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International Journal of Geophysics

Volume 2011 (2011), Article ID 174396, 10 pages

http://dx.doi.org/10.1155/2011/174396

## Hydrological Excitation of Polar Motion Derived from GRACE Gravity Field Solutions

^{1}CNRS/UMR8630, Observatoire de Paris, 61 avenue de l'Observatoire, 75014 Paris, France^{2}Space Research Center, Polish Academy of Sciences, Bartycka 18 A, 00-716 Warsaw, Poland

Received 1 October 2010; Accepted 29 March 2011

Academic Editor: Petr Vaníček

Copyright © 2011 L. Seoane et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The influence of the continental water storage on the polar motion is not well known. Different models have been developed to evaluate these effects and compared to geodetic observations. However, previous studies have shown large discrepancies mainly attributed to the lack of global measurements of related hydrological parameters. Now, from the observations of the GRACE mission, we can estimate the polar motion excitation due to the global hydrology. Data processing of GRACE data is carried out by several centers of analysis, we focus on the new solution computed by the Groupe de Recherche de Géodésie Spatiale. At annual scales, excitations derived from GRACE data are in better agreement with geodetic observations than models estimates. The main contribution to the hydrological excitation comes from the monsoon climates regions where GRACE and models estimates are in a very good agreement. Still, the effect of the north high latitudes regions, where the principal areas of snow cover are found, cannot be neglected. At these regions, GRACE and models estimated contributions to polar motion excitations show significant discrepancies. Finally, GRACE-based excitations reveal the possible influence of water storage variations in exciting polar motion around the frequency of 3 cycles per year.

#### 1. Introduction

The excitation of polar motion is, to a large extent, related to the mass redistribution of geophysical fluids. The importance of atmospheric and oceanic angular momentum signals at monthly and seasonal periods is well known. The contribution of the continental hydrological signals, originating from land water, snow, and ice, is, however, less known. A number of previous studies have estimated hydrological excitation from climatological measurements, numerical climate models, and global hydrology models based upon the observed distribution of surface water, snow, ice, and soil moisture [1–5].

The hydrological part of polar motion excitation can also be obtained, as a residual series, by removing atmospheric and oceanic signals from the geodetic excitation of polar motion. The general conclusion of these studies is that the change in continental water storage plays a major role in the seasonal polar motion although the results of the hydrological models do not agree with each other and with observed polar motion [6, 7]. This is mainly due to the lack of global measurements of related hydrological parameters which are difficult to predict (like evaporation, run-off, groundwater, and snow/ice mass change).

Other analyses show that hydrological signals seem to exert a substantial influence at interannual scales [7, 8].

Thanks to the gravity recovery and climate experiment (GRACE) mission, the mass redistributions are observed over whole Earth. Atmospheric mass variations and the corresponding oceanic response are largely removed during GRACE data processing, then the obtained time-variable gravity fields reflect hydrological phenomena (i.e., terrestrial water storage variations from the soil water, groundwater, and snow/ice sheets) plus other non-modeled effects like postglacial rebound, earthquakes, and baroclinic oceanic signal. Thus, considering gravity field variations over continents mainly due to water and ice mass change, we have a new approach to evaluate the effect of the continental Earth's hydrology on polar motion. Other studies [9] show that GRACE observations are useful to evaluate oceanic and hydrological polar motion excitations in order to close global mass budget.

Our main objective is to compare the hydrological excitations computed from different data sets to better understand the influence of water mass variations on polar motion. Additionally, GRACE can help to located significant hydrological mismodelling effects. The data sets used in our study are geodetic observations of polar motion (IERS C04 polar motion series), GRACE gravity field solutions provided by the Groupe de Recherche de Géodésie Spatiale (GRGS), the Climate Prediction Center (CPC) [10] hydrological model, and the newer surface modelling system global land data assimilation system (GLDAS) [11].

#### 2. Data Sets

##### 2.1. Hydrological Models

Latitude-longitude grids providing the charge of continental water by surface unit are predicted by the CPC and the surface model GLDAS.

The CPC uses the Noah land surface model [10] forced by observed precipitation derived from CPC daily and hourly precipitation analyses, downward solar and long-wave radiation, surface pressure, humidity, temperature, and horizontal wind speed from the atmospheric model reanalysis of the National Centers for Environmental Prediction (NCEP). The net water storage at a grid point is estimated using the conservation equation [12] where , and are precipitation, evapotranspiration, and run-off. CPC water storage grids are estimated from January 1948 to December 2007 with a monthly resolution.

The GLDAS generates optimal fields of land surface states and fluxes by integrating ground- and satellite-based observational data products, using advanced land surface modelling and data assimilation techniques [11]. GLDAS has resulted in a massive archive of modelled and observed global surface meteorological data, parameter maps, and output which includes 1 and 0.25 degrees resolution of the 1979 to present simulations of the Noah, community land (CLM), mosaic, and variable infiltration capacity (VIC) land surface models [13]. In this case, water storage is the sum of soil moisture, snow water equivalent, and canopy surface water not counting changes in groundwater below the depth defined by the model [12], that is, variations below 2 meters depth. Hydrological excitation functions can be computed from the monthly fields of global water storage from January 1979 to February 2008.

##### 2.2. Gravimetric Data

The GRACE time-variable gravity field solutions of the GRGS are provided at 10 day intervals from July 29 2002 to May 27 2008 in the last release RL02 [14]. They use a different data processing strategy than those applied by the other analysis centers (CSR, GFZ, and JPL). The GRGS gravity field solution is computed by a combination of GRACE and LAGEOS-1 and 2 observations. LAGEOS data provide over 90% of the information on the (2,0) degree coefficients [14]. GRACE data provide nearly 100% of the information on all other harmonic coefficients. A different background model is used mainly concerning the nontidal oceanic model. The GRGS uses a barotropic oceanic model Modèle 2D d’Ondes de Gravité (MOG2D). Lastly, it is known that the geoid’s height difference plots show a north-south streaking due to systematic errors in higher degree coefficients. To avoid this problem, GRGS constrained the higher degrees coefficients gradually to those of the static solution [15]. The other centers (CSR, GFZ, and JPL) use instead a filtering procedure for avoiding this problem [16].

Usually, the excitation based on gravimetric observations is derived from the and coefficients of the gravity field solution using the classical methodology (see, e.g., [17]). However, these coefficients contain hydrological variations and also residuals over oceans, in our case, this is a baroclinic signal. In this paper, we propose to estimate the hydrological GRACE-based excitation in a different way employing equivalent water height maps (EWH) restricted to continents in order to exclude oceanic effects. In fact, GRGS provides converted maps into meters of EWH from which we estimate the terrestrial water storage grids by where kg m^{−3} is the water density.

##### 2.3. Geodetic Residuals

The International Earth Rotation and Reference Systems Service (IERS) provides a combined time series C04 of the Earth Orientation Parameters (EOP) at daily intervals [18, 19], in particular the pole coordinates and . The geodetic polar motion excitation in polar motion can be written as where is the complex pole coordinate obtained from C04 series and is the frequency of the Chandler pulsation ( rad/days) with an adopted quality factor of 175 [20]. We derived the geodetic excitation according to Wilson [21].

The hydrological influences are obtained by removing atmospheric and oceanic signals from the geodetic excitation. For computing these geodetic residuals, we use the atmospheric excitation series based on the NCEP/NCAR reanalysis [22] and the oceanic excitation series derived from the ECCO model [23]. In order to match the temporal spectral consistency with GRACE gravity field solutions, geodetic, atmospheric, and oceanic excitations are smoothed using Vondrak filter [24, 25] and interpolated every 10 days.

#### 3. Analysis and Results

##### 3.1. Hydrological Polar Motion Excitations

According to Chen and Wilson [7] formulation, by integrating the grids of water thickness of the CPC and GLDAS models over continents (Greenland and Antarctica are excluded), we have reconstituted the hydrological excitation function reduced to its mass term as follows: where is the Earth’s mean radius, and are the Earth’s principal moments of inertia, and () is the latitude and longitude. The factor 1.098 accounts the combined effects of the yielding of the solid Earth to surface load, core-mantle decoupling, and rotational deformation [26]. The series are interpolated to the GRACE temporal resolution. In the same way, that is, integrating over continents the terrestrial water storage derived from GRACE (3), we obtain another approach of the hydrological excitation. From November 2002 to February 2003 are the main GRACE data gaps, and so, our study period is restricted to March 2003 until December 2007, which is the last common date with the hydrological models time span.

Figure 1 shows the estimates of the hydrological excitation (GRACE grids were integrated over continents) and the oceanic residuals (GRACE grids were integrated over oceans only). We can notice significant oceanic variations that we will not consider in our study. Spatial spectral leakage due to using a [0 or 1] mask is expected to be negligible over large regions.

Figure 2 shows the excitation functions obtained from residual geodetic observations, GRACE gravity field solutions, and models estimates. Means and linear trends are removed from all data sets. As expected, we observe that the hydrological signals are dominated by the annual fluctuations. GRACE-based excitations are in agreement with the residual geodetic excitations mainly at annual scales, and both show variations between . Hydrological models underestimate variations, probably because some mismodeled process, except for the component derived from CPC.

##### 3.2. Seasonal Variations

Seasonal fluctuations are estimated by least-square fitting (Table 1 and corresponding phaser plots Figure 3). The annual variations of GRACE-based and the residual geodetic excitations are in good agreement for the both components and . Phase differences are more important in the case of but not large ( versus ); however, CPC model is closer in phase ( versus 3°). The is more sensitive to the ocean mass redistributions and the uncertainties of the ocean models used for estimating residual geodetic series can probably be a cause of disagreement. To the contrary, is affected by the Earth hydrology due to the location of main continents [7]. Whereas, considering the hydrological models predictions with respect to GRACE observations and geodetic residual, there are larger discrepancies in amplitude and the modeled annual signals are generally underestimated. Except for computed from the CPC model, which has an amplitude of nearly 3 mas larger than the GRACE estimate. Phases agree quite well. In conclusion, the annual hydrological budget estimated by GRACE is more consistent with the geodetic observations than models predictions. In the case of the semiannual oscillations, they have lower amplitudes (up to 4 mas). It seems that there is a reasonably agreement between models predictions and GRACE observations.

Phasor diagram (Figure 3) confirms that GRACE-based excitation is in better agreement at geodetic residuals (phases are similar and amplitude difference is about 2 mas). However in the case of the semiannual signal, GRACE and models-based excitation are in agreement, but geodetic residuals are large different probably due to atmospheric or oceanic models errors at this frequency.

##### 3.3. Regional Hydrology Contributions at Annual Scale

In order to find the Earth’s regions, where models CPC and GLDAS do not predict consistent annual variations with respect to GRACE observations, the amplitudes and phases for every grid point are computed by least-square fitting (Figure 4). In Figure 4, we note that the prominent annual signals are due to the monsoonal climates [27] situated at latitudes smaller than . The monsoon regions are located in the Amazon, Central Africa, South Africa, North Australia, India, and Indochina. We observe that CPC model provides stronger amplitudes than the GLDAS model. The groundwater storage not counting in the GLDAS model seems to be the cause of the lower amplitudes over major river basins [12]. In fact, GLDAS model is defined with a surface layer of 2 m depth, then groundwater variations below are not taken into account. So, what is the contribution of the monsoonal climate regions to the polar motion excitation? To answer this question, we compute the hydrological excitations restricting the integration of the water storage grids of CPC, GLDAS, and GRACE (see (3)) over those latitudes smaller than . Results are shown in Figure 5. As expected, annual oscillations are clearly dominant, and there is a very good agreement between the GRACE observations and models. Generally, the contribution of this Earth domain does not explain the hydrological annual budget found in Table 1, thus influences of the north high latitudes regions must not be neglected. At these latitudes (latitudes ), we find the main areas of snow cover and continental climates. We notice the large discrepancies between the hydrological excitations computed from models and GRACE (Figure 5), especially concerning , come from this region, where models snow water estimations seems to be inaccurate.

##### 3.4. Interannual Polar Motion Excitations

The hydrology plays an important role at low frequencies. Chen and Wilson [7] have shown significant interannual variations which seem to be of hydrological nature. From wavelet analysis of the excitation functions derived from the geodetic residuals and the hydrological model predictions, Fernández et al. [8] have found strong energy values around 4 years in the retrograde band.

For obtaining interannual variations, we remove seasonal signals (annual and semiannual) from geodetic, CPC, GLDAS, and GRACE-based hydrological excitations. Afterward, we applied a low pass digital filter of cutoff frequency 1 year to the residuals. The interannual signals are shown in Figure 6. For the component, models and GRACE-based excitations are well correlated with the geodetic residuals (Table 2). Future longer series of GRACE observations and improvements in the data processing can help to gain a greater understanding of the hydrology influences on polar motion at interannual scales.

##### 3.5. Intraseasonal Polar Motion Excitations

Various studies note the important influence of the atmosphere and oceans on polar motion excitations at interseasonal scales [22, 28–31]. Gross et al. [32] have observed that a third of the geodetic excitation was not explained by atmospheric and oceanic phenomenon. They attribute this discrepancy to the uncertainties in the data sets and also to the effect of other excitation process not considered like the continental hydrology. However, models do not predict enough power at those frequencies. To obtain the intraseasonal variations we removed from all series the annual, semiannual signals, and low frequency fluctuations. The latter are estimated in the previous section. Figure 7 shows the spectrum of the different hydrological excitation data sets. GRACE observations provide more power than hydrological models, especially in the prograde and retrograde bands around the frequency of 3 cycles per year. At those frequencies, the power of the hydrological excitation derived from GRACE is comparable to those derived from geodetic residual and the hydrology seems to be a nonnegligible process of intraseasonal polar motion excitation.

#### 4. Conclusion

This study explores the hydrological excitation of the polar motion computed from GRACE gravity field observations. So far, the excitation produced by the water storage variations was estimated using advanced hydrological models. These models include algorithms to assimilate observations of terrestrial hydrology. However, the main causes of errors are the lack of the global measurements of related hydrological parameters. The GRACE mission provides continental water change with unprecedented accuracy. After removing the atmospheric and oceanic effect from geodetic observations, we compare these residual signals to the excitations computed by GRACE estimates. At the annual timescale, we find that the GRACE-based excitations are in better agreement with geodetic residuals than the excitations predicted by the hydrological models. The prominent annual excitation is mainly due to the monsoon regions located at latitudes smaller than , where GRACE and models are in a very good agreement, in particular for CPC. In fact, we note that the groundwater variations unaccounted in the GLDAS model can have significant influences. Moreover, the annual signal observed by GRACE and obtained by the models at the high latitudes regions show important discrepancies probably due to the inaccurate snow water and ice estimations. We find also considerable interannual variations which confirms that the continental hydrology exerts a significant influence on the variations at low frequencies. Even so, the models or the GRACE solutions cannot explain the fluctuations of the geodetic residuals especially concerning the component. Finally, from the spectral analysis of interseasonal variations, GRACE observations show that continental hydrology can excite polar motion at frequencies of about 3 cpy.

In conclusion, mass water variations of terrestrial water storage components (like groundwater or ice/snow sheets) are very difficult to model precisely. The mismodelling signals have a significant impact in the determination of hydrological influence on polar motion. Still, terrestrial water storage variations are observed by the GRACE mission, and it could be useful to constrain the models. We can expect that data processing improvements and longer series of GRACE observations will help in the understanding of polar motion excitation caused by the Earth’s hydrology and closing the global mass budget.

#### Abbreviations

CLM: | Community land model |

CSR: | Center for Space Research |

CPC: | Climate Prediction Center |

ECCO: | Estimating the circulation and climate of the ocean |

EOP: | Earth orientation parameters |

EWH: | Equivalent water height |

G-A-O: | Geodetic-atmospheric-oceanic excitations |

GFZ: | Geoforschungs Zentrum |

GLDAS: | Global land assimilation system |

GRACE: | Gravity recovery and climate experiment |

GRGS: | Groupe de Recherche de Géodésie Spatiale |

IERS: | International Earth Rotation and Reference Systems Service |

JPL: | Jet Propulsion Laboratory |

MOG2D: | Modèle 2D d’Ondes de Gravité |

NCAR: | National Centers for Atmospheric Research |

NCEP: | National Centers for Environmental Prediction |

LAGEOS: | Laser geodynamics satellite |

SH: | Spherical harmonics |

VIC: | Variable infiltration capacity. |

#### Acknowledgments

The authors are grateful to Jean Michel Lemoine for providing different GRGS data sets and David Salstein for his suggestions. During her stay in Paris, J. Nastula was sponsored by the Observatoire de Paris. J. Nastula acknowledges the support of Project no. N526 140 735 from the Polish Ministry of Science and Higher Education.

#### References

- T. E. A. Van Hycklama,
*Water Balance and Earth Unbalance*, vol. 92, IASH AISH, 1970. - L. A. Hinnov and C. R. Wilson, “An estimate of the water storage contribution to the excitation of polar motion,”
*Geophysical Journal Royal Astronomical Society*, vol. 88, no. 2, pp. 437–459, 1987. View at Google Scholar · View at Scopus - B. F. Chao and W. P. O'Connor, “Global surface-water-induced seasonal variations in the Earth's rotation and gravitational field,”
*Geophysical Journal*, vol. 94, no. 2, pp. 263–270, 1988. View at Google Scholar · View at Scopus - J. Kuehne and C. R. Wilson, “Terrestrial water storage and polar motion,”
*Journal of Geophysical Research*, vol. 96, no. 3, pp. 4337–4345, 1991. View at Google Scholar · View at Scopus - J. L. Chen, C. R. Wilson, B. F. Chao, C. K. Shum, and B. D. Tapley, “Hydrological and oceanic excitations to polar motion and length-of-day variation,”
*Geophysical Journal International*, vol. 141, no. 1, pp. 149–156, 2000. View at Publisher · View at Google Scholar · View at Scopus - J. Nastula, B. Kolaczek, and W. Popiński, “Comparisons of hydrological angular momentum (HAM) of different models,” in
*Proceedings of the Journées*, A. Brzeziński, N. Capitaine, and B. Kolaczek, Eds., pp. 207–210, 2005. - J. L. Chen and C. R. Wilson, “Hydrological excitations of polar motion, 1993–2002,”
*Geophysical Journal International*, vol. 160, no. 3, pp. 833–839, 2005. View at Publisher · View at Google Scholar · View at Scopus - L. I. Fernández, H. Schuh, M. Schmidt, and F. Seitz, “Effects of inter-annual water storage variations on polar motion,”
*Geophysical Journal International*, vol. 169, no. 1, pp. 12–18, 2007. View at Publisher · View at Google Scholar · View at Scopus - S. Jin, D. P. Chambers, and B. D. Tapley, “Hydrological and oceanic effects on polar motion from GRACE and models,”
*Journal of Geophysical Research B*, vol. 115, no. 2, Article ID B02403, 2010. View at Publisher · View at Google Scholar · View at Scopus - Y. Fan, H. van den Dool, K. Mitchel, and D. Lohmann, “A 51-year reanalysis of the US land-surface hydrology,”
*GEWEX News*, vol. 13, no. 2, pp. 6–10, 2003. View at Google Scholar - M. Rodell, P. R. Houser, U. Jambor et al., “The global land data assimilation system,”
*Bulletin of the American Meteorological Society*, vol. 85, no. 3, pp. 381–394, 2004. View at Publisher · View at Google Scholar · View at Scopus - J. L. Chen, M. Rodell, C. R. Wilson, and J. S. Famiglietti, “Low degree spherical harmonics influences on Gravity Field Recovery and Climate Experiment (GRACE) water storage,”
*Geophysical Research Letters*, vol. 32, p. L14405, 2005. View at Google Scholar - H. Fang, “Readme document for Global Data Assimilation System (GLDAS) products,” 2008.
- R. Biancale, J. M. Lemoine, G. Balmino et al., 6 years of gravity variations from GRACE and LAGEOS data at 10-day intervals over the period from July 29th 2002 to November 2008, http://bgi.cnes.fr:8110/geoid-variations/README.html.
- J. M. Lemoine, S. Bruinsma, S. Loyer et al., “Temporal gravity field models inferred from GRACE data,”
*Advances in Space Research*, vol. 39, no. 10, pp. 1620–1629, 2007. View at Publisher · View at Google Scholar · View at Scopus - S. Swenson and J. Wahr, “Post-processing removal of correlated errors in GRACE data,” in
*Geophysical Research Letters*, vol. 33, L08402, 2006. View at Google Scholar - J. L. Chen, C. R. Wilson, B. D. Tapley, and J. C. Ries, “Low degree gravitational changes from GRACE: validation and interpretation,”
*Geophysical Research Letters*, vol. 31, no. 22, Article ID L22607, 5 pages, 2004. View at Publisher · View at Google Scholar · View at Scopus - D. Gambis, “Monitoring Earth orientation using space-geodetic techniques: state-of-the-art and prospective,”
*Journal of Geodesy*, vol. 78, no. 4-5, pp. 295–303, 2004. View at Publisher · View at Google Scholar · View at Scopus - C. Bizouard and D. Gambis, “The combined solution C04 for Earth Orientation Parameters consistent with International Terrestrial Reference Frame 2005,” Technical Note of IERS Earth Orientation Center, 2007.
- C. R. Wilson and R. O. Vicente, “Maximum likelihood estimates of polar motion parameters,” in
*Variations in Earth Rotation*, D. D. McCarthy and W. Carter, Eds., vol. 53 of*Geophysical Monograph Series*, pp. 151–155, AGU, Washington, DC, USA, 1990. View at Google Scholar - C. R. Wilson, “Discrete polar motion equations,”
*Geophysical Journal Royal Astronomical Society*, vol. 80, no. 2, pp. 551–554, 1985. View at Google Scholar · View at Scopus - D. A. Salstein, D. M. Kann, A. J. Miller, and R. D. Rosen, “The sub-bureau for atmospheric angular momentum of the International Earth Rotation Service: a meteorological data center with geodetic applications,”
*Bulletin of the American Meteorological Society*, vol. 74, no. 1, pp. 67–80, 1993. View at Google Scholar · View at Scopus - R. S. Gross, “An improved empirical model for the effect of long-period ocean tides on polar motion,”
*Journal of Geodesy*, vol. 83, no. 7, pp. 635–644, 2009. View at Publisher · View at Google Scholar · View at Scopus - J. Vondrak, “A contribution to the problem of smoothing observational data,”
*Bulletin of the Astronomical Institutes of Czechoslovakia*, vol. 20, p. 349, 1969. View at Google Scholar - J. Vondrak, “Problem of smoothing observational data II,”
*Bulletin of the Astronomical Institutes of Czechoslovakia*, vol. 28, pp. 84–89, 1977. View at Google Scholar - T. M. Eubanks, “Variations in the orientation of the Earth,” in
*Contributions of Space Geodesy to Geodynamic: Earth Dynamics*, D. Smith and D. Turcotte, Eds., vol. 24 of*Geodynamics Series*, pp. 1–54, AGU, Washington, DC, USA, 1993. View at Google Scholar - Y. Fan and H. van den Dool, “Climate Prediction Center global monthly soil moisture data set at 0.5° resolution for 1948 to present,”
*Journal of Geophysical Research D*, vol. 109, no. 10, p. D10102, 2004. View at Publisher · View at Google Scholar · View at Scopus - B. Kolaczek, W. Kosek, and H. Schuh, “Short-period oscillations of Earth rotation,” in
*Polar Motion: Historical and Scientific Problems*, S. Dick, D. McCarthy, and B. Luzum, Eds., vol. 178 of*IAU Colloquia*, pp. 533–544, Astronomical Society of the Pacific, San Francisco, Calif, USA, 2000. View at Google Scholar - B. Kołaczek, M. Nuzhdina, J. Nastula, and W. Kosek, “El Niño impact on atmospheric polar motion excitation,”
*Journal of Geophysical Research B*, vol. 105, no. 2, pp. 3081–3087, 2000. View at Google Scholar · View at Scopus - R. M. Ponte, D. Stammer, and J. Marshall, “Oceanic signals in observed motions of the Earth's pole of rotation,”
*Nature*, vol. 391, no. 6666, pp. 476–479, 1998. View at Publisher · View at Google Scholar · View at Scopus - J. Nastula, R. M. Ponte, and D. A. Salstein, “Regional signals in atmospheric and oceanic excitation of polar motion,” in
*Proceedings of the 178th IAU Colloquium, Polar Motion: Historical and Scientific Problems*, pp. 463–472, Cagliari Sardinia, Italy, 2000. - R. S. Gross, I. Fukumori, and D. Menemenlis, “Atmospheric and oceanic excitation of the Earth's wobbles during 1980–2000,”
*Journal of Geophysical Research B*, vol. 108, no. 8, pp. 6–16, 2003. View at Google Scholar · View at Scopus