Skip to main content
SpringerLink
Log in

Statistical and Optimization Techniques in Climate Modeling

  • Chapter
  • First Online:
Impact of Climate Change on Water Resources

Part of the book series: Springer Climate ((SPCL))

  • 1172 Accesses

Abstract

This chapter presents data compression techniques, namely, cluster and fuzzy cluster analysis, Kohonen neural networks for clustering GCMs and principal component analysis for transforming a set of observations of possible correlation into a set of linearly uncorrelated variables applying an orthogonal transformation. F--statistic test which can be used as the basis for finding optimal clusters is also discussed. Trend detection techniques, namely, Kendall’s rank correlation and turning point test along with mathematical background are also briefed with the objective to ascertain the quality of the hydrological or climatological records. In addition, optimization techniques, namely, linear and non-linear programming and genetic algorithms along with mathematical description are also discussed. The reader is expected to understand various statistical and optimization techniques along with their applicability by studying this chapter.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Bashiri-Atrabi H, Qaderi K, Rheinheimer DE, Sharifi E (2015) Application of harmony search algorithm to reservoir operation optimization. Water Resour Manage 29:5729–5748

    Article  Google Scholar 

  • Bezdek J (1981) Pattern recognition with fuzzy objective function algorithms. Plenum, New York

    Google Scholar 

  • Burn DH (1989) Cluster analysis as applied to regional flood frequency. J Water Resour Plann Manag 115:567–582

    Article  Google Scholar 

  • Das S, Mullick SS, Suganthan PN (2016) Recent advances in differential evolution—an updated survey. Swarm Evol Comput 27:1–30

    Article  Google Scholar 

  • Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Anal Mach Intell 1(4):224–227

    Article  Google Scholar 

  • Deb K, Agarwal RB (1995) Simulated binary crossover for continuous search space. Complex Syst 9:115–148

    MathSciNet  MATH  Google Scholar 

  • Deb K (1999) An introduction to genetic algorithms. Sadhana 24(4):293–315

    Article  MathSciNet  MATH  Google Scholar 

  • Deb K (2002) Multi-objective optimization using evolutionary algorithms, 1st edn. Wiley

    Google Scholar 

  • Dunn JC (1974) Well separated clusters and optimal fuzzy partitions. J Cybern 4:95–104

    Article  MathSciNet  MATH  Google Scholar 

  • Garousi-Nejad I, Bozorg-Haddad O, Loáiciga HA, Marino MA (2016) Application of the firefly algorithm to optimal operation of reservoirs with the purpose of irrigation supply and hydropower production. J Irrig Drain Eng 142(10):04016041-1–04016041-12. doi:10.1061/(ASCE)IR.1943-4774.0001064

  • Genetic Algorithm (2017) https://in.mathworks.com/help/gads/genetic-algorithm.html. Accessed on 31 Jan 2017

  • Goldberg DE (1989) Genetic algorithms in search. Optimization and Machine Learning, Addison-Wesley, New York

    MATH  Google Scholar 

  • Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice-Hall, Englewood Cliffs, New Jersey

    MATH  Google Scholar 

  • Jain SK, Singh VP (2003) Water resources systems planning and management. Elsevier B.V, The Netherlands

    Google Scholar 

  • Kendall MG (1975) Rank correlation methods. Charless Griffin, London

    MATH  Google Scholar 

  • Khare A, Rangnekar S (2013) A review of particle swarm optimization and its applications I in solar photovoltaic system. Appl Soft Comput 13:2997–3006

    Article  Google Scholar 

  • Kohonen T (1989) Self organization and associative memory. Springer, Berlin

    Book  MATH  Google Scholar 

  • Loucks DP, Stedinger JR, Haith DA (1981) Water resources systems planning and analysis. Prentice–Hall, NJ

    Google Scholar 

  • Mann HB (1945) Nonparametric tests against trend. Econometrica 13:245–259

    Article  MathSciNet  MATH  Google Scholar 

  • Mujumdar PP, Nagesh Kumar D (2012) Floods in a changing climate: hydrologic modeling. Cambridge University Press, International Hydrology Series

    Book  Google Scholar 

  • Nagesh Kumar D (2017) Optimization methods. http://nptel.ac.in/syllabus/105108127/. Accessed on 31 Jan 2017

  • Patra KC (2010) Hydrology and water resources engineering. Narosa Publishing House

    Google Scholar 

  • Price K, Storn R, Lampinen J (2005) Differential evolution—a practical approach to global optimization. Springer, Germany

    MATH  Google Scholar 

  • Raju KS, Nagesh Kumar D (2014) Multicriterion analysis in engineering and management. Prentice Hall of India, New Delhi

    Google Scholar 

  • Rao SS (2003) Engineering optimization: theory and practice. New Age International (P) Limited, New Delhi

    Google Scholar 

  • Raschka (2015) Implementing a principal component analysis (PCA) in Python step by step http://sebastianraschka.com/Articles/2014_pca_step_by_step.html. Accessed on 31 Jan 2017

  • Ravindran A, Phillips DT, Solberg JJ (2001) Operations research—principles and practice. Wiley, New York

    MATH  Google Scholar 

  • Ross TJ (2011) Fuzzy logic with engineering applications. Wiley

    Google Scholar 

  • Sonali P, Nagesh Kumar D (2013) Review of trend detection methods and their application to detect temperature changes in India. J Hydrol 476:212–227

    Article  Google Scholar 

  • Taha HA (2005) Operations research—an introduction. Prentice-Hall of India Pvt. Ltd., New Delhi

    Google Scholar 

  • The Climate Data Guide: Empirical Orthogonal Function (EOF) Analysis and Rotated EOF Analysis (2017). https://climatedataguide.ucar.edu/climate-data-tools-and-analysis/empirical-orthogonal-function-eof-analysis-and-rotated-eof-analysis#sthash.RBGslgxN.dpuf. Accessed on 31 Jan 2017

  • Vedula S, Mujumdar PP (2005) Water resources systems: modelling techniques and analysis. Tata McGraw Hill, New Delhi

    Google Scholar 

  • Yang XS (2010) Nature-inspired metaheuristic algorithms. Lunvier Press, United Kingdom

    Google Scholar 

  • Yegnanarayana B (1998) Artificial neural networks. Prentice Hall of India, New Delhi

    Google Scholar 

Suggested Further Reading

  • Hamed KH, Rao AR (1998) A modified Mann-Kendall trend test for auto correlated data. J Hydrol 204:219–246

    Article  Google Scholar 

  • Haan CT (1977) Statistical methods in hydrology. Iowa State University Press, Ames, Iowa, p 378

    Google Scholar 

  • Hastie T, Tibshirani R (2011) The elements of statistical learning: data mining, inference, and prediction. Springer Series in Statistics

    Google Scholar 

  • Helsel DR, Hirsch RM (2002) Statistical methods in water resources techniques of water resources investigations, book 4, chapter A3, US geological survey, pp 522

    Google Scholar 

  • Khaliq MN, Ouarda TBMJ, Gachon P, Sushama L, St.-Hilaire A (2009) Identification of hydrologic trends in the presence of serial and cross correlations. A review of selected methods and their application to annual flow regimes of Canadian rivers. J Hydrol 368:117–130

    Article  Google Scholar 

  • Lettenmaier DP (1976) Detection of trend in water quality data from record with dependent observations. Water Resour Res 12:1037–1046

    Article  Google Scholar 

  • Milton JS, Arnold JC (2007) Introduction to probability and statistics. Tata McGraw-Hill

    Google Scholar 

  • North GR, Bell TL, Cahalan RF, Moeng FJ (1982) Sampling errors in the estimation of empirical orthogonal functions. Mon Weather Rev 110:699–706

    Article  Google Scholar 

  • Shrestha S, Anal AK, Salam PA, van der Valk M (eds) (2015) Managing water resources under climate uncertainty: examples from Asia, Europe, Latin America, and Australia. Springer Water, pp 438

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Birla Institute of Technology and Science-Pilani, Hyderabad, Telangana, India

    Komaragiri Srinivasa Raju

  2. Department of Civil Engineering, Centre for Earth Sciences, Divecha Centre for Climate Change, Interdisciplinary Centre for Water Research, Indian Institute of Science, Bangalore, Karnataka, India

    Dasika Nagesh Kumar

Authors
  1. Komaragiri Srinivasa Raju
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dasika Nagesh Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Komaragiri Srinivasa Raju .

4.1 Electronic Supplementary Material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PPT 949 kb)

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Srinivasa Raju, K., Nagesh Kumar, D. (2018). Statistical and Optimization Techniques in Climate Modeling. In: Impact of Climate Change on Water Resources . Springer Climate. Springer, Singapore. https://doi.org/10.1007/978-981-10-6110-3_4

Download citation

Publish with us

Policies and ethics

Search

Navigation