Terrestrial Water Storage Variations from GRACE
As a major component of global water cycle, terrestrial water is defined as an integrated mea-sure of all forms of water stored on and below the surface of the Earth, which includes surface water, soil moisture and permafrost, groundwater, snow and ice, and wet biomass. Early, based on some simulations from hydrological, oceanic, and atmospheric models, Wahr et al.  validated the detectability of TWS variation signal using GRACE and proposed the basic method for constructing mass variations from the GRACE gravity coefficients. Later, Swenson and Wahr  devised spatial averaging kernels to extract regional mass variations from GRACE. Since its launch in 2002, GRACE has proven to be an extremely useful tool for observing TWS variations [Tapley et al., 2004; Wahr et al., 2004]. As the largest drainage basin in the world, Amazon River basin exhibits large-scale TWS variations, which is prone to be observed by GRACE firstly [Tapley et al., 2004]. Significant seasonal variability of TWS in the Amazon River basin was detected by GRACE, and was in general agreement with the predictions of a hydrological model [Wahr et al., 2004] . With the increase of GRACE ob-servations and the improvement of data processing methods, interannual variations of TWS in the Amazon River basin are further validated based on GRACE observations. The drought events in 2005 and 2010 and the flood in 2009 in the Amazon River basin are detected by GRACE [Chen et al., 2010a, 2009b; Feng et al., 2012; Frappart et al., 2012]. By comparing with in situ river level records, precipitation observations, and hydrological models, GRACE has proven to successfully capture both seasonal and interannual variations of TWS in the Amazon River basin [Alsdorf et al., 2010; Becker et al., 2011; Xavier et al., 2010; Zeng et al., 2008]. Additionally, GRACE-observed TWS variations even have the potential to improve the fire forecasts for the southern Amazon [Chen et al., 2013]. Besides the Amazon river basin, GRACE also detects hydrological signals in many parts of the world, e.g., the Congo River basin [Crowley et al., 2006], the Lower Ob basin [Frappart et al., 2010], the Yangtze River basin[Hu et al., 2006; Zhong et al., 2009], the Illinois and Texas of U.S. [Long et al., 2013; Swenson et al., 2006], the East African great lakes region [Becker et al., 2010], the North America and Scandinavia [Wang et al., 2013], and the central Europe [Andersen et al., 2005].
Groundwater, soil water and surface water are three main components of terrestrial water. With the development of remote sensing and the increase of ground observation data, surface water and soil water can be observed or modeled at different spatial and temporal resolutions [Crétaux et al., 2011; Famiglietti, 2004; Kerr et al., 2001; Rodell et al., 2004; Sheffield et al., 2009]. As an important component of global water cycle, groundwater is a vital source of fresh water for agriculture, industry, public supply, and ecosystems in many parts of the world. However, there are no extensive ground-based networks for monitoring large-scale groundwa-ter storage (GWS) variations. Globally, groundwater provides more than 50% of drinking water, 40% of industrial water, and 20% of irrigation water [Zektser and Everett Lorne, 2004]. Over-exploitation of groundwater has resulted in groundwater depletion and pollution as well as soil salinization and land subsidence, particularly in places where groundwater-based irri-gation is intensive, such as in the North China Plain (NCP), northern India, and the central United States [Scanlon et al., 2007; Shah et al., 2000; Wada et al., 2010]. However, informa-tion regarding the spatial and temporal variability of GWS is extremely limited [Shah et al., 2000]. The impact of groundwater on global water cycle is still veiled. Preliminary study in-dicates that global groundwater depletion rate since 2000 is ∼145 km3/yr (equivalent to 0.40 mm/yr of sea-level rise, or 13% of the reported rate of 3.1 mm/yr) [Konikow, 2011]. However, Wada et al. ’s results show that the contribution of groundwater depletion to sea-level rise is about 0.57 ± 0.09 mm/yr in 2000, which is significant larger than that from Konikow . The latest estimate based on WaterGAP global hydrological model from Döll et al.  is 113 km3/yr (equivalent to 0.31 mm/yr of sea-level rise) for the period 2000-2009, which is smaller than other two estimates derived from different global hydrological modeling [Konikow, 2011; Wada et al., 2012]. So the modeling uncertainties of global groundwater depletion rate remain high.
Global Sea Level Variations from Altimetry and GRACE
By defining the sea level relative to the Earth’s geocenter (i.e., geocentric sea level), the phys-ical causes of sea level change can be expressed as either the ocean volume change or ocean-basin shape change [Willis et al., 2010]. Changes of ocean-basin shape mainly result from the Glacial Isostatic Adjustment (GIA) effect, which is the Earth’s viscoelastic response to the last deglaciation [Lambeck and Nakiboglu, 1984; Peltier, 1986]. GIA effect causes a net sinking of ocean basin relative to the Earth’s geocenter, which would imply, if the surface of the sea remained at a constant distance to the center of the Earth, a globally averaged sea level rise rate of 0.3 mm/yr [Peltier, 2009]. Usually, this effect is therefore added to global sea level change observed by altimetry and tide gauges. So, in a general sense, global sea level change refers to the changes in the ocean’s volume.
Global mean sea level (GMSL) change results from two major processes: (i) thermal ex-pansion caused by heating of the global ocean (i.e., thermosteric sea level), and (ii) ocean mass change caused by the exchange of water between oceans and other reservoirs (i.e., glaciers and ice caps, ice sheets, and other land water reservoirs) [IPCC AR5, 2013] . Although haline ef-fects might be significant in some regional ocean, the globally averaged salinity content stay relatively constant [Antonov et al., 2002; Munk, 2003]. Thus, the net increase of ocean heat content and the freshwater imports from continents are the two dominant reasons of global sea level rise.
Based on tide gauge measurements, global sea level rise rate over the 20th century is about 2 mm/yr, as released by the latest IPCC Fifth Assessment Report (AR5) . However, the number and spatial distribution of tide gauge observations are highly limited [Mitchum et al., 2010]. In addition, since tide gauge observes the sea level variations relative to the land, the crustal deformation in the tide gauge station need to be estimated, which is still difficult for many tide gauge stations. Figure 1.5 shows the estimated, observed, and projected global sea level rise from 1800 to 2100 [Shum et al., 2008; Willis et al., 2010], which exhibits a significant acceleration in sea level rise since about 1900. Since early 1990s, satellite altimetry provides a high coverage of the spatial and temporal variations of the sea level globally. The GMSL rise rate during 1993-2013 observed by satellite altimetry is about 3.2 mm/yr. This GMSL rise rate is relatively stable since 1993 [Ablain et al., 2009; Cazenave et al., 2009; Kuo, 2006; Leuliette and Scharroo, 2010; Nerem et al., 2010; Shum et al., 2008; Willis et al., 2010]. Although the quality and quantity of sea level observations have improved significantly in recent two decades, the projected sea level rise remains controversial, especially from semi-empirical models [Gregory et al., 2006; Grinsted et al., 2010; Holgate et al., 2007; Rahmstorf, 2007; Schmith et al., 2007; Taboada and Anadon, 2010; Vermeer and Rahmstorf, 2009, 2010].
It is worth noting that the global sea level rise rate is inhomogeneous in spatial domain [Cazenave and Llovel, 2010]. As shown in Figure 1.6a, in some regions, such as the Western Pacific Ocean, sea level rises rapidly; while in the eastern coast of Northern Pacific Ocean, sea level falls. Additionally, sea level exhibit rise and drop alternately in oceans, where there are high-speed currents, e.g., Kuroshio Current, Gulf Stream, and Antarctic Circumpolar Current. When the global mean sea level rise rate of 3.2 mm/yr is removed, the nonuniform distribu-tion of regional sea level trends relative to GMSL rise is further highlighted (Figure 1.6b). For example, sea level rise rate in the warm pool region of the Western Pacific Ocean is sig-nificantly larger than the global mean value. Keep in mind that this inhomogeneous pattern of sea level rise rate also contains the response of sea level to climate change events on in-terannual to decadal timescales, e.g., El Niño-Southern Oscillation (ENSO), North Atlantic Oscillation (NAO), and Pacific Decadal Oscillation (PDO). Thus, it is worthwhile to analyze the nonuniform sea level change in different ocean regions.
Although altimetry provides the temporal and spatial variations of global sea level, it is not able to isolate the steric sea level variations (SLV) and mass-induced SLV. Steric SLV can be calculated from ocean temperature and salinity data based on oceanographic observations or ocean models [Fukumori, 2002; Ishii et al., 2006; Levitus et al., 2005]. The Argo project is a global ocean observing system for measuring temperature and salinity in the Earth’s oceans since the early 2000s [Guinehut et al., 2004; Hadfield et al., 2007; Roemmich and Owens, 2000]. Since 2007, the Argo array contains more than 3000 high-quality temperature and salinity profiles in or near real time, which significantly improve the coverage of global oceanographic observations (http://www.argo.ucsd.edu/).
In spatial domain, original unconstrained monthly gravity field observed by GRACE shows north-south stripes, which represent the correlated errors in the gravity coefficients. As a example, spatial pattern of mass variations in October 2013 from original GRACE Stokes coefficients is shown in Figure 2.2. Swenson and Wahr  found that, for a given order m, Stokes coefficients of the same parity are correlated with each other. They proposed a method to reduce this correlation by using quadratic polynomial in a moving window of width w centered at degree l . For example, for Cl,m, they used the Stokes coefficients Cl−2α ,m, …, Cl−2,m, Cl,m, Cl+2,m, …, Cl+2α ,m to fit a quadratic polynomial, and removed the fitted value from original Cl,m to derive the de-correlated Cl,m. The relation between the width of moving window w (i.e., the number of coefficients used for quadratic polynomial fitting) and α is w = 2α + 1. In Swenson and Wahr ’s paper, the detailed algorith to determine the width of moving window was not provided. Referring to Swenson and Wahr’s unpublished results, Duan et al.  provided the window width in the form of w = max(Ae− m +1,5) (2.17).
where m is order (≥5), max() takes the larger one of the two arguments. Swenson and Wahr  have empirically chose A = 30 and K = 10 based on a trial-and-error procedure.
To estimate ocean mass change using GRACE, Chambers  modified the algorithm described above. For RL02 GRACE solutions, they keep 7 × 7 portion of the coefficients unchanged, and fit a 7th order polynomial to the remaining coefficients to degrees with the same parity for each order up to 50. In their method, only one polynomial is used for each odd or even set for a given order, unlike the method from Swenson and Wahr . For RL04 GRACE solutions, they keep 11 × 11 portion of the coefficients unchanged, and a 5th order polynomial is applied. For latest RL05 GRACE solutions, the optimal parameterization based on the model test is to start filtering at degree 15, and adopt a 4th polynomial [Chambers and Bonin, 2012]. This processing method is denoted as P4M15.
Chen et al. [2007a] used the P3M6 method to process GRACE data and estimated coseismic and post-seismic deformation from the Sumatra-Andaman earthquake using GRACE. Later, they adopted the P4M6 method to estimate mass balance in ice caps, mountain glaciers, and terrestrial water storage change [Chen et al., 2009a, 2010a, 2007b, 2008, 2009b, 2010b].
Different from the above methods, Duan et al.  determined the unchanged portion of coefficients based on the error pattern of the coefficients. Their unchanged portion of coef-ficients and the width of moving window depend on both degree and order in a more complex way. As a example, Figure 2.2 shows the global mass variations in October 2013 from GRACE Stokes coefficients based on different destriping methods. As shown in Figure 2.2(c-f), there is a general agreement among results from different destriping methods. In addition, destriping process suppresses the north-south stripes more efficiently, comparing the results with only the Gaussian smoothing applied.
Combination of Altimetry, GRACE and Oceanographic Data
Satellite altimetry can observe the total SLV over the global ocean, while GRACE and oceano-graphic data can be used to estimate mass-induced SLV and steric SLV respectively. Never-theless, to study the global sea level budget using these three independent observations, some attention should be paid to make these observations in a self-consistent way.
Elastic Loading Deformation
Owing to the elastic loading effect, mass change in the water column produces a vertical dis-placement in the ocean bottom, which may not be negligible in some regional ocean [Kuo et al., 2008]. This elastic loading deformation should be removed from altimetry, when com-paring with GRACE results. The following equation is used to calculate this loading deforma-tion: ∞l hl ΔH (θ , λ ) = a ∑ ∑ Plm(cos θ ) ΔClm cos(mλ ) + ΔSlm sin(mλ ) (2.38) 1 + kl l=0 m=0.
where a is the Earth’s radius, θ , λ are co-latitude and longitude respectively, l is degree and m is order, Plm(cos θ ) is the fully normalized associated Legendre function, ΔClm, ΔSlm are geopotential spherical harmonics respectively, kl is potential Love number, and hl is vertical Love number.
Stokes coefficients from GRACE products are employed to compute the vertical loading deformation in the ocean bottom. Figure 2.7 shows the vertical loading deformation in the ocean bottom in January 2003 based on GRACE-observed ocean mass variations in the same month.
Table of contents :
1.1 Terrestrial Water Storage Variations from GRACE
1.2 Global Sea Level Variations from Altimetry and GRACE
1.3 Outline of the Thesis
2.1 Basics of Temporal Gravity Field
2.2 Post-processing Methods
2.2.1 Gaussian Smoothing
2.2.2 Destriping Methods
2.2.3 GRACE Measurement Error
2.2.4 Basin-scale Mass Variations from Temporal Gravity Field
2.3 Combination of Altimetry, GRACE and Oceanographic Data
2.3.1 Steric Sea Level Variations
2.3.2 Glacial Isostatic Adjustment
2.3.3 Elastic Loading Deformation
2.3.4 Inverted Barometer Corrections
2.3.5 Boussinesq Approximation
3 Groundwater Storage Variations in North China from GRACE
3.2 Data and Methods
3.2.1 GRACE Data and Processing
3.2.2 Land Surface Models
3.2.3 Ground-based Measurements
3.2.4 Groundwater Model
3.3.1 Seasonal GWS Variations
3.3.2 Interannual GWS Variations
3.3.3 Long-term GWS Variations
3.3.4 Error Estimation of GRACE-based GWS Variations
4 Regional Sea Level Variations from GRACE
4.2 Sea Level Variations in China Seas
4.2.2 Study Region
4.2.3 Spatial Patterns of Seasonal Sea Level Variations in China Seas
4.2.4 Sea Level Variations in the South China Sea
4.2.5 Sea Level Variations in the East China Sea and Yellow Sea
4.2.6 Discussion and Summary
4.3 Sea Level Variations in the Red Sea
4.3.2 Data and Processing
4.3.3 GRACE Data
4.3.4 Steric-corrected Altimetry Data
4.3.5 Bottom Pressure Records
4.3.6 Results and Discussion
5 Conclusions and Future Work
5.2 Future Work