Detectability of variations in continental water storage from satellite observations of the time dependent gravity field

Continental water storage is a key variable in the Earth system that has never been adequately monitored globally. Since variations in water storage on land affect the time dependent component of Earth's gravity field, the NASA Gravity Recovery and Climate Experiment (GRACE) satellite mission, which will accurately map the gravity field at 2–4 week intervals, may soon provide global data on temporal changes in continental water storage. This study characterizes water storage changes in 20 drainage basins ranging in size from 130,000 to 5,782,000 km2 and uses estimates of uncertainty in the GRACE technique to determine in which basins water storage changes may be detectable by GRACE and how this detectability may vary in space and time. Results indicate that GRACE will likely detect changes in water storage in most of the basins on monthly or longer time steps and that instrument errors, atmospheric modeling errors, and the magnitude of the variations themselves will be the primary controls on the relative accuracy of the GRACE‐derived estimates.


Introduction
Soil moisture, groundwater, snow and ice, lake and river water, and vegetative water are the principal components of continental (or terrestrial, total) water storage.Although it constitutes only about 3.5% of the water in the hydrologic cycle, continental water storage has a tremendous influence on climate and weather as well as being fundamental to life on land. .
The importance of soil water in Earth's climate system has been demonstrated using general circulation models (GCMs) and documented by numerous authors [e.g., Manabe, 1969; Shukla and Mintz, 1982;Milly and Dunne, 1994;Dirmeyer, 1995] (see also Entekhabi et al. [1996] for a recent review).For example, soil water links the water, energy, and biogeochemical cycles; its high heat capacity provides thermal inertia over multiple timescales; and it fuels evapotranspiration, which helps to sustain storms through the process of precipitation recycling [Brubaker et al., 1993;Eltahir and Bras, 1996].
Frozen water and liquid water stored below soils in aquifers play important roles in the Earth system and hold practical significance for society.Seasonal melts replenish soils and streams, while groundwater provides base flow to streams and sustains deep-rooted plants through periods of drought.Predicting the magnitudes of spring melts and the availability of groundwater is critical for natural hazard preparedness and for agricultural and domestic water resources management.
Mass redistribution associated with changes in water storage on land has additional effects on the Earth system beyond those described above.For example, Chao and O'Connor [1988] and Kuehne and Wilson [1991] showed that changes in terrestrial water storage effect Earth rotation variations, and Chen et al. [1998] showed that the redistribution of water from the continents to the oceans is the primary driver of sea level nique.Toward that end, 20 continental-scale drainage basins were identified for detailed study.Mean changes in water storage were computed on monthly, seasonal, and annual bases for each basin using 12 modeled data sets.Uncertainties in hypothetical GRACE-derived water storage variation measurements were estimated as the sum of three individual error sources.The results presented in this paper have implications for how the detectability of water storage variations by GRACE and the level of precision of GRACE-derived AS estimates change with geographic location and with the time period A T.

Background
The gravitational force experienced at the surface of Earth varies in space and time, so that the gravity field of the whole Earth can be visualized as a not-quite-smooth ellipsoid.Spatial variations in Earth's gravity field arise primarily from irregularities in the mass distribution near the surface of Earth, e.g., continents, mountains, and depressions in the crust.The Earth's gravity field is said to have both static and time variable components, the static component being orders of magnitude stronger and encompassing all the factors that only vary on geologic timescales, e.g., the total mass of Earth and the distribution of the continents.Jeffreys [1952] was among the first to report the existence of the time variable component, noting that mass movements such as ocean tides could effect temporal changes in the gravity field.At that time, spatial variations in the gravity field were observed primarily with the aid of pendulums.
Mapping spatial irregularities in Earth's gravity field was facilitated by the first artificial satellites, which began orbiting in the late 1950s.Satellite tracking via optical and Doppler techniques allowed scientists to compute departures from predicted orbits, and these departures were attributed to previously unobserved factors affecting the paths of the satellites, irregularities in the static gravity field in particular.For the past two decades, orbit determination has been accomplished by ground to satellite laser ranging.The increased accuracy afforded by this technique has allowed more detailed assessments of the gravity field.Yoder et al. [1983] reported that the orbit of the LAGEOS satellite was sensitive to temporal variations in the gravity field in addition to static, spatial variations.They believed that the primary sources of these temporal variations were redistributions of groundwater and air mass and changes in sea level.Gutierrez and Wilson [1987]  tracking integrated with Global Positioning System receivers will measure range perturbations between the satellites caused by spatial variations in the gravity field, while nongravitational accelerations will be monitored by onboard accelerometers [Tapley, 1997].The high degree of precision afforded by this technique will enable GRACE to map the gravity field at intervals of 2 weeks or longer, with an accuracy equivalent to a few millimeters of water (note that 1 mm water depth is equivalent to 1 kg/m 2 water mass, given a constant density of 1 g/cm2).
In order to use GRACE gravitational measurements to estimate changes in continental water storage, certain operations will be necessary.The following describes these operations in a very general manner (see Wahr et al. [1998] for a more detailed explanation).For a particular averaging period (the time period during which GRACE observations contributing to a single global gravity field are gathered), GRACE observations will be used to estimate thousands of coefficients of a spherical harmonic expansion that describes Earth's total (static plus time variable) gravity field as the shape of a geoid.To estimate changes in water storage, a global field of temporal gravitational variations must first be computed from two such total gravity fields.Postglacial rebound (PGR) and changes in the distribution of atmospheric mass also will influence the time dependent gravity signal over land, so that models of surface pressure changes and PGR must supply the data necessary to remove their effects.On monthly to annual timescales, other factors influencing the time variable gravity signal over inland regions (e.g., the solid Earth tide) are assumed to be negligible.This paper advances the investigation of GRACE's potential to produce accurate estimates of changes in continental water storage in three ways.First, the analysis is global, with 20 regions of varying dimate and spatial extent examined individually.Second, to improve understanding of the nature of terrestrial water storage variations themselves, 12 global time series are assessed with a critical eye toward the realism of the estimates, with results from five independent water balance studies included for comparison.Third, GRACE's potential is evaluated for three timescales commonly encountered in hydroclimatology: 30, 90, and 365 days.

Study Areas
Twenty continental-scale drainage basins were selected for detailed study.These are shown in Figure 1 and listed in Table 1 from largest to smallest drainage area (this is the order used in most of the subsequent figures and tables).Drainage basins, rather than grid squares or circular regions, were chosen as the units over which to analyze GRACE's potential to measure variations in terrestrial water storage because they are fundamental subdivisions of the land surface from a hydrological perspective.Furthermore, the future use of GRACE data to compute changes in storage over watersheds will facilitate comparisons to runoff measurements.The 20 basins were chosen to encompass an array of climates, from wet equatorial (Amazon) to dry subtropical (Murray-Darling) to boreal/ tundra (Ob).Also desirable was the existence of Global Energy and Water Cycle Experiment (GEWEX) projects and other large-scale experiments in the regions (e.g., in the Mississippi, Mackenzie, and Amazon basins).The basins range in size from 5,782,000 to 130,000 kJn 2 and include four internally draining basins.They were delineated with the aid of a geographic information system using the Terrain Base 5 arc min global digital elevation model [Row et al., 1995].

Water Storage Data
Twelve modeled data series of soil moisture and snow water were acquired.Ten series were modeled by Global Soil Wetness Project (GSWP) contributing groups on 1 ø global grids, spanning the 24 month period beginning January 1, 1987 [Dirmeyer et al., 1999].GSWP is an ongoing GEWEX project that serves as a pilot study of the feasibility of producing a global data set of soil wetness for use in global climate models.Water storage changes ZIS were derived over specific intervals zX T (i.e., the time step) for each of the time series of water storage S described above.This was necessary because GRACE will not measure the total magnitude of water storage in the land at any given time; rather, GRACE will allow changes in water storage over specific intervals to be determined by comparing gravity fields measured over different averaging periods.Note that when time series of water storage changes are derived by comparing GRACE measurements from consecutive averaging periods, the measurement averaging period and the series time step ZIT will be equivalent in length; therefore in this paper the descriptors "monthly," "seasonal," and "annual" when modifying "change" or "error" will refer to both the averaging period and the time step.
The following approach was used to construct time series of water storage changes from the modeled data.First, because

GRACE
will not be able to differentiate between soil water and snow water, the two were combined to represent total terrestrial water storage.Second, changes in storage were computed as the backward difference between average terrestrial water storage for each 30-, 90-, or 365-day period corresponding to a GRACE measurement averaging period, and average terrestrial water storage for the immediately preceding period, for the duration of each modeled time series and for each of the basins.This approach was designed to be consistent with the manner in which GRACE will measure water storage where E.q is the atmospheric error in the storage change and E.q,1 and E.q,2 are the atmospheric errors in GRACE measurements for averaging periods 1 and 2, respectively.While temporal correlation in the atmospheric errors may exist, it is assumed to be small (K.Trenberth, NCAR, personal communication, 1998).Equation (3) results in an estimate of the atmospheric uncertainty that is conservative in that it does not account for future improvements in the models.Uncertainty resulting from the use of modeled PGR rates, EpcR, was assessed as a uniform 20% error in the rebound rates of a PGR model [Peltier, 1994[Peltier, , 1995]], which were converted to equivalent units of water mass change.Total uncertainty in the change in storage ET was taken as the sum of the Terrestrial water storage data produced by the 10 GSWP models appear to be more realistic than the reanalysis data.Figure 3  Additional information on water storage variations was derived from five terrestrial and combined atmosphericterrestrial water balance studies [Matsuyarna, 1995;Oki et al., 1995;Rasrnusson, 1968;Roads, 1994;Ropelewski andYarosh, 1997, 1988] in order to compare the GSWP time series to  4).
Nevertheless, the amplitudes of the storage cycles determined by these water balances should be, for our purposes, reasonable approximations of the actual amplitudes.Note that only Oki et al. [1995] extended their study beyond North America.GSWP amplitudes are generally smaller but rarely by more than 50%.From this analysis it seems reasonable to conclude that actual variations in total terrestrial water storage may be underestimated to some extent by GSWP modeled soil moisture and snow water variations, but these estimates would be of the correct order of magnitude.Further, the use of GSWP estimates in this study is well justified: when the estimated errors derived in section 3.4 are imposed upon GSWP estimates of changes in water storage, use of these lower amplitude storage estimates may provide a conservative, upper bound on relative error.

Chao
Table 4 also compares the average GSWP estimate of the annual change in continental water storage over the Mississippi River basin to estimates of the annual change from the water balance studies.Six other estimates are shown.An annual change is defined here as the difference between two consecutive values of mean annual water storage.The GSWP annual variation, 18 mm, is smaller than all of the water balance estimates, which range from 23 to 58 mm, but it is within the same order of magnitude.As before, it is speculated that the GSWP value is.smaller because it only includes variations in surface soil and snow water storage and because it was computed as the change between two drier-than-normal years.A longer time series would be more appropriate for determining a representative value of the annual variation.Lacking other estimates for comparison, it is difficult to draw conclusions about the GSWP annual variations seen in the other basins.Considering that these variations do not include the effects of deeper soil moisture and groundwater, it is hypothesized that they are low, order-of-magnitude estimates of typical annual variations, although some may be substantially smaller than the true mean variations.

Potential Accuracy of GRACE-Derived AS Estimates
As described in section 3.3, uncertainty in the GRACEderived estimates of water storage changes will arise from also imply that annual variations in water storage will be undetectable by GRACE in seven of the basins, including the Amazon.However, these water storage change estimates may not be reliable because in addition to neglecting deeper groundwater they result from a single year-to-year cycle.

Discussion
Table 7 lists the number of time intervals during which water storage changes are detectable by GRACE (relative error, Er/AS < 1) within each basin for monthly, seasonal, and annual averaging periods, given the data in Figures 4-6 Relative error (uncertainty), and therefore detectability, in the GRACE-derived estimates will depend mainly on the size of the region (which is inversely related to the instrument uncertainty), the atmospheric modeling errors, and the magnitude of the variations themselves.The temporal resolution of the change in storage estimates will also affect relative uncertainty.Monthly total uncertainty is always larger than seasonal uncertainty, which in turn, is larger than annual uncertainty because the instrument and atmospheric errors decrease with increasing averaging period (long-term average modeled pressure estimates should approach measured mean values).PGR errors show the opposite trend, increasing linearly with timescale, but as seen in Table 5, uncertainty due to PGR is typically 2 orders of magnitude smaller than total uncertainty in the regions of this study.
In the Wisla, Great Salt Lake, and Odra basins, where water storage changes are expected to be undetectable (i.e., AS _< Er), instrument errors will be large and will tend to dominate Future circumstances, such as the evolution of the mission specifications, advances in technology, and improvements in atmospheric modeling capability, may influence the uncertainty in GRACE-derived water storage change estimates.Furthermore, the effects that hourly to daily water storage and atmospheric mass variations might have on the gravity measurements remains to be explored.It should be recalled that total terrestrial water storage variations may be significantly larger than those represented in the GSWP data, so that water storage variations may be detectable in more of the basins and at a higher level of relative accuracy than indicated by this study.The lack of a global-scale groundwater fluctuation data set has precluded a more thorough analysis of variations in total terrestrial water storage and the potential for monitoring these variations.The water storage changes listed in Table 6 may have been quite different if groundwater fluctuations were taken into account.This inadequacy implicates the need for further study in this area, but it also exemplifies the shortcomings in our basic understanding of large-scale hydrologic processes, some of which may be reconciled by GRACE.

Summary
Global time series of continental water storage were obtained from 12 modeled data sets.Two sources were eliminated because they were not believed to be representative of actual conditions.The 10 remaining data sets compared favorably with independent water balance studies and were shown to provide conservative estimates of actual water storage variations.Based on these data sets, time series of changes in continental water storage were produced for 20 drainage basins ranging in size from 130,000 to 5,782,000 km 2 on monthly, seasonal, and annual time steps.The modeled changes in water storage were compared to the expected total uncertainty in GRACE-derived estimates of the changes.Estimated errors from the GRACE instruments, atmospheric modeling, and postglacial rebound modeling all contributed to the total uncertainty estimates.The primary controls on the relative accuracy of GRACE-derived water storage change estimates were determined to be instrument errors and therefore the area of the region, atmospheric modeling errors in the region, and the magnitude of the variations themselves.Monthly changes in continental water storage were predicted to be detectable on average in 16 of the 17 basins of area 201,000 km 2 and greater; seasonal changes were predicted to be detectable on average in 17 of the 18 basins of area 184,000 km 2 and greater; and annual changes were predicted to be detectable in 13 of the 17 basins of area 201,000 km 2 and greater.
water balance for each basin, based upon archived precipitation data and published coefficients for runoff and evapotranspiration.By comparing their solutions with the observed orbits, they were able to confirm that seasonal variations in terrestrial water storage do influence the time variable gravity field enough to induce predictable satellite orbit perturbations.Chao and O'Connor [1988] reached a similar conclusion in their study of the effects of seasonal changes in surface water on Earth's rotation, length of day, and gravity field.More recent studies have attempted to define the global gravity field and its fluctuations more precisely [e.g., Ries et al., 1989; Nerem et al., 1993], but significant future improvements demand the utilization of advanced technologies.Recently, Dickey et al. [1997] assessed several possible mission scenarios for a dedicated satellite gravity mission and highlighted the potential benefits to research in hydrology (i.e., quantifying changes in continental water storage using gravity field observations), oceanography, and solid earth processes, as well as geodesy.Mission scenarios were evaluated based on trade-offs between expected mission lifetime at a particular altitude, measurement resolution, and maturity of the required technologies.Dickey et al. [1997] helped to crystallize the plans that soon became the Gravity Recovery and Climate Experiment.GRACE is sponsored jointly by NASA, as part of its Earth System Science Pathfinder Project, and two German agencies: GeoForschungsZentrum Potsdam and Deutsche Forschungsanstalt fiir Luft und Raumfahrt.Mission design is being led by scientific teams at the University of Texas Center for Space Research and NASA's Jet Propulsion Laboratory.GRACE is scheduled for launch in July 2001 with a nominal duration of 5 years.The instrument will consist of two satellites in a tandem orbi't 100-400 km apart at about 450 km altitude.Microwave

Figure 1 .
Figure 1.Locations of the 20 continental-scale drainage basins examined in this study (Robinson projection).

Figure 2 .
Figure 2. Instrument errors (millimeters of water equivalent) versus area of the region for monthly, seasonal, and annual averaging periods.

Figure 3 .
Figure 3. Two-year time series of terrestrial water storage (as deviation from mean) averaged over the areas of the drainage basins.Included are results from 10 GSWP models.See Table 2 for definition of model name abbreviations.
into this matter revealed that the ECMWF model does not allow soil moisture in the deeper layers to vary above wilting point values even during episodes of flooding, as in the midwestern United States in 1993.Because of this unrealistic constraint, water storage data from ECMWF were omitted from this analysis.In comparison, the NCEP/NCAR Reanalysis allows soil moisture to vary over a larger, more realistic range.However, examination of this time series showed that only minor variations in the amplitude and timing of the annual cycle exist, resulting from a dependence on a prescribed climatology.In the NCEP/NCAR model, soil moisture is nudged toward the Mintz and Serafini [1992] climatology, which is not governed by the model water and energy balances, and additionally, no observations which directly affect soil moisture are assimilated into the model [Kalnay et al., 1996].Therefore the NCEP/ NCAR water storage data were also eliminated from this analysis.

Figure 4 .
Figure 4. Two-year time series of GSWP median monthly terrestrial water storage changes, with error bars that represent the total uncertainty in GRACE-derived estimates of the change in water storage.

Figure 5 .Figure 6 .
Figure 4. (continued) estimate being 52 mm.That the GSWP amplitude is at the low end of the range may be explained by two factors: (1) it only reflects surface soil moisture and snow variations, while results from the independent water balance studies implicitly include deeper soil water, groundwater, vegetative water, and lake and river channel storage variations; and (2) the GSWP years, 1987 and 1988, were dry in terms of precipitation for the Mississippi basin, which may have caused storage variations to be subdued.Comparing the estimated amplitudes of Oki et al. [1995] to those from GSWP in 17 other basins shows a similar result.

Figure 7 .
Figure 7. Mean monthly atmospheric uncertainty, computed as the 15-year average difference between ECMWF and NCEP/NCAR model values divided by 2 m, for each of the 20 drainage basins and each month of the year.
. The table shows that monthly water storage variations are detectable between 50% and 91% of the time in 15 of the 17 basins of area 201,000 km 2 and greater; that seasonal variations are detectable between 50% and 100% of the time in 17 of the 18 basins of area 184,000 km 2 and greater; and that annual variations are detectable in 13 of the 17 basins of area 201,000 km 2 and greater.Close inspection of Table 6 reveals that when mean error is compared to mean change in storage, a similar pattern emerges: water storage variations are detectable in 16, 17, and 13 basins on monthly, seasonal, and annual timescales, respectively.

Figure 8 .
Figure 8. Global map of the annual amplitude of the terrestrial water storage cycle, based on data from the Japan Meteorological Agency's Modified SiB model (Robinson projection).

CSU SiB2 NOAA National Center for Environmental Protection M6t6o-France Centre National de Recherches M6t6orologiques Japan Meteorological Agency Hydrological Sciences Branch, NASA Goddard Space Flight Center (GSFC) Mesoscale Atmospheric Processes Branch, NASA/GSFC Climate and Radiation Branch, NASA/GSFC Center for Ocean-Land-Atmosphere Studies Center for Climate System Research, University of Tokyo/National Institute for Environmental Studies Department of Hydrology and Water Resources, University of Arizona Department of Atmospheric Science, Colorado State University Ten independent groups used a common data set of model parameters, meteorological observations, and analyses to drive state-of-the-art land surface models, which produced fields of soil moisture, snow, and other variables. The 10 GSWP con- tributing groups and their models are listed in Table 2. The two other series are products of the European Centre for Medium- Range
Weather Forecasts (ECMWF) Re-analysis [ECMWF, 1996] and the joint National Center for Environmental Prediction (NCEP) and National Center for Atmospheric Research (NCAR) Reanalysis Project [Kalnay et al., 1996].