Mark E. Tamisiea

New Data Systems and Products at the Permanent Service for Mean Sea Level

ABSTRACT Holgate, S.J.; Matthews, A.; Woodworth, P.L.; Rickards, L.J.; Tamisiea, M.E.; Bradshaw, E.; Foden, P.R.; Gordon, K.M.; Jevrejeva, S., and Pugh, J., 2013. New data systems and products at the Permanent Service for Mean Sea Level. Sea-level rise remains one of the most pressing societal concerns relating to climate change. A significant proportion of the global population, including many of the worlds large cities, are located close to the coast in potentially vulnerable regions such as river deltas. The Permanent Service for Mean Sea Level (PSMSL) continues to evolve and provide global coastal sea-level information and products that help to develop our understanding of sea-level and land motion processes. Its work aids a range of scientific research, not only in long-term change, but also in the measurement and understanding of higher frequency variability such as storm surges and tsunamis. The PSMSL has changed considerably over the past 10 years, and the aim of this paper is to update the community about these changes as well as provide an overview of our continuing work.

Causes for Contemporary Regional Sea Level Changes

Regional sea level changes can deviate substantially from those of the global mean, can vary on a broad range of timescales, and in some regions can even lead to a reversal of long-term global mean sea level trends. The underlying causes are associated with dynamic variations in the ocean circulation as part of climate modes of variability and with an isostatic adjustment of Earths crust to past and ongoing changes in polar ice masses and continental water storage. Relative to the coastline, sea level is also affected by processes such as earthquakes and anthropogenically induced subsidence. Present-day regional sea level changes appear to be caused primarily by natural climate variability. However, the imprint of anthropogenic effects on regional sea level-whether due to changes in the atmospheric forcing or to mass variations in the system-will grow with time as climate change progresses, and toward the end of the twenty-first century, regional sea level patterns will be a superposition of climate variability modes and natural and anthropogenically induced static sea level patterns. Attribution and predictions of ongoing and future sea level changes require an expanded and sustained climate observing system.

On seasonal signals in geodetic time series

We explore implications for modeling and noise analysis of stochastic seasonal processes of climatic origin in geodetic time series. Seasonal signals are generally modeled as sinusoids with annual periods (and harmonics thereof), each with constant amplitude and phase. However, environmental noise that underlies the seasonal signal in geodetic time series has a reddened power spectral density (PSD). We investigate the form of the PSD of a time series having a stochastic seasonal component and find that for frequencies greater than the nominal seasonal frequency, the PSD of the time series reflects the PSD of the seasonal amplitudes. For example, if the PSD of the seasonal amplitudes can be expressed as an inverse power law, then the PSD of the time series will behave as an inverse power law for high frequencies. Stochastic seasonal variability will also induce a peak near the nominal seasonal frequency in addition to that of the mean seasonal signal and will be relatively flat below this frequency. It is therefore possible that some of the noise in Global Navigation Satellite Systems (GNSS) time series reported by others may be associated with neglecting the stochastic component of the seasonal signal. We use a GNSS time series from site ZIMM as an example to demonstrate the existence of a variable seasonal signal (without attributing its cause), and we use an example Gravity Recovery and Climate Experiment (GRACE) time series from Alaska to demonstrate that use of a nonstochastic seasonal model can have a significant impact on the value and uncertainty of time-variable rates estimated from the time series.

Global geoid and sea level changes due to present-day ice mass fluctuations

We predict gravitationally self-consistent global geoid and relative sea level (RSL) perturbations due to present-day melting of ice complexes, including the Antarctic and Greenland ice sheets and a suite of mountain glaciers and ice sheets. Classic analyses of sea level change indicate that these perturbations will depart significantly from eustatic (i.e., geographically uniform) trends [e.g., Woodward, 1888; Farrell and Clark, 1976], although this result has not always been appreciated in modern analyses. Mass flux of individual ice reservoirs will produce unique geometries of sea level change, and this distinctiveness admits the possibility of using global geoid, sea surface, and RSL signatures of recent climate change to infer the ongoing mass balance of each reservoir rather than simply the net mass flux. As an example, we show that perturbations to the geoid arising from noneustatic water loads associated with each ice reservoir are sufficiently large (at low degrees) to be theoretically measurable within 5 years by the GRACE satellite mission. We complete the study by reanalyzing tide gauge data at 23 sites selected by Douglas [1997] in a recent analysis of global RSL rise. Traditionally, estimates of global sea level rise are generated by taking the mean of a set of secular tide gauge trends that have been corrected for the influence of ongoing glacial isostatic adjustment (GIA) related to the late Pleistocene glacial cycles. The common assumption in such studies is that the geographic scatter in the residual, GIA-corrected trends is due to errors in the GIA model or unmodeled processes (e.g., tectonics). We consider a large suite of GIA model predictions and apply a least squares approach to the GIA-corrected tide gauge trends to estimate the weighting of various present-day sea level signatures. We find that the fit to the residual RSL trends is significantly improved and that the procedure is able to resolve a long-standing observation of anomalously low sea level rates in Europe. This preliminary analysis, which is relatively insensitive to changes in the assumed geometry of the present-day mass balance, assumes that ocean thermal expansion is globally uniform. However, the procedure can be easily extended to incorporate a realistic steric contribution once the geometry of the process is sufficiently well constrained.

Impact of self-attraction and loading on the annual cycle in sea level

The annual exchange of water between the continents and oceans is observed by GPS, gravimetry, and altimetry. However, the global average amplitude of this annual cycle (observed amplitude of ∼8 mm) is not representative of the effects that would be observed at individual tide gauges or at ocean bottom pressure recorders because of self-attraction and loading effects (SAL). In this paper, we examine the spatial variation of sea level change caused by the three main components that load the Earth and contribute to the water cycle: hydrology (including snow), the atmosphere, and the dynamic ocean. The SAL effects cause annual amplitudes at tide gauges (modeled here with a global average of ∼9 mm) to vary from less than 2 mm to more than 18 mm. We find a variance reduction (global average of 3 to 4%) after removing the modeled time series from a global set of tide gauges. We conclude that SAL effects are significant in places (e.g., the south central Pacific and coastal regions in Southeast Asia and west central Africa) and should be considered when interpreting these data sets and using them to constrain ocean circulation models.

Combination of geodetic observations and models for glacial isostatic adjustment fields in Fennoscandia

We demonstrate a new technique for using geodetic data to update a priori predictions for Glacial Isostatic Adjustment (GIA) in the Fennoscandia region. Global Positioning System (GPS), tide gauge, and Gravity Recovery and Climate Experiment (GRACE) gravity rates are assimilated into our model. The technique allows us to investigate the individual contributions from these data sets to the output GIA model in a self‐consistent manner. Another benefit of the technique is that we are able to estimate uncertainties for the output model. These are reduced with each data set assimilated. Any uncertainties in the GPS reference frame are absorbed by reference frame adjustments that are estimated as part of the assimilation. Our updated model shows a spatial pattern and magnitude of peak uplift that is consistent with previous models, but our location of peak uplift is slightly to the east of many of these. We also simultaneously estimate a spatially averaged rate of local sea level rise. This regional rate (∼1.5 mm/yr) is consistent for all solutions, regardless of which data sets are assimilated or the magnitude of a priori GPS reference frame constraints. However, this is only the case if a uniform regional gravity rate, probably representing errors in, or unmodeled contributions to, the low‐degree harmonic terms from GRACE, is also estimated for the assimilated GRACE data. Our estimated sea level rate is consistent with estimates obtained using a more traditional approach of direct “correction” using collocated GPS and tide gauge sites.

Weighing the ocean: Using a single mooring to measure changes in the mass of the ocean

[1] Combining ocean and earth models, we show that there is a region in the central Pacific ocean where ocean bottom pressure is a direct measure of interannual changes in ocean mass, with a noise level for annual means below 3 mm water equivalent, and a trend error below 1 mm/yr. We demonstrate this concept using existing ocean bottom pressure measurements from the region, from which we extract the annual cycle of ocean mass (amplitude 8.5 mm, peaking in late September), which is in agreement with previous determinations based on complex combinations of global data sets. This method sidesteps a number of limitations in satellite gravity-based calculations, but its direct implementation is currently limited by the precision of pressure sensors, which suffer from significant drift. Development of a low-drift method to measure ocean bottom pressure at a few sites could provide an important geodetic constraint on the earth system. Citation: Hughes, C. W., M. E. Tamisiea, R. J. Bingham, and J. Williams (2012), Weighing the ocean: Using a single mooring to measure changes in themass ofthe ocean, Geophys. Res. Lett., 39, L17602, doi:10.1029/2012GL052935.

Long Wavelength Sea Level and Solid Surface Perturbations Driven by Polar Ice Mass Variations: Fingerprinting Greenland and Antarctic Ice Sheet Flux

Rapid ice mass variations wiihin the large polar ice sheets lead to distinct and highly nonuniform sea-level changes that have come to be known as ‘sea-level fingerprints’. We explore in detail the physics of these fingerprints by decomposing the total sea-level change into contributions from radial perturbations in the two bounding surfaces: the gcoid (or sea surface) and the solid surface. In the case of a melting event, the sea-level fingerprint is characterized by a sea-level fall in the near-field of the ice complex and a gradually increasing sea-level rise (from 0.0 to 1,3 times the eustalic value) as one considers sites at progressively greater distances (up to ∼ 90° or so) from the ice sheet. The far-field redistribution is largely driven by the relaxation of I he sea-surface as the gravitational pull of the ablating ice sheet weakens. The near-field sea-level fall is a consequence of both this relaxation and ocean-plus-ice unloading of the solid surface. We argue that the fingerprints provide a natural explanation for geographic variations in sea-level (e.g., tide gauge, satellite) observations. Therefore, they furnish a methodology for extending traditional analyses of these observations to estimate not only the globally averaged sea-level rate but also the individual contributions to this rate (i.e., the sources).

A method for detecting rapid mass flux of small glaciers using local sea level variations

There is increasing evidence that the global reservoir of small (or mountain) glaciers is presently experiencing an accelerated phase of net melting, perhaps linked to climatic warming. We argue that relative sea level and sea surface fingerprints local to such events provide a potentially powerful, integrated diagnostic for the mass imbalance. For example, we demonstrate, using an inference of glacier mass balance near Alaska over the last 50 years, that the present-day relative sea level fall at nearby sites can reach amplitudes that are ∼2 orders of magnitude greater than the ongoing eustatic sea level rise associated with the melting. The peak sea surface subsidence is a factor of ∼15 greater than the eustatic amplitude. We find that the predicted present-day sea surface change arising from the 50-year loading history is sensitive only to the ongoing rate of accelerated melting. In contrast, the present-day relative sea level fingerprint becomes increasingly sensitive to the ‘history’ of the recent loading when the viscosity of the asthenosphere adopted in the prediction is progressively reduced below 1020 Pa s. Specifically, the relative sea level fingerprint becomes more localized, and reaches higher amplitudes, close to the glacier system as viscous effects become active. Our results have application in efforts to constrain small glacier mass balance using tide gauge records of relative sea level change or satellite-derived constraints on sea surface (geoid) rates.

Reply to comment by W. R. Peltier et al. on “Ocean mass from GRACE and glacial isostatic adjustment”

[1] We examine geoid rates and ocean mass corrections from two published global glacial isostatic adjustment (GIA) models, both of which have been used in previous studies to estimate ocean mass trends from Gravity Recovery and Climate Experiment (GRACE) satellite gravity data. These two models are different implementations of the same ice loading history and use similar mantle viscosity profiles. The model results are compared with each other and with geoid rates determined from GRACE during August 2002 to November 2009. When averaged over the global ocean, the two models have rates that differ by nearly 1 mm yr of ocean mass, with the first model giving a correction closer to 2 mm yr and the second closer to 1 mm yr. By comparing the two models, we have discovered that 50% of the difference is caused by a global (land + ocean) mean in the first model. While it is appropriate to include this mean when subtracting GIA effects from measurements of sea level change measured by tide gauges or satellite altimetry, the mean should not be included when subtracting GIA effects from ocean mass variations derived from satellite gravity data. When this mean is removed, the ocean mass corrections from the two models still disagree by 0.4 mm yr. We trace the residual difference to the fact that the first model also has large trends over the ocean related to large rates in its predicted degree 2, order 1 geoid coefficients. Such oceanic trends are not observed by GRACE nor are they predicted by the second model, and they are shown to be inconsistent with the polar wander rates predicted by the first model itself. If these two problems are corrected, we find that the two model predictions agree at the 3% level. On the basis of this analysis, we conclude that the ocean mass correction for GRACE is closer to 1 mm yr than 2 mm yr, although significant uncertainties remain.