Methodology

Methodology

The Gravity Recovery and Climate Experiment (GRACE) satellite mission has been monitoring Earth's time variable gravity field with extremely high precision since March 2002. For the first time, a space-based system is capable of resolving changes in the Earth’s gravity field to permit the direct monitoring of surface mass flux of sufficient temporal and spatial resolution to be considered another unique form of remote sensing of the four dimensional Earth system. Fields of terrestrial water storage variations (or, similarly, anomalies) are now being derived from GRACE gravity observations. This new, independent source of data is valuable for refining our understanding of the terrestrial water cycle, because it provides information on water stored at depths not resolvable using space-borne radar or radiometers. This portal is devoted to making these data specifically available to the hydrology and broader Earth science community.

Currently, a major thrust of time variable gravity recovery from GRACE is focused on monthly gravity recovery through global spherical harmonic solutions [Tapley et al, 2004a]. Although this has been largely successful, this approach has not exploited the fundamental resolution of the GRACE observations and the standard products produced by the Project must undergo some form of a posteriori smoothing to cope with spatial aliasing to eliminate spurious, largely north-to-south striping features. At NASA/Goddard Space Flight Center, we have developed a method for local time-dependent gravity recovery through mass concentration blocks (mascons) which yields submonthly resolution while preserving high spatial resolution.

Mascon solutions from GRACE that are based on block parameters enjoy some advantages that are either difficult or impossible to exploit in global spherical harmonic solutions. The mass anomalies (with respect to a multi-year mean gravity field) are directly solved and require no additional a posteriori processing, smoothing, or other forms of manipulation which affect their quantitative assessment. Also, parameters describing the mean value of a gravity parameter in a block over an interval of time easily lend themselves to a type of least squares neighbor constraint which helps stabilize the solution within the estimation process itself. This type of constraint causes pairs of parameters which describe the same phenomenon but at different times or in close spatial proximity to have a defined correlative relationship and enables improved temporal resolution [e.g.Luthcke et al, 2003].These constraints permit solutions every 10 days. The mathematical details of the mascon representation and constraints are provided below in the Mathematical Description.

Our methodology for the analysis of the GRACE data and estimation of mass anomalies directly from the K-Band intersatellite range-rate data is described in Rowlands et al, (2005). There are three innovative approaches which we have introduced in our analysis of the GRACE data:

The mascons and orbit parameters are exclusively estimated from the KBRR data themselves. This is made possible by solving for a reduced set of orbit parameters that completely accommodate the orbit sensitivity as projected into the inter-satellite vector and its orientation (c.f. Rowlands et al, 2002).
Through an extensive calibration procedure, we are able to remove spurious values, biases, and trends in the accelerometer data which are used to isolate the gravitational forcing experienced by the GRACE satellite pair. When the corrected accelerometer data are used, we find it totally unnecessary to introduce extraneous empirical parameters to “correct” the KBRR data. As far as we can discern, all other investigations are solving for empirical correction parameters for the KBRR data which degrades their strength in gravity solutions
We directly solve for the mascons and orbit parameters in a simultaneous least squares solution. This yields a direct estimate of the mass flux over a given region over a specific time interval. Since we are not solving for a global functional representation of the gravity model, we can restrict the KBRR data being analyzed to the local area of interest.

Our analysis method is able to provide sub-monthly (approximately 10-day) measures of the change in continental water storage over all of the Earth’s land areas with a resolution of 4x4 degrees at the equator. While a finer spatial resolution is possible over higher latitude regions, we are initially releasing a 4x4 degree grid of anomalies over all continental regions over the entire duration of the GRACE mission where data are available. The mass flux anomalies are represented as a surface layer of water within each rectangular cell and have accuracies of ±1-3 cm. Given the polar character of the GRACE orbits, as the ground tracks converge and data density significantly increases at higher latitudes, improved spatial resolution will be obtained for ice covered regions like Greenland and Antarctica which will be reported elsewhere. For ice covered regions we use the slope of the topography to define specific drainage basins which become the boundaries of the mascons (see Luthcke et al, 2006). This effort will provide critical environmental data records especially for the hydrologists that were not previously available.

The Earth is a dynamic system of land, ocean, atmosphere and cryosphere interactions. Mass movement is a key component of this system as each of these components of the Earth’s system responds to various forms of forcing and interact with one another. Figure 1 below provides insight into the forms of mass motion ongoing within the Earth’s systems in terms of their spatial and temporal components.

Figure 1 Temporal and Spatial Resolution of Mass Flux Phenomena of Geophysical Interest

For 10 day changes on approximately 400 km time scales, the dominant mass movement arises in the hydrological system, but also changes in regional atmospheric pressure, and solid Earth and ocean tides are important on these spatial and temporal scales. Thereby, to isolate hydrospheric signals, we must eliminate tidal and atmospheric variations on comparable time scales. This is accomplished using forward modeling approaches. The relatively rapid seasonal and sub-seasonal mass movements are occurring against a background of much longer period effects, some of which appear secular, like the post glacial rebound ongoing in the Earth’s lithosphere and upper mantle as the Earth returns to isostatic equilibrium after the melting of the ice during the last ice age.

We are fortunate that the Earth and ocean tides are extremely well known and can be modeled in our GRACE analyses. This removes these signals to a very high degree of accuracy. Atmospheric pressure changes are also very well known over the continents where direct barometric readings are continuously taken and reported. They are less well known over the oceans, where the atmospheric loading is somewhat compensated for by the resulting flow in the ocean as it responds to this loading. While the ocean’s response is approximated by an “inverted barometer”, the accuracy of the GRACE system requires a significantly more sophisticated modeling of the ocean’s response. In our analysis, we model the atmospheric mass anomalies over the entire Earth’s surface with a resolution of 6 hrs. This allows us to capture the dominant semi-diurnal (S2) and diurnal (S1) atmospheric “tides”. To a very significant extent, the forward modeling for atmospheric pressures removes these signals over the continents. Accompanied by our utilization of KBRR data limited to the specific region of interest, modeling over the ocean is of small concern to the analysis reported herein. By applying these forward models in a rigorous fashion, the mass anomalies we recover isolate the resulting hydrological signal, including the very important ground water level changes.

To accompany the 10-daily, 4° gridded mass anomaly fields derived from GRACE, numerically modeled soil moisture and snow mass fields from the Global Land Data Assimilation System (GLDAS; Rodell et al., 2004a) are provided with identical spatial and temporal characteristics. The availability of both products greatly facilitates interpretation of the GRACE data from a hydrological perspective. These independent GRACE-derived hydrological mass flux estimates provide a significant advancement to hydrological system monitoring especially when coupled with improved hydrometeorological flux estimates obtained from other remote sensing techniques (MODIS, TRIMM, AMSR). The products to be derived from GRACE expand and strengthen the interconnectedness and reuse of key satellite system technologies and make these products available within the wider Earth System Science communities.