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Determination of Water Level and Tides Using Interferometric Observations of GPS Signals

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Determination of Water Level and Tides Using Interferometric Observations of GPS Signals 1118 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 Determination of Water Level and Tides Using Interferometric Observations of GPS Signals KENNETH D. ANDERSON Space and Naval Warfare Systems Center San Diego, San Diego, California (Manuscript received 4 May 1999, in ®nal form 17 September 1999) ABSTRACT A nonintrusive remote sensing method to measure water level is examined. It relies on the fact that water is a good re¯ector of radio frequency energy, thus, on a satellite-to-ground path when the satellite is near the horizon, a readily detectable interference pattern is formed as the satellite moves through its orbit. Provided that the elevation angles from the ground-based receiver to the satellite are small enough for good re¯ection but not so small that atmospheric refractive effects contribute, the shape of this interference pattern is strongly related to the geometry of propagation. Results from interferometric observations of Global Positioning System (GPS) satellite signals are presented for two sets of measurements where the receiving antenna varied from 7 to 10 m above the nominal water surface. These results, compared to in situ or nearby tide gauges, show that water level is measured to an accuracy of about 12 cm. A GPS receiver, a laptop computer, and a clear over- water path to the horizon are all that is needed to provide an affordable means for tracking water levels or ocean tides. 1. Introduction location of interest is far away from a tide gauge, errors in estimating the hydrology can signi®cantly affect the Along the shoreline of oceans, or seas, determining calculations relating the height of the water surface to the height of a land-based object above the water surface the vertical datum. This paper focuses on using inter- to an accuracy of less than a meter requires a leveling ferometry of GPS satellite radio frequency (RF) trans- survey from the water surface to the object in question. Tidal changes in water level are usually measured with missions to relate easily and accurately water level to a direct sensor such as a ¯oat or an acoustic transducer the height of a land-based object above the water sur- (acoustic transducers are included in the direct sensing face. category because they require a stilling well that pen- Lakes and rivers are often subject to the whims of etrates the water surface), and these sensors are leveled nature and man. Short-term effects, such as snowmelt to a vertical datum. In North America, these sensors, or or water release from dams upstream, make lake and tide gauges, are typically referenced to data such as the river levels unpredictable without knowledge of these North American Vertical Datum of 1988 (NAVD88) or effects. On the other hand, ocean tides are dominated the National Geodetic Vertical Datum of 1929 by gravitational effects. The motion of the earth and (NGVD29), which are commonly found on topographic moon about the sun are well known and readily pre- maps. Differential GPS surveys, which can establish dictable. With this astronomical information and secular relative (X, Y, Z) positions to subcentimeter accuracy, data from tide gauges along shorelines, techniques are have made leveling surveys much easier, but a Global routinely developed for predicting tides. Tide tables are Positioning System (GPS) relies on yet another datum, produced for hundreds of sites worldwide, and knowing the World Geodetic System 1984 (WGS-84). So for a the bathymetry makes it possible to estimate the tides GPS survey to determine a position with respect to a at sites having no local tide gauge. However, these tables water surface, WGS-84 must be related to NAVD88 or do not account for perturbations caused by storm surges NGVD29, which must be related to the water surface. or other changes to the circulation pattern that also affect This is practical near an existing tide gauge but, if the tides. For example, the 1998 El NinÄo raised the average water level in the Southern California offshore area by about 10 cm. Although tide predictions are generally good, direct or remote sensing techniques are necessary Corresponding author address: Kenneth D. Anderson, Propagation to accurately determine water level. Division, SPAWAR SYSCEN-SD D858, 49170 Propagation Path, San Diego, CA 92152-7385. Because they are in contact with the water, direct E-mail: [email protected] sensors are placed in sheltered coves or on piers to Unauthenticated | Downloaded 09/30/21 01:04 AM UTC AUGUST 2000 ANDERSON 1119 protect them from rough surf or storm damage. How- ever, in many cases, the water level outside of the pro- tected environment is of interest. In areas exposed to potential surf or storm damage, pressure sensors, which measure the height of a water column by sensing water pressure, are used. Because these sensors are placed underwater on the sea¯oor, they are not affected by storms overhead, but they are expensive to install and maintain. One dif®culty in using pressure sensors is establishing the relationship between what the pressure sensor measures (the height of the water column) and a reference point on dry land. Some form of direct mea- surement must be performed to relate the water surface to a land-based reference. Another dif®culty in using pressure sensors is the timeliness of the data. For near- real-time processing of bottom pressure recordings, the data must be transmitted to the surface, which exposes cables or buoy mounted equipment to wave or storm damage. For long-term recording, the pressure data col- FIG. 1. The basic concept of using interferometry to determine lection unit is placed on the bottom with the sensor but antenna height above water. As the source (a GPS satellite, for ex- this negates real-time processing and has the attendant ample) moves through its orbit, the pathlength difference between risk that any failure would not be noticed until the units the direct and re¯ected paths changes many wavelengths so the re- are recovered. ceiver sees an interference pattern. For moderately low elevation angles to the satellite, about 28 to 78 above the horizon, the spacing Sea surface height is sensed remotely by satellite- between the interference fringes is strongly related to the antenna borne radar altimeters; TOPEX and ERS-1/2 are cur- height above the water surface. rently active. These altimeters determine sea surface height by differencing the radar range to the sea surface end the computed height of the satellite above a ref- when plotted as a function of time or subsatellite range, erence ellipsoid. A comparison of TOPEX sea surface which is the range from the receiver to the nadir point heights to sea levels measured by in situ tide gauges of the satellite on the earth. For very low-elevation an- (Mitchum 1994) indicates rms differences of 5 to 10 gles from the receiver to the satellite (less than a few cm. Although there is excellent agreement between sat- degrees or so) atmospheric refractive effects, such as ellite observations and sea level, the data are not avail- ducting, strongly in¯uence the spacing between peaks able in real time. For TOPEX, swath data are dumped (or nulls) in the interference pattern. However, at higher every 8 h, and the revisit time is 10 days. elevation angles (above a few degrees or so), refractive Interferometric techniques are widely used in optics effects are minimal, and the spacing between peaks in for spectroscopy and metrology and have been applied the interference pattern is almost entirely due to the at radio frequencies. R. K. Crane (1998, personal com- height of the antenna above the re¯ecting surface. munication), circa 1961, used RF interferometry on a Therefore, by making careful measurements and by ex- satellite-to-ground path for sensing water levels. Glaz- amining the shape of the interference pattern one can man (1981) proposed using ground-based RF transmit- deduce the height of the antenna above the surface, ters and receivers, where the path between them ex- which implies a practical remote sensing tide gauge. tended over water, for measuring water levels. Anderson GPS is dedicated to providing both precise time and (1982) used RF interferometry on a satellite-to-ground location information worldwide; its success in both mil- path to infer the vertical atmospheric refractive pro®le. itary and commercial sectors has been staggering. In the Recent work by Anderson (1994) strongly suggests that past 20 years GPS receivers have evolved from rack- interferometric measurements of GPS signals can be mounted equipment costing half a million dollars to used to directly determine the height of the antenna pocket-size receivers costing under a hundred dollars. above a water surface, that is, as a tide gauge. Figure Equipment volume has decreased by better than a factor 1 illustrates the concept. There are two paths for the of 1000 and the cost has decreased by a factor of at signal from the GPS satellite to a ground-based receiver least 5000 making GPS truly affordable to the average when there is a water surface between the receiver and person. Although delivery vehicles and personal auto- the horizon where the satellite rises or sets. One is the mobiles are now routinely equipped with GPS to assist direct path, or direct ray; the other is the re¯ected path, in navigating, other exciting bene®ts of the technology or the re¯ected ray. As the satellite moves along its orbit, are emerging. Particularly in the area of using GPS as the pathlength difference between the direct ray and the a remote sensing tool. For example, Hoeg et al. (1995), re¯ected ray changes many wavelengths.
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