Abstract
Precipitation prediction is one of the most effective management aspects for rehabilitating dried water resources such as Urmia Lake, Iran. This study was conducted to investigate the efficiency of the first-order multi-site autoregressive [MSAR (1)] model in the spatiotemporal simulation of annual precipitation in the Urmia Lake basin. To determine the model parameters, data from the period of 47 years (1961–2007) were used. These parameters were obtained by computing the lag-zero (lag 0) and lag-one (lag1) correlation among the annual precipitation time series of stations. A 12-year period (2008–2019) was used to evaluate the model. The region's precipitation in a year (t) was estimated based on its precipitation in the previous year (t − 1). The mean absolute error percentage (MAPE) for the test data was 16.7%. Also, the statistical characteristics of the generated and historical data were similar and their differences were not significant. Therefore, considering the appropriate efficiency of the MSAR (1) model in forecasting and generating annual precipitation, its application is recommended to help better manage water resources in this area.
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Data availability
All data used for this study are available from public institutions (Meteorological Organization of Iran).
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The software programs used in this research were free.
References
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19(6):716–723. https://doi.org/10.1109/tac.1974.1100705
Barideh R, Nasimi F (2022) Investigating the changes in agricultural land use and actual evapotranspiration of the Urmia Lake basin based on FAO’s WaPOR database. Agr Water Manag 264:107509. https://doi.org/10.1016/j.agwat.2022.107509
Box G, Jenkins F (1976) Times series analysis: forecasting and control. Holden-Day, Oakland
Bradley JV (1968) Distribution-free statistical tests. Prentice-Hall, Englewood Cliffs
Brissette FP, Khalili M, Leconte R (2007) Efficient stochastic generation of multi-site synthetic precipitation data. J Hydrol 345:121–133. https://doi.org/10.1016/j.jhydrol.2007.06.035
Faghih H, Behmanesh J, Khalili K (2018) Simulation of spatiotemporal annual precipitation using stochastic models. J Water Soil Sci 22(1):367–386 (In Persian)
Faghih H, Behmanesh J, Rezaei H, Khalili K (2021) Changes in climatic variables and their effect on wheat water requirement in Urmia Lake Basin. J Agric Sci Technol 23(5):1179–1191
Faghih H, Behmanesh J, Rezaie H, Khalili K (2022) Application of artificial intelligence in agrometeorology: a case study in Urmia Lake basin, Iran. Theor Appl Climatol. https://doi.org/10.1007/s00704-022-04104-6
Farajzadeh J, Fakheri Fard A, Lotf S (2014) Modeling of monthly rainfall and runoff of Urmia lake basin using “feed-forward neural network” and “time series analysis” model. Water Resour Ind 7–8:38–48. https://doi.org/10.1016/j.wri.2014.10.003
Golub GH, Van Loan CF (2013) Matrix computations, 4th edn. The Johns Hopkins University Press, Baltimore
Grubbs FE (1969) Procedures for detecting outlying observations in samples. Technometrics 11(1):1–21. https://doi.org/10.2307/1266761
Härdle WK, Simar L (2015) Applied multivariate statistical analysis. Springer, Verlag Berlin Heidelberg. https://doi.org/10.1007/978-3-662-45171-7
Hellassa S, Souag-Gamane D (2019) Improving a stochastic multi-site generation model of daily rainfall using discrete wavelet de-noising: a case study to a semi-arid region. Arab J Geosci. https://doi.org/10.1007/s12517-018-4168-0
Jarque CM, Bera AK (1987) A test for normality of observations and regression residuals. Int Stat Rev 55(2):163–172. https://doi.org/10.2307/1403192
Karamouz M, Szidarovszky F, Zahraie B (2003) Water resources system analysis. LEWIS PUBLISHERS, Boca Raton
Khalili M, Brissette F, Leconte R (2009) Stochastic multi-site generation of daily weather data. Stoch Environ Res Risk Assess 23:837–849. https://doi.org/10.1007/s00477-008-0275-x
Khalili M, Brissette F, Leconte R (2011) Effectiveness of multi-site weather generator for hydrological modeling. J Am Water Resour Assoc 47(2):303–314
Kigobe M, McIntyre N, Wheater H, Chandler R (2011) Multi-site stochastic modeling of daily rainfall in Uganda. Hydrol Sci J 56(1):17–33. https://doi.org/10.1080/02626667.2010.536548
Kim S, Kim H (2016) A new metric of absolute percentage error for intermittent demand forecasts. Int J Forecast 32:669–679
Komornık J, Komornıkova M, Mesiar R, Szokeova D (2006) Comparison of forecasting performance of nonlinear models of hydrological time series. Phys Chem Earth 31:1127–1145
Lawrance AJ, Kottegoda NT (1977) Stochastic modeling of river flow time series. J R Stat Soc Ser A 140, part 1, p.1.
Markovic D et al (2019) Multivariate and multi-scale generators based on non-parametric stochastic algorithms. J Hydroinform 21(6):1102–1117. https://doi.org/10.2166/hydro.2019.071
Matalas NC (1967) Mathematical assessment of synthetic hydrology. Water Resour Res 3(4):937–945
Medda S, Bhar KK (2019) Comparison of single-site and multi-site stochastic models for streamflow generation. Appl Water Sci 9(67):1–14. https://doi.org/10.1007/s13201-019-0947-3
Nasrollahi H, Shirazizadeh R, Shirmohammadi R, Pourali O, Amidpour M (2021) Unraveling the water-energy-food-environment nexus for climate change adaptation in Iran: Urmia Lake Basin case-study. Water 13:1282. https://doi.org/10.3390/w13091282
Olea RA (1999) Geostatistics for engineers and earth scientists. Springer, New York. https://doi.org/10.1007/978-1-4615-5001-3
Oliveira B, Maia R (2018) Stochastic generation of streamflow time series. J Hydrol Eng 23(10):04018043. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001695
Papalexiou SM, Serinaldi F, Porcu E (2021) Advancing space-time simulation of random fields: from storms to cyclones and beyond. Water Resour Res. https://doi.org/10.1029/2020WR029466
Paschalis A, Molnar P, Fatichi S, Burlando P (2013) A stochastic model for high-resolution space-time precipitation simulation. Water Resour Res 49:8400–8417. https://doi.org/10.1002/2013WR014437
Peleg N, Fatichi S, Paschalis A, Molnar P, Burlando P (2017) An advanced stochastic weather generator for simulating 2-D high-resolution climate variables. J Adv Model Earth Syst 9:1595–1627. https://doi.org/10.1002/2016MS000854
Pohlert T (2020) Non-parametric trend tests and change-point detection. Accessed 25 Nov 2020 from https://cran.r-project.org/web/packages/trend/vignettes/trend.pdf
Rasmussen PF (2013) Multisite precipitation generation using a latent autoregressive model. Water Resour Res 49:1845–1857. https://doi.org/10.1002/wrcr.20164
Saada N (2014) Time series modeling of monthly rainfall in arid areas: a case study for Saudi Arabia. Am J Environ Sci 10(3):277–282
Saada N, Abu-Romman A (2017) Multi-site modeling and simulation of the standardized precipitation index (SPI) in Jordan. J Hydrol Reg Stud 14:83–91. https://doi.org/10.1016/j.ejrh.2017.11.002
Shumway RH, Stoffer DS (2000) Time series analysis and its applications. Springer, New York. https://doi.org/10.1007/978-1-4757-3261-0
Srikanthan R, McMahon TA (1985) Stochastic generation of rainfall and evaporation data. AWRC 84:301
Thomas H, Fiering M (1962) Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation. In: Maass A, Marglin S, Fair G (eds) Design of water resources systems. Harvard University Press, Cambridge
Wang H, Wang C, Lin X, Kang J (2014) An improved ARIMA model for precipitation simulations. Nonlinear Process Geophys 21:1159–1168
Young GK, Pisano WC (1968) Operational hydrology using residuals. J Hydraul Div Amer Soc Civil Eng 94(HY4):909–923
Yue S, Wang C (2004) The Mann-Kendall test modified by effective sample size to detect trends in serially correlated hydrological series. Water Resour Manag 18:201–218
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The authors would like to thank the Editorial Board and anonymous reviewers for their helpful comments. The authors also appreciate the support of the Iran Meteorological Organization (IMO) for providing climatic data.
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The authors contributed to the study's conception and design. Material preparation, data collection, and analysis were performed by HF. The first draft of the manuscript was written by HF and JB commented on previous versions of the manuscript. The authors read and approved the final manuscript.
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Faghih, H., Behmanesh, J. Spatiotemporal simulation of annual precipitation in the Urmia Lake basin. Stoch Environ Res Risk Assess 37, 4215–4227 (2023). https://doi.org/10.1007/s00477-023-02503-3
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DOI: https://doi.org/10.1007/s00477-023-02503-3