Probabilistic Estimation of Multivariate Streamflow Using Independent Component Analysis and Climate Information

Seth Westra School of Civil and Environmental Engineering, University of New South Wales, Sydney, New South Wales, Australia

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Ashish Sharma School of Civil and Environmental Engineering, University of New South Wales, Sydney, New South Wales, Australia

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Abstract

A statistical estimation approach is presented and applied to multiple reservoir inflow series that form part of Sydney’s water supply system. The approach involves first identifying sources of interannual and interdecadal climate variability using a combination of correlation- and wavelet-based methods, then using this information to construct probabilistic, multivariate seasonal estimates using a method based on independent component analysis (ICA). The attraction of the ICA-based approach is that, by transforming the multivariate dataset into a set of independent time series, it is possible to maintain the parsimony of univariate statistical methods while ensuring that both the spatial and temporal dependencies are accurately captured.

Based on a correlation analysis of the reservoir inflows with the original sea surface temperature anomaly data, the principal sources of variability in Sydney’s reservoir inflows appears to be a combination of the El Niño–Southern Oscillation (ENSO) phenomenon and the Pacific decadal oscillation (PDO). A multivariate ICA-based estimation model was then used to capture this variability, and it was shown that this approach performed well in maintaining the temporal dependence while also accurately maintaining the spatial dependencies that exist in the 11-dimensional historical reservoir inflow dataset.

Corresponding author address: Seth Westra, Water Research Centre, School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia. Email: s.westra@unsw.edu.au

Abstract

A statistical estimation approach is presented and applied to multiple reservoir inflow series that form part of Sydney’s water supply system. The approach involves first identifying sources of interannual and interdecadal climate variability using a combination of correlation- and wavelet-based methods, then using this information to construct probabilistic, multivariate seasonal estimates using a method based on independent component analysis (ICA). The attraction of the ICA-based approach is that, by transforming the multivariate dataset into a set of independent time series, it is possible to maintain the parsimony of univariate statistical methods while ensuring that both the spatial and temporal dependencies are accurately captured.

Based on a correlation analysis of the reservoir inflows with the original sea surface temperature anomaly data, the principal sources of variability in Sydney’s reservoir inflows appears to be a combination of the El Niño–Southern Oscillation (ENSO) phenomenon and the Pacific decadal oscillation (PDO). A multivariate ICA-based estimation model was then used to capture this variability, and it was shown that this approach performed well in maintaining the temporal dependence while also accurately maintaining the spatial dependencies that exist in the 11-dimensional historical reservoir inflow dataset.

Corresponding author address: Seth Westra, Water Research Centre, School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia. Email: s.westra@unsw.edu.au

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  • Ashok, K., Guan Z. , and Yamagata T. , 2003: Influence of the Indian Ocean Dipole on the Australian winter rainfall. Geophys. Res. Lett., 30 , 1821. doi:10.1029/2003GL017926.

    • Search Google Scholar
    • Export Citation
  • Barros, A. P., and Bowden G. J. , 2008: Toward long-lead operational forecasts of drought: An experimental study in the Murray-Darling River Basin. J. Hydrol., 357 , 349367.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cai, W., Whetton P. H. , and Pittock A. B. , 2001: Fluctuations of the relationship between ENSO and northeast Australian rainfall. Climate Dyn., 17 , 421432.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chiew, F. H. S., and McMahon T. A. , 2002: Global ENSO-streamflow teleconnection, streamflow forecasting and interannual variability. Hydrol. Sci. J., 47 , 505522.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chiew, F. H. S., Piechota T. C. , Dracup J. A. , and McMahon T. A. , 1998: El Niño/Southern Oscillation and Australian rainfall, streamflow and drought: Links and potential for forecasting. J. Hydrol., 204 , 138149.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chiew, F. H. S., Zhou S. L. , and McMahon T. A. , 2003: Use of seasonal streamflow forecasts in water resources management. J. Hydrol., 270 , 135144.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Colman, A. W., and Davey M. K. , 2003: Statistical prediction of global sea-surface temperature anomalies. Int. J. Climatol., 23 , 16771697.

  • Cordery, I., and Opoku-Ankomah Y. , 1994: Temporal variation of relations between tropical sea-surface temperatures and New South Wales rainfall. Aust. Meteor. Mag., 43 , 7380.

    • Search Google Scholar
    • Export Citation
  • Cordery, I., and McCall M. , 2000: A model for forecasting drought from teleconnections. Water Resour. Res., 36 , 763768.

  • Drosdowsky, W., 1993: Potential predictability of winter rainfall over southern and eastern Australia using Indian Ocean sea-surface temperature anomalies. Aust. Meteor. Mag., 42 , 16.

    • Search Google Scholar
    • Export Citation
  • Drosdowsky, W., 2002: SST phases and Australian rainfall. Aust. Meteor. Mag., 51 , 112.

  • Drosdowsky, W., and Chambers L. E. , 2001: Near-global sea surface temperature anomalies as predictors of Australian seasonal rainfall. J. Climate, 14 , 16771687.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dutta, S. C., Ritchie J. W. , Freebairn D. M. , and Abawi G. Y. , 2006: Rainfall and streamflow response to El Niño Southern Oscillation: A case study in a semiarid catchment, Australia. Hydrol. Sci. J., 51 , 10061020.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Filho, F. A. S., and Lall U. , 2003: Seasonal to interannual ensemble streamflow forecasts for Ceara, Brazil: Applications of a multivariate, semiparametric algorithm. Water Resour. Res., 39 , 1307. doi:10.1029/2002WR001373.

    • Search Google Scholar
    • Export Citation
  • Goddard, L., Mason S. J. , Zebiak S. E. , Ropelewski C. F. , Basher R. , and Cane M. A. , 2001: Current approaches to seasonal-to-interannual climate predictions. Int. J. Climatol., 21 , 11111152.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hamlet, A. F., Huppert D. , and Lettenmaier D. P. , 2002: Economic value of long-lead streamflow forecasts for Columbia River hydropower. J. Water Resour. Plann. Manage., 128 , 91101.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hyvärinen, A., Karhunen J. , and Oja E. , 2001: Independent Component Analysis. John Wiley, 481 pp.

  • Jain, S., and Lall U. , 2001: Floods in a changing climate: Does the past represent the future? Water Resour. Res., 37 , 31933205.

  • Jevrejeva, S., Moore J. C. , and Grinsted A. , 2003: Influence of the Arctic Oscillation and El Niño-Southern Oscillation (ENSO) on ice conditions in the Baltic Sea: The wavelet approach. J. Geophys. Res., 108 , 4677. doi:10.1029/2003JD003417.

    • Search Google Scholar
    • Export Citation
  • Jevrejeva, S., Moore J. C. , and Grinsted A. , 2004: Oceanic and atmospheric transport of multiyear El Niño–Southern Oscillation (ENSO) signatures to the polar regions. Geophys. Res. Lett., 31 , L24210. doi:10.1029/2004GL020871.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaplan, A., Cane M. A. , Kushnir Y. , Clement A. C. , Blumenthal M. B. , and Rajagopalan B. , 1998: Analyses of global sea surface temperature 1856–1991. J. Geophys. Res., 103 , (C9). 1856718589.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kiem, A. S., Franks S. W. , and Kuczera G. , 2003: Multi-decadal variability of flood risk. Geophys. Res. Lett., 30 , 1035. doi:10.1029/2002GL015992.

    • Search Google Scholar
    • Export Citation
  • Lettenmaier, D. P., and Wood E. F. , 1993: Hydrologic forecasting. Handbook of Hydrology, D. R. Maidment, Ed., McGraw-Hill, 26.1–26.30.

    • Search Google Scholar
    • Export Citation
  • Mantua, N. J., and Hare S. R. , 2002: The Pacific decadal oscillation. J. Oceanogr., 58 , 3544.

  • Mantua, N. J., Hare S. R. , Zhang Y. , Wallace J. M. , and Francis R. C. , 1997: A Pacific interdecadal climate oscillation with impacts on salmon production. Bull. Amer. Meteor. Soc., 78 , 10691079.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nicholls, N., 1985: Towards the prediction of major Australian droughts. Aust. Meteor. Mag., 33 , 161166.

  • Nicholls, N., 1989: Sea surface temperatures and Australian winter rainfall. J. Climate, 2 , 965973.

  • Nicholls, N., Lavery B. , Frederiksen C. , Drosdowsky W. , and Torok S. , 1996: Recent apparent changes in relationships between the El Niño-Southern Oscillation and Australian rainfall and temperature. Geophys. Res. Lett., 23 , 33573360.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Piechota, T. C., Chiew F. H. S. , Dracup J. A. , and McMahon T. A. , 1998: Seasonal streamflow forecasting in eastern Australia and the El Niño–Southern Oscillation. Water Resour. Res., 34 , 30353044.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Piechota, T. C., Chiew F. H. S. , Dracup J. A. , and McMahon T. A. , 2001: Development of exceedance probability streamflow forecast. J. Hydrol. Eng., 6 , 2028.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pittock, A. B., 1975: Climatic change and the patterns of variation in Australian rainfall. Search, 6 , 498504.

  • Power, S., Tseitkin F. , Torok S. , Lavery B. , Dahni R. , and McAvaney B. , 1998: Australian temperature, Australian rainfall and the Southern Oscillation, 1910-1992: Coherent variability and recent change. Aust. Meteor. Mag., 47 , 85101.

    • Search Google Scholar
    • Export Citation
  • Power, S., Casey T. , Folland C. , Colman A. , and Mehta V. , 1999a: Inter-decadal modulation of the impact of ENSO on Australia. Climate Dyn., 15 , 319324.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Power, S., Tseitkin F. , Mehta V. , Torok S. , and Lavery B. , 1999b: Decadal climate variability in Australia during the twentieth century. Int. J. Climatol., 19 , 169184.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ropelewski, C. F., and Halpert M. S. , 1987: Global and regional scale precipitation patterns associated with the El Niño/Southern Oscillation. Mon. Wea. Rev., 115 , 16061626.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Saji, N. H., and Yamagata T. , 2003: Possible impacts of Indian Ocean Dipole mode events on global climate. Climate Res., 25 , 151169.

  • Saji, N. H., Goswami B. N. , Vinayachandran P. N. , and Yamagata T. , 1999: A dipole mode in the tropical Indian Ocean. Nature, 401 , 360363.

  • Sharma, A., 2000a: Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: Part 1—A strategy for system predictor identification. J. Hydrol., 239 , 232239.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sharma, A., 2000b: Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: Part 3—A nonparametric probabilistic forecast model. J. Hydrol., 239 , 249258.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sharma, A., Lall U. , and Tarboton D. G. , 1998: Kernel bandwidth selection for a first order nonparametric streamflow simulation model. Stochastic Hydrol. Hydraul., 12 , 3352.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sharma, A., Luk K. C. , Cordery I. , and Lall U. , 2000: Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: Part 2 — Predictor identification of quarterly rainfall using ocean-atmosphere information. J. Hydrol., 239 , 240248.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Torrence, C., and Compo G. P. , 1998: A practical guide to wavelet analysis. Bull. Amer. Meteor. Soc., 79 , 6178.

  • Trenberth, K. E., 1997: The definition of El Niño. Bull. Amer. Meteor. Soc., 78 , 27712777.

  • Van den Dool, H. M., Huang J. , and Fan Y. , 2003: Performance and analysis of the constructed analogue method applied to U.S. soil moisture over 1981–2001. J. Geophys. Res., 108 , 8617. doi:10.1029/2002JD003114.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Verdon, D. C., and Franks S. W. , 2005: Indian Ocean sea surface temperature variability and winter rainfall: Eastern Australia. Water Resour. Res., 41 , W09413. doi:10.1029/2004WR003845.

    • Search Google Scholar
    • Export Citation
  • Verdon, D. C., Wyatt A. M. , Kiem A. S. , and Franks S. W. , 2004: Multidecadal variability of rainfall and streamflow: Eastern Australia. Water Resour. Res., 40 , W10201. doi:10.1029/2004WR003234.

    • Search Google Scholar
    • Export Citation
  • Wang, B., and Wang Y. , 1996: Temporal structure of the Southern Oscillation as revealed by waveform and wavelet analysis. J. Climate, 9 , 15861598.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Westra, S., and Sharma A. , 2006: Dominant modes of interannual variability in Australian rainfall analyzed using wavelets. J. Geophys. Res., 111 , D05102. doi:10.1029/2005JD005996.

    • Search Google Scholar
    • Export Citation
  • Westra, S., Brown C. , Lall U. , and Sharma A. , 2007: Modeling multivariable hydrological series: Principal component analysis or independent component analysis? Water Resour. Res., 43 , W06429. doi:10.1029/2006WR005617.

    • Search Google Scholar
    • Export Citation
  • Westra, S., Sharma A. , Brown C. , and Lall U. , 2008: Multivariate streamflow forecasting using independent component analysis. Water Resour. Res., 44 , W02437. doi:10.1029/2007WR006104.

    • Search Google Scholar
    • Export Citation
  • Westra, S., Brown C. , Lall U. , Koch I. , and Sharma A. , 2009: Interpreting variability in global SST data using independent component analysis and principal component analysis. Int. J. Climatol., doi:10.1002/joc.1888, in press.

    • Search Google Scholar
    • Export Citation
  • White, W. B., Gershunov A. , Annis J. L. , McKeon G. , and Syktus J. , 2004: Forecasting Australian drought using Southern Hemisphere modes of sea-surface temperature variability. Int. J. Climatol., 24 , 19111927.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yao, H., and Georgakakos A. , 2001: Assessment of Folsom Lake response to historical and potential future climate scenarios: 2. Reservoir management. J. Hydrol., 249 , 176196.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, Y., Wallace J. M. , and Battisti D. S. , 1997: ENSO-like interdecadal variability: 1900–93. J. Climate, 10 , 10041020.

    • Crossref
    • Search Google Scholar
    • Export Citation
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