Low degree gravitational changes from earth rotation and geophysical models

1. Introduction

[2] Earth's rotational changes at periods of a few years and less are forced mainly by mass redistribution and movement in the atmosphere, oceans, and hydrosphere/cryosphere, via the conservation of angular momentum of the Earth system. These polar motion and length of day (LOD) excitations may be divided into contributions from (1) surface mass load variations due to changes of atmospheric surface pressure, continental water storage (including snow and ice), and ocean bottom pressure, and (2) mass movements associated with wind and ocean current variations causing angular momentum exchange between the solid Earth and the surrounding geophysical fluids. Angular momentum exchange related to flow in terrestrial rivers and streams is likely to contribute negligibly.

[3] When rotational deformation on the gravity field is neglected, excitations of X, Y, and LOD due to surface mass load variations are proportional to changes in degree 2 spherical harmonic (Stokes) coefficients of the gravity field, ΔC₂₁, ΔS₂₁, and ΔC₂₀ [e.g., Wahr, 1982; Eubanks, 1993; Chen et al., 2000]. Thus estimates of ΔC₂₁, ΔS₂₁, and ΔC₂₀ from accurately measured Earth rotational changes are possible, provided that we can effectively estimate and subtract wind and ocean current contributions. Earth rotation variations are observable at time scales as short as a few hours by some techniques (such as GPS), providing unique measurements of high-frequency variations in the degree 2 gravity fields. Neither satellite laser ranging (SLR) nor GRACE is capable of resolving gravity variations at such high frequencies. The relationship between normalized ΔC₂₁, ΔS₂₁, and ΔC₂₀ and mass load driven X, Y, and LOD excitations (χ_i^mass, i = 1, 2, 3) is [Eubanks, 1993 (equation A3-1, 3-3); Chen et al., 2000 (equation 1)],

in which, M and R are the mass and mean radius of the Earth, C and A the two principal inertia moments of the Earth. k₂′ is the degree 2 load Love number (−0.301), accounting for elastic deformational effects on gravitational change. Equation (1) is a modified version of the equation (1) of Chen et al. [2000] with normalization and load deformation are considered. A recent study by Dickman [2003] derived slightly different representation of the computation of effective excitations, which will lead to a few percents of difference in equation (1). χ_i^mass can be computed from χ_i^mass = χ_i^obs − χ_i^motion, where, χ_i^obs are observed excitations computed from X, Y, and LOD, collectively termed Earth Orientation Parameters (EOP) time series, and χ_i^motion are excitations by atmospheric winds and ocean currents that must be estimated from atmospheric and oceanic models. Chen et al. [2000] estimated degree 2 gravitational changes from rotational variations in this way, and compared them with SLR observations and geophysical model predictions. They found that at intraseasonal time scales, EOP-derived ΔC₂₁ and ΔS₂₁ are probably superior to SLR estimates, because they agreed better with atmosphere, ocean, and water storage model predictions. However at seasonal time scales, the conclusion was less strong.

[4] The Chen et al. [2000] study was clearly limited by the oceanic and hydrological models available at the time. For example, the parallel Ocean Climate Model (POCM) [Stammer et al., 1996] had been reported to under-estimate oceanic mass variability [e.g., Johnson et al., 1999]. The hydrologic estimate has also been shown to be poor, as it was computed from soil and snow fields of the National Center for Environmental Prediction (NCEP) reanalysis atmospheric model. NCEP soil and snow fields significantly over-estimate water storage variability [e.g., Chen et al., 2001].

[5] Recent advancements in both ocean general circulation models (OGCM) and hydrological models provide an opportunity to re-estimate time variations in degree 2 gravity coefficients and compare them with EOP-derived values. We use here the data assimilating OGCM [Fukumori et al., 2000], developed at NASA's Jet Propulsion Laboratory, as a partner in the Estimating the Circulation and Climate of the Ocean (ECCO) program. Hereafter this model is denoted simply as ECCO. ECCO is used to estimate ocean current contributions as well as ocean mass redistribution. A recent study by Chen et al. [2003a] indicates that the data assimilating ECCO model is superior to many previous OGCMs in its ability to model large scale current and ocean bottom pressure (OBP) variability. Soil water storage fields are taken from the Land Data Assimilation System (LDAS) model, a surface hydrological model newly developed at the NCEP Climate Prediction Center (CPC).

2. Data and Models

3. Results

[11] The 3 panels of Figure 1 (a, b, c) show ΔC₂₁, ΔS₂₁, and ΔC₂₀ time series (in blue curves) estimated from the residual excitations of X, Y, and LOD. Geophysical model predictions, the sum of atmosphere, ocean, and water (AOW) effects are shown in red. All time series are interpolated to 10-day intervals. EOP-derived ΔS₂₁ matches the geophysical model predictions almost perfectly over a broad frequency band and ΔC₂₁ estimates agree nearly as well. The EOP-derived ΔC₂₀ show a large semiannual signal and some interannual variability during 1997–1999. This semiannual variation is not likely due to ΔC₂₀ change, but instead from incomplete removal of wind and current effects from the LOD data [Chen et al., 2000]. Atmospheric wind effects are so dominant in driving LOD, that small errors in wind field estimates, especially in the upper atmosphere, significantly contaminate the residual used to compute ΔC₂₀. If this semiannual signal is removed using least squares, the remainder (the green curve in Figure 1c) agrees considerably better with model predictions (at annual and other intraseasonal time scales). The relatively larger discrepancies during 1997–1999 are apparently associated with the 1997/1998 El Niño and the follow-on La Niña event. Atmospheric models are expected to show relatively larger uncertainties during these abnormal periods, especially in modeling wind circulation.

[12] Amplitudes and phases of annual and semiannual variations are estimated by least squares for each time series and given in Table 1. Similar estimates from Chen et al. [2000] and SLR measured ΔC₂₀ from Cox and Chao [2002] are presented for comparison. For a clearer presentation, Figures 2a, 2b, and 2c show the vector plots of annual ΔC₂₁, ΔS₂₁, and ΔC₂₀ variations as listed in Table 1. EOP derived annual ΔC₂₁ and especially ΔS₂₁ variations agree very well with AOW model predictions. These ΔC₂₁ and ΔS₂₁ estimates from both EOP and new AOW models, however do not agree with SLR observations of Chen et al. [2000], and in particularly show large phase differences, which appears indicating that there might be large phase errors in these SLR determined ΔC₂₁ and ΔS₂₁ variations. LOD derived ΔC₂₀ from this study agrees considerably better with both model predictions and SLR measurements than that of Chen et al. [2000] does. The improved agreements between EOP derived and model predicted ΔC₂₁, ΔS₂₁, and ΔC₂₀ come from two aspects: (1) a better determination of ocean current excitations using the advanced ECCO data assimilation system [Chen et al., 2003a, 2003b]; and (2) a better modeling of oceanic mass (or OBP) change of ECCO and land water storage change of LDAS.

[13] We compute cross correlation coefficients between EOP derived ΔC₂₁, ΔS₂₁, and ΔC₂₀ time series and model predictions. Signals of seasonal or longer periods are first removed from all time series using least squares. A strong peak of correlation coefficients at zero phase lag, well beyond the 99.9% significance level is found in all 3 cases. Both ΔC₂₁ and ΔC₂₀ estimates from this study show improved agreement with model predictions at intraseasonal time scales compared with those of Chen et al. [2000], e.g., (0.69 vs. 0.42) for ΔC₂₁ and (0.64 vs. 0.54) for ΔC₂₀. This improvement apparently comes from the use of the ECCO model. Hydrological model predictions are dominated by seasonal change and the LDAS monthly averaged soil water data does not contribute much to intraseasonal variability.

4. Discussion

[14] The improved agreement between EOP derived results and model predictions supports the conclusion that ECCO provides more accurate estimates of global scale current and OBP variations than POCM at both intraseasonal and seasonal time scales [e.g., Chen et al., 2003b]. Improved agreement at seasonal time scale indicates that LDAS is superior in representing large scale surface water storage change compared with the NCEP reanalysis.

[15] EOP based estimates of gravity change may be affected by errors in EOP measurements, but we suspect this is a relatively minor contaminant. Instead, improper estimates of atmospheric wind and ocean currents are a more significant error source. EOP estimated of ΔS₂₁ show larger seasonal variability and agree better with model predictions, evidently dominated by the hydrological model. The larger seasonal signal in ΔS₂₁ is related to the geographical orientation of continents, which align more closer along the Y axis (±90° longitude). Atmospheric pressure changes over the oceans are mostly canceled out by the IB response of the oceans.

[16] This study further demonstrates the advantages of using Earth rotational observations to study low degree gravitational variations. Combining accurately determined EOP time series with atmospheric and oceanic general circulation models creates a unique and successful method to estimate degree 2 gravitational variations independently of satellite-based methods such as GRACE. These should be useful in validation of low degree GRACE observations, and in strengthening overall time variable gravity solutions.