To date, GRACE has principally been used to improve both stationary and monthly-resolved spherical harmonic models of the gravity field (Tapley et al., 2004; Wahr et al., 2004). When a common spherical harmonic model of the gravity field is computed from multiple years of GRACE data, like GGM02C, the resulting field is an improvement of nearly two orders of magnitude over any pre-GRACE fields like EGM-96 (Lemoine et al, 1998). Monthly harmonic models have been used as a proof of concept to demonstrate the resolving power of GRACE to monitor mass flux globally. Although monthly gravity models have produced intriguing results, information at submonthly time scales is lost and spatial and temporal aliasing through the estimation of static global parameters has been a major stumbling block for the exploitation of the GRACE data. We have investigated the origins of these aliasing effects and have developed an analysis procedure which significantly reduces their manifestations.
NASA/Goddard Space Flight Center has produced new monthly estimates of the Earth's gravity field which are based on the following innovations:
- These monthly solutions are determined solely from GRACE inter-satellite range-rate measurements
- We utilize an improved method to calibrate the GRACE accelerometers
- We have adopted a “baseline” state parameterization which are the reduced set of orbit parameters which isolate those parts of the orbit position that the GRACE intersatellite data can sense (Rowlands et al, 2002)
- We apply and/or solve for no empirical parameters on the KBRR data
Our methodology exploits the inherent power of the inter-satellite range-rate data at the expense of the GPS data, which are used solely for establishing an accurate orbital reference and for calibrating accelerometers. Resulting gravity solutions show significantly less error than previously published GRACE solutions, especially for spherical harmonic terms of degree 2 and terms of order 15,16 (Luthcke et al, 2005).
The GRACE satellites are equipped with two basic tracking systems. A K-band inter-satellite link provides information about the relative motion of the GRACE satellites while GPS receivers tie each GRACE satellite to the terrestrial reference frame. Most global fields derived from GRACE, as in Tapley et al. (2004a and 2004b), have been based on solutions that combine tracking data from both systems. However, the inter-satellite measurement is of much higher precision (nearly 3 orders of magnitude) than GPS data and can degrade the value of the KBRR data when included in the spherical harmonic recovery. We have validated the processing used in Rowlands et al. (2005) by extending that processing to the estimation of monthly global gravity fields comprised of standard Stokes coefficients. These fields have been compared to the GRACE project monthly fields in Luthcke et al, (2006) and have significantly less aliasing. We find that our new fields compare very closely with the GRACE project fields from degree 5 through 12. However, the new fields have two significant improvements: (1) more realistic recovery of information at the very lowest degrees and (2) fewer problems above degree 14 especially at order 15 and 16 (the source of North-South streaking seen in standard GRACE models). We relate these improvements to the two major differences in our processing: (1) a new parameteriztion of the accelerometer calibration and K-band inter-satellite range-rate (KBRR) reduction that does not require the estimation of KBRR measurement empirical parameters and (2) the exclusion of GPS data during gravity reductions.
Figure 1 compares the variance of the GRACE monthly spherical harmonic models with respect to the annual mean field over the time period of July 2003 through July 2004 for our GSFC and the University of Texas’ Center for Space Research (CSR) Release 1 fields. The higher variance seen for the resonance orders (14-15, 30-31, 44-45) in the CSR models, we believe, arise from the corrupting influence of the GPS data and the need to give additional weight to these data when combining them with KBRR in these solutions.
Figure 1. Coefficient Variances (for each degree and order) of 12 monthly fields with respect to the 12 month average for Center for Space Research (CSR) and GSFC solutions. Much higher noise levels, especially for resonance orders are seen in the CSR fields
It should be noted that our parameterization of the accelerometer calibration and KBRR reduction is quite different from previous investigations. Our approach results in KBRR residuals that do not require additional adjustment of empirical KBRR measurement model parameters such as those used in Tapley et al. 2004a and Reigber et al. 2005. For example, Tapley et al. 2004a estimate the following empirical measurement model parameters: KBRR bias and bias drift every half orbital revolution and KBRR one-cycle-per-revolution (1CPR) parameters every orbital revolution. In total our calibration and KBRR reduction process uses nearly a factor of three times fewer parameters than that found in Tapley et al 2004a and a factor of 1.5 times fewer than Reigber et al. 2005 for each gravity solution. Presumably, our processing strategy better preserves the low degree gravitational signal in the GRACE inter-satellite range-rate observations by not removing signal from the KBRR data through the estimation of empirical measurement parameters
In an attempt to isolate the geophysically unreasonable signal, or presumably noise in these solutions, we have removed a trend, annual and semi-annual signal from the monthly equivalent water fields computed from the monthly gravity fields out to degree and order 20. This model accounts for most of signal variance, thus leaving mostly noise and stochastic variability. Figure 2 presents the RMS of these residual monthly fields over our test time period and shows the CSR Release 1 solutions have significantly more noise variance than the GSFC solutions. The CSR fields have a global residual RMS of 3.7 cm and a maximum of 12.0 cm, while the GSFC fields have a global residual RMS of 2.2 cm and a maximum of 5.6 cm. The variance in the CSR is dominated by north south streaking corresponding to the problems throughout orders 15 and 16 and particularly at degrees 15 and 16 as observed in the CSR coefficients of these degrees and orders (Figure 1)
Figure 2 A comparison of aliasing in the GSFC and CSR monthly gravity fields after removal of the dominant geophysical signals -- a linear trend, annual and semi-annual term for each harmonic as compared to the mean annual field.
