Lake Water Level Prediction Model Based on Autocorrelation Regressive Integrated Moving Average and Kalman Filtering Techniques – An Empirical Study on Lake Volta Basin, Ghana

Yıl 2021, Cilt: 3 Sayı: 1, 1 - 11, 15.12.2020

Michael Stanley Peprah Edwin Kojo Larbı

Öz

The continuous decline in lake water levels is not only a major concern but also a daunting challenge to policymakers, demanding a backup technological and policy interventions in context of broader political and socio-economic realities. This study used Lake Volta hydrological system to shed light on the extensive and flexible modelling and simulation capabilities of stochastic models to understand the bigger picture of water level (WL) dynamics. The study used Autocorrelation Regressive Integrated Moving Average (ARIMA) and Kalman Filtering (KF) techniques as the proposed optimal stochastic models for the study area. The first order ARIMA (0, 1, 1) was found suitable for predicting the future monthly Lake Volta WL in the presented study based on expert advice and recommendations from existing studies. The statistical performance indicators used were minimum residual error (rmin), maximum residual error (rmax), arithmetic mean error (AME), arithmetic mean squared error (AMSE), arithmetic mean absolute percentage deviation (AMAPD), and arithmetic standard deviation (ASD). Based on the results achieved in this study, ARIMA (0, 1, 1) achieved AME, AMSE, AMAPD and ASD of -0.1268 m, 0.0037 m, 0.5749 m, and 0.0033 m respectively. Ensemble of ARIMA and KF was further used to forecast the upcoming monthly WL trends up to December 2048. ARIMA (0, 1, 1) model is found suitable for forecasting Lake Volta WL which shows positive trend up to December 2048. The study further predicted that Lake Volta WL will increase from the current average level of 0.2272 m to an average of 9.1366 m for the next 28 years. The ensuing conclusions stressed the need for checks against over-release of WL for hydropower production and measures for sustainable land and water management in the entire basin. This study can potentially enhance our understanding of hydrodynamic processes in Lake Volta and support water resource management.

Anahtar Kelimeler

Lake Volta, Kalman Filter, Stochastic Models, Time Series Analysis, Water Levels

Kaynakça

• Abban, E.K., 1999. Integrated Development of Artisanal Fishes. Integrated Development of Artisanal Fisheries Project, GHA/93/008, 1-43.
• Abeho, D.R., Hipkin, R., Tulu, B.B., 2014. Evaluation of EGM08 by means of GPS levelling Uganda. South African Journal of Geomatics 3 (3), 272-284.
• Adnan, R., Ruslan, F.A., Samad, A.M., Zain, Z.M., 2012. Artificial Neural Network Modelling and Flood Water Level Prediction Using Extended Kalman Filter. 2012 IEEE International Conference on Control System, Computing and Engineering, 23-25 November 2012, Penang, Malaysia, 535-538.
• Akyen, T., Boye, C.B., Ziggah, Y.Y., 2016. Municipal Solid Waste Estimation and Landfill Lifespan Prediction. 4th UMaT Biennial International Mining and Mineral Conference, Tarkwa, Ghana, GG127-133.
• Al-Krargy, E.M., Mohamed, H.F., Hosney, M.M., Dawod, G.M., 2017. A High-Precison Geoid for Water Resources Management: A Case Study in Menofia Governorate, Egypt. National Water Research Center (NWRC) Conference on: Research and Technology Development for Sustainable Water Resources Management, Cairo, Egypt, 1-13.
• Akurut, M., Williams, P., Niwagaba, C.B., 2014. Potential Impacts of Climate Change on Precipitation Over Lake Victoria, East Africa, in the 21st Century. Water 6, 2634-2659.
• Amin, M.M., 2003. An up to Date Precise 5´ * 5´ Geoid Grid for Egypt by Collocation Tecnique. Port-Said Engineering Research Journal (PSERT), Published by faculty of Engineering, Suez Canal University, Port-Said, Egypt, 1-22.
• Andersen, O.B., Knudsen, P., 1998. Global marine gravity field from the ERS1 and Geosat geodetic mission. J Geophys Res, 103, 8129–8137.
• Arabelos, D., Tziavos, I.N., 1996. Combination of ERS1 and TOPEX altimetry for precise geoid and gravity recovery in the Mediterranean Sea. Geophysical Journal International 125, 285-302.
• Awange, J.L., Forootan, E., Kusche, J., Kiema, J.B.K., Omondi, P.A., Heck, B., Fleming, K., Ohanga, S O., Goncalves, R.M. 2013. Understanding the Decline of Water Storage Across the Ramsev-Lake Naivasha Using Satellite-Based Methods. Advances in Water Resources, 60, 7-23.
• Bekhtaovi, Z., Abdelkrim, M., Mohammed, D., Abed-Meraim, K., 2017. Maneuvering Target Tracking Using q-Learning Based Kalman Filter. The 5th International Conference on Electrical Engineering-Boumerdes (ICEE-B) October 29-31 2017, Boumerdes, Algeria, 1-5.
• Béné, C., 2007. Diagnostic study of the Volta Basin fisheries Part 1 - Overview of the fisheries resources. Volta Basin Focal Project Report No 6. World Fish Center Regional Offices for Africa and West Asia, Cairo Egypt, and CPWF, Colombo, Sri Lanka, 1-31.
• Béné, C., Russell, A.J.M., 2007. Diagnostic study of the Volta Basin fisheries. Part 1 - Livelihoods and poverty analysis, current trends and projections. Volta Basin Focal Project Report No 7. World Fish Center Regional Offices for Africa and West Asia, Cairo Egypt, and CPWF, Colombo, Sri Lanka, 1-67.
• Béné, C., Obirih-Opareh, N., 2009. Social and Economic Impacts of Agricultural Productivity Intensification: The Case of Brush Park Fisheries in Lake Volta. Agricultural Systems, 102, 1-10.
• Box, G.E.P., Jenkins, G.M., 1976. Time Series Analysis: Forecasting and Control, Holden-Day, Boca Raton, Fla, USA.
• Boye, P., Ziggah, Y.Y., 2020. A Short-Term Stock Exchange Prediction Model Using Box-Jenkins Approach. Journal of Applied Mathematics and Physics 8, 766-779. Braimah, L.I., 2003. Fisheries Management Plan for the Volta Lake, Ministry of Food and Agriculture, Directorate of Fisheries, Accra, Ghana, 1-77.
• Cazenave, A., Schaeffer, P., Berge, M., Brosier, C., Dominh, K., Genero, M.C. 1996. High-resolution mean sea surface computed with altimeter data of ERS1 (Geodetic Mission) and TOPEX/POSEION. Geophysical Journal International 125, 696-704.
• Chen, W., Hill, C. 2005. Evaluation Procedure for Coordinate Transformation. Journal of Surveying Engineering, 43-49.
• Coe, M.T., Birkett, C.M., 2004. Calculation of River Discharge and Prediction of Lake Height from Satellite Radar Altimetry: Example for the lake Chad Basin. Water Resources Research 40 (W10205), 1-11.
• Demir, V., Ulke Keskin, A., 2020. Height Modelling with Artificial Neural Networks (Samsun_Mert River Basin). Journal of Engineering Sciences, 6 (1), 54-61.
• Dickson, K. B., Benneh, G., 1977. A New Geography of Ghana. Longman Group, London, UK, 1-173.
• El-Shazly, A.H., 2005. The Efficiency of Neural Networks to Model and Predict Monthly Mean Sea Level from Short Spans Applied to Alexandria Tide Gauge. From Pharaohs to Geoinformatics, FIG Working Week 2005 and GSDI-8, Cairo, Egypt, April 16-21, 2005, 1-13.
• Farajzadeh, J., Fard, A.F., Lotfi, S., 2014. Modelling of Monthly Rainfall and Runoff of Urmia Lake Basin Using Feed-Forward Neural Network and Time Series Analysis Model. Water Resources and Industry 7 (8), 38-48.
• Fernandez, F.R.Q., Montero, N.B., III, R.B.P., Addawe, R.C., Diza, H.M.R., 2018. Forecasting Manila South Harbour Mean Sea Level Using Seasonal ARIMA Models. Journal of Technology Management and Business 5 (1), 1-7.
• Fernandez, F.R., III, R.P., Montero, N., Addawe, R., 2017. Prediction of South China Sea Level Using Seasonal ARIMA Models. Proceedings of the 13th IMT-GT International Conference on Mathematics, Statistics and their Applications (ICMSA 2017), 050018-1-050018-6.
• Grgic, S.M., Jukic, S., Nerem, R.S., Basic, S.T. 2017. The Assessment of an Impact of Mean Sea Level change in the Mid-Adriatic Region Based on Satellite Altimeter Records. 17th International Multidisciplinary Scientific Geoconference SGEM 2017, Section Photogrammetry and Remote Sensing, 263-270.
• Gyau-Boakye, P., 2001. Environmental Impacts of the Akosombo Dam and Effects of Climate Change on the Lake Levels. Environment, Development and Sustainability 3 (1), 17-29.
• Hassan, O., Elnazeer, E., Zomrawi, N., 2015. Application of Artificial Neural Network for Height Modelling. International Journal of Recent and Innovation Trends in Computing and Communication 3 (3), 1374-1377.
• Hirsch, P.E., Schillinger, S., Weigt, H., Burkhardt-Holm, P., 2014. A Hydro-Economic Model for Water Level Fluctuations: Combining Limnology with Economics for Sustainable Development of Hydropower. PLoS ONE, 9 (12), 1-26.
• Jian-Jun, S., 2003. Prediction and Analysis of Tides and Tidal Currents. International Hydrographic Review, 4 (2), 24-29.
• Kaloop, M.R., Beshr, A.A.A., Zarzoura, F., Ban, W.H., Hu, J.W., 2020. Predicting Lake Wave Height Based on Regression and Multi Input-Single Output Soft Computing Models. Arabian Journal of Geosciences 13 (591), 1-14.
• Kranenburg, W., Tiessen, M., Veenstra, J., de Graaff, R., Uittenbogaard, R., Bouffard, D., Sakindi, G., Umutoni, A., Van de Walle, J., Thiery, W., 2020. 3D-Modelling of Lake Kivu: Horizontal and Vertical Flow and Temperature Structure Under Spatially Variable Atmospheric Forcing. Journal of Great Lakes Research 46 (4), 947-960.
• Kim, Y., Bang, H., 2018. Introduction to Kalman Filter and Its Application. Published Book, Korea Advanced Institute of Science and Technology, Daejeon, South Korea, 1-19.
• Lawson, G.W., 1970. Lessons of the Volta - A New Man-made Lake in Tropical Africa. Africa Biological Conservation 2 (2), 91-96.
• Lemoine, F.G., Kenyon, S.C., Factor, J.K., Trimmer, R.G., Pavlis, N.K., Chinn, D.S., Cox, C., Klosko, S.M., Luthcke, S.B., Torrence, M.H., Wang, Y.M., Williamson, R.G., Pavlis, E.C., Rapp, R.H., Olson, T.R., 1998. The development of the join NASA GSFC and NIMA geopotential model EGM96. NASA Technical Paper, 1-4.
• Makwinja, R., Phiri, T., Kosamu, I.B.M., Kaonga, C.C., 2017. Application of Stochastic Models in Predicting Lake Malawi Water Levels. International Journal of Water Resources and Environmental Engineering 9 (9), 191-200.
• Makarynskyy, O., Kuhn, M., Makarynska, D., Featherstone, W.E., 2004. The Use of Artificial Neural Networks to Retrieve Sea Level Information from Remote Data Sources. IAG International Symposium: Gravity, Geoid and Space Missions, Porto, Portugal, August 30-September 3, 2004, Springer Verlag, Berlin, Germany, 1-4.
• Mitchum, G.T., 2000. An Improved Calibration of Satellite Altimetric Heights using Tide Gauge Sea Levels with Adjustment for land Motion. Marine Geodesy 23, 145-166.
• Mohinder, S.G. Angus, P.A., 2001. Kalman Filtering: Theory and Practice Using MATLAB. Wiley-Interscience Publication, New York, 1-410.
• Muthuwatta, L.P., 2004. Long Term Rainfall-Runoff-Lake Level Modelling of the Lake Naivasha Basin, Kenya. Published MSc Dissertation, Water Resources Survey and Environmental Systems Analysis and Management, International Institute for Geo-Information Science and Earth Observation, Enschede, The Netherlands, 1-89.
• Ndehedehe, C.E., Awange, J.L., Kuhn, M., Agutu, N.O., Fukuda, Y., 2017. Analysis of Hydrological Variability over the Volta River Basin using in-situ Data and Satellite Observations. Journal of Hydrology: Regional Studies, 12, 88-110.
• Ni, S., Cehn, J., Wilson, C.R., Hu, X., 2017. Long-Term Water Storage Changes of Lake Volta from GRACE and Satellite Altimetry and Connections with Regional Climate, Remote Sensing 9 (842), 1-15.
• Okwuashi, O., Olayinka, D.N., 2017. Tide Modelling Using the Kalman Filter. Journal of Spatial Science, 62(2), 353-365.
• Owusu, K., Waylen, P., Qiu, Y., 2008. Changing Rainfall Inputs in the Volta Basin: Implications for Water Sharing in Ghana. GeoJournal, 71(4), 201-210.
• Pashova, L., Popova, S., 2011. Daily Sea Level Forecast at Tide Gauge Burgas, Bulgaria Using Artificial Neural Networks. Journal of Sea Research 66, 154-161.
• Peprah, S.M., Yevenyo, Y.Y., Issaka, I., 2017. Performance Evaluation of the Earth Gravitational Model (EGM2008) – A Case Study. South African Journal of Geomatics 6 (1), 47-72.
• Poku-Gyamfi, Y., 2009. Establishment of GPS Reference Network in Ghana. Published MPhil Dissertation, Universitat Der Bundeswehr Munchen Werner Heisenberg-Weg 39, 85577, Germany, 1-218.
• Qi, L., Huang, J., Gao, J., Cui, Z., 2019. Modelling the Impacts of Bathymetric Changes on Water Level in China’s Largest Freshwater Lake. Water 11 (1469), 1-16.
• Rezaifard, E., Abbasi, P., 2017. Inertial Navigation System Calibration Using GPS Based on Extended Kalman Filter. 25th Iranian Conference on Electrical Engineering (ICEE), May 2017, Iran, 1-5.
• Ribeiro, M.I., 2004. Kalman and Extended Kalman Filters: Concept, Derivation and Properties. Institute for Systems and Robotics, Av. Rovisco Pais, 1, 14049-001 Lisboa Portugal, 1-44.
• Rodgers, C., Van de Giesen, N., Laube, W., Vick, P.L.G., Youkhana, E., 2007. The GLOWA Volta Project: A Framework for Water Resources Decision-making and Scientific Capacity Building in a Transnational West African Basin. In Integrated Assessment of Water Resources and Global Change: A North-South Analysis, Springer: Dordrecht, The Netherlands, 295-313.
• Rummel, R., Sanso, F., 1993. Satellite Altimetry in Geodesy and Oceanography. Springer-Verlag, Berlin Heidelberg, 1-469.
• Smith, K. A., Semazzi, F.H.M., 2014. The Role of the Dominant Modes of Precipitation Variability Over Eastern Africa in Modelling the Hydrology of Lake Victoria. Advances in Meteorology 2014 (516762), 1-11.
• Srivastava, P.K., Islam, T., Singh, S.K., Petropoulos, G.P., Gupta, M., Dai, Q., 2016. Forecasting Arabian Sea Level Rise Using Exponential Smoothing State Space Models and ARIMA from Topex and Jason Satellite Radar Altimeter Data. Meteorological Applications 23, 633-639.
• Thiery, W., Gudmundison, L., Bedka, K., Semazzi, F.H.M., Lhermitte, S., Willems, P., Van Lipzig, N. P. M., Seneviratne, S. I., 2017. Early Warnings of Hazardous Thunderstorms Over Lake Victoria. Environmental Research Letters 12, 1-9.
• Tolkatchev, A., 1996. Global Sea Level Observing System. Marine Geodesy, 19, 21-62.
• Turner, J.F., Iliffe, J.C., Ziebart, M.K., Jones, C., 2013. Global Ocean Tide Models: Assessment and use Within a Surface Model of Lowest Astronomical Tide. Marine Geodesy 36, 123-137.
• Tziavos, I.N., Vergos, G.S., Kotzev, V., Pashova, L., 2005. Mean Sea Level and Sea Level Variation Studies in the Black Sea and the Aegean. Gravity, Geoid and Space Missions, 254-259.
• Vainu, M., Terasmaa, J., 2014. Changes in Climate, Catchment Vegetation and Hydrogeology as the Causes of Dramatic Lake-Level Fluctuations in the Kurtna Lake District, NE Estonia. Estonia Journal of Earth Sciences 63 (1), 45-61.
• Vanderkelen, I., Van Lipzig, N.P.M., Thiery, W., 2018. Modelling the Water Balance of Lake Victoria (East Africa) – Part 2: Future Projections. Hydrology and Earth System Sciences, 22, 5527-5549.
• Vergos, G.S., Tziavos, I.N., Andritsanos, V.D., 2004. On the Determination of Marine Models by Least Squares Collocation and Spectral Methods using Heterogeneous Data. International Association of Geodesy Symposia 128, 1-382.
• Vergos, G.S., Tziavos, I.N., Andritsanos, V.D., 2003. On the Determination of Marine Geoid Models by Least Squares Collocation and Spectral Methods using Heterogeneous Data. Presented at Session G03 of the 2004 IUGG General Assembly, Sapporo, Japan, July 2-8, 2003, 1-5.
• Welch, G., Bishop, G., 2001. An Introduction to the Kalman Filter. Published Lecture Book, Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3175, 1-50.
• Wenzel, H.G., 1998. Ultra-high degree geopotential model GPM3E97 to degree and order 1800 tailored to Europe. Presented at the 2nd Continental Workshop on the geoid in Europe, Budapest, Hungary, 1-4.
• Yakubu, I., Ziggah, Y.Y., Peprah, M.S. 2018a. Adjustment of DGPS Data using artificial intelligence and classical least square techniques. Journal of Geomatics 12 (1), 13-20.
• Yakubu, I., Ziggah, Y.Y., Baafi, K.A., 2018. Prediction of Tidal Effect in Crustal Deformation Monitoring: A Geodetic Perspective. Ghana Journal of Technology 2 (2), 63-69.
• Yusof, F., Kane, I.L., Yusof, Z., 2013. Hybrid of ARIMA-GARCH Modelling in Rainfall Time Series. Journal Teknologi (Sciences and Engineering) 63 (2), 27-34.