Advancement of Science and Technology: Materials and Energy 3031336097, 9783031336096

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Green Energy and Technology

Bereket Haile Woldegiorgis Kibret Mequanint Muluken Zegeye Getie Eshetu Getahun Mulat Addisu Alemayehu Assegie   Editors

Advancement of Science and Technology Materials and Energy

Green Energy and Technology

Climate change, environmental impact and the limited natural resources urge scientific research and novel technical solutions. The monograph series Green Energy and Technology serves as a publishing platform for scientific and technological approaches to “green”—i.e. environmentally friendly and sustainable—technologies. While a focus lies on energy and power supply, it also covers “green” solutions in industrial engineering and engineering design. Green Energy and Technology addresses researchers, advanced students, technical consultants as well as decision makers in industries and politics. Hence, the level of presentation spans from instructional to highly technical. **Indexed in Scopus**. **Indexed in Ei Compendex**.

Bereket Haile Woldegiorgis Kibret Mequanint • Muluken Zegeye Getie Eshetu Getahun Mulat Addisu Alemayehu Assegie Editors

Advancement of Science and Technology Materials and Energy

Editors Bereket Haile Woldegiorgis Faculty of Mechanical and Industrial Engineering Bahir Dar Institute of Technology Bahir Dar, Ethiopia Muluken Zegeye Getie Faculty of Mechanical and Industrial Engineering Bahir Dar Institute of Technology Bahir Dar, Ethiopia

Kibret Mequanint Department of Chemical and Biochemical Engineering University of Western Ontario Ontario, Canada Eshetu Getahun Mulat Faculty of Chemical and Food Engineering Bahir Dar University Bahir Dar, Ethiopia

Addisu Alemayehu Assegie School of Materials Science and Engineering Bahir Dar University Bahir Dar, Ethiopia

ISSN 1865-3529 ISSN 1865-3537 (electronic) Green Energy and Technology ISBN 978-3-031-33609-6 ISBN 978-3-031-33610-2 (eBook) https://doi.org/10.1007/978-3-031-33610-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

It is a great honor for us to introduce the proceedings of the tenth edition of the EAI – International Conference on Advancements of Science and Technology (EAI ICAST 2022). EAI ICAST 2022 is an annual conference that takes place at Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia. The conference covers topical science and technology issues and has brought together researchers, engineers, developers, practitioners, scholars, scientists, and academicians from around the world. The technical program of EAI ICAST 2022 was organized from seven main tracks: Track 1, Sustainable Processes for Green Technologies; Track 2, Artificial Intelligence and Digitalization for Sustainable Development; Track 3, River Basin Management and Trans-boundary Cooperation; Track 4, Agro-Mechanization and Manufacturing Systems; Track 5, Advances in Electrical and Computer Engineering; Track 6, Advances in Green Energy Technologies; and Track 7, Materials for Emerging Technologies. We have received a total of 217 full papers, from which 90 papers were accepted in a peer-reviewed process. Each paper was reviewed by, on average, three reviewers who are experts in the area. After a thorough evaluation process, the final technical program included 64 high-quality full research papers for oral presentation sessions in the seven main conference tracks. In this book edition of the Green Energy and Technology volume, out of the 85 papers initially submitted to the tracks related to sustainable energy and advanced materials, 25 papers were accepted for publication. In addition to the technical sessions, the technical program featured two general session keynote and ten track session keynote speeches along with exhibitions and poster presentations. The two keynote speakers were Sossina Haile, from Materials Science and Engineering at Northwestern University, Evanston, IL, USA, and Asregedew Kassa Woldesenbet, from Construction Management at Ethiopian Institute of Architecture Building Construction and City Development, Addis Ababa University. The keynote speakers shared their research and industry experience, respectively, in electrochemistry and construction. We sincerely appreciate the work of the Steering Committee Chair and members; the Organizing Committee chair, Kibret Mequanint; and the Organizing Committee co-chairs, for v

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Preface

their constant support and guidance that ensured the success of the conference. It was also a great pleasure to work with such an excellent team of the Organizing Committee. We are grateful to the Technical Program Committee Chair and TPC Co-chairs, Zenamarkos Bantie, Abdulkerim Mohammed, Birhanu Kebede, Assefa Asmare, Teketay Mulu, Eshetu Getahun, and Addisu Alemayehu. The team performed exceptionally well to handle the peer-review process and design a highquality technical program. We are also grateful to the conference manager, Veronika Kissova, for her support and guidance throughout the process; EAI Publications Coordinator, Carlos Valiente, for his determined work to facilitate the publication; and all the authors who submitted their papers to the EAI ICAST 2022 conference. We believe that the EAI ICAST 2022 conference provided the platform for the scientific communities to discuss all science and technology aspects relevant to each track. We also expect that future EAI ICAST conferences will be as successful and stimulating, as indicated by the contributions presented in this volume. Bahir Dar, Ethiopia Ontario, Canada

Bereket Haile Woldegiorgis Kibret Mequanint Muluken Zegeye Getie Eshetu Getahun Mulat Addisu Alemayehu Assegie

Contents

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s Amhara Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Teshome B. Kotu, Venkata R. Ancha, Abdulkadir A. Hassen, and Solomon W. Fanta Investigation and Optimization of the Energy Band Gap of PAM/PVP/Al2O3 Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Negese Yazie Amogne, Delele Worku Ayele, and Nigus Gabbiye Habtu Characterization of False Banana Fiber as a Potential Reinforcement Material for Geopolymer Composites . . . . . . . . . . . . . . . Lulseged Belay Addis, Zenamarkos Bantie Sendekie, Nigus Gabbiye Habtu, Dirk W. Schubert, Judith A. Roether, and Aldo R. Boccaccini Drying Characteristics and Kinetic Study of Coffee Cherries (Coffee arabica) in Convective Hot Air Dryer . . . . . . . . . . . . . . Zelalem M. Salehudress, Nigus G. Habtu, Bimrew T. Admasu, Mulugeta A. Delele, and Aynadis M. Asemu Effect of Partial Replacement of Cement by Metakaolin on Engineering Properties of Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . Mitiku Damtie Yehualaw, Meseret Asrade Fentie, and Begashaw Worku Yifru

1

33

49

65

89

Engineering Properties of Concrete with Partial Replacement Cement and Coarse Aggregate by Waste Glass Powder and Steel Slag Aggregate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Yohannes Berhane Abreha, Begashaw Worku Yifru, and Mitiku Damtie Yehualaw

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Contents

Experimental Investigation on Properties of Mortar Containing Waste Marble as Fine Aggregate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Mitiku Damtie Yehualaw, Akelilu Musback Eshetie, Begashaw Worku Yifru, and Duy-Hai Vo Investigation on Utilizing of Steel Slag as a Partial Replacement of Natural River Sand as a Fine Aggregate in Concrete Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Mitiku Damtie Yehualaw, Degsera Fantahun, Solomon Asrat Endale, Shumet Getahun, and Duy-Hai Vo Effect of Filtering Techniques in Manufacturing of Optimal Topologies Using Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . 167 Hailu Shimels Gebremedhen, Dereje Engida Woldemichael, Fakhruldin M. Hashim, Khuram Altaf, and Hue Cin Chong Optimal Placement and Size of Multiple PV-DG Units for Power Loss Reduction and Voltage Profile Improvement in Dilla Distribution Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Assen Beshr Alyu and Tefera Terefe Yetayew Technological Development and Adoption Rates of Injera Baking Stoves: A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Lamesgin Addisu Getnet, Addisu Alamirew Meku, Muluken Zegeye Getie, and Mekete Mulualem Mebratu Experimental Investigation of Solar Cooker Using Parabolic Dish Collector for Indoor Cooking Application . . . . . . . . . . . . . . . . . . . 225 Mulat S. Alem, Bimrew T. Admasu, Temesgen A. Minale, Muluken Z. Getie, and Hailemariam M. Wassie Economic Feasibility Study of Biogas Production from Cladodes of Cactus (Opuntia ficus-indica) . . . . . . . . . . . . . . . . . . . . . . . . 243 Jemal Beshir Belay, Nigus Gabbiye Habtu, and Venkata Ramayya Ancha Zn(NO3)2.6H2O/Urea Composite Deep Eutectic Solvents Derived Through Facile and Green Synthesis Approach as an Electrolyte for Rechargeable Zinc Air Batteries . . . . . . . . . . . . . . 253 Fentahun Adamu Getie, Delele Worku Ayele, Nigus Gabbiye Habtu, Temesgen Atnafu Yemata, and Fantahun Aklog Yihun Experimental Investigation of Parabolic Solar Dish Concentrator-Based Solar Dryer Assisted with Thermal Energy Storage System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Hailemariam M. Wassie, Bimrew T. Admasu, Muluken Z. Getie, and Mulat S. Alem

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Performance Evaluation and Comparison of Mixed-Mode Natural Convection Solar Dryer With and Without Solar Air Heater for Green Banana Flour Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Betelihem Zemedkun Lodamo, Kamil Dino Adem, and Fiseha Kedir Jemal Evaluation of Planetary Ball Milling and Mild-Alkaline Pretreatment for Enhanced Fermentable Sugar Production from Sugarcane Bagasse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 Yalew Woldeamanuel Sitotaw, Nigus Gabbiye Habtu, and Tom Van Gerven Mechanical Response Prediction of Fiber-Reinforced Composites by Using Machine Learning Models: A Review . . . . . . . . . . . . . . . . . . . 329 Mekete Mulualem, Addisu Alamirew Meku, and Lamesgin Addisu Getnet Review on Recent Advancements in Mechanical Properties of Cross-Laminated Timber (CLT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 Tamirat Semu Yihune and Dawit Wagnebachew Nega Utilization of Starch from Waste Avocado Seed for the Manufacture of Sustainable Bio-Based Adhesive Reinforced with Clay Particles . . . . . 367 Asmare Tezera Admase, Mequannt Demeke Aynalem, Tessafa Abrham Ashagrie, Yemsrach Mintesnot Melaku, and Surafiel Aregahegn Agdew Investigating Rutting Performance Characteristics of Ethiopian Jute Fiber-Modified Asphalt Binder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 Yohannes Sisay Zeleke and Zelalem Alebel Arega Preparation of Thermal Insulation Material from Plastic Scrap, Sawdust, and Gypsum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Yemsrach Mintesnot Melaku, Mequanint Demeke Aynalem, Surafel Argahegn Agdew, Belete Adane Mandie, and Asmare Tezera Admase Partial Replacement of Cement with Marble and Ceramic Waste Powders in Normal Strength Concrete . . . . . . . . . . . . . . . . . . . . . 407 Abrham Gebre Tarekegn, Rihanna Nuru, and Yisihak Gebre Evaluation of the Impact of Wing Span and Wing Chord Length on the Aerodynamic Performance of Cessna 172-R Aircraft . . . . . . . . . . 419 Addisu Alamirew Meku, D. K. Nageswara Rao, Mekete Mulualem Mebratu, and Lamesgin Addisu Getnet

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Investigation of Existing Building Condition for Maintenance: Prolonging Its Service Life: The Case of CBE Bure Branch . . . . . . . . . . 435 Habtamu A. Tadesse, Seto M. Haile, Samuel D. Shiferaw, Tamirat S. Yihun, Alemayehu G. Gualu, and Nakachew A. Kebede Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s Amhara Region Teshome B. Kotu, Venkata R. Ancha, Abdulkadir A. Hassen, and Solomon W. Fanta

1 Introduction The Amhara Region is located in northwest Ethiopia, between 8°45′ and 13°45′ north latitudes and 36° 20′ and 40° 20′ longitudes. According to current information, the region lacks fossil fuel energy resources. The predominant energy source in the region is biomass, which is largely utilized for cooking. The method of utilizing biomass energy resources for cooking is through the use of inefficient and polluting three-stone fires. In rural families in the region, kerosene is still utilized as a source of light, leading to indoor air pollution. Agriculture, in the traditional sense, contributes significantly to the region’s economy. Despite having plenty of irrigation water, the region’s agricultural production is heavily dependent on the rainy season because modern agriculture is impractical without electricity. Only 17% of the region’s population resides in metropolitan areas with grid power. The remainder of the population lives in rural areas without access to electricity [1]. On the other hand, the Amhara Region is endowed with solar energy, a clean and sustainable source of energy. Each day, the region receives between 4.5 and 7.5 KWh/m2.day. With regard to solar energy potential, it is critical for the Amhara T. B. Kotu (✉) Faculty of Mechanical and Industrial Engineering, Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia V. R. Ancha Jimma Institute of Technology, Jimma University, Jimma, Ethiopia A. A. Hassen School of Mechanical and Industrial Engineering, Addis Ababa Institute of Technology, Addis Ababa University, Addis Ababa, Ethiopia S. W. Fanta Faculty of Chemical and Food Engineering, Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. H. Woldegiorgis et al. (eds.), Advancement of Science and Technology, Green Energy and Technology, https://doi.org/10.1007/978-3-031-33610-2_1

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T. B. Kotu et al.

Region to harness solar energy to support growth while also conserving the region’s valuable and vulnerable ecology. In order to utilize solar radiation, the specific site’s resources are essential for designing the energy conversion mechanisms. However, this information is not available in the majority of the region [1, 2]. Solar radiation that strikes the earth is the most fundamental renewable energy source in nature. Solar energy is one of the most important alternative energy sources that may provide a considerable quantity of energy to the planet. The growing interest in solar energy as a renewable energy source has raised the need for solar radiation and climatological data for use in system design and performance evaluation. Solar energy-related activities such as solar energy system design and construction, lighting buildings, open water evaporation, evapotranspiration from the land surface, crop growth, plant photosynthesis, irrigation water yields, irrigation drainage system design, and available water levels all need solar radiation data for a precise place. For various solar energy applications, including solar furnaces, concentrating collectors, and interior lighting of homes, solar engineers, building designers, agriculturists, and hydrologists need reasonably accurate data of the availability of the sun resource at any location. Despite the importance of solar radiation data, it is not widely available due to the cost of the measurement device, as well as the maintenance and calibration needs. As a result of these factors, solar radiation measurements are only collected in a few areas in impoverished nations such as Ethiopia. This leads to the establishment of several empirical models utilizing easily available meteorological parameters [2–5]. Different solar radiation models were proposed to estimate the global solar radiation using easily accessible metrological data in locations where solar radiation data are not available. The most frequent environmental factors for the estimation of solar radiation data are sunshine hours, maximum and lowest temperatures, cloud cover, and relative humidity. Among them, sunshine-based models are commonly accepted and they typically offer more precise results. Sunshine duration may be readily and precisely measured and data are widely available. The most widely used method is that of Angstrom who proposed a linear relationship between the ratio of average daily global radiation to the corresponding value on a completely clear day and the ratio of average daily sunshine duration to the maximum possible sunshine duration. The main challenge with this approach was the inability to obtain clear-day data. The Prescott letter proposed a method that substitutes extraterrestrial radiation for clear-day data. Following that, an Angstrom-Prescott model was developed and has been widely used since then [4, 6–10]. Girma Dejene implemented several equations to estimate the monthly average daily global solar radiation from sunshine hours and measured temperature in Tepi, Ethiopia. In his study, he concluded that the correlation models give better performance and can be used for estimating the global solar radiation in Tepi and its surroundings with similar climate conditions [11]. Despite the extensive work that has gone into developing empirical correlations for determining monthly averaged daily global solar radiation in locations across Ethiopia, no empirical correlations for Amhara Region have been found in the open literature, and the global solar radiation data in this region has not been thoroughly

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . .

3

examined. Therefore, the major objectives of this study are to estimate and validate the monthly average daily global radiation on a horizontal surface from sunlight using previously proposed models such as linear, quadratic, cubic, logarithmic, and exponential, and to select the most appropriate model for the stations investigated in this study.

2 Materials and Methods 2.1

Study Area

The study area consists of selected stations from the Amhara Regional State. The region shares an international border with Sudan in the northwest, as well as local borders with Tigray in the northeast, Afar in the east, Oromia in the south, and Benshangul Gumuz in the west (Fig. 1).

2.2

Data

The goal of this study was to use existing Angstrom models to predict global solar radiation in Ethiopia’s Amhara Region. To include representative locations in the

Fig. 1 Study area

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T. B. Kotu et al.

Table 1 Location and other parameters of the study area Stations Amdework Bahir Dar Chagni Dangla Debre Birhan Debre Markos Kombolcha Mehal Meda Mekane Selam Metema Mota Simada Sirinka Tistiska Wegel Tena Were Ilu

Latitude (N) 12.35° 11.36° 10.97° 11.25° 9.67° 10.33° 11.09° 10.23° 10.74° 12.78° 11.07° 11.30° 11.75° 12.77° 11.59° 10.60°

Longitude (E) 38.75° 37.24° 36.50° 36.85° 39.53° 37.74° 39.72° 39.68° 38.76° 36.41° 37.87° 38.18° 39.61° 38.80° 39.22° 39.43°

Elevation (m) 2421 1850 1583 2138 2840 2446 1831 3132 1827 685 2487 2209 2015 1589 3010 2699

Observation period 2016–2020 2011–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020 2016–2020

region, we requested sunshine duration and global solar radiation data for all firstclass (synoptic) stations in the Amhara Region from Ethiopia’s national meteorological agency. Multiple metrological variables, such as sunshine durations, precipitation, daily maximum and minimum temperatures, global solar radiation, and so on, are recorded by first-class stations. However, since the majority of stations are unable to record data on global solar radiation, we were unable to obtain complete data of many stations to cover the whole region. As a result, at least one station is chosen from each of the region’s 11 administrative zones. In this study, the measured daily data of the global solar radiation and sunshine duration at Amdework, Bahir Dar, Chagni, Dangla Debre Markos, Debre Brehan, Mehal Meda, Kombolcha, Mehal Meda, Mekane Selam, Metema, Mota, Simada, Tistiska, Wegel Tena, and Wereilu stations in the Amhara Region are gathered from the National Metrological Agency of Ethiopia. The row data from the stations are then processed to generate monthly average daily global radiation data. The collected row sunshine duration data were reprocessed to make it more convenient for the calculation. Ethiopia’s national metrological agency used a CMP3 Kipp-Zonen Pyranometer to measure global solar radiation. The metrological stations used a Campbell-Stokes sunshine recorder to record the sunshine hours. The measured metrological data cover 5 years, from 2016 to 2020. Table 1 provides detailed location information for the 16 stations under consideration.

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . .

5

Table 2 The regression models used in the study Models Linear Quadratic Cubic Logarithmic Exponential 1 Exponential 2 Power

2.3

Regression equations H/Ho = a + b(S/So) H/Ho = a + b(S/So) + c(S/So)2 H/Ho = a + b(S/So) + c(S/So)2 + d(S/So)3 H/Ho = a + b log(S/So) H/Ho = a exp(b * S/So) H/Ho = a + b exp(S/So) H/Ho = a(S/So)b

Source Angstrom-Prescott [9, 10] Aknoglu and Ecevit [12] Bhel et al. [13] Ampratwum and Dorvlo [14] Elagib and Mansell [15] Almorox and Hontoria [16] Kadir Bakirci [4]

Empirical Models

In this study, several regression models taken from the literature are investigated and validated in order to estimate monthly average daily global radiation from extraterrestrial radiation and duration of sunshine. Linear, quadratic, cubic, logarithmic, exponential 1, exponential 2, and exponent models are studied. The first recommended model for this study was the Angstrom-Prescott linear regression model (Table 2) [9, 10]. Akinoglu et al. [12] developed a quadratic regression model, which was used as the second model in this study. The cubic regression model, proposed by Bahel et al. [13] was chosen third in this study. The fourth regression model used in this study is logarithmic, and it was adopted by Ampratwum et al. [14]. Exponential 1 regression model which was proposed by Elagib et al. [15] took the fifth place in this study. Exponential 2 and power regression models, proposed by Almorex et al. [16] and Bakirci et al. [4] took the sixth and seventh place in this study, respectively. The correlation coefficients of the models under consideration are derived from the long-term average ratios of measured monthly global radiation to extraterrestrial radiation (H/Ho) and measured sunshine duration to daylight duration (S/So). The following formulas are used to calculate Ho and So [17]. Where H is the measured monthly average daily global radiation Ho is extraterrestrial radiation So is measured monthly average sunshine duration S is daylight hours

Ho =

24I sc 360n 1 þ 0:033 cos π 365

where Isc (Solar Constant) = 1367 W/m2 n is the day number of the year ϕ is the latitude of the stations

cos ϕ cos δ sin ωs þ

2πωs sin ϕ sin δ 360

ð1Þ

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δ is the solar declination angle ωs is the sunset hour angle δ = 23:15 sin 360

n þ 284 365

ωs = cos - 1 ð- tan ϕ tan δÞ

ð 3Þ

2 ω 15 s 2π S0 = ω 15 s

ð4Þ

ωs =

2.4

ð2Þ

ð5Þ

Testing Goodness of the Model

The regression coefficients of the 16 stations are obtained by a curve fitting method using Origin Pro software. The variables used in the software to find the regression coefficients are H/Ho versus S/So. To validate the models, various statistical methods such as coefficient of determination (R2), root mean square error (RMSE), percentage error (PE), mean percentage error (MPE), mean bias error (MBE), mean absolute bias error (MABE), and t-Statistic methods (tstat) are used [18, 19] (Fig. 2). The calculated and measured clearness index data set ratios were used in the statistical method to assess the goodness of each model. The coefficient of determination (R2) is a popular statistical method for determining the linear relationship between measured and estimated values. The following equation is used to calculate this value. n

R = 2

i=1 n i=1

ðH i,m - H i,c Þ2 H i,m - H i,m

2

ð6Þ

where Hi, m, Hi, c, and H i,m are the measured clearness index, estimated clearness index, and average of the measured clearness index. Taking the square root of the coefficient of determination R2 yields the correlation coefficient R. The coefficient of determination is used to determine how well the measured results are replicated by the model. The coefficient of determination has values ranging from 0 to 1. The correlation coefficient (R) is a statistical value that is used to determine the linear relationship between measured and predicted values. The correlation coefficient ranges from -1 to +1, and a value of 0 or close to 0 indicates that there is no relationship between the measured and predicted values. Similarly, if the value is ±1 or close to ±1, there is a strong relationship between the variables [20].

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . .

7

The percentage error is another statistical parameter used to determine the strength of the relationship between the measured and calculated values. Percentage error is the measured-estimated variations in an individual month and is calculated from the following equation. The values range from positive to negative, indicating over- and underestimation, respectively. According to the literature, the percentage error threshold value ranges between 10% and -10%. The model is accepted if the calculated value of the percentage error is within the range of the threshold value [21, 22].

Fig. 2 Annual variations in H/Ho and S/So measured at stations

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Fig. 2 (continued)

The mean percentage error (MPE), mean absolute percentage error (MAPE), root mean square error (RMSE), mean bias error (MBE), and mean absolute bias error (MABE) are other statistical methods used to evaluate the relationship between measured and predicted values by the model and are calculated from the following equations [15].

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . .

9

Fig. 2 (continued)

The root mean square error gives information on the correlations’ short-term performance by enabling a term-by-term similarity of the real deviation between estimated and measured values. The mean bias error test provides information on the long-term performance of the model. H i,m - H i,c 100 H i,m

PE = MPE = MAPE =

1 n 1 n

MSE =

n

H i,m - H i,c 100 H i,m

i=1 n

H i,m - H i,c H i,m

i=1

1 n

ð7Þ

100

ð8Þ ð9Þ

n

ðH i,m - H i,c Þ2 i=1

ð10Þ

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T. B. Kotu et al.

MBE = MABE =

1 n 1 n

n

ðH i,m - H i,c Þ

ð11Þ

ðjH i,m - H i,c jÞ

ð12Þ

i=1 n i=1

The t-statistic is another statistical method used in this study to test the performance of the models. This test compares models while also indicating whether or not a model’s estimates are statistically significant at a given confidence level. The confidence level in the tsta is taken as 0.05. It is calculated from the following equation. t sta =

ðn - 1ÞMBE2 RMSE2 - MBE2

ð13Þ

Except for R and R2, the ideal values of the aforementioned statistical methods are 0 or close to 0 [23].

3 Results and Discussion 3.1

The Stations’ Model Performance

Amdework The calculated correlation coefficient of the linear, quadratic, cubic, exponential 1, logarithmic, exponential 2, and exponent regression models obtained from Amdework’s H/Ho and S/So data sets ranges from 0.9065 (exponent 2) to 0.9194 (cubic). The correlation coefficients obtained from the measured and calculated H/ Ho clearness index are the same as the value obtained from the H/Ho and S/So data sets. The cubic model yielded the highest value of the correlation coefficient for this station which is 0.9194. The lowest percentage error -16.7144 is obtained from the exponential 2 regression model while the highest percentage error 8.0410 is obtained from the logarithmic model. All the positive values of the percentage error are within the 10% threshold. On the other hand, all the lowest percentage error values are below the threshold value of -10%. The best value of the percentage error for this station is -13.4486 and 6.1970 obtained from the cubic regression model. The cubic model yields the lowest values of statistical tests such as MPE, MAPE, MBE, MABE, and RMSE for this station, which are -0.4155, 5.3277, -0.0001, 0.0328, and 0.0493, respectively (see Table 4). Bahir Dar As shown in Table 3, the cubic model yields the highest correlation coefficient of 0.9809, while the logarithmic model yields the lowest value of 0.9569 from the data

Dangla

Chagni

Bahir Dar

Station Amdework

Model Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1

a 0.2259 0.1733 0.7772 0.3089 0.7383 0.0080 0.7651 0.2227 0.2637 0.5409 0.2816 0.6332 0.04865 0.6512 0.2263 0.258 0.5549 0.2838 0.6305 0.05496 0.648 0.2159 0.2934 0.0219 0.2903

Table 3 The regression models’ Angstrom coefficients for stations 0.5592 0.7497 -2.6110 0.9739 0.3139 0.2993 0.5831 0.4445 0.2983 -1.198 0.8995 0.256 0.238 0.5367 0.4377 0.3246 -1.278 0.8862 0.2522 0.2344 0.5285 0.5756 0.2739 1.904 1.077

b

c

0.2703 -2.816

0.09212 2.821

0.119 2.664

-0.1575 5.64

1.859

-1.482

-1.381

-3.16

d

R2 0.8341 0.8359 0.8454 0.8223 0.8253 0.8218 0.8348 0.9772 0.9784 0.9809 0.9776 0.9569 0.9772 0.9709 0.9778 0.9785 0.9814 0.9774 0.9592 0.9769 0.9721 0.9348 0.9382 0.9401 0.9384

(continued)

R 0.9133 0.9143 0.9194 0.9068 0.9084 0.9065 0.9137 0.9885 0.9891 0.9904 0.9888 0.9782 0.9886 0.9853 0.9888 0.9892 0.9907 0.9886 0.9794 0.9884 0.9859 0.9669 0.9686 0.9696 0.9687

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . . 11

Kombolcha

Debre Markos

Debre Birhan

Station

Table 3 (continued)

Model Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power

b 0.2994 0.3271 0.5854 0.6966 -0.654 4.208 1.243 0.3876 0.3876 0.7119 0.5754 0.2128 1.838 1.104 0.2847 0.3294 0.5804 0.5874 0.8911 -28.37 1.448 0.3093 0.3093 0.9256

a 0.7254 -0.0414 0.7633 0.1677 0.5421 -0.3312 0.2731 0.7906 -0.1283 0.8472 0.2112 0.2988 0.0470 0.2813 0.7185 -0.0536 0.7581 0.0291 -0.06526 6.066 0.1589 0.5736 -0.1842 0.6127

c

-0.2388 45.67

-2.876

1.143 -7.453

1.97

4.859

-23.71

d

R2 0.9089 0.9384 0.9273 0.8984 0.9487 0.9579 0.9300 0.8341 0.9248 0.8823 0.9571 0.9637 0.9676 0.9641 0.9177 0.9639 0.9452 0.7887 0.7995 0.8407 0.7927 0.7973 0.7953 0.7988

R 0.9534 0.9687 0.9629 0.9478 0.9740 0.9579 0.9643 0.9113 0.9617 0.9393 0.9783 0.9817 0.9836 0.9819 0.9580 0.9818 0.9722 0.8937 0.8941 0.9169 0.8903 0.8929 0.8918 0.8938

12 T. B. Kotu et al.

Mota

Metema

Mekane Selam

Mehal Meda

Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponen 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2

-0.0361 -0.9022 -1.346 0.2097 0.8863 -0.3911 0.9564 0.1993 0.1932 0.0113 0.271 0.7255 -0.0848 0.7673 0.3591 0.2311 -0.1579 0.3927 0.6658 0.2395 0.6729 0.2868 0.1469 0.1581 0.3515 0.7137 0.1364 0.9924 3.78 5.896 1.6273 0.6273 0.5198 1.048 0.5991 0.6277 1.958 1.155 0.2773 0.3451 0.5823 0.3287 0.7689 2.767 0.574 0.1986 0.1716 0.3544 0.4517 0.8968 0.8438 0.7628 0.2906 0.2294 -0.2548

-0.3508 -3.607

-0.0282 -2.846

-2.191 -5.512

-0.040

1.7

1.801

1.715

0.8147 0.8380 0.8381 0.7941 0.8284 0.8029 0.8139 0.9716 0.9716 0.9780 0.9634 0.9497 0.9653 0.9694 0.9283 0.9479 0.9533 0.9165 0.9486 0.9061 0.9438 0.8433 0.8449 0.8449 0.8297 0.8450 0.8263 (continued)

0.9026 0.9154 0.9155 0.8912 0.9102 0.8960 0.9022 0.9857 0.9857 0.9889 0.9816 0.9745 0.9825 0.9846 0.9635 0.9736 0.9764 0.9573 0.9739 0.9519 0.9715 0.9183 0.9192 0.9192 0.9109 0.9192 0.9090

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . . 13

Tistiska

Sirinka

Simada

Station

Table 3 (continued)

Model Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent1 Logarithmic Exponent 2 Power

b 0.5017 0.6107 0.7659 6.829 1.039 0.3409 0.3347 0.6062 0.3007 1.7099 -1.3192 0.7018 0.3953 0.1676 0.4043 0.6345 0.8479 9.257 1.042 0.3895 0.3343 0.6537

a 0.7254 0.2221 0.1792 -0.91 0.3121 0.7734 -0.0275 0.808 0.2501 -0.1424 0.4135 0.2821 0.5200 0.1241 0.5306 0.2051 0.1409 -1.599 0.3106 0.7949 -0.0287 0.8228 -0.1689 -13.3

-1.2349 4.1842

-0.132 -10.87

c

6.086

6.672

-3.188

d

R2 0.8433 0.8571 0.8579 0.8741 0.8493 0.8540 0.8497 0.8586 0.7702 0.8368 0.8385 0.7584 0.7960 0.7531 0.7863 0.9262 0.9269 0.9341 0.9210 0.9259 0.9212 0.9272

R 0.9183 0.9258 0.9262 0.9350 0.9216 0.9241 0.9218 0.9266 0.8776 0.9147 0.9157 0.8708 0.8922 0.8678 0.8867 0.9624 0.9628 0.9665 0.9596 0.9622 0.9598 0.9629

14 T. B. Kotu et al.

Were Ilu

Wegel Tena

Linear Quadratic Cubic Exponent1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent1 Logarithmic Exponent 2 Power

0.1502 0.1624 -0.067 0.2759 0.7935 -0.110 0.8326 0.2913 0.1002 0.1617 0.366 0.7854 0.0674 0.8129

0.6965 0.655 1.875 1.18 0.4119 0.3682 0.7363 0.5532 1.277 0.8908 0.872 0.2954 0.3014 0.5019 -0.6335 0.1115

0.0332 -2.026

-0.4486

1.114

0.911 0.911 0.911 0.905 0.896 0.907 0.908 0.7977 0.8320 0.8323 0.7676 0.8275 0.7626 0.8196

0.9542 0.9542 0.9545 0.9516 0.9464 0.9524 0.9536 0.8931 0.9122 0.9123 0.8761 0.9097 0.8733 0.9053

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . . 15

16

T. B. Kotu et al.

set of H/Ho and S/So. All the values of the percentage error calculated for this station are below the threshold value of ±10%. For the Bahir Dar station, the PE calculated using the cubic model is -3.8378 and 2.6310. The cubic model calculates the minimum value of the statistical tests (MPE, MAPE, MBE, MABE, and RMSE) as 1.6386, -0.0709, 0.0087, -0.001, and 0.0126. Chagni The maximum and minimum correlation coefficient values for the Chagni station from the H/Ho and S/So data sets are 0.9814 for the cubic model and 0.9592 for the logarithmic model (Table 3). As shown in Table 4, all of the values of the percentage error calculated by the models are less than ±10% threshold and range from -5.9289 to 3.8764. The MAPE, MPE, MABE, MBE, and RMSE have the lowest values of 1.6001 (cubic), -0.0216 (exponential 2), 0.0085 (cubic), 0 (all), and 0.0123 (logarithmic), respectively. Dangla For the Dangla station, the highest value of the correlation coefficient obtained by data set of H/Ho and S/So is 0.9696 by cubic model and the lowest value is 0.9533 by logarithmic model (Table 3). Table 4 shows that the PE values range between 12.1253 for the logarithmic model and 7.8186 for the exponential 2 model. The PE values obtained from the cubic model, -8.0170 and 6.6109, are within the 10% threshold. The positive values of the entire PE model are all within the threshold value, but the negative values of the PE obtained by logarithmic and exponent are slightly beyond. This implies that the values of global solar radiation are underestimated in these models. The Dangla station has the lowest MAPE, MPE, MAPE, MBE, and RMSE values of 3.0003 (cubic), -0.1972 (logarithmic), 0.0170 (cubic), 0.0000 (linear, quadratic, and exponential 2), and 0.0248 (exponential 1 and exponential 2), respectively. The coefficient of determination values of the linear, quadratic, cubic, exponential 1, logarithmic, exponential, and exponent models ranges from 0 and 1. Debre Birhan The cubic model yielded the highest correlation coefficient of 0.9740, while the logarithmic model yielded the lowest value of 0.9113 as shown in Table 3. For the Debre Birhan station, the negative value of the PE ranges from -16.7440 to -9.0981. The value of the PE which is close to the threshold value is -9.8585 and 5.6236 obtained by the cubic model. The PE calculated from the quadratic model is -9.0981 and 8.4767, both of which are within the range of the threshold value. Other statistical tests, such as MAPE, MPE, MAPE, MBE, and RMSE, have the lowest values of 3.181 (cubic), -0.0824 (exponential 1), 0.0236 (cubic), 0 (logarithmic), and 0.0270 (cubic), respectively. The cubic model shows the highest coefficient of determination of 0.9579. Debre Markos The calculated correlation coefficient of the models obtained from the data sets of H/Ho and S/So varies between 0.9580 (logarithmic) and 0.9840 (cubic). Table 3 shows that the cubic regression model has the highest value of 0.9840 for the Debre

Dangla

Chagni

Bahir Dar

Stations Amdework

Model Linear Quadratic Cubic Exponent 1 Logarithmic Exponent2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent1

PEmin -15.4112 -14.5969 -13.4486 -16.4733 -12.9277 -16.7144 -14.4571 -4.2379 -3.5189 -3.8372 -3.0130 -6.3220 -2.8670 -5.2058 -3.9064 -3.3554 -3.8113 -2.7832 -5.9289 -2.8312 -4.8867 -9.6694 -8.3745 -8.0170 -8.1688 PEmax 6.9923 6.7189 6.1970 7.6190 8.0410 7.5741 6.7173 2.7375 2.9321 2.6310 3.2350 3.9939 3.31487 3.2231 2.8514 2.9997 2.4930 3.1963 3.8764 3.2618 3.0878 6.9415 7.7797 6.6109 7.8186

Table 4 The regression models’ statistical results for stations MAPE 5.8604 6.0062 5.3277 5.7552 6.4492 5.6656 6.0817 1.7788 1.7237 1.6386 1.7400 2.7476 1.7571 2.2030 1.6899 1.6689 1.6011 1.7285 2.6091 1.7473 2.1139 3.3054 3.1437 3.0003 3.1694

MPE -0.4452 -0.4208 -0.4155 -0.5745 -0.4340 -0.5389 -0.4122 -0.0470 -0.0469 0.0357 -0.0458 -0.0709 -0.0366 -0.0112 -0.0324 -0.0304 -0.0375 -0.0609 -0.0543 -0.0373 -0.0216 -0.1497 -0.1634 -0.0977 -0.1545

MABE 0.0354 0.0361 0.0328 0.0348 0.0384 0.0384 0.0365 0.0094 0.0093 0.0087 0.0094 0.0137 0.0095 0.0112 0.0090 0.0090 0.0085 0.0094 0.0130 0.0095 0.0108 0.0187 0.0176 0.0170 0.0177

MBE 0.0001 0.0000 -0.0001 -0.0001 0.0000 0.0000 0.0001 -0.0001 0.0000 0.0004 0.0000 -0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0004 0.0001

RMSE 0.0457 0.0479 0.0493 0.0473 0.0469 0.0473 0.0456 0.0127 0.0130 0.0130 0.0126 0.0174 0.0127 0.0143 0.0123 0.0127 0.0126 0.0124 0.0166 0.0125 0.0138 0.0255 0.0262 0.0274 0.0248

R 0.9133 0.9143 0.9194 0.9068 0.9084 0.9065 0.9137 0.9885 0.9891 0.9904 0.9887 0.9782 0.9886 0.9853 0.9888 0.9892 0.9907 0.9886 0.9794 0.9884 0.9859 0.9669 0.9686 0.9696 0.9687

(continued)

t 0.0038 0.0033 0.0055 0.0055 0.0020 0.0034 0.0039 0.0155 0.0072 0.1002 0.0101 0.0125 0.0206 0.0153 0.0031 0.0121 0.0045 0.0098 0.0012 0.0204 0.0025 0.0031 0.0036 0.0441 0.0139

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . . 17

Mehal Meda

Kombolcha

Debre Markos

Debre Birhan

Stations

Model Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear

Table 4 (continued)

PEmin -12.1253 -8.2834 -10.6804 -13.9712 -9.0981 -9.8585 -11.9416 -16.7440 -12.4215 -14.5933 -7.5877 -6.5228 -7.1576 -6.5349 -11.8494 -6.4106 -9.2659 -12.3886 -12.7594 -15.2646 -11.6641 -13.0609 -11.8931 -12.4308 -9.0633 PEmax 5.1014 7.7667 6.1702 7.1207 8.4767 5.6236 7.7642 9.9926 7.3713 9.1573 5.4411 4.9861 4.1111 4.8026 7.4609 4.6385 6.0854 8.7400 8.4861 7.7272 9.2565 8.2903 9.0877 8.7134 11.7381

MAPE 4.3966 3.1482 3.7951 5.0942 3.3497 3.1817 4.1286 6.4060 4.2745 5.6199 3.2662 3.0899 2.5029 3.0551 4.6504 3.0648 3.7684 5.6237 5.5182 4.7509 5.8124 5.4330 5.7575 5.6092 6.0717

MPE -0.1972 -0.1607 -0.1069 -0.2332 -0.2080 -0.1309 -0.0824 -0.3848 -0.1669 -0.1095 -0.0975 -0.1312 -0.0560 -0.1280 -0.1701 -0.1271 -0.0004 -0.4327 -0.4198 -0.7355 -0.4783 -0.4373 -0.4395 -0.4280 -0.5059

MABE 0.0241 0.0176 0.0210 0.0293 0.0190 0.0180 0.0236 0.0370 0.0246 0.0320 0.0185 0.0173 0.0146 0.0171 0.0253 0.0172 0.0207 0.0232 0.0227 0.0189 0.0241 0.0223 0.0239 0.0232 0.0386

MBE 0.0000 0.0000 0.0001 0.0000 -0.0002 0.0002 0.0002 0.0000 0.0001 0.0004 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0003 0.0000 0.0000 -0.0017 -0.0001 -0.0001 0.0000 0.0000 0.0000

RMSE 0.0302 0.0248 0.0270 0.0375 0.0281 0.0270 0.0312 0.0480 0.0323 0.0405 0.0247 0.0240 0.0240 0.0226 0.0342 0.0227 0.0280 0.0298 0.0313 0.0297 0.0302 0.0299 0.0300 0.0298 0.0479

R 0.9533 0.9687 0.9629 0.9478 0.9740 0.9787 0.9643 09133 0.9617 0.9393 0.9783 0.9817 0.9836 0.9819 0.9580 0.9818 0.9722 0.8937 0.8941 0.9169 0.8903 0.8929 0.8918 0.8938 0.9026

t 0.0033 0.0064 0.0178 0.0035 0.0193 0.0220 0.0265 0.0020 0.0052 0.0356 0.0006 0.0010 0.0423 0.0053 0.0027 0.0057 0.0325 0.0035 0.0002 0.1875 0.0104 0.0067 0.0012 0.0008 0.0002

18 T. B. Kotu et al.

Mota

Metema

Mekane Selam

Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power

-11.8894 -11.6709 -11.3411 -10.0380 -9.9461 -9.2303 -6.2915 -6.3923 -6.3268 -12.0038 -8.7231 -10.5548 -7.0993 -3.6646 -4.7981 -4.5365 -4.5029 -4.3494 -4.8703 -3.9493 -11.5644 -10.7601 -10.7605 -11.8576 -10.7698 -12.0244 -11.1641 10.8127 11.0435 12.2998 11.4202 12.0048 11.8130 4.2902 4.3785 5.6018 5.8810 6.9723 5.6689 5.2148 3.6497 2.8356 3.2753 3.9699 2.9488 4.2162 3.1828 5.5679 5.4077 5.3953 5.7202 5.4812 5.7361 5.5154

5.5027 5.2608 6.5270 5.6315 6.3393 6.1216 3.5821 3.5347 2.6855 4.7990 4.9877 4.5964 3.1260 2.5523 1.7668 1.6540 2.7708 1.9085 2.9208 2.1425 3.7559 3.7884 3.7891 3.7468 3.7720 3.7376 3.7661

-0.4111 -0.2600 -0.6210 -0.4490 -0.5555 -0.5632 -0.1798 -0.1880 -0.0963 -0.4933 -0.0565 -0.3712 0.0083 -0.0736 -0.0438 -0.0095 -0.1103 -0.0469 -0.0922 -0.0608 -0.2107 -0.2003 -0.2042 -0.2487 -0.1978 -0.2411 -0.2051 0.0342 0.0340 0.0408 0.0363 0.0399 0.0387 0.0201 0.0199 0.0160 0.0239 0.0269 0.0232 0.0186 0.0146 0.0103 0.0098 0.0158 0.111 0.0166 0.0124 0.0225 0.0228 0.0228 0.0224 0.0227 0.0223 0.0226

-0.0002 0.0007 0.0001 0.0000 0.0000 -0.0001 0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000 0.0002 0.0000 0.0000 0.0002 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0472 0.0501 0.0505 0.0461 0.0494 0.0480 0.0252 0.0266 0.0249 0.0287 0.0336 0.0279 0.0262 0.0165 0.0148 0.0149 0.0178 0.0140 0.0189 0.0146 0.0308 0.0318 0.0337 0.0316 0.0301 0.0319 0.0303

0.9154 0.9155 0.8912 0.9102 0.8960 0.9022 0.9857 0.9857 0.9889 0.9816 0.9745 0.9825 0.9846 0.9635 0.9736 0.9764 0.9573 0.9739 0.9519 0.9715 0.9156 0.9192 0.9192 0.9109 0.9192 0.9090 0.9183 (continued)

0.0126 0.0488 0.0037 0.0020 0.0002 0.0098 0.0081 0.0061 0.0029 0.0085 0.0030 0.0041 0.0285 0.0086 0.0082 0.0417 0.0077 0.0063 0.0172 0.0026 0.0052 0.0010 0.0031 0.0027 0.0003 0.0012 0.0023

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . . 19

Wegel Tena

Tistiska

Sirinka

Stations Simada

Table 4 (continued)

Model Linear Quadratic Cubic Exponenti 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1 Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponent 1

PEmin -9.2132 -9.6920 -12.0558 -11.1501 -11.4823 -10.8097 -10.0582 -6.0089 -6.3036 -6.5290 -5.9378 -6.0936 -5.9381 -6.0456 -7.0657 -6.5475 -5.1696 -8.3295 -5.5922 -8.1538 -6.5363 -8.2554 -8.2884 -9.1733 -8.9824 PEmax 12.1519 11.9646 9.4047 12.3383 10.8444 12.4254 11.73 3.9998 3.6168 3.3963 4.0713 3.9014 4.1592 3.9527 6.3967 6.3005 3.8632 6.3834 5.7879 6.4608 6.2271 6.9266 6.8784 6.9273 6.4773

MAPE 4.8437 4.9314 4.6685 4.9488 5.3753 4.8957 5.0036 2.2217 1.7455 1.6446 2.2740 2.0768 2.2965 2.1372 3.3634 3.4535 3.3609 3.2992 3.5974 3.3073 3.4481 4.5139 4.4847 4.5128 4.4341

MPE -0.4201 -0.4030 -0.0855 -0.4904 -0.3778 -0.4820 -0.3994 -0.0910 -0.0599 -0.0585 -0.1006 -0.0785 -0.1000 -0.0863 -0.1637 -0.1478 -0.3808 -0.1862 -0.1394 -0.1965 -0.1560 -0.2509 -0.2552 -0.2601 -0.3798

MABE 0.0274 0.0279 0.0266 0.0278 0.0309 0.0275 0.0284 0.0096 0.0076 0.0072 0.0098 0.0090 0.0099 0.0093 0.0206 0.0212 0.0209 0.0202 0.0223 0.0202 0.0212 0.0278 0.0277 0.0275 0.0272

MBE 0.0000 0.0000 0.0016 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0017 0.0000 0.0000 -0.0001 0.0000 0.0000 0.0000 0.0000 -0.0003

RMSE 0.0390 0.0410 0.0410 0.0401 0.0395 0.0400 0.0388 0.0139 0.0124 0.0130 0.0143 0.131 0.0144 0.0134 0.0257 0.0269 0.0272 0.0266 0.0257 0.0265 0.0255 0.0348 0.0367 0.0388 0.0358

R 0.9258 0.9262 0.9349 0.9216 0.9241 0.9218 0.9266 0.8776 0.9147 0.9157 0.8708 0.8922 0.8678 0.8867 0.9624 0.9628 0.9665 0.9596 0.9622 0.9598 0.9629 0.9542 0.9542 0.9545 0.9516

t 0.0013 0.0023 0.1331 0.0013 0.0009 0.0046 0.0011 0.0009 0.0009 0.0005 0.0027 0.0002 0.0024 0.0011 0.0029 0.0036 0.2036 0.0055 0.0030 0.0112 0.0028 0.0003 0.0007 0.0034 0.0271

20 T. B. Kotu et al.

Were Ilu

Logarithmic Exponent 2 Power Linear Quadratic Cubic Exponential 1 Logarithmic Exponential 2 Power

-9.0661 -8.6138 -8.1181 -13.8842 -13.1038 -12.5524 -15.3184 -14.2551 -14.9301 -13.9761 8.2680 6.4905 7.1231 14.0643 11.8718 11.7916 14.7971 12.3259 14.9719 13.1782

5.0448 4.3404 4.6605 5.4258 5.2049 5.1409 6.2177 5.2019 6.3437 4.8169

-0.2342 -0.3142 -0.2179 -0.5966 -0.4218 -0.4215 -0.8060 -0.4381 -0.7365 -0.5452 0.0305 0.268 0.0285 0.0321 0.0309 0.0307 0.0362 0.0307 0.0372 0.0289

0.0000 -0.0001 0.0000 0.0000 0.0000 0.0000 -0.0002 0.0000 0.0000 -0.0001

0.0376 0.0355 0.0351 0.0477 0.0458 0.0486 0.0512 0.0441 0.0517 0.0451

0.9464 0.9524 0.9536 0.8931 0.9122 0.9123 0.8761 0.9097 0.8733 0.9053

0.0018 0.0075 0.0043 0.0013 0.0007 0.0004 0.0160 0.0035 0.0008 0.0077

Prediction of Global Solar Radiation Based on Sunshine Hours in Ethiopia’s. . . 21

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T. B. Kotu et al.

Markos station. The percentage error values for this station range from -11.8494 to 7.4609 (logarithmic). The cubic model ensures optimal PE values of -7.1576 and 4.1111. The logarithmic model yields the highest PE error as -11.8490 to 7.4609. The regression models’ lowest values for MAPE, MPE, MAPE, MBE, and RMSE are 2.5029 (cubic), -0.056 (cubic), 0.0146 (cubic), 0 (all models), and 0.0240 (cubic), respectively. The cubic model has the highest coefficient of determination of all models, with a value of 0.9676, and the logarithmic model has the lowest value, with a value of 0.9177 (Table 4). Kombolcha The cubic model has the highest correlation coefficient of all the models (0.9170), while the exponential 1 model has the lowest (0.8900), as determined by the H/Ho and S/So data sets (Table 3). The negative values of all the models are beyond the threshold value of -10% with the lowest value as -11.6641 from the calculation of the exponential 2 model while the highest value in this set is -15.2646 by the cubic model. The lowest positive value of the PE error is calculated as 7.7272 by the cubic model. According to the exponential 2 model, the best percentage error value for Kombolcha station is -1.6641 and 9.2565. The models’ lowest MAPE, MPE, MAPE, MBE, and RMSE values are 4.7509 (cubic), -0.4198 (quadratic), 0.0189 (cubic), 0 (all models), and 0.0297 (cubic), respectively. The cubic model obtains the highest coefficient of determination from the H/Ho and S/So data set of 0.9169, while the exponential 2 model obtains the lowest value of 0.8918. Mehal Meda The cubic model yields the highest correlation coefficient of 0.9155 for the Mehal Meda station, while the exponential 2 model yields the lowest value of 0.8912. The PE value varies between -11.8890 for the quadratic model and 12.3000 for the exponential 2 model, as shown in Table 4. According to the linear model, the optimal PE value for this station is -9.0633 and 11.7381. The lowest results from statistical tests such as MAPE, MPE, MAPE, MBE, and RMSE are 5.2608 (cubic), -0.2600 (cubic), 0.034 (cubic), 0 (all), and 0.0480 (power) model, respectively. The cubic model yielded the highest correlation coefficient of 0.9155 from the data set of measured and predicted global solar radiation (Table 4). The highest coefficient of determination calculated for the Mehal Meda station by the cubic model is 0.9155, which is the same as the value obtained by the data set of measured and calculated solar radiation. Mekane Selam According to the results in Table 3, the cubic model has the highest value of the correlation coefficient of the Mekane Selam station at 0.9889. The logarithmic model yielded the lowest correlation coefficient for this station, which is 0.9745. Table 4 shows that the PE value ranges between -12.0038 (exponential 2) and 6.9723 (logarithmic). Except for the exponential 1 and exponential 2 models, all of the PE values are within the ±10% threshold. The deviation of these values from the threshold value is not significant, and based on this statistical test, all of the models adequately fit the data and can be used to determine global solar radiation under

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23

similar climatic conditions. According to the MAPE, MPE, MAPE, MBE, and RMSE statistical tests, the models’ lowest values are 2.6855 (cubic), 0.0083 (power), 0.0160 (cubic), 0 (all), and 0.02520 (linear). The highest value of the coefficient of determination from the data sets H/Ho and S/So is 0.9780 by the cubic model. The cubic and quadratic models obtained the highest correlation coefficient from the data set of measured and predicted values of global solar radiation from the entire models, which is 0.9857. Metema The cubic model yielded the highest value of the correlation coefficient obtained from the data set of H/Ho and S/So, which is 0.9764, as shown in Table 3. The lowest correlation coefficient obtained from each regression, on the other hand, is 0.9573 for the Metema station. The correlation coefficients for each station are all greater than 0.9500, indicating that there is a strong positive relationship between sunshine duration and global solar radiation. The PE value of this station ranges between 4.8703 and 4.2162 based on the results of the exponential 2 model. The optimal value of the PE for this station is the one obtained from the linear model and it is between -3.6646 and 3.6497. All of the percentage error values obtained from the entire models are within the ±10% threshold. According to the calculated data in Table 4, the MAPE, MPE, MAPE, MBE, and RMSE models have the lowest values of 1.6540 (cubic), -0.0095 (cubic), 0.0098 (cubic), 0 (all), and 0.0140 (logarithmic), respectively. The cubic model yielded 0.9533 as the highest coefficient of determination for the station from the data set of H/Ho and S/So. Metema station has the highest correlation coefficient of 0.9764 obtained from the cubic model from the data set of measured and predicted global solar radiation. Mota The highest value of the correlation coefficient from the data set of H/Ho and S/So for Mota station is 0.91912 by quadratic, cubic, and logarithmic models. The correlation coefficient for this station has the lowest value of 0.9090 across all models. According to the PE statistical test, the value ranges between -12.0244 and 5.7361, both by the exponential 2 model. The negative percentage value for this station from the entire model exceeds the -10% threshold. On the other hand, all of the positive PE values for this station are within the 10% threshold. The cubic model yields the best PE values for this station, which are -10.7610 and 5.3930. The lowest values for statistical tests such as MAPE, MPE, MAPE, MBE, and RMSE are 3.7468 (exponential 1), 0.1978 (logarithmic), 0.0223 (exponential 2), 0 (all), and 0.0301 (logarithmic), respectively. The highest coefficient of determination obtained from the H/Ho and S/So data set for this station is 0.8449 from the quadratic and cubic models. The quadratic, cubic, and logarithmic models have the highest coefficient of determination calculated from the data set of measured and predicted global solar radiation, which is 0.9192. Simada The cubic model yielded the highest correlation coefficient of 0.9352 for this station from the data set of H/Ho and S/So. From the exponential 2 model, the lowest value

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of the correlation coefficient for this station is 0.9216. Table 4 shows that the statistical test of the PE for the Simada station ranges between -12.0560 (cubic) and 12.4250 (exponential 2). Table 4 shows that the linear model for the Simada station produces the best PE values of -9.2132 and 12.1519. Except for the linear and quadratic models, all negative PE values at this station exceed the threshold value. Again, with the exception of the cubic model, all positive values exceed the threshold value. The lowest values of the MAPE, MPE, MAPE, MBE, and RMSE statistical tests are 4.6685 (cubic), -0.0855 (cubic), 0.0266 (cubic), 0 (all), and 0.0390 (linear) models, respectively. In terms of the coefficient of determination, the highest value for station is obtained from the cubic model, which is 0.8579. When we examine the correlation coefficients from the data set of measured and predicted values for this station, the cubic model yields the highest value of 0.8741. Sirinka The cubic model produces the highest correlation coefficient 0.9157 from the data set of H/Ho and S/So at Srinika station. The lowest correlation coefficient for this station, on the other hand, is 0.8678 from the exponential 2 model. According to the statistical test of the PE for this station, its value ranges between -6.5290 (cubic) and 4.1592 by the exponential 2 model. All the values of the PE obtained from the models are within the threshold value of ±10%. The quadratic model yielded the best PE values for this station: -6.3036 and 3.6168. Statistical tests such as MAPE, MPE, MAPE, MBE, and RMSE yielded the lowest values of 1.6446 (cubic), 0.0585 (cubic), 0.0072 (cubic), 0 (all), and 0.0124 (quadratic), as shown in Table 4. The cubic model yields the highest value of 0.8385 for the coefficient of determination from the data set of H/Ho and S/So . Meanwhile, the cubic model yielded the highest correlation coefficient of 0.9157 from the data set of measured and calculated global solar radiation. Tistiska In this station, the cubic model yielded a correlation coefficient of 0.9665 from the data set of H/Ho and S/So , which was chosen as the highest of all models. On the other hand, the lowest correlation coefficient is 0.9598 from the exponential 2 model. Table 4 shows that the PE test result ranges between -8.3295 (exponential 1) and 6.4608 (exponential 2). All of the PE values from all of the models are within the ±10% threshold. The cubic model has the best PE values of -5.1696 and 3.8632 in Table 4 of the statistical test results. The MAPE, MPE, MAPE, MBE, and RMSE have the lowest values of 3.9292 (exponential 1), -0.1394 (logarithmic), 0.0202 (exponential 1 and 2), 0 (all), and 0.0255 (logarithmic), respectively. When the coefficients of determination obtained from the data set of H/Ho and S/So of all the models are compared, 0.9341 is found to be the highest. Similarly, the cubic model yields the highest correlation coefficient of 0.9545 from the data set of measured and predicted global solar radiation. Wegel Tena According to Table 3, the cubic model produces the highest correlation coefficient from the data set of H/Ho and S/So, which is 0.9545. The exponential 2 model yields

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the lowest value of 0.9524. Table 4 shows that the value of the PE ranges between 9.1733 and 6.9273 using the cubic model. For this station, the entire PE values are within the 10% threshold. The best PE values from all models from these stations are -8.1181 and 7.1231. The lowest values obtained from statistical tests of MAPE, MPE, MAPE, MBE, and RMSE were 4.3404 (exponential 1), 0.2179 (power), 0.2680 (exponential 2), 0 (all), and 0.0348 (linear) models, respectively. The cubic model has the highest coefficient of determination of the entire models used for this station, 0.9111, from the data set of H/Ho and S/So. According to the cubic model, the best correlation coefficient for the station from the data set of measured and predicted global solar radiation is 0.9545. Were Ilu According to the statistical tests and results in Table 3, the cubic model has the highest correlation coefficient from the data set of H/Ho and S/So, which is 0.9123. According to the same table, the Were Ilu station has the lowest correlation coefficient from the cubic model analysis, which is 0.8733. Statistical test result of the PE shows that the values are ranging between -15.3180 (exponential 1) and 14.9720 (exponential 2). All of the PE values exceed the ±10% threshold, indicating that the models appear to be relatively poor for determining global solar radiation in the area of this station. The best values for the PE among the models are -12.5520 and 11.7920. The minimum values of the MAPE, MPE, MAPE, MBE, and RMSE for the Were Ilu station are 5.1409 (cubic), -0.4215 (cubic), 0.0307 (cubic), 0 (all), and 0.0441 (logarithmic), respectively, as shown in Table 4. The cubic model yields the best coefficient determination value of 0.8323 from the data set of H/Ho and S/So. Similarly, the cubic model yields the highest value of the correlation coefficient from the data set of measured and predicted global solar radiation: 0.9123. Class of PE (%) -14 to -16 -12 to -14 -10 to -12 -8 to -10 -6 to -8 -4 to -6 -2 to -4 -2 to 0 0 to 2 2 to 4 4 to 6 6 to 8 8 to 10 10 to 12 12 to 14 14 to 16

Frequency (%) Linear Quadratic 1 1 3 3 3 2 8 8 10 10 17 16 22 18 25 29 32 36 41 41 14 16 11 6 2 3 1 3 1 0 1 0

Cubic 1 3 3 6 8 14 19 35 40 40 13 6 2 2 0 0

Exp. 1 2 1 7 10 7 14 21 30 30 32 24 9 2 0 2 1

Logarithmic 2 4 5 5 13 20 19 21 29 36 17 13 5 2 1 0

Exp. 2 2 2 5 12 6 13 23 29 33 27 27 8 2 0 2 1

Power 2 2 5 6 14 11 27 18 32 37 22 10 3 2 1 0

(continued)

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Class of PE (%) Under estimation Over estimation -10 to 10

3.2

Frequency (%) Linear Quadratic 46.35 45.31 53.65 54.69 94.79 95.31

Cubic 46.35 53.65 95.31

Exp. 1 47.92 52.08 93.23

Logarithmic 46.35 53.65 92.71

Exp. 2 47.92 52.08 93.75

Power 44.27 55.73 93.75

Choosing the Best Regression Model for the Stations

The models are statistically significant, according to all of the statistical studies. However, as seen in Table 3, some stations, including Kombolcha, Simada, and Sirinka, have slightly lower correlation coefficients than the other stations. The quality of the data can be one cause for the low correlation coefficient. The inadequate organization of the data for these stations may be seen from the row data received from Ethiopia’s national metrological station. Every regression equation yields excellent results. However, every level of accuracy, including MBE, MABE, MPE, MAPE, RMSE, and tstat, uses different values from one regression model to another for the same station. Although the difference appears to be significant, it is actually quite little. The frequency analysis was used to evaluate the prediction accuracy of each of the seven regression models using the PE calculation data from each of the 16 stations. According to the results of the frequency analysis, indicated in Table 3, linear, cubic, and logarithmic regression models produce the same frequency results for underestimation and overestimation, which are 46.35% and 53.65%, respectively. The quadratic model’s under- and overestimation frequency ranges are calculated to be 45.31% and 54.69%, respectively. The power model’s under- and overestimation frequency ranges are calculated to be 44.27% and 53.73%, respectively. Exponential 1 and exponential 2’s under- and overestimation frequency ranges are calculated to be 47.92% and 52.08%, respectively. According to the literature, the percentage cut-off value is up to around ±10%. In this study, 95.31% frequency value of the quadratic and cubic model residues between ±10%. The frequencies of PE values for linear, exponential 1 and logarithmic models are calculated as 94.79%, 93.23%, and 92.71%, respectively. The PE frequency of the exponential 2 and power models is 95.73%. Figure 3 depicts the differences in observed and estimated values (H/Ho and S/So) for 16 stations. As shown in Fig. 3, there are no statistically significant differences between the observed and estimated values. In order to figure out the optimum regression models for the entire stations, seven regression models have been classified by ranking from each performance parameter such as MPE, MAPE, MABE, RMSE, R, and tta. For all evaluated stations having Angstrom coefficients, the cubic regression model can be used as indicated in Table 5.

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Fig. 3 Comparison of measured and calculated monthly average daily global solar radiation prediction for 16 locations using regression models

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Fig. 3 (continued)

T. B. Kotu et al.

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Table 5 Equations obtained from regression analysis to predict global solar radiation of the Amhara Region Amdework Bahir Dar Chagni Dangla Debre Birhan Debre Markos Kombolcha Mehal Meda Mekane Selam Metema Mota Simada Sirinka Tistiska Wegel Tena Were Ilu

H/Ho = 0.78 - 2.61(S/So) + 5.64(S/So)2 - 3.16(S/So)3 H/Ho = 0.54 - 1.20(S/So) + 2.66(S/So)2 - 1.38(S/So)3 H/Ho = 0.55 - 1.28(S/So) + 2.82(S/So)2 - 1.48(S/So)3 H/Ho = 0.22 + 1.90(S/So) - 2.82(S/So)2 + 1.86(S/So)3 H/Ho = -0.33 + 4.21(S/So) - 7.45(S/So)2 + 4.86(S/So)3 H/Ho = 0.05 + 1.84(S/So) - 2.88(S/So)2 + 1.97(S/So)3 H/Ho = 6.07 - 28.37(S/So) + 45.67(S/So)2 - 23.71(S/So)3 H/Ho = -1.34 + 5.91(S/So) - 5.51(S/So)2 + 1.72(S/So)3 H/Ho = 0.01 + 1.96(S/So) - 2.47(S/So)2 + 1.80(S/So)3 H/Ho = -0.16 + 2.77(S/So) - 3.61(S/So)2 + 1.70(S/So)3 H/Ho = 0.16 + 0.85(S/So) - 0.25(S/So)2 - 0.04(S/So)3 H/Ho = -0.91 + 6.83(S/So) - 10.87(S/So)2 + 6.09(S/So)3 H/Ho = 0.41 - 1.32(S/So) + 4.18(S/So)2 - 3.19(S/So)3 H/Ho = -1.60 + 9.26(S/So) - 13.30(S/So)2 + 6.67(S/So)3 H/Ho = -0.07 + 1.88(S/So) - 2.03(S/So)2 + 1.11(S/So)3 H/Ho = 0.16 + 0.89(S/So) + 0.12(S/So)2 - 0.045(S/So)3

4 Conclusion In order to predict monthly average daily global solar radiation on horizontal surface for 16 stations in the Amhara Region, Ethiopia, seven regression models based on the sunshine duration ratio were used. All regression models investigated in this study produce extremely good results for estimating global solar radiation on the horizontal surface at all stations. The statistical studies (MBE, MABE, MPE, MAPE, RMSE, and tsta) show that all regression equations may be used to estimate monthly average daily global solar radiation for all stations. However, the best-fit regression equations for predicting monthly average daily global solar radiation on horizontal surfaces are the cubic and quadratic regression models. Acknowledgments The authors would like to thank the National Meteorological Agency of Ethiopia, as well as the branch offices of the Western and Eastern Amhara Metrological Agencies, for providing the data.

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References 1. Hailu, A. D., & Kumsa, D. K. (2020). Ethiopia renewable energy potentials and current state. AIMS Energy, 9(1), 1–14. https://doi.org/10.3934/ENERGY.2021001 2. Tucho, G. T., Weesie, P. D. M., & Nonhebel, S. (2014). Assessment of renewable energy resources potential for large scale and standalone applications in Ethiopia. Renewable and Sustainable Energy Reviews, 40, 422–431. https://doi.org/10.1016/j.rser.2014.07.167 3. Duzen, H., & Aydin, H. (2012). Sunshine-based estimation of global solar radiation on horizontal surface at Lake Van region (Turkey). Energy Conversion and Management, 58, 35–46. https://doi.org/10.1016/j.enconman.2011.11.028 4. Bakirci, K. (2009). Correlations for estimation of daily global solar radiation with hours of bright sunshine in Turkey. Energy, 34(4), 485–501. https://doi.org/10.1016/j.energy.2009. 02.005 5. Almorox, J., Bocco, M., & Willington, E. (2013). Estimation of daily global solar radiation from measured temperatures at Cañada de Luque, Córdoba, Argentina. Renewable Energy, 60, 382–387. https://doi.org/10.1016/j.renene.2013.05.033 6. Ranganathan, S., Senthilkumar, A., & Durgalakshmi, K. (2015). Global solar radiation estimation using sunshine duration in Pollachi area. International Journal of Applied Engineering Research, 10(7), 17459–17467. https://doi.org/10.1016/j.enconman.2003.08.022 7. Bakirci, K. (2015). Models for the estimation of diffuse solar radiation for typical cities in Turkey. Energy, 82, 827–838. https://doi.org/10.1016/j.energy.2015.01.093 8. Bulut, H., & Büyükalaca, O. (2007). Simple model for the generation of daily global solarradiation data in Turkey. Applied Energy, 84(5), 477–491. https://doi.org/10.1016/j.apenergy. 2006.10.003 9. Angstrom, A. (1924). Solar and terrestrial radiation. Quarterly Journal of the Royal Meteorological Society, 50(121), 5. 10. Prescott, J. A. (1940). Evaporation from a water surface in relation to solar radiation. Transactions of the Royal Society of South Australia, 64(114), 25. 11. Nage, G. D. (2018). Estimation of monthly average daily solar radiation from meteorological parameters: sunshine hours and measured temperature in Tepi, Ethiopia. International Journal of Energy and Environmental Science, 3(1), 19–26. https://doi.org/10.11648/j.ijees. 20180301.12 12. Akinoǧlu, B. G., & Ecevit, A. (1990). Construction of a quadratic model using modified Ångstrom coefficients to estimate global solar radiation. Solar Energy, 45(2), 85–92. https:// doi.org/10.1016/0038-092X(90)90032-8 13. Bahel, V., Bakhsh, H., & Srinivasan, R. (1987). A correlation for estimation of global solar radiation. Energy, 12(2), 131–135. https://doi.org/10.1016/0360-5442(87)90117-4 14. Ampratwum, D. B., & Dorvlo, A. S. S. (1999). Estimation of solar radiation from the number of sunshine hours. Applied Energy, 63(3), 161–167. https://doi.org/10.1016/S0306-2619(99) 00025-2 15. Elagib, N. A., & Mansell, M. G. (2000). New approaches for estimating global solar radiation across Sudan. Energy Conversion and Management, 41(5), 419–434. https://doi.org/10.1016/ S0196-8904(99)00123-5 16. Almorox, J., & Hontoria, C. (2004). Global solar radiation estimation using sunshine duration in Spain. Energy Conversion and Management, 45(9–10), 1529–1535. https://doi.org/10.1016/j. enconman.2003.08.022 17. Duffie, J. A., Beckman, W. A., & McGowan, J. (1985). Solar engineering of thermal processes. American Journal of Physics, 53(4). 18. Badescu, V. (2008). Modeling solar radiation at the earth’s surface. Springer. 19. Yorukoglu, M., & Celik, A. N. (2006). A critical review on the estimation of daily global solar radiation from sunshine duration. Energy Conversion and Management, 47(15–16), 2441–2450. https://doi.org/10.1016/j.enconman.2005.11.002

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Investigation and Optimization of the Energy Band Gap of PAM/PVP/Al2O3 Composites Negese Yazie Amogne, Delele Worku Ayele, and Nigus Gabbiye Habtu

1 Introduction Nowadays, polymeric materials have gained great attention owing to their possible applications in diverse fields, such as batteries, solar cells, capacitors, optoelectronics, and others, on the basis of their electrical and optical properties, low costs, ease of fabrication, lightweight, and others [1–6]. The characteristics of polymers may be altered/enhanced through different approaches such as blending polymers, incorporating fillers into the polymeric matrices, and others [2, 7–10]. By combining polymers with ceramic fillers, such as metal oxide particles, new classes of materials can be made. The effect of fillers on polymer matrices depends on their nature, size, and concentration [11]. The inclusion of metal oxide fillers, such as Al2O3, into the polymer matrices produced polymer composites with excellent electrical, mechanical, and optical properties [12, 13]. In addition, the synthesized polymer composites revealed a variety of characteristics such as ease of processing, stiffness, and organic functionality. Further, the metal oxide fillers/particles possess impressive properties N. Y. Amogne Department of Chemical Engineering, Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia Dire Dawa Institute of Technology, Dire Dawa University, Dire Dawa, Ethiopia D. W. Ayele (✉) Departments of Chemistry, College of Science, Bahir Dar University, Bahir Dar, Ethiopia Energy Research Center, Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia N. G. Habtu Department of Chemical Engineering, Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia Energy Research Center, Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. H. Woldegiorgis et al. (eds.), Advancement of Science and Technology, Green Energy and Technology, https://doi.org/10.1007/978-3-031-33610-2_2

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not found in polymer materials, including stiffness, and transparency, along with good thermal, chemical, and mechanical stability [14]. Consequently, the composite materials composed of polymeric materials and metallic oxide fillers have properties of both components (based on weight percentages) to produce novel materials with superior characteristics [14, 15]. Polymeric composite thin films are gaining considerable attention recently owing to their attractive features and potential application in optical lenses, energy storage devices, UV screening, photodetectors, corrosion protection, and many other fields [12]. Therefore, considerable attention has been paid to developing novel polymer composite thin films as they play a vital role in synthesizing devices with impressive properties like customized energy band gap, ionic conductivity, refractive index, absorption/transmission characteristics, and others [16]. Metal oxide fillers in polymeric materials frequently cause transparency losses due to the scattering of filler particle agglomerates, raising the refractive index [16]. In addition to their refractive index, incorporating fillers like metal oxides into polymeric materials can significantly change the energy band gap and crystallinity tendency of the polymeric hosts, which in turn determines their applications. Polymer composites with small band gaps are preferable for optoelectronic and photonic uses [7]. Further, the decline in Eg values enhances the amorphousness in polymer composites [17], which improves the ionic conductivity of polymeric membranes when utilized as hosts for polymer electrolytes. In addition to their thermal stability and high dielectric constant, aluminum oxide particles have strong mechanical properties, excellent corrosion resistance, and excellent electrical conductivity [18]. Polyvinyl pyrrolidone (PVP), an amorphous polymer, can be greatly modified through polymer blending [19]. In addition, PVP offers chemical inertness, non-toxicity, environmental stability, and high transparency along with dopant-dependent characteristics [20], making it a special choice among conjugated polymers for optoelectronics applications. Polyacrylamide (PAM) is a water-soluble polymer that absorbs large quantities of water, forming a soft gel upon hydration and can undergo multiple chemical modifications [21]. PAM is used to produce soft contact lenses and in other applications. The purpose of this research was to investigate the effect of alumina fillers on the energy band gap of PAM/PVP blend films and to optimize the energy band gap of the prepared polymer composites using simplex lattice mixture experiment design methods. Our work includes assessing the optical properties of the synthesized samples, along with identifying the principal vibrational modes found in the polymer blend and optimized polymer composite thin films and Al2O3 fillers. Besides these properties, the transmittance, reflectance, and absorbance of the composites were also examined.

Investigation and Optimization of the Energy Band Gap of PAM/PVP/Al2O3. . .

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2 Experimental Section Polyacrylamide/polyvinyl pyrrolidone (50:50) blend films and aluminum oxide were used as hosting materials and fillers, respectively. PVP and PAM were provided by Samir Tech-Chem Pvt. Ltd, while aluminum oxide was obtained from Blulux, India. The aluminum oxide particles range in size from micrometers to millimeters.

2.1

Preparation of the Polymer/Al2O3 Composites Using SLMD

The polymer composite samples with different proportions of PVP/PAM blend (50: 50) and Al2O3 recommended by the simplex lattice mixture design (SLMD) method were prepared. For preparing the polymer composites, the appropriate amounts of PAM and PVP were dissolved in distilled water separately at ambient temperature for 10 minutes. After stirring magnetically, the PVP solutions were added to the PAM solutions and then the required amounts of Al2O3 powder were incorporated into the PAM/PVP solutions, and the mixture was stirred magnetically for 2 and ½ hours at ambient temperature. Then, the obtained solution was cast on a plastic petri dish and subjected to drying at 45 °C overnight to remove the solvent and the dried polymer composite films were detached from the petri dish and stored in a desiccator for later use (i.e., characterization).

2.2

Experimental Design and Statistical Analysis

We utilized simplex lattice mixture design (SLMD) to optimize the formulation factors since the response changes as a function of the relative proportions of the components. In these experiments, two factors were evaluated by changing their proportions (in weight percentage) simultaneously while keeping the total concentration constant (i.e., 0.5 g) in each run. The amount of polyvinyl pyrrolidone/ polyacrylamide blend (50:50 wt %) and aluminum oxide were used as input factors, with the energy band gap serving as the output response. The effect of each input factor on the energy band gap of the composites was statistically determined using SLMD and the formulations were optimized using a polynomial model Eq. (1) [22]. Experimental designs, models, and analyses were performed using Design Expert software (Stat-Ease Inc., Minneapolis, USA). Table 1 shows the upper and lower limits of the input factors.

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Table 1 An experimental design with the input factor levels

Independent factors X1, PAM/PVP proportion (%) X2, Al2O3 proportion (%)

q

y=

0 87.5 12.5

1 100 25

q

β i xi þ i=1

Levels -1 75 0

βij xi xj

ð1Þ

i80%) and low reflectance (