• Akaike, H., 1974: A new look at the statistical model identification. IEEE Trans. Autom. Control, 19, 716723, doi:10.1109/TAC.1974.1100705.

    • Search Google Scholar
    • Export Citation
  • Anderson, T. W., 1962: On the distribution of the two-sample Cramer–von Mises criterion. Ann. Math. Stat., 33, 11481159, doi:10.1214/aoms/1177704477.

    • Search Google Scholar
    • Export Citation
  • Andreadis, K. M., and Lettenmaier D. P. , 2006: Trends in 20th century over the continental United States. Geophys. Res. Lett., 33, L10403, doi:10.1029/2006GL025711.

    • Search Google Scholar
    • Export Citation
  • Bárdossy, A., 2006: Copula-based geostatistical models for groundwater quality parameters. Water Resour. Res., 42, W11416, doi:10.1029/2005WR004754.

    • Search Google Scholar
    • Export Citation
  • Bárdossy, A., and Li J. , 2008: Geostatistical interpolation using copulas. Water Resour. Res., 44, W07412, doi:10.1029/2007WR006115.

  • 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, doi:10.1016/j.jhydrol.2008.05.026.

    • Search Google Scholar
    • Export Citation
  • Blenkinsop, S., and Fowler H. J. , 2007: Changes in drought frequency, severity and duration for the British Isles projected by the PRUDENCE regional climate models. J. Hydrol., 342 (1–2), 5071, doi:10.1016/j.jhydrol.2007.05.003.

    • Search Google Scholar
    • Export Citation
  • Brown, J. D., and Seo D. J. , 2010: A nonparametric postprocessor for bias correction of hydrometeorological and hydrologic ensemble forecasts. J. Hydrometeor., 11, 642665.

    • Search Google Scholar
    • Export Citation
  • Burke, E. J., Perry R. H. J. , and Brown S. J. , 2010: An extreme value analysis of UK drought and projections of change in the future. J. Hydrol., 388, 131143, doi:10.1016/j.jhydrol.2010.04.035.

    • Search Google Scholar
    • Export Citation
  • Cancelliere, A., Mauro G. D. , Bonaccorso B. , and Rossi G. , 2007: Drought forecasting using the standardized precipitation index. Water Resour. Manag., 21, 801819.

    • Search Google Scholar
    • Export Citation
  • Carbone, G. J., and Dow K. , 2005: Water resource management and drought forecasts in South Carolina. J. Amer. Water Resour. Assoc., 41, 145155, doi:10.1111/j.1752-1688.2005.tb03724.x.

    • Search Google Scholar
    • Export Citation
  • Day, G. N., 1985: Extended streamflow forecasting using NWSRFS. J. Water Resour. Plan. Manage., 111 (2), 157170, doi:10.1061/(ASCE)0733-9496(1985)111:2(157).

    • Search Google Scholar
    • Export Citation
  • DeChant, C., and Moradkhani H. , 2011: Improving the characterization of initial condition for ensemble streamflow prediction using data assimilation. Hydrol. Earth Syst. Sci., 15, 33993410, doi:10.5194/hess-15-3399-2011.

    • Search Google Scholar
    • Export Citation
  • DeChant, C., and Moradkhani H. , 2012: Examining the effectiveness and robustness of data assimilation methods for calibration and quantification of uncertainty in hydrologic forecasting. Water Resour. Res., 48, W04518, doi:10.1029/2011WR011011.

    • Search Google Scholar
    • Export Citation
  • Dupuis, D. J., 2007: Using copulas in hydrology: Benefits, cautions, and issues. J. Hydrol. Eng., 12, 381393, doi:10.1061/(ASCE)1084-0699(2007)12:4(381).

    • Search Google Scholar
    • Export Citation
  • Embrechts, P., Lindskog F. , and McNeil A. J. , 2003: Modelling dependence with copulas and applications to risk management. Handbook of Heavy Tailed Distributions in Finance, S. T. Rachev, Ed., Elsevier Science, 329–384.

  • Favre, A. C., Adlouni S. E. , Perreault L. , Thiéonge N. , and Bobée B. , 2004: Multivariate hydrological frequency analysis using copulas. Water Resour. Res., 40, W01101, doi:10.1029/2003WR002456.

    • Search Google Scholar
    • Export Citation
  • Genest, C., and Rémillard B. , 2008: Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models. Annal. Inst. Henri-Poincaré, 44, 10961127.

    • Search Google Scholar
    • Export Citation
  • Genest, C., Rémillard B. , and Beaudoin D. , 2009: Goodness-of-fit tests for copulas: A review and a power study. Insur. Math. Econ., 44, 199213, doi:10.1016/j.insmatheco.2007.10.005.

    • Search Google Scholar
    • Export Citation
  • Ghosh, S., and Mujumdar P. P. , 2007: Nonparametric methods for modeling GCM and scenario uncertainty in drought assessment. Water Resour. Res., 43, W07405, doi:10.1029/2006WR005351.

    • Search Google Scholar
    • Export Citation
  • Halmstad, A., Najafi M. R. , and Moradkhani H. , 2012: Analysis of precipitation extremes with the assessment of regional climate models over the Willamette River Basin, USA. Hydrol. Processes,27, 2579–2590, doi:10.1002/hyp.9376.

  • Huang, W. C., and Chou C. C. , 2005: Drought early warning system in reservoir operation: Theory and practice. Water Resour. Res., 41, W11406, doi:10.1029/2004WR003830.

    • Search Google Scholar
    • Export Citation
  • Huang, W. C., and Chou C. C. , 2008: Risk-based drought early warning system in reservoir operation. Adv. Water Resour., 31, 649660, doi:10.1016/j.advwatres.2007.12.004.

    • Search Google Scholar
    • Export Citation
  • Hwang, Y., and Carbone G. J. , 2009: Ensemble forecasts of drought indices using a conditional residual resampling technique. J. Appl. Meteor. Climatol., 48, 12891301, doi:10.1175/2009JAMC2071.1.

    • Search Google Scholar
    • Export Citation
  • Jaeger, W. K., and Coauthors, 2013: Toward a formal definition of water scarcity in natural-human systems. Water Resour. Res., 49, 4506–4517, doi:10.1002/wrcr.20249.

    • Search Google Scholar
    • Export Citation
  • Joe, H., 1997: Multivariate Models and Dependence Concepts. Chapman & Hall, 399 pp.

  • Kao, S., and Govindaraju R. S. , 2008: Trivariate statistical analysis of extreme rainfall events via Plackett family of copulas. Water Resour. Res., 44, W02415, doi:10.1029/2007WR006261.

    • Search Google Scholar
    • Export Citation
  • Kao, S., and Govindaraju R. S. , 2010: A copula-based joint deficit index for droughts. J. Hydrol., 380, 121134, doi:10.1016/j.jhydrol.2009.10.029.

    • Search Google Scholar
    • Export Citation
  • Karl, T., Quinlan F. , and Ezell D. S. , 1987: Drought termination and amelioration: Its climatological probability. J. Climate Appl. Meteor., 26, 11981209, doi:10.1175/1520-0450(1987)026<1198:DTAAIC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kendall, J. R., and Dracup D. A. , 1992: On the generation of drought events using an alternating renewal-reward model. Stochastic Hydrol. Hydraul., 6, 5568, doi:10.1007/BF01581675.

    • Search Google Scholar
    • Export Citation
  • Kolmogorov, A. N., 1933: Sulla Determinazione Empirca di una Legge di Distribuzione, Giornale dell’. Istituto Italiano degli Attuari, 4, 8391.

    • Search Google Scholar
    • Export Citation
  • Leavesley, G. H., Lichty R. W. , Troutman B. M. , and Saindon L. G. , 1983: Precipitation-runoff modeling system: User’s manual. U.S. Geological Survey Water-Resources Investigations Rep. 83-4238, 207 pp.

  • Li., C., Singh V. P. , and Mishra A. K. , 2013: Monthly river flow simulation with a joint conditional density estimation network. Water Resour. Res.,49, 3229–3242, doi:10.1002/wrcr.20146.

  • Liu, W. T., and Kogan F. N. , 1996: Monitoring regional drought using the vegetation condition index. Int. J. Remote Sens., 17, 27612782, doi:10.1080/01431169608949106.

    • Search Google Scholar
    • Export Citation
  • Loaiciga, H. A., and Leipnik R. B. , 1996: Stochastic renewal model of low-flow streamflow sequences. Stochastic Hydrol. Hydraul., 10, 6585, doi:10.1007/BF01581794.

    • Search Google Scholar
    • Export Citation
  • Lohani, V. K., and Loganathan G. V. , 1997: An early warning system for drought management using the palmer drought index. J. Amer. Water Resour. Assoc., 33, 13751386, doi:10.1111/j.1752-1688.1997.tb03560.x.

    • Search Google Scholar
    • Export Citation
  • Lott, N., and Ross T. , 2000: A climatology of recent extreme weather and climate events. NCDC Tech. Rep. 2000-02, 17 pp.

  • Lott, N., and Ross T. , 2006: Tracking and evaluating U.S. billion dollar weather disasters, 1980–2005. Extended Abstracts, AMS Forum: Environmental Risk and Impacts on Society: Successes and Challenges, Atlanta, GA, Amer. Meteor. Soc., 1.2. [Available online at https://ams.confex.com/ams/Annual2006/techprogram/paper_100686.htm.]

  • Madadgar, S., and Moradkhani H. , 2011: Drought analysis under climate change using copula. J. Hydrol. Eng., 18 (7), 746–759, doi:10.1061/(ASCE)HE.1943-5584.0000532.

    • Search Google Scholar
    • Export Citation
  • Madadgar, S., Moradkhani, H., and Garen D. , 2013: Towards improved post-processing of hydrologic forecast ensembles. Hydrol. Processes,doi:10.1002/hyp.9562, in press.

  • Massey, F. J., 1951: The Kolmogorov-Smirnov test for goodness of fit. Amer. Stat. Assoc., 46 (253), 6878, doi:10.1080/01621459.1951.10500769.

    • Search Google Scholar
    • Export Citation
  • McKee, T. B., Doesken N. J. , and Kleist J. , 1993: The relationship of drought frequency and duration to time scales. Preprints, Eighth Conf. on Applied Climatology, Anaheim, CA, Amer. Meteor. Soc., 179–184.

  • Mishra, A. K., and Desai V. R. , 2005: Drought forecasting using stochastic models. Stochastic Environ. Res. Risk Assess., 19 (5), 326339, doi:10.1007/s00477-005-0238-4.

    • Search Google Scholar
    • Export Citation
  • Mishra, A. K., and Desai V. R. , 2006: Drought forecasting using feed-forward recursive neural network. Ecol. Modell., 198, 127138, doi:10.1016/j.ecolmodel.2006.04.017.

    • Search Google Scholar
    • Export Citation
  • Mishra, A. K., and Singh V. P. , 2010: A review of drought concepts. J. Hydrol., 391, 202216, doi:10.1016/j.jhydrol.2010.07.012.

  • Moradkhani, H., and Meier M. , 2010: Long-lead water supply forecast using large-scale climate predictors and independent component Analysis. J. Hydrol. Eng., 15, 744762.

    • Search Google Scholar
    • Export Citation
  • Moradkhani, H., Baird R. G. , and Wherry S. , 2010: Assessment of climate change impact on floodplain and hydrologic ecotones. J. Hydrol., 395, 264278, doi:10.1016/j.jhydrol.2010.10.038.

    • Search Google Scholar
    • Export Citation
  • Moradkhani, H., DeChant C. M. , and Sorooshian S. , 2012: Evolution of ensemble data assimilation for uncertainty quantification using the particle filter–Markov Chain Monte Carlo method. Water Resour. Res., 48, W12520, doi:10.1029/2012WR012144.

    • Search Google Scholar
    • Export Citation
  • Najafi, M. R., Moradkhani H. , and Piechota T. , 2012: Ensemble streamflow prediction: Climate signal weighting vs. climate forecast system reanalysis. J. Hydrol., 442–443, 105116, doi:10.1016/j.jhydrol.2012.04.003.

    • Search Google Scholar
    • Export Citation
  • Nelsen, R. B., 1999: An Introduction to Copulas. Springer, 216 pp.

  • Niemeyer, S., 2008: New drought indices. Proc. First Int. Conf. on Drought Management: Scientific and Technological Innovations, Zaragoza, Spain, CIHEAM, 267–274.

  • Özger, M., Mishra A. K. , and Singh V. P. , 2012: Long lead time drought forecasting using a wavelet and fuzzy logic combination model: A case study in Texas. J. Hydrometeor., 13, 284297, doi:10.1175/JHM-D-10-05007.1.

    • Search Google Scholar
    • Export Citation
  • Palmer, W. C., 1965: Meteorologic drought. U.S. Department of Commerce, Weather Bureau, Research Paper 45, 58 pp.

  • Palmer, W. C., 1968: Keeping track of crop moisture conditions, nationwide: The new crop moisture index. Weatherwise, 21, 156161, doi:10.1080/00431672.1968.9932814.

    • Search Google Scholar
    • Export Citation
  • Parrish, M., Moradkhani H. , and DeChant C. M. , 2012: Towards reduction of model uncertainty: Integration of Bayesian model averaging and data assimilation. Water Resour. Res., 48, W03519, doi:10.1029/2011WR011116.

    • Search Google Scholar
    • Export Citation
  • Risley, J., Moradkhani H. , Hay L. , and Markstrom S. , 2011: Statistical comparisons of watershed-scale response to climate change in selected basins across the United States. Earth Interact., 15, 126, doi:10.1175/2010EI364.1.

    • Search Google Scholar
    • Export Citation
  • Russell, S. J., and Peter N. , 2009: Artificial Intelligence: A Modern Approach. 3rd ed. Prentice Hall, 1152 pp.

  • Salvadori, G., and De Michele C. , 2006: Statistical characterization of temporal structure of storms. Adv. Water Resour., 29, 827842, doi:10.1016/j.advwatres.2005.07.013.

    • Search Google Scholar
    • Export Citation
  • Salvadori, G., and De Michele C. , 2010: Multivariate multiparameter extreme value models and return periods: A copula approach. Water Resour. Res., 46, W10501, doi:10.1029/2009WR009040.

    • Search Google Scholar
    • Export Citation
  • Schaake, J. C., and Coauthors, 2007: Precipitation and temperature ensemble forecasts from single-value forecasts. Hydrol. Earth Syst. Sci. Discuss., 4, 655717.

    • Search Google Scholar
    • Export Citation
  • Shafer, B. A., and Dezman L. E. , 1982: Development of a Surface Water Supply Index (SWSI) to assess the severity of drought conditions in snowpack runoff areas. Preprints, 50th Annual Western Snow Conf., Reno, NV, Colorado State University, 164–175.

  • Sheffield, J., and Wood E. F. , 2007: Characteristics of global and regional drought, 1950–2000: Analysis of soil moisture data from off-line simulation of the terrestrial hydrologic cycle. J. Geophys. Res., 112, D17115, doi:10.1029/2006JD008288.

    • Search Google Scholar
    • Export Citation
  • Sheffield, J., and Wood E. F. , 2008: Projected changes in drought occurrence under future global warming from multi-model, multi-scenario, IPCC AR4 simulations. Climate Dyn., 31, 79105, doi:10.1007/s00382-007-0340-z.

    • Search Google Scholar
    • Export Citation
  • Shiau, J. T., 2006: Fitting drought duration and severity with two-dimensional copulas. Water Resour. Manage., 20, 795815, doi:10.1007/s11269-005-9008-9.

    • Search Google Scholar
    • Export Citation
  • Showstack, R., 2012: Drought research and monitoring program is focus of congressional hearing. Eos, Trans. Amer. Geophys. Union, 93 (32), 310, doi:10.1029/2012EO320002.

    • Search Google Scholar
    • Export Citation
  • Shukla, S., Steinemann A. C. , and Lettenmaier D. P. , 2011: Drought monitoring for Washington State: Indicators and applications. J. Hydrometeor., 12, 6683, doi:10.1175/2010JHM1307.1.

    • Search Google Scholar
    • Export Citation
  • Sklar, K., 1959: Fonctions de repartition à n Dimensions et Leura Marges. Publ. Inst. Stat. Univ. Paris,8, 229–231.

  • Steinemann, A., 2003: Drought indicators and triggers: A stochastic approach to evaluation. J. Amer. Water Resour. Assoc., 39, 12171233, doi:10.1111/j.1752-1688.2003.tb03704.x.

    • Search Google Scholar
    • Export Citation
  • Steinemann, A., 2006: Using climate forecasts for drought management. J. Appl. Meteor. Climatol., 45, 13531361, doi:10.1175/JAM2401.1.

    • Search Google Scholar
    • Export Citation
  • Thulasiraman, K., and Swamy M. N. S. , 1992: Graphs: Theory and Algorithms. John Wiley and Son, 460 pp.

  • Twedt, T. M., Schaake J. C. , and Peck E. L. , 1977: National Weather Service extended streamflow prediction. Proc. 45th Western Snow Conf., Albuquerque, NM, 52–57.

  • van Huijgevoort, M. H. J., Hazenberg P. , van Lanen H. A. J. , and Uijlenhoet R. , 2012: A generic method for hydrological drought identification across different climate regions. Hydrol. Earth Syst. Sci., 16, 24372451, doi:10.5194/hess-16-2437-2012.

    • Search Google Scholar
    • Export Citation
  • Van Loon, A. F., and Van Lanen H. A. J. , 2012: A process-based typology of hydrological drought. Hydrol. Earth Syst. Sci., 16, 19151946, doi:10.5194/hess-16-1915-2012.

    • Search Google Scholar
    • Export Citation
  • Wong, G., Lambert M. F. , Leonard M. , and Metcalfe A. V. , 2010: Drought analysis using trivariate copulas conditional on climatic states. J. Hydrol. Eng., 15 (2), 129141, doi:10.1061/(ASCE)HE.1943-5584.0000169.

    • Search Google Scholar
    • Export Citation
  • Wood, A. W., and Lettenmaier D. P. , 2008: An ensemble approach for attribution of hydrologic prediction uncertainty. Geophys. Res. Lett., 35, L14401, doi:10.1029/2008GL034648.

    • Search Google Scholar
    • Export Citation
  • WWA and NIDIS, 2012: The 2012 Drought in Colorado, Utah and Wyoming: A July 2012 update from the Western Water Assessment and the National Integrated Drought Information System, WWA and NIDIS, 2 pp. [Available online at http://www.drought.gov/imageserver/NIDIS/DEWS/UCRB/docs/WWA-NIDIS_July_2012_Drought_update.pdf.]

  • Zhang, L., and Singh V. P. , 2007a: Trivariate flood frequency analysis using the Gumbel–Hougaard copula. J. Hydrol. Eng., 12, 431439, doi:10.1061/(ASCE)1084-0699(2007)12:4(431).

    • Search Google Scholar
    • Export Citation
  • Zhang, L., and Singh V. P. , 2007b: Gumbel–Hougaard copula for trivariate rainfall frequency analysis. J. Hydrol. Eng., 12, 409419, doi:10.1061/(ASCE)1084-0699(2007)12:4(409).

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 544 506 33
Full Text Views 61 61 3
PDF Downloads 40 40 4

A Bayesian Framework for Probabilistic Seasonal Drought Forecasting

View More View Less
  • 1 Department of Civil and Environmental Engineering, Portland State University, Portland, Oregon
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

Seasonal drought forecasting is presented within a multivariate probabilistic framework. The standardized streamflow index (SSI) is used to characterize hydrologic droughts with different severities across the Gunnison River basin in the upper Colorado River basin. Since streamflow, and subsequently hydrologic droughts, are autocorrelated variables in time, this study presents a multivariate probabilistic approach using copula functions to perform drought forecasting within a Bayesian framework. The spring flow (April–June) is considered as the forecast variable and found to have the highest correlations with the previous winter (January–March) and fall (October–December). Incorporating copula functions into the Bayesian framework, two different forecast models are established to estimate the hydrologic drought of spring given either the previous winter (first-order conditional model) or previous winter and fall (second-order conditional model). Conditional probability density functions (PDFs) and cumulative distribution functions (CDFs) are generated to characterize the significant probabilistic features of spring droughts. According to forecasts, the spring drought is more sensitive to the winter status than the fall status, which approves the results of prior correlation analysis. The 90% predictive bound of the spring-flow forecast indicates the efficiency of the proposed model in estimating the spring droughts. The proposed model is compared with the conventional forecast model, the ensemble streamflow prediction (ESP), and it is found that their forecasts are generally in agreement with each other. However, the forecast uncertainty of the new method is more reliable than the ESP method. The new probabilistic forecast model can provide insights to water resources managers and stakeholders to facilitate the decision making and developing drought mitigation plans.

Corresponding author address: Hamid Moradkhani, Room 202J, 1930 SW 4th Avenue, Portland, OR 97201. E-mail: hamidm@cecs.pdx.edu

This article is included in the Advancing Drought Monitoring and Prediction Special Collection.

Abstract

Seasonal drought forecasting is presented within a multivariate probabilistic framework. The standardized streamflow index (SSI) is used to characterize hydrologic droughts with different severities across the Gunnison River basin in the upper Colorado River basin. Since streamflow, and subsequently hydrologic droughts, are autocorrelated variables in time, this study presents a multivariate probabilistic approach using copula functions to perform drought forecasting within a Bayesian framework. The spring flow (April–June) is considered as the forecast variable and found to have the highest correlations with the previous winter (January–March) and fall (October–December). Incorporating copula functions into the Bayesian framework, two different forecast models are established to estimate the hydrologic drought of spring given either the previous winter (first-order conditional model) or previous winter and fall (second-order conditional model). Conditional probability density functions (PDFs) and cumulative distribution functions (CDFs) are generated to characterize the significant probabilistic features of spring droughts. According to forecasts, the spring drought is more sensitive to the winter status than the fall status, which approves the results of prior correlation analysis. The 90% predictive bound of the spring-flow forecast indicates the efficiency of the proposed model in estimating the spring droughts. The proposed model is compared with the conventional forecast model, the ensemble streamflow prediction (ESP), and it is found that their forecasts are generally in agreement with each other. However, the forecast uncertainty of the new method is more reliable than the ESP method. The new probabilistic forecast model can provide insights to water resources managers and stakeholders to facilitate the decision making and developing drought mitigation plans.

Corresponding author address: Hamid Moradkhani, Room 202J, 1930 SW 4th Avenue, Portland, OR 97201. E-mail: hamidm@cecs.pdx.edu

This article is included in the Advancing Drought Monitoring and Prediction Special Collection.

Save