Skip to main content
Log in

Probabilistic forecasting of drought: a hidden Markov model aggregated with the RCP 8.5 precipitation projection

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

The creeping characteristics of drought make it possible to mitigate drought’s effects with accurate forecasting models. Drought forecasts are inevitably plagued by uncertainties, making it necessary to derive forecasts in a probabilistic framework. In this study, we proposed a new probabilistic scheme to forecast droughts that used a discrete-time finite state-space hidden Markov model (HMM) aggregated with the Representative Concentration Pathway 8.5 (RCP) precipitation projection (HMM-RCP). The standardized precipitation index (SPI) with a 3-month time scale was employed to represent the drought status over the selected stations in South Korea. The new scheme used a reversible jump Markov chain Monte Carlo algorithm for inference on the model parameters and performed an RCP precipitation projection transformed SPI (RCP-SPI) weight-corrected post-processing for the HMM-based drought forecasting to perform a probabilistic forecast of SPI at the 3-month time scale that considered uncertainties. The point forecasts which were derived as the HMM-RCP forecast mean values, as measured by forecasting skill scores, were much more accurate than those from conventional models and a climatology reference model at various lead times. We also used probabilistic forecast verification and found that the HMM-RCP provided a probabilistic forecast with satisfactory evaluation for different drought categories, even at long lead times. In a drought event analysis, the HMM-RCP accurately predicted about 71.19 % of drought events during the validation period and forecasted the mean duration with an error of less than 1.8 months and a mean severity error of <0.57. The results showed that the HMM-RCP had good potential in probabilistic drought forecasting.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Belayneh A, Adamowski J, Khalil B, Ozga-Zielinski B (2014) Long-term SPI drought forecasting in the Awash River Basin in Ethiopia using wavelet neural network and wavelet support vector regression models. J Hydrol 508(16):418–429

    Article  Google Scholar 

  • Bellone E, Hughes JP, Guttorp P (2000) A hidden Markov model for downscaling synoptic atmospheric patterns to precipitation amounts. Clim Res 15(1):1–12

    Article  Google Scholar 

  • Bordi I, Sutera A (2007) Drought monitoring and forecasting at large scale. In: Rossi G, Vega T, Bonaccorso B (eds) Methods and tools for drought analysis and management, vol 62. Springer, Berlin, pp 3–27

    Chapter  Google Scholar 

  • Bracken C, Rajagopalan B, Zagona E (2014) A hidden Markov model combined with climate indices for multidecadal streamflow simulation. Water Resour Res 50(10):7836–7846

    Article  Google Scholar 

  • Brémaud P (1999) Markov chains. Springer, New York

    Book  Google Scholar 

  • Cancelliere A, Mauro GD, Bonaccorso B, Rossi G (2007) Drought forecasting using the standardized precipitation index. Water Resour Manag 21(5):801–819

    Article  Google Scholar 

  • Chambers DW, Baglivvo JA, Ebel JE, Kafka AL (2012) Earthquake forecasting using hidden Markov models. Pure Appl Geophys 169(4):625–639

    Article  Google Scholar 

  • Chebud Y, Melesse A (2011) Operational prediction of groundwater fluctuation in south Florida using sequence based Markovian stochastic model. Water Resour Manag 25(9):2279–2294

    Article  Google Scholar 

  • Cutore P, Di Mauro G, Cancelliere A (2009) Forecasting Palmer Index using neural networks and climate indexes. J Hydrol Eng 14(6):588–595

    Article  Google Scholar 

  • Epstein ES (1969) A scoring system for probability forecasts of ranked categories. J Appl Meteorol 8(6):985–987

    Article  Google Scholar 

  • Gales MJF (1998) Maximum likelihood linear transformation for HMM-based speech recognition. Comput Speech Lang 12(2):75–98

    Article  Google Scholar 

  • Gelman A, Rubin DB (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4):457–511

    Article  Google Scholar 

  • Ghahramani Z (2001) An introduction to hidden Markov models and Bayesian networks. Int J Pattern Recogn 15(1):9–42

    Article  Google Scholar 

  • Green PJ (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82(4):711–732

    Article  Google Scholar 

  • Hassan MR, Nath B, Kirley M (2007) A fusion model of HMM, ANN and GA for stock market forecasting. Expert Syst Appl 33(1):171–180

    Article  Google Scholar 

  • Hokimoto T, Shimizu K (2014) A non-homogeneous hidden Markov model for predicting the distribution of sea surface elevation. J Appl Stat 41(2):294–319

    Article  Google Scholar 

  • Kharin VV, Zwiers FW (2003) On the ROC score of probability forecasts. J Clim 16(24):4145–4150

    Article  Google Scholar 

  • Kim TW, Valdés JB (2003) Nonlinear model for drought forecasting based on a conjunction of wavelet transforms and neural networks. J Hydrol Eng 8(6):319–328

    Article  Google Scholar 

  • Korner-Nievergelt F, Roth T, von Felten S, Guélat J, Almasi B, Korner-Nievergelt P (2015) Bayesian data analysis in ecology using linear models with R, BUGS, and Stan. Elsevier, London

    Google Scholar 

  • Lohani VK, Loganathan GV, Mostaghimi S (1998) Long-term analysis and short-term forecasting of dry spells by the Palmer Drought Severity Index. Nord Hydrol 29(1):21–40

    Google Scholar 

  • Mallya G, Tripathi S, Kirshner S, Govindaraju RS (2013) Probabilistic assessment of drought characteristics using hidden Markov model. J Hydrol Eng 18(7):834–845

    Article  Google Scholar 

  • McFarland JM, Hahn TTG, Mehta MR (2011) Explicit-duration hidden Markov model inference of up–down states from continuous signals. PLoS One 6(6):e21606

    Article  CAS  Google Scholar 

  • McKee TB, Doesken NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales. In: Proceedings of the 8th conference on applied climatology, American Meteorological Society, Boston

  • Mishra AK, Singh VP (2010) A review of drought concepts. J Hydrol 391(1–2):202–216

    Article  Google Scholar 

  • Mishra AK, Desai VR, Singh VP (2007) Drought forecasting using a hybrid stochastic and neural network model. J Hydrol Eng 12(6):626–638

    Article  Google Scholar 

  • Modarres R (2007) Streamflow drought time series forecasting. Stoch Environ Res Risk Assess 21(3):223–233

    Article  Google Scholar 

  • Moradkhani H (2015) Statistical-dynamical drought forecast within Bayesian networks and data assimilation: how to quantify drought recovery. Geophysical research abstracts, vol 17, EGU2015-2849

  • Olivier C, Eric M, Tobias R (2005) Inference in hidden Markov models (Springer series in statistics). Springer, Lund University, Lund

    Google Scholar 

  • Oscar MR, Ramon DU (2006) A flexible statistical method for detecting genomic copy-number changes using hidden Markov models with reversible jump MCMC. http://biostates.bepress.com/cobra/art9

  • Rabiner LR (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE 77(2):257–286

    Article  Google Scholar 

  • Robert CP, Rydén T, Titterington DM (2000) Bayesian inferences in hidden Markov models through the reversible jump Markov chain Monte Carlo method. J R Statist Soc B 62(1):57–75

    Article  Google Scholar 

  • Robertson AW, Moron V, Swarinoto Y (2009) Seasonal predictability of daily rainfall statistics over Indramayu district, Indonesia. Int J Climatol 29(10):1449–1462

    Article  Google Scholar 

  • Saidane M, Lavergne C (2009) Optimal prediction with conditionally heteroskedastic factor analysed hidden Markov models. Comput Econ 34(4):323–364

    Article  Google Scholar 

  • Schneider G, Fechner U (2004) Advances in the prediction of protein targeting signals. Proteomics 4(6):1571–1580

    Article  CAS  Google Scholar 

  • Stephen PB, Andrew G (1998) General methods for monitoring convergence of iterative simulations. J Comput Graph Stat 7(4):434–455

    Google Scholar 

  • Thyer M, Kuczera G (2003) A hidden Markov model for modeling long-term persistency in multi-site rainfall time series. 2. Real data analysis. J Hydrol 275(1–2):27–48

    Article  Google Scholar 

  • Trambauer P, Werner M, Winsemius HC, Maskey S, Dutra E, Uhlenbrook S (2015) Hydrological drought forecasting and skill assessment for the Limpopo River basin, southern Africa. Hydrol Earth Syst Sci 19(4):1695–1711

    Article  Google Scholar 

  • Verbist K, Robertson AW, Cornelis WM, Gabriels D (2010) Seasonal predictability of daily rainfall characteristics in central northern Chile for dry-land management. J Appl Meteor Climatol 49(9):1938–1955

    Article  Google Scholar 

  • Wilks DS (1995) Statistical methods in the atmospheric sciences an introduction. Academic, San Diego

    Google Scholar 

  • Zucchini W, Guttorp P (1991) A hidden Markov model for space-time precipitation. Water Resour Res 27(8):1917–1923

    Article  Google Scholar 

  • Zucchini W, MacDonald IL (2009) Hidden Markov models for time series: an introduction using R. CRC/Taylor & Francis, Boca Raton

    Book  Google Scholar 

Download references

Acknowledgments

This study was supported by a Grant (14AWMP-B082564-01) from the Water Management Research Program funded by Ministry of Land, Infrastructure and Transport, Republic of Korea.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tae-Woong Kim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, S., Shin, J.Y. & Kim, TW. Probabilistic forecasting of drought: a hidden Markov model aggregated with the RCP 8.5 precipitation projection. Stoch Environ Res Risk Assess 31, 1061–1076 (2017). https://doi.org/10.1007/s00477-016-1279-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-016-1279-6

Keywords

Navigation