Deriving scaling factors using a global hydrological model to restore GRACE total water storage changes for China's Yangtze River Basin

Remote Sensing of Environment 168 (2015) 177–193

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Deriving scaling factors using a global hydrological model to restore GRACE total water storage changes for China's Yangtze River Basin Di Long a,⁎, Yuting Yang b, Yoshihide Wada c,d,e, Yang Hong a,f, Wei Liang g, Yaning Chen h, Bin Yong i, Aizhong Hou j, Jiangfeng Wei k, Lu Chen l a

State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China CSIRO Land and Water, Black Mountain, Canberra, ACT 2601, Australia Department of Physical Geography, Utrecht University, Utrecht, The Netherlands d NASA Goddard Institute for Space Studies, New York, NY 10025, United States e Center for Climate Systems Research, Columbia University, New York, NY, United States f Department of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019, United States g Department of Tourism and Environmental Sciences, Shaanxi Normal University, Xi'an, Shaanxi 710119, China h State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi, Xinjiang 830011, China i State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Jiangsu 210098, China j Bureau of Hydrology, Ministry of Water Resources, Beijing 100053, China k Department of Geological Sciences, The University of Texas at Austin, Austin, TX 78712, United States l College of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China b c

a r t i c l e

i n f o

Article history: Received 18 September 2014 Received in revised form 30 May 2015 Accepted 1 July 2015 Available online xxxx Keywords: GRACE Scaling factor PCR-GLOBWB CLM4.0 GLDAS-1 Noah Yangtze River China

a b s t r a c t This study used a global hydrological model (GHM), PCR-GLOBWB, which simulates surface water storage changes, natural and human induced groundwater storage changes, and the interactions between surface water and subsurface water, to generate scaling factors by mimicking low-pass filtering of GRACE signals. Signal losses in GRACE data were subsequently restored by the scaling factors from PCR-GLOBWB. Results indicate greater spatial heterogeneity in scaling factor from PCR-GLOBWB and CLM4.0 than that from GLDAS-1 Noah due to comprehensive simulation of surface and subsurface water storage changes for PCR-GLOBWB and CLM4.0. Filtered GRACE total water storage (TWS) changes applied with PCR-GLOBWB scaling factors show closer agreement with water budget estimates of TWS changes than those with scaling factors from other land surface models (LSMs) in China's Yangtze River basin. Results of this study develop a further understanding of the behavior of scaling factors from different LSMs or GHMs over hydrologically complex basins, and could be valuable in providing more accurate TWS changes for hydrological applications (e.g., monitoring drought and groundwater storage depletion) over regions where human-induced interactions between surface water and subsurface water are intensive. © 2015 Elsevier Inc. All rights reserved.

1. Introduction The total water storage (TWS) change, defined as changes in all water components stored on the surface (e.g., lakes, reservoirs, rivers, and snow water equivalent), in the entire soil profile, and in aquifers, is one of the most critical state variables in the hydrological cycle (Famiglietti & Rodell, 2013; Landerer & Swenson, 2012; Long, Longuevergne, & Scanlon, 2015). In conventional water budget calculations, the TWS change is often assumed negligible on multiple-year scales (steadystate storage) but becomes critical due to appreciable changes at monthly and seasonal scales (transient storage change). In this case, the assumption of steady-state storage can lead to great errors in water budget estimates. Traditional measurements of TWS change components, e.g., surface water storage (SWS) changes, soil moisture storage (SMS) ⁎ Corresponding author. E-mail address: [email protected] (D. Long).

http://dx.doi.org/10.1016/j.rse.2015.07.003 0034-4257/© 2015 Elsevier Inc. All rights reserved.

changes, and groundwater storage (GWS) changes are made at point scales. It was impossible to directly measure TWS changes at regional and even larger scales. Since its launch in 2002, Gravity Recovery and Climate Experiment (GRACE) satellites realize for the first time in history detection of TWS changes on a 10-day or monthly basis by measuring changes in the Earth's gravity field (Tapley, Bettadpur, Ries, Thompson, & Watkins, 2004), providing valuable state variable information for a range of hydrological studies and applications. GRACE-derived TWS changes have been widely used for monitoring droughts (Leblanc, Tregoning, Ramillien, Tweed, & Fakes, 2009; Long et al., 2013) and floods (Chen, Wilson, & Tapley, 2010; Reager & Famiglietti, 2009), evaluating groundwater variations (Rodell, Velicogna, & Famiglietti, 2009; Rodell et al., 2007; Scanlon et al., 2012; Scanlon, Longuevergne & Long, 2012; Yeh, Swenson, Famiglietti, & Rodell, 2006) and glacier and snow melting (Chen, Wilson, & Tapley, 2013), and improving land surface models (LSMs) through data assimilation (Houborg, Rodell, Li, Reichle, & Zaitchik, 2012; Lo, Famiglietti, Yeh, &

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Syed, 2010) over the past decade. Efforts have also been made to reconstruct and predict TWS anomalies beyond the GRACE period (Forootan et al., 2014; Long et al., 2014; Xavier et al., 2010). More recently reported results suggest that GRACE-observed TWS changes can be useful in interpreting variations in surface greenness across continental Australia (Yang et al., 2014). GRACE is especially suitable for quantifying TWS changes at spatial resolution greater than its footprint of ~200,000 km2 which is limited by the altitude (McVicar & Körner, 2013) of GRACE satellites of ~450 km and the distance between the two satellites of ~200 km (Chen, Li, Zhang, & Ni, 2014; Tapley et al., 2004). The fundamental problem in use of GRACE data is to reduce the bias (or leakage-out error) and leakage (or leakage-in error) errors in GRACE-derived TWS changes that result from low-pass filtering for removing high-frequency noise in GRACE signal (Longuevergne, Scanlon, & Wilson, 2010; Swenson & Wahr, 2006). There are generally four approaches to reduce the bias and leakage effects. The first approach uses filtered and unfiltered TWS changes from synthetic data (e.g., from LSMs) to create scaling factors, i.e., the scaling factor approach. The bias and leakage effects can be corrected by multiplying the filtered GRACE TWS changes with the corresponding scaling factor for a basin or the scaling factors for each grid cell of a basin. GRACE Level 3 TWS change products (1° × 1° gridded) are based on the scaling factor approach (Landerer & Swenson, 2012) and have been widely used in the hydrological community. The second approach takes advantage of LSMs to correct for the bias and leakage errors of filtered GRACE signals separately, i.e., the additive correction approach (Longuevergne et al., 2010). The third approach is based on the assumption of uniform distribution of TWS changes within a basin and a multiplicative factor, which does not depend largely on LSMs, termed the multiplicative correction approach (Longuevergne et al., 2010; Swenson & Wahr, 2007; Velicogna & Wahr, 2006). The fourth approach is data assimilation by sequentially adjusting hydrological components from LSMs and ground measurements based on respective uncertainties (van Dijk, Renzullo, & Rodell, 2011; van Dijk, Renzullo, Wada, & Tregoning, 2014). The scaling factor approach is to perform forward modeling of LSM or global hydrological model (GHM) output. TWS changes from LSMs or GHMs are filtered by the same low-pass filtering as applied to GRACE data. Scaling factors can therefore be derived by least square fit between the filtered and unfiltered modeled TWS changes at basin scales or grid cell scales. It is noted that the scaling factor is not aimed to make the filtered GRACE TWS changes equivalent to modeled TWS changes, but makes use of pattern information in modeled TWS changes to restore signal losses in GRACE data. The widely used gridded GRACE TWS anomaly products (Landerer & Swenson, 2012) have popularized the use of GRACE data by hydrologists without geodesy background. Scaling factors for the products were derived from NCAR's Community Land Model 4.0 (CLM4.0) (Gent et al., 2011; Lawrence et al., 2011), which accounts for natural discharge and recharge of groundwater and river storage changes that are not simulated in many LSMs. Human activities, e.g., irrigation with surface water and groundwater, may result in water redistribution in the soil profile and changes in the interactions of moisture between soil layers and aquifers. Accurate simulation of these complex processes between natural and human systems remains a big challenge. LSMs, e.g., Noah (Ek et al., 2003), Mosaic (Koster & Suarez, 1994, 1996), Variable Infiltration Capacity (VIC) (Liang, Lettenmaier, Wood, & Burges, 1994), and CLM (Dai et al., 2003) in Global Land Data Assimilation System-1 (GLDAS1) (Rodell et al., 2009), have been widely used to provide estimates of SMS changes at regional/basin scales. GWS change scan be disaggregated from GRACE-observed TWS changes, LSM-simulated SMS changes, and in situ SWS measurements or satellite altimetry-based water levels for deriving SWS changes using mass balance (Rodell et al., 2007; Strassberg, Scanlon, & Chambers, 2009; Voss et al., 2013). LSMsimulated TWS estimates approximated by SMS changes, snow water equivalent, and canopy interception are also used to correct for the bias and leakage effects (Longuevergne et al., 2010). It is noted that

the LSMs in GLDAS-1 do not simulate GWS changes and human impacts (e.g., irrigation) on water storage changes. Therefore, LSMs or GHMs that account for human activities seem more suited for depicting these complex interactions and may provide more reliable hydrological state and flux variables over regions with intensive human activities (Döll et al., 2014; Pokhrel et al., 2015; Wada, van Beek, & Bierkens, 2012; Wada, Wisser, & Bierkens, 2014). PCR-GLOBWB is one of the GHMs able to simulate TWS changes by depicting water storage changes on the surface in rivers, lakes, reservoirs and wetlands, two vertically stacked soil layers, and an underlying groundwater layer, as well as exchange between the layers and between the top layer and the atmosphere (van Beek, Wada, & Bierkens, 2011; Wada et al., 2011; Wada et al., 2014). PCR-GLOBWB output may therefore be more accurate to represent reality in basins with intensive human activities and useful in deriving more effective scaling factors for restoring GRACE signals. Evaluation of GRACE-observed TWS changes is critical before applying to resolve water-related issues (Famiglietti et al., 2011; Long, Longuevergne & Scanlon, 2014). It is, however, extremely difficult to directly evaluate TWS changes on a basin scale using limited point-based measurements of TWS components (e.g., limited soil moisture sampling and groundwater monitoring networks). One of practical ways for the evaluation is based on surface water budget calculation, in which evapotranspiration (ET) is one of the most uncertain variables that may cause failures of water budget estimates of TWS changes (Syed, Famiglietti, & Chambers, 2009). There are generally three types of remote sensing-based models for ET estimation (Kalma, McVicar, & McCabe, 2008). The first approach mainly incorporates land surface temperature (LST) from thermal infrared remote sensing to solve the energy balance equation (Anderson, Norman, Mecikalski, Otkin, & Kustas, 2007; Bastiaanssen, Menenti, Feddes, & Holtslag, 1998; Long & Singh, 2012; Norman, Kustas, & Humes, 1995; Su, 2002). The second approach takes advantages of the correlation among evaporative fraction (EF, defined as the ratio of the latent heat flux to the sum of latent heat and sensible heat flux), LST, and fractional vegetation cover (fc) to calculate EF within a characteristic triangular or trapezoidal space constituted by LST and fc (e.g., Carlson, 2007; Jiang & Islam, 2001; Long, Singh & Scanlon, 2012; Moran, Clarke, Inoue, & Vidal, 1994). These models are constrained to work under clear sky conditions. The third approach is based on the Penman–Monteith equation, in which parameters associated with surface and canopy conductance are related to the remotely sensed vegetation index (VI). Because the VI derived from visible and near infrared band information is less affected by cloud contamination and shows relatively slower variations compared with instantaneous LST, the third approach is suitable to generate global ET products, e.g., the MOD16 ET product (Mu, Zhao, & Running, 2011) and the Advanced Very High Resolution Radiometer (AVHRR) ET product (Zhang, Kimball, Nemani, & Running, 2010). The Yangtze River in China (6300 km long) is the third longest river in the world, with a contributing area of ~1,800,000 km2 that sustains ~ 400 million people. Climate change and extreme events, including droughts and floods, in combination with intensive surface water irrigation have been profoundly influencing terrestrial water resources, and in turn, resulted in great impacts on natural and human systems (Long, Scanlon, Fernando, Meng & Quiring, 2012; Wang, Sheng, Gleason, & Wada, 2013). Quantification of TWS changes from GRACE observations and land surface/hydrological modeling could be extremely helpful for developing a better understanding of GRACE signal restoration over hydrologically complex basins and therefore guiding integrative water resource management at basin scales. The objectives of this study were twofold: (1) generating scaling factors of the Yangtze River basin for restoring GRACE signals using PCR-GLOBWB and forward modeling; and (2) evaluating GRACE TWS changes using a water balance approach, satellite ET and precipitation products, and in situ stream flow data. This study should be valuable in providing implications for hydrological drought monitoring over the Yangtze River basin using the restored GRACE TWS changes, and

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providing reference for large water diversion projects (e.g., the Project of Water Diversion from the South to the North of China) and integrative water resource management for one of the most populous large river basins in the world. 2. Method and materials 2.1. Study region The Yangtze River originates from Qinghai Province, with its mainstream flowing across 11 provinces of China from the west to the east and its outlet at Shanghai. The Yangtze River basin is one of the largest river basins in the world in terms of its gross amount of water resources of ~976 km3, with an area of ~1,800,000 km2 that accounts for ~one fifth of China's territory (Fig. 1). The climate of the major portion of the Yangtze River basin is subtropical monsoon, with mean annual precipitation of ~ 960 mm from the satellite precipitation product (TMPA 3B43). Similar seasonal cycles of rainfall and temperature favor the well development of agriculture across the Yangtze River basin which now sustains ~ 400 million people. The grain production accounts for ~ 40% of China, in which rice production shares 70% and cotton takes up ~ one third across the country. Around 8% of the Yangtze River basin (~ 144,000 km2) is equipped for irrigation (Fig. 2a), and 85% of the equipped areas (~122,240 km2) are actually irrigated (Fig. 2b) according to AQUASTAT data of the Food and Agricultural Organization of the United Nations (http://www.fao.org/nr/water/aquastat/irrigationmap/ index10.stm).Most of the areas equipped for irrigation are concentrated in the Chengdu Plains of the Upper Yangtze and the plains of the middle and lower reaches of the Yangtze River (Fig. 2a). Areas irrigated with surface water account for 96% of the areas equipped for irrigation, and only 4% of the equipped areas are irrigated with groundwater (Fig. 2c and d) over this region. Traditionally, the contributing area above the Yichang gauging station (Yichang station hereafter) on the mainstream is termed the Upper Yangtze River basin (~1,000,000 km2), the contributing area between the Yichang station and the Hukou gauging station (Hukou station hereafter) is termed the Central Yangtze River basin (~680,000 km2), and the remaining part is termed the Lower Yangtze River basin (~180,000 km2). Given the relatively small contributing area of the Lower Yangtze relative

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to the footprint of GRACE observations over 200,000 km2 and the large leakage error from the ocean into the Lower Yangtze River basin, in this study, we combine the Central and Lower Yangtze basins into an integrated part and term the Lower Yangtze River basin for convenience of discussion. Major surface water bodies in the Yangtze River basin from the east to the west are Lakes Taihu (near the outlet of the Yangtze River), Poyang (near the Hukou station), and Dongting in the Central Yangtze River basin (Fig. 1). The Three Gorges Reservoir (TGR) with a total reservoir capacity of 39.3 km3 forms a large manmade lake surface with an area of 1084 km2 when the water level achieves the elevation of 175 m. The associated hydroelectric power station with a total installed capacity of 22,500 MW including 32 main turbines and 2 small generators is the largest in the world. 2.2. Method 2.2.1. Scaling factors from forward modeling Applying filtering to a synthetic mass distribution is referred to as forward modeling and generates a mass distribution similar to what GRACE sees (Scanlon, Longuevergne & Long, 2012). In Landerer and Swenson (2012b), the scaling factor for a basin of interest was derived by least square fit between spatially averaged filtered and unfiltered modeled TWS anomaly time series. The filtered GRACE TWS anomaly for the basin was subsequently multiplied with the scaling factor for reducing the bias and leakage effects, termed the basin-integrated approach here. Following Landerer and Swenson (2012), gridded scaling factors of the global land surface at the 1° × 1° scale were also generated using forward modeling and LSM/GHM output in this study. Landerer and Swenson (2012) suggested that the gridded scaling factors were applied to the corresponding filtered GRACE TWS anomalies for each grid cell within the basin, and then the rescaled TWS anomalies for all grid cells were spatially averaged to obtain the TWS anomaly for the basin. This processing was intended to provide scaling factors for arbitrary regions of interest to hydrologists without geophysical background. Given the large footprint of GRACE signals (200,000 km2) than the 1° × 1° scale, rescaling of filtered GRACE TWS anomalies at 1° × 1° scale may be problematic. We compared scaling factors from the basin-integrated approach with spatially averaged scaling factors

Fig. 1. Location of the Yangtze River basin (Upper and Lower basins) in China, with showing streams and lakes, gauging stations (Yichang, Hukou, and Datong), the Three Gorges Dam (TGD), China's provinces and their capitals, and elevations of the Yangtze River basin.

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Fig. 2. Area equipped for irrigation expressed as percentage of total area (a), area actually irrigated expressed as percentage of area equipped for irrigation (b), area irrigated with surface water expressed as percentage of total area equipped for irrigation (c), and area irrigated with groundwater expressed as percentage of total area equipped for irrigation from AQUASTAT of the Food and Agricultural Organization of the United Nations.

across the basins examined. The spatially averaged scaling factor can be taken as a proxy of the scaling factor for a basin and then was used to rescale the spatially averaged filtered GRACE TWS anomalies for the basin, termed the spatially averaging approach. Forward modeling mimics low-pass filtering of GRACE spherical harmonic (SH) solutions. The low-pass filtering includes: (1) destriping using a least square fit of degree 4 polynomial for orders 6–40 of SH coefficients, (2) truncation at the maximum degree and order of 60, and (3) filtering of high-degree and order SH coefficients using a 300 km Gaussian filter. The Earth's gravity field is often expressed in terms of SH expression of the geoid that is the equipotential surface corresponding to the mean sea level (Chao & Gross, 1987; Wahr, Molenaar, & Bryan, 1998): ∞ X l X P˜ lm cosðθÞ  ½C lm cosðmλÞ þ Slm sinðmλÞ H ðθ; λÞ ¼ a

ð1Þ

l¼0 m¼0

where θ and λ are the colatitude and longitude, respectively; a is the Earth mean radius (6371 km); P˜ is the fully normalized associated lm

Legendre polynomials of degree l and order m; and Clm and Slm are SH coefficients that can be provided by GRACE satellites. Variations in SH coefficients can be expressed as following by assuming mass variations to be near the surface (10–15 km, from the top of the atmosphere to the bottom of oceans) and considering the load deformation effects (Wahr et al., 1998): 

ΔC lm ΔSlm

 ¼

a kl þ 1  M e 2l þ 1

Z

Δσ ðθ; λÞ  P~ lm cosðθÞ 



cosðmλÞ sinðmλÞ

  sinðθÞ  dθ  dλ

ð2Þ

where Me is the mass of the Earth (5.97219 × 1024 kg); Δσ(θ, λ) is the mass load changes (in kg/m2); and kl are elastic load Love numbers of the solid Earth. TWS changes from synthetic data (GLDAS-1 Noah and PCR-GLOBWB TWS outputs to be explained later) at each grid cell (1° × 1° in this study) in a discrete and limited-degree way can therefore be expressed as (Wahr et al., 1998): Δσ ðθ; λÞ ¼

N X l Me X 2l þ 1 ~  P cosðθÞ  ½ΔC lm cosðmλÞ þ ΔSlm sinðmλÞ: 4πa2 l¼0 m¼0 kl þ 1 lm

ð3Þ An initial expansion to degree and order 120 was used in this study, i.e., converting the gridded LSM output into the spectral domain at the maximum degree and order of 120. N is the truncated maximum degree of SH coefficients, i.e., 60 for CSR RL05 and 90 for JPL and GFZ RL05 in this study. Degrees 0 and 1 were set to zero because of mass conservation (degree 0) and no available data (degree 1). The degree-2 zonal harmonic coefficients (C20) have higher uncertainties and were replaced by satellite laser ranging estimates provided by the Center for Space Research (CSR) at The University of Texas at Austin (Cheng & Tapley, 2004). Low-pass filtering should be performed to suppress noise in longitudinal stripes in GRACE signals (correlated error) and high degree and order of SH coefficients (random error). Longitudinal stripes were reduced by an effective data-adaptive polynomial filter developed by Swenson and Wahr (2006), with a fourth-degree polynomial being fit for SH orders 6 to 40 (Longuevergne et al., 2010). For suppressing the random error in GRACE signals, the fixed parameter isotropic Gaussian filter with the half-length radius r = 300 km was

D. Long et al. / Remote Sensing of Environment 168 (2015) 177–193

used to convolute with TWS changes from GRACE or synthetic data in Eq. (3): Δσ ðθ; λÞ ¼

N X l Me X 2l þ 1  W l  P~ lm cosðθÞ  ½ΔC lm cosðmλÞ þ ΔSlm sinðmλÞ 4πa2 l¼0 m¼0 kl þ 1

ð4Þ 2

ðlr Þ W l ¼ exp − 4 ln ð2Þa2

!

inflow and outflow (mm/month) for a specific region of interest; and ET is the monthly evapotranspiration (mm/month). P, Rin, Rout, and ET are obtained by other satellite-based products and in situ measurements given in Section 2.3.3. The GRACE-based TWS change is computed from GRACE-observed TWS anomalies (mm) whose reference is the mean gravity field for a calculation period (e.g., January 2003–Jul 2013 in this study) (Long, Longuevergne, et al., 2014):

ð5Þ dS=dt ¼

where Wl is the Gaussian weight for all orders of spherical harmonics of degree l. After the forward modeled LSM output is obtained, scaling factors for each grid cell or basin can be computed by least square fit between the filtered and unfiltered (original data) TWS anomalies (Landerer & Swenson, 2012). In this study, the Noah and PCR-GLOBWB-based scaling factors from forward modeling were compared with those derived from NCAR's CLM4.0 and provided by the GRACE Tellus website (http://grace.jpl.nasa.gov/data/gracemonthlymassgridsland/). A flowchart for the derivation of scaling factors using forward modeling is given in Fig. 3. Uncertainties in GRACE-derived TWS anomalies include: (1) uncertainties in GRACE L1 measurements which were quantified by the approach (Wahr, Swenson, & Velicogna, 2006), and (2) bias and leakage corrections due to uncertainties in SMS changes from LSMs. Uncertainty in SMS was estimated from the standard deviation of SMS from 4 LSMs (Noah, Mosaic, VIC, and CLM) in GLDAS-1 (Longuevergne et al., 2010). Total errors of GRACE TWS anomalies for each month were consequently quantified by summarizing measurement and bias and leakage errors in quadrature and rescaled by the scaling factor (Joodaki, Wahr, & Swenson, 2014). 2.2.2. Evaluation of GRACE-derived total water storage changes GRACE-observed TWS changes restored by scaling factors from LSMs should be evaluated before applying to resolve water-related issues. The ‘ground truth’ of TWS changes is difficult to obtain and in most cases represented by water budget estimates of TWS changes from remotely sensed variables and/or ground-based observations. In this study, we evaluated GRACE-derived TWS changes using surface water budget calculation under the assumption of no net groundwater flow across the boundaries of the Yangtze River basin and its sub-basins: dS=dt ¼ P þ Rin −Rout −ET

ð6Þ

Where dS/dt is the TWS change at the monthly scale (mm/month); P is the monthly precipitation (mm/month); Rin and Rout are the surface

TWSAðt þ 1Þ−TWSAðt−1Þ : 2t

2.3. Data 2.3.1. GRACE data The gridded GRACE TWS anomaly products (1° × 1°) derived from SH solution RL05 provided by three processing centers, i.e., the Center for Space Research at The University of Texas at Austin (CSR), Jet Propulsion Laboratory (JPL), and German Research Center (GFZ) were obtained for use in this analysis. Processing of the GRACE data includes: (1) replacement of C20 (degree 2 and order 0) coefficients with the solutions from Satellite Laser Ranging (Cheng & Tapley, 2004) because of larger uncertainties in the C20 coefficient values from GRACE, (2) degree 1 coefficients (geocenter) derived from those in (Swenson, Chambers, & Wahr, 2008), (3) glacial isostatic adjustment (GIA) correction based on the model from (Geruo, Wahr, & Zhong, 2013), (4) a destriping filter to reduce the effect of correlated error in the GRACE signal that forms north–south stripes, and (5) a 300 km Gaussian filter that is intended to dampen random errors in high degree and order of SH coefficients. GRACE gridded products from the three processing centers totaling

Filtered TWSA

CSR SH coefficients RL05

Destriping

Filtered GRACE TWSA

PCRGLOBWB TWSA

Truncation Lmax=60

Back to spatial domain

Filtered PCR-GLOBWB TWSA

To spectral domain

GLDAS-1 Noah

300 km

Gaussian filtering

ð7Þ

Uncertainties in GRACE-based TWS change for a specific month t were quantified by summarizing uncertainties in GRACE-derived TWS anomalies before and after the month in quadrature. In addition to examining different approaches for the entire period (2003–2013), we paid particular attention to the evaluation of restored GRACE TWS changes under extremely dry conditions when LSMs and satellite products may poorly perform (Long et al., 2013). The extreme drought was defined based on both meteorological and hydrologic conditions (Thomas, Reager, Famiglietti, & Rodell, 2014), i.e., two criteria are met concurrently: (1) the Palmer Drought Severity Index (PDSI) (Dai, Trenberth, & Qian, 2004) is less than − 2 over 6 consecutive months or longer, and (2) the TWS deficit for a month is 20% larger than the climatology for the month over 6 consecutive months or longer. Based on the two criteria, two periods, i.e., Jul–Dec 2006 and Apr–Nov 2011, were identified as the extreme droughts for the Yangtze River basin.

Low-pass filtering

Data input

181

Filtered GLDAS-1 Noah

Generated k

Output

Scaling factors (k) from PCRGLOBWB

Restored GRACE TWSA using PCRGLOBWB k

Scaling factors (k) from GLDAS-1 Noah

Restored GRACE TWSA using GLDAS-1 Noah k

Least square fit

Fig. 3. Flowchart of the derivation of scaling factors to restore GRACE TWS anomaly signals from CSR Release 5 (RL05) spherical harmonic coefficients using PCR-GLOBWB and GLDAS-1 Noah models in this study. Note that scaling factors from NCAR's CLM4.0 were directly provided by the JPL website (http://grace.jpl.nasa.gov/data/gracemonthlymassgridsland/).

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121 months spanning from Jan 2003 through Jul 2013 were used. Data of six months during the study period are not available, i.e., Jun 2003, Jan 2011, Jun 2011, May 2012, Oct 2012, and Mar 2013, which were interpolated by simply averaging the values of two months before and after the month with missing data. A separate file of scaling factors derived from NCAR's CLM4.0 was also obtained (http://grace.jpl.nasa.gov/ data/gracemonthlymassgridsland/) to correct for GRACE signals during the low-pass filtering (i.e., destriping, truncation, and filtering). 2.3.2. Land surface and global hydrological models LSMs and associated outputs used in this study include: (1) SMS and snow water equivalent from GLDAS-1 Noah at a spatial resolution of 0.25° × 0.25° on a monthly scale for the period Jan 2003–Dec 2009 (Rodell et al., 2004) (resampled to 1° × 1°) for generating scaling factors using forward modeling for comparison with those derived from NCAR's CLM4.0; (2) SMS changes from Noah, Mosaic, VIC, and CLM in GLDAS-1 at a spatial resolution of 1° × 1° to quantify variations in SMS for the study period Jan 2003–Jul 2013 (Rodell et al., 2004); and (3) TWS changes from PCR-GLOBWB at a spatial resolution of 0.5° × 0.5° (resampled to 1° × 1°) for the period 2003–Dec 2009 for deriving scaling factors using forward modeling. TWS changes from PCR-GLOBWB for the period 1960–2010 were also used to illustrate the effect of low-pass filtering on signal dampening. PCR-GLOBWB (van Beek et al., 2011; Wada et al., 2010; Wada et al., 2014) is a conceptual, process-based water balance model of the terrestrial part of the hydrological cycle except Antarctica. It simulates for each grid cell (0.5° × 0.5° globally) and for each time step (daily) the water storage in two vertically stacked soil layers and an underlying groundwater layer, as well as the water exchange between the layers and between the top layer and the atmosphere (rainfall, evaporation, and snow storage). Fluxes between the lower soil reservoir and the groundwater reservoir are mostly downward (i.e., deep percolation), except for areas with shallow groundwater tables, where fluxes from the groundwater reservoir to the soil reservoirs are possible (i.e., capillary rise) during periods of low soil moisture content (Wada et al., 2014). The total runoff for a cell consists of saturation excess surface runoff, melt water that does not infiltrate, runoff from the second soil reservoir (interflow), and groundwater runoff (base flow) from the lowest groundwater reservoir. Direct runoff, interflow, and base flow are summed and routed along the drainage network on the basis of DDM30 (Doll & Lehner, 2002) by using the kinematic wave approximation of the Saint-Venant equation. The effect of open water evaporation, storage changes by lakes, attenuation by floodplains and wetlands, and reservoir operations (i.e., water supply, flood control, hydropower and navigation) are taken into account as well. This effect should be prominent for the Yangtze River because large surface water storage changes may occur, e.g., water impoundment or release from reservoirs and seasonal variations in water storage in rivers and lakes. The PCR-GLOBWB model has been used to estimate nonrenewable groundwater abstraction globally by simulating gross crop water demand for irrigated crops, available blue and green water to meet this demand, downscaled country statistics of groundwater abstraction, and groundwater recharge including return flow from irrigation (Wada et al., 2012). Fig. S1 in the Supporting Information shows the model structure of PCRGLOBWB. However, GLDAS-1 Noah does not simulate groundwater flow and groundwater storage changes. CLM4.0 does not consider human impact on water storage changes, including surface water and groundwater abstractions for irrigation and return flow. Forcing of PCR-GLOBWB includes precipitation and air temperature derived from the CRU TS 2.1 monthly data set (Mitchell & Jones, 2005), downscaled to daily scale by ERA40 re-analysis data (Uppala et al., 2005), incoming shortwave and long wave radiation and U and V components of wind speed derived from the CRU CLIM1.0 climatology data set (New, Lister, Hulme, & Makin, 2002). Details of the forcing of GLDAS-1 can be found in (Rodell et al., 2004). Model outputs are different due to both forcing data and model mechanisms; scaling factors

derived from different modeling systems can therefore be different. The purpose of this study was to identify the most suited model for TWS changes and subsequently to derive scaling factors for the Yangtze River basin, given the basin characteristic of intensive irrigation with surface water.

2.3.3. Ancillary data The satellite precipitation product (Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis, TMPA 3B43, research product that is post-real time and gauged-corrected) at a spatial resolution of 0.25° × 0.25° and a monthly timescale was used as an input of Eq. (6) for evaluating GRACE-derived TWS changes for the Yangtze River basin. Both the MOD16 ET product (2000 to present) and the AVHRRNDVI-based ET product (1983 to 2006) (http://www.ntsg.umt. edu/data) were jointly used to derive optimized ET time series for the Yangtze River basin and its sub-basins during the period Jan 2003 through Jul 2013 (Long, Longuevergne, et al., 2014). The two products are based on the Penman–Monteith equation and linking the Leaf Area Index (LAI, for MOD16 ET) or Normalized Difference Vegetation Index (NDVI, for AVHRR ET) to canopy and surface conductance. Evaporation from water bodies may be critical over the study region because of a large number of reservoirs and lakes. The MOD16 product does not, however, contain evaporation from water bodies. The AVHRR ET product simulates evaporation from water bodies with the Priestley–Taylor equation (Zhang et al., 2010). MOD16 ET and AVHRR ET products were reported a root mean square difference (RMSD) with ground flux measurements of 25 mm/ month (Mu et al., 2011) and 28 mm/month (Zhang et al., 2010), respectively. Daily stream flow measurements at Yichang and Datong stations for the period Jan 2003–Jul 2013 were obtained for use in the water budget calculation in combination with TRMM precipitation and the remotely sensed ET products.

3. Results 3.1. Scaling factors from forward modeling 3.1.1. Effects of low-pass filtering using PCR-GLOBWB To illustrate the effect of low-pass filtering applied to GRACE data, TWS anomalies from PCR-GLOBWB for the period 1960–2010 were performed the same processing for GRACE SH coefficients (see Section 2.2.1). Standard deviations of TWS anomaly time series for each grid for the Yangtze River basin indicate a marked heterogeneity in TWS changes (Fig. 4a), showing the maximum of 325 mm and the minimum of 5 mm, with a spatial mean of 73 mm. Apparently, relatively high variations in TWS occur along the mainstream of the Yangtze River, where surface water withdrawals for irrigation are intensive. Seasonal variations in TWS combined with human-induced variations in SWS changes resulted in the relatively high TWS variations across the Yangtze River basin. After performing the low-pass filtering to TWS anomalies from PCRGLOBWB, variations in TWS were greatly dampened by 26% in terms of the spatial mean of the standard deviations of TWS anomalies, showing the maximum of 87 mm, the minimum of 17 mm, and a spatial mean of 54 mm (73 mm for the original TWS changes). More importantly, the local features and processes of the TWS changes were essentially removed due to the smoothing, especially those features with relatively higher or lower TWS variations. Exhibited in Fig. 4(b) is only a general pattern of amplitudes of TWS anomalies that is dominated by the seasonal cycle of climate, e.g., the lower the latitudes, the higher the amplitudes of TWS variations dictated by the South Asia monsoon and the East Asia monsoon over South China. The low-pass filtering applied to the synthetic data also indicates that the use of the filtered TWS changes without signal restoration could result in substantial reductions in both seasonal cycles and long-term trends in TWS changes.

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Fig. 4. Standard deviations (mm) of TWS changes from the PCR-GLOBWB (a denotes the original data and b denotes the filtered data with the same low-pass filtering of GRACE data applied) from 1960 to 2000 for the Yangtze River basin. Standard deviations greater than 200 mm were set to 200 mm.

3.1.2. Scaling factors from different land surface models at the grid cell scales Scaling factors derived from PCR-GLOBWB TWS changes through forward modeling exhibit a marked spatial heterogeneity that reflects characteristics of TWS changes of the Yangtze River basin (Fig. 5a). Similar to Fig. 4, grid cells along the mainstream of the Yangtze River show relatively higher magnitudes of the scaling factors. Scaling factors over the TGR, the Lake Taihu region, as well as the outlet of the Yangtze River show values over 3. These results are reasonable because the TWS change along the mainstream is highest compared to other parts of the basin (Fig. 4a); signal loss for the mainstream is consequently highest due to the low-pass filtering and requires higher values of the scaling factors to restore the signal loss. Striking is the magnitude of the scaling factor (~ 7) for the grid cell at the outlet of the Yangtze, which is likely due to the combined effect of the reason above and the leakage effect of the East China Sea. The ocean dampened the amplitude of TWS changes for the outlet and therefore a much higher value of the scaling factor was needed to restore the signal loss. In addition, groundwater abstractions over the Suzhou–Wuxi–Changzhou region in the Lower Yangtze River basin resulting in subsidence (Hu, Shi, Inyang, Chen, & Sui, 2009) should also contribute to the greater spatial heterogeneity in the Lower Yangtze River basin as reflected by PCR-GLOBWB that simulates both the natural and human-induced GWS changes.

Looking at scaling factors from NCAR's CLM4.0, a similar pattern as the scaling factors from PCR-GLOBWB was found (Fig. 5b), i.e., the magnitudes of the scaling factors along the lower reaches of the Yangtze River are relatively higher than other grid cells and even higher than PCR-GLOBWB. This coincides with larger surface water and groundwater storage changes over these regions that are explicitly parameterized in PCR-GLOBWB and CLM4.0. However, the upper reaches of the Yangtze River do not show such higher scaling factors for CLM4.0 due mostly to not considering water storage changes in reservoirs and lakes, e.g., the TGR. The relatively higher scaling factors along the lower reaches and the lower scaling factors along the upper reaches of the Yangtze for CLM4.0 led to the highest variability in scaling factor over the Yangtze River basin in the three models examined. In addition to the Yangtze River basin, CLM4.0 shows very large scaling factors along the large rivers globally, e.g., the Amazon and Nile (Fig. 6). However, scaling factors from PCR-GLOBWB of the global land surface have a higher spatial variability than CLM4.0 (standard deviation: 1.41 for PCR-GLOBWB and 1.02 for CLM4.0; mean scaling factor: 1.36 for PCR-GLOBWB and 1.02 for CLM4.0). This is likely due to the comprehensive accommodation of human impacts on surface and subsurface water storage changes for PCR-GLOBWB, resulting in a more heterogeneous variability in TWS changes and consequently scaling factors than CLM4.0.

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Fig. 5. Scaling factors from PCR-GLOBWB (a), NCAR's CLM4 (b), and GLDAS-1 Noah (c).

Noah model-derived scaling factors do not show any characteristic of TWS changes along the mainstream of the Yangtze River as opposed to the scaling factors from the other two models (Fig. 5c). Lack of mechanisms to characterize natural recharge and discharge of groundwater, and human-induced surface and groundwater storage changes in Noah resulted in a relatively homogeneous distribution of the scaling factors, especially over the Lower Yangtze River basin. Comparison

between TWS anomaly time series from PCR-GLOBWB and GLDAS-1 four LSMs for the Yangtze River basin and its sub-basins further highlights the differences in modeled TWS anomalies (Fig. S2 in the Supporting Information). The Noah model will thus be precluded from the following discussion because of its inability to characterize the features of TWS changes and its large differences with PCR-GLOBWB that comprehensively simulates the hydrological cycle.

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3.1.3. Scaling factors from PCR-GLOBWB and CLM4.0 at basin scales There are appreciable differences in scaling factor between PCRGLOBWB and CLM4.0 for the entire Yangtze River basin (i.e., PCRGLOBWB: 1.00; CLM4.0: 1.37, Table 1). The differences become larger for the Lower Yangtze River basin (i.e., PCR-GLOBWB: 0.92; CLM4.0: 1.66). Furthermore, the scaling factor from PCR-GLOBWB for the Upper Yangtze River basin (1.22) is higher than the Lower Yangtze River basin (0.92). However, this is reversed for CLM4.0 that the scaling factor for the Upper Yangtze basin (1.19) is lower than that for the Lower Yangtze River basin (1.66). For PCR-GLOBWB, a scaling factor higher than 1 for the Upper Yangtze River basin and a scaling factor lower than 1 for the Lower Yangtze River basin indicate signal leakage from the Upper Yangtze River basin and the surrounding of the Lower Yangtze River basin into the lower reaches. However, this is not the case for CLM4.0 that there is signal leakage from the Lower Yangtze

River basin especially along the mainstream into the surrounding and therefore it requires a relatively higher scaling factor (1.66) to restore the signal loss. The differences in scaling factor can be attributed to: (1) differences in model mechanisms (e.g., simulation of SWS changes and whether human-induced changes in surface and subsurface water are accommodated) and (2) differences in forcing data the two models use (Long, Longuevergne, et al., 2014; Long et al., 2013). In addition, relative differences in the derived scaling factors from the basin-integrated approach and the spatially averaging approach range from 5%–15% (Table 1), which agrees with what Landerer and Swenson (2012) found that the two approaches lead to relative differences in scaling factor within 20% over the study basins they examined. The reason for the similarity between the basin-integrated approach and the spatially averaging approach for the entire Yangtze River basin is that timing of TWS changes for grid cells across the basin is

Table 1 Scaling factors derived from PCR-GLOBWB and CLM4.0 for the Yangtze River basin and its sub-basins. Relative difference was defined as the absolute relative difference in scaling factor between the basin-integrated and spatially averaging approaches with respective to the scaling factor for the basin-integrated approach. Basin name

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generally similar to those for the entire basin. This is demonstrated by:(1) the correlation coefficients between TWS anomaly time series from PCR-GLOBWB at grid cells (local dynamics) and the TWS anomaly time series from PCR-GLOBWB over the entire basin (large-scale climate patterns) are generally high (the mean correlation coefficient: 0.63), especially along the mainstream of the Yangtze River (Fig. 7a); (2) the

correlation coefficients between the filtered TWS anomaly time series from PCR-GLOBWB across all grid cells and the filtered TWS anomaly time series from PCR-GLOBWB for the entire basin (Fig. 7b, mean correlation coefficient: 0.86) further highlight the finding that the local processes and dynamics of TWS changes are generally similar to those for the entire basin; and (3) the generally good correspondence (mean

Fig. 7. (a) Correlation coefficients between TWS anomalies from PCR-GLOBWB at grid cells and the TWS anomaly from PCR-GLOBWB for the entire Yangtze River basin (left) and its frequency distribution (right), (b) correlation coefficients between filtered TWS anomalies from PCR-GLOBWB at grid cells and the filtered PCR-GLOBWB TWS anomaly for the entire Yangtze River basin (left) and its frequency distribution (right), and (c) correlation coefficients between filtered GRACE TWS anomalies and filtered PCR-GLOBWB TWS anomalies at grid cells (left) and its frequency distribution (right).

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correlation coefficient: 0.70) between the filtered TWS anomaly time series from PCR-GLOBWB and the filtered GRACE TWS anomaly time series at grid cells suggests that the GHM coincides temporally with GRACE observations well. Use of the GHM to create gridded scaling factors to correct for GRACE signals seems feasible in capturing large-scale hydrological dynamics in this case. It is therefore possible for hydrologists without geophysical background to correct for GRACE TWS changes using gridded scaling factors for arbitrary shapes of the study regions that have been reported in the literature. However, it should be noted that the correspondence between the local processes and the large-scale hydrological dynamics of TWS changes is markedly reduced over the Lower Yangtze River basin (especially the southeast part) where a greater heterogeneity in TWS changes from PCR-GLOBWB at grid cells with respect to the entire basin is shown (Fig. 7a–b). Spatially averaging rescaled gridded TWS anomalies/scaling factors to derive the TWS anomaly for a basin depends on the assumption of the high correlation between TWS changes across grid cells and those for the entire basin. In other words, TWS changes for a study region should be generally homogeneous. This can explain why the spatially averaging approach differs somewhat from the basin-integrated approach for the Lower Yangtze River basin using PCR-GLOBWB (basin-integrated: 0.92; spatially averaging: 1.06, Table 1). It would therefore be problematic by simply averaging rescaled gridded TWS anomalies/scaling factors for basins with highly spatial and/or temporal heterogeneity in TWS changes. In the following discussion, only the basin-integrated scaling factors from PCR-GLOBWB and CLM4.0 are discussed. 3.2. Evaluation of GRACE-derived total water storage changes 3.2.1. Satellite-observed and in situ measurements of hydrological flux variables Evaluation of GRACE-derived TWS changes in this study is based on surface water budget calculation (Section 2.2.2). Monthly TMPA precipitation, NOAA-AVHRR ET, and in situ stream flow measurements for the Yangtze, the Upper Yangtze, and the Lower Yangtze basins during the period from Jan 2003 through Jul 2013 are shown in Fig. 8. In general, precipitation in the Upper Yangtze is lower than that in the Lower Yangtze, showing mean annual precipitation of 782 mm and 1348 mm, respectively, for the period 2003–2013. The mean annual precipitation for the entire Yangtze is 1017 mm. Consequently, ET for the Upper Yangtze is generally lower than the Lower Yangtze, showing mean annual ET of 436 mm, 529 mm, and 476 mm for the Upper Yangtze, Lower Yangtze, and entire Yangtze basins, respectively, for the period 2003–2013. MOD16 ET shows ~ 34% (582 mm) and ~ 46% (773 mm) higher magnitudes than AVHRR ET for the Upper and Lower Yangtze basins, respectively. Published studies indicate that the MOD16 ET product may have relatively higher uncertainties in the humid region (Long, Longuevergne, et al., 2014; Long, Shen, et al., 2014). Therefore, MOD16 ET was precluded from the following analysis and discussion. Mean annual runoff from the in situ data was 393 mm and 628 mm, resulting in runoff ratios of 0.50 and 0.46 for the Upper and Lower Yangtze River basins, respectively. The monthly time series of ET and stream flow also indicate a more responsive characteristic of stream flow to precipitation than ET. The satellite-based ET product, however, shows a relatively weak response to precipitation and a general stationarity, even during 2006 and 2011 droughts. This implies a possible limitation in remotely sensed vegetation index-derived ET products whose algorithms are not able to completely reflect the effect of soil moisture constraint on ET processes especially during drought (Long, Longuevergne, et al., 2014). These uncertainties in remotely sensed P and ET, and in situ R consequently result in uncertainties in the water budget estimates of TWS changes. However, as discussed in (Long, Longuevergne, et al., 2014), the magnitude of these uncertainties should be lower than the magnitude of uncertainties in GRACE-derived TWS changes, leading to the legitimacy

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of using hydrological fluxes to evaluate GRACE TWS changes at basin scales.

3.2.2. Comparison of GRACE TWS anomalies applied with different scaling factors Comparison of GRACE-derived TWS anomalies from three processing centers, i.e., CSR, JPL, and GFZ indicates an excellent consistency over the Yangtze and its sub-basins (Figure S3 in the Supporting Information), showing mean correlation coefficients of ~ 0.92 for all basins examined. For the convenience of discussion, only gridded CSR TWS anomalies applied with scaling factors from PCR-GLOBWB and CLM4.0 will be used in the subsequent analysis and discussion. GRACE TWS anomalies for the Yangtze River basin and its sub-basins for the period Jan 2003 through Jul 2013 were restored by the scaling factors from PCR-GLOBWB and CLM4.0 using the basin-integrated approach, and compared with those without signal restoration (i.e., filtered TWS anomalies) (Fig. 9). Apparently, GRACE TWS anomalies applied with the PCR-GLOBWB scaling factor of 1 overlap the filtered GRACE TWS anomalies for the Yangtze River basin. The synthetic data from PCR-GLOBWB demonstrate that the leakage-in and leakage-out errors are offset for the entire Yangtze River basin. Therefore, signal restoration may not be critical for the entire basin. However, the CLM4.0-based scaling factor of 1.37 results in 37% higher (p b 0.001, one-way analysis of variance, ANOVA, note that absolute values of TWS anomaly time series were used for the ANOVA test since different scaling factors can only result in different amplitudes of TWS changes and will not change the phases) amplitudes of the restored GRACE signal relative to the PCR-GLOBWB-based scaling factor. The large absolute differences between the two restored GRACE TWS anomaly time series were found during wet (Jul–Sep) and dry (Dec–Apr) periods of each year, with the mean absolute differences of 17.7 mm and 11.2 mm, respectively. For the Upper Yangtze River basin, PCR-GLOBWB and CLM4.0 resulted in very similar scaling factors (1.22 VS 1.19) and therefore the restored GRACE TWS anomalies using the two scaling factors are almost overlapped without showing a statistically significant difference (p = 0.718). The filtered GRACE TWS anomalies are generally within the uncertainty estimates (shading areas of Fig. 9) of the restored TWS anomalies. Deviating from the entire basin and Upper Yangtze River basin, the Lower Yangtze River basin exhibits relatively large differences in restored GRACE signals using PCRGLOBWB and CLM4.0-based scaling factors. Again, TWS anomalies restored by the CLM4.0-derived scaling factor (1.66) resulted in 66% higher (p b 0.001) amplitudes of TWS anomalies than the filtered GRACE TWS anomalies. However, TWS anomalies applied with the PCR-GLOBWB scaling factor (0.92) appear to be overlapping the filtered GRACE TWS anomalies. Discrepancies between PCR-GLOBWB and CLM4.0 over the Lower Yangtze River basin are exacerbated, with the mean absolute differences of 33.1 mm and 21.1 mm for the wet and dry (drought) periods, respectively (Fig. 9). Relative uncertainties of GRACE TWS anomalies for the entire Yangtze, Upper Yangtze, and Lower Yangtze basins were estimated to be 20%, 28%, and 31%, increasing with decreasing areas of the basins examined. The PDSI time series from 2003 through 2012 for each basin examined were superimposed to the TWS anomaly time series in Fig. 9. In general, the PDSI corresponds to the peak values of TWS anomaly time series well (wet cases). However, the PDSI leads the relatively low values of TWS anomaly time series for 1 to 2 months (dry cases). Though the hydrological drought (characterized by TWS changes in this study) is linked partially with the meteorological drought (characterized by the PDIS in this study), there is indeed a time lag between the two types of drought. The propagation of meteorological drought to the upper layer of soil (e.g., 1 m characterized by the PDSI) is relatively fast, but becomes much slower in hydrological drought. This is because water retention and groundwater storage act as low-pass filters on the terrestrial hydrological cycle that gradually remove high frequency variability associated with atmospheric forcing as depth increases (Eltahir

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& Yeh, 1999), and therefore trigger a slower response to the meteorological drought. 3.2.3. Comparison of GRACE TWS changes with water budget estimates of TWS changes Comparison of water budget estimates of TWS changes (Eq. 6) and the counterparts from GRACE satellites (Eq. 7) indicates a generally good correspondence (Fig. 10). Coefficients of determination (R2) between the GRACE-derived TWS changes and water budget estimates of TWS changes are 0.77, 0.68, and 0.63 for the Yangtze, Upper Yangtze, and Lower Yangtze River basins, respectively (Figs. 11 and S4). The

larger the study basin, the higher the correspondence between the GRACE-derived TWS changes and the water budget estimates of TWS changes. This may be attributed to the fact that the large area smooths more uncertainties in GRACE signals, remotely sensed precipitation and ET, and in situ stream flow measurements. It is noted that the scaling factor does not impact the R2 between the two time series of TWS changes, but does result in differences in amplitude of the GRACEderived TWS changes from reality that is represented by water budget estimates of TWS changes in this study. GRACE TWS changes applied with the scaling factors from PCR-GLOBWB improved the correspondence with water budget estimates in terms of a lower RMSD than the

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counterparts from CLM4.0. Taking the entire Yangtze River basin as an example, the RMSD of 10.2 mm/month for the GRACE-derived TWS changes applied with the PCR-GLOBWB scaling factor (1.0) is relatively lower (~ 30% reduction) than the RMSD of 14.6 mm/month for the GRACE-derived TWS changes applied with the CLM4.0 scaling factor (Fig. 11). This improvement was also found in the Lower Yangtze River basin where GRACE TWS changes applied with the PCRGLOBWB scaling factor (0.92) show a lower RMSD of 22.1 mm/month than those applied with the CLM4.0 scaling factor with an RMSD of 25.0 mm/month, i.e., ~ 12% reduction. The mean biases (MBS) for these comparisons also show similar improvement. For the Upper

Yangtze River basin, GRACE TWS changes applied with the CLM4.0 scaling factor (1.19) have a slightly lower discrepancy with water budget estimates of TWS changes than GRACE TWS changes applied with the PCR-GLOBWB scaling factor (1.22). Discrepancies between the GRACE-derived TWS changes and water budget estimates of TWS changes become relatively larger for the high (wet) and low (dry) magnitudes of TWS changes, especially for the Upper Yangtze basin (Fig. 10). During these periods, the magnitudes of the water budget estimates of TWS changes are relatively lower than those of the GRACE TWS changes. These discrepancies may be attributed to: (1) a weak response of remotely sensed ET to variations in

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Fig. 10. Water budget estimates of TWS changes (Eq. 6) and TWS changes from GRACE TWSA anomalies applied with the scaling factors from PCR-GLOBWB and CLM4.0 (Eq. 7). Shaded areas are uncertainties in TWS changes from GRACE.

precipitation, (2) uncertainties in remotely sensed precipitation, and (3) the assumption of no net groundwater flow across the boundaries of basins in the surface water balance equation. 4. Discussion 4.1. GRACE signal restoration GRACE signal restoration is challenging for hydrological studies and applications, e.g., drought and groundwater depletion monitoring, though it is sometimes not critical for large river basins. Forward modeling of synthetic data can be used to determine if the filtered GRACE TWS anomalies are required to be rescaled and/or to what extent the TWS anomalies need to be rescaled, i.e., the magnitude of scaling factors is

critical. As concluded from the analysis of PCR-GLOBWB, the scaling factor of 1 for the entire Yangtze River basin demonstrates that rescaling of filtered GRACE TWS anomalies for the Yangtze River basin is not required. However, this is not the case at the sub-basin scales, especially for the Lower Yangtze River basin where there are large seasonal SWS changes and intensive surface water irrigation may directly and indirectly impact the interactions between surface water and subsurface water. There have been studies that investigated impact of climatic variability and extremes on the hydrological processes of the Yangtze River basin.Hu et al. (2006) investigated seasonal amplitudes of GRACEderived TWS changes for the Yangtze River basin for the period Apr 2002–Dec 2003, showing a similar seasonal cycle of filtered GRACE TWS changes (34 mm) with the filtered output of the Climate Prediction

D. Long et al. / Remote Sensing of Environment 168 (2015) 177–193 100

80 60

TWSC GRACE (mm/mo)

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Fig. 11. Scatterplots of water budget estimates of TWS changes and GRACE-derived TWS changes applied with scaling factors from PCR-GLOBWB and CLM4.0 using the basin-integrated approach for the Yangtze, Upper Yangtze, and Lower Yangtze River basin for the periods Jan 2003 through Jul 2013, with showing statistics of the comparisons including coefficients of determination (R2), root mean square errors (RMSD), and mean biases (MBS).

Center (CPC) model of NOAA (41 mm) and GLDAS (27 mm). Zhao et al. (2011) investigated TWS changes over the Yangtze River basin for the period Feb 2003–May 2008 using the first release of the Delft Institute of Earth Observation and Space Systems Mass Transport (DMT-1) model based on GRACE data. TWS anomalies for the Yangtze River basin reached lowest in Jan 2004, which is consistent with what we found in this study (see Fig. 9). However, the great impact of the 2006 drought on the TWS over the Yangtze River basin was not detected in (Zhao et al., 2011), which may be related to a greater uncertainty in the early release of GRACE Level 2 data and different processing strategies. In addition, the scaling factor of 0.98 from GLDAS-1 Noah in (Zhao et al., 2011) suggests that LSMs in GLDAS-1 slightly dampened TWS changes in the Yangtze River basin compared with other more sophisticated GHM/LSM models (i.e., PCR-GLOBWB and NCAR's CLM4, also see Fig. S2) due to lack of surface and groundwater storage components and therefore resulted in a lower scaling factor than PCR-GLOBWB and CLM4.0. Ferreira et al. (2013) showed that TWS changes estimated by the GRACE-observed gravity field are not negligible in total discharge estimation using a water budget calculation at the monthly scale in the Yangtze River basin and also derived a scaling factor of ~1 for the Yangtze River basin. It should be noted that use of different scaling factors not only impacts the signal restoration for the seasonal amplitudes but also the secular trends in TWS changes. Rescaling of GRACE TWS changes can be more critical for quantifying groundwater storage depletion (Longuevergne, Wilson, Scanlon, & Crétaux, 2012; Scanlon et al., 2012; Shamsudduha, Taylor, & Longuevergne, 2012; Swenson, Yeh, Wahr, & Famiglietti, 2006; Yeh et al., 2006). The scaling factor can definitely impact the estimation of the drought severity using the deficit approach (Thomas et al., 2014) due to different seasonal amplitudes of TWS anomalies restored with different scaling factors. This reinforces the importance of selecting an appropriate processing strategy (or LSM/GHM) to restore GRACE signals, given the characteristics of TWS distribution, composition, and variation for a basin of interest. 4.2. Evaluation of GRACE total water storage changes Lack of complete TWS measurements makes validation and interpretation of GRACE signals a great challenge. The water balance approach is one of the practical ways to evaluate GRACE-derived TWS changes. Sahoo et al. (2011) and Pan et al. (2011) developed water budgets for large river basins globally using a range of satellite and/or ground-based monitoring of P, R, ET, and GRACE-derived TWS changes. Large water budget non-closure errors ranging from 5% to 25% of P were attributed primarily to errors in satellite-derived P and TWS changes (−35–50 mm for the Yangtze River basin). The RMSD of 10 mm/month and R2 of 0.77

between GRACE-derived TWS changes applied with the PCR-GLOBWB scaling factor and water budget estimates of TWS changes for the Yangtze River basin in our study appear to be relatively better than other river basins globally, e.g., a humid basin in the South Central US (RMSD = 27 mm/month and R2 = 0.64) (Long, Longuevergne, et al., 2014). One of the reasons may be attributed to its large size (~1,800,000 km2 for the Yangtze River basin) that has filtered more uncertainties in all satellitebased retrievals and ground-based measurements than those for relatively small basins (e.g., ~200,000 km3). In addition, the use of GRACE RL05 SH coefficients that have shown a reduction in 40% uncertainty with respect to RL04 data (Long et al., 2013) may also improve the water budget calculation in our study. 5. Conclusion Signal restoration for filtered GRACE TWS anomalies is challenging because of uncertainties in synthetic data (LSM or GHM output) that are used to generate scaling factors. This study makes an attempt to use a state-of-the-art GHM, PCR-GLOBWB, which simulates comprehensively SWS, natural and human induced GWS changes, and the interactions between surface water and subsurface water, to generate scaling factors by mimicking low-pass filtering of GRACE signals (forward modeling). Results indicate that scaling factors from PCRGLOBWB and CLM4.0 can reflect marked spatial heterogeneity due to large seasonal and human-induced surface and subsurface variations in water storage. However, the GLDAS-1 Noah model does not show such spatial heterogeneity in scaling factor due to the inability to simulate SWS and GWS changes. GRACE TWS changes multiplied by PCRGLOBWB scaling factors show closer agreement with water budget estimates of TWS changes than those multiplied by CLM4.0 scaling factors (PCR-GLOBWB: RMSD = 10.2 mm/month and R2 = 0.77; CLM4.0: RMSD = 14.6 mm/month and R2 = 0.77) in China's Yangtze River basin. Results of this study could be valuable in providing a basis for more accurate TWS change time series for drought monitoring and water resource management over regions where human-induced interactions between surface water and subsurface water are intensive. Acknowledgement This study was jointly supported by the National Science Foundation of China Major Research Programs (No. 91437214 and No. 71461010701), and the Open Research Fund Program of the State Key Laboratory of Hydroscience and Engineering at Tsinghua University (Grant No. sklhse-2014-A-02 and sklhse-2014-A-01). We thank Dr. Laurent Longuevergne with Université de Rennes in France for helping with learning forward modeling techniques. We are grateful to editors

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and four reviewers for their valuable comments and constructive suggestions. This paper has been greatly improved as a result of their efforts.

Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.rse.2015.07.003.

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