OCEAN SURFACE TOPOGRAPHY 455 motion of the ocean has a wide range of spatial and OCEAN SURFACE TOPOGRAPHY temporal scales. We all have the experience of watching ocean surface and being awed by the ever-changing Lee-Lueng Fu waves and their breaking into turbulence and white caps. Jet Propulsion Laboratory, California Institute of In order to measure the velocity of an ocean current, we Technology, Pasadena, CA, USA must average out these wave effects. At longer periods, there are ocean tides. If the timescales of our interests Definition are longer than tides, we must also average out the The deviation of the height of the ocean surface from effects of tides. Fortunately, there is a dynamic property the geoid is known as the ocean surface topography. of large-scale ocean currents called the geostrophic bal- The geoid is a surface on which the Earth’s gravity field ance. This balance occurs when the Rossby number, is uniform. The ocean surface topography is caused by defined as U/fL, is much smaller than unity. In the nota- ocean waves, tides, currents, and the loading of atmo- tion, U is the speed of the current, L is the spatial scale, spheric pressure. The main application of ocean surface and f is the Coriolis parameter defined as f ¼ 2O sinj, topography is for the determination of large-scale ocean where O is the Earth’s rotation rate (7.292 Â 10À5 rad/s) circulation. and j is the latitude. For example, if U ¼ 50 cm/s at 45 latitude, geostrophic balance occurs when L » 5 km. Introduction Then the geostrophic velocity of the current at ocean sur- The determination of global ocean circulation has been face can be computed from the pressure at ocean surface a challenging goal of physical oceanographers. The fluid as follows: Satellite Orbit Instrument Corrections • tracker bias • waveform sampler gain calibration biases • antenna gain pattern • AGC attenuation • Doppler shift Atmospheric Refraction • range acceleration Corrections • oscillator drift • dry gases R • pointing angle/sea state • water vapor • ionospheric electrons H External Geophysical Adjustments • geoid height hg Sea-State Bias • ocean tidal height hT • atmospheric pressure loading h Corrections a • EM bias • skewness bias hd=h-hg-hT-ha h=H-R Sea Surface Reference Ellipsoid Bottom Topography Ocean Surface Topography, Figure 1 Schematic illustration of the measurement system of satellite altimetry (From Chelton et al., 2001). 456 OCEAN SURFACE TOPOGRAPHY 80′N 40′N 0′ 80′S 80′S 160′W 120′W80′W40′W0′ 40′E80′E120′E 160′E −80 −60 −40 −200 20406080100 120 140 160 180 200 220 240 260 cm Ocean Surface Topography, Figure 2 OST derived from a combined analysis of satellite altimeter data, surface drifter data, and a geoid model (From Rio and Hernandez, 2004). @ the Earth’s surface can be computed from the gradient of ¼ 1 p fv r @ (1) the atmospheric surface pressure; similarly, the speed x and direction of large-scale ocean surface currents can be @ computed from the gradient of OST as shown by ¼1 p fu r @ (2) Equations 1 and 2. OST has been traditionally estimated y from the density field of the ocean as follows: where p is the pressure, r is the density of sea water, and 0 1 Z0 Z0 u and v are the zonal and meridional velocity components, @r @r ¼1 @ 0 þ 0 A respectively. The large-scale ocean currents are also in s r @ T dz @ S dz (3) hydrostatic balance, namely, p ¼ g , where is the 0 T S Àh Àh elevation of the ocean surface topography (denoted by OST hereafter), defined as the deviation of the ocean where T’ and S’ are the temperature and salinity deviations surface from the geoid, and g is the Earth’s gravity from their mean values, and r and ro are the density and acceleration. The geoid is defined as the ocean surface its depth average, respectively, and h is the depth of the on which the Earth’s gravity field is uniform. In the ocean. This quantity, s, has been traditionally referred absence of any motions, the ocean surface would be to as the steric sea level, which is an approximation of conformed to the geoid. OST. In most places, the steric sea level is predominantly The role of OST for ocean currents is thus equivalent to determined by temperature, and therefore is a good the role of atmospheric surface pressure for winds. indicator of the heat content of the water column of the The speed and direction of large-scale wind blowing at ocean. OST is also influenced by other factors such as OCEAN SURFACE TOPOGRAPHY 457 70 60 50 40 30 20 10 0 −10 −20 −30 −40 −50 −60 −70 0 30 60 90 120 150 180 210 240 270 300 330 360 −20 −15 −10 −5 0 5 101520 Ocean Surface Topography, Figure 3 A snapshot (May 30, 2007) of the temporal change of OST from its time-mean value. The unit is cm. wind, atmospheric pressure, and tides. However, our oceanography community. Oceanographers began to knowledge of OST has primarily been obtained through realize the potential of observing the global ocean circula- shipboard measurement of ocean temperature and salinity tion from OST determined from space. using Equation 3 until the recent development of satellite The challenges of determining OST from satellite altimetry (Fu and Cazenave, 2001). altimetry were the measurement accuracies. For example, an error of 1 cm in OST is capable of producing an error in the mass transport by ocean current of the magnitude Satellite altimetry of several million tons per second, which is a significant The concept of using a radar altimeter for measuring fraction of the transport of major ocean currents. The the height of sea surface was developed in the 1960s. technique of satellite altimetry is conceptually straightfor- The measurement of the round-trip travel time of a radar ward, but there are numerous sources for measurement pulse from a satellite to the surface of the ocean allows errors as illustrated in Figure 1. Corrections for these the determination of the distance between the satellite errors constitute the enterprise of precision altimetry and the ocean surface. If the location of the satellite in beginning with the TOPEX/Poseidon Mission. The reader orbit is also known in an Earth-fixed coordinate, then the is referred to Chelton et al. (2001) for a treatise of the height of the sea surface is determined in this coordinate details. Only the major components of the measurement and so is the OST if the knowledge of the geoid is system are briefly described in this entry. available as well. The first satellite altimeter was carried First,thefreeelectronsintheEarth’s ionosphere slow by Skylab launched in the early 1970s. The first satellite down the radar signals and have a net effect of more than altimeter with sufficient precision for detecting OST was 20 cm in error if not corrected. To correct for this error, radar onboard Seasat, which was launched in 1978 returning altimeter must transmit in two channels, for example, the Ku only about 100 days of data. However, the first image of band (13.6 GHz) and the C band (5.3 GHz) as the TOPEX/ the ocean reflecting the variability of OST caused by Poseidon altimeter. The signal delays are different for the ocean currents provided a revolutionary impact on the measurements made at the two channels, which are used 458 OCEAN SURFACE TOPOGRAPHY 65 55 45 35 25 15 5 −5 −15 −25 −35 −45 −55 −65 0306090 120 150 180 210 240 270 300 330 360 0 5 10 15 20 25 30 Ocean Surface Topography, Figure 4 The standard deviation of the temporal change of OST in unit of centimeters. to determine the total electron content and the signal delay. to continue the precision altimetry data record. In the Second, the water vapor in the Earth’s troposphere also mean time, the other satellite altimeters from the ERS, has the effect of delaying radar signals by more than ENVISAT, and Geosat Follow-On (GFO) missions have 40 cm in the tropics. The approach of the TOPEX/Poseidon contributed to the measurement of sea surface height Mission was to carry a three-frequency microwave and OST by providing enhanced spatial and temporal radiometer for making measurement of the water vapor con- resolutions. These missions have, however, benefited tent and the corresponding signal delay of the altimeter. from the cross-calibration with the precision missions for Third, the precise location of the satellite in orbit must be correcting for large-scale errors such as orbit errors determined. This requires onboard precision tracking and tidal effects. It has been recognized by the altimetry systems and well-maintained geodetic ground systems. For community that the continuation of precision missions example, the TOPEX/Poseidon Mission carries three (e.g., Jason) in combination with other missions independent orbit tracking systems: laser retroreflectors, (e.g., ENVISAT) is essential for the measurement of GPS receivers, and a Doppler system called DORIS. OST for a variety of applications. After Seasat, there were two satellite altimeters flown without the full suite of capabilities of error corrections: the US Geosat and the European Remote-Sensing Satellite Ocean general circulation (ERS). The first satellite altimeter mission that was dedi- The measurement of sea surface height from satellite altim- cated to optimal measurement of OST was the joint Amer- etry is not sufficient for the determination of OST. The ican/French TOPEX/Poseidon Mission, launched in 1992. missing link is the geoid. Direct measurement of the Earth’s Aside from the complete measurement system, the 66 gravity field for geoid determination is limited to orbit inclination was chosen for the determination of a resolution of 300 km at present (Jayne, 2000).