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

1118 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17

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 overwater 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 protected 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 measurement 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 2Њ to 7Њ 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. So, at the re- Kursinski et al. (1996), and Rocken et al. (1997) ex- ceiver, the signal will appear as an interference pattern amine a low-earth-orbiter-based GPS receiver to extract

Unauthenticated | Downloaded 09/30/21 01:04 AM UTC 1120 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 atmospheric and ionospheric properties; Businger et al. (1996) examine the potential of ground-based GPS receivers in atmospheric monitoring; Garrison et al. (1998) report on the potential of GPS to determine sea surface roughness; Kavak et al. (1998) use a ground based GPS receiver to estimate surface permittivity; and Komjathy et al. (1999) use an airborne GPS receiver to extract sea surface wind speed. Using GPS as a remote sensor shows great potential. This paper concentrates on using GPS as a remote sensor of water levels and ocean tides. The following sections review the fundamentals of ray optics and develop a model of the received signal interference pattern. Tide heights derived from GPS FIG. 2. The path of a ray in a vertical plane through the source measurements are compared to directly measured tide assuming cylindrical symmetry. Here, ␤ is the local ray elevation heights, and errors, primarily from pattern recognition angle, ␳ is the earth-centered (EC) distance to a height z above the problems, are examined. Results to date indicate that earth's surface, ␴ is the slant range, and ␪ is the interior EC angle. the technique of determining water level from GPS mea- Subsatellite range, de®ned as the distance along the earth's surface surements has promise and is a workable solution for from the receiver to the nadir point of the satellite, is a␪. implementing a remote sensing tide gauge with a height sensing accuracy (1 ␴) of about 12 cm. sponding to the progression of the ray from p to p ϩ dp, and ␰ is shorthand notation for pn(p)/a. Rearranging 2. Methodology terms and integrating gives Determining the height of a water surface in relation dp ␪ ϭ C . (3) to a vertical datum using RF interferometry relies on ͵ p͙␰ 22Ϫ C modeling RF propagation through the atmosphere, modeling the interaction of the re¯ected signal with the water The ground or subsatellite range is simply a␪, which surface, and a method to compare the observations to is the distance from the receiver to the nadir point of the modeled data. Raytracing, developed in the 1700s the satellite as measured along the surface of the earth. for propagation of light through lenses or ®lters, is read- Following the same lines as the development of (3), the ily applied to RF propagation through a refractive me- geometric slant pathlength S and the optical pathlength dium such as the atmosphere and is quickly reviewed. O are written as Surface re¯ection from a water surface and refractive dp characteristics of the atmosphere are well known and S ϭ d␴ ϭ ␰ (4) 22 brie¯y described. Correlation, a well-known signal pro- ͵͵͙␰ Ϫ C cessing technique, is described as it applies to extracting height above the water surface from observations. O ϭ ͵ nd␴ a. Raytracing and propagation fundamentals ϭ ͵͵pn cos(␤) d␪ ϩ n sin(␤) dp. (5) Snell's law in a spherically symmetric medium can be expressed as Equations (3) and (4) are solved analytically when n(p) is expressed as linear segments but written in terms pn(p) cos(␤) ϭ C, (1) of 1/p (Gradshteyn and Ryzhik 1980). Errors introduced a by approximating a linear n segment using the reciprocal of p are discussed later, but for now, it is suf®cient to where p is the distance from the earth's center (EC) to say that these errors are negligible. The optical path- a height z above the earth's surface, a is the earth's radius length is readily found using simple algebraic combi- (6378.135 km), n(p) is the refractive index at height z, nations of ␪,S,and p. Above 50 km, de®ned as z , the ␤ is the local elevation angle of the ray, and C is the ␷ atmosphere is treated as a vacuum; so ␪,S,and O are ray characteristic, a constant (Freehafer 1951). The path easily found from geometry. of a ray in the meridian plane, assuming cylindrical Calculations for the direct ray are straightforward for symmetry, is illustrated in Fig. 2. From geometry a speci®ed ray elevation angle at the receiver. Calcu- dp Ϯ͙␰ 22Ϫ C lations for the re¯ected ray are more dif®cult because ϭ p , (2) the procedures involve an iteration scheme to ®nd the d␪ C re¯ected ray elevation angle such that ␪ is identical where d␪ is the earth's interior incremental arc corre- (within a tolerance of 1 part in 1013) on the two paths.

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Surface roughness is not a factor in using interferometry to determine the antenna height above water. In the capillary regime (water wavelengths less than about 1.7 cm) the effect of surface roughness is a reduction in the amplitude of the re¯ected component, suggesting that interferometry may be able to sense surface wind speed as well as height above the surface. For gravity waves (water wavelengths greater than about 1.7 cm), there is essentially no effect as the time average of height of these waves is zero. One of the serious shortcomings of raytracing is its inability to trace a ray at all elevation angles. For example, the pattern in Fig. 3 should continue out to subsatellite ranges greater than 8600 km, which corresponds to a ray elevation angle at the receiver of about FIG. 3. Propagation factors computed for a GPS satellite-to-ground Ϫ0.8Њ. Depending on the vertical refractive index pro-

path in four refractive environments. Signi®cant changes in the in- ®le, there is a cutoff elevation angle, ␤c (and a corre- terference pattern due to different refractive conditions begin to occur sponding cutoff incidence angle ␺c) below which ray- only when subsatellite range exceeds about 8200 km. tracing fails to yield a solution. In a normal atmosphere,

raytracing works down to where ␤c ഠ ␺c ഠ 0.1Њ, which The iteration normally uses a Newton technique. How- corresponds roughly to ␦ ഠ ¼ wavelength (Reed and ever, at the lowest elevation angles, a binary-tree search Russel 1964). has been more effective (Press et al. 1993). In addition, Although raytracing has its limitations, it is adequate assuming the re¯ecting surface is seawater and account- for the determination of water level. For incidence an- ing for polarization, the incidence angle of the re¯ected gles less than about 7Њ and circular polarization the mag- ray on the earth's surface, ␺, and the complex Fresnel nitude of R is greater than 0.4, which yields a useful re¯ection coef®cient, R ∠ ␽, must be computed (where interference pattern. For incidence angles much greater R is the magnitude and ␽ is the phase lag of the Fresnel than 7Њ, R approaches 0 and no interference pattern is re¯ection coef®cient; see Reed and Russel 1964). The observed. For incidence angles below about 2Њ, but well

total phase lag between the direct ray and the re¯ected above ␺c, the vertical refractive index pro®le begins to ray is de®ned as ␾ and the difference between the re- distort the interference pattern. So, the approximate use- ¯ected and direct optical pathlengths is de®ned as ␦. ful range of elevation angles is from 2Њ to 7Њ above the The total phase lag is the sum of the wavenumber times horizon. ␦ and the phase lag from surface re¯ection. The pattern In Fig. 3 there are eight interference fringes between propagation factor (Kerr 1951) F, assuming isotropic subsatellite ranges of 7700 to 8200 km, which roughly antennas and ignoring divergence, is correspond to the ␤s of interest. A good rule of thumb F ϭ [1 ϩ R21/2ϩ 2R cos(␾)] is that the number of interference fringes is linear with height, so for an antenna 5 m above the surface, we 1/2 2␲␦ expect about four fringes whereas, for an antenna 50 m ϭ 1 ϩ R2 ϩ 2R cos ϩ ␽ . (6) above the surface, we expect some 40 fringes. GPS ␭ []΂΃ satellites are in 12-h orbits, so the ground velocity is a Although GPS signals are right-hand circularly po- little less than 1 km sϪ1. With a GPS receiver at 50 m larized, F is computed using horizontal polarization be- and operating at a 1-s sample rate, there are some 13 cause the phase difference between the two propagation samples per fringe, which is about the minimum number factors (right-hand circular and horizontal) is insignif- for positive identi®cation. Therefore, using GPS as a icant for this analysis. (The magnitude of the re¯ection tide gauge, or water-level detector, is feasible for an- coef®cient changes, which changes the peak-to-null tenna heights between approximately 5 to about 50 m depth, but this change is not important as shown later.) above the water surface. Figure 3 shows the pattern propagation factors in deci- bels, equal to 20 log(F), computed for reception of the b. Refractivity GPS L1 frequency (1575.420 MHz) on a satellite-to- ground path in four refractive environments where the The radio frequency refractive index of air at the receiver is 10 m above the sea. The interference pat- earth's surface is very close to unity (typically about ternÐconsisting of peaks and nulls, or fringes, in FÐ 1.000 320), and it is convenient to express it as refrac- is clearly evident. More importantly, there is very little tivity, N, where N ϭ (n Ϫ 1) ϫ 106. It is also common difference in the interference pattern when the subsat- to express the vertical refractivity pro®le in the lowest ellite range is less than 8200 km, which suggests in- portions of the atmosphere as linear segments, or slabs sensitivity to the refractive conditions. of constant dN/dz, and assume spherical (cylindrical)

Unauthenticated | Downloaded 09/30/21 01:04 AM UTC 1122 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 symmetry. In this analysis the refractivity pro®le from the earth's surface to GPS satellite altitudes is modeled as three regions; linear, exponential, and constant (vacuum). The linear region extends from the surface to an altitude of 4.85 km, where the top of the linear region is de®ned as ze. The exponential region extends from ze to z␷ (50 km). The constant region (where the refractivity is zero) extends from z␷ to the GPS satellite altitude. Refractivity in the linear region may vary consider- ably, both temporally and spatially (Hitney et al. 1985). However, as demonstrated earlier, the effects are minimal for subsatellite ranges between 7700 and 8200 km. For the tide gauge analysis, the linear region is treated as a single layer such that the gradient of refractivity, dN/dz, is Ϫ27N kmϪ1. Bean and Dutton (1968) found that the refractivity N FIG. 4. The modeled refractivity pro®le, which approximates linear in the region from 9 to 50 km above North America segments of refractivity in terms of 1/␳, and the percent difference behaves as from the ``exact'' pro®le. The worst-case difference is less than 1% and occurs at a height where the refractivity is very nearly zero, N ϭ 105 exp[Ϫ0.1424(z Ϫ 9)], (7) which corresponds to propagation through a vacuum. where z is expressed in kilometers. Experience with refractive measurements along the coast of Southern Cal- c. Errors modeling N in terms of 1/p ifornia has shown that (7) is a reasonably good ®t for Figure 4 shows the modeled refractivity pro®le used heights down to 4.85 km. [As (7) is extended down- in this analysis. The linear region, extending from the wards to z ϭ 4.85 km, the gradient approaches that surface to 4.85 km, is a single slab of constant refrac- expected in an adiabatic atmosphere, about Ϫ27N tivity gradient where dN/dz ϭϪ27N kmϪ1. Above the kmϪ1.] The exponential region refractive pro®le is lin- linear region is the exponential region where refractivity earized into 60 segments (spaced logarithmically) to fa- is computed from Bean and Dutton's model (7). Dots cilitate the ray optics calculations. on the solid curve show where the pro®le is partitioned Implicit in (7) is the fact that the refractivity pro®le into segments. In the linear region, simple calculus is nearly zero for z Ͼ z␷ (n ϭ 1.000 000 306 at z ϭ z␷ ); shows that the maximum difference between computing therefore, the atmosphere above z␷ (50 km) is safely N in linear terms and in terms of 1/p is found at p ϭ 1/2 treated as a vacuum. Refractivity in the linear region is (p1p 2) where p1 is the EC distance to the bottom of forced to terminate at N(ze) ϭ 189.6. This affords an the slab and p 2 is the EC distance to the top of the slab. opportunity to precompute ␪,S,and O for a wide range For each of the 60 slabs in the exponential region, the of ray elevation angles at ze and to interpolate these maximum difference between computing N from (7) and results for fast raytracing above ze. in terms of 1/p is found numerically. The dashed line Returning to Fig. 3, F is calculated for four refrac- in Fig. 4 shows the maximum differences expressed as tivity pro®les, where each pro®le extends from the sur- a percentage. There is no appreciable difference so er- face to the satellite. Three of these pro®les are single rors in modeling N in terms of 1/p are insigni®cant. slabs in the linear region where dN/dz takes on values of Ϫ19, Ϫ27, and Ϫ35 N kmϪ1, which covers a broad range of realistic refractivity pro®les. The fourth pro®le d. Extracting antenna height from observations consists of three slabs in the linear region forming a Figure 5 illustrates the propagation factor surface 200-m-thick surface-based duct (Hitney et al. 1985, is computed for antenna heights from 5 to 30 m above the an excellent review of ducting). For subsatellite ranges water and for subsatellite ranges from 7700 to about less than about 8200 km, there is almost no difference 8500 km. Here F was arbitrarily limited to a minimum between Fs computed for these four pro®les, which val- of Ϫ5 dB for convenience in viewing. Contours of F, idates the claim that the received signal pattern is in- projected onto the X±Y plane, show its sensitivity to sensitive to the refractivity pro®le at ␤s greater than a antenna height. few degrees. For ranges greater than about 8200 km, Interferometric observations of real GPS signals, dis- which corresponds to receiver ␤s less than 2.5Њ, refrac- cussed in later sections, contain noise that arises from tivity pro®les clearly affect F. This implies that, with several sources. Wind ruf¯ing of the re¯ecting surface extensions to overcome the raytracing limitations, in- scatters the re¯ected ray, causing some slight variations terferometry can be used to infer the refractive pro®le in R, hence F, and is the major source of noise for and is the subject of another paper. determining height (but this noise might be used with

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FIG. 5. The propagation factor F computed using the environment speci®ed by Fig. 4 for a GPS satellite-to-ground path where the antenna is positioned 5±30 m above the water surface. Even a coarse examination of the contour plot shows that the interference pattern, or spacing between fringes, for differing antenna heights is unique, which implies that observations of the interference pattern are a reliable means to infer the antenna height.

FIG. 6. The location of the Scripps Pier test site is designated by SIO. It is located at the Scripps Institution of Oceanography, La Jolla, other techniques to estimate both R and surface wind CA. The azimuthal radials indicate where selected GPS satellites rise speed). Spatial and temporal variations in the refractiv- or set on the ocean's horizon. ity, predominately in the ®rst few kilometers above the surface, also cause the rays to wander, but this is a minor e. GPS problem because the rays traverse a relatively short path. In the ionosphere, the direct and re¯ected rays travel on A quality GPS receiver updates its position and time nearly the same path, so the pathlength difference ␦ is at a 1-Hz rate or faster. And, at the same rate, the receiver not affected by variations in ionospheric refractivity. reports the output value of all locked correlators, which Another source of noise, which can be signi®cant, is is proportional to the pattern propagation factor F. Some additional signal re¯ections into the antenna from near- receivers report correlator output as signal-to-noise ratio by objects, or multipath, but proper antenna siting can (SNR). Other receivers report correlator output as reduce or eliminate these problems. counts. SNR is directly proportional to F, whereas Although there are numerous signal processing tech- counts must be calibrated in terms of F for useful com- niques for identi®cation, correlation is simple, robust, parisons. The receivers used in this analysis are Allen and relatively insensititive to absolute amplitude (e.g., Osborne and Associates (AOA) SNR-8000 Turbo- the depth of the nulls). It is implemented by Rouges, which report correlator output as SNR in volts per volt at a 1-Hz rate. n

xyij ͸iϭ0 3. Measurements rk ϭ , nn xy22 a. San Diego, California ͸͸ij Ίiϭ0 iϭ0 Many sets of interferometric GPS measurements have j ϭ i, i Ϯ 1, i Ϯ 2,...,i Ϯ k, (8) been made in the San Diego, California, area but the most important of these sets were made at Scripps Pier, where x is the debiased (zero mean) computed propa- which is located at the Scripps Institution of Ocean- gation factor for a speci®c antenna height sampled in ography (SIO). Figure 6 shows the geographic location 1-km steps of subsatellite range (normally from 7700 of the SIO site. Radial lines emanating from the SIO to 8200 km); y is the debiased and ®ltered measured site indicate the azimuthal direction where selected GPS signal strength, sampled in the same manner as x from satellites rise or set at the horizon. the subsatellite ranges calculated using either the GPS Observations at SIO were made in conjunction with satellite ephemerides or precise orbit data; and k is the an in situ tide gauge operated by the National Oceanic lag. The correlation coef®cient, rk, varies from Ϫ1to and Atmospheric Administration's National Ocean Ser- ϩ1, where rk ϭ 1 indicates a perfect positive correlation, vice's Center for Operational Oceanographic Products rk ϭϪ1 indicates a perfect negative correlation, and rk and Services (CO-OPS). Data from CO-OPS gauges are ϭ 0 indicates no correlation. sampled once every second, averaged, and reported ev-

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FIG. 7. Observed, ®ltered, and best-®t data for GPS-14 measure- FIG. 8. Time series comparison for SIO measurements. The light ments made at SIO (1925±1953 UTC 23 Sep 1998). The small gray gray solid curve is the mean water level, referred to the mean lower- crosses represent measurements of the C/A signal-to-noise ratio low water (MLLW) mark as reported by the Scripps Pier tide gauge. (SNR) as reported by an Allen Osborne Associates SNR-8000 This SIO gauge samples water level once every second and is reported TurboRouge receiver at a 1-Hz sample rate. The light gray solid curve as an average of the samples over a 6-min period. The vertical gray is a locally weighted and smoothed version of the C/A SNR, which lines represent the standard deviation of the samples about the mean is sampled at a 1-km subsatellite range spacing and correlated with (uncorrected near-real-time data reported by CO-OPS). Two GPS re- computed F factors (e.g., Fig. 5). The best-®t correlation to F is ceivers were used to record low elevation angle interference patterns indicated by the dark solid line and corresponds to an antenna height (e.g., Fig. 7) for GPS-22, Ϫ15, Ϫ14, Ϫ31, Ϫ16, Ϫ18, Ϫ19, and Ϫ27. of 10.30 m above the water surface. Results of converting these measurements to antenna height above water and scaling to the SIO tide gauge MLLW mark are shown by the crosses (for receiver #4) and the diamonds (for receiver #5). The standard error in the comparison of GPS measurements to the in situ ery 6 min. Near-real-time, 6-min data are available on- SIO tide gauge is less than 12 cm, which is less than the typical line at their Web site (http://www.co-ops.nos.noaa.gov). standard deviation of the tide gauge measurements. A vertical reference point, Bench Mark 2030P,is located at the western end of the pier and it is precisely 10.22 m above the station's current mean lower-low water smooth each point and the ®ltered data are shown as (MLLW) mark. This reference mark was used to level the solid line. The smoothed data were debiased and two GPS antennas with respect to the station's MLLW correlated with debiased F computed for antenna heights mark. One antenna was located 11.54 m above MLLW from 9 to 12 m in 1-cm steps. The maximum correlation and the second antenna was located 10 cm higher. A found by a search of this F surface was 0.7623 and high performance Dorn-Margollan Choke Ring antenna corresponds to an antenna 10.30 m above the surface. was used with one receiver, simply known as #4, and As receiver #4 was 11.54 m above MLLW, the tide, a standard AOA antenna was used with the other re- referenced to MLLW, was 1.24 m for this time period. ceiver, #5. Both antennas were tilted 20Њ from the zenith The propagation factor F, offset by 42 dB for better toward the west and had clear, unobstructed views of visualization for an antenna 10.30 m above the surface, eight GPS satellites rising or setting at the horizon. (The is shown as the dashed line in Fig. 7. The ®t is good tilt is needed to improve reception of the re¯ected ray, as it should be with such a high correlation coef®cient. essentially defeating the purpose of the choke ring.) Figure 8 shows a time series of results from mea- Figure 7 shows the results for one typical measure- surements made on 23 September 1998 (The measurement that was made at SIO on 23 September 1998. GPS ment using GPS-14, show in Fig. 7, is represented as a Satellite 14, or GPS-14, was ®rst detected rising on the cross with ``14'' below). The solid line is the tide (ref- ocean horizon at 1925 UTC (14 designates the PRN erenced to MLLW) reported by the SIO gauge and the code transmitted by this satellite). Its azimuth, geometric error bars indicate one standard deviation of its mea- elevation angle and subsatellite range relative to the surements in a 6-min period (near-real time data pro- pier-mounted antennas were 284Њ, Ϫ0.36Њ, and 8518 km, vided by CO-OPS is unveri®ed but should be accurate respectively. Some 28 min later, GPS-14 was 7.1Њ above to a few centimeters). Crosses and diamonds are the the horizon at a subsatellite range of 7700 km. Figure results calculated from observations by receivers #4 and 7 shows the measured C/A SNR for GPS-14 as light #5 respectively, which, in 10 out of 13 cases, fall within gray crosses. These measurements were smoothed by one standard deviation of SIO's gauge measurement. A applying a locally weighted regression-smoothing ®lter linear regression on this data yields a regression coef- (Cleveland and Devlin 1988) to an interpolated version ®cient of 0.930 and a standard deviation of 0.116 m. of C/A SNR, which was sampled at 1-km subsatellite These results show that the standard deviation found range spacing. A total of 11 samples were used to by comparing interferometric GPS tide gauge measure-

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FIG. 9. Wallops Island, VA, test site and radials to GPS satellites rising or setting on the horizon. The small cross to the west south west of the test site is the location of the Wallops Island tide gauge, FIG. 10. Comparison of GPS measurements made at Wallops Island, which was operational for two months in 1969. Measurements from VA, from 4 to 18 Mar 1998, to the scaled Wachapreague, VA, tide this tide gauge were compared to the currently active Wachapreague, gauge MLLW reference. The boxed crosses represent measurements VA, tide gauge, located some 30 km southwest of the site, to deter- made for GPS-18 that rose on the horizon at an azimuth of 198.5Њ. mine time and amplitude offsets for scaling Wachapreague tide gauge In the analysis of GPS-18 it was found that the sand beach, in the data to Wallops Island. direction of 198.5Њ, was uncovered when MLLW was less than about 0.4 m, so these outliers are some complicated measurement of antenna height above a wet to damp sand beach and should be ignored. Ex- cluding these three outliers of GPS-18, the standard deviation in ments to a highly calibrated, in situ, direct measuring comparing to the scaled Wachapreague data is 10.2 cm. tide gauge is less than 12 cm, which, in this case, is comparable to the standard deviation of the in situ gauge measurements. site and its location is shown as the gray cross in Fig. 9. From this analysis, it was determined that Wachap- b. Wallops Island, Virginia reague tides lead Wallops tides by 66 min and must be reduced in amplitude by a factor of 0.891. These cor- Measurements at Wallops Island, Virginia, were made rection factors needed to be veri®ed so a GPS receiving to support a radio frequency propagation experiment antenna was installed on top of a rock seawall about 50 conducted by the Naval Surface Warfare Center, Dahl- m south of the MPMS tower and about 7 m above the gren Division (NSWCDD) in March 1998. Figure 9 water. As in the previous measurements, the antenna shows the geographic location of the test site and the was tilted 20Њ from the zenith in the seaward direction. horizon radials where GPS satellites rise or set. The height difference between the GPS antenna and a NSWCDD's Microwave Propagation Measurement Sys- reference mark on the MPMS tower was determined to tem (MPMS) consists of four vertically spaced receiving be 4.13 m. (All MPMS receiving antenna heights were antennas and 10 vertically spaced transmitting antennas. referenced to this mark.) The transmitters step in frequency from 2 to 18 GHz Results from the interferometric GPS measurements and, by slightly offsetting the transmit frequency to each made between 4 and 18 March 1998 are shown in Fig. antenna, MPMS is capable of receiving signals on 40 10, which compares the Wachapreague tide gauge data, simultaneous propagation paths. The transmitters were translated to Wallops Island using the CO-OPS factors, mounted on a 10-m tower separated in height by 1 m to the GPS results translated to MLLW. For comparison, and the tower was installed on a boat. The receiving the dashed gray line indicates a perfect match between antennas were installed on a 30-m tower at the test site the two. Results from observations of GPS-18 are shown and were located at nominal heights of 5.8, 16.5, 21.0, as boxed-crosses, whereas results from all other GPS and 25.6 m above the sea. As the heights of the antennas satellites are shown as crosses. One striking feature is relative to the sea surface are critical for analysis of the outliers associated with GPS-18 when the Wach- propagation data, the local tides needed to be measured. apreague gauge indicates a tide of about 0.4 m (MLLW) The nearest active tide gauge is located at Wachap- or less. GPS-18 set on the horizon at an azimuth of reague, Virginia, which is about 30 km southwest of the 198.5Њ, which intercepts a large portion of beach when site. CO-OPS was asked to determine the time and the tide is out. When the tide is below about 0.4 m, height scale factors appropriate for translating data from GPS-18's signal is re¯ected from sand, not the water Wachapreague to Wallops Island. CO-OPS analyzed two surface. When the tide is higher than 0.4 m, GPS-18's months of data recorded by a tide gauge that was in- signal is re¯ected from a water surface. Excluding these stalled temporarily on Wallops Island in 1969. This three outliers, a linear regression indicates a best-®t gauge was located about 3 km west-southwest of the slope of 0.98 with a standard deviation of 10.2 cm. The

Unauthenticated | Downloaded 09/30/21 01:04 AM UTC 1126 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 conclusion is that the CO-OPS translation factors are ments a practical candidate for many water level or tide appropriate and reliable for converting Wachapreague gauge applications. tide gauge data to the sea offshore of Wallops Island. From the analysis presented there are several possi- bilities for future investigation. By observing the depth of the measured interference nulls (see Fig. 7) one can 4. Conclusions and discussions estimate the Fresnel re¯ection coef®cient R, and, ac- counting for grazing angle dependencies, therefore es- A nonradiating, nonintrusive, remote sensing method timate surface wind speed as R is related to the square to measure changes in water height is examined. Results of the surface wind speed (Ament 1953). Another pos- to date indicate that determining water level from in- sibility is using the very lowest elevation angle infor- terferometric GPS measurements has promise and is a mation to extract qualitative, and perhaps quantitative, workable solution for a remote sensing tide gauge. The data on the vertical distribution of refractivity and hu- method has a number of advantages. First, it can be midity in the lower troposphere. For example, Anderson easily set up and it can be operating in a short period (1998) shows that this technique readily discriminates of time. Second, the equipment package is small, about between surface-based ducting and normal refractive the size of two briefcases, easily transportable, and ame- conditions. However, as raytracing fails at these low nable to low-power operation. Third, there is no re- elevation angles, a more robust propagation model is quirement to install equipment in the water to measure needed to extract quantitative data. One candidate is the changes in water height. And ®nally, the method does so-called parabolic equation (PE) or paraxial approxi- not depend on established vertical data. mation to the wave equation (Barrios 1994), which has Interferometric measurements of GPS satellite signals advantages over raytracing in that it ef®ciently handles to determine height above water compared to a collo- range-dependent refractivity and terrain effects, which cated tide gauge (i.e., the SIO measurements) show a possibly could reduce some of the limitations presented standard deviation of less than 12 cm. Although the here. remote sensing update rate of water level is very much less than the update rate of the tide gauge (about 1 h Acknowledgments. This work is sponsored by Dr. compared to about 6 min), the size, ease of installation, Scott Sandgathe, Code 322MM, of the Of®ce of Naval and accuracy makes these interferometric measurements Research. attractive. The method has two basic limitations. First, the satellite transmission frequency sets both an upper and a REFERENCES lower limit to the antenna height above water. Using Ament, W. D., 1953: Toward a theory of re¯ection by a rough surface. GPS satellites, which transmit at 1575.42- and 1227.6- Proc. IRE, 41, 142±146. MHz, the effective maximum height is ഠ50 m above Anderson, K. D., 1982: Inference of refractivity pro®les by satellite- to-ground measurements. Radio Sci., 17 (3), 653±663. water and the effective minimum height is about ഠ5m. , 1994: Tropospheric refractivity pro®les inferred from low-el- However, reducing the satellite transmission frequency evation angle measurements of Global Positioning System (GPS) by a factor of 2 doubles both the upper and lower heights Signals. Advisory Group for Aerospace Research and Devel- and provides some ¯exibility in antenna positioning but opment, Note CP 567, 364 pp. [Available from 7 Rue Ancelle, 92200, Neuilly sur Seine, France.] at potentially great cost (i.e., sacri®cing the ease of use , 1998: Using the Global Positioning System to detect surface- associated with GPS). The second limitation is the re- based ducts. Proc. 1997 Battlespace Atmospherics Conf. 2±4 quirement for both a large water surface and a large Dec. 1997, K. D. Anderson and J. H. Richter, Eds., Space and azimuthal ®eld-of-view (AFOV). There must be a clear Naval Warfare Systems Center San Diego, 557±562. overwater path between the receiving antenna and the Barrios, A. E., 1994: A terrain parabolic equation model for propagation in the troposphere. IEEE Trans. Antennas Propag., 42 satellite when the satellite is between about 2Њ and 7Њ (1), 90±98. above the horizon. For an antenna z m above the water, Bean, B. R., and E. J. Dutton, 1968: Radio Meteorology. Dover, 435 the antenna must be positioned within ഠ5 z horizontally pp. from the edge of the water surface and the water surface Businger, S., and Coauthors, 1996: The Promise of GPS in Atmo- spheric Monitoring. Bull. Amer. Meteor. Soc., 77, 5±18. must extend out to at least ഠ30 z. The AFOV establishes Cleveland, W. S., and S. J. Devlin, 1988: Locally weighted Regres- how many satellites are seen by the receiver, which sion: An approach to regression analysis by local ®tting. J. Amer. determines the update rate of the surface height mea- Stat. Assoc., 83, 596±610. surements. Approximately 40 satellites per day are seen Freehafer, J. E., 1951: Geometrical optics. Propagation of Short Radio Waves, D. E. Kerr, Ed., McGraw-Hill, 41±58. for an east- or west-facing antenna with an AFOV of Garrison, J. L., S. J. Katzberg, and M. I. Hill, 1998: Effect of sea 180Њ. 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