Seasat Altimeter Data Research Articles

Generation of DEMs over A Part of Antarctica Using Altimetry Data and their Implications

Recent advancements in remote sensing techniques have made it possible to monitor and understand the activities of polar ice sheets, which exert profound influence in controlling global climate. Techniques such as laser altimetry, radar altimetry, InSAR, GPS etc. have been used for generation of DEMs, calculation of ice‐sheet mass balance, retrieval of snow‐water equivalent and other snow/ice related studies. In the present study, DEMs were generated using SEASAT altimeter data over parts of Antarctica and the maximum height variations in the studied area have been observed as high as 3200 m. From the analysis of the surface slopes, an attempt was made to qualitatively estimate the magnitude and direction of the ice‐sheet movement vectors. Coupled with temporal data, both field and satellite derived, the results obtained can be used for modelling of ice‐sheet mass balance over Antarctica.

Ice sheet altimeter processing scheme

Abstract The analysis of altimeter data over non-ocean surfaces is complicated by the effects of topography and the dielectric properties of the surface. The philosophy behind the processing (for the U.K.-Earth Observation Data Centre) of altimeter data over ice sheets and shelves is explained and a description of the function and performance of the algorithms used is provided. The methods available for waveform retracking and slope correction, which represent the primary difference between ocean and land altimeter data analysis, are discussed in detail. Results from their operation with Seasat altimeter data and a simulated surface profile are provided to indicate their likely performance with ERS-1 data. The contents and structure of the ice sheet data product is described and its intended applications discussed. Future modifications and calibration/validation of the data are also considered.

Collinear and cross-over adjustment of Geosat ERM and Seasat altimeter data in the Mediterranean Sea

The computation of mean sea surface heights from a set of collinear Geosat ERM altimeter data tracks was carried out in a collinear adjustment, where 1 cy/rev cosine and sine coefficients for each track are estimated, so the differences between the collinear tracks are minimized. Then bias/tilt cross-over adjustments of stacked Geosat and Seasat altimetry were carried out. The problems with the free surface in the cross-over adjusted altimetric surface were treated using the absolute sea surface heights relative to the geoid model OSU89B. In a combined adjustment of the two altimeter data sets using cross-over and height informations simultaneously a RMS of the cross-overs of 0.080 m and a RMS of the sea surface heights relative to OSU89B of 0.611 m were obtained.

Deformation of the oceanic crust between the North American and South American Plates

Fracture zone trends and magnetic anomalies in the Atlantic Ocean indicate that the North American plate must have moved with respect to the South American plate during the opening of the Atlantic. A comparison of plate tectonic flow lines with fracture zones identified from Geosat and Seasat altimeter data suggests that the North American‐South American plate boundary migrated northward from die Guinea‐Demarara shear margin to the Vema Fracture Zone before chron 34 (84 Ma), to north of the Doldrums Fracture Zone before chron 22 (51.9 Ma), and to north of the Mercurius Fracture Zone between chron 32 (72.5 Ma) and chron 13 (35.5 Ma). The paleoridge offset through time identified from magnetic anomalies and the computed cumulative strike slip motion in the plate boundary area, indicate that the triple junction may have been located between the Mercurius and the Fifteen‐Twenty fracture zones after 67 Ma (chron 30). Plate reconstructions indicate a Late Cretaceous phase of transtension, followed by transpression in the Tertiary for the Tiburon/Barracuda Ridge area south of the Fifteen‐Twenty Fracture Zone. The ocean floor in this area is characterized by a series of ridges and troughs with large Bouguer gravity anomalies (up to ∼135 mGal). We use smoothing spline estimation to invert Bouguer anomalies for crustal layer structure. Our model results suggest that the Moho is uplifted 2–4 km over short wavelengths (∼70 km) at the Barracuda and Tiburon ridges and imply large anelastic strains. The severely thinned crust at the two ridges implies that crustal extension must have taken place before they were uplifted. We propose that the North‐South American plate boundary migrated to the latitude of the Tiburon Ridge, bounded by the Vema and Marathon fracture zones, before chron 34 (84 Ma). Post‐chron 34 crustal thinning during a transtensional tectonic regime may have been localized at preexisting structural weaknesses such as the Vema, Marathon, Mercurius, and Fifteen‐Twenty fracture zone troughs, but reaching the Fifteen‐Twenty Fracture Zone and future Barracuda Ridge area only after chron 32 (72.5 Ma). This interpretation concurs with our crustal structural model, which shows stronger crustal thinning underneath the Tiburon Ridge than at the Barracuda Ridge. Subsequent transpression may have continued along the existing zones of weakness in the Tertiary, creating the presently observed crustal deformation and uplift of the Moho, accompanied by anelastic failure of the crust. Middle‐Eocene‐Upper Oligocene turbidites on the slope of the Tiburon Ridge, now located 800 m above the abyssal plain, suggest that most of its uplift occurred at post‐Oligocene times. The unusually shallow Moho underneath the Tiburon and Barracuda ridges represents an unstable density distribution, which may indicate that compressive stresses are still present to maintain these anomalies, and that the North American‐South American plate boundary may still be located in this area.

Evidence of Time-dependent Sverdrup Circulation in the South Pacific from the Seasat Scatterometer and Altimeter

Abstract Seasat scatterometer and altimeter data are analyzed to investigate time-dependent Sverdrup dynamics in the Southern Ocean (40°S to 60°S) over seasonal time scales. Sverdrup dynamics are shown to be inadequate to describe the circulation in the South Atlantic and Indian oceans. The Sverdrup circulation in the South Pacific is reasonable north of 55°S. The changes in Sverdrup circulation from July to September 1978 indicate an eastward acceleration along 55°S and westward acceleration along 40°S, suggesting a southward shift in the subpolar eastward flow. Sea level in the South Pacific is estimated for July and September 1978 from scatterometer vector wind data based on Sverdrup dynamics assuming a flat-bottom ocean with barotropic flow. The changes in Sverdrup sea level are compared with the changes in sea level observed by the altimeter for the same time period. Both estimates indicate a rise in sea level along a zonal band centered at about 50°S. This sea level rise inferred from both the scatt...

A global mean sea surface based upon GEOS 3 and Seasat altimeter data

A mean sea surface relative to the International Union of Geodesy 1980 Geodetic Reference System reference ellipsoid has been derived from Seasat and GEOS 3 altimeter measurements. This surface, called MSS‐9012, has been computed on a grid of 1/8° resolution. Each elevation value was calculated by fitting all data within 111 km to a local biquadratic surface using Bayesian least squares. Individual data points were weighted inversely to the square of the distance to the grid location in the gridding process. The surface covers the global ocean between 70°N and 72°S. In the vicinity of sea ice the altimeter heights have been corrected for the on‐board tracker error that occurs over non‐Gaussian surfaces. Comparisons are made between MSS‐9012 and ocean bathymetry. The eastern extent of the Chain Fracture Zone in the Gulf of Guinea is more apparent in the altimetry than in the bathymetry data, as are many other features. The combination of data from the two satellites has successfully retrieved more information about the sea surface than was previously possible using only Seasat data.

An assessment of the capability of the satellite radar altimeter for measuring ice sheet topographic change

Abstract The monitoring of surface topography has frequently been cited as the most important application of the satellite radar altimeter over the ice sheets. The potential of the instrument in this respect is examined in detail using Seasat and Geosat altimeter data recorded over the Wilkes plateau in East Antarctica. The precision of the range measurements is optimized by the use of an improved retracking technique. However, although the r.m.s. precision of range measurements indicated at orbit crossovers, after orbit adjustment, is 20-30 cm, tilt and bias orbit adjustment techniques are shown to leave errors in the measurement of surface elevation change, with magnitudes of the order of tens of centimetres, depending on the location. Additional orbit error, which cannot be identified from crossover residuals, is almost certainly present in the difference measurements. Variable mispointing of the Geosat antenna is considered the most likely explanation for an apparent change in surface scattering prope...

Simultaneous Estimation of the Gravity Field and Sea Surface Topography From Satellite Altimeter Data By Least-Squares Collocation

SUMMARY The signal content of Seasat altimeter data is evaluated with respect to magnitude and wavelength. Based on this information covariance functions associated with the different signals/errors have been determined. the covariance function associated with the sea surface heights contains covariances associated with the geoid, the stationary sea surface topography, and the time-varying sea surface topography. These three components have been estimated from Seasat altimeter data in the Faeroe Islands region using least-squares collocation. In the solution error covariances associated with errors in the orbits, corrections for instrumental, atmospherical, and tidal effects, and sea state related bias are taken into account. the accuracies of the solutions are evaluated by computing error estimates and error correlations. A special effort has been made to evaluate the correlations between the estimated geoid and the other signals/errors. the results show that geoid undulations may be estimated with an accuracy of 0.13–0.16m. Approximately 50 per cent of the error variance has a long-wavelength signature, which is mainly correlated with errors in the estimation of the permanent sea surface topography. the short-wavelength part of the error is mainly correlated with errors due to liquid water in rain and clouds. Free air gravity anomalies may be estimated with an accuracy of 8.8–11.7 times 10-5 ms-2. This error has a short-wavelength signature which is mainly correlated with errors due to liquid water in rain and clouds. However, a comparison with gravity observations resulted in an agreement of 7.8 times 10-5 ms-2. Both the permanent and the time-varying sea surface topography may be estimated with accuracies of about 0.21 m.

Dynamic sea surface topography, gravity, and improved orbit accuracies from the direct evaluation of Seasat altimeter data

A gravitational model incorporating Seasat altimetry, surface gravimetry, and satellite tracking data has been determined in terms of global spherical harmonics complete to degree and order 50. This model, PGS‐3337, uses altimeter data as a dynamic observation of the satellite's height above the sea surface. A solution for the ocean's dynamic topography is recovered simultaneously with the orbit parameters, gravity, and ocean tidal terms. The recovered dynamic topography reveals the global long wavelength circulation of the oceans with a resolution of 2000 km and is very similar to the mean upper ocean dynamic height derived from historical ship observations. The PGS‐3337 geoid has an uncertainty of 60 cm rms globally but only 25 cm rms over the ocean because of the altimeter measurements. Seasat orbits determined in this solution have an estimated accuracy for the radial position of 20 cm rms. The difference between the altimeter observed sea height and the geoid plus dynamic topography model is 30 cm rms. Contained in these residuals are the sea height variability, as well as errors from the geoid, orbits, tidal models, and altimeter range measurement. This performance level is 2 to 3 times better than that achieved with previous Goddard gravitational models.

A preliminary estimate of geoid‐induced variations in repeat orbit satellite altimeter observations

Altimeter satellites are often maintained in a repeating orbit to facilitate the separation of sea height variations from the geoid. However, atmospheric drag and solar radiation pressure cause a satellite orbit to drift. For Geosat this drift causes the ground track to vary by ±1 km about the nominal repeat path. This misalignment leads to an error in the estimates of sea surface height variations because of the local slope in the geoid. We have estimated this error globally for the Geosat Exact Repeat Mission using a mean sea surface constructed from Geos 3 and Seasat altimeter data. Over most of the ocean the geoid gradient is small, and the repeat track misalignment leads to errors of only 1 to 2 cm. However, in the vicinity of trenches, continental shelves, islands, and seamounts, errors can exceed 20 cm. The estimated error is compared with direct estimates from Geosat altimetry, and a strong correlation is found in the vicinity of the Tonga and Aleutian trenches. This correlation increases as the orbit error is reduced because of the increased signal‐to‐noise ratio.

High‐resolution inversion for South Atlantic Plate kinematics using joint altimeter and magnetic anomaly data

We present an inversion for plate kinematics that solves for finite rotation parameters using fracture zone (FZ) and magnetic anomaly location data jointly. We define misfit functions that incorporate properties unique to each data type; in particular, the FZ misfit function does not depend upon alignment of conjugate FZ traces in the same way as magnetic lineations under the finite rotations. This property is useful for FZ locations, in which the signals on conjugate sides of the ridge may include systematic differences, or where data from one side of the ridge are sparse or missing. Formal error bounds estimated for the pole parameters show that the magnetic and FZ data are complementary in their information content. Error bounds computed for the joint inversion are substantially smaller than for either the FZ or magnetics data used separately, indicating that simultaneous use of the data in an inversion is crucial. We apply this method to Seasat altimeter data and magnetic anomaly picks in the South Atlantic. We solve for finite poles corresponding to magnetic anomalies 5, 6, 8, 13, 21, 22, 25, 30, 33, 33r, and 34; these define a smooth path over the past 84 m.y. indicating that the plate motions have not been as erratic as found previously.

On the source of cross‐grain lineations in the central Pacific gravity field

Subtle lineations in the marine gravity field of the central Pacific derived from Seasat altimeter data were observed by Haxby and Weissel (1986). They suggested that these “cross‐grain” lineations were evidence of small‐scale convection beneath the Pacific plate. We have examined these features by comparing multiple, collinear gravity and bathymetry profiles in the Fourier transform domain. Our nine gravity profiles were each obtained by stacking (averaging) three or more individual, repeat Geosat/ERM altimeter passes. Prior to stacking, the individual Geosat passes were fit to a cubic spline and then differentiated along track to produce along‐track deflections of the vertical (or horizontal gravity). Corresponding bathymetric profiles were produced by projecting, onto Geosat ground tracks, bathymetric observations from six R/V Thomas Washington legs and three R/V Conrad legs that virtually coincide with these Geosat tracks. After Fourier transforming the resulting gravity and bathymetry profiles, we estimate admittances of gravity to bathymetry. These admittances are generally low; they also tend to be negative at very short wavelengths (λ<50 km). They are consistent with models of flexural isostatic compensation by a very thin lithosphere (approximately 2 km). They are not consistent with models of dynamic compensation. We suggest, therefore, that either (1) these cross‐grain lineations began to form very near the East Pacific Rise or (2) they formed on older, anomalously weak lithosphere. We also suggest that the gravity lineations result primarily from loads beneath the seafloor in combination with, secondarily, loads on the seafloor. Depths of these subseafloor loads appear not to exceed significantly typical Moho depths.

Seasat altimetry and the South Atlantic Geoid: 2. Short‐wavelength undulations

This paper is a discussion of the short‐wavelength (25–100 km) undulations of the geoid recovered from Seasat altimeter data in the South Atlantic. These undulations are known to be highly correlated to seafloor topography, and they considerably improve our knowledge about global bathymetry of the South Atlantic, which remains poorly surveyed. The orientation of fracture zones (FZ) with respect to the Seasat profiles ensures an efficient recovery of the FZ pattern in the younger (<65 Ma) parts of the South Atlantic between 20°N and 50°S. We used 22 well‐marked FZs regularly distributed between 12°N and 47°S to compute Eulerian poles describing the finite relative movement between Africa and South America. From the present back to 35 Ma, FZ trends south of the equator are well accounted for with a single rotation, and standard statistical tests do not indicate a need for distinct and successive rotations. However, these tests indicate an improvement of the fit when distinct poles are adjusted to separate subsets of our 22 FZs (either FZs north and south of the equator, or FZs north and south of Tristan da Cunha). This points out the possibility of the existence of either “corridors” in which slight relative movements occur, or diffuse elastic deformation over the entire South Atlantic, although this is really a second‐order effect. We also present and discuss a map of the roughness of the geoid (for the 25‐ to 110‐km wave band). Strong disagreements between the roughness map and the GEBCO maps exist in regions of sparse ship track coverage; for example, the Rio Grande Rise has an associated roughness feature which appears elongated and more symmetric with respect to the Walvis Ridge than what is displayed on the GEBCO maps. The roughness map also clearly documents a long‐wavelength (∼400 km) segmentation of the Mid‐Atlantic Ridge between the equator and 35°S.

Sea height wave form in equatorial waves and its interpretation

In a previous paper a variation in sea slope of 1.6±0.6 cm per degree of latitude between 2°N and 4°N in Seasat altimeter data was associated with the passage of two temperature crests between 113°W and 130°W in the equatorial Pacific. This work has been extended to include variations in sea height between 1.5°S and 9°N with arbitrary phase in the wave. A mean wave pattern was found with maximum amplitude of 5 cm near 6°N. When the analysis was repeated for a range of wave periods, two preferred values are selected by minimum residuals. A period of 38.6±2.2 days corresponds with the passage of two observed temperature crests. A period of 22.2±0.9 days includes both these two crests and a possible intermediate crest of smaller amplitude. Fluctuating velocities in geostrophic equilibrium with the mean wave height are combined with a mean zonal flow to derive streamlines in a coordinate system moving westward with the phase velocity of the mean wave. One streamline shows the trochoidal form of the temperature front at about the appropriate latitude. Velocity field dependent estimates of the latitude of the crest and the angle of the crest are made. Flow immediately north of this streamline exhibits clockwise gyres near each trough. I suggest that this is the basic pattern of the observed form and motions in the waves. Also, selected streamlines are used to compute idealized drifter trajectories and compared with observations.

An experiment to invert Seasat altimetry for the Mediterranean and Black Sea mean surfaces

SUMMARY The high accuracy mapping of the mean sea surface (MSS) from satellite altimetry requires efficiency, flexibility and mathematical transparency from the data analysis. This paper argues that so does the least squares inverse method. Prior to the data inversion, models of covariance functions are constructed for the expected residual mean sea surface relative to a starting map and for the various error sources in the data including the radial orbit errors, instrument noise and sea height variability. The unique optimum solution is then restored from the data in a single step analysis, with formal error estimates and, possibly, local a posteriori covariances (‘resolving kernels’). Numerical experiments are performed to obtain the Mediterranean and Black Sea mean surfaces by an inversion of the Seasat altimeter data. In our present computational environment, the constraint raised by the cost of a run leads us to degrade the rigorous data analysis strategy. Owing to these limitations, and to the assumed covariance models and data coverage, the MSS is mapped with an accuracy of -12121x1 for wavelengths greater than 335 km. The supplementary error related to shorter scales is -70 cm. The inverse MSS solution is compared with another model computed at the Bureau Gravimetrique International in a classical way (crossing arc analysis plus data filtering) from Geos3 and Seasat. Then, neglecting the dynamic heights of the sea circulation, we invert the Seasat data set to map the equivalent free air gravity anomalies. The cross-covariance used is consistently derived from the a priori power spectrum of the MSS. The gravity anomalies are recovered with an accuracy of 1 mGal. Moreover, a large error of -25 mGal is expected from the smoothing of the shorter scales. An external comparison made with the gravimetric map of Torge, Weber & Wenzel (1983) broadly agrees with our formal error estimates. Several prospective specifications concerning the covariance models and the numerical procedure are drawn from these preliminary experiments and comparisons.

A plate-kinematic framework for models of Caribbean evolution

We define the former relative positions and motions of the plates whose motions have controlled the geological evolution of the Caribbean region. Newly determined poles of rotation defining the approximate spreading histories of the central North and the South Atlantic oceans are given. For the late Jurassic-Early Cretaceous anomaly sequence of the central North Atlantic, we have used previously published ∗ ∗ Klitgord and Schouten (1987). definitions of fracture-zone traces and magnetic anomaly picks, redetermining the pole positions and angular rotations for various isochrons on an Evans and Sutherland interactive graphics system. For magnetic anomalies younger than the Cretaceous Quiet Period in both oceans, we (1) used Seasat altimeter data to help define fracture-zone traces, and (2) identified and used marine magnetic anomalies to determine the positions of spreading isochrons along the flowlines indicated by the fracture zones. By the finite difference method, the relative paleopositions and the relative motion history between North and South America were computed. This analysis defines the size and shape (and the rate at which the size and shape changed) of the interplate region between North and South America since the Middle Jurassic. Thus, a plate-kinematic framework is provided for the larger plates pertaining to the Caribbean region, in which can be derived more detailed scenarios for Gulf of Mexico and Caribbean evolution. North and South America diverged to approximately their present relative positions from Late Triassic? to Early Campanian (about 84 m.y. ago) time. This is the period during which the Gulf of Mexico and a Proto-Caribbean seaway were formed. Since the Campanian, only minor relative motion has occurred; from Early Campanian through to Middle Eocene times. South America diverged only another 200 km, and since the Middle Eocene, minor N-S convergence has occurred. These very minor post-Early Campanian motions have probably been accommodated by imperfect shear and compression along the Atlantic fracture zones to the east of the Lesser Antilles, and along the northern and southern borders of the Caribbean Plate. Accordingly, it is suggested that from Campanian time to the present, the relative motions between the North and South American plates have had only minor effects on the structural development of the Caribbean region. Primarily using the data of Engebretson et al. ∗∗ ∗∗ Engebretson (1982); Engebretson et al. (1985). , the convergence history of Pacific plates with North America was calculated for two points near the western Caribbean. By completing finite difference solutions, the convergence history of the Pacific plates with the Caribbean and South American plates can be approximated. The direction and rate of convergence of the Pacific plates with the Americas may have controlled the style of subduction and possible microplate migration along the North American, South American and western Caribbean boundaries that define the eastern Pacific plate margin.

Marine gravity

The U.S. Navy satellite, GEOSAT (Figure 1) is third in the series of microwave altimeter satellites which make, or made, precise, direct observations of the marine geoid. GEOSAT, launched March 1985, is active today. Its two predecessors are NASA's Geos‐3 mission which operated from 1975 through 1978 and NASA's SEASAT mission which functioned only during the summer of 1978. Each of the three has provided highly significant, abundant, new information about the gravity field of the oceans. As such, these missions have begun a revolution in marine geodesy and geophysics. One exemplary result of this ongoing revolution is the global map of marine gravity constructed from SEASAT altimeter data by Haxby [1987]. In fact, members of the marine geophysical community were, and, in some cases, still are, largely unaware of the spate of gravity field information coming from these satellites. Our purpose here is to help assure that this same community is aware of the very major increase in our knowledge of the marine gravity field which will come from GEOSAT, and that this increase will come on top of the gains made from SEASAT and Geos‐3!

PLATE KINEMATICS OF THE SOUTH ATLANTIC: CHRON C34 TO PRESENT

A high‐resolution seafloor spreading history of the South Atlantic since chron C34 is constrained by a combination of Seasat altimeter data and underway marine geophysical data. A set of 45 finite rotation poles defines the relative position of Africa and South America at roughly 2‐m.y. intervals. A set of 12 stage poles constrain the relative motion of these two plates at 5‐ to 10‐m.y. intervals. The position of the stage poles continuously migrates, reflecting the continuously changing azimuths of the fracture zones. Major changes in spreading direction are observed in the Late Cretaceous and early Cenozoic as the fracture zones sweep out broad S‐shaped curves similar to the pattern seen on the Kane fracture zone in the central Atlantic. Small offset fracture zones were found to be the most accurate recorders of changes in plate motion; large offset fracture zones, such as the Agulhas‐Falkland fracture zone, were the least reliable recorders. At 30°S, spreading rates decrease throughout the Late Cretaceous from a high of 75 mm/yr at the end of chron C34 to a low of 30 mm/yr around chron C27. A period of slow spreading between chron C30 and chron C20 corresponds to a zone of fracture zone proliferation, an increase in the amplitude of geoid anomalies over fracture zones, greater relief on topographic profiles, and locally, evidence of intraplate crustal deformation. Spreading rates increase at chron C20 to about 50 mm/yr and then gradually decrease during the late Paleogene and Neogene. A comparison of synthetic fracture zones based on the South Atlantic stage poles to the observed trends of fracture zones in the equatorial Atlantic indicates that the Vema and Marathon fracture zones were generated by South Atlantic spreading, as opposed to central Atlantic spreading, at least as far back as 35 m.y. ago and possibly 50 m.y. ago.

Circulation from a joint gravity field solution determination of the general ocean

With the development of satellite altimetry, it is possible to infer the geostrophic velocity of the surface ocean currents, if the geoid and the position of the satellite are known accurately. Errors in current geoid models and orbit computations, both due primarily to errors in the Earth's gravity field model, have limited the use of altimeter data for this purpose. The objective of this investigation is to demonstrate that altimeter data can be used in a joint solution to simultaneously estimate the quasi‐stationary sea surface topography, ζ, and the model for the gravity field. Satellite tracking data from twelve satellites were used along with Seasat altimeter data for the solution. The estimated model of ζ compares well at long wavelengths with the hydrographic model of ζ. Covariance analysis indicates that the geoid is separable from ζ up to degree 9, at which point geoid error is comparable to the signal of ζ.

An investigation of small‐offset fracture zone geoid waveforms

Approximately 1,500 geoid cross sections across 15 small‐offset South Atlantic fracture zones (FZ's) are compiled from Seasat altimeter data and organized according to crustal age; these profiles provide a basis for the comparison of the different FZ's, and the evolution of each over geological time. I use an empirical orthogonal function decompostion to investigate the dependence of profile shape and amplitude upon crustal age. The geoid cross sections are found to be coherent in form down the length of each FZ, and possess amplitudes that are inversely related to the relative spreading rate at the time of formation. This observation is consistent with a simple model in which the active portion of a fracture zone (the transform fault) remains a fixed spatial length, yielding a variable age offset across the FZ.