Extensive Continuous Mass of Ice on Continental Scale
Summary
A simulation of monthly global gravity coefficients has been created that represents time-variable hydrology, ice mass loss and global mean sea level rise. Hydrology variations are from a numerical model, whereas the ice mass variations are based on recently observed rates and patterns of melt for glaciers, Greenland and Antarctica. A eustatic sea level variation consistent to balance the mass variations over land is added. This simulation is then used to test the capability of recovering trends in ocean mass, continental water storage and Greenland and Antarctica melting, using methods used to determine these from GRACE data. We find that ocean mass trends can be significantly biased low by the large melting rates from Greenland, Antarctica and glaciers, unless data within 300 km of continents is ignored. Any smoothing of the data beyond a truncation to degree/order 60 will also slightly bias the result. Trends of continental water storage and Antarctica mass loss also tend to be biased due to the sea level rise signal leaking into the estimate. Greenland melting rates are not affected.
1 Introduction
The Gravity Recovery and Climate Experiment (GRACE) has delivered a nearly continuous time-series of global gravity coefficients since 2002 August. These data have been used by numerous authors to study changes in land water storage (e.g. Ramillien et al. 2004; Rodell et al. 2004a; Syed et al. 2005; Swenson et al. 2006), ocean mass ( Chambers et al. 2004; Lombard et al. 2007; Willis et al. 2008) and changes in land-locked ice, including glaciers ( Tamisiea et al. 2005; Chen et al. 2007), the Greenland ice sheet (Velicogna & Wahr 2005, 2006a; Chen et al. 2006; Luthcke et al. 2006; Ramillien et al. 2006) and the Antarctic ice sheet ( Ramillien et al. 2006; Velicogna & Wahr 2006b). However, because the GRACE coefficients do not represent the full spatial structure of the water storage changes and because the errors increase at smaller wavelengths, it is necessary to both smooth the results to reduce noise and to scale the data to restore power reduced by the smoothing and truncation (e.g. Swenson & Wahr 2002)
In a previous study ( Chambers et al. 2007), we examined the effect large trends in melting of continental ice have on determining trends in ocean mass when such smoothing and truncation is required. The results were based on a relatively crude simulation, assuming uniform melting over Greenland, Antarctica and glaciers. Based on this assumption and the observed rates at the time, we found that an ocean kernel that masked out areas within 300 km of land and smoothed with a 300 km radius Gaussian function should be used to estimate ocean mass from GRACE. This would still cause a slight underestimation of the true trend in mean sea level (MSL) rise by 0.1 mm yr−1, but it represented a reasonable compromise. With more smoothing, the trend error was greater; with less smoothing, the trend error was less, but other errors were larger.
In the last year since the study was published, it has become more evident that Greenland is not melting uniformly, but has much higher rates near the edges ( Chen et al. 2006; Luthcke et al. 2006). Similar studies for Antarctica suggest that most of the melting is coming from the West Antarctic ice sheet and the Antarctic Peninsula (Shepherd & Wingham 2007). A recent study of glacier melt ( Meier et al. 2007) suggests an even higher rate than we originally used, and that glaciers in Alaska may explain nearly 1/3 of the rate ( Tamisiea et al. 2005).
The simulation of Chambers et al. (2007) was also done assuming GRACE Release-01 errors. Since then, Release-04 has been distributed. These data have significantly smaller predicted errors than the previous releases. For example, the estimated error in the monthly calculation of ocean mass is 3.9 mm of water thickness for Release-01 accumulated to degree/order 60 with no smoothing and 1.3 mm after 300 km smoothing, based on calibrated sigmas (e.g. Swenson & Wahr 2002). The cumulative error of Release-04 coefficients for the same global ocean basin is only 1.1 mm with no smoothing and 0.5 mm with 300 km smoothing. Thus, unsmoothed Release-04 coefficients give a comparable result to smoothed Release-01 coefficients, when averages are computed over areas as large as the global ocean.
Because of these changes in both the accuracy of the GRACE data and our understanding of the ice-melting patterns and rates, we have created an updated simulation. We have included models of non-uniform melting of Greenland and Antarctica and glaciers. We have also added seasonal and interannual fluctuations in land water storage from a numerical model. The specifics of the models used to create simulated global gravity coefficients are discussed in the following section.
Our previous study was also limited to the effects in estimating ocean mass. As we pointed out, the same problem will affect the estimation of trends in continental water storage and ice loss from Greenland and Antarctica, albeit at different magnitudes. In this new study, we will also examine trend errors in continental water storage and Greenland and Antarctica mass loss from GRACE.
2 Description of Simulation
The base model for the new simulation was monthly average land water storage variations from the GLDAS/NOAH hydrologic model ( Rodell et al. 2004b) for 2003 January until 2005 December. This hydrology model has a reasonable mean seasonal variation in continental water storage with some year-to-year changes but no significant trend over the 3 yr period. It does not model changes in ice mass, so, has very little or no variability over Greenland, Antarctica or glaciers. We added the negative of the monthly GLDAS/NOAH water mass to the oceans to balance the variation on land. The mass was added as a eustatic rise or fall in sea level, which is consistent with observations of the effect of the global, seasonal water cycle on ocean mass (e.g. Chambers et al. 2004). We have not included the effects of localized ocean bottom pressure variations in the simulation, since for GRACE processing this is simulated with a numerical model and removed during processing (Flechtner 2007). When computing ocean mass change or continental water storage, GRACE coefficients relative to this background model are used (e.g. Chambers et al. 2004; Velicogna & Wahr 2005).
No numerical model is perfect, however, and errors in the model may leak into the estimates of water mass variation. To simulate this, we have added the monthly difference between two ocean models to the eustatic change in sea level predicted by GLDAS. The models utilized are one run at Jet Propulsion Laboratory (JPL) as part of the Estimating the Circulation and Climate of the Ocean (ECCO) consortium ( Fukumori et al. 1999) and the Ocean Model for Circulation and Tides (OMCT) that is used to de-alias GRACE data during processing (Thomas 2002). To be consistent with the GRACE processing, the average of the models over the ocean is removed so that the spatial average difference of the two models is exactly zero.
The Greenland model is derived from the latest rates computed from GRACE coefficients for 2003 January until 2007 December (Fig. 1). We have not smoothed or filtered the data to remove the north–south 'stripes' that dominate below 60° latitude (e.g. Swenson & Wahr 2006). Such filtering dramatically reduces the melting signal on the coastlines because it is predominantly north–south, and the filters are designed to remove north–south correlated signals. The apparent gain of mass in the interior may be a residual stripe, although Luthcke et al. (2006) have reported evidence of some small gains of mass in the interior. For this analysis, we have assumed the GRACE map within the boundaries of Greenland is representative of the melting signal, which is arguably better than just assuming a uniform melting. It is at least consistent with other estimates of the patterns and sizes of Greenland melting (Shepherd & Wingham 2007).
Figure 1.
Rates of mass loss (in cm of water) estimated from GRACE gravity coefficients from 2003 January until 2007 December. The coefficients are from the Release-04 data set processed by the Center for Space Research. Data have not been smoothed or 'de-striped' (e.g. Swenson & Wahr 2006) but have only been expanded to degree/order 60. A glacial isostatic adjustment model from Paulson et al. (2007) has been applied to the data to remove postglacial rebound signals.
However, because the GRACE data are truncated at degree/order 60, Fig. 1 does not represent the full size of the mass loss; at best it shows the cumulative mass loss up to degree/order 60. To represent the complete mass loss, we estimated a forward model that, when truncated to degree/order 60, had minimal residuals with the GRACE map over Greenland (Fig. 2). The model was iterated several times to minimize the residuals. The model assumed two narrow regions on the west and east coasts where mass was being lost, with a third region in the middle of the east coast to account for the larger GRACE trend observed there and two regions in the interior where mass was being gained. All other areas were set to zero. As can be seen, the truncated forward model is very similar to that of GRACE (Fig. 2), even showing similar leakage of signals into the ocean. The forward model is loosing an equivalent of 0.46 mm yr−1 of equivalent sea level, which is consistent with recent observations from GRACE for 2003 January until 2007 December, using the methodology of Velicogna & Wahr (2006a). To balance this loss in the model, we added it uniformly to the global ocean.
Figure 2.
Rates of mass loss from a forward model based on GRACE. The rates are shown for the full model (top) and model truncated to degree/order 60 (bottom).
The change from the Greenland model used in Chambers et al. (2007) is significant. The previous model assumed a uniform melting, which implied 6.8 cm yr−1 equivalent water loss on the coastline, whereas the new model has a mass loss of more than 40 cm yr−1 along the east coast. Such an increase can cause significantly more leakage into the ocean than in the previous model.
We did not compute a forward model for Antarctica because there are still large uncertainties in the glacial isostatic adjustment correction there (e.g. Rammillien et al. 2006). Instead, we have assumed all the mass loss was from the two regions where the largest losses have been observed (Shepherd & Wingham 2007)—north of 80°S and between 220°E and 270°E and on the peninsula north of 73°S. The mean mass loss in these areas was assumed to be the same and estimated from recent estimates of Antarctica's contribution to sea level rise of 0.35 mm yr−1 for 2003 January until 2007 December, based on the method of Velicogna & Wahr (2006b). The rest of the continent was assumed to be zero. The difference between the new Antarctica model and the previous one is not as large as for Greenland but is still significant. A uniform melting model implies a 0.8 cm yr−1 mass loss on the coastline, whereas the new model has a mass loss of more than 11.8 cm yr−1 along a smaller area.
The glaciers model is similar to the one we used in Chambers et al. (2007), except we assumed that the glaciers along the coastline of Alaska were melting at a rate that would contribute 0.3 mm yr−1 to sea level rise, based on the observations reported by Tamisiea et al. (2005). The other glaciers in the database (National Snow and Ice Data Center 2005) were assumed to be melting at a rate that would contribute to a 0.8 mm yr−1 sea level rise, which is based on the most recent estimation by Meier et al. (2007), neglecting the Alaskan glaciers. We assumed that all glaciers (except Alaska and those on Greenland and Antarctica) melted at the same average mass density rate, which is the same assumption used by Dyurgerov & Meier (2005) and Meier et al. (2007).
We added the separate Greenland, Antarctica and glacier melting-rate models to the monthly land/ocean water mass grids by integrating the trends in time and adding the value to the appropriate land grid. We added the equivalent sea level rise of 1.9 mm yr−1 uniformly to the ocean grids. This is 0.3 mm yr−1 higher than the value assumed in Chambers et al. (2007). The monthly grids of water thickness anomalies were then converted into global gravity coefficients as described in Chambers et al. (2007).
3 Results and Analysis
The simulated gravity coefficients can then be combined with various basin kernels to determine the recovered mean signal and compared with the known full signal. We expand the simulated gravity coefficients to degree/order 60 because this is the maximum degree reported by Center for Space Research Processing Center. Truncation of the spherical harmonic expansion and the smoothing kernel will both tend to reduce the amplitude of any estimated variation. However, there tends to be a linear relationship between the true signal and truncated/smooth signal (e.g. Swenson & Wahr 2002); so, it is relatively easy to compute a linear scaling parameter from our simulated data set (Fig. 3) to restore most of the power lost by the truncation/smoothing. Note that the scaling parameter differs significantly depending on the size of the basin and level of smoothing. Small regions (like Greenland) require a scaling parameter much larger than 1, whereas large regions (like the global oceans) require a scaling parameter closer to 1. Likewise, using a large smoothing radius will require a larger scaling parameter. Finally, we have found that including smaller scale, time-varying variations within the basin in our simulation leads to significantly different scaling parameters than assuming a uniform change over the basin, as suggested by Swenson & Wahr (2002). Any analysis of GRACE data to recover accurate basin-scale averages has to compute such scaling parameters from a simulated data set (e.g. Velicogna & Wahr 2006a,b). All results presented here represent the estimate after scaling to restore power.
Figure 3.
Estimated ocean mass for a kernel that excludes coastal water within 300 km of continents versus the true ocean mass in the simulation. The slope of the linear trend for the unscaled data is 0.84, whereas it is 0.99 after a linear scaling.
Table 1 lists the trends for several different basin kernels compared with the input trend. The trend of the difference (estimated – truth) is also listed; positive values mean that the estimate is biased high, whereas negative values mean the estimate is biased low. Uncertainties are formal errors of the fit only, where trends were estimated simultaneously with a bias and annual and semi-annual sinusoids. The uncertainties on the differences reflect that much of the seasonal signal is differenced out; so, formal errors of the fit are smaller.
Table 1.
Recovered trends from simulation for various averaging kernels compared to the truth.
Because of the truncation at degree/order 60 and resulting leakage of the large ice-melting rates to the coastal regions, using a full ocean-averaging kernel underestimates the true trend by 16 per cent, or more than 0.3 mm yr−1. By ignoring the coastal water, one can recover the true ocean rate almost exactly. However, if the kernel is also smoothed more than ∼100 km, land signals will leak in and tend to bias the estimate too low, although still not as much as using a full ocean kernel. This is significantly different than the conclusion reached by Chambers et al. (2007) using a model of uniform mass loss from Greenland and Antarctica. They found that a kernel ignoring coastal waters and smoothed with a 300 km Gaussian had an error in ocean mass rate of less than 0.1 mm yr−1.
The results for the continents excluding Greenland and Antarctica show the effects of the MSL rise leaking into the results. Even with no additional smoothing, the truncation of the coefficients causes the estimate to be biased too high by about 21 per cent. Smoothing does not improve this significantly, however. Masking off coastal land areas only increases the bias (not shown) since most of the large trends are within a few hundred kilometres of the coast. These results suggest that one cannot infer the trend in continental water storage to better than 20 per cent, unless the leakage of MSL rise is accounted for.
The optimal averaging kernel used by Velicogna & Wahr (2006a) is excellent at recovering the trends over Greenland. This clearly is because the mass losses there are so large compared with the leakage of MSL rise; the ratio is more than 200 to 1. The optimal averaging kernel for Antarctica (Velicogna & Wahr 2006b) does not fare as well because the ratio of mass loss to MSL rise is smaller. It is interesting to note that the simulated Antarctica signal was only a linear trend, whereas the estimated variation has seasonal and interannual variability of up to 0.2 mm. This can only arise from leakage of the ocean signal into the Antarctica estimate. Velicogna & Wahr (2006b) attempted to remove this leakage by using an estimate of ocean mass variability based on a balance with GLDAS hydrology, which will remove most of the seasonal leakage, but not the trend. Over the period used in this simulation, the trend in GLDAS hydrology averaged over the ocean is 0 mm yr−1. Thus, this simulation suggests that the estimates of mass loss from Antarctica may be underestimated by up to 20 per cent, and should be re-examined in light of this.
4 Conclusions
If mountain glaciers and ice sheets in Greenland and Antarctica have the rates and patterns we have assumed in this simulation, then one has to take care in computing mass trends from GRACE data to avoid the leakage of the signals of both the ice-sheets and MSL rise from systematically biasing any estimated trends. We find that for estimates of ocean mass, an unsmoothed ocean kernel that ignores the oceans within 300 km of land, will not bias the trend within the formal error. The optimal kernel derived by Velicogna & Wahr (2006a) for Greenland will also not bias the trend estimate. However, kernels for Antarctica and all other land areas appear to have problems with leakage of the ocean mass trends. For the amount of MSL rise used in this simulation (1.93 mm yr−1), the continental water storage trends are biased high by 21 per cent, whereas the trends for Antarctica are biased more positive by approximately the same amount. We note, however, that these results are based on assuming a 1.93 mm yr−1 rise in MSL from addition of ocean mass; recent estimates from GRACE suggest the value is closer to 1 mm yr−1 ( Lombard et al. 2007; Willis et al. 2008), although these may be biased slightly low because of the averaging functions used. This simulation indicates that continental and Antarctica averages will tend to be too positive for any non-zero rise in ocean mass.
Finally, as we mentioned in our previous study, different kernels will affect the results differently; so, one should test their own kernel using a similar simulation. This same sort of effect will occur for someone interested in examining trends in land water storage in a region bordered by any large glacier or the ocean. We advise any investigator interested in studying mass trends from GRACE over any region to perform a similar simulation for their particular application to address the potential error.
Acknowledgments
This research was supported by grants from the NASA Interdisciplinary Science and Energy- and Water-Cycle Sponsored Research programs and the NASA GRACE Science Team. We would like to thank I. Velicogna for sharing her averaging kernels for Greenland and Antarctica. We would also like to thank J. Wahr for his comments on this paper during the review process, which led to a better revision.
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© 2008 The Authors Journal compilation © 2008 RAS
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