R. Steven Nerem

Calibration of TOPEX/Poseidon and Jason Altimeter Data to Construct a Continuous Record of Mean Sea Level Change

Jason, the successor to the TOPEX/POSEIDON (T/P) mission, has been designed to continue seamlessly the decade-long altimetric sea level record initiated by T/P. Intersatellite calibration has determined the relative bias to an accuracy of 1.6 mm rms. Tide gauge calibration of the T/P record during its original mission shows a drift of −0.1 ± 0.4 mm/year. The tide gauge calibration of 20 months of nominal Jason data indicates a drift of −5.7 ± 1.0 mm/year, which may be attributable to errors in the orbit ephemeris and the Jason Microwave Radiometer. The analysis of T/P and Jason altimeter data over the past decade has resulted in a determination of global mean sea level change of +2.8 ± 0.4 mm/year.

Density and Winds in the Thermosphere Deduced from Accelerometer Data

With the emergence and increased use of highly accurate accelerometers for geodetic satellite missions, a new opportunity has arisen to study nonconservative forces acting on a number of satellites with high temporal resolution. As the number of these satellite missions increases, so does our ability to determine the spatial characteristics and time response of total density and winds in the thermosphere. This paper focuses on the derivation and methodology of inferring density and winds from along-track and cross-track accelerometer measurements, with themain goal of determining the feasibility of this data set. The principal sources of error such as solar radiation pressure, the unknown coefficients of drag and lift, instrument precision and biases, and unaccounted-for winds are discussed in the context of both density and winds. In the context of our treatment of errors, density errors are generally less than 15%, whereas wind-speed errors are more substantial. Finally, comparisons of results to existing empirical models (i.e., horizontal wind model 93) and to self-consistent numerical models (i.e., thermosphere–ionosphere electrodynamic general circulation model) are provided. Comparisons of results to ion drift velocities (as measured by Defense Meteorological Satellite Program) are also provided.

Distributed Deformation across the Rio Grande Rift, Great Plains, and Colorado Plateau

We use continuous measurements of GPS sites from across the Rio Grande Rift, Great Plains, and Colorado Plateau to estimate present-day surface velocities and strain rates. Velocity gradients from five east-west profiles suggest an average of ∼1.2 nanostrains/yr east-west extensional strain rate across these three physiographic provinces. The extensional deformation is not concentrated in a narrow zone centered on the Rio Grande Rift but rather is distributed broadly from the western edge of the Colorado Plateau well into the western Great Plains. This unexpected pattern of broadly distributed deformation at the surface has important implications for our understanding of how low strain-rate deformation within continental interiors is accommodated.

Sea-Level Rise by 2100

In his News and Analysis piece reporting on the newly released fifth assessment report (AR5) by Working Group I (WGI) of the Intergovernmental Panel on Climate Change (IPCC) (“A Stronger IPCC Report,” 4 October, p. [23][1]), R. A. Kerr highlights three fundamental conclusions about climate change that were assessed with equal or greater confidence than in previous IPCC reports. He also points to three “contentious points” on which he states that the AR5 “took a moderate line.” Kerr includes sea-level projections among these points, and reports “a rise of 40 to 60 centimeters by late in the century and a worst case of 1 meter by 2100, [which is] higher than in 2007 but far below the meter or two of sea-level rise that some expect.” As the authors of the IPCC WGI AR5 chapter on “Sea-Level Change,” we wish to clarify that for the highest emission scenario considered (RCP8.5), the AR5 reported a “likely” range of 0.45 to 0.82 m for sea-level projections for the late 21st century (average over 2081 to 2100) and of 0.52 to 0.98 m by 2100. The difference in sea level between these two periods is large because in 2081 to 2100, the “likely” rate of rise is 8 to 16 mm per year, which is up to about 10 times the average rate of rise during the 20th century. In the calibrated uncertainty language of the IPCC, this assessed likelihood means that there is roughly a one-third probability that sea-level rise by 2100 may lie outside the “likely” range. That is, the AR5 did not exclude the possibility of higher sea levels. However, we concluded that sea levels substantially higher than the “likely” range would only occur in the 21st century if the sections of the Antarctic ice sheet that have bases below sea level were to collapse. We determined with medium confidence that “this additional contribution would not exceed several 10ths of a meter of sea-level rise during the 21st century.” We could not define this possible contribution more precisely because “there is currently insufficient evidence to evaluate the probability of specific levels above the assessed ‘likely’ range.” The upper boundary of the AR5 “likely” range should not be misconstrued as a worst-case upper limit, as was done in Kerrs story as well as elsewhere in the media and blogosphere. For policy and planning purposes, it may be necessary to adopt particular numbers as an upper limit, but according to our assessment, the current state of scientific knowledge cannot give a precise guide. ![Figure][2] CREDIT: ANDREW MANDEMAKER/WIKIMEDIA COMMONS [1]: /lookup/doi/10.1126/science.342.6154.23-b [2]: pending:yes

An inversion of gravity and topography for mantle and crustal structure on Mars

Analysis of the gravity and topography of Mars presently provides our primary quantitative constraints on the internal structure of Mars. We present an inversion of the long-wavelength (harmonic degree ≤ 10) gravity and topography of Mars for lateral variations of mantle temperature and crustal thickness. Our formulation incorporates both viscous mantle flow (which most prior studies have neglected) and isostatically compensated density anomalies in the crust and lithosphere. Our nominal model has a 150-km-thick high-viscosity surface layer over an isoviscous mantle, with a core radius of 1840 km. It predicts lateral temperature variations of up to a few hundred degrees Kelvin relative to the mean mantle temperature, with high temperature under Tharsis and to a lesser extent under Elysium and cool temperatures elsewhere. Surprisingly, the model predicts crustal thinning beneath Tharsis. If correct, this implies that thinning of the crust by mantle shear stresses dominates over thickening of the crust by volcanism. The major impact basins (Hellas, Argyre, Isidis, Chryse, and Utopia) are regions of crustal thinning, as expected. Utopia is also predicted to be a region of hot mantle, which is hard to reconcile with the surface geology. An alternative model for Utopia treats it as a mascon basin. The Utopia gravity anomaly is consistent with the presence of a 1.2 to 1.6 km thick layer of uncompensated basalt, in good agreement with geologic arguments about the amount of volcanic fill in this area. The mantle thermal structure is the dominant contributor to the observed geoid in our inversion. The mantle also dominates the topography at the longest wavelengths, but shorter wavelengths (harmonic degrees ≥4) are dominated by the crustal structure. Because of the uncertainty about the appropriate numerical values for some of the models input parameters, we have examined the sensitivity of the model results to the planetary structural model (core radius and core and mantle densities), the mantles viscosity stratification, and the mean crustal thickness. The model results are insensitive to the specific thickness or viscosity contrast of the high-viscosity surface layer and to the mean crustal thickness in the range 25 to 100 km. Models with a large core radius or with an upper mantle low-viscosity zone require implausibly large lateral variations in mantle temperature.

Investigation of glacial isostatic adjustment in the northeast U.S. using GPS measurements

[1] We have been observing three-dimensional site velocities at over 60 permanent GPS stations in the northeastern U.S for the purpose of inferring mantle viscosity and thus improving current models of glacial isostatic adjustment (GIA). We estimate the upper and lower mantle viscosity by comparing radial site velocities from a subset of continuous GPS measurements with numerical GIA predictions. Our inferences are consistent with previous esti-mates obtained using different methods and data sets.

Interannual and latitudinal variability of the thermosphere density annual harmonics

[1] In this paper we investigate the intra-annual variation in thermosphere neutral density near 400 km using 4 years (2002–2005) of CHAMP measurements. The intra-annual variation, commonly referred to as the ‘‘semiannual variation,’’ is characterized by significant latitude structure, hemispheric asymmetries, and interannual variability. The magnitude of the maximum yearly difference, from the yearly minimum to the yearly maximum, varies by as much as 60% from year to year, and the phases of the minima and maxima also change by 20–40 days from year to year. Each annual harmonic of the intraannual variation, namely, annual, semiannual, terannual and quatra-annual, exhibits a decreasing trend from 2002 through 2005 that is correlated with the decline in solar activity. In addition, some variations in these harmonics are correlated with geomagnetic activity, as represented by the daily mean value of Kp. Recent empirical models of the thermosphere are found to be deficient in capturing most of the latitude dependencies discovered in our data. In addition, the solar flux and geomagnetic activity proxies that we have employed do not capture some latitude and interannual variations detected in our data. It is possible that these variations are partly due to other effects, such as seasonallatitudinal variations in turbopause altitude (and hence O/N2 composition) and ionosphere coupling processes that remain to be discovered in the context of influencing the intraannual variations depicted here. Our results provide a new data set to challenge and validate thermosphere-ionosphere general circulation models that seek to delineate the thermosphere intra-annual variation and to understand the various competing mechanisms that may contribute to its existence and variability. We furthermore suggest that the term ‘‘intra-annual’’ variation be adopted to describe the variability in thermosphere and ionosphere parameters that is well-captured through a superposition of annual, semiannual, terannual, and quatra-annual harmonic terms, and that ‘‘semiannual’’ be used strictly in reference to a pure 6-monthly sinusoidal variation. Moreover, we propose the term ‘‘intraseasonal’’ to refer to those shorter-term variations that arise as residuals from the above Fourier representation.

Interannual mean sea level change and the Earth's water mass budget

The relationship between interannual global mean sea level change and the Earths water mass budget is examined between 1993 and 1998 by removing the steric (thermal) component from mean sea level computed with TOPEX/Poseidon (T/P) altimetry. The steric component is calculated from subsurface temperatures measured by expendable bathythermographs and interpolated to a global grid by empirical orthogonal function (EOF) reconstruction. Results indicate that from late-1995 to early-1998, the thermal expansion of sea level was significantly higher than the total sea level change measured by T/P, suggesting that fresh water mass was lost from the ocean. The size of the maximum water mass lost is equivalent to about 18 mm of sea level. An error analysis indicates that this value is significant at the 95% confidence level. Results from numerical models show similar magnitudes of water mass change in the ocean at interannual periods, but at different phases.

A harmonic analysis of Martian topography

The topography of Mars is represented by a spherical harmonic model complete to degree and order 50. The data source is a recently revised U.S. Geological Survey compilation which encompasses a diverse array of spacecraft measurements and Earth-based radar ranges. Because of the disparate nature of the original data sources, it is difficult to obtain reliable estimates of the likely errors in Martian topography. However, the variance spectrum has a shape similar to that found for other terrestrial planets, and the topography correlates well with recent estimates of the gravitational field of Mars. Both of these considerations suggest that the existing data provide a reasonable approximation to the true topography of Mars. Nevertheless, a detailed topographic mapping of the planet, such as will be provided by the Mars Global Surveyor, will be required before significant advances are made in understanding the relationship between topography and gravity on Mars.

Surfaces of zero velocity in the restricted problem of three bodies

Recent uses of computer graphics allow the representation of the three-dimensional surfaces of zero velocity, also known as Hills or the Jacobian surfaces. The purpose of this paper is to show the actual surfaces rather than their projections which are available in the standard literature. The analytical properties of the surfaces are also available; therefore, this paper offers the pertinent references rather than the derivations.