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Unmixing grain-size distributions in lake sediments: a new method of endmember modeling using hierarchical clustering

Published online by Cambridge University Press:  16 October 2017

Xiaonan Zhang ,
Aifeng Zhou ,
Xin Wang ,
Mu Song ,
Yongtao Zhao ,
Haichao Xie ,
James M. Russell  and
Fahu Chen
Xiaonan Zhang*
Affiliation:
Key Laboratory of Western China’s Environmental Systems (Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China
Aifeng Zhou
Affiliation:
Key Laboratory of Western China’s Environmental Systems (Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China
Xin Wang
Affiliation:
Key Laboratory of Western China’s Environmental Systems (Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China
Mu Song
Affiliation:
Department of Earth Sciences, The University of Hong Kong, Hong Kong 999077, China
Yongtao Zhao
Affiliation:
Key Laboratory of Western China’s Environmental Systems (Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China
Haichao Xie
Affiliation:
Key Laboratory of Western China’s Environmental Systems (Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China
James M. Russell
Affiliation:
Department of Earth, Environmental, and Planetary Sciences, Brown University, Providence, Rhode Island 02912, USA
Fahu Chen*
Affiliation:
Key Laboratory of Western China’s Environmental Systems (Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China Institute of Tibetan Plateau Research, Chinese Academy of Science, Beijing 100101, China
*
*Corresponding authors at: Key Laboratory of Western China’s Environmental Systems (Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China. E-mail addresses: fhchen@lzu.edu.cn (F. Chen); zhangxn2012@lzu.edu.cn (X. Zhang).
*Corresponding authors at: Key Laboratory of Western China’s Environmental Systems (Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China. E-mail addresses: fhchen@lzu.edu.cn (F. Chen); zhangxn2012@lzu.edu.cn (X. Zhang).
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Abstract

The grain-size distribution (GSD) of sediments provides information on sediment provenance, transport processes, and the sedimentary environment. Although a wide range of statistical parameters have been applied to summarize GSDs, most are directed at only parts of the distribution, which limits the amount of environmental information that can be retrieved. Endmember modeling provides a flexible method for unmixing GSDs; however, the calculation of the exact number of endmembers and geologically meaningful endmember spectra remain unresolved using existing modeling methods. Here we present the methodology hierarchical clustering endmember modeling analysis (CEMMA) for unmixing the GSDs of sediments. Within the CEMMA framework, the number of endmembers can be inferred from agglomeration coefficients, and the grain-size spectra of endmembers are defined on the basis of the average distance between the samples in the clusters. After objectively defining grain-size endmembers, we use a least squares algorithm to calculate the fractions of each GSD endmember that contributes to individual samples. To test the CEMMA method, we use a grain-size data set from a sediment core from Wulungu Lake in the Junggar Basin in China, and find that application of the CEMMA methodology yields geologically and mathematically meaningful results. We conclude that CEMMA is a rapid and flexible approach for analyzing the GSDs of sediments.

Keywords

Grain-size distributionEndmemberHierarchical clustering analysisUnmixingLake sediments

Information

Type
Research Article
Information
Quaternary Research , Volume 89 , Issue 1: Tribute to Daniel Livingstone and Paul Colinvaux , January 2018 , pp. 365 - 373
Copyright
Copyright © University of Washington. Published by Cambridge University Press, 2017 

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References

REFERENCES

Blott, S.J., Pye, K., 2001. GRADISTAT: a grain size distribution and statistics package for the analysis of unconsolidated sediments. Earth Surface Processes and Landforms 26, 1237–1248.Google Scholar
Boulay, S., Colin, C., Trentesaux, A., Pluquet, F., Bertaux, J., Blamart, D., Buehring, C., Wang, P., 2003. Mineralogy and sedimentology of Pleistocene sediments on the South China Sea (ODP Site 1144). In: Prell, W.L., Wang, P., Blum, P., Rea, D.K., Clemens, S.C. (Eds.), Proceedings of the Ocean Drilling Program: Scientific Results. Vol. 184. Ocean Drilling Program, Texas A&M University, College Station, pp. 1–21.Google Scholar
Chen, F., Chen, J., Holmes, J., Boomer, I., Austin, P., Gates, J.B., Wang, N., Brooks, S.J., Zhang, J., 2010. Moisture changes over the last millennium in arid central Asia: a review, synthesis and comparison with monsoon region. Quaternary Science Reviews 29, 1055–1068.CrossRefGoogle Scholar
Chen, F., Yu, Z., Yang, M., Ito, E., Wang, S., Madsen, D.B., Huang, X., et al., 2008. Holocene moisture evolution in arid central Asia and its out-of-phase relationship with Asian monsoon history. Quaternary Science Reviews 27, 351–364.Google Scholar
Chiu, T., Fang, D., Chen, J., Wang, Y., Jeris, C., 2001. A robust and scalable clustering algorithm for mixed type attributes in large database environment. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, pp. 263–268.Google Scholar
Clark, M.W., 1976. Some methods for statistical analysis of multimodal distributions and their application to grain-size data. Journal of the International Association for Mathematical Geology 8, 267–282.Google Scholar
Court, A., 1949. Separating frequency distributions into two normal components. Science 110, 500–501.CrossRefGoogle ScholarPubMed
Dietze, E., Hartmann, K., Diekmann, B., Ijmker, J., Lehmkuhl, F., Opitz, S., Stauch, G., Wünnemann, B., Borchers, A., 2012. An end-member algorithm for deciphering modern detrital processes from lake sediments of Lake Donggi Cona, NE Tibetan Plateau, China. Sedimentary Geology 243–244, 169–180.Google Scholar
Donato, S.V., Reinhardt, E.G., Boyce, J.I., Pilarczyk, J.E., Jupp, B.P., 2009. Particle-size distribution of inferred tsunami deposits in Sur Lagoon, Sultanate of Oman. Marine Geology 257, 54–64.Google Scholar
Everitt, B.S., Landau, S., Leese, M., Stahl, D., 2011. Hierarchical clustering. In: Everitt, B.S., Landau, S., Leese, M., Stahl, D. (Eds.), Cluster Analysis. 5th ed. John Wiley and Sons, Chichester, UK, pp. 71–110.Google Scholar
Folk, R.L., Ward, W.C., 1957. Brazos River bar: a study in the significance of grain size parameters. Journal of Sedimentary Research 27, 3–26.Google Scholar
Fournier, J., Gallon, R.K., Paris, R., 2014. G2Sd: a new R package for the statistical analysis of unconsolidated sediments. Géomorphologie: Relief, Processus, Environnement 20, 73–78.Google Scholar
Ghosh, J.K., Mazumder, B.S., 1981. Size distribution of suspended particles—unimodality, symmetry and lognormality. In: Taillie, C., Patil, G.P., Baldessari, B.A. (Ed.), Statistical Distributions in Scientific Work. Vol. 6. Applications in Physical, Social, and Life Sciences. D. Reidal, Dordrecht, the Netherlands, pp. 21–32.Google Scholar
Grimm, E.C., Donovan, J.J., Brown, K.J., 2011. A high-resolution record of climate variability and landscape response from Kettle Lake, northern Great Plains, North America. Quaternary Science Reviews 30, 2626–2650.Google Scholar
Gruvaeus, G., Wainer, H., 1972. Two additions to hierarchical cluster analysis. British Journal of Mathematical and Statistical Psychology 25, 200–206.CrossRefGoogle Scholar
He, Y., Zhao, C., Song, M., Liu, W., Chen, F., Zhang, D., Liu, Z., 2015. Onset of frequent dust storms in northern China at ~AD 1100. Scientific Reports 5, 17111. http://dx.doi.org/10.1038/srep17111.Google Scholar
Hill, E.W., Brennan, J.F., Wolman, H.L., 1998. What is a central city in the United States? Applying a statistical technique for developing taxonomies. Urban Studies 35, 1935–1969.Google Scholar
Inman, D.L., 1952. Measures for describing the size distribution of sediments. Journal of Sedimentary Research 22, 125–145.Google Scholar
Johnson, S.C., 1967. Hierarchical clustering schemes. Psychometrika 32, 241–254.Google Scholar
Kaufman, L., Rousseeuw, P.J., 2009. Finding Groups in Data: An Introduction to Cluster Analysis. John Wiley and Sons, Hoboken, NJ.Google Scholar
Langfelder, P., Zhang, B., Horvath, S., 2008. Defining clusters from a hierarchical cluster tree: the Dynamic Tree Cut package for R. Bioinformatics 24, 719–720.Google Scholar
Liu, J., Rühland, K.M., Chen, J., Xu, Y., Chen, S., Chen, Q., Huang, W., Xu, Q., Chen, F., Smol, J.P., 2017. Aerosol-weakened summer monsoons decrease lake fertilization on the Chinese Loess Plateau. Nature Climate Change 7, 190–194.Google Scholar
Liu, X., Herzschuh, U., Shen, J., Jiang, Q., Xiao, X., 2008. Holocene environmental and climatic changes inferred from Wulungu Lake in northern Xinjiang, China. Quaternary Research 70, 412–425.CrossRefGoogle Scholar
Nelson, P.A., Bellugi, D., Dietrich, W.E., 2014. Delineation of river bed-surface patches by clustering high-resolution spatial grain size data. Geomorphology 205, 102–119.CrossRefGoogle Scholar
Ordóñez, C., Ruiz-Barzola, O., Sierra, C., 2016. Sediment particle size distributions apportionment by means of functional cluster analysis (FCA). Catena 137, 31–36.Google Scholar
Passega, R., 1964. Grain size representation by CM patterns as a geological tool. Journal of Sedimentary Research 34, 830–847.Google Scholar
Paterson, G.A., Heslop, D., 2015. New methods for unmixing sediment grain size data. Geochemistry, Geophysics, Geosystems 16, 4494–4506.Google Scholar
Qiang, M., Chen, F., Zhou, A., Xiao, S., Zhang, J., Zhang, J., 2007. Impacts of wind velocity on sand and dust deposition during dust storm as inferred from a series of observations in the northeastern Qinghai–Tibetan Plateau, China. Powder Technology 175: 82–89.CrossRefGoogle Scholar
Qin, X., Cai, B., Liu, T., 2005. Loess record of the aerodynamic environment in the east Asia monsoon area since 60,000 years before present. Journal of Geophysical Research: Solid Earth 110, B01204. http://dx.doi.org/10.1029/2004JB003131.Google Scholar
Renner, R.M., 1991. An examination of the use of the logratio transformation for the testing of endmember hypotheses. Mathematical Geology 23, 549–563.CrossRefGoogle Scholar
Rodriguez, A., Laio, A., 2014. Clustering by fast search and find of density peaks. Science 344, 1492–1496.CrossRefGoogle ScholarPubMed
Salvador, S., Chan, P., 2004. Determining the number of clusters/segments in hierarchical clustering/segmentation algorithms. In: Proceedings 16th IEEE International Conference on Tools with Artificial Intelligence, Boca Raton, FL, pp. 576–584.Google Scholar
Singer, A., 1984. The paleoclimatic interpretation of clay minerals in sediments—a review. Earth-Science Reviews 21, 251–293.CrossRefGoogle Scholar
Sun, D., Bloemendal, J., Rea, D.K., Vandenberghe, J., Jiang, F., An, Z., Ruixia, S., 2002. Grain-size distribution function of polymodal sediments in hydraulic and aeolian environments, and numerical partitioning of the sedimentary components. Sedimentary Geology 152, 263–277.Google Scholar
Tibshirani, R., Walther, G., Hastie, T., 2001. Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63, 411–423.Google Scholar
Visher, G.S., 1969. Grain size distributions and depositional processes. Journal of Sedimentary Research 39, 1074–1106.Google Scholar
Weltje, G.J., 1997. End-member modeling of compositional data: numerical-statistical algorithms for solving the explicit mixing problem. Mathematical Geology 29, 503–549.Google Scholar
Weltje, G.J., Prins, M.A., 2003. Muddled or mixed? Inferring palaeoclimate from size distributions of deep-sea clastics. Sedimentary Geology 162, 39–62.Google Scholar
Weltje, G.J., Prins, M.A., 2007. Genetically meaningful decomposition of grain-size distributions. Sedimentary Geology 202, 409–424.Google Scholar
Wu, J., Ma, L., Zeng, H., 2013. Water quantity and quality change of Ulungur Lake and its environmental effects. [In Chinese with English abstract.]. Journal of Nature Resources 28, 844–853.Google Scholar
Xu, R., Wunsch, D., 2005. Survey of clustering algorithms. IEEE Transactions on Neural Networks 16, 645–678.CrossRefGoogle ScholarPubMed
Yu, S., Colman, S.M., Li, L., 2015. BEMMA: a hierarchical Bayesian end-member modeling analysis of sediment grain-size distributions. Mathematical Geosciences, 1–19.Google Scholar
Zhang, X., Zhou, A., Zhang, C., Hao, S., Zhao, Y., An, C., 2016. High-resolution records of climate change in arid eastern central Asia during MIS 3 (51 600–25 300 cal a BP) from Wulungu Lake, north-western China. Journal of Quaternary Science 31, 577–586.Google Scholar
Zhou, D., Chen, H., Lou, Y., 1991. The logratio approach to the classification of modern sediments and sedimentary environments in northern South China Sea. Mathematical Geology 23, 157–165.Google Scholar
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