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Seasonal excitation of polar motion
Journal of Geodynamics 62 (2012) 8–15
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Seasonal excitation of polar motion J.L. Chen a,c,∗ , C.R. Wilson a,b , Y.H. Zhou c a
Center for Space Research, University of Texas at Austin, Austin, TX, United States Jackson School of Geosciences, Department of Geological Sciences, University of Texas at Austin, Austin, TX, United States c Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China b
a r t i c l e
i n f o
Article history: Received 17 May 2011 Received in revised form 21 October 2011 Accepted 5 December 2011 Available online 13 December 2011 Keywords: Earth rotation Polar motion Excitation Atmosphere Ocean Hydrology GRACE
a b s t r a c t We estimate geophysical excitations (1 and 2 ) of polar motion using multiple sources of data, including recent atmospheric, oceanic, and hydrological models, satellite gravity measurements from the Gravity Recovery and Climate Experiment (GRACE), and compare geophysical excitations with observed polar motion excitations from space geodetic techniques. At seasonal time scales, both model-estimated excitations from the geophysical fluids envelope (i.e., atmosphere, ocean, and hydrosphere) and GRACEobserved excitations agree remarkably well with polar motion observations in the 2 component, and in the 1 component, model estimates and observed geodetic excitations show significant discrepancies. However, mass excitations estimated from GRACE show significantly better agreement with observed excitations than those from models, especially in 1 , due to better quantification of terrestrial water storage and oceanic mass changes using GRACE data. Furthermore, GRACE satellite gravity measurements offer a unique means for quantifying contributions from cryospheric angular momentum (CAM) change, a component mostly neglected in previous studies due to the lack of adequate observations or reliable ice sheets models. Based on GRACE estimates, CAM excitations appear a minor, but not negligible contributor to seasonal excitations of polar motion. The significantly better agreement in 2 (than that in 1 ) between observations and model excitations is related to the higher sensitivity of 2 excitations to atmospheric pressure and terrestrial water changes over the Eurasia and North American continents, because of the special relationship between the S21 spherical harmonic coefficient (proportional to 2 ) mass model and the locations of the two continents. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction Variations of Earth rotation are driven by mass redistribution and movement within the Earth system, including the solid Earth, atmosphere, ocean, hydrosphere, and cryosphere. Under the conservation of angular momentum, any variations of atmospheric angular momentum (AAM), oceanic angular momentum (OAM), hydrological angular momentum (HAM) can change Earth’s rotation via exchange of angular momentum between the solid Earth and its geophysical fluid envelope. At interannual or shorter (e.g., longer than 1-day) time scales, variations of atmospheric pressure and wind, ocean bottom pressure (OBP) and currents, and terrestrial water storage (TWS) change (plus ice mass change over polar ice sheets and mountain glaciers) are primary driving forces of Earth rotational changes, which include polar motion (X, Y) and length-of-day (LOD), representing respectively equatorial and axial components of Earth Orientation Parameters (EOP).
∗ Corresponding author at: Center for Space Research, University of Texas at Austin, Austin, TX, United States. E-mail address: [email protected] (J.L. Chen). 0264-3707/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jog.2011.12.002
AAM variations have long been recognized as the dominant driving force of LOD change, accounting for about 90% of observed LOD variability, and as a primary cause of polar motion (e.g. Barnes et al., 1983; Eubanks, 1993; Gross et al., 2004). Contributions from the oceans and land hydrology have also been shown to play important roles in driving Earth’s rotational change (e.g. Dickey et al., 1993; Ponte et al., 1998; Gross et al., 2004; Chen et al., 2004a; Nastula et al., 2007). Data assimilating atmospheric and oceanic general circulation models and (hydrological) land surface models are useful data sources for quantifying geophysical excitations of polar motion and LOD from the three major components of the geophysical fluid envelope. In addition, satellite altimetry sea surface height data have also been used to estimate oceanic contribution to Earth rotational change due to non-steric sea level (OBP) change (Chen et al., 2004b). However, except for LOD variations, observed excitations of polar motions X and Y are far from being satisfactorily explained, due to relatively large uncertainty in current oceanic and hydrological models and satellite measurements. Since its launch in February 2002, the Gravity Recovery and Climate Experiment (GRACE) has been measuring changes in Earth gravity on approximately a monthly basis, with unprecedented accuracy (Tapley et al., 2004). GRACE time-variable gravity
J.L. Chen et al. / Journal of Geodynamics 62 (2012) 8–15
measurements can be used to estimate large-scale mass variations on Earth surface (Wahr et al., 1998). The 9+ year time series of GRACE data provides a unique means for quantifying large-scale TWS and OBP change, and offers an alternative data source for studying hydrologic and oceanic excitations of earth rotation (e.g., Nastula et al., 2007; Jin et al., 2010). In addition, GRACE satellite gravity measurements can be used to quantify cryospheric angular momentum (CAM) variation, a component that has been neglected in previous studies due to the lack of adequate observations or reliable ice sheet models. GRACE observed degree-2 and order-2 spherical harmonics (C21 and S21 ) can be directly used to quantify global mass excitations of polar motion (e.g., Nastula et al., 2007). However, spatial leakage effect of GRACE data is expected to affect GRACE-estimated hydrologic and cryospheric excitations of polar motion. This leakage issue has not been appropriately addressed in previous studies (e.g., Jin et al., 2010). In this study, we estimate atmospheric, oceanic, hydrologic, and cryospheric excitations of polar motion using estimates from numerical models of the atmosphere, ocean, and land hydrology, and GRACE time-variable gravity observations (with improved data analyzing method). We focus on seasonal time scales. The main purpose is to explore how well we can close the seasonal excitation budget of polar motion, and improve understanding of major error sources in quantifying geophysical excitation of polar motion. 2. Data processing 2.1. Observed polar motion excitations Polar motion (X, Y) time series are taken from the International Earth Rotation and Reference Systems Service (IERS) combined EOP time series (C05) (Gambis, 2004), derived from various space geodetic observations by a Kalman filter combination (Eubanks et al., 1988). The data are daily values from September 1962 to the present. Excitation functions (1 and 2 ) are computed from (X, Y) using the discrete linear polar motion filter developed by Wilson (1985) using a Chandler frequency of 0.843 cycles per year (cpy) and a quality factor (Q) of 175. In order to match the temporal resolution of the GRACE results introduced later, the daily 1 and 2 time series are averaged into monthly intervals. 2.2. Atmospheric model and AAM excitations Atmospheric pressure and wind excitations (1 and 2 ) of polar motion are computed using atmospheric surface pressure and wind fields from the National Centers for Environmental Prediction (NCEP) reanalysis atmospheric model (Kalnay et al., 1996), following the formulation given by Eubanks (1993). The data are provided as daily averages for the period January, 1948 to present, on a uniform Gaussian grid, about 1.904◦ latitude by 1.875◦ longitude. The zonal winds include 17 layers from the surface at 1000 mb to the top at 10 mb. When computing atmospheric pressure excitations, an inverted barometer (IB) correction is applied so that over the oceans, atmospheric pressure at any point is replaced by mean pressure over the oceans (not including in-land seas) (Greatbatch, 1994). The wind integration is from the surface (defined by surface pressure) to the top of the model (10 mb). Daily atmospheric excitations (1 and 2 ) are averaged into monthly intervals, again to match GRACE temporal sampling. 2.3. Oceanic model and OAM excitations Oceanic excitations, including OBP and ocean current contributions are computed from model estimated OBP and ocean current
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fields (following the formulation given by Eubanks, 1993) from the data assimilating Ocean General Circulation Model developed at NASA’s Jet Propulsion Laboratory (JPL), a partner in the Estimating the Circulation and Climate of the Ocean (ECCO) program. The ECCO OGCM is based on the parallel version of the Massachusetts Institute of Technology general circulation model and an approximate Kalman filter method (Fukumori et al., 2000). The ECCO model (run kf080a) assimilates T/P SSH observations. The model coverage is nearly global from 79.5◦ S to 78.5◦ N and has a telescoping meridional grid with 1/3◦ resolution in the tropics (20◦ S to 20◦ N) that gradually increases to a 1◦ resolution away from the equator. The resolution in longitude is 1◦ . There are 46 vertical levels with 10-m resolution within 150 m of the surface. The model is forced by National Centers for Environmental Prediction (NCEP) reanalysis products (Kalnay et al., 1996) (12-h interval wind stress data and daily heat and fresh water fluxes) with time means replaced by those of the Comprehensive Ocean-Atmosphere Data Set. Temperature and salinity at the model sea surface are relaxed toward observed values. The ECCO model provides near real-time estimates of physical changes of the ocean, including current, sea surface height (SSH), temperature (T), salinity (S), and OBP. Model fields are available at 10-day intervals (as 10-day averages). SSH and OBP are also available at 12-h intervals (as instantaneous values). The ECCO values used here include 10-day averaged OBP, SSH, zonal (U), and meridional (V) velocities from January 2003 to December 2009. The ECCO model employs the Boussinesq approximation to conserve total ocean volume. This will cause changes of estimated total ocean mass unrelated to any oceanographic effect. To correct this, we enforce ECCO mass conservation by removing a mean OBP (over the oceans) at each time step (Greatbatch, 1994). The 10day current and 12-hourly OBP excitations are both averaged into monthly intervals, in order to be compared with other time series later.
2.4. Land surface model and HAM excitations Hydrological (or HAM) excitations are computed from model estimated TWS changes from the WaterGAP Global Hydrological Model (WGHM) (Döll et al., 2003; Güntner et al., 2007). The WGHM model simulates the continental water cycle by conceptual formulations of the major hydrological processes. The details of the conceptual model equations are described by Döll et al. (2003) and Hunger and Döll (2008). The WGHM model provides daily (and also monthly) estimates of water storage changes in soil and snow, surface water reservoirs, and groundwater reservoirs, with a 0.5◦ × 0.5◦ spatial resolution. Monthly TWS changes are computed as the sum of soil and snow water, surface water, and groundwater. Following the equations in Chen et al. (2004, Eq. (1)), we compute monthly hydrological excitations (1 and 2 ) on polar motions from WGHM TWS estimates for the period January 2003 through December 2009. Global water mass conservation is applied by adding a uniform layer of water over the ocean, equal to the negative of integrated total water mass over land. This procedure is necessary, as we had enforced a mass conservation of the ECCO ocean model (see Section 2.3) by the Greatbatch correction (Greatbatch, 1994). So the total mass of the ocean from the ECCO model remains as a constant. In reality, there is a clear water mass exchange between land hydrology and ocean, as part of the global water cycle (Chen et al., 1998; Minster et al., 1999; Cazenave et al., 2009). This global mass conservation has a minor impact on estimated hydrological and oceanic excitations on polar motion. However, it plays a much more important role in correctly estimating excitations of LOD (not discussed in the present study) (Chen, 2005).
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2.5. GRACE gravity observations GRACE data used here include 83 monthly release 4 (RL04) fields for the period January 2003 to December 2009, provided by the Center for Space Research (CSR) at the University of Texas of Austin (Bettadpur, 2007a). Each monthly field consists of fully normalized spherical harmonic coefficients to degree and order 60. Atmospheric, oceanic, and tidal effects have been removed during GRACE processing using geophysical models (Bettadpur, 2007b). The July 2003 solution is not available due to inadequate data, and the gap is filled using linear interpolation. Over (non-glaciated) land areas, GRACE gravity change mainly represents contributions from TWS, which includes changes of surface water storage in soil, snow, and surface reservoirs (rivers and lakes), and groundwater storage, and residual atmospheric or tidal mass changes due to imperfect removal during GRACE data processing. Long-term variability of some low-degree spherical harmonics (e.g., C20 , C30 , C40 , C21 , and S21 ), removed from GRACE gravity solutions has been restored (Bettadpur, 2007b). Degree-1 spherical harmonics (geocenter variations) are zero in the RL04 solutions. We neglect geocenter effects in the analysis due to the lack of reliable estimates from other types of data. We use GRACE time-variable gravity measurements to estimate polar motion excitation (1 and 2 ) using two different methods. GRACE TWS change estimates can be used to quantify hydrological excitation of polar motion, and GRACE-derived ice mass changes over polar ice sheets and mountain glaciers provide a unique means for quantifying cryospheric (i.e., CAM) contributions. However, leakage effects in GRACE estimates, arising from required spatial filterings (and a limited degree and order range of spherical harmonic coefficients) will affect TWS and especially ice mass estimates (Chen et al., 2006, 2008). Therefore, appropriate corrections for leakage effects are needed. The two methods reflect alternate ways to minimize leakage. One is to only apply a decorrelation filter to reduce the longitudinal stripes in GRACE data (Swenson and Wahr, 2006), but without the typically applied Gaussian smoothing (to further reduce errors). The other is to apply a forward modeling method to reduce the leakage effect and restore true signal amplitude. More information about the forward modeling method can be found in previous studies (e.g., Chen et al., 2006, 2008, 2009). A second approach is to directly use GRACE degree-2 and order-1 spherical harmonic coefficients (C21 and S21 ) to quantify polar motion excitation. When atmospheric and oceanic contributions to GRACE C21 and S21 (removed during the GRACE dealiasing process) are restored using the GAC products provided by the GRACE project (Bettadpur, 2007b), GRACE C21 and S21 variations directly represent the change of the two inertia tensors of the Earth, which govern polar motion excitations due to mass change (x1mass and x2mass ) via the McCullagh’s formula (e.g., Munk and McDonald, 1960; Chen et al., 2000)
mass 1
1 · =− (1 + k2 )
mass 2
1 · =− (1 + k2 )
5 1.098R2 M · C21 · 3 (C − A)
(1)
5 1.098R2 M · S21 · 3 (C − A)
Here M and R are mass and mean radius of the Earth, C and A (C − A = 2.61 × 1035 kg m2 ) the two principal inertia moments of the Earth, and Cm (7.1236 × 1037 kg m2 ) the principal inertia moment of Earth’s mantle (Eubanks, 1993). k’2 is the degree-2 load Love number (−0.301), accounting for a secondary change in the gravity potential due to elastic deformations of the Earth.
Fig. 1. Monthly excitations of polar motion (a) 1 and (b) 2 , from geodetic observation (Obs.), atmospheric angular momentum (AAM), oceanic angular momentum (OAM), hydrological angular momentum (HAM), and cryospheric angular momentum (CAM). AAM, OAM, and HAM are estimated from numerical models for the atmosphere, ocean, and land hydrology and CAM is estimated from GRACE observed polar ice sheets mass change. Units are in radians.
3. Results and comparisons 3.1. Excitations from individual contributors The two panels of Fig. 1 compare observed (Obs.) monthly excitations (1 and 2 ) of polar motion, and contributions from AAM, OAM, HAM, and CAM, representing angular momentum excitations from the four major components of Earth’s geophysical fluids envelope (i.e., atmosphere, ocean, hydrosphere, and cryosphere). AAM, OAM, and HAM are computed from numerical models as we introduced in the above sections, and CAM is from GRACE (based on forward modeling), which includes contributions from the Antarctic and Greenland ice sheets and a few major mountain glacier complexes (Alaskan Glaciers and Patagonia Icefields). Apparently, the atmosphere plays a more significant role in driving polar motion, especially in the Y component (i.e., 2 ), but contributions from ocean and land hydrology are also important. Ice mass change, (CAM) appears to play a relatively minor role (relative to other sources), but its contribution is not negligible. In order to examine and compare hydrological excitations estimated from the WGHM model and GRACE, we remove AAM and OAM excitations from polar motion observations, and compare the residual excitations (Obs. – AAM – OAM) with two HAM excitations
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Fig. 2. Comparison between residual excitations (i.e., Obs. – AAM – OAM) of (a) 1 and (b) 2 , with WGHM HAM, GRACE HAM and CAM contributions. (c) and (d) show similar comparisons, but with combined HAM and CAM (i.e., HAM + CAM) contributions.
(plus CAM) in the top two panels of Fig. 2. GRACE estimates (shown here) of HAM and CAM are based on forward modeling. GRACE and WGHM HAM excitations show significant differences, especially in 1 (the X component), and for much of the period (2003–2009), seasonal cycles are out of phase. Reasonable agreement between the two HAM estimates can be found for 2 . In addition, GRACE estimates agree much better with residual polar motion excitations, in particular 1 . And, CAM appears to play a larger role in 2 relative to 1 . The bottom two panels of Fig. 2 show similar comparisons, but with GRACE CAM added to HAM estimates from WGHM and GRACE (i.e., WGHM HAM + CAM and GRACE HAM + CAM). GRACE combined HAM and CAM excitations (HAM + CAM) agree very well with residual excitations in both 1 and 2 , over a broad band of frequencies (from intraseasonal, seasonal, to long-term time scales). However, although WGHM HAM (plus GRACE CAM) does agree well with residual excitations in 2 , it fails to show satisfactory agreement with 1 . This is likely due to deficiencies in the land surface models. GRACE combined HAM and CAM excitations (HAM + CAM) can explain 76% of the variance of residual excitations of 1 (Obs. – AAM – OAM), with a peak correlation coefficient (at zero phase lag) of ∼0.88, compared to the 42% reduction from WGHM HAM + CAM and a zero-phase-lag correlation coefficient of ∼0.68. However, in 2 excitations, although both GRACE and WGHM HAM (+CAM) show reasonable correlation with residual excitations (with zerophase-lag correlation coefficients of ∼0.48 and 0.50, respectively), removing these two contributions (GRACE HAM + CAM or WGHM HAM + CAM) does not really reduce the residual variance, likely due to the large high frequency noise in GRACE data and uncertainty in the WGHM hydrological model.
We also compare two different GRACE estimates of HAM (plus CAM) based on forward modeling and decorrelation filtering (Fig. 3). GRACE HAM estimates from decorrelation (green curves in Fig. 3a and b) includes contributions from all land areas (which includes both land hydrology and ice mass change). Although results from both methods agree well with residual polar motion excitations, the forward modeling results (red curves) show apparently better agreement with residual polar motion excitations than estimates based on the decorrelation filter, especially in 1 . Previous studies (Chen et al., 2006, 2008, 2009; Wouters et al., 2008) have demonstrated that forward modeling is more effective in removing leakage error in GRACE data, which tends to be a problem associated with longer period polar ice sheet changes, and therefore can better determine GRACE HAM and CAM excitations, in particularly at interannual and longer time scales. 3.2. Excitations from global mass redistribution We separate mass-related excitations of polar motion by removing atmospheric wind and ocean current excitations from IERS observations, and compare (Obs. – Wind – Current) with combined mass-contributions from the atmosphere, ocean, and land hydrology (denoted as AOW), and with cryospheric contributions included (denoted as AOWC) (see Fig. 4). Wind and ocean current excitations are estimated from the NCEP and ECCO models (see Sections 2.2 and 2.3). AOW excitations (in Fig. 4) represent the sum of contributions from NCEP atmospheric pressure, ECCO OBP, and WGHM TWS change (and AOWC = AOW + GRACE CAM). When wind and current effects are removed, observed massterm excitations agree remarkably well with both AOW (from
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Fig. 3. Comparison between residual excitations (i.e., Obs. – AAM – OAM) of (a) 1 and (b) 2 , with two GRACE estimates of HAM (and CAM) contributions.
models) and GRACE estimates, especially in 2 (reflecting mostly polar motion Y). GRACE results show significantly better agreement with observed 1 excitations than model estimates (AOW) do. Again, the improvement appears more evident (from visual examination) at longer periods (e.g., longer than a few years), consistent with the analysis in Section 3.1. 3.3. Seasonal budget of polar motion excitations To further examine the seasonal budget on mass-term polar motion excitations, we estimate annual and semiannual amplitudes and phases (along with the long-term trends) of the observed excitations and contributions from AOW, AOWC, and GRACE using unweighted least squares fit, and list the results in Table 1. Fig. 5a and b illustrates the comparisons and agreements of annual amplitudes and phases for 1 and 2 , using phasor diagrams. Consistent with visual examination of Fig. 4, observed mass-term excitations and the three geophysical excitations (AOW, AOWC, and GRACE) agree remarkably well in the 2 component. However, there is a significant phase difference (of about 60◦ ) between model-based excitations (AOW and AOWC) and observations in the 1 component, but GRACE total mass excitations of 1 agree significantly better with observations. To better understand annual excitations from different components of the Earth system and likely major error sources in estimates of 1 , we show the individual annual phasor vectors in
Fig. 4. Mass excitations of (a) 1 and (b) 2 , from observations (i.e., Obs. minus wind and ocean current contributions), combined contributions from the atmosphere, ocean with land water (AOW) from models, AOW plus cryosphere (AOWC), and GRACE observed mass change.
AOWC and GRACE excitations (see the dashed arrows in Fig. 6). The ECMWF atmospheric excitation is from the GRACE GAC solutions, which are based on the ECMWF atmospheric model. The NCEP and ECMWF atmospheric excitations agree very well. However, the two hydrological excitations, i.e., WGHM and GRACE (GRC) show large differences in both amplitude and phase, and the same is true for ECCO and GRACE oceanic excitations. CAM plays a smaller role in annual contributions to 1 . Clearly, the large difference between observed and AOWC (or AOW) mass-term contributions to 1 is mostly related to deficiencies in WGHM and ECCO models. 3.4. Sensitivity analysis of polar motion excitations There are distinctively different concordances between observations (i.e., EOP – Wind/Current) and model (AOW) and GRACE excitations for 1 and 2 components. That is, with a large difference for 1 , the same models yield near perfect agreement with observed 2 (see Figs. 4 and 5). Part of the difference may be that annual amplitudes in 2 are larger than in 1 , so a fixed noise level will have less effect for 2 (see Fig. 4b). However, the difference between AOWC and observed 1 is much larger than for 2 (see Fig. 5a and b), suggesting that WGHM and ECCO do a relatively poor job with 1 . On the other hand, GRACE excitations agree well with observations for both 1 and 2 . This indicates that
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Table 1 Amplitudes and phases of annual and semiannual mass-term excitations of 1 and 2 from space geodetic observations (Obs. – Wind/Current), combined geophysical contributions (AOW or AOWC), and GRACE-observed excitations during the period Jan. 2003 to Dec. 2009. The phase is defined as in sin (2(t − t0 ) + ), where t0 refers to h0 on January 1. Polar motion excitations (1 & 2 )
Obs. – Wind/Current (1 ) AOW (1 ) AOWC (1 ) GRACE (1 ) Obs. – Wind/Current (2 ) AOW (2 ) AOWC (2 ) GRACE (2 )
Annual
Semiannual
Amplitude (×108 )
Phase (deg)
Amplitude (×108 )
Phase (deg)
4.08 4.69 4.70 4.85 13.66 12.34 12.68 13.16
343 279 281 346 296 291 294 288
0.98 0.23 0.29 1.69 4.34 2.22 2.34 2.42
314 336 332 308 75 102 105 60
the distinctive agreements in 1 and 2 may be tied to the geographical sampling of the two components and numerical model performance in different regions. For comparisons, similar AOW2 excitations (covering the same time span, January 2003 through December 2009) which are based on combined GLDAS hydrological model (Rodell et al., 2004) estimates and GRACE GAC atmospheric and oceanic contributions are also included in the annual phasor diagrams. The computation of AOW2 excitations follows the exact same procedures of Chen and Wilson (2008).
1 and 2 are proportional to C21 and S21 (see Eq. (1)), which sample the earth as illustrated in the bottom two panels of Fig. 5. For S21 (Fig. 5d), the maxima of the two mass signals in the northern hemisphere fall in the centers of Eurasian and North American continents. In contrast, the maximum C21 sensitivity (in the northern hemisphere) is mostly over the oceans. This suggests that S21 may be more sensitive (than C21 ) to mass changes over land, and C21 is more sensitive to mass changes over the oceans. This is useful in addressing the following questions.
Fig. 5. Phasor diagram of annual mass excitations of (a) 1 and (b) 2 . The four vectors in each panel represent annual mass excitations from observations (EOP – Wind/Current), AOW, AOWC, and GRACE. Separate estimates of AOW2 based on GLDAS land water and GRACE GAC atmosphere and ocean (Chen and Wilson, 2008) are also included for comparisons. Units are in radians (×10−8 ). Each annual excitation is described by a sine and a cosine component, projected in the Y and X axes of the Cartesian coordinates. (c) and (d) Mass change modes of spherical harmonics C21 and S21 , corresponding to mass excitations of 1 and 2 , respectively. The four maximums of the C21 mode fall mostly in ocean areas, and the two northern hemispheric maximums of the S21 mode fall over the Eurasian and North American continents, suggesting the different sensitivities of these two mass change modes to atmospheric and oceanic contributions (due to the IB response over the oceans, atmospheric pressure effects are dominated by contributions from land).
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Fig. 6. Phasor diagram of individual contributions to annual mass excitations of 1 . The solid vectors show mass excitations from EOP – Wind/Current (blue), models (green), and GRACE (GRC) (red), and dashed vectors show individual components. Ice contributions are from GRACE. Units are in radians (×10−8 ). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
(1) Why do 2 (mass-term) excitations have larger variability than 1 ? Seasonal variations in the atmosphere clearly play a more dominant role in polar motion excitation (see Fig. 1a and b). At seasonal time scales, atmospheric pressure changes over the oceans are mostly cancelled by the IB effect. That means atmospheric pressure change over land and TWS change are the most significant seasonal forces driving polar motion. As 2 is more sensitive to mass load change over land, 2 is expected to show larger variability, mainly due to atmospheric and land water mass changes over the Eurasian and North American continents. (2) Why do observations and AOWC excitations agree better for 2 than in 1 ? Atmospheric pressure change plays a more important role in 2 than in 1 , and modern atmospheric models (e.g., ECMWF and NCEP) are considerably more mature than oceanic and hydrological models, and there are more available in situ and satellite meteorological observations to assimilate. This yields relatively better agreement for 2 (between observations and AOWC). In addition, 1 is more sensitive to seasonal variability of OBP, which is significantly smaller than atmospheric pressure and has relatively larger uncertainty. This will also contribute to poorer agreement for 1 . 4. Summary and discussion We estimate geophysical excitations of polar motion (1 and 2 ) using multiple sources of data, including recent numerical models for the atmosphere, ocean, and land hydrology, and GRACE satellite gravity measurements. At seasonal time scales, modelestimated AOW (or AOWC) excitations agree very well with polar motion observations for 2 , but show significant differences for 1 . However, GRACE-derived excitations agree remarkably well with observed geodetic excitations in both 1 and 2 , due to superior GRACE estimates of terrestrial water storage and oceanic mass changes. GRACE time-variable gravity measurements also provide a means for quantifying excitations from ice mass change (i.e., CAM) over polar ice sheets and mountain glaciers, largely omitted in previous studies due to the lack of adequate observations or reliable ice sheets models. GRACE estimates indicate that CAM excitations are small but not negligible contributors to seasonal excitations of polar motion.
Leakage corrections are important for quantifying hydrological and cryospheric excitations of polar motion from GRACE data. It has been demonstrated that the forward modeling method is effective in correcting the leakage effect and restoring the true magnitudes of TWS ice mass changes. The effect on ice mass changes is especially important (Fig. 3a and b). Better accounting for 2 (relative to 1 ) is apparently tied to the greater importance of relatively well determined atmospheric pressure and TWS changes over the Eurasian and North American continents, because S21 is proportional to 2 . This special sensitivity and the more significant seasonal mass load changes over land also contribute to the larger 2 amplitude. This study demonstrates inadequacies in current ocean and land surface models in forming estimates of large-scale mass changes. Of course, GRACE estimates suffer from a number of limitations as well, including low spatial resolution, contamination by longitudinal stripes, leakage effects, residual errors, and relatively large uncertainty in low degrees spherical harmonic coefficients. However, when measuring very large scale mass changes (C21 and S21 ) GRACE clearly out-performs oceanic and land surface models, and comes closer to balancing the seasonal excitation budget of polar motion.
Acknowledgments The authors would like to thank the two anonymous reviewers for their insightful comments, which lead to improved presentation of the results. We are grateful to Dr. Andreas Güntner for providing the WGHM data. This study was supported by the National Geospatial Intelligence Agency (under NURI Grant HM1582-07-1-2032), and National Science Foundation (under grants ANT-0632195 and ANT-1043750). Additional support was provided by the Shanghai Astronomical Observatory, Chinese Academy of Sciences and the Geology Foundation of the Jackson School of Geosciences, University of Texas Austin.
References Barnes, R., Hide, R., White, A., Wilson, C., 1983. Atmospheric angular momentum functions, length-of-day changes and polar motion. Proc. R. Soc. Lond. A 387, 31–73. Bettadpur, S., 2007a. Level-2 Gravity Field Product User Handbook. GRACE 327-734, The GRACE Project, Center for Space Research, University of Texas at Austin. Bettadpur, S., 2007b. CSR Level-2 Processing Standards Document for Product Release 04. GRACE 327-742, The GRACE Project, Center for Space Research, University of Texas at Austin. Cazenave, A., Dominh, K., Guinehut, S., Berthier, E., Llovel, W., Ramillien, G., Ablain, M., Larnicol, G., 2009. Sea level budget over 2003–2008: A reevaluation from GRACE space gravimetry, satellite altimetry and Argo. Global Planetary Change 65, 83–88. Chen, J.L., 2005. Global Mass Balance and the Length-of-day Variation. J. Geophys. Res. 110, B08404, doi:10.1029/2004JB003474. Chen, J.L, Wilson, C.R., Chambers, D.P., Nerem, R.S., Tapley, B.D., 1998. Seasonal global water mass budget and mean sea level variations. Geophys. Res. Lett. 25 (19), 3555–3558. Chen, J.L., Wilson, C.R., Eanes, R.J., Tapley, B.D., 2000. A new assessment of long wavelength gravitational variations. J. Geophys. Res. 105 (B7), 16271–16278. Chen, J.L., Wilson, C.R., Hu., X.G., Zhou, Y.H., Tapley, B.D., 2004a. Oceanic effects on polar motion determined from an ocean model and satellite altimetry: 1993–2001. J. Geophys. Res. 109 (B2), B02411, doi:10.1029/2003JB002664. Chen, J.L., Wilson, C.R., Tapley, B.D., Ries, J.C., 2004b. Low degree gravitational changes from GRACE: validation and interpretation. Geophys. Res. Lett. 31, L22607, doi:10.1029/2004GL021670. Chen, J.L., Wilson, C.R., Tapley, B.D., 2006. Satellite gravity measurements confirm accelerated melting of greenland ice sheet. Science 313, doi:10.1126/science.1129007. Chen, J.L., Wilson, C.R., Tapley, B.D., Blankenship, D., Young, D., 2008. Antarctic regional ice loss rates from GRACE. Earth Planet. Sci. Lett. 266, 140–148, doi:10.1016/j.epsl.2007.10.057. Chen, J.L., Wilson, C.R., 2008. Low degree gravitational changes from GRACE, Earth 380 Rotation, geophysical models, and satellite laser ranging. J. Geophys. Res. 113, B06402, doi:10.1029/2007JB005397.
J.L. Chen et al. / Journal of Geodynamics 62 (2012) 8–15 Chen, J.L., Wilson, C.R., Blankenship, D.D., Tapley, B.D., 2009. Accelerated Antarctic ice loss from satellite gravity measurements. Nature Geosci. 2, 859–862, doi:10.1038/NGEO694. Dickey, J.O., Marcus, S.L., Johns, C.M., Hide, R., Thompson, S.R., 1993. The oceanic contribution to the Earth’s seasonal angular momentum budget. Geophys. Res. Lett. 20 (24), 2953–2956. Döll, P., Kaspar, F., Lehner, B., 2003. A global hydrological model for deriving water availability indicators: model tuning and validation. J. Hydrol. 270, 105–134. Eubanks, T.M., Steppe, J.A., Dickey, J.O., Rosen, R.D., Salstein, D.A., 1988. Causes of rapid motions of the Earth’s pole. Nature 334, 115–119. Eubanks, T.M., 1993. Variations in the orientation of the earth. In: Smith, D., Turcotte, D. (Eds.), Contributions of Space Geodesy to Geodynamic: Earth Dynamics. Geodyn. Ser., vol. 24. AGU, Washington, D.C., pp. 1–54. Fukumori, I., Lee, T., Menemenlis, D., Fu, L.-L., Cheng, B., Tang, B., Xing, Z., Giering, R., 2000. A dual assimilation system for satellite altimetry. In: Joint TOPEX/POSEIDON and Jason-1 Science Working Team Meeting, Miami Beach, Florida, 15–17 November 2000. Gambis, G., 2004. Monitoring Earth Orientation at the IERS using space-geodetic observations. J. Geod. 78, 295–303. Greatbatch, R.J., 1994. A note on the representation of steric sea level in models that conserve volume rather than mass. J. Geophys. Res. 99, 12767–12771. Gross, R.S., Fukumori, I., Menemenlis, D., Gegout, P., 2004. Atmospheric and oceanic excitation of length-of-day variations during 1980–2000. J. Geophys. Res. 109, B01406, doi:10.1029/2003JB002432. Güntner, A., Stuck, J., Werth, S., Döll, P., Verzano, K., Merz, B., 2007. A global analysis of temporal and spatial variations in continental water storage. Water Resources Res. 43 (5), W05416, doi:10.1029/2006WR005247. Hunger, M., Döll, P., 2008. Value of river discharge data for global-scale hydrological modeling. Hydrol. Earth Syst. Sci. 12, 841–861.
15
Jin, S., Chambers, D.P., Tapley, B.D., 2010. Hydrological and oceanic effects on polar motion from GRACE and models. J. Geophys. Res. 115 (B2), 1–11, doi:10.1029/2009JB006635. Kalnay, E., et al., 1996. The NCEP/NCAR 40-year reanalysis project. Bull. Am. Meteorol. Soc. 77, 437–471. Minster, J.F., Cazenave, A., Serafini, Y.V., Mercier, F., Gennero, M.C., Rogel, P., 1999. Annual cycle in mean sea level from TOPEX-Poseidon and ERS-1: inference on the global hydrological cycle. Global Planetary Change 20, 57–66. Munk, W.H., McDonald, G.J.F., 1960. The Rotation of the Earth. Cambridge Univ. Press, Cambridge, U.K. Nastula, J., Ponte, R.M., Salstein, D.A., 2007. Comparison of polar motion excitation series derived from GRACE and from analyses of geophysical fluids. Geophys. Res. Lett. 34, L11306, doi:10.1029/2006GL028983. Ponte, R.M., Stammer, D., Marshall, J., 1998. Oceanic signals in observed motions of the Earth’s pole of rotation. Nature 391, 476–479. Rodell, M., et al., 2004. The global land data assimilation system. Bull. Am. Meteorol. Soc. 85 (3), 381–394. Swenson, S., Wahr, J., 2006. Post-processing removal of correlated errors in GRACE data. Geophys. Res. Lett. 33, L08402, doi:10.1029/2005GL025285. Tapley, B.D., Bettadpur, S., Watkins, M.M., Reigber, C., 2004. The gravity recovery and climate experiment; mission overview and early results. Geophys. Res. Lett. 31 (9), L09607, doi:10.1029/2004GL019920. 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, doi:10.1029/98JB02844. Wilson, C.R., 1985. Discrete polar motion equations. Geophys. J. R. Astron. Soc. 80, 551–554. Wouters, B., Chambers, D., Schrama, E.J.O., 2008. GRACE observes small-scale mass loss in Greenland. Geophys. Res. Lett. 35, L20501, doi:10.1029/2008GL034816.
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Journal of Geodynamics journal homepage: http://www.elsevier.com/locate/jog
Seasonal excitation of polar motion J.L. Chen a,c,∗ , C.R. Wilson a,b , Y.H. Zhou c a
Center for Space Research, University of Texas at Austin, Austin, TX, United States Jackson School of Geosciences, Department of Geological Sciences, University of Texas at Austin, Austin, TX, United States c Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China b
a r t i c l e
i n f o
Article history: Received 17 May 2011 Received in revised form 21 October 2011 Accepted 5 December 2011 Available online 13 December 2011 Keywords: Earth rotation Polar motion Excitation Atmosphere Ocean Hydrology GRACE
a b s t r a c t We estimate geophysical excitations (1 and 2 ) of polar motion using multiple sources of data, including recent atmospheric, oceanic, and hydrological models, satellite gravity measurements from the Gravity Recovery and Climate Experiment (GRACE), and compare geophysical excitations with observed polar motion excitations from space geodetic techniques. At seasonal time scales, both model-estimated excitations from the geophysical fluids envelope (i.e., atmosphere, ocean, and hydrosphere) and GRACEobserved excitations agree remarkably well with polar motion observations in the 2 component, and in the 1 component, model estimates and observed geodetic excitations show significant discrepancies. However, mass excitations estimated from GRACE show significantly better agreement with observed excitations than those from models, especially in 1 , due to better quantification of terrestrial water storage and oceanic mass changes using GRACE data. Furthermore, GRACE satellite gravity measurements offer a unique means for quantifying contributions from cryospheric angular momentum (CAM) change, a component mostly neglected in previous studies due to the lack of adequate observations or reliable ice sheets models. Based on GRACE estimates, CAM excitations appear a minor, but not negligible contributor to seasonal excitations of polar motion. The significantly better agreement in 2 (than that in 1 ) between observations and model excitations is related to the higher sensitivity of 2 excitations to atmospheric pressure and terrestrial water changes over the Eurasia and North American continents, because of the special relationship between the S21 spherical harmonic coefficient (proportional to 2 ) mass model and the locations of the two continents. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction Variations of Earth rotation are driven by mass redistribution and movement within the Earth system, including the solid Earth, atmosphere, ocean, hydrosphere, and cryosphere. Under the conservation of angular momentum, any variations of atmospheric angular momentum (AAM), oceanic angular momentum (OAM), hydrological angular momentum (HAM) can change Earth’s rotation via exchange of angular momentum between the solid Earth and its geophysical fluid envelope. At interannual or shorter (e.g., longer than 1-day) time scales, variations of atmospheric pressure and wind, ocean bottom pressure (OBP) and currents, and terrestrial water storage (TWS) change (plus ice mass change over polar ice sheets and mountain glaciers) are primary driving forces of Earth rotational changes, which include polar motion (X, Y) and length-of-day (LOD), representing respectively equatorial and axial components of Earth Orientation Parameters (EOP).
∗ Corresponding author at: Center for Space Research, University of Texas at Austin, Austin, TX, United States. E-mail address: [email protected] (J.L. Chen). 0264-3707/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jog.2011.12.002
AAM variations have long been recognized as the dominant driving force of LOD change, accounting for about 90% of observed LOD variability, and as a primary cause of polar motion (e.g. Barnes et al., 1983; Eubanks, 1993; Gross et al., 2004). Contributions from the oceans and land hydrology have also been shown to play important roles in driving Earth’s rotational change (e.g. Dickey et al., 1993; Ponte et al., 1998; Gross et al., 2004; Chen et al., 2004a; Nastula et al., 2007). Data assimilating atmospheric and oceanic general circulation models and (hydrological) land surface models are useful data sources for quantifying geophysical excitations of polar motion and LOD from the three major components of the geophysical fluid envelope. In addition, satellite altimetry sea surface height data have also been used to estimate oceanic contribution to Earth rotational change due to non-steric sea level (OBP) change (Chen et al., 2004b). However, except for LOD variations, observed excitations of polar motions X and Y are far from being satisfactorily explained, due to relatively large uncertainty in current oceanic and hydrological models and satellite measurements. Since its launch in February 2002, the Gravity Recovery and Climate Experiment (GRACE) has been measuring changes in Earth gravity on approximately a monthly basis, with unprecedented accuracy (Tapley et al., 2004). GRACE time-variable gravity
J.L. Chen et al. / Journal of Geodynamics 62 (2012) 8–15
measurements can be used to estimate large-scale mass variations on Earth surface (Wahr et al., 1998). The 9+ year time series of GRACE data provides a unique means for quantifying large-scale TWS and OBP change, and offers an alternative data source for studying hydrologic and oceanic excitations of earth rotation (e.g., Nastula et al., 2007; Jin et al., 2010). In addition, GRACE satellite gravity measurements can be used to quantify cryospheric angular momentum (CAM) variation, a component that has been neglected in previous studies due to the lack of adequate observations or reliable ice sheet models. GRACE observed degree-2 and order-2 spherical harmonics (C21 and S21 ) can be directly used to quantify global mass excitations of polar motion (e.g., Nastula et al., 2007). However, spatial leakage effect of GRACE data is expected to affect GRACE-estimated hydrologic and cryospheric excitations of polar motion. This leakage issue has not been appropriately addressed in previous studies (e.g., Jin et al., 2010). In this study, we estimate atmospheric, oceanic, hydrologic, and cryospheric excitations of polar motion using estimates from numerical models of the atmosphere, ocean, and land hydrology, and GRACE time-variable gravity observations (with improved data analyzing method). We focus on seasonal time scales. The main purpose is to explore how well we can close the seasonal excitation budget of polar motion, and improve understanding of major error sources in quantifying geophysical excitation of polar motion. 2. Data processing 2.1. Observed polar motion excitations Polar motion (X, Y) time series are taken from the International Earth Rotation and Reference Systems Service (IERS) combined EOP time series (C05) (Gambis, 2004), derived from various space geodetic observations by a Kalman filter combination (Eubanks et al., 1988). The data are daily values from September 1962 to the present. Excitation functions (1 and 2 ) are computed from (X, Y) using the discrete linear polar motion filter developed by Wilson (1985) using a Chandler frequency of 0.843 cycles per year (cpy) and a quality factor (Q) of 175. In order to match the temporal resolution of the GRACE results introduced later, the daily 1 and 2 time series are averaged into monthly intervals. 2.2. Atmospheric model and AAM excitations Atmospheric pressure and wind excitations (1 and 2 ) of polar motion are computed using atmospheric surface pressure and wind fields from the National Centers for Environmental Prediction (NCEP) reanalysis atmospheric model (Kalnay et al., 1996), following the formulation given by Eubanks (1993). The data are provided as daily averages for the period January, 1948 to present, on a uniform Gaussian grid, about 1.904◦ latitude by 1.875◦ longitude. The zonal winds include 17 layers from the surface at 1000 mb to the top at 10 mb. When computing atmospheric pressure excitations, an inverted barometer (IB) correction is applied so that over the oceans, atmospheric pressure at any point is replaced by mean pressure over the oceans (not including in-land seas) (Greatbatch, 1994). The wind integration is from the surface (defined by surface pressure) to the top of the model (10 mb). Daily atmospheric excitations (1 and 2 ) are averaged into monthly intervals, again to match GRACE temporal sampling. 2.3. Oceanic model and OAM excitations Oceanic excitations, including OBP and ocean current contributions are computed from model estimated OBP and ocean current
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fields (following the formulation given by Eubanks, 1993) from the data assimilating Ocean General Circulation Model developed at NASA’s Jet Propulsion Laboratory (JPL), a partner in the Estimating the Circulation and Climate of the Ocean (ECCO) program. The ECCO OGCM is based on the parallel version of the Massachusetts Institute of Technology general circulation model and an approximate Kalman filter method (Fukumori et al., 2000). The ECCO model (run kf080a) assimilates T/P SSH observations. The model coverage is nearly global from 79.5◦ S to 78.5◦ N and has a telescoping meridional grid with 1/3◦ resolution in the tropics (20◦ S to 20◦ N) that gradually increases to a 1◦ resolution away from the equator. The resolution in longitude is 1◦ . There are 46 vertical levels with 10-m resolution within 150 m of the surface. The model is forced by National Centers for Environmental Prediction (NCEP) reanalysis products (Kalnay et al., 1996) (12-h interval wind stress data and daily heat and fresh water fluxes) with time means replaced by those of the Comprehensive Ocean-Atmosphere Data Set. Temperature and salinity at the model sea surface are relaxed toward observed values. The ECCO model provides near real-time estimates of physical changes of the ocean, including current, sea surface height (SSH), temperature (T), salinity (S), and OBP. Model fields are available at 10-day intervals (as 10-day averages). SSH and OBP are also available at 12-h intervals (as instantaneous values). The ECCO values used here include 10-day averaged OBP, SSH, zonal (U), and meridional (V) velocities from January 2003 to December 2009. The ECCO model employs the Boussinesq approximation to conserve total ocean volume. This will cause changes of estimated total ocean mass unrelated to any oceanographic effect. To correct this, we enforce ECCO mass conservation by removing a mean OBP (over the oceans) at each time step (Greatbatch, 1994). The 10day current and 12-hourly OBP excitations are both averaged into monthly intervals, in order to be compared with other time series later.
2.4. Land surface model and HAM excitations Hydrological (or HAM) excitations are computed from model estimated TWS changes from the WaterGAP Global Hydrological Model (WGHM) (Döll et al., 2003; Güntner et al., 2007). The WGHM model simulates the continental water cycle by conceptual formulations of the major hydrological processes. The details of the conceptual model equations are described by Döll et al. (2003) and Hunger and Döll (2008). The WGHM model provides daily (and also monthly) estimates of water storage changes in soil and snow, surface water reservoirs, and groundwater reservoirs, with a 0.5◦ × 0.5◦ spatial resolution. Monthly TWS changes are computed as the sum of soil and snow water, surface water, and groundwater. Following the equations in Chen et al. (2004, Eq. (1)), we compute monthly hydrological excitations (1 and 2 ) on polar motions from WGHM TWS estimates for the period January 2003 through December 2009. Global water mass conservation is applied by adding a uniform layer of water over the ocean, equal to the negative of integrated total water mass over land. This procedure is necessary, as we had enforced a mass conservation of the ECCO ocean model (see Section 2.3) by the Greatbatch correction (Greatbatch, 1994). So the total mass of the ocean from the ECCO model remains as a constant. In reality, there is a clear water mass exchange between land hydrology and ocean, as part of the global water cycle (Chen et al., 1998; Minster et al., 1999; Cazenave et al., 2009). This global mass conservation has a minor impact on estimated hydrological and oceanic excitations on polar motion. However, it plays a much more important role in correctly estimating excitations of LOD (not discussed in the present study) (Chen, 2005).
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2.5. GRACE gravity observations GRACE data used here include 83 monthly release 4 (RL04) fields for the period January 2003 to December 2009, provided by the Center for Space Research (CSR) at the University of Texas of Austin (Bettadpur, 2007a). Each monthly field consists of fully normalized spherical harmonic coefficients to degree and order 60. Atmospheric, oceanic, and tidal effects have been removed during GRACE processing using geophysical models (Bettadpur, 2007b). The July 2003 solution is not available due to inadequate data, and the gap is filled using linear interpolation. Over (non-glaciated) land areas, GRACE gravity change mainly represents contributions from TWS, which includes changes of surface water storage in soil, snow, and surface reservoirs (rivers and lakes), and groundwater storage, and residual atmospheric or tidal mass changes due to imperfect removal during GRACE data processing. Long-term variability of some low-degree spherical harmonics (e.g., C20 , C30 , C40 , C21 , and S21 ), removed from GRACE gravity solutions has been restored (Bettadpur, 2007b). Degree-1 spherical harmonics (geocenter variations) are zero in the RL04 solutions. We neglect geocenter effects in the analysis due to the lack of reliable estimates from other types of data. We use GRACE time-variable gravity measurements to estimate polar motion excitation (1 and 2 ) using two different methods. GRACE TWS change estimates can be used to quantify hydrological excitation of polar motion, and GRACE-derived ice mass changes over polar ice sheets and mountain glaciers provide a unique means for quantifying cryospheric (i.e., CAM) contributions. However, leakage effects in GRACE estimates, arising from required spatial filterings (and a limited degree and order range of spherical harmonic coefficients) will affect TWS and especially ice mass estimates (Chen et al., 2006, 2008). Therefore, appropriate corrections for leakage effects are needed. The two methods reflect alternate ways to minimize leakage. One is to only apply a decorrelation filter to reduce the longitudinal stripes in GRACE data (Swenson and Wahr, 2006), but without the typically applied Gaussian smoothing (to further reduce errors). The other is to apply a forward modeling method to reduce the leakage effect and restore true signal amplitude. More information about the forward modeling method can be found in previous studies (e.g., Chen et al., 2006, 2008, 2009). A second approach is to directly use GRACE degree-2 and order-1 spherical harmonic coefficients (C21 and S21 ) to quantify polar motion excitation. When atmospheric and oceanic contributions to GRACE C21 and S21 (removed during the GRACE dealiasing process) are restored using the GAC products provided by the GRACE project (Bettadpur, 2007b), GRACE C21 and S21 variations directly represent the change of the two inertia tensors of the Earth, which govern polar motion excitations due to mass change (x1mass and x2mass ) via the McCullagh’s formula (e.g., Munk and McDonald, 1960; Chen et al., 2000)
mass 1
1 · =− (1 + k2 )
mass 2
1 · =− (1 + k2 )
5 1.098R2 M · C21 · 3 (C − A)
(1)
5 1.098R2 M · S21 · 3 (C − A)
Here M and R are mass and mean radius of the Earth, C and A (C − A = 2.61 × 1035 kg m2 ) the two principal inertia moments of the Earth, and Cm (7.1236 × 1037 kg m2 ) the principal inertia moment of Earth’s mantle (Eubanks, 1993). k’2 is the degree-2 load Love number (−0.301), accounting for a secondary change in the gravity potential due to elastic deformations of the Earth.
Fig. 1. Monthly excitations of polar motion (a) 1 and (b) 2 , from geodetic observation (Obs.), atmospheric angular momentum (AAM), oceanic angular momentum (OAM), hydrological angular momentum (HAM), and cryospheric angular momentum (CAM). AAM, OAM, and HAM are estimated from numerical models for the atmosphere, ocean, and land hydrology and CAM is estimated from GRACE observed polar ice sheets mass change. Units are in radians.
3. Results and comparisons 3.1. Excitations from individual contributors The two panels of Fig. 1 compare observed (Obs.) monthly excitations (1 and 2 ) of polar motion, and contributions from AAM, OAM, HAM, and CAM, representing angular momentum excitations from the four major components of Earth’s geophysical fluids envelope (i.e., atmosphere, ocean, hydrosphere, and cryosphere). AAM, OAM, and HAM are computed from numerical models as we introduced in the above sections, and CAM is from GRACE (based on forward modeling), which includes contributions from the Antarctic and Greenland ice sheets and a few major mountain glacier complexes (Alaskan Glaciers and Patagonia Icefields). Apparently, the atmosphere plays a more significant role in driving polar motion, especially in the Y component (i.e., 2 ), but contributions from ocean and land hydrology are also important. Ice mass change, (CAM) appears to play a relatively minor role (relative to other sources), but its contribution is not negligible. In order to examine and compare hydrological excitations estimated from the WGHM model and GRACE, we remove AAM and OAM excitations from polar motion observations, and compare the residual excitations (Obs. – AAM – OAM) with two HAM excitations
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Fig. 2. Comparison between residual excitations (i.e., Obs. – AAM – OAM) of (a) 1 and (b) 2 , with WGHM HAM, GRACE HAM and CAM contributions. (c) and (d) show similar comparisons, but with combined HAM and CAM (i.e., HAM + CAM) contributions.
(plus CAM) in the top two panels of Fig. 2. GRACE estimates (shown here) of HAM and CAM are based on forward modeling. GRACE and WGHM HAM excitations show significant differences, especially in 1 (the X component), and for much of the period (2003–2009), seasonal cycles are out of phase. Reasonable agreement between the two HAM estimates can be found for 2 . In addition, GRACE estimates agree much better with residual polar motion excitations, in particular 1 . And, CAM appears to play a larger role in 2 relative to 1 . The bottom two panels of Fig. 2 show similar comparisons, but with GRACE CAM added to HAM estimates from WGHM and GRACE (i.e., WGHM HAM + CAM and GRACE HAM + CAM). GRACE combined HAM and CAM excitations (HAM + CAM) agree very well with residual excitations in both 1 and 2 , over a broad band of frequencies (from intraseasonal, seasonal, to long-term time scales). However, although WGHM HAM (plus GRACE CAM) does agree well with residual excitations in 2 , it fails to show satisfactory agreement with 1 . This is likely due to deficiencies in the land surface models. GRACE combined HAM and CAM excitations (HAM + CAM) can explain 76% of the variance of residual excitations of 1 (Obs. – AAM – OAM), with a peak correlation coefficient (at zero phase lag) of ∼0.88, compared to the 42% reduction from WGHM HAM + CAM and a zero-phase-lag correlation coefficient of ∼0.68. However, in 2 excitations, although both GRACE and WGHM HAM (+CAM) show reasonable correlation with residual excitations (with zerophase-lag correlation coefficients of ∼0.48 and 0.50, respectively), removing these two contributions (GRACE HAM + CAM or WGHM HAM + CAM) does not really reduce the residual variance, likely due to the large high frequency noise in GRACE data and uncertainty in the WGHM hydrological model.
We also compare two different GRACE estimates of HAM (plus CAM) based on forward modeling and decorrelation filtering (Fig. 3). GRACE HAM estimates from decorrelation (green curves in Fig. 3a and b) includes contributions from all land areas (which includes both land hydrology and ice mass change). Although results from both methods agree well with residual polar motion excitations, the forward modeling results (red curves) show apparently better agreement with residual polar motion excitations than estimates based on the decorrelation filter, especially in 1 . Previous studies (Chen et al., 2006, 2008, 2009; Wouters et al., 2008) have demonstrated that forward modeling is more effective in removing leakage error in GRACE data, which tends to be a problem associated with longer period polar ice sheet changes, and therefore can better determine GRACE HAM and CAM excitations, in particularly at interannual and longer time scales. 3.2. Excitations from global mass redistribution We separate mass-related excitations of polar motion by removing atmospheric wind and ocean current excitations from IERS observations, and compare (Obs. – Wind – Current) with combined mass-contributions from the atmosphere, ocean, and land hydrology (denoted as AOW), and with cryospheric contributions included (denoted as AOWC) (see Fig. 4). Wind and ocean current excitations are estimated from the NCEP and ECCO models (see Sections 2.2 and 2.3). AOW excitations (in Fig. 4) represent the sum of contributions from NCEP atmospheric pressure, ECCO OBP, and WGHM TWS change (and AOWC = AOW + GRACE CAM). When wind and current effects are removed, observed massterm excitations agree remarkably well with both AOW (from
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Fig. 3. Comparison between residual excitations (i.e., Obs. – AAM – OAM) of (a) 1 and (b) 2 , with two GRACE estimates of HAM (and CAM) contributions.
models) and GRACE estimates, especially in 2 (reflecting mostly polar motion Y). GRACE results show significantly better agreement with observed 1 excitations than model estimates (AOW) do. Again, the improvement appears more evident (from visual examination) at longer periods (e.g., longer than a few years), consistent with the analysis in Section 3.1. 3.3. Seasonal budget of polar motion excitations To further examine the seasonal budget on mass-term polar motion excitations, we estimate annual and semiannual amplitudes and phases (along with the long-term trends) of the observed excitations and contributions from AOW, AOWC, and GRACE using unweighted least squares fit, and list the results in Table 1. Fig. 5a and b illustrates the comparisons and agreements of annual amplitudes and phases for 1 and 2 , using phasor diagrams. Consistent with visual examination of Fig. 4, observed mass-term excitations and the three geophysical excitations (AOW, AOWC, and GRACE) agree remarkably well in the 2 component. However, there is a significant phase difference (of about 60◦ ) between model-based excitations (AOW and AOWC) and observations in the 1 component, but GRACE total mass excitations of 1 agree significantly better with observations. To better understand annual excitations from different components of the Earth system and likely major error sources in estimates of 1 , we show the individual annual phasor vectors in
Fig. 4. Mass excitations of (a) 1 and (b) 2 , from observations (i.e., Obs. minus wind and ocean current contributions), combined contributions from the atmosphere, ocean with land water (AOW) from models, AOW plus cryosphere (AOWC), and GRACE observed mass change.
AOWC and GRACE excitations (see the dashed arrows in Fig. 6). The ECMWF atmospheric excitation is from the GRACE GAC solutions, which are based on the ECMWF atmospheric model. The NCEP and ECMWF atmospheric excitations agree very well. However, the two hydrological excitations, i.e., WGHM and GRACE (GRC) show large differences in both amplitude and phase, and the same is true for ECCO and GRACE oceanic excitations. CAM plays a smaller role in annual contributions to 1 . Clearly, the large difference between observed and AOWC (or AOW) mass-term contributions to 1 is mostly related to deficiencies in WGHM and ECCO models. 3.4. Sensitivity analysis of polar motion excitations There are distinctively different concordances between observations (i.e., EOP – Wind/Current) and model (AOW) and GRACE excitations for 1 and 2 components. That is, with a large difference for 1 , the same models yield near perfect agreement with observed 2 (see Figs. 4 and 5). Part of the difference may be that annual amplitudes in 2 are larger than in 1 , so a fixed noise level will have less effect for 2 (see Fig. 4b). However, the difference between AOWC and observed 1 is much larger than for 2 (see Fig. 5a and b), suggesting that WGHM and ECCO do a relatively poor job with 1 . On the other hand, GRACE excitations agree well with observations for both 1 and 2 . This indicates that
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Table 1 Amplitudes and phases of annual and semiannual mass-term excitations of 1 and 2 from space geodetic observations (Obs. – Wind/Current), combined geophysical contributions (AOW or AOWC), and GRACE-observed excitations during the period Jan. 2003 to Dec. 2009. The phase is defined as in sin (2(t − t0 ) + ), where t0 refers to h0 on January 1. Polar motion excitations (1 & 2 )
Obs. – Wind/Current (1 ) AOW (1 ) AOWC (1 ) GRACE (1 ) Obs. – Wind/Current (2 ) AOW (2 ) AOWC (2 ) GRACE (2 )
Annual
Semiannual
Amplitude (×108 )
Phase (deg)
Amplitude (×108 )
Phase (deg)
4.08 4.69 4.70 4.85 13.66 12.34 12.68 13.16
343 279 281 346 296 291 294 288
0.98 0.23 0.29 1.69 4.34 2.22 2.34 2.42
314 336 332 308 75 102 105 60
the distinctive agreements in 1 and 2 may be tied to the geographical sampling of the two components and numerical model performance in different regions. For comparisons, similar AOW2 excitations (covering the same time span, January 2003 through December 2009) which are based on combined GLDAS hydrological model (Rodell et al., 2004) estimates and GRACE GAC atmospheric and oceanic contributions are also included in the annual phasor diagrams. The computation of AOW2 excitations follows the exact same procedures of Chen and Wilson (2008).
1 and 2 are proportional to C21 and S21 (see Eq. (1)), which sample the earth as illustrated in the bottom two panels of Fig. 5. For S21 (Fig. 5d), the maxima of the two mass signals in the northern hemisphere fall in the centers of Eurasian and North American continents. In contrast, the maximum C21 sensitivity (in the northern hemisphere) is mostly over the oceans. This suggests that S21 may be more sensitive (than C21 ) to mass changes over land, and C21 is more sensitive to mass changes over the oceans. This is useful in addressing the following questions.
Fig. 5. Phasor diagram of annual mass excitations of (a) 1 and (b) 2 . The four vectors in each panel represent annual mass excitations from observations (EOP – Wind/Current), AOW, AOWC, and GRACE. Separate estimates of AOW2 based on GLDAS land water and GRACE GAC atmosphere and ocean (Chen and Wilson, 2008) are also included for comparisons. Units are in radians (×10−8 ). Each annual excitation is described by a sine and a cosine component, projected in the Y and X axes of the Cartesian coordinates. (c) and (d) Mass change modes of spherical harmonics C21 and S21 , corresponding to mass excitations of 1 and 2 , respectively. The four maximums of the C21 mode fall mostly in ocean areas, and the two northern hemispheric maximums of the S21 mode fall over the Eurasian and North American continents, suggesting the different sensitivities of these two mass change modes to atmospheric and oceanic contributions (due to the IB response over the oceans, atmospheric pressure effects are dominated by contributions from land).
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Fig. 6. Phasor diagram of individual contributions to annual mass excitations of 1 . The solid vectors show mass excitations from EOP – Wind/Current (blue), models (green), and GRACE (GRC) (red), and dashed vectors show individual components. Ice contributions are from GRACE. Units are in radians (×10−8 ). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
(1) Why do 2 (mass-term) excitations have larger variability than 1 ? Seasonal variations in the atmosphere clearly play a more dominant role in polar motion excitation (see Fig. 1a and b). At seasonal time scales, atmospheric pressure changes over the oceans are mostly cancelled by the IB effect. That means atmospheric pressure change over land and TWS change are the most significant seasonal forces driving polar motion. As 2 is more sensitive to mass load change over land, 2 is expected to show larger variability, mainly due to atmospheric and land water mass changes over the Eurasian and North American continents. (2) Why do observations and AOWC excitations agree better for 2 than in 1 ? Atmospheric pressure change plays a more important role in 2 than in 1 , and modern atmospheric models (e.g., ECMWF and NCEP) are considerably more mature than oceanic and hydrological models, and there are more available in situ and satellite meteorological observations to assimilate. This yields relatively better agreement for 2 (between observations and AOWC). In addition, 1 is more sensitive to seasonal variability of OBP, which is significantly smaller than atmospheric pressure and has relatively larger uncertainty. This will also contribute to poorer agreement for 1 . 4. Summary and discussion We estimate geophysical excitations of polar motion (1 and 2 ) using multiple sources of data, including recent numerical models for the atmosphere, ocean, and land hydrology, and GRACE satellite gravity measurements. At seasonal time scales, modelestimated AOW (or AOWC) excitations agree very well with polar motion observations for 2 , but show significant differences for 1 . However, GRACE-derived excitations agree remarkably well with observed geodetic excitations in both 1 and 2 , due to superior GRACE estimates of terrestrial water storage and oceanic mass changes. GRACE time-variable gravity measurements also provide a means for quantifying excitations from ice mass change (i.e., CAM) over polar ice sheets and mountain glaciers, largely omitted in previous studies due to the lack of adequate observations or reliable ice sheets models. GRACE estimates indicate that CAM excitations are small but not negligible contributors to seasonal excitations of polar motion.
Leakage corrections are important for quantifying hydrological and cryospheric excitations of polar motion from GRACE data. It has been demonstrated that the forward modeling method is effective in correcting the leakage effect and restoring the true magnitudes of TWS ice mass changes. The effect on ice mass changes is especially important (Fig. 3a and b). Better accounting for 2 (relative to 1 ) is apparently tied to the greater importance of relatively well determined atmospheric pressure and TWS changes over the Eurasian and North American continents, because S21 is proportional to 2 . This special sensitivity and the more significant seasonal mass load changes over land also contribute to the larger 2 amplitude. This study demonstrates inadequacies in current ocean and land surface models in forming estimates of large-scale mass changes. Of course, GRACE estimates suffer from a number of limitations as well, including low spatial resolution, contamination by longitudinal stripes, leakage effects, residual errors, and relatively large uncertainty in low degrees spherical harmonic coefficients. However, when measuring very large scale mass changes (C21 and S21 ) GRACE clearly out-performs oceanic and land surface models, and comes closer to balancing the seasonal excitation budget of polar motion.
Acknowledgments The authors would like to thank the two anonymous reviewers for their insightful comments, which lead to improved presentation of the results. We are grateful to Dr. Andreas Güntner for providing the WGHM data. This study was supported by the National Geospatial Intelligence Agency (under NURI Grant HM1582-07-1-2032), and National Science Foundation (under grants ANT-0632195 and ANT-1043750). Additional support was provided by the Shanghai Astronomical Observatory, Chinese Academy of Sciences and the Geology Foundation of the Jackson School of Geosciences, University of Texas Austin.
References Barnes, R., Hide, R., White, A., Wilson, C., 1983. Atmospheric angular momentum functions, length-of-day changes and polar motion. Proc. R. Soc. Lond. A 387, 31–73. Bettadpur, S., 2007a. Level-2 Gravity Field Product User Handbook. GRACE 327-734, The GRACE Project, Center for Space Research, University of Texas at Austin. Bettadpur, S., 2007b. CSR Level-2 Processing Standards Document for Product Release 04. GRACE 327-742, The GRACE Project, Center for Space Research, University of Texas at Austin. Cazenave, A., Dominh, K., Guinehut, S., Berthier, E., Llovel, W., Ramillien, G., Ablain, M., Larnicol, G., 2009. Sea level budget over 2003–2008: A reevaluation from GRACE space gravimetry, satellite altimetry and Argo. Global Planetary Change 65, 83–88. Chen, J.L., 2005. Global Mass Balance and the Length-of-day Variation. J. Geophys. Res. 110, B08404, doi:10.1029/2004JB003474. Chen, J.L, Wilson, C.R., Chambers, D.P., Nerem, R.S., Tapley, B.D., 1998. Seasonal global water mass budget and mean sea level variations. Geophys. Res. Lett. 25 (19), 3555–3558. Chen, J.L., Wilson, C.R., Eanes, R.J., Tapley, B.D., 2000. A new assessment of long wavelength gravitational variations. J. Geophys. Res. 105 (B7), 16271–16278. Chen, J.L., Wilson, C.R., Hu., X.G., Zhou, Y.H., Tapley, B.D., 2004a. Oceanic effects on polar motion determined from an ocean model and satellite altimetry: 1993–2001. J. Geophys. Res. 109 (B2), B02411, doi:10.1029/2003JB002664. Chen, J.L., Wilson, C.R., Tapley, B.D., Ries, J.C., 2004b. Low degree gravitational changes from GRACE: validation and interpretation. Geophys. Res. Lett. 31, L22607, doi:10.1029/2004GL021670. Chen, J.L., Wilson, C.R., Tapley, B.D., 2006. Satellite gravity measurements confirm accelerated melting of greenland ice sheet. Science 313, doi:10.1126/science.1129007. Chen, J.L., Wilson, C.R., Tapley, B.D., Blankenship, D., Young, D., 2008. Antarctic regional ice loss rates from GRACE. Earth Planet. Sci. Lett. 266, 140–148, doi:10.1016/j.epsl.2007.10.057. Chen, J.L., Wilson, C.R., 2008. Low degree gravitational changes from GRACE, Earth 380 Rotation, geophysical models, and satellite laser ranging. J. Geophys. Res. 113, B06402, doi:10.1029/2007JB005397.
J.L. Chen et al. / Journal of Geodynamics 62 (2012) 8–15 Chen, J.L., Wilson, C.R., Blankenship, D.D., Tapley, B.D., 2009. Accelerated Antarctic ice loss from satellite gravity measurements. Nature Geosci. 2, 859–862, doi:10.1038/NGEO694. Dickey, J.O., Marcus, S.L., Johns, C.M., Hide, R., Thompson, S.R., 1993. The oceanic contribution to the Earth’s seasonal angular momentum budget. Geophys. Res. Lett. 20 (24), 2953–2956. Döll, P., Kaspar, F., Lehner, B., 2003. A global hydrological model for deriving water availability indicators: model tuning and validation. J. Hydrol. 270, 105–134. Eubanks, T.M., Steppe, J.A., Dickey, J.O., Rosen, R.D., Salstein, D.A., 1988. Causes of rapid motions of the Earth’s pole. Nature 334, 115–119. Eubanks, T.M., 1993. Variations in the orientation of the earth. In: Smith, D., Turcotte, D. (Eds.), Contributions of Space Geodesy to Geodynamic: Earth Dynamics. Geodyn. Ser., vol. 24. AGU, Washington, D.C., pp. 1–54. Fukumori, I., Lee, T., Menemenlis, D., Fu, L.-L., Cheng, B., Tang, B., Xing, Z., Giering, R., 2000. A dual assimilation system for satellite altimetry. In: Joint TOPEX/POSEIDON and Jason-1 Science Working Team Meeting, Miami Beach, Florida, 15–17 November 2000. Gambis, G., 2004. Monitoring Earth Orientation at the IERS using space-geodetic observations. J. Geod. 78, 295–303. Greatbatch, R.J., 1994. A note on the representation of steric sea level in models that conserve volume rather than mass. J. Geophys. Res. 99, 12767–12771. Gross, R.S., Fukumori, I., Menemenlis, D., Gegout, P., 2004. Atmospheric and oceanic excitation of length-of-day variations during 1980–2000. J. Geophys. Res. 109, B01406, doi:10.1029/2003JB002432. Güntner, A., Stuck, J., Werth, S., Döll, P., Verzano, K., Merz, B., 2007. A global analysis of temporal and spatial variations in continental water storage. Water Resources Res. 43 (5), W05416, doi:10.1029/2006WR005247. Hunger, M., Döll, P., 2008. Value of river discharge data for global-scale hydrological modeling. Hydrol. Earth Syst. Sci. 12, 841–861.
15
Jin, S., Chambers, D.P., Tapley, B.D., 2010. Hydrological and oceanic effects on polar motion from GRACE and models. J. Geophys. Res. 115 (B2), 1–11, doi:10.1029/2009JB006635. Kalnay, E., et al., 1996. The NCEP/NCAR 40-year reanalysis project. Bull. Am. Meteorol. Soc. 77, 437–471. Minster, J.F., Cazenave, A., Serafini, Y.V., Mercier, F., Gennero, M.C., Rogel, P., 1999. Annual cycle in mean sea level from TOPEX-Poseidon and ERS-1: inference on the global hydrological cycle. Global Planetary Change 20, 57–66. Munk, W.H., McDonald, G.J.F., 1960. The Rotation of the Earth. Cambridge Univ. Press, Cambridge, U.K. Nastula, J., Ponte, R.M., Salstein, D.A., 2007. Comparison of polar motion excitation series derived from GRACE and from analyses of geophysical fluids. Geophys. Res. Lett. 34, L11306, doi:10.1029/2006GL028983. Ponte, R.M., Stammer, D., Marshall, J., 1998. Oceanic signals in observed motions of the Earth’s pole of rotation. Nature 391, 476–479. Rodell, M., et al., 2004. The global land data assimilation system. Bull. Am. Meteorol. Soc. 85 (3), 381–394. Swenson, S., Wahr, J., 2006. Post-processing removal of correlated errors in GRACE data. Geophys. Res. Lett. 33, L08402, doi:10.1029/2005GL025285. Tapley, B.D., Bettadpur, S., Watkins, M.M., Reigber, C., 2004. The gravity recovery and climate experiment; mission overview and early results. Geophys. Res. Lett. 31 (9), L09607, doi:10.1029/2004GL019920. 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, doi:10.1029/98JB02844. Wilson, C.R., 1985. Discrete polar motion equations. Geophys. J. R. Astron. Soc. 80, 551–554. Wouters, B., Chambers, D., Schrama, E.J.O., 2008. GRACE observes small-scale mass loss in Greenland. Geophys. Res. Lett. 35, L20501, doi:10.1029/2008GL034816.