Abstract
Drought is a global phenomenon that occurs virtually in all landscapes causing significant damage both in natural environment and in human lives. Due to the random nature of contributing factors, occurrence and severity of droughts can be treated as stochastic in nature. Early indication of possible drought can help to set out drought mitigation strategies and measures in advance. Therefore drought forecasting plays an important role in the planning and management of water resource systems. In this study, linear stochastic models known as ARIMA and multiplicative Seasonal Autoregressive Integrated Moving Average (SARIMA) models were used to forecast droughts based on the procedure of model development. The models were applied to forecast droughts using standardized precipitation index (SPI) series in the Kansabati river basin in India, which lies in the Purulia district of West Bengal state in eastern India. The predicted results using the best models were compared with the observed data. The predicted results show reasonably good agreement with the actual data, 1–2 months ahead. The predicted value decreases with increase in lead-time. So the models can be used to forecast droughts up to 2 months of lead-time with reasonably accuracy.
Similar content being viewed by others
References
Abramowitz M, Stegun A (1965) Handbook of mathematical formulas, graphs, and mathematical tables. Dover Publications Inc., New York
Akaike H (1974) A look at the statistical model identification. IEEE Trans Automatic Control AC 19:716–723
Bartlett MS (1946) On the theoretical specification of sampling properties of auto correlated time series. J R Stat Soc B8:27
Box GEP, Jenkins GM (1976) Time series analysis forecasting and control. Holden-Day, San Francisco
Box GEP, Jenkins GM, Reinsel GC (1994) Time series analysis, ‘forecasting and control.’ Prentice Hall, Englewood Cliffs, NJ
Brace MC, Schmidt J, Hadlin M (1991) Comparison of the forecasting accuracy of neural networks with other established techniques. In: Proceedings of the 1st forum on application of neural networks to power systems. Seattle, WA, pp 31–35
Bras RL, Rodriguez-Iturbe I (1985) Random functions and hydrology. Addison-Wesley, Reading MA, USA
Bussay A, Szinell C, Szentimery T (1999) Investigation and measurements of droughts in Hungary. Hungarian Meteorological Service, Budapest
Caire P, Hatabian G, Muller C (1992) Progress in forecasting by neural networks. In: Proceedings of the international joint conference on neural networks, vol. 2, pp540–545
Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. Mcgraw-Hill Book Company, New York
Chung CH, Salas JD (2000) Drought occurrence probabilities and risks of dependent hydrological processes. J Hydrol Eng ASCE 5(3):259–268
Cline TB (1981) Selecting seasonal streamflow models. Water Resour Res 17(4):975–984, Company Inc., New York, p 478
De Groot C, Wurtz D (1991) Analysis of univariate time series with connectionist nets: a case study of two classical examples. Neurocomputing 3:177–192
Durbin J (1960) The fitting of time series models, review of the international institute of Statistics, vol. 28, pp 233–140
Edwards DC, McKee TB (1997) Characteristics of 20th century drought in the United States at multiple timescales. Colorado State University Fort Collins, Climatology Report No. 97-2
Foster WR, Collopy F, Ungar LH (1992) Neural network forecasting of short, noisy time series. Comput Chem Eng 16(4):293–297
Gorr WL, Nagin D, Szczypula J (1994) Comparative study of artificial neural network and statistical models for predicting student grade point averages. Int J Forecast 10:17–34
Govindaswamy R (1991) Univeriate Box-Jenkins forecasts of water discharge in Missouri river. Water Resour Dev 7(3):168–177
Haan CT (1977) Statistical methods in hydrology. Iowa State Press, Iowa
Hayes MJ, Svoboda MD, Wilhite DA, Vanyarkho OV (1999) Monitoring the 1996 drought using the standardized precipitation index. Bull Am Meterol Soc 80:429–438
Hughes BL, Saunders MA (2002) A drought climatology for Europe. Int J Climatol 22:1571–1592
Kendel DR, Dracup JA (1992) On the generation of drought events using an alternating renewal-reward model. Stochastic Hydro Hydr 6(1):55–68
Kim T, Valdes JB (2003) Nonlinear model for drought forecasting based on a conjunction of wavelet transforms and neural networks. J Hydrol Eng ASCE 8(6):319–328
Lana X, Serra C, Burgue~no A (2001) Patterns of monthly rainfall shortage and excess in terms of the standardized precipitation index. Int J Climatol 21:1669–1691
Lewis PAW, Ray BK (2002) Nonlinear modeling of periodic threshold autoregressions using TSMARS. J Time Ser Anal 23(4):459–471
Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrica 65:297–303
Loaiciga HA, Leipnik RB (1996) Stochastic renewal model of low-flow stream sequences. Stochastic Hydro Hydr 10(1):65–85
Lohani VK, Loganathan GV (1997) An early warning system for drought management using the Palmer drought index. J Am Water Resour Assoc 33(6):1375–1386
Makridakis S, Wheelwright SC, Hyndman R (2003) Forecasting methods and applications. Wiley (ASIA) Pvt Ltd., Singapore
McKee TB, Doesken NJ, Kliest J (1993) The relationship of drought frequency and duration to time scales. In: Proceedings of the 8th conference on applied climatology 17–22 January, Anaheim, CA. American Meteorological Society, Boston, MA, pp 179–184
McKerchar AI, Dellur JW (1974) Application of seasonal parametric linear stochastic models to monthly flow data. Water Resour Res 10(2):246–255
Mishra AK, Desai VR (2005) Spatial and temporal drought analysis in the Kansabati river basin, India. Int J River Basin Manag IAHR 3(1):31–41
Moye AL, Kapadia AS, Cech IM, Hardy RJ (1988) The theory of run with application to drought prediction. J Hydrol 103:127–137
Panu US, Sharma TC (2002) Challenges in drought research: some perspectives and future directions. Hydrol Sci 47(S)
Panu US, Unny TE, Ragade RK (1978) A feature prediction model in synthetic hydrology based on concepts of pattern recognition. Water Resour Res 14(2):335–344
Rao AR, Padmanabhan G (1984) Analysis and modelling of Palmers drought index series. J Hydrol 68:211–229
Saldariaga J, Yevjevich V (1970) Application of run-lengths to hydrologic series Hydrol Paper. Colorado State University Publication, Colorado State University, Fort Collins, CO
Schwartz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464
Sen Z (1976) Wet and dry periods of annual flow series. J Hydrol Div ASCE 106(HY1):99–115
Sen Z (1977) Run sums of annual flow series. J Hydrol 35:311–324
Sen Z (1990) Critical drought analysis by second order Markov chain. J Hydrol 120:183–202
Szalai S, Szinell C (2000) Comparison of two drought indices for drought monitoring in Hungary—a case study. In: Vogt JV, Somma F (eds) Drought and drought mitigation in Europe. Kluwer, Dordrecht, pp 161–166
Thom HCS (1958) A note on gamma distribution. Monthly Weather Rev 86:117–122
Wei WWS (1990) Time series analysis. Addison-Wesley Publishing, Reading, MA
Wilhite DA, Glantz MH (1985) Understanding the drought phenomenon: the role of definations. Water Int 10:111–120
Wilhite DA, Rosenberg NJ, Glantz MH (1986) Improving federal response to drought. J Climate Appl Meteorol 25:332–342
Yevjevich V (1967) An objective approach to definitions and investigations of continental hydrologic droughts. Hydrol Papers Colorado State University, Fort Collins, CO
Yurekli K, Kurunc K, Ozturk F (2005) Application of linear stochastic models to monthly flow data of Kelkit Stream. Ecol Model 183:67–75
Acknowledgments
The authors would like to thank two anonymous reviewers for giving valuable suggestions for improving the quality of the paper. The authors would also like to acknowledge the editor G. Christakos for the timely handling the review processes of the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mishra, A.K., Desai, V.R. Drought forecasting using stochastic models. Stoch Environ Res Ris Assess 19, 326–339 (2005). https://doi.org/10.1007/s00477-005-0238-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-005-0238-4