WHU-Grace01s: A new temporal gravity field model recovered from GRACE KBRR data alone

g e o d e s y a n d g e o d y n a m i c s 2 0 1 5 , v o l 6 n o 5 , 3 1 6 e3 2 3

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WHU-Grace01s: A new temporal gravity field model recovered from GRACE KBRR data alone Zhou Haoa, Luo Zhicaia,b,*, Zhong Boa,b a

School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China

b

article info

abstract

Article history:

A new temporal gravity field model called WHU-Grace01s solely recovered from Gravity

Received 9 June 2015

Recovery and Climate Experiment (GRACE) K-Band Range Rate (KBRR) data based on dy-

Accepted 15 July 2015

namic integral approach is presented in this paper. After meticulously preprocessing of the

Available online 28 August 2015

GRACE KBRR data, the root mean square of its post residuals is about 0.2 micrometers per second, and seventy-two monthly temporal solutions truncated to degree and order 60 are

Keywords:

computed for the period from January 2003 to December 2008. After applying the combi-

Temporal gravity field model

nation filter in WHU-Grace01s, the global temporal signals show obvious periodical change

Gravity Recovery and Climate

rules in the large-scale river basins. In terms of the degree variance, our solution is smaller at

Experiment (GRACE)

high degrees, and shows a good consistency at the rest of degrees with the Release 05 models

Dynamic integral approach

from Center for Space Research (CSR), GeoForschungsZentrum Potsdam (GFZ) and Jet Pro-

K-Band Range Rate (KBRR)

pulsion Laboratory (JPL). Compared with other published models in terms of equivalent

Satellite gravity

water height distribution, our solution is consistent with those published by CSR, GFZ, JPL,

Spherical harmonics

Delft institute of Earth Observation and Space system (DEOS), Tongji University (Tongji),

Equivalent water height

Institute of Theoretical Geodesy (ITG), Astronomical Institute in University of Bern (AIUB)

Geopotential determination

and Groupe de Recherche de Geodesie Spatiale (GRGS), which indicates that the accuracy of WHU-Grace01s has a good consistency with the previously published GRACE solutions. © 2015, Institute of Seismology, China Earthquake Administration, etc. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1.

Introduction

The successful implementation of Gravity Recovery and Climate Experiment (GRACE) mission opens a new era of the Earth's internal structure comprehension and the shallow

layer mass transport. Since the first released set of monthly gravity field model by Wahr [1], the study on global or local terrestrial water storage change, glacier melting and accumulation based on GRACE products have obtained fruitful research results [2e8], which has great significance

* Corresponding author. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China. E-mail address: [email protected] (Luo Z.). Peer review under responsibility of Institute of Seismology, China Earthquake Administration.

Production and Hosting by Elsevier on behalf of KeAi

http://dx.doi.org/10.1016/j.geog.2015.07.004 1674-9847/© 2015, Institute of Seismology, China Earthquake Administration, etc. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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g e o d e s y a n d g e o d y n a m i c s 2 0 1 5 , v o l 6 n o 5 , 3 1 6 e3 2 3

in the development of Geophysics, Geodesy, Oceanography, Glaciology and other fields. Since the comprehensive influence of payload errors, massive observations processing and complicated calculation during the temporal gravity field model determination, only a few international agencies can finish this complex task. They are Center for Space Research (CSR) [9], GeoForschungsZentrum Potsdam (GFZ) [10], Jet Propulsion Laboratory (JPL) [11], Institute of Theoretical Geodesy (ITG) [12], Delft institute of Earth Observation and Space system (DEOS) [13], Astronomical Institute in University of Bern (AIUB) [14], Groupe de Recherche de Geodesie Spatiale (GRGS) [15], Tongji University (Tongji) [16] and Chinese Academy of Sciences (CAS) [17] etc. Table 1 presents the statistical information of released temporal gravity field models, which indicates that most of these agencies selected dynamic integral approach to determine the temporal gravity field models. Furthermore, considering the advantages of GRACE K-Band Range Rate (KBRR) data in temporal gravity field models inversion [18], we will select dynamic integral approach and solely KBRR data to recover a new set of purely GRACE temporal gravity field models.

2. Principle of dynamic integral approach for gravity field inversion GRACE constellation consists of two identical satellites which flies almost in the same orbit plane but separated at a distance of few hundred kilometers in the approximate northesouth direction. This mission realizes satellite-to-satellite tracking in low-low mode (LL-SST) with KBRR system, which allows to detect inter-satellite range rate variation with the precision of submicron meter per second. The range r and range rate r_ which relate to the location and velocity of two GRACE identical satellites can be described as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  2 ðxa  xb Þ2 þ ya  yb þ ðza  zb Þ2    ðxa  xb Þðx_a  x_b Þ þ ya  yb y_a  y_b þ ðza  zb Þðz_a  z_b Þ r_ ¼ r r¼

(1)

where XA ðxa ;ya ;za ; x_a ; y_a ; z_a Þ and XB ðxb ;yb ;zb ; x_b ; y_b ; z_b Þ are the state vector of GRACE A and GRACE B satellite respectively.

On the basis of equation (1), the partial derivatives of intersatellite range rate with respect to the state vector of GRACE A can be computed by the following equation:   8 vr_ 1 r_ vr_ ðxa  xb Þ > > ðx_a  x_b Þ  ðxa  xb Þ ; ¼ ¼ > > _a vx r r v x r a > > >   >   <  r_   vr_ ya  yb vr_ 1  y_a  y_b  ya  yb ; ¼ ¼ > r vya r vy_a r > > >   > > vr_ > 1 r_ vr_ ðza  zb Þ > : ðz_a  z_b Þ  ðza  zb Þ ; ¼ ¼ vza r r vz_a r

(2)

In addition, the relationship between the partial derivatives of range rate with respect to two satellite state vectors can be illustrated as follows: vr_ vr_ ¼ A vXB vX

(3)

In the dynamic integral approach, we use the discrepancy between the observations and integral value to update the reference earth gravity field model. During integration, the major part of the discrepancy is derived from the initial state error and priori force model parameter error. Hence, the residual of inter-satellite range rate Dr_ can be expressed as a linear combination of initial state error DXA0 , DXB0 and priori force model parameter error Dp as follows: Dr_ ¼

vr_ vr_ vr_ DXA0 þ B DXB0 þ Dp vp vXA0 vX0

(4)

According to the chain rule of partial derivative, the partial derivative of inter-satellite range rate with respect to initial state error can be illustrated as follows: vr_ vr_ vXA vr_ vr_ vXB ¼ A ; B ¼ B A A vX0 ð16Þ vX ð16Þ vX0 ð66Þ vX0 ð16Þ vX ð16Þ vXB0 ð66Þ

(5)

vr_ where vXvr_A and vX B can be obtain from equation (2) and equation A B and vX can be (3),while the state transition matrix vX vXA vXB0 0 computed by efficient numerical integrator [18]. Considered that the Earth gravity field impacts the state of two satellites simultaneously, the partial derivative of intersatellite range rate with respect to spherical harmonic coefficients can be expressed as:

vr_ vr_ vXa vr_ vXb ¼ þ vc ð1npÞ vXað16Þ vc ð6npÞ vXbð16Þ vc ð6npÞ

(6)

Table 1 e Statistical information of released time-variable gravity field models. Model CSR-Release04 CSR-Release05 GFZ-Release 04 GFZ-Release05 JPL-Release04 JPL-Release05 ITG-Grace2010 DEOS AIUB GRGS Tongji-GRACE01 IGG-CAS

Time span

Truncated degree

Approach

May 2002eApril 2011 April 2002eJune 2014 August 2002eApril 2011 April 2002eMay 2014 April 2002eFebruary 2011 April 2002eMay 2014 August 2002eAugust 2009 February 2003eAugust 2009 July 2003eDecember 2009 January 2003eDecember 2012 January 2003eAugust 2011 January 2004eDecember 2010

60 96 120 90 120 90 120 120 60 80 60 60

Dynamic integral Dynamic integral Dynamic integral Dynamic integral Dynamic integral Dynamic integral Short arc Acceleration Celestial mechanics Dynamic integral Short arc Short arc

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Particularly, in terms of the parameters which related to the single satellite state respectively, e.g., accelerometer calibration parameters, the calculation pattern of their partial derivatives is the same as equation (5). While in terms of the parameters which related to two satellites simultaneously, e.g., tidal model parameters and three body gravitational perturbation parameters, the calculation pattern of their partial derivatives is the same as equation (6). Through the discussion mentioned above, the earth gravity field model can be updated by the discrepancy between the original inter-satellite range rate observations and integral values. Finally, after removing the average value of the solutions from each month, we can extract the global or regional temporal signal of each month directly.

3.

GRACE data processing

Precise temporal gravity field model inversion is based on extracting inter-satellite range rate residual accurately. It indicates that the reference inter-satellite range rate which computed from the integral dynamic orbit should be highly accurate. To this end, the efficiency integrator and precise background force models, which are closely related to the accuracy of purely dynamic orbit, are selected. In the process of temporal gravity field model inversion, a high-efficiency Gauss-Jackson integrator is adopted to minimize integral error [19]. Moreover, the accurate GRACE Level1b observations of Release02 version provided by JPL are used. As it is shown in Table 2, the appropriate force models are selected. Specifically, the priori mean gravity field model GGM05s is a purely GRACE solution determined by approximately ten years GRACE data [20]. A notable difference is that the newest Release05 edition of the so-called Atmosphere and Ocean De-aliasing (AOD1B) is applied to remove the influence of non-tidal signal [21]. IERS (International Earth Rotation Service) 2003 conventions are used in coordinate transformation. Since the orbit of the GRACE twin satellites is analogous, the structures of partial derivatives of inter-satellite range rate with respect to two initial state vectors are similar to each other. If the temporal gravity field model is solely determined from inter-satellite range rate, the condition number of

normal equation coefficient matrix would be too big to estimate the spherical harmonic coefficients steadily. There are two schemes to solve this problem. One is to bring in the orbit observations to change the structure of normal equation coefficient matrix, and the other is to separate the processes of local parameters and global parameters determination. In this paper, the initial state vector and accelerometer calibration parameters are estimated at first. Subsequently, the precise orbits are computed by the Gauss-Jackson integrator using a pure dynamic strategy and the relative reference inter-satellite range rate is computed by equation (1). After removing the reference values from the KBRR observations, the residuals can be used to estimate the spherical harmonic coefficients directly. The root mean square (RMS) values of KBRR residual in April 2005 are displayed in Fig. 1 It is obvious that the precision of KBRR residual for all arcs is around 0.2 micrometer per second, which is corresponding to the official nominal precision of KBRR system. After GRACE data preprocessing mentioned above, the monthly temporal gravity field models are inversed by dynamic integral approach presented in Section 2, and least square method is used in the adjustment process. On the basis of the processed KBRR residuals, the spherical harmonic coefficients are estimated for each month, which are finally gathered as a set of monthly temporal gravity field models and named as WHU-Grace01s.

4. Analysis and discussion of WHUGrace01s WHU-Grace01s are all truncated to degree and order 60. Fig. 2 displays the equivalent water heights computed from the temporal gravity field models of April 2005, and truncated to degree and order 10, 20, 30, 40, 50 and 60, respectively. With the increase of truncated degree and order, it is obvious that the northesouth stripe errors gradually submerge the temporal signal. In the map of model truncated to degree 10 and 20, the temporal signal is bigger than the high-frequency noise. When the truncated degree is 60, stripe error thoroughly submerged the temporal signal.

Table 2 e Summary of force models for satellite motion. Force model Mean gravitational field N-body perturbation Solid Earth tides Ocean tides Polar tides Atmosphere tides Non-tidal signals General relativity effects Non-gravitational accelerations Linear trends in low-degree coefficients

Description

Parameters and remarks

GGM05s DE405 IERS2003 EOT08A IERS2003 GOT4.8 AOD1B IERS2003 Accelerometer observations IERS2003

Truncated to degree 180 Only consider the point mass attractions from Sun and Moon The frequency-independent part is considered in degree 2, 3 and 4 Truncated to degree 120 The polar motion is considered in C2,1 and S2,1 The tidal constituent S2 is considered in C2,2 and S2,2 RL05 edition, truncated to degree 100 General theory of relativity Initial bias and scaling parameters are provided by JPL. The 3D bias and scaling parameters are determined per 24-h arc The linear trends of C2,0, C2,1, S2,1, C3,0 and C4,0

g e o d e s y a n d g e o d y n a m i c s 2 0 1 5 , v o l 6 n o 5 , 3 1 6 e3 2 3

Fig. 1 e RMS of post KBRR residual in April 2005.

In order to comprehend the formation of stripe error, a simulation study of temporal gravity field model inversion in error free condition is implemented. In the simulation, the earth gravity field model added by GGM05s and Global Land Data Assimilation System (GLDAS) is treated as a true model to generate the real inter-satellite range rate observations, while GGM05s is treated as a reference model to integrate the reference inter-satellite range rate. The KBRR residuals are then used to estimate the spherical harmonic coefficients by the dynamic integral approach. Fig. 3a and Fig. 3b display the equivalent water height computed from the GLDAS and determined solutions respectively. It is obvious that the determined solution is almost identical to the real model. Fig. 3c displays the discrepancy of these two models in terms of equivalent water height. The magnitude of this discrepancy is merely about 1 mm, which indicates that the

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temporal gravity field models can be precisely recovered with our software. In addition, it is noted that even in the error free condition in GRACE mission configuration, the discrepancy in Fig. 3c still present a north-south error pattern. Considering that the two GRACE identical satellites are tracking in the northesouth direction, we can attribute the stripe error to the non-uniform distribution of the observations, that is, the observations in polar area are denser than the ones near equator. Simultaneously, only one direction rather than three dimensions of range rate observations is the other reason for the stripe errors shown in error free condition. Furthermore, in the real measurement condition, the observation error from accelerometer and aliasing error from tidal and non-tidal signal also contaminate gravity fields of GRACE, which consequently cause the north-south stripe errors. In order to extract the temporal signal from the contaminated values in Fig. 2, a combined filter contains 500 km Fan filter and de-correlated filter P3M6 is used. The final equivalent water height in 2005 computed from WHUGrace01s is shown in Fig. 4. The hydrological signals in the continental area can be clearly observed throughout a year. The most obvious mass transportation area is the Amazon River Basin. Since it steps into the dry season in July, the equivalent water height gradually decreases and reaches a minimum in October. Following by the rainy season, the water storage begins to accumulate after October and shows a positive peak in April. In addition, according to the division of global basins by Oki and Su [22], the water storage variations in the river basins of Orinoco, Tocantins, Mississippi, Mackenzie, Nile, Congo, Danube, Ob, Yangtze, Ganges can also be observed in our solutions. Due to the snow melting and accumulation, the water storage in these river basins shows a seasonal periodicity and a same pattern year by year.

Fig. 2 e Equivalent water heights computed from WHU-Grace01s truncated to different degrees and orders in April 2005.

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Fig. 3 e Equivalent water height computed from (a) GLDAS signal, (b) solution recovered from simulated GRACE data in noise free condition, (c) discrepancy between (a) and (b).

Fig. 4 e Surface mass anomalies in the units of cm of equivalent water height for WHU-Grace01s from January to December in 2005. (500 km Fan filter and P3M6 filter was applied).

g e o d e s y a n d g e o d y n a m i c s 2 0 1 5 , v o l 6 n o 5 , 3 1 6 e3 2 3

5.

Comparison with other GRACE solutions

This section makes a comparison of the WHU-Grace01s with other published GRACE solutions in terms of degree variance and global water storage variations. It should be mentioned that all the models are computed up to degree and order 60. The degree variance is frequently used as an important index to compare different gravity field models. We compute the degree variance of WHU-Grace01s and compare it with JPL RL05, CSR RL05 and GFZ RL05 which are all determined by traditional dynamic integral approach. The result of degree variance for different models is shown in Fig. 5. Importantly, the distribution of global mass in Fig. 2 indicates that the low degree part, i.e., between 0 to about 30, is related to the main part of temporal signal, while the degrees above 40 contain more noise, and degrees between noise and signal parts mix noise and signal. Compared with JPL RL05, CSR RL05 and GFZ RL05 which are the solutions derived from the combination of orbits and range rate observations, as it is shown in Fig. 5, the degree variance in the noise part of WHU-Grace01s stands at the highest precise level, which can be treated as successfully avoiding orbit error contamination in the final solution. Due to the different background force models and processing strategy of observations processing, the differences of degree variance in the mix part in different solutions are clearly, while WHU-Grace01s model is very similar to JPL RL05, leveling at the middle of these four solutions. The degree variance of each solution is very similar to each other between degree 2 to 20, and this phenomenon is especially remarkable between WHU-Grace01s and JPL RL05, which demonstrates that these four solutions have potential to extract almost the same temporal gravity signal with individual spherical harmonic coefficients. The largest difference occurs after degree 30. According to the

Fig. 5 e Comparison of degree variance for different temporal gravity field models in August, 2015.

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discussion by Luthcke et al. [18], we can attribute this discrepancy to the different observation processing strategy and solely exploiting GRACE KBRR data for spherical harmonic coefficients determination. Particularly, compared the degree variance of each solution at degree 60, WHUGrace01s perform better than JPL RL05, CSR RL05 and GFZ RL05. Fig. 6 shows the equivalent water height computed from nine different temporal gravity field models. We distinguish these models with the abbreviation of their published agency. During the conversion from Stokes coefficients to global mass distribution, the same combination filter, i.e., 500 km Fan filter and P3M6 de-correlation filter, is applied. Although the models are determined by different background models, different processing strategy of GRACE observations and different inversion approaches, the distribution of global mass concentration computed from these nine models shows remarkable consistency. This fact leads to a conclusion that our solution WHUGrace01s can be used for temporal signal extraction exactly as the other models did. Nevertheless, as it mentioned in the degree variance discussion, these differences during the spherical harmonic coefficients determination also bring tiny discrepancies in equivalent water height. The discrepancies are particularly clear at the southeast corner of the Indian Ocean, where there are positive mass blocks in CSR, ITG, AIUB solutions rather than in the left six solutions. Moreover, at the middle of Pacific Ocean, the equivalent water height RMS of WHUGrace01s are only 0.6 cm, while it is 1.0 cm, 0.9 cm, 1.0 cm for CSR, GFZ and JPL, respectively.

6.

Conclusion

We presented a new temporal gravity field model WHUGrace01s, which is solely determined by GRACE KBRR data. The monthly gravity field solution currently is truncated to degree and order 60 for the period from January 2003 to December 2008. Our major focus points are: (i) fundamental of temporal gravity field model determination, (ii) strategy of data processing, (iii) analysis of model accuracy and (iv) comparison with other GRACE solutions. On the basis of dynamic integral approach, the statistic errors of post GRACE KBRR residuals are about 0.2 micrometers per second, which is consistent with the official observation accuracy of K-band system. Due to the GRACE configuration and background force model error, the temporal signals gradually submerged by noise with the increasing of truncated degrees. Hence, the spatial filter and de-correlation filter should be applied during the conversion from Stokes coefficients to mass variations. After applying combination filter, the global temporal signals show periodical change rules. In terms of the degree variance, our solution shows a good consistency with other published solutions, especially with JPL RL05. This consistency is inconformity after degree 50, where our solution is more accuracy than CSR RL05, JPL RL05 and GFZ RL05. Compared with other published models in

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Fig. 6 e Comparison of equivalent water height computed from different temporal gravity field models in April 2005 (500 km Fan filter and P3M6 filter was applied).

terms of equivalent water height distribution, our solutions show a good potential to estimate consistency global mass variations.

Acknowledgements This research was jointly supported by the National 973 Program of China (2013CB733302), the National Natural Science Foundation of China (41131067, 41174020, 41374023, 41474019), the Open Research Fund Program of the State Key Laboratory of Geodesy and Earth's Dynamics (SKLGED2015-13-E), the open fund of State Key Laboratory of Geographic Information Engineering (SKLGIE2013-M-1-3), the open fund of Key Laboratory of Geospace Environment and Geodesy, Ministry of Education (13-02-05).

references

[1] Wahr J, Swenson S, Zlotnicki V, Isabella V. Time-variable gravity from GRACE: first results. Geophys Res Lett 2004;31(11):L11501.

[2] Chen JL, Wilson CR, Tapley BD, Famiglietti JS, Rodell M. Seasonal global mean sea level change from satellite altimeter GRACE, and geophysical models. J Geodesy 2005;79(9):532e9. [3] Chen JL, Wilson CR, Tapley BD, Blankenship D, Young D. Antarctic regional ice loss rates from GRACE. Earth Planet Sci Lett 2008;266(1):140e8. [4] Luthcke SB, Zwally HJ, Abdalati W, Rowlands DD, Ray R, Nerem RS, et al. Recent Greenland ice mass loss by drainage system from satellite gravity observations. Science 2006;314(5803):1286e9. [5] Hu XG, Chen JL, Zhou YH, Huang C, Liao XH. Seasonal water storage change of the Yangtze River basin detected by GRACE. Sci China Ser D 2006;49(5):483e91. [6] Zhong M, Duan JB, Hsu HT, Peng P, Yan HM, Zhu YZ. Trend of China land water storage redistribution at medi-and largespatial scales in recent five years by satellite gravity observations. Chin Sci Bull 2009;54(5):816e21. [7] Luo ZC, Li Q, Zhang K, Wang HH. Trend of mass change in the Antarctic ice sheet recovered from the GRACE temporal gravity field. Sci China Earth Sci 2012;55(1):76e82. [8] Li Qiong, Luo Zhicai, Zhong Bo, Wang Haihong. Terrestrial water storage changes of the 2010 southwest China drought detected by GRACE temporal gravity field. Chin J Geophys 2013;56(6):1843e9 [in Chinese]. [9] Bettadpur S. UTCSR level-2 processing standards document for level-2 product release 0005. Center for Space Research.

g e o d e s y a n d g e o d y n a m i c s 2 0 1 5 , v o l 6 n o 5 , 3 1 6 e3 2 3

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

Technical Report GRACE. The University of Texas at Austin; 2012. Flechtner F. GFZ level-2 processing standards document for level-2 product release 0004. GeoForschungsZentrum Potsdam, Rev 2007:1. Bettadpur S. UTCSR level-2 processing standards document for level-2 product release 0004. Center for Space Research. Technical Report GRACE. The University of Texas at Austin; 2007. Mayer-Gu¨rr T. Gravitationsfeldbestimmung aus der Analyse € gen am Beispiel der Satellitenmissionen kurzer Bahnbo CHAMP und GRACE. Dissertation. University of Bonn; 2006. Liu X, Ditmar P, Siemes C, Slobbe DC, Revtova E, Klees R, et al. DEOS Mass Transport model (DMT-1) based on GRACE satellite data: methodology and validation. Geophys J Int 2010;181(2):769e88. € ggi A, Beutler G. Monthly gravity field solutions Meyer U, Ja based on GRACE observations generated with the Celestial Mechanics Approach. Earth Planet Sci Lett 2012;345:72e80. Lemoine JM, Bruinsma S, Loyer S, Biancalea R, Martya JC, Perosanza F, et al. Temporal gravity field models inferred from GRACE data. Adv Space Res 2007;39(10):1620e9. Shen Y, Chen Q, Hsu H, Zhang XF, Lou LZ. A modified short arc approach for recovering gravity field model. GRACE Science Meeting, Center for Space Research, University of Texas; 2013. Ran Jiangjun, Xu Houze, Zhong Min, Feng Wei, Shen Yunzhong, Zhang Xingfu, et al. Global temporal gravity field recovery using GRACE data. Chin J Geophys 2014;57(4):1032e40 [in Chinese].

323

[18] Luthcke SB, Rowlands DD, Lemoine FG, Klosko SM, Chinn D, McCarthy JJ. Monthly spherical harmonic gravity field solutions determined from GRACE inter-satellite range-rate data alone. Geophys Res Lett 2006;33(2):L02402. [19] Luo Zhicai, Zhou Hao, Zhong Bo, Zhang Kun. Analysis and validation of Gauss-Jackson integral algorithm. Geomatics Inf Sci Wuhan Univ 2013;38(11):1364e8 [in Chinese]. [20] Tapley BD, Flechtner F, Bettadpur SV, Watkins MM. The status and future prospect for GRACE after the first decade. AGU Fall Meet Abstr 2013. G22A -01. [21] Flechtner F, Dobslaw H. Gravity Recovery and Climate Experiment, AOD1B product description document for product release 05. Rev. 4.0. Technical report. Potsdam: GFZ German Research Centre for Geosciences; 2013. [22] Oki T, Sud YC. Design of Total Runoff Integrating Pathways (TRIP)-A global river channel network. Earth Interact 1998;2(1):1e37.

Zhou Hao, a PhD student studying in School of Geodesy and Geomatics, Wuhan University, majors in satellite gravimetry. He mainly works on satellite gravity field models recovery on the basis of GRACE and GOCE mission solely and jointly. He also studies in the determination of GRACE temporal gravity field models.