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Evaluation of Markov Chain Based Drought Forecasts in an Andean Regulated River Basin Using the Skill Scores RPS and GMSS

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On behalf of the decision-makers of Andean regulated river basins a drought index was developed to predict the occurrence and extent of drought events. Two stochastic models, the Markov Chain First Order (MCFO) and the Markov Chain Second Order (MCSO) model, predicting the frequency of monthly droughts were applied and the performance checked using two skill scores, respectively the ranked probability score (RPS) and the Gandin-Murphy skill score (GMSS). Data of the Chulco River basin (3200–4300 m.a.s.l.), situated in the Ecuadorian southern Andes, were employed to test the performance of both models. Results indicate that events with greater drought severity were more accurately predicted. The study also revealed the importance of verifying the quality of the forecasts and to have an assessment of the likely performance of the forecasting models before adopting any model and accepting the resulting information for decision-making.

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  1. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Contr 19:716–723. doi:10.1109/TAC.1974.1100705

  2. Banimahd SA, Khalili D (2013) Factors influencing markov chains predictability characteristics, utilizing SPI, RDI, EDI and SPEI drought indices in different climatic zones. Water Resour Manag 27:3911–3928. doi:10.1007/s11269-013-0387-z

  3. Barua S, Asce SM, Ng AWM, Perera BJC (2011) Comparative evaluation of drought indexes : case study on the Yarra River catchment in Australia. J Water Resour Plan Manag 137:215–226. doi:10.1061/(ASCE)WR.1943-5452.0000105

  4. Barua S, Ng A, Perera B (2012) Drought assessment and forecasting: a case study on the Yarra River catchment in Victoria, Australia. Aust J Water Resour 15:95–108. doi:10.7158/W10-848.2012.15.2

  5. Beniston M (2003) Climatic change in mountain regions: a review of possible impacts. Clim Chang 59:5–31

  6. Buytaert W, Célleri R, De Bièvre B et al (2006a) Human impact on the hydrology of the Andean páramos. Earth Sci Rev 79:53–72. doi:10.1016/j.earscirev.2006.06.002

  7. Buytaert W, Celleri R, Willems P (2006b) Spatial and temporal rainfall variability in mountainous areas: a case study from the south Ecuadorian Andes. J Hydrol 329:413–421. doi:10.1016/j.jhydrol.2006.02.031

  8. Cancelliere A, Di Mauro G, Bonaccorso B, Rossi G (2007) Drought forecasting using the Standardized Precipitation Index. Water Resour Manag 21:801–819. doi:10.1007/s11269-006-9062-y

  9. Celleri R, Willems P, Buytaert W, Feyen J (2007) Space – time rainfall variability in the Paute Basin, Ecuadorian Andes. Hydrol Process 21:3316–3327. doi:10.1002/hyp.6575

  10. Gandin LS, Murphy AH (1992) Equitable Skills scores for categorical forecast. Mon Weather Rev 120:361–370

  11. Gerrity JP (1992) A note on Gandin and Murphy’s Equitable Skill Scores. Mon Weather Rev 120:2709–2712

  12. Keyantash JA, Dracup JA (2004) An aggregate drought index: assessing drought severity based on fluctuations in the hydrologic cycle and surface water storage. Water Resour Res 40:1–13. doi:10.1029/2003WR002610

  13. Khalili D, Farnoud T, Jamshidi H et al (2011) Comparability analyses of the SPI and RDI meteorological drought indices in different climatic zones. Water Resour Manag 25:1737–1757. doi:10.1007/s11269-010-9772-z

  14. Labadie JW, Asce M (2004) Optimal operation of multireservoir systems : state-of-the-art review. J Water Resour Plan Manag 130:93–111. doi:10.1061/(ASCE)0733-9496(2004)130:2~93!

  15. Lee S-E, Seo K-H (2013) The development of a statistical forecast model for changma. Weather Forecast 28:1304–1321. doi:10.1175/WAF-D-13-00003.1

  16. Liu Y, Gupta H, Springer E, Wagener T (2008) Linking science with environmental decision making: experiences from an integrated modeling approach to supporting sustainable water resources management. Environ Model Softw 23:846–858. doi:10.1016/j.envsoft.2007.10.007

  17. Lohani VK, Loganathan GV (1997) An early warning system for drought management using the Palmer drought index. J Am Water Resour Assoc 33:1375–1386

  18. Mason SJ (2004) On using “Climatology” as a reference strategy in the brier and ranked probability skill scores. Mon Weather Rev 132:1891–1895

  19. Mauget S, Ko J (2008) A two-tier statistical forecast method for agricultural and resource management simulations. J Appl Meteorol Climatol 47:1573–1589. doi:10.1175/2007JAMC1749.1

  20. McKee TB, Doesken NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales. Proc. 8th Conf. Appl. Climatol. American Meteorological Society Boston, MA, pp 179–183

  21. Mishra a K, Desai VR (2005) Drought forecasting using stochastic models. Stoch Environ Res Risk Assess 19:326–339. doi:10.1007/s00477-005-0238-4

  22. Mishra AK, Singh VP (2010) Review paper A review of drought concepts. J Hydrol 391:202–216. doi:10.1016/j.jhydrol.2010.07.012

  23. Mishra AK, Desai VR, Singh VP, Asce F (2007) Drought forecasting using a hybrid stochastic and neural network model. J Hydrol Eng 12:626–638. doi:10.1061/(ASCE)1084-0699(2007)12:6(626)

  24. Moreira EE, Coelho C, Paulo A a et al (2008) SPI-based drought category prediction using loglinear models. J Hydrol 354:116–130. doi:10.1016/j.jhydrol.2008.03.002

  25. Muller WA, Appenzeller C, Doblas-Reyes FJ, Liniger MA (2005) A debiased ranked probability skill score to evaluate probabilistic ensemble forecasts with small ensemble sizes. J Clim 18:1513–1523. doi:10.1175/JCLI3361.1

  26. Murphy A (1971) A note on the ranked probability score. J Appl Meteorol 10:155–156

  27. Murphy AH (1977) The value of climatological, categorical and probabilistic forecasts in the cost-loss ratio situation. Mon Weather Rev 105:803–816. doi:10.1175/1520-0493(1977)105<0803:TVOCCA>2.0.CO;2

  28. Nalbantis I, Tsakiris G (2009) Assessment of hydrological drought revisited. Water Resour Manag 23:881–897. doi:10.1007/s11269-008-9305-1

  29. Palmer W (1965) Meteorological drought. Paper 45:65

  30. Panu US, Sharma TC (2002) Challenges in drought research: some perspectives and future directions. Hydrol Sci J 47:S19–S30. doi:10.1080/02626660209493019

  31. Paulo A, Pereira LS (2007) Prediction of SPI drought class transitions using Markov chains. Water Resour Manag 21:1813–1827. doi:10.1007/s11269-006-9129-9

  32. Ries H, Schlünzen KH, Brümmer B et al (2010) Impact of surface parameter uncertainties on the development of a trough in the Fram Strait region. Tellus A 62:377–392. doi:10.1111/j.1600-0870.2010.00451.x

  33. Robertson DE, Wang QJ (2013) Seasonal forecasts of unregulated inflows into the Murray River, Australia. Water Resour Manag 27:2747–2769. doi:10.1007/s11269-013-0313-4

  34. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464

  35. Shukla S, Wood AW (2008) Use of a standardized runoff index for characterizing hydrologic drought. Geophys Res Lett 35:1–7. doi:10.1029/2007GL032487

  36. Steinemann A (2003) Drought indicators and triggers: a stochastic approach to evaluation. J Am Water Resour Assoc 39:1217–1233

  37. Steinemann AC, Cavalcanti LF (2006) Developing multiple indicators and triggers for drought plans. J Water Resour Plan Manag 132:164–174. doi:10.1061/(ASCE)0733-9496(2006)132:3(164)

  38. Svoboda M, Hayes M, Wilhite D, Tadesse T (2004) Recent advances in drought monitoring. Drought Mitig Cent Fac Publ 6

  39. Tsakiris G, Vangelis H (2005) Establishing a drought index incorporating evapotranspiration. Eur Water 9:3–11

  40. Vicente-Serrano SM, Beguería S, López-Moreno JI (2010) A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. J Clim 23:1696–1718. doi:10.1175/2009JCLI2909.1

  41. Viviroli D, Archer DR, Buytaert W et al (2011) Climate change and mountain water resources: overview and recommendations for research, management and policy. Hydrol Earth Syst Sci 15:471–504. doi:10.5194/hess-15-471-2011

  42. Westphal KS, Laramie RL, Borgatti D, Stoops R (2007) Drought Management Planning with Economic and Risk Factors. J Water Resour Plan Manag 133:351–362. doi:10.1061/(ASCE)0733-9496(2007)133:4(351)

  43. Wilks DS (2011) Statistical methods in the atmospheric sciences. Third Edit. 704

  44. Zhang H, Casey T (2000) Verification of categorical probability forecasts. Weather Forecast 15:80–89

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The research was conducted within the frame of the projects “Meteorological Cycles and Evapotranspiration along the Altitudinal Gradient of the Cajas National Park” and “Identification of hydro-meteorological processes that trigger extreme floods in the city of Cuenca using precipitation radar”. Both projects were funded by the University of Cuenca and the Public Municipal Company of Water Supply from Cuenca (ETAPA). Thanks are due to INAMHI and CBRM for providing the information of the Chulco river basin.

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Correspondence to Alex Avilés.

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Avilés, A., Célleri, R., Paredes, J. et al. Evaluation of Markov Chain Based Drought Forecasts in an Andean Regulated River Basin Using the Skill Scores RPS and GMSS. Water Resour Manage 29, 1949–1963 (2015). https://doi.org/10.1007/s11269-015-0921-2

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  • Drought index
  • Probabilistic forecast
  • Markov Chains
  • Forecast evaluation
  • Andean basins