Hydrological Sciences-Journal-des Sciences Hydrologiques, 44(3) June 1999 407

Gravity and the hydrosphere: new frontier

JEAN O. DICKEY1, CHARLES R. BENTLEY2, ROGER BILHAM3, JAMES A. CARTON4, RICHARD J. EANES5, THOMAS A. HERRING6, WILLIAM M. KAULA7, GARY S. E. LAGERLOEF8, STUART ROJSTACZER9, WALTER H. F. SMITH10, HUGO M. VAN DEN DOOL11; JOHN M. WAHR12, MARIA T. ZUBER13 Members of the US National Research Council/National Academy of Science Committee on Earth Gravity from Space

Abstract Satellite gravity measurements expected in the next few years will provide unprecedented views of the Earth's gravity field and, given sufficient duration, its changes with time. Gravity changes directly reflect changes in the masses of the ocean (thus allowing the separation of steric (heat induced) and non-steric contributions to sea-level rise), the Greenland and Antarctic ice sheets, and the water stored in the continents. Not only can measurements of those changes provide a truly global integrated view of the Earth, they have, at the same time, sufficient spatial resolution to aid in the study of individual regions of the Earth. These data should yield information on water cycling previously unobtainable and be useful to both fundamental studies of the hydrologie cycle and practical assessments of water availability and distribution. Together with complementary geophysical data, satellite gravity data represent a new frontier in studies of the Earth and its fluid envelope. La gravimétrie et l'hydrosphère: de nouvelles perspectives Résumé Les mesures gravimétriques satellitaires que l'on peut espérer obtenir dans quelques années fourniront un vision sans précédent du champ de gravité de la Terre, ainsi que de ses variations au cours du temps. Les variations du champ de gravité de la Terre reflètent directement les modifications de la masse des océans (permettant de distinguer les contributions d'origine thermique à l'élévation du niveau des mers), des couches de glace du Groenland et de l'Antarctique et de l'eau stockée sur les continents. Ces mesures peuvent non seulement fournir une vision globale de la Terre, mais elles ont aussi une résolution spatiale suffisante pour permettre l'étude de régions particulières. Ces données devraient permettre d'obtenir des informations sur le cycle hydrologique jusqu'ici inabordables, qui seront utiles tant pour l'étude fondamentale du cycle de l'eau que pour l'évaluation de la répartition et de la disponibilité de l'eau.

Jet Propulsion Laboratory/California Institute of Technology, Pasadena, California 91109, USA, jean.dickey@jpl.nasa.gov - University of Wisconsin-Madison, Madison, Wisconsin 53706, USA, [email protected] CIRES, University of Colorado, Boulder, Colorado 80309, USA, [email protected] University of Maryland, College Park, Maryland 20742, USA, [email protected] University of Texas, Austin, Texas 78722, USA, [email protected] Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA, [email protected] University of California, Los Angeles, California 90024-1567, USA, [email protected] Earth and Space Research, Seattle, Washington 98102, USA, [email protected] Duke University, Durham, North Carolina 27708-0230, USA, [email protected] NOAA Geosciences Laboratory, Silver Spring, Maryland 20910-3281, USA, [email protected] NOAA Climate Prediction Center, Camp Spring, Maryland 20746, USA, [email protected] University of Colorado, Boulder, Colorado 80309, USA, [email protected] Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA, [email protected]

Open for discussion until 1 December 1999 408 Jean O. Dickey et al.

En liaison avec d'autres données géophysiques, la gravimétrie satellitaire ouvre de nouvelles perspectives à l'étude de la Terre et de son enveloppe fluide.

INTRODUCTION

The Earth's gravity field provides a record of the mass distribution within the Earth's system that can be used to understand the evolution and dynamics needed to maintain that distribution. Processes that affect the distribution of mass in the Earth produce variations in the Earth's gravitational field on a variety of spatial and temporal scales (Fig. 1). Highly accurate measurements of the Earth's gravity field made with appropriate spatial and temporal sampling can thus be used to better understand the processes that move mass within, on, and above the Earth. The inversion of the gravity signals to obtain the mass distribution and an understanding of the dynamics that cause them are not straightforward problems. However, through a combination of spatial and temporal analyses as well as auxiliary land-based measurements for ground truth, knowledge of the gravity field and its temporal variations can provide insights into the processes involved. The reliability of these inferences depends on the accuracy, spatial and temporal resolution, and duration of the gravity measurements.

ADVANCES IN UNDERSTANDING GLOBAL GRAVITY

In a recently released report of the US National Research Council (NRC, 1997), the Committee on Earth Gravity from Space explored the scientific questions that could be addressed with a better determination of the global gravity field, examined generic mission scenarios developed from approximately a dozen mission concepts, and deduced the expected advances that would flow from each. Traditionally, the gravity field has been treated as essentially steady-state, or static, over human lifetimes because over 99% of the anomalous gravity field (the departure of the field from a simple ellipsoidal model) is static in historic time. The static field is dominated by irregularities in the solid Earth caused by convective processes that deform the solid Earth on time scales of thousands to millions of years. Spaceborne gravity measurements have already led to dramatic advances in recent years in the understanding of those processes and their relationships to the structure and dynamics of the core and mantle, the thermal and mechanical structure of the lithosphère, ocean circulation, and plate tectonics. While we expect that static-field studies will yield significant future results, we envision that the most dramatic advances arising from the next generation of gravity satellites will arise from the examination of the remaining anomalous gravity field. Temporal variations, which have time scales ranging from hours to secular changes, are caused by a variety of phenomena that redistribute mass. Many of these are related to the hydrosphere; processes range from sub-daily oscillations (e.g. tides) to longer- term trends (e.g. aquifer depletion). The cryosphere (the part of the Earth's surface that is perennially frozen) also has seasonal and inter-annual variations, as well as a long- term secular change. Particularly exciting from a hydrological standpoint is the Gravity and the hydrosphere: new frontier 409

Spatial and Temporal Scales of Geoid Variations

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1 - - I -1— T 10,000 1000 100 10 1 Wavelength (km) Fig. 1 (a) Geophysical phenomena that cause measurable temporal and spatial variations in the Earth's gravity field (adapted from Bettadpur & Tapley, 1996); and (b) summary of requirements for static gravity-measurement accuracy as a function of wavelength (adapted from NASA, 1987). potential to study sea-level changes and their causes and changes to groundwater and surface water (including soil moisture) in continental regions (NRC, 1997; Dickey et al, 1998). Satellite gravity data that have accumulated over several decades have been used to produce complex interpretative models of the Earth's gravity field (Nerem et ah, 1995). Doppler tracking of close satellites (e.g. SPOT) and laser tracking of distant 410 Jean O. Dickey et al. satellites (e.g. LAGEOS), augmented by satellite radar altimetry and GPS measurements on TOPEX/POSEIDON, have been the primary data source. The approval of two new missions based on improved measurement techniques places the study of the global gravity field at the opening of a new era. CHAMP, a German-led mission with US involvement scheduled for launch in 1999, will utilize a high-satellite-to-low-satellite tracking scheme to improve the long- wavelength component of gravity. NASA's Gravity Recovery and Climate Experiment (GRACE; launch date 2001 (Tapley, 1997; Stanton et al, 1998)) features the first use of still more accurate low-satellite-to-low-satellite microwave tracking. GRACE'S low altitude (480-300 km) as well as its long lifetime (planned for five years), will provide measurements of both the static and temporal components of the gravity field with an unprecedented spatial and temporal accuracy. High-satellite-to-low-satellite tracking is a scenario where one satellite is at relatively high altitude and other is positioned at a low altitude, while low-satellite-to-low-satellite tracking is a scheme where both satellites are located at low altitude, allowing a more robust resolution. In the remainder of this article, we will focus on expected advances in time-variable-gravity measurement that we believe will be of interest to the hydrological community. Advances in other areas have been highlighted by Dickey et al (1998) and a full treatment is given in the NRC report (NRC, 1997).

GRAVITY MEASUREMENTS FOR THE HYDROLOGICAL APPLICATIONS

Continental Water Variation Gravity missions can provide estimates of changes in water storage over spatial scales of several hundred kilometres and larger, which would be accurate to 10 mm or better (Fig. 2). These would be useful to hydrologists for connecting hydrological processes at traditional length scales (tens of kilometres and less) to those at longer scales. The main measurables related to these processes are soil moisture, groundwater and snow pack. The issue of whether GRACE gravity solutions can be inverted to solve for those changes in water storage depends on the amplitude of this hydrological gravity signal, and on whether the hydrological contributions can be separated from changes in gravity caused by other types of mass variability. The atmospheric signal is a particular problem because GRACE would be incapable of distinguishing between a change in water storage in a region and a change in atmospheric mass integrated vertically above that region. The atmospheric contributions will be removed from the GRACE results prior to the hydrological solutions by using the global pressure fields available from meteorological forecast centres. To illustrate the capabilities of GRACE for providing hydrological information in the presence of both GRACE measurement errors and contamination from other signals, Fig. 3 shows the results of an inversion of simulated GRACE data (reconstructing mass distribution from the gravity signal) from Wahr et al. (1998). For this inversion, five years of synthetic, monthly GRACE gravity solutions were constructed, consisting of a realization of the expected GRACE measurement errors, plus the estimated gravity contributions from soil moisture (using a global, gridded soil moisture data set constructed as described by Huang et al, 1996), océanographie Gravity and the hydrosphere: new frontier 411

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0.001 SSI errors for 400-km attitude 10 20 30 40 Spherical Harmonic Degree Fig. 2 The degree amplitudes (in mass), expressed as the thickness of a water layer, for the annually-varying terms (averaged over 5 years of data) from continental hydrology, oceanography, and changes in Antarctic and Greenland ice mass. To estimate the Antarctic and Greenland contributions, annually-varying changes in thickness of 1 and 8 cm, respectively, were assumed for the two ice sheets, which are in reasonable agreement with the results of Bromwich et al. (1993, 1995). (SST refers to a low- satellite-to-low-satellite tracking mission which is a GRACE-like mission utilizing GPS; SSI describes results that would be obtained by the low-satellite-to-low-satellite tracking mission using laser interferometry; correspondingly SSGE refers to results expected from an extended mission of spaceborne gravity gradiometer.) processes (using output from the Los Alamos POP ocean general circulation model of Dukowicz & Smith, 1994), and errors in the atmospheric pressure corrections (estimated as the difference between European Center for Medium-Range Weather Forecasts (ECMWF) and National Centers for Environmental Prediction (NCEP) 412 Jean O. Dickey et al.

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(ci : 0.01 1000 100 averaging radius (km) Fig. 3 The results of simulations in which synthetic GRACE data are used to recover the hydrological signal at Manaus, Brazil (Amazon River basin) (from Wahr et al., 1998). (a) and (b) show five years of monthly values for two averaging radii (the solid line is the hydrology signal that went into the simulation, and the dotted line is the signal inferred from the synthetic GRACE data); and (c) shows the rms of five years of monthly data as a function of averaging radius (the solid line is the estimate from the hydrology data; the dashed line represents the accuracy of the GRACE results, estimated as the rms of the difference between the GRACE recovered values and the hydrology signal.). The simulated geoid data include the GRACE geoid errors, as well as contributions from hydrology and oceanography, and our estimated errors in the atmospheric pressure data. pressure fields, divided by sqrt(2)). The synthetic gravity solutions were used to infer monthly changes in water storage averaged over a disc centred on Manaus, Brazil (in the Amazon River basin), and the results are compared in Fig. 3 with the correct results, i.e. with the results predicted from the soil moisture data set used in the simulation. The results are shown in terms of the thickness of a water layer. The results in the upper two panels show comparisons for five years of monthly values for two different averaging discs (radii of 500 and 230 km). The bottom panel shows the rms Gravity and the hydrosphere: new frontier 413 both of the predicted signal at this location and of the errors in the GRACE recovery of this signal, as a function of averaging radius. Note that the GRACE errors are smaller than the signal at radii of about 200 km and larger, are smaller than 1 cm at radii in excess of about 280 km, and reduce to about 2-3 mm at radii of 400 km and larger. The 2-3 mm limit comes from the estimated atmospheric pressure errors, and is equi­ valent to a 0.2-0.3 mbar rms pressure error. The degradation of the results with decrea­ sing radius is due to the increase in GRACE measurement error with decreasing scale. The results shown in Fig. 3 are fairly typical of the expected GRACE performance at most locations. The inferences are that GRACE should be able to provide useful estimates of changes in continental water storage at scales of a few hundred km and larger and at time scales of two weeks and longer, and that GRACE has the potential of delivering monthly values of water mass with accuracies of better than 10 mm in water thickness at large scales. These water storage estimates can be used both for monitoring purposes and to improve understanding of hydrological and climate-related processes. Because GRACE measurements will consist of averages over hundreds of km, they will complement traditional ground-based hydrological measurements, which tend to be restricted to the scales of individual catchments. The GRACE results can also complement space-based microwave and infrared soil moisture measurements. The latter provide information on only the upper few cm of water in the soil, whereas the GRACE estimates reflect changes in water storage throughout the water column. What GRACE does allow is closure of the total water budget over large regions. This should permit the assessment and improvement of regional-scale hydrological models and of the hydrological components of climate and meteorological models. It could prove useful also for helping to monitor the water available for agricultural purposes and to help in assessing flood and drought danger over large regions. Sea Level Rise and Glaciology Satellite observations of time-dependent gravity could constrain changes in global sea-level in two ways. First, they could be used to help identify the thermal-expansion component of sea-level rise by using the observations to solve directly for the mass increase in the ocean. From the GRACE mission (five-year duration assumed), an increasing mass of water in the ocean equivalent to 0.1 mm year"1 of sea-level rise can be measured. That will be a major improvement over the uncertainty at present, which is almost an order of magnitude larger. Second, they could help identify the continental sources of water transferring into the ocean, through continual monitoring of the mass of ice sheets, continental glaciers, and groundwater aquifers. Using GRACE to monitor liquid water on land was outlined above. Probably even more important to sea level are temporal variations in the masses of glaciers, ice caps, and ice sheets (the term "ice sheet" is reserved for the vast ice covers of Antarctica and Greenland).

GRAVITY FIELD AND THE CRYOSPHERE

Ice bodies on land can shrink in two ways—by excess melting and liquid water runoff and by breaking off as icebergs. In either case the mass lost soon reaches the ocean. Conversely, ice bodies can gain mass only by an excess of snowfall on their surfaces; the moisture source is evaporation from the oceans. Thus, the measurement of the total 414 Jean O. Dickey et al. mass balance (deviation from constant mass through time) of the ice on land is a direct, though partial measure of the changes of water mass in the oceans. There are two immense advantages of gravity measurements for large-scale mass- balance studies. The first is that since gravity depends simply on mass, changes in gravity provide a direct measure of ice-mass balance that is independent of changes in the mean density of the ice bodies, which can change with time. Secondly, gravity serves as an automatic integrating tool, thus obviating the huge difficulty that glaciologists face in extrapolating results from field studies in a few areas to much larger regions, especially to the entirety of the vast ice sheets. Changes in the masses of the Antarctic and Greenland ice sheets may be major contributors to sea-level change. Unfortunately, the large-scale mass balances of the ice sheets are currently only poorly known. Estimates of their contributions to the global sea-level rise during this century are in the range of -1.4 to 1.4 mm year"1 for Antarctica and -0.4 to 0.4 mm year"1 for Greenland (Warrick et al., 1996)—not even the sign is known. GRACE will be sensitive to changes in the overall mass of Greenland and Antarctica to an almost unbelievable accuracy, equivalent to better than 0.01 mm year"1 of sea-level rise corresponding to each ice sheet! However, there are ambiguities in interpreting gravity signals over ice sheets because of problems in separating the effects of ice sheet changes from the effects of isostatic rebound (i.e. creep in the mantle in response to the geologically recent removal of ice sheets) and inter-annual variations in snow accumulation rates and atmospheric pressure, which preclude the attainment of that high accuracy. Fortunately, these ambiguities will be much reduced by the determinations of the present-day changes in the heights of the ice sheets that laser-altimeter measurements from NASA's planned ICES AT mission will yield. That is because, for a given mass increase, the ratio of surface-height change to mass change differs widely for isostatic uplift, changes in solid ice, changes in snow accumulation at the surface, and atmospheric pressure changes. The combined measurements will make it possible to determine the contribution of the ice sheets to sea-level rise with an error of only one or two tenths of a millimetre per year. (For a more extensive discussion see Bentley & Wahr, 1998.) Satellite gravity measurements are capable of yielding valuable information also about the mass balance of individual drainage systems within the Antarctic ice sheet, as well as of the ice sheet as a whole. Glaciologists could use such information to test models of ice dynamics, which are essential to the prediction of future sea-level change. Satellite gravity could be used to study secular, inter-annual, and seasonal changes in the mass of ice and snow in regions characterized by a large number of glaciers and ice caps. A prime example is the glacier system that runs from the Kenai Peninsula in southern Alaska down to the coastal ranges of the Yukon and British Columbia.

CONCLUDING REMARKS

Satellite gravity measurements can provide unprecedented views of the Earth's gravity field and, given sufficient duration, its changes with time. Not only can they provide a Gravity and the hydrosphere: new frontier 415

truly global integrated view of the Earth, they have, at the same time, sufficient spatial resolution to aid in the study of individual regions of the Earth. In many cases, the gravity data will be exploited best by assimilating them, together with other geophysical data, into geophysical models of known processes. Examples of processes that require ancillary data to better interpret the gravity data are structure and evolution of the mantle and plumes, structure and evolution of the crust and lithosphère (including regional deformation of the sea floor and continents, structure of passive margins, and the continent-ocean transition), and ice-sheet mass balance.

REFERENCES

Bentley, C. R. & Wahr, J. M. ( 1998) Satellite gravity and the mass balance of the Antarctic ice sheet. J. Gluciol. 44( 147), 207-213. Bettadpur, S. V. & Tapley, B. D. (1996) Accuracy assessments of dedicated geopotential mapping missions. Supplement to EOS, Trans. AGU 77(46), F140. Bromwich, D. H., Robasky, F. M., Keen, R. A. & Bolzan, J. F. (1993) Modulated variations of precipitation over the Greenland ice sheet. J. Climate 6(7), 1253-1268. Bromwich, D. H., Robasky, F. M., Cullather, R. 1. & Van Woert, M. L. (1995) The atmospheric hydrologie cycle over the Southern Ocean and Antarctica from operational numerical analyses. Mon. Weath. Rev. 123(12), 3518-3538. Dickey, J. O., Bentley, C. R., Bilham, R., Carton, J. A., Eanes, R. J., Herring, T. A., Kaula, W. M., Lagerloef, G. S. E., Rojstaczer, S., Smith, W. H. F., van den Dool, H. M., Wahr, J. M. & Zuber, M. T. (1998) Satellite gravity and the geosphere: contributions to the solid Earth and its fluid envelope. Eos, Trans. AGU 79(20), 237-243. Dukowicz, J. K. & Smith, R. D. (1994) Implicit free-surface method for the Bryan-Cox-Semtner ocean model. J. Geophys. Res. 99(C4), 7991-8014. Huang, J., van den Dool, H. M. & Georgakakos, K. G. (1996) Analysis of model-calculated soil moisture over the US (1931-1993) and applications to long range temperature forecasts. J. Climate 9, 1350-1362. NASA ( 1987) Geophysical and geodetic requirements for global gravity field measurements, 1987-2000. Report of a Gravity Workshop, Colorado Springs, Colorado, USA. NASA Geodynamics Branch, Division of Earth Science and Applications, Washington, DC. NRC (1997) Satellite Gravity and the Geosphere: Contributions to the Study of the Solid Earth and its Fluid Earth. National Academy Press, Washington, DC. Nerem, R. S., Jekeli, C. & Kaula, W. M. (1995) Gravity field determination and characteristics: retrospective and prospective. J. Geophys. Res. 100(B8), 15,053-15,074. Stanton, R., Bettadpur, S., Dunn, C, Renner, K.-P. & Watkins, M. (1998) Gravity Recovery and Climate Experiment (GRACE) science & mission requirements. Document 327-200, ./PL D-I5928. Jet Propulsion Lab., California Institute of Technology, Pasadena, California, USA. Tapley, B. (1997) The Gravity Recovery and Climate Experiment (GRACE). EOS, Trans. AGU 78(46), Supplement, 163. Wahr, J., Molenaar, M. & Bryan, F. (1998) Time-variability of the Earth's gravity field: hydrological and oceanic effects and their possible detection using GRACE. J. Geophys. Res. 103, 30205-30230. Warrick, R. A., Le Provost, C, Meier, M., Oerlemans, J. & Woodworm, P. L. (1996) Changes in sea level. In: Climate Change 1995: The Science of Climate Change (ed. by J. i\ Houghton, L. G. Meira Filho, B. A. Callander, N. Harris, A. Kattenberg & K. Maskell) (Contribution of Working Group I to the Second Assessment Report of the Intergovernmental Panel on Climate Change), 359-^105. Cambridge University Press, Cambridge, UK.

Received 1 December 1998; accepted 10 February 1999