Christoph Dahle

Revisiting the Contemporary Sea Level Budget on Global and Regional Scales

Significance Understanding sea-level change is of paramount importance because it reflects climate-related factors, such as the ocean heat budget, mass changes in the cryosphere, and natural ocean/atmosphere variations. Furthermore, sea-level rise directly affects coastal areas, which has ramifications for its population and economy. From a novel combination of Gravity Recovery And Climate Experiment and radar altimetry data we find over the last 12 y: (i) a larger global steric sea-level rise as previously reported, (ii) a mass contribution to global sea level consistent with mass loss estimates from the world’s ice sheets, glaciers, and hydrological sources, and (iii) regionally resolved sea-level budget components which differ significantly from that of the global sea-level budget. Dividing the sea-level budget into contributions from ice sheets and glaciers, the water cycle, steric expansion, and crustal movement is challenging, especially on regional scales. Here, Gravity Recovery And Climate Experiment (GRACE) gravity observations and sea-level anomalies from altimetry are used in a joint inversion, ensuring a consistent decomposition of the global and regional sea-level rise budget. Over the years 2002–2014, we find a global mean steric trend of 1.38 ± 0.16 mm/y, compared with a total trend of 2.74 ± 0.58 mm/y. This is significantly larger than steric trends derived from in situ temperature/salinity profiles and models which range from 0.66 ± 0.2 to 0.94 ± 0.1 mm/y. Mass contributions from ice sheets and glaciers (1.37 ± 0.09 mm/y, accelerating with 0.03 ± 0.02 mm/y2) are offset by a negative hydrological component (−0.29 ± 0.26 mm/y). The combined mass rate (1.08 ± 0.3 mm/y) is smaller than previous GRACE estimates (up to 2 mm/y), but it is consistent with the sum of individual contributions (ice sheets, glaciers, and hydrology) found in literature. The altimetric sea-level budget is closed by coestimating a remaining component of 0.22 ± 0.26 mm/y. Well above average sea-level rise is found regionally near the Philippines (14.7 ± 4.39 mm/y) and Indonesia (8.3 ± 4.7 mm/y) which is dominated by steric components (11.2 ± 3.58 mm/y and 6.4 ± 3.18 mm/y, respectively). In contrast, in the central and Eastern part of the Pacific, negative steric trends (down to −2.8 ± 1.53 mm/y) are detected. Significant regional components are found, up to 5.3 ± 2.6 mm/y in the northwest Atlantic, which are likely due to ocean bottom pressure variations.

The Release 04 CHAMP and GRACE EIGEN Gravity Field Models

In this article we highlight the advances in gravity field recovery with CHAMP and GRACE, leading to the new GFZ release 04 (RL04) EIGEN (European Improved Gravity field of the Earth by New techniques) models. RL04 consists of time series of monthly CHAMP and GRACE gravity models, pure weekly GRACE solutions and combined static fields from satellite-only and terrestrial data. Additionally a new mean CHAMP-only gravity field model has been generated. It becomes obvious that the improvements in the RL04 background modelling, processing standards and strategies have led to significant improvements in the reprocessed gravity field models. These new RL04 EIGEN models, available for nearly the whole CHAMP and GRACE mission periods, provide an important data base to monitor mass transport and mass distribution phenomena in the system Earth, such as the continental hydrological cycle, ice mass loss in Antarctica and Greenland, ocean mass changes or the ocean surface topography.

Changes in total ocean mass derived from GRACE, GPS, and ocean modeling with weekly resolution

[1] We derive changes in ocean bottom pressure (OBP) and ocean mass by combining modeled ocean bottom pressure, weekly GRACE-derived models of gravity change, and large-scale deformation patterns sensed by a global network of GPS stations in a joint least squares inversion. The weekly combination allows a consistent estimation of geocenter motion, loading mass harmonics up to degree 30, and a spatially uniform mass correction term, which serves as a correction for forcing of the ocean model. We provide maps and time series of ocean mass and bottom pressure variations. Furthermore, we discuss the estimated geocenter motion and the estimated model correction. Our results indicate that the total ocean mass change is predominantly annual, with a maximum amplitude corresponding to 7.4 mm in October, which is in line with earlier work. The mean ocean bottom pressure (i.e., ocean plus atmospheric mass) shows an annual amplitude of 8.7 mm and is shifted forward by about 1.5 months. In addition, the solution exhibits typical autocorrelation times of about 2 weeks. A comparison with in situ bottom pressure time series in the southern Indian Ocean shows a good agreement, with correlations of 0.7-0.8. Based on these comparisons, we see that our results monitor realistic submonthly variations, which are strongest at high latitudes. The addition of GRACE data in the inversion is found to improve these high-latitude variations and enables better separability of the geocenter motion from other unknowns. Increasing the OBP model error from 3 cm to 4.8 cm affects mainly the higher-degree coefficients.

EIGEN-6C: A High-Resolution Global Gravity Combination Model Including GOCE Data

GOCE satellite gradiometry data were combined with data from the satellite missions GRACE and LAGEOS and with surface gravity data. The resulting high-resolution model, EIGEN-6C, reproduces mean seasonal variations and drifts to spherical harmonic degree and order (d/o) 50 whereas the mean spherical harmonic coefficients are estimated to d/o 1420. The model is based on satellite data up to d/o 240, and determined with surface data only above degree 160. The new GOCE data allowed the combination with surface data at a much higher degree (160) than was formerly done (70 or less), thereby avoiding the propagation of errors in the surface data over South America and the Himalayas in particular into the model.

GFZ RL05: An Improved Time-Series of Monthly GRACE Gravity Field Solutions

After publishing its release 04 (RL04) time-series of monthly GRACE gravity field solutions starting end of 2006, GFZ has reprocessed this time-series based on numerous changes covering reprocessed instrument data, observation and background models as well as updated processing environment and standards. The resulting GFZ RL05 time-series features significant improvements of about a factor of two compared to its precursor. By analyzing 72 monthly solutions for the time span 2005 till 2010, a remarkable noise reduction and a noticeably higher spatial resolution become obvious. The error level has significantly decreased and is now only about a factor of six above the pre-launch simulated baseline accuracy. GFZ RL05 solutions are publically available at ISDC and PO.DAAC archives.

Submonthly GRACE Solutions from Localizing Integral Equations and Kalman Filtering

An alternative approach for the analysis of GRACE inter-satellite range observations being processed in combination with current best knowledge GRACE orbits from improved GPS relative integer ambiguity fixing has been elaborated. The observations are first reduced by available background geophysical models and subsequently inverted as well as downward continued by a rigorous formulation in terms of reproducing kernel functions. Additionally, time-variable gravity field anomaly maps with respect to the subtracted background data have been derived. The observation equations are due to their spatial representation well suited for a Kalman-filter solution that can possibly enhance time resolution towards sub-monthly time series. The theoretical foundation of the method along with first numerical results and comparison to standard GRACE products are presented.

Estimating Sub-Monthly Global Mass Transport Signals Using GRACE, GPS and OBP Data Sets

In an effort to learn more about the sub-monthly variations in the global mass transport processes of the Earth, a study has been performed in which the feasibility of using weekly GRACE gravity solutions, in combination with GPS displacement data and ocean bottom pressure (OBP) models, is examined. A sensitivity study was conducted in which a range of solutions using different combinations of these three data sets were compared to each other, and with the time span of each combination ranging from 1 to 4 weeks. Data sets included weekly GFZ RL04 GRACE covariance matrices, as well as IGS GPS solutions and a new FESOM global OBP model, developed at AWI. The results showed that the temporal resolution of the solutions could be increased, while still maintaining reasonable levels of accuracy, if either GPS or OBP data were included in the combination. In particular, a 2-week triple combination of GRACE, GPS and OBP data was found to have approximately the same accuracy over land as a standard monthly GRACE solution, up to degree and order 30. These results provide encouraging support for future work involving real-data combinations.

A Geocenter Time Series from a Combination of LAGEOS and GRACE Observations

The geocenter motion can be inferred by evaluating Satellite Laser Ranging (SLR) observations to the LAGEOS satellites. Within the dynamic orbit determination process the degree 1 coefficients of a spherical harmonic expansion of the Earth’s gravity field are estimated. In a combined approach covering the years 2006–2011, GRACE mission GPS, K-band inter-satellite range-rate, and SLR observations are added to the LAGEOS solution via normal equations to examine possible improvements of the geocenter estimates. The particular effects on the estimates by each of the GRACE observation types are analyzed and the combined solutions are assessed and discussed. It turns out that adding GRACE data degrades the LAGEOS geocenter time series while at the same time consuming considerable computational resources.

Gravity Field Mapping from GRACE: Different Approaches—Same Results?

GFZ as part of the GRACE Science Data System (SDS) is routinely processing time-variable global gravity field models on monthly and weekly basis throughout the whole GRACE mission period. These operational products consist of spherical harmonic coefficients which are calculated based on the so-called dynamic method, i.e. integration of variational equations. As a matter of fact, these coefficients are imperfect due to different error sources such as inaccurate background models, instrument noise and inhomogeneous sampling and thus have to be filtered during post-processing in an appropriate way. Nevertheless, the current release named GFZ RL05 shows significant improvements compared to its precursors with an average error level of only about a factor of 6 above the pre-launch estimated baseline accuracy.

Improvement in GPS Orbit Determination at GFZ

Precise orbits of the GPS satellites are required at GFZ for generation of Earth’s gravity field models, precise determination of baselines between Low Earth Orbiters (LEOs) such as TerraSAR-X and TanDEM-X, for processing of various LEO radio occultation data as well as in research following the integrated approach where ground and space-borne GPS data are used together to estimate parameters needed for determination of a geodetic terrestrial reference frame. For this GFZ has implemented many GPS modelling improvements including GPS phase wind-up and attitude model, improved ambiguity fixing, absolute antenna phase centre offsets and variations, global constrains for the terrestrial reference system, frame transformation according to IERS Conventions 2010, higher order ionospheric corrections and improvements in the parameterization of the solar radiation pressure model. In this paper the influence of all these modelling improvements on the accuracy of the GPS orbits is presented. It is shown, that the application of the new models reduced the mean 3D difference of our orbits from 7.76 to 3.01 cm when compared to IGS final orbits.