Roelof Rietbroek

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.

A mascon approach to assess ice sheet and glacier mass balances and their uncertainties from GRACE data

The purpose of this paper is to assess the mass changes of the Greenland Ice Sheet (GrIS), Ice Sheets over Antarctica, and Land glaciers and Ice Caps with a global mascon method that yields monthly mass variations at 10,242 mascons. Input for this method are level 2 data from the Gravity Recovery and Climate Experiment (GRACE) system collected between February 2003 and June 2013 to which a number of corrections are made. With glacial isostatic adjustment (GIA) corrections from an ensemble of models based on different ice histories and rheologic Earth model parameters, we find for Greenland a mass loss of −278 ± 19 Gt/yr. Whereas the mass balances for the GrIS appear to be less sensitive to GIA modeling uncertainties, this is not the case with the mass balance of Antarctica. Ice history models for Antarctica were recently improved, and updated historic ice height data sets and GPS time series have been used to generate new GIA models. We investigated the effect of two new GIA models for Antarctica and found −92 ± 26 Gt/yr which is half of what is obtained with ICE-5G-based GIA models, where the largest GIA model differences occur on East Antarctica. The mass balance of land glaciers and ice caps currently stands at −162 ± 10 Gt/yr. With the help of new GIA models for Antarctica, we assess the mass contribution to the mean sea level at 1.47 ± 0.09 mm/yr or 532 ± 34Gt/yr which is roughly half of the global sea level rise signal obtained from tide gauges and satellite altimetry.

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.

Comparison of in situ bottom pressure data with GRACE gravimetry in the Crozet-Kerguelen region

Two time series of deep ocean bottom pressure records (BPRs) in between the Crozet Islands and Kerguelen are compared with GRACE (Gravity Recovery And Climate Experiment) equivalent water heights. An analysis of the correlation is performed for four time series: 1) monthly averages of the equivalent water height at the Crozet Islands, 2) the same near the Kerguelen Islands, 3) the mean of the two preceding series and 4) the difference between the two locations expressed in terms of geostrophic transport. We find that smoothed GRACE solutions are strongly correlated with the BPR data with correlation coefficients in the order of 0.7–0.8. Consequently GRACE measures real oceanic mass variations in this region.

Improving mass redistribution estimates by modeling ocean bottom pressure uncertainties

Weekly ocean bottom pressure anomalies (OBP) are modeled using the Finite Element Sea-ice Ocean Model FESOM). The models OBP error, mostly unknown so far, is assessed by comparing two model simulations, each forced by different atmospheric forcing data sets. The mean estimated error of modeled OBP is found to be 0.04 m per 1.5° × 1.5° grid cell. The error varies strongly from 0.003 m in the equatorial region to 0.31 m in the Weddell and Ross Seas. We believe that the spatial variations of the errors are an important improvement over previous error models. The new error estimates are implemented in a joint inversion of Gravity Recovery and Climate Experiment (GRACE) gravity measurements, GPS site displacements and modeled OBP, resulting in a larger overall OBP weight in the inversion, most notably in the Polar Regions. Additionally, the inversion provides a global mass correction term to adjust the ocean mass budget of the model. The estimated term is used to correct the models fresh water balance, making it consistent with GRACE and GPS on seasonal and longer timescales. All model results, weekly GRACE estimates and the inverse solutions are compared with measurements from in situ bottom pressure recorders. The newly estimated error model of the combination solution results in higher correlations than the previously used constant error model of the combination solution.

Uncertainty in geocenter estimates in the context of ITRF2014

Uncertainty in the geocenter position and its subsequent motion affects positioning estimates on the surface of the Earth and downstream products such as site velocities, particularly the vertical component. The current version of the International Terrestrial Reference Frame, ITRF2014, derives its origin as the long-term averaged center of mass as sensed by Satellite Laser Ranging (SLR), and by definition, it adopts only linear motion of the origin with uncertainty determined using a white noise process. We compare weekly SLR translations relative to the ITRF2014 origin, with network translations estimated from station displacements from surface mass transport models. We find that the proportion of variance explained in SLR translations by the model-derived translations is on average less than 10%. Time-correlated noise and non-linear rates, particularly evident in the Y and Z components of the SLR translations with respect to the ITRF2014 origin, are not fully replicated by the model-derived translations. This suggests that translation-related uncertainties are underestimated when a white noise model is adopted, and that substantial systematic errors remain in the data defining the ITRF origin. When using a white noise model, we find uncertainties in the rate of SLR X, Y and Z translations of ±0.03, ±0.03 and ±0.06 respectively, increasing to ±0.13, ±0.17 and ±0.33 (mm/yr, one sigma) when a PLW noise model is adopted.

Regional sea level change in response to ice mass loss in Greenland, the West Antarctic and Alaska

Besides the warming of the ocean, sea level is mainly rising due to land ice mass loss of the major ice sheets in Greenland, the West Antarctic, and the Alaskan Glaciers. However, it is not clear yet how these land ice mass losses influence regional sea level. Here, we use the global Finite Element Sea-ice Ocean Model (FESOM) to simulate sea surface height (SSH) changes caused by these ice mass losses and combine it with the passive ocean response to varying surface loading using the sea level equation. We prescribe rates of fresh water inflow, not only around Greenland, but also around the West Antarctic Ice Sheet and the mountain glaciers in Alaska with approximately present-day amplitudes of 200, 100, and 50 Gt/yr, respectively. Perturbations in sea level and in freshwater distribution with respect to a reference simulation are computed for each source separately and in their combination. The ocean mass change shows an almost globally uniform behavior. In the North Atlantic and Arctic Ocean, mass is redistributed toward coastal regions. Steric sea level change varies locally in the order of several centimeters on advective time- scales of decades. Steric effects to local sea level differ significantly in different coastal locations, e.g., at North American coastal regions the steric effects may have the same order of magnitude as the mass driven effect, whereas at the European coast, steric effects remain small during the simulation period.

Sea level budget in the Bay of Bengal (2002–2014) from GRACE and altimetry

Sea level rise is perceived as a major threat to the densely populated coast of the Bay of Bengal. Addressing future rise requires understanding the present-day sea level budget. Using a novel method and data from the Gravity Recovery and Climate Experiment (GRACE) satellite, we partition altimetric sea level rise (6.1 mm/a over 2002–2014) into mass and steric components. We find that current mass trends in the Bay of Bengal are slightly above global mean, while steric trends appear much larger: 2.2–3.1 mm/a if we disregard a residual required to close the budget, and 4.3–4.6 mm/a if, as an upper bound, we attribute this residual entirely to steric expansion. Our method differs from published approaches in that it explains altimetry and GRACE data in a least squares inversion, while mass anomalies are parameterized through gravitationally self-consistent fingerprints, and steric expansion through EOFs. We validate our estimates by comparing to Argo and modeling for the Indian Ocean, and by comparing total water storage change (TWSC) for the Ganges and Brahmaputra basins to the conventional GRACE approach. We find good agreement for TWSC, and reasonable agreement for steric heights, depending on the ocean region and Argo product. We ascribe differences to weaknesses of the Argo data, but we also find the inversion to be to some extent sensitive with respect to the EOFs. Finally, combining our estimates with CMIP5-simulations, we estimate that Bay of Bengal absolute sea level may rise for additional 37 cm under the RCP4.5 scenario and 40 cm under RCP8.5 until 2050, with respect to 2005.

Passive‐ocean radial basis function approach to improve temporal gravity recovery from GRACE observations

We present a state-of-the-art approach of passive-ocean Modified Radial Basis Functions (MRBFs) that improves the recovery of time-variable gravity fields from GRACE. As is well known, spherical harmonics (SHs), which are commonly used to recover gravity fields, are orthogonal basis functions with global coverage. However, the chosen SH truncation involves a global compromise between data coverage and obtainable resolution, and strong localized signals may not be fully captured. Radial basis functions (RBFs) provide another representation, which has been proposed in earlier works to be better suited to retrieve regional gravity signals. In this paper, we propose a MRBF approach by embedding the known coastal geometries in the RBF parameterization and imposing global mass conservation and equilibrium behavior of the oceans. Our hypothesis is that, with this physically justified constraint, the GRACE-derived gravity signals can be more realistically partitioned into the land and ocean contributions along the coastlines. We test this new technique to invert monthly gravity fields from GRACE level-1b observations covering 2005-2010, for which the numerical results indicate that: (1) MRBF-based solutions reduce the number of parameters by approximately 10%, and allow for more flexible regularization when compared to ordinary RBF solutions; and (2) the MRBF-derived mass flux is better confined along coastal areas. The latter is particularly tested in the Southern Greenland, and our results indicate that the trend of mass loss from the MRBF solutions is approximately 11% larger than that from the SH solutions, and approximately 4% ∼ 6% larger than that of RBF solutions.

Consistency of Geoid Models, Radar Altimetry, and Hydrodynamic Modelling in the North Sea

ABSTRACT Radar altimetry, when corrected for tides, atmospheric forcing of the sea surface, and the effects of density variations and mean and time-variable currents, provides an along-track realization of the marine geoid. In this study we investigate whether and how such an ‘altimetric-hydrodynamic’ geoid over the North Sea can serve for validating satellite-gravimetric geoids. Our results indicate that, using ERS-2 and ENVISAT along-track altimetry and water levels from the high-resolution operational circulation model BSHcmod, we do find distinct differences in RMS fits for various state-of-the art satellite-only models (beyond degree 145 for GRACE-only, and beyond degree 185 for GOCE models) and for combined geoid models, very similar as seen in GPS-levelling validations over land areas. We find that, at spectral resolution of up to about 200, an RMS fit as low as about 7 cm can be obtained for the most recent GOCE-derived models such as GOCO05S. This is slightly above what we expect from budgeting individual errors. Key to the validation is a proper treatment of the spectral mismatch between satellite-gravimetric and altimetric-hydrodynamic geoids. Comparison of data fits and error budget suggests that geoid truncation errors residual to EGM2008 (i.e. EGM2008 commission and omission error) may amount up to few cm.