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Principal Component Regression, Time Series, ARIMA, SARIMA, Measures of Adequacy

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Principal Component Regression, Time Series, ARIMA, SARIMA, Measures of Adequacy International Journal of Statistics and Applications 2018, 8(6): 332-340 DOI: 10.5923/j.statistics.20180806.07 Use of Principal Components Regression and Time-Series Analysis to Predict the Water Level of the Akosombo Dam Level Isaac Ofori Asare1,*, Dorothy Anima Frempong2, Paul Larbi3 1Mathematics Department, Kwame Nkrumah University of Science and Technology, Ghana 2Computer science Department, Accra Technical University, Ghana 3Kwame Nkrumah University of Science and Technology, Kumasi, Ghana Abstract Knowing the water level of the Akosombo Dam would help Ghanaian since we depend heavily on hydroelectric power. When the future of the water level is known, society would be able to plan on the usage of electricity for the industries, society, individuals who use some of the water storage for irrigation, water supply purposes. The study employed rainfall from the 12 catchment areas to the River Volta and the daily water level of the dam for a period of 78-years. Principal Component Regression was applied to the input variables for the reduction of its large size to a few principal components to explain the variations in the original dataset. The outcome of the PCR extraction was two principal components. Time Series using Seasonal Autoregressive Integrated Moving Average was used to model the data. The appropriate model that fit the data well was ARIMA (2,1,2) (1,0,0) [12] after comparing other models AICs. The model with the smallest AIC and the least number of parameters was selected as the best model. Keywords Principal Component Regression, Time series, ARIMA, SARIMA, Measures of Adequacy rains and their impact on the water level of the Akosombo 1. Introduction dam. Also, as a major source of hydro-power, there is the need to be able to forecast the water level at a time accurately The hydroelectric project is a physical structure and precisely to determine the amount of energy that might constructed for the generation of hydropower. They have be produced at a particular point in time, daily, weekly, been used as a structural mechanism to regulate the flow of monthly or even yearly. A result of that there was the need to water for storages purposes. The structure (hydro project) are have good forecasting tool that could help forecast the water made to reduce the fast flow of water to the dam. The level of the dam accurately and precisely. hydroelectric projects are capable of storing flow of At the beginning of the year 2007, Ghanaians were rainwater to ensure water supply for hydro-power generation worried and raised concerns about the limited hydro-power and for other economic purposes such as for agro-business, generation (electricity) or supply from the generation plant household and industry usage. During raining season, the (dam) due to the low water levels in the Lake Volta reservoir, dam is able to get enough water for it intended purposes, reports from the dam site indicating that the project was production of enough hydropower. When there is drought, functioning below its capacity due to the problems of the water level of the dam reduces which limit the production drought due to global warming. It implies that when there is of electricity as Ghanaians depend largely on hydropower for minuscule or no rains from the river catchment areas to feed domestic and industrial usage. The dam level depends it, the Akosombo dam level would be low and as a result, the largely on rainfall from some catchment's areas of Ghana. dam would not be able to perform up to expectation. When it rains in these areas the water flow into the tributaries In the year 2010, the country experienced high rains and as and then move to the river Volta. There is the need to know a result, the Akosombo dam site recorded the highest water the contribution of each of these catchment areas when it level due to heavy rainfalls in a catchment area contributing to the dam, the reservoir elevation went above it expected a * Corresponding author: value of 84.73 m (278.0 ft). Due to the raised in the water [email protected] (Isaac Ofori Asare) level of the dam, it caused management of the dam site to let Published online at http://journal.sapub.org/statistics Copyright © 2018 The Author(s). Published by Scientific & Academic Publishing some of the water flow out by allowing some of the water to This work is licensed under the Creative Commons Attribution International pass through the floodgates at a basin elevation of 84.45 m License (CC BY). http://creativecommons.org/licenses/by/4.0/ (277 ft), and for several days, weeks, water was still International Journal of Statistics and Applications 2018, 8(6): 332-340 333 spattering from the river, creating some flooding in the from its catchment areas to operate effectively for nearby communities along the dam site. generating of hydroelectric power and production of water According to the Ghanaian times on June 7, 2016, at the for domestic consumption and industrial usage to time when the report has been filed, the dam level of the Ghanaians and other nearby countries. According to the reservoir was approximately 237.27 ft, just a little below the Ghana Metro-logical Agency, the Akosombo Dam takes its 240 ft the accepted level that can enhance the operation of volume of water from about 12 catchment areas (stations) the plant a situation the VRA has been threatened with all when it rains in these areas, therefore contribute this while. The Corporate Affairs Manager at the VRA, Mrs significantly to the water level of the dam. They are as Getrude N. Koomson, in a formal interview with one of the follows; Kintampo, Bui, Tamale, Yendi, Akuse, Navrongo, new papers; the Ghanaian Times indicated that the situation Salaga, Kate-Karachi, Bole, Atebubu, Kpando and Ho. was causing the machinery to underperform. Ghana depends so much on the Akosombo Hydroelectric This news indicates that until the water level appreciates power for its activities there is the need to get a model that to up to certain level to empower all the six turbines run can improve the older models used in predicting the water concurrently, then the alternative they would be left with was level. The study adopted Principal Component analysis to to relying on or cope with the little inflow and to ensure that reduce these rainfall stations to few stations that could be the engineers keep at most four of the turbines running used to describe the variation explained by all the stations. subject to the demand of hydro-power in the country (Ghana). Though the traditional time series model does not consider This is as a result of low rainfalls in the country. When there nonlinear inputs, hence giving out inconsistency results in are rains from the catchment areas especially the medium or its anticipation as indicated by Rani and Parekh (2014). The the central belt and the northern zones of the country. The traditional time series technique is efficient and effective for situation the dam is experiencing could change if there are a long time, but there was a deficiency that they suffer that rains from these areas. is the issue of stationary and linearity. Though the ARIMA The water level of the dam is mainly for hydropower and model does not take into consideration nonlinear data, the other purposes such as water storage which has been process of transformation could be applied to the data to employed for irrigation needs and water supply for domestic make it linearize. Also differencing could be applied to the use are some key importance of the dam, therefore there is data if the dataset is non-stationary to make it stationary. the need to knowing the water level of the dam for effective Ghana depends heavily on hydropower (Akosombo) for and efficient planning and the need to knowing the electricity, there is the need to get model that could be used contributions water from the various catchment areas to the to forecast the water level of the Akosombo Dam at any dam for the desired performance. This could be done when given time been daily, monthly or year based for proper we know the main contribution of the various catchment planning of the power issues in the country. areas to the water level in the dam and based on it the Planning for the hydroelectric project is a very essential forecasting techniques can be employed to ensure effective step for success in the evolution of Ghana since we depend and accurate result when we know the contribution of water mainly on hydro-power. This progress would be successful by the catchment areas can be obtained. if the water level of the dam is determined correctly or There are factors that influence the water level negatively checking for accuracy of the dam water level. As a result of such as evaporation, soil moisture and human activities this prediction; the study adopted Principle Component along the banks of the river, these are factors that need to be Regression (PCR) and variable importance using the considered in forecasting of the water level. Marino et al random forest technique in the determination of the (2017) climate change can cause the distribution of rainfall important rainfall catchment area having an impact on the patterns, with potential effect for the water bodies. Changes water level. in water bodies' level are as a result of factors such as like rains and other atmospheric conditions such as temperature, evaporation and humidity. When there is continuous wet and 3. Specific Objectives of the Study cold condition over a period of time, the volume of water 1.
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