refract the GPS signal. The GPS signal will travel on a curved path instead of a straight line. Both of these effects are due to the changing refractivity of the lower atmosphere in the ray path of the GPS signal. [Bevis et al., 1992; Yuan et al., 1993] Excess Path Length al., 1993] The excess path length is given by the path integral [Bevis et al., 1992; Yuan et L = n() s ds G (2.1) L where n(s) is the refractive index as a function of position, s, along the path L and G is the straight line geometric path length through the atmosphere. Simplified, Equation 2.1 can be expressed as [Bevis et al., 1992; Yuan et al., 1993] 19

28 L = n() s 1 ds [ S G] (2.2) L [ ] + where S is the path length along L. This separates the change in travel length into the first term, which is the delay due to the slowing effect of the troposphere and the second term, which is the added path length due to the bending of the signal. For most elevations over 15, S G is less than a centimeter, meaning the first term is the bulk of the excess length. Refractivity It is mathematically easier to use the atmospheric refractivity, N, instead of refractive index, n, in Equation 2.2 utilizing the relation [Bevis et al., 1992; Yuan et al., 1993] ( ) 6 N = 10 n 1 (2.3) where N can be related empirically to temperature, T, pressure, P and water vapor pressure P v by [Hofmann-Wellenhof et al., 1997; Smith and Weintraub, 1953] P Pv N = T * 10 5 (2.4) 2 T or a more accurate and complex representation [Thayer, 1974] 20

29 Pd N k T Z k Pv T Z k Pv = 1 d + 1 v Z 2 T 1 v (2.5) in which k 1 = ( ± 0.014) K/mbar, k 2 = (64.79 ± 0.08) K/mbar, k 3 = (3.776 ± 0.004) K 2 /mbar, P d is the partial pressure of dry air (in mbar), and Z -1 d and Z -1 v are inverse compressibility factors for dry air and water vapor. Because of the extreme difficulty in finding values for many of the parameters in Equations 2.4 and 2.5, the total atmospheric delay is divided into a hydrostatic delay and a wet delay [Saastamoinen, 1972]. This method of dividing the delay is ideal for utilizing GPS to measure atmospheric water vapor. How GPS Can be Used to Measure Water Vapor Basics of the Signal Delay For a given measured distance from the ground to the satellite (using both pseudorange and carrier phase from Equations 1.1 and 1.2), the difference between the measured range and the actual range can be extremely simplified to R = ρ+ εi + ε t (2.6) εt = εh + εw (2.7) where R is the measured range from GPS antenna, ρ is actual range, ε i is the ionospheric error, ε t is the tropospheric error, ε w is the wet delay error, and ε h is the 21

30 hydrostatic delay. If the satellite orbit and receiver location are known to a good degree of accuracy, then an estimate of ρ is known. ε i can be estimated due to the frequency dependent nature of the ionospheric delay using a mathematical combination of the two GPS frequencies. Then, we compute ε h from the atmospheric measurements and measure R from the GPS data leaving the only unknown to be the error caused by the wet component of the atmosphere, ε w. Separation of Wet Delay from the Hydrostatic Delay The hydrostatic delay is the cause of the bulk of the total GPS signal delay due to the troposphere. It can be accurately estimated by measuring local surface pressure and using the formula [Bevis et al., 1992; Yuan et al., 1993] L h ( ) 6 = ZHD = ± Ps f λ, h ( ) (2.8) where P s is surface pressure in mbar and f(λ,h) is the station latitude and height dependent gravitation function [Bevis et al., 1992] f( λ, h)= ( * cos 2λ h) (2.9) and is close to unity. The wet delay varies much more in time and space than the hydrostatic delay. It is also much more difficult to measure using atmospheric data 22

31 exclusively. The formula for calculating it is [Bevis et al., 1996; Bevis et al., 1992; Yuan et al., 1993] Pv L ZWD k T dz k Pv T dz w = = 10 6 ' (2.10) in which k 2 = (17 ± 10) K/mbar, k 3 = (3.776 ± 0.03)*10 5 K 2 /mbar (same as Equation 2.5), P v is the partial pressure of water vapor (only available through radiosondes), and T is the temperature (K) Since the integral of the partial pressure cannot be measured in near real time, it is easier to measure the total delay from GPS measurements, then correct it using the much more easily calculable hydrostatic delay. The remaining portion of the total delay is the wet delay. Mapping the Delay to the Zenith For GPS measurement of zenith precipitable water vapor, the signal delay in each direction to each GPS satellite is not generally estimated individually. Instead, the individual delays are mapped from each individual satellite direction to a single zenith delay. This mapping method assumes that the delay is independent of azimuth. However, it does not assume that the delay is independent of elevation. This assumption could never be made, because of the significant increase in delay that is seen when the signal travels through much more of the atmosphere at lower 23

32 elevations. Mapping functions take the delay seen by each satellite and map them to the zenith direction. Examples of mapping functions are the Niell, Lanyi, and Lanyi- C. For the GIPSY-OASIS processing in this PWV application, Niell mapping functions are used to map delays to the zenith. Niell mapping functions are dependent upon site latitude and height and not atmospheric models as some other mapping functions are. The Niell mapping function is [Niell, 1996] 1 a 1 + b 1 + m( ε) = 1 + c 1 a sin( ε)+ b sin( ε )+ sin( ε)+ c (2.11) where a, b, and c are given by Table 2.1 for hydrostatic delay, Table 2.2 for wet delay, and are dependent upon site latitude. All values were calculated using experimental data and have an amplitude of order 10-5 dependent upon the day of year. 24

33 Latitude (all values are 10-3 ) Coefficient a b c Table Coefficients of the Hydrostatic Mapping Function [Niell, 1996] Latitude (all values are 10-4 ) Coefficient a b c Table Coefficients of the Wet Mapping Functions [Niell, 1996] The mapping function is adjusted for the height above geoid with [Niell, 1996] dm( ε) 1 = f ε aht bht cht dh ( ε) (,,, ) (2.12) sin where f is Equation 2.11 for a b c ht ht ht = 253. E 5 = 549. E 3 = 114. E 3 giving a mapping function height correction of [Niell, 1996] 25

34 m( ε )= where H is the height of the site above geoid. ( ) dm ε dh H (2.13) Calculation of PWV from Zenith Delay Once a zenith delay due to the wet portion of the atmosphere has been determined, then it can be mathematically converted into total precipitable water vapor. The two are related by the formula [Bevis et al., 1996; Bevis et al., 1993; Bevis et al., 1992; Kruse et al., 1999; Ware et al., 1997; Yuan et al., 1993] where dimensionless k is PWV ZWD = (2.14) k k k = ' + k2 R T m v (2.15) R v is the specific gas constant for water vapor, and k 2 and k 3 are from Equation T m is mean temperature from [Bevis et al., 1996; Bevis et al., 1993; Bevis et al., 1992; Yuan et al., 1993] 26

35 T m = 2 Pv T dz Pv T dz (2.16) which again is difficult to calculate because of the near impossible task of measuring the values to integrate. However, the mean temperature has been estimated linearly [Bevis et al., 1993; Bevis et al., 1992; Yuan et al., 1993]: T m T (2.17) s where T s is surface temperature in Kelvin. T m has an rms deviation of 4.7 K which contributes to errors in the measurement of PWV with GPS, but not significantly, as the dependence upon temperature is weak [Bevis et al., 1996]. Errors in Measuring Water Vapor Error estimations for PWV measurement using GPS have been performed previously and this section summarizes these results. GPS Orbits GPS orbit errors affect the calculation of receiver-satellite range in Equation 2.6. There are several different levels of accuracy of GPS orbits produced by various centers around the world (e.g. Jet Propulsion Laboratory, International GPS Service, GeoForschungsZentrum). First, there are predicted orbits, which are satellite 27

36 positions extrapolated into the future. These orbits decrease in accuracy from less than 1 m up to 3 m in satellite position after three days [Gregorius, 1996]. Predicted orbits are primarily used for near real time applications. Secondly, a slightly more accurate, quick-time, orbit is available about a day after data is gathered. These orbits, which are accurate to about cm, can be used to post-process GPS data within a few days after they are gathered. Thirdly, in about ten days to two weeks, the satellites are calculated to their most precise positions, which can then be used for precise GPS applications. The precise orbits are accurate to cm. In addition to these calculated or extrapolated orbits, there are orbit data broadcast by the GPS satellites that can be used for real time positioning and near real time geodetic measurements. These orbits, with SA implemented, have accuracy which allow positioning to only within 100 m horizontal in real time [Hofmann- Wellenhof et al., 1997]. Orbit errors of 1 in 100 million (centimeter level errors in satellite location) yield an error of approximately 0.1 mm error in PWV [Rocken et al., 1993; Ware et al. 1997]. For predicted orbit error of 1 m, the PWV error jumps to 1-3 mm. Multipath Errors Multipath errors affect the measurement of pseudorange and carrier phase in Equation 2.6. Multipath occurs when a GPS signal reflects off of another surface, thus reaching the receiver by more than one path [Hofmann-Wellenhof et al., 1997; 28

37 Rocken et al., 1993]. Multipath is best reduced by antenna design, site location, and data processing. Most antennas used in precise-positioning have a choke ring, which helps mitigate multipath. Also, by not locating the antenna near tall buildings or other reflective surfaces, multipath effects can be significantly reduced. Quality check software used to improve the quality of GPS data also looks for multipath and can help eliminate it. Multipath is difficult to quantify when discussing the measurement of water vapor [Rocken et al., 1993]. The aforementioned UNAVCO-Colorado experiment showed repeated inaccuracy with respect to hour of the day, when comparing PWV estimated from WVRs and GPS, due to multipathing. Because similar degrees of inaccuracy were observed the same time each (sidereal) day (when satellites are in almost exactly the same position), multipath can be considered the primary source for this error. Figure 2.1 contains PWV time series for five separate days of data. Please note that data from each day are arbitrarily offset from one another. For the UNAVCO experiment, about 1 mm of error was attributed to multipath. 29

38 Figure 2.1 Multipath Coherence for Five Separate Days [Rocken et al., 1993] WVR Errors Errors in instrument calibration can also cause errors in WVR measurements. There is a necessary calibration period once a WVR is set up for atmospheric measurement [Radiometrics, 1999]. As in any instrument calibration, there is a limit to the accuracy. This calibration inaccuracy can lead to about 0.3 mm of difference between a WVR and GPS measured PWV [Rocken et al., 1993]. Another error, when comparing WVR data and GPS data, is that a WVR can measure variance in azimuth directions of atmospheric water vapor. As mentioned before, azimuth asymmetry can lead to a 20% error in positioning repeatability [Bar- Sever et al., 1998]. 30

39 Pressure Sensor Errors Pressure sensor errors affect the calculation of the hydrostatic delay, ε d, in Equation 2.6. As with any measurement device, there are very small errors in calibration. For an error of 1 mbar, the error in PWV can be about 0.5 mm [Rocken et al., 1993]. Total Errors For the major error sources listed above, error in PWV from GPS measurement when compared to actual PWV is approximately 1.6 mm using precise orbits. When comparing to WVR measurements, the error is 1.9 mm. The error can increase to over 3 mm when using less accurate, predicted orbits. Table 2.3 displays the PWV error values. Error Source PWV Error (GPS PWV Error (GPS vs. Absolute) vs. WVR) GPS Orbits Errors mm mm Multipath Errors 1 mm 1 mm WVR Errors N/A 0.3 mm Pressure Sensor 0.5 mm 0.5 mm Expected RMS Error mm mm TOTAL ERROR mm mm Table Error Budget for PWV Calculations 31

40

41 Chapter 3 The GPS Network and Computational Procedure The GPS Network The Continuously Operating Reference Stations (CORS) network gathers data from 16 GPS receivers in Texas and its surrounding states for near real time PWV processing. For this project, four additional receivers specifically were placed strategically to fill in geographical gaps left by the CORS receivers. Because an Internet connection for data upload was needed at each receiver location, colleges and universities were ideal choices for these GPS sites. There is no CORS antenna located near Austin, Texas, with data available hourly (data from the CORS site, AUS5, is only published once a day), so a GPS antenna was placed on the roof of the building in which CSR is located. The other permanent GPS sites were installed at universities in Wichita Falls, Brownwood, and Laredo, Texas. More detail will be presented in the next section regarding the specifics of the site installations. Table 3.1 shows a complete list of GPS sites used for near real time PWV processing, and the agency responsible for their maintenance and upkeep. Figure 3.1 shows a map displaying the location of each receiver used for the experiment. 32

42 Site Location Lat. Long. Responsible Agency ARP3 Aransas Pass, Texas U.S. Coast Guard AZCN Aztec, New Mexico Forecast Systems Lab BRWD Brownwood, Texas Center for Space Research CSR1 Austin, Texas Center for Space Research DQUA Dequeen, Arkansas Forecast Systems Lab ENG1 English Turn, Louisiana U.S. Coast Guard GAL1 Galveston, Texas U.S. Coast Guard HKLO Morris, Oklahoma Forecast Systems Lab JTNT Jayton, Texas Forecast Systems Lab LMNO Lamont, Oklahoma Forecast Systems Lab LRDO Laredo, Texas Center for Space Research MDO1 Ft. Davis, Texas International GPS Service PATT Palestine, Texas Forecast Systems Lab PRCO Purcell, Oklahoma Forecast Systems Lab SJT2 San Angelo, Texas FAA/NTSB TCUN Tucumcari, New Mexico Forecast Systems Lab VCIO Vici, Oklahoma Forecast Systems Lab WNFL Winnfield, Louisiana Forecast Systems Lab WSMN White Sands, New Mexico Forecast Systems Lab WTFL Wichita Falls, Texas Center for Space Research Table Antenna Site Locations and Responsible Agencies 33

43 Symbol Legend CSR FSL USCG IGS FAA/NTSB Figure Map of GPS Receiver Locations [Whitlock et al., 1999] GPS Site Installation Representatives from Howard Payne University in Brownwood, Texas A&M International University in Laredo, and Midwestern State University in Wichita Falls 34

44 agreed to assist the project by hosting GPS equipment at their respective campuses. For each of these three sites, a Trimble choke ring antenna and Paroscientific MET3 sensor were installed on the roof. Antenna and meteorological sensor cables connected the antenna to the receiver/pc located in a lab, then the PC was connected to the Internet for data upload. Site Requirements For each potential GPS site location, several criteria must be satisfied to receive, log, and transfer GPS data. In order to receive good data, the potential GPS antenna location must have a clear view of the sky. Also, there must not be any interference in the L-band ( MHz and MHz for L1 and L2) that would worsen the signal-to-noise ratio of the GPS signal as received by the antenna. The GPS receiver and PC must be in a secure environment, with power and Internet access. Finally, a physical pathway to connect the cable from the antenna and meteorological sensor on the roof to the receiver in the lab must be established. Hardware for Each CSR Installed Site The following were the major hardware items taken and installed at each site: 1 Trimble choke ring GPS antenna with spherical raydome and 30 meters of cable 1 Trimble 4000SSi receiver with an Office Support Module 2 (OSM2) power unit 1 Paroscientific MET3 Sensor with 30 to 60 meters of cable 35

45 1 Linux platform Personal Computer (PC) with monitor 1 Uninterrupted Power Supply (UPS) These hardware items were purchased for the project and installed at the three selected sites in Brownwood, Wichita Falls, and Laredo. These same items were installed in Austin at the Center for Space Research facility, except that the cable was longer (100 m) and needed two signal and DC voltage boosters installed along the cable. The MET3 cable was also 100 m, and instead of a Linux based PC, a Hewlett Packard workstation was used. The configuration for the hardware is diagrammed later, in Figure 3.4. Antenna Installation For each antenna installation, a threaded rod was placed in a drilled hole and fixed with epoxy. A plate (Figure 3.2) to allow for fine leveling of the antenna was locked onto the threaded rod with thread-locking cement. Once locked onto the plate, the antenna is leveled and the raydome cover installed to protect the antenna from the elements (Figure 3.3). The Paroscientific MET3 meteorological sensor was installed near the antenna, and the antenna and MET3 cables were run together to reach the receiver and PC in a secure laboratory. 36

46 Figure Leveling Plate (BRWD) Figure Complete Antenna with Raydome (BRWD) 37

47 Receiver and PC Set Up Prior to installation, each receiver and PC was configured and tested to ensure proper functionality. For installation at each remote site, the antenna and meteorological sensor were installed on the roof and connected to the receiver, which was located below in a secure laboratory. The receiver was connected to an OSM2, which allows interface between the PC and the receiver and provides power. Connecting the PC to the Internet was the final step to begin logging and uploading data. Once the hardware was installed and connected, an Internet protocol address had to be assigned to the PC, and Linux had to be reconfigured for the local universities Internet server in order to upload the data from the PC back to the central GPS lab at the CSR facility for processing with the other GPS sites. Internet Conn. UPS MET3 Antenna Data Power Power Power Data Power Power Data Data Data PC OSM2 Receiver Figure Hardware Configuration 38

48 Firmware Configuration Each Trimble 4000SSi receiver is configured to sample observation data every 15 seconds with a 4 satellite elevation mask. Through the Control Menu via the MET/TILT Interface, the Repeat String is set for "05 *9900P9N" which samples the pressure, temperature, and relative humidity automatically every five minutes, and writes them to the data file. Data files are continuously taken at 60 minute increments. The data file that is downloaded hourly contains observation, meteorological, and navigation RINEX data. Computational Procedure Figure 3.5 summarizes the overall processing procedure. Before the GPS data is processed for PWV calculations, pre-established positions for the antenna sites must be estimated. To fix the coordinates of each GPS antenna, the RINEX data for the entire day for each available GPS site are processed with GIPSY-OASIS from the Jet Propulsion Laboratory (JPL). This position is then fixed for PWV estimation purposes for the entire subsequent day. GIPSY-OASIS is also used to process the near real time GPS data to eventually estimate a tropospheric zenith delay for each receiver, which are translated into PWV by using the equations in Chapter 2. Time series for PWV, as well as temperature and pressure, are then produced. For PWV contour mapping purposes, PWV values are averaged over the hour. This single PWV value, along with antenna latitude and longitude, is input into Generic Mapping Tools 39

49 24 hours of RINEX data for day 0 for 21 sites G-O II proc. for sta-pos Predicted orbit data Fixed sta-pos for 21 sites 3 hours of RINEX Predicted orbit data G-O II proc for indiv. Calc. a priori TZD site TZD corrections TZD corrections for each site A priori TZD TZD for each site for each site Chapter 2 equations G-O II = GIPSY OASIS II TZD = Total Zenith Delay PWV For Each Site PWV time series Sta-pos = station position Near real time PWV map Figure Processing Flow Diagram for Any Hour of Day 1 (GMT) 40

50 software, which produces a detailed map of PWV over Texas and its surrounding states [Wessel and Smith, 2000]. These maps and time series are then placed on the Internet in near real time for the public to use. Downloading GPS Data GPS RINEX data are gathered from the CORS network at ftp://cors.ngs.noaa.gov/cors/rinex The Trimble receivers installed by the Center for Space Research upload their data every hour (on the hour) to personal computers at each specific site. Figure 3.6 outlines the data gathering and processing algorithm performed hourly to quality check and convert the raw data to RINEX format for each CSR installed site. Local Automated Process for Downloading of Global Sites (LAPDOGS) software, from UNAVCO, is used to take the raw data from the Trimble 4000 SSi receiver and place it on the hard drive of the computer. Rfile Utilities software, a series of executable files acquired from Trimble, is needed to run the LAPDOGS program. The downloaded data is in r00 format (filename.r00) and must be converted using runpkr00 (one of the executable files in the Rfile utilities) to data file format (filename.dat, filename.eph, filename.mes, filename.ion). Next, teqc, also distributed by UNAVCO, performs a quality check on the data, and converts it to the RINEX format that is ASCII readable and the data format input to GIPSY-OASIS. Both meteorological and observation data are converted to RINEX using this procedure. 41

51 r00 (with met and obs data) file on receiver LAPDOGS RFILE Utilities r00 on PC RUNPKR00 Data file on PC Teqc Met and obs in RINEX on PC Internet upload RINEX at GPS laboratory Figure Data Flow Diagram for CSR Sites 42

52 Finally, the observation and meteorological RINEX files are uploaded to a computer in the GPS lab at the Center for Space Research for combined processing. Daily Station Position Runs Once data for an entire day is available, GIPSY-OASIS takes the site position and velocity from CORS site log files as a priori, then estimates a new station position. This position is used for initializing the scheme for the daily PWV estimation. Initial experimentation showed that fixing the position in this manner gave more stable PWV estimates, especially when compared to independently determined PWV data [Gabor, 1997]. Estimation Background Observations, z, are modeled as a function of parameters, x, as [Gregorius, 1996] z = F(x) + Data Noise + Mismodeling (3.1) where F(x) must be linearized using Taylor expansion to z = F( x) F( x0) + F' ( x0)( x x0) + O( x0 ) (3.2) or δz = Aδx (3.3) where δz = z - F(x 0 ), A = F (x 0 ), and δx = (x - x 0 ). x 0 are the nominal values of the model parameters and A is their matrix of change. GIPSY-OASIS tries to find the best 43

53 solution to Equation 3.3, which is the best least squares agreement between the model and observations. Next, we introduce pre-fit residuals, v, to Equation 3.3 (and drop the δ s for convenience) to get z = Ax+ v (3.4) where z now represents the observed minus the computed values, A is the partial derivative matrix of parameters, or design matrix, and then solve for x. This set of equations yields one equation per observation. We define the parameter covariance matrix as T Pˆ = ( A WA) x 1 (3.5) where W is the a priori weight matrix of the observations and is the inverse of the covariance of observational errors. The values in W cannot be computer mathematically, but instead from previous experience. The weighted least squares of residuals is then T vwv ˆ ˆ = min. (3.6) The estimate of the corrections to the initial values assumed for the parameters is then where from the normal equations, giving the final solution t xˆ = Pt (3.7) xˆ T = A Wz (3.8) * T 1 T x = x + Pt ˆ = x + ( A WA) A Wz 0 x 0 (3.9) 44

54 where x 0 is the initial parameter values matrix. When a priori information are included (call x the a priori value and P the a priori covariance), we get x = x+ v (3.10) again where v are the pre-fit (a priori) residuals. Next, the equation is normalized with the square root of P, S, for which we define S by R = S 1 P = ( R T R ) 1 (3.11) such that Equation 3.10 becomes and substituting z Rx = Rx + Rv (3.12) Rx and v Rv, a new observation equation is included as z = Rx + v (3.13) which can be added to Equation 3.4 to yield a set of equations z R z A x v = + v. (3.14) Tropospheric Delay Estimation The tropospheric delay is estimated by GIPSY-OASIS as a stochastic parameter using the Kalman-Bucy filter, which combines batch and sequential filter methods [Kalman and Bucy, 1961]. The filtering processes the measurements forward through time, accumulates the solution, then computes smoothing coefficients for each batch. The parameters are assumed to be piecewise constant within the 45

55 batch, then the time is updated and a new batch is processed. The user can input the length of the batches for estimation. For this processing of PWV, data were processed in 600 second batches, meaning a value for zenith delay was estimated every 600 seconds. The sequential filter used is a numerically stable and computationally fast Square Root Information Filter, which is needed for the quantity of data processed in the near real time PWV calculations [Gregorius, 1996]. The dynamic system is linearized by Taylor expansion and the parameters in GIPSY-OASIS are split into three categories: satellite states, stochastic parameters, and constant bias parameters. The state vector, X, (x from above) is defined as [GIPSY, 1999] X x = x x sat sto bia (3.15) where r x sat contains the state of the satellite, r x sto contains the stochastic parameters (including tropospheric delay) to be estimated, and the vector constant bias parameters that corrupt the satellite state. r x bia contains the r X includes the individual state and process noise vectors and the common parameters between satellites, such as station coordinates. The linearized state propagation (from time t k-1 to t k ) and observation state equations, with process noise added is the system can be represented by [GIPSY, 1999; Gregorius, 1996]. 46

56 x x x sat sto bia ( tk ) ( tk ) ( t ) k ( ) ( ) ( ) d s b Φsat tk, tk sat tk tk sat tk tk 1 Φ, 1 Φ, 1 x = 0 Φsto( tk, tk 1) 0 x 0 0 I x sat sto bia ( tk 1) ( tk 1) ( t ) k 1 0 wt k 1 (3.16) 0 + ( ) where Φ d sat(t k,t k-1 ) is the deterministic portion of the satellite-state update, Φ s sat (t k,t k-1 ) is the stochastic portion of the satellite-state update, Φ b sat(t k,t k-1 ) is the constant bias parameter portion of the satellite-state update, Φ sto (t k,t k-1 ) is the stochastic parameters transition matrix, and I is the identity matrix, as the bias parameters are constants. w(t k-1 ) is a Gauss-Markov random walk noise vector with zero mean. The GPS data are processed to estimate the stochastic parameter of correction to an initial guess of zenith tropospheric delay. The a priori guess for zenith tropospheric delay has both a wet component and hydrostatic component. The hydrostatic guess is [GIPSY, 1999] * e * h meters (3.17) which is dependent solely upon the station height above the geoid, as higher elevation sites have less atmosphere through which the signal travels (meaning less hydrostatic delay). The wet component guess is 0.10 meters and is a constant. These are just initial guesses for the GIPSY-OASIS filter and need not be extremely accurate. For example, the station in Wichita Falls, TX is about m above the geoid. The a priori estimate of dry delay would be m based upon Equation 47

57 3.17, adjusted to m to include the wet component guess. The station position is held fixed while the correction to the a priori (2.328 m) tropospheric delay is then estimated through time, in 600 second (10 minute) increments. The clock drift of each receiver clock must also be estimated. To estimate these drifts, the CORS station in Algonquin Park, Ontario, is included as the reference clock in the processing as it has a highly accurate hydrogen maser clock. By using a stable clock, the drift for the other clocks can accurately be estimated. Post-GIPSY-OASIS Processing First, the corrections to the initial guess of total zenith atmospheric delay are combined with the GIPSY-OASIS tropospheric zenith delay output for a corrected zenith troposphere delay estimate. Once the atmospheric data are gathered, any meteorological data point and tropospheric zenith delay data point within 100 seconds of one another are considered a sample point. The surface pressure value from the meteorological data is used to estimate hydrostatic zenith delay, which is subtracted off of the corrected tropospheric zenith delay. The remaining value is the wet tropospheric zenith delay. This is converted to zenith PWV using Equation See Appendix A for a sample calculation of PWV using pressure, temperature, and zenith delay. Several PWV values are gathered over each hour of interest and the PWV values are averaged over the hour to obtain a single value to include on the contour map. All PWV values that are estimated are included in the time series 48

58 graphs. The hourly value of zenith PWV for each site is input into the GMT software package and a map in JPEG format is produced detailing water vapor over the Texas region. Then, the PWV, surface pressure, and surface temperature are graphed in time series using MATLAB for placement on the Internet. 49

59

60 Chapter 4 - Water Vapor Results Automated computer routines were implemented to process all the available GPS sites once an hour, every hour of every day. For the purpose of data processing in this project, Greenwich Mean Time (GMT) is the time standard used. This eliminates any problems with time zone differences and daylight savings time and is also the method that the GPS networks reference their data with regard to day of year and GPS week. RINEX data from the non-csr GPS sites are available in hour long files about minutes after the hour. Once the data files are posted, the automatic script gathers all of the available meteorological and observation data. Any time the observation data are available, the site is included for processing regardless of the availability of the meteorological data. Predicted orbits for the GPS satellites are downloaded, then the data from the most recent three hours are processed. The GIPSY-OASIS filter seemed most stable when more than one hour was processed, but the data to be processed were limited to three hours to save computation time. Once GIPSY-OASIS has completed processing the data, the output from the most recent hour is converted from zenith delay to PWV. A time series of 24 hours of PWV for each site is constructed by taking 23 hours of previously converted PWV and adding the PWV data from the most recent hour to the end. A near real time PWV map and individual site 24 hour time series graphs are placed on the Internet at: 50

61 In addition to showing how near real time PWV measurement could be done with GPS, some selected data were post-processed to determine the accuracy of predicted orbits in the near real time application. A comparison of GPS orbit accuracy was done for February 26, 2000 in order to see how the PWV results are affected by predicted orbit inaccuracies. Near Real Time Results The contour maps and PWV time series are produced quickly and accurately. The data are automatically processed hourly, and accurate PWV estimations within one hour are produced with no human interaction required. Time Series of Maps Figure 4.1 is several hourly PWV maps for February 26, The data from this day is interesting because it can be seen how rapidly water vapor can change in time. February 26, 2000, began relatively moist but as a slight cold front pushed through the Texas region, noticeably dryer air was present by the end of the day. A significant drop in temperature (up to 9 C) was seen by the GPS sites that experienced the most significant PWV decrease (Figure 4.2). For these maps and time series presented here, predicted orbit files were used. Later in the chapter, the result of changing the type of orbit used will be discussed. 51

62 Figure Near Real Time Maps 52

63 Figure Near Real Time Maps (continued) 53