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Stochastic ARIMA model for annual rainfall and maximum temperature forecasting over Tordzie watershed in Ghana

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Warianty tytułu
PL
Stochastyczny model ARIMA do prognozowania rocznego opadu i maksymalnej temperatury w zlewni Tordzie w Ghanie
Języki publikacji
EN
Abstrakty
EN
The forecast of rainfall and temperature is a difficult task due to their variability in time and space and also the inability to access all the parameters influencing rainfall of a region or locality. Their forecast is of relevance to agriculture and watershed management, which significantly contribute to the economy. Rainfall prediction requires mathematical modelling and simulation because of its extremely irregular and complex nature. Autoregressive integrated moving average (ARIMA) model was used to analyse annual rainfall and maximum temperature over Tordzie watershed and the forecast. Autocorrelation function (ACF) and partial autocorrelation function (PACF) were used to identify the models by aid of visual inspection. Stationarity tests were conducted using the augmented Dickey–Fuller (ADF), Mann–Kendall (MK) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests respectively. The chosen models were evaluated and validated using the Akaike information criterion corrected (AICC) and also Schwartz Bayesian criteria (SBC). The diagnostic analysis of the models comprised of the independence, normality, homoscedascity, P–P and Q–Q plots of the residuals respectively. The best ARIMA model for rainfall for Kpetoe and Tordzinu were (3, 0, 3) and (3, 1, 3) with AICC values of 190.07 and 178.23. That of maximum temperature for Kpetoe and Tordzinu were (3, 1, 3) and (3, 1, 3) and the corresponding AICC values of 23.81 and 36.10. The models efficiency was checked using sum of square error (SSE), mean square error (MSE), mean absolute percent error (MAPE) and root mean square error (RMSE) respectively. The results of the various analysis indicated that the models were adequate and can aid future water planning projections.
PL
Prognozowanie opadu i temperatury jest trudnym zadaniem z powodu zmienności tych parametrów w czasie i przestrzeni, a także nieznajomości wszystkich czynników wpływających na opady w regionie czy w danej miejscowości. Prognozowanie opadów jest ważne dla rolnictwa i gospodarki zlewniowej, mających znaczący wkład w gospodarkę regionu. Przewidywanie opadu wymaga modelowania matematycznego i symulacji z powodu jego skrajnie nieregularnego i złożonego charakteru. Do analizy i prognozowania rocznych opadów i maksymalnej temperatury w zlewni Tordzie wykorzystano autoregresyjny zintegrowany model średniej ruchomej (ARIMA). Do zidentyfikowania modeli metodą oglądu wizualnego użyto funkcji autokorelacji (ACF) i cząstkowej autokorelacji (PACF). Testy stacjonarności przeprowadzono za pomocą testów Dickeya–Fullera (ADF), Manna–Kendalla (MK) i Kwiatkowskiego–Phillipsa–Schmidta–Shina (KPSS). Wybrane modele poddano ocenie i walidacji z użyciem skorygowanego kryterium Akaike (AICC) i Bayesowskiego kryterium Schwartza (SBC). Diagnostyczna analiza modeli obejmowała niezależność, normalność, homoscedastyczność, wykresy P–P i Q–Q dla reszt. Najlepsze modele ARIMA dla opadu w Kpetoe i Tordzinu miały postać (3, 0, 3) i (3, 1, 3), gdy wartości AICC równe odpowiednio 190,07 i 178,23. Modele dla maksymalnej temperatury w Kpetoe i Tordzinu miały postać (3, 1, 3) i (3, 1, 3), a ich odpowiednie wartości AICC wynosiły 23,81 i 36,10. Wydajność modelu sprawdzano, wykorzystując sumę błędu kwadratowego (SSE), średni błąd kwadratowy (MSE), średni bezwzględny błąd procentowy (MAPE) i pierwiastek ze średniego błędu kwadratowego (RMSE). Wyniki różnych analiz wykazały, że modele są odpowiednie i mogą stanowić pomoc w przyszłej gospodarce wodnej.
Wydawca
Rocznik
Tom
Strony
127--140
Opis fizyczny
Bibliogr. 37 poz., rys., tab.
Twórcy
autor
  • Ho Technical University, Department of Agricultural Engineering, Ho, Volta Region, Box 217, Ghana, doga_nyatuame@yahoo.com
autor
  • Kwame Nkrumah University of Science and Technology, Department of Agricultural and Biosystems Engineering, Kumasi, Ashanti Region, Ghana, skagodzo7@usa.net
Bibliografia
  • ABDUL-AZIZ A., ANOKYE M., KWAME A., MUNYAKAZI L., NSOWAH-NUAMAH N. 2013. Modeling and forecasting rainfall pattern in Ghana as a seasonal ARIMA process: The case of Ashanti region. International Journal of Humanities and Social Science. Vol. 3. No. 3 p. 224–233.
  • AFRIFA-YAMOAH E. 2015. Application of ARIMA models in forecasting monthly average surface temperature of Brong Ahafo Region of Ghana. International Journal of Statistics and Applications. Vol. 5. No. 5 p. 237–246.
  • AFRIFA-YAMOAH E., SAEED B.I., KARIM A. 2016. Sarima modelling and forecasting of monthly rainfall in the Brong Ahafo Region of Ghana. World Environment. Vol. 6(1) p. 1–9.
  • AKAIKE H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control. Vol. 19. Iss. 6 p. 716-723.
  • AKROUR N., CHAZOTTES A., VERRIER S., MALLET C., BARTHES L. 2015. Simulation of yearly rainfall time series at microscale resolution with actual properties: Intermittency, scale invariance, and rainfall distribution. Water Resources Research. Vol. 51. Iss. 9 p. 7417–7435. DOI 10.1002/2014WR016357.
  • ALAM N., MISHRA P., JANA C., ADHIKARY P.P. 2014. Stochastic model for drought forecasting for Bundelkhand region in Central India. Indian Journal of Agricultural Sciences. Vol. 84(1) p. 79–84.
  • ASAMOAH-BOAHENG M. 2014. Using SARIMA to forecast monthly mean surface air temperature in the Ashanti Region of Ghana. International Journal of Statistics and Applications. Vol. 4(6) p. 292–298.
  • BĄK B., KUBIAK-WÓJCICKA K. 2017. Impact of meteorological drought on hydrological drought in Toruń (central Poland) in the period of 1971–2015. Journal of Water and Land Development. No. 32 p. 3–12. DOI 10.1515/jwld-2017-0001.
  • BOX G. E., JENKINS G.M., REINSEL G.C., LJUNG G.M. 2015. Time series analysis: forecasting and control. 5th ed. John Wiley & Sons. ISBN 1118675029 pp. 712.
  • FENG Q., WEN X., LI J. 2015. Wavelet analysis-support vector machine coupled models for monthly rainfall forecasting in arid regions. Water Resources Management. Vol. 29. Iss. 4 p. 1049–1065.
  • GALAVI H., MIRZAEI M., SHUI L.T., VALIZADEH N. 2013. Klang river-level forecasting using ARIMA and ANFIS models [online]. Journal of America Water Works Association. Vol. 105. Iss. 9 p. E496–E506. DOI 10.5942/jawwa.2013.105.0106.
  • GEORGE J., LETHA J., JAIRAJ P. 2016. Daily rainfall prediction using generalized linear bivariate model – A case study. Procedia Technology. Vol. 24 p. 31–38.
  • HASMIDA H. 2009. Water quality trend at the upper part of Johor River in relation to rainfall and runoff pattern. MSc Thesis. Universiti Teknologi Malaysia pp. 155.
  • HENDRY D.F., PRETIS F. 2016. All change! The implications of non-stationarity for empirical modelling, forecasting and policy. Unviversity of Oxford, Oxford Martin School Policy Paper Series pp. 28.
  • HUANG Y.F., MIRZAEI M., YAP W.K. 2016. Flood analysis in Langat River Basin using stochatic model. International Journal of GEOMATE. Vol. 11 p. 2796–2803.
  • JUNG K., SHAH N.H. 2015. Implications of non-stationarity on predictive modeling using EHRs. Journal of Biomedical Informatics. Vol. 58 p. 168-174.
  • KAPOOR P., BEDI S.S. 2013. Weather forecasting using sliding window algorithm. ISRN Signal Processing. Vol. 2013 (2013). Article ID 156540 pp. 5.
  • KENITZER S., ROSENFELD J., HEIDEMAN K. 2007. Bulletin of the America Meteorological Society: Annual Report 2006. Boston 88.4 (Apr 2007) p. 1–27.
  • KHADR M. 2011. Water resources management in the context of drought (An application to the Ruhr River Basin in Germany). PhD Dissertation. Civil Engineering Department. University of Wuppertal, Germany (edited).
  • KUMARI K.A., BOIROJU N.K., GANESH T., REDDY P.R. 2012. Forecasting surface air temperature using neural networks. International Journal of Mathematics and Computer Applications Research. Vol. 3 p. 65–78.
  • LOGAH F., OBUOBIE E., OFORI D., KANKAM-YEBOAH K. 2013. Analysis of rainfall variability in Ghana. International Journal of Latest Research in Engineering and Computing. Vol. 1. Iss. 1 p. 1–8.
  • ŁABĘDZKI L., BĄK B. 2017. Impact of meteorological drought on crop water deficit and crop yield reduction in Polish agriculture. Journal of Water and Land Development. No. 34 p. 181–190. DOI 10.1515/jwld-2017-0052.
  • MISHRA A.K., DESAI V.R. 2005. Drought forecasting using stochastic models. Stochastic Environmental Research and Risk Assessment. Vol. 19. Iss. 5 p. 326–339.
  • MONTGOMERY D.C; JENNINGS C.L; KULAHCI M. 2008. Introduction to time series analysis and forecasting. John Wiley and Sons, Inc. ISBN 0471653977 pp. 472.
  • NIRMALA M. 2015. Computational models for forecasting annual rainfall in Tamilnadu. Applied Mathematical Sciences. Vol. 9. Iss. 13 p. 617–621.
  • NKRUMAH F., KLUTSE N.A.B., ADUKPO D.C., OWUSU K., QUAGRAINE K.A., OWUSU A., GUTOWSKI W. 2014. Rainfall variability over Ghana: Model versus rain gauge observation. International Journal of Geosciences. Vol. 5. Iss. 7 p. 673–683.
  • NOBRE S.J., SINGER M.J. 2007. Residual analysis for linear mixed models. Biometrical Journal. Vol. 49. Iss. 6 p. 863–875.
  • NYATUAME M., AGODZO S. 2017. Analysis of extreme rainfall events (drought and flood) over Tordzie Watershed in the Volta Region of Ghana. Journal of Geoscience and Environment Protection. Vol. 05. No. 09 p. 275–295.
  • NYATUAME M., OWUSU-GYIMAH V., AMPIAW F. 2014. Statistical analysis of rainfall trend for Volta Region in Ghana. International Journal of Atmospheric Sciences. Vol. 2014. Article ID 203245 pp. 11.
  • OWUSU K., WAYLEN P.R. 2009. Trends in spatio‐temporal variability in annual rainfall in Ghana (1951–2000). Weather. Vol. 64. Iss. 5 p. 115–120.
  • OWUSU K., WAYLEN P.R. 2013. The changing rainy season climatology of mid-Ghana. Theoretical and Applied Climatology. Vol. 112. Iss. 3–4 p. 419–430.
  • RADHAKRISHNAN P., DINESH S. 2006. An alternative approach to characterize time series data: Case study on Malaysian rainfall data. Chaos, Solitons and Fractals. Vol. 27. Iss. 2 p. 511–518.
  • RAMANA R.V., KRISHNA B., KUMAR S., PANDEY N. 2013. Monthly rainfall prediction using wavelet neural network analysis. Water Resources Management. Vol. 27. Iss. 10 p. 3697–3711.
  • SCHWARZ G. 1978. Estimating the dimension of a model. The Annals of Statistics. Vol. 6(2) p. 461–464.
  • SOMVANSHI V., PANDEY O., AGRAWAL P., KALANKER N., PRAKASH M.R., CHAND R. 2006. Modeling and prediction of rainfall using artificial neural network and ARIMA techniques. The Journal of Indian Geophysical Union. Vol. 10. No. 2 p. 141–151.
  • VALIZADEH N., EL-SHAFIE A., MIRZAEI M., GALAVI H., MUKHLISIN M., JAAFAR O. 2014. Accuracy enhancement for forecasting water levels of reservoirs and river streams using a multiple-input-pattern fuzzification approach. The Scientific World Journal. Vol. 2014. Article ID 432976 pp. 9.
  • WRC 2010. Annual report. Water Resources Commission. ISBN 978-0-621-40211-7 pp. 156.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-dff3af07-955a-4acb-bdff-d2db87fad49f
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