MAXIMUM LIKELIHOOD ESTIMATION OF THE WATER LEVELS IN THE TONO DAM, GHANA
Keywords:
Weibull distribution, reservoir, probability distribution, validation
Abstract
The quest of this research is to find the most appropriate probability distribution function that
best approximates the water level in the Tono dam. The data used consist daily water level
recordings from January 2010 to January, 2017. The sample size of the data is 2570. However,
2195 data points were used in the analysis whilst the remaining 375 was used for validation.
After various probability distribution functions were fitted to the data, it was observed that the
Weibull distribution best fits the data. From the Weibull distribution fitted, it can be observed
that the level of the water in the Tono dam is dwindling with time.
References
Akaike, H., (1977). On entropy maximization principle. In: Krishnaiah, P.R. (Editor). Applications
of Statistics, North-Holland, Amsterdam, pp. 27–41.
Alam S., Khan S. M. & Rahat S., H., (2015). A study on selection of probability distributions of
extreme hydrologic parameters for the peripheral river system of Dhaka City. 15th World
International conference, Bangkok, Thailand, pp. 29 – 34.
Alfarra A., Kemp-Benedict E., Hötzl H., Sader N., & Sonneveld B. (2012). Modeling Water Supply
and Demand for Effective Water Management Allocation in the Jordan Valley. Journal of the
American Statistical Association, 1(1), pp. 1-7, World Academic Publishing.
Bessa R.J., Miranda V., Sumaili J., Botterud A., Zhou Z., & Wang J., (2011). Wind Power
Forecasting with Probability Density Estimation: A Tool for the Business, Windpower 2011
Conference and Exhibition, Anaheim, CA – USA.
Ding Y., Li S. & Li L., 2009. An analysis on chaos behavior of currency exchange rate undulation.
First international workshop on education technology and computer science, Wuhan, Hubei,
vol., 2, pp. 599-602. [doi: 10.1109.ETCS.2009.394].
Garba H., Ismail A., & Tsoho U., (2013). Fitting probability distribution functions to discharge
variability of Kaduna River. International journal of modern engineering research (IJMER), 3(5),
pp. 2848 – 2852.
Ghana Statistical Service (2012). 2010 Population & housing census. Sakoa Press Limited.hosh, S. K., Chowdary, V. M., Saikrishnaveni, A, & Sharma R. K. (2016). A Probabilistic
Nonlinear Model for Forecasting Daily Water Level in Reservoir, Water Resources Management,
30(9), pp. 3107–3122.
Gradojevic, N. and Yang, J., (2006). Non-linear, non-parametric, non-fundamental exchange rate
forecasting. J. Forecast. No. 25, 227–245.
Huang, S.C., Chuang, P. J., & Wu, C.F., (2010). Chaos-based support vector regressions for
exchange rate forecasting. Expert Systems with Applications 37 (12), 8590 –8598.
Ishak W., Hussain, W., Ku-Ruhanan K-M & Norita M. N., (2010). Reservoir water level
forecasting model using neural network. International Journal of Computational Intelligence, 6
(4). pp. 947-952. ISSN 0973-1873
Izinyon O. C. & Ajumuka N. H., (2013). Probability distribution models for flood predictions in
Upper Benue river basin-part II. Civil and environmental research 3(2), pp. 62 – 74.
Lai C. D., PraMurthy D. N., & Xie M., (2006). Weibull distributions and its applications. In
Springer handbook of engineering statistics; Pham, H., ed.; Springer-Verlag: London, U. K., pp.
63 – 78.
Lin C-S, Chiu S-H & Lin T-Y, (2012). Empirical mode decomposition–based least squares support
vector regression for foreign exchange rate forecasting. Economic Modelling 29, 2583 – 2590.
Nwobi-Okoye C. C., & Igboanugo (2013). Predicting water levels at Kainji dam using artificial
neural networks. Nigeria Journal of Technology (NIJOTECH), PP. 129 – 136.
Radhwan A., Kamel M., Dahab M. Y., & Hassanien A, (2015). Forecasting exchange rates: A
chaos-based regression approach. International Journal of Rough Sets and Data Analysis, 2(1),
38 – 57.
Rani S. & Parekh F., (2014). Predicting reservoir water level using artificial neural network.
International journal of innovative research in science, engineering and technology (IJIRSET),
3(7), pp. 14489 – 14496.
Schwarz, G. E. (1978). Estimating the dimension of a model. Annals of Statistics 6 (2): 461–464.
doi:10.1214/aos/1176344136. MR468014.
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 MultipleInput-Pattern Fuzzification Approach. The Scientific World Journal, doi:10.1155/2014/432976.
Vivekanandam N., (2015). Estimation of maximum flood discharge using Gamma and extreme
value family of probability distributions. International journal of world research (IJWR), 1(16),
pp. 16 – 23.
of Statistics, North-Holland, Amsterdam, pp. 27–41.
Alam S., Khan S. M. & Rahat S., H., (2015). A study on selection of probability distributions of
extreme hydrologic parameters for the peripheral river system of Dhaka City. 15th World
International conference, Bangkok, Thailand, pp. 29 – 34.
Alfarra A., Kemp-Benedict E., Hötzl H., Sader N., & Sonneveld B. (2012). Modeling Water Supply
and Demand for Effective Water Management Allocation in the Jordan Valley. Journal of the
American Statistical Association, 1(1), pp. 1-7, World Academic Publishing.
Bessa R.J., Miranda V., Sumaili J., Botterud A., Zhou Z., & Wang J., (2011). Wind Power
Forecasting with Probability Density Estimation: A Tool for the Business, Windpower 2011
Conference and Exhibition, Anaheim, CA – USA.
Ding Y., Li S. & Li L., 2009. An analysis on chaos behavior of currency exchange rate undulation.
First international workshop on education technology and computer science, Wuhan, Hubei,
vol., 2, pp. 599-602. [doi: 10.1109.ETCS.2009.394].
Garba H., Ismail A., & Tsoho U., (2013). Fitting probability distribution functions to discharge
variability of Kaduna River. International journal of modern engineering research (IJMER), 3(5),
pp. 2848 – 2852.
Ghana Statistical Service (2012). 2010 Population & housing census. Sakoa Press Limited.hosh, S. K., Chowdary, V. M., Saikrishnaveni, A, & Sharma R. K. (2016). A Probabilistic
Nonlinear Model for Forecasting Daily Water Level in Reservoir, Water Resources Management,
30(9), pp. 3107–3122.
Gradojevic, N. and Yang, J., (2006). Non-linear, non-parametric, non-fundamental exchange rate
forecasting. J. Forecast. No. 25, 227–245.
Huang, S.C., Chuang, P. J., & Wu, C.F., (2010). Chaos-based support vector regressions for
exchange rate forecasting. Expert Systems with Applications 37 (12), 8590 –8598.
Ishak W., Hussain, W., Ku-Ruhanan K-M & Norita M. N., (2010). Reservoir water level
forecasting model using neural network. International Journal of Computational Intelligence, 6
(4). pp. 947-952. ISSN 0973-1873
Izinyon O. C. & Ajumuka N. H., (2013). Probability distribution models for flood predictions in
Upper Benue river basin-part II. Civil and environmental research 3(2), pp. 62 – 74.
Lai C. D., PraMurthy D. N., & Xie M., (2006). Weibull distributions and its applications. In
Springer handbook of engineering statistics; Pham, H., ed.; Springer-Verlag: London, U. K., pp.
63 – 78.
Lin C-S, Chiu S-H & Lin T-Y, (2012). Empirical mode decomposition–based least squares support
vector regression for foreign exchange rate forecasting. Economic Modelling 29, 2583 – 2590.
Nwobi-Okoye C. C., & Igboanugo (2013). Predicting water levels at Kainji dam using artificial
neural networks. Nigeria Journal of Technology (NIJOTECH), PP. 129 – 136.
Radhwan A., Kamel M., Dahab M. Y., & Hassanien A, (2015). Forecasting exchange rates: A
chaos-based regression approach. International Journal of Rough Sets and Data Analysis, 2(1),
38 – 57.
Rani S. & Parekh F., (2014). Predicting reservoir water level using artificial neural network.
International journal of innovative research in science, engineering and technology (IJIRSET),
3(7), pp. 14489 – 14496.
Schwarz, G. E. (1978). Estimating the dimension of a model. Annals of Statistics 6 (2): 461–464.
doi:10.1214/aos/1176344136. MR468014.
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 MultipleInput-Pattern Fuzzification Approach. The Scientific World Journal, doi:10.1155/2014/432976.
Vivekanandam N., (2015). Estimation of maximum flood discharge using Gamma and extreme
value family of probability distributions. International journal of world research (IJWR), 1(16),
pp. 16 – 23.
Published
2018-11-30
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