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Solar Energy Fundamentals, Zekai ¸Sen, Notas de estudo de Engenharia Elétrica

energia solar, energia renovável

Tipologia: Notas de estudo

2014

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Baixe Solar Energy Fundamentals, Zekai ¸Sen e outras Notas de estudo em PDF para Engenharia Elétrica, somente na Docsity! Pe IN) or dao) Fundamentals and Modeling Techniques PATA Ico ae LA TVS (Open ENS a Springer Solar Energy Fundamentals and Modeling Techniques Bismillahirrahmanirrahim In the name of Allah the most merciful and the most beneficial Preface Atmospheric and environmental pollution as a result of extensive fossil fuel ex- ploitation in almost all human activities has led to some undesirable phenomena that have not been experienced before in known human history. They are varied and include global warming, the greenhouse affect, climate change, ozone layer deple- tion, and acid rain. Since 1970 it has been understood scientifically by experiments and research that these phenomena are closely related to fossil fuel uses because they emit greenhouse gases such as carbon dioxide (CO2) and methane (CH4) which hin- der the long-wave terrestrial radiation from escaping into space and, consequently, the earth troposphere becomes warmer. In order to avoid further impacts of these phenomena, the two main alternatives are either to improve the fossil fuel quality thus reducing their harmful emissions into the atmosphere or, more significantly, to replace fossil fuel usage as much as possible with environmentally friendly, clean, and renewable energy sources. Among these sources, solar energy comes at the top of the list due to its abundance and more even distribution in nature than other types of renewable energy such as wind, geothermal, hydropower, biomass, wave, and tidal energy sources. It must be the main and common purpose of humanity to de- velop a sustainable environment for future generations. In the long run, the known limits of fossil fuels compel the societies of the world to work jointly for their re- placement gradually by renewable energies rather than by improving the quality of fossil sources. Solar radiation is an integral part of different renewable energy resources, in general, and, in particular, it is the main and continuous input variable from the practically inexhaustible sun. Solar energy is expected to play a very significant role in the future especially in developing countries, but it also has potential in de- veloped countries. The material presented in this book has been chosen to provide a comprehensive account of solar energy modeling methods. For this purpose, ex- planatory background material has been introduced with the intention that engineers and scientists can benefit from introductory preliminaries on the subject both from application and research points of view. The main purpose of Chapter 1 is to present the relationship of energy sources to various human activities on social, economic and other aspects. The atmospheric vii viii Preface environment and renewable energy aspects are covered in Chapter 2. Chapter 3 pro- vides the basic astronomical variables, their definitions and uses in the calculation of the solar radiation (energy) assessment. These basic concepts, definitions, and derived astronomical equations furnish the foundations of the solar energy evalua- tion at any given location. Chapter 4 provides first the fundamental assumptions in the classic linear models with several modern alternatives. After the general review of available classic non-linear models, additional innovative non-linear models are presented in Chapter 5 with fundamental differences and distinctions. Fuzzy logic and genetic algorithm approaches are presented for the non-linear modeling of solar radiation from sunshine duration data. The main purpose of Chapter 6 is to present and develop regional models for any desired location from solar radiation measure- ment sites. The use of the geometric functions, inverse distance, inverse distance square, semivariogram, and cumulative semivariogram techniques are presented for solar radiation spatial estimation. Finally, Chapter 7 gives a summary of solar energy devices. Applications of solar energy in terms of low- and high-temperature collectors are given with future research directions. Furthermore, photovoltaic devices are dis- cussed for future electricity generation based on solar power site-exploitation and transmission by different means over long distances, such as fiber-optic cables. An- other future use of solar energy is its combination with water and, as a consequence, electrolytic generation of hydrogen gas is expected to be another source of clean energy. The combination of solar energy and water for hydrogen gas production is called solar-hydrogen energy. Necessary research potentials and application possi- bilities are presented with sufficient background. New methodologies that are bound to be used in the future are mentioned and, finally, recommendations and sugges- tions for future research and application are presented, all with relevant literature reviews. I could not have completed this work without the support, patience, and assistance of my wife Fatma Şen. İstanbul, Çubuklu 15 October 2007 Contents xi 5 Non-Linear Solar Energy Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.2 Classic Non-Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.3 Simple Power Model (SPM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.3.1 Estimation of Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . 157 5.4 Comparison of Different Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 5.5 Solar Irradiance Polygon Model (SIPM) . . . . . . . . . . . . . . . . . . . . . . . 160 5.6 Triple Solar Irradiation Model (TSIM) . . . . . . . . . . . . . . . . . . . . . . . . . 168 5.7 Triple Drought–Solar Irradiation Model (TDSIM) . . . . . . . . . . . . . . . 172 5.8 Fuzzy Logic Model (FLM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 5.8.1 Fuzzy Sets and Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 5.8.2 Fuzzy Algorithm Application for Solar Radiation . . . . . . . . . 179 5.9 Geno-Fuzzy Model (GFM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5.10 Monthly Principal Component Model (MPCM) . . . . . . . . . . . . . . . . . 188 5.11 Parabolic Monthly Irradiation Model (PMIM) . . . . . . . . . . . . . . . . . . . 196 5.12 Solar Radiation Estimation from Ambient Air Temperature . . . . . . . 202 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 6 Spatial Solar Energy Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 6.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 6.2 Spatial Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 6.3 Linear Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 6.4 Geometric Weighting Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 6.5 Cumulative Semivariogram (CSV) and Weighting Function . . . . . . . 216 6.5.1 Standard Spatial Dependence Function (SDF) . . . . . . . . . . . . 217 6.6 Regional Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 6.6.1 Cross-Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 6.6.2 Spatial Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 6.7 General Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 7 Solar Radiation Devices and Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 7.2 Solar Energy Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 7.3 Heat Transfer and Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 7.3.1 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 7.3.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 7.3.3 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 7.4 Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 7.4.1 Flat Plate Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 7.4.2 Tracking Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 7.4.3 Focusing (Concentrating) Collectors . . . . . . . . . . . . . . . . . . . . 250 7.4.4 Tilted Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 7.4.5 Solar Pond Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 7.4.6 Photo-Optical Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 xii Contents 7.5 Photovoltaic (PV) Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 7.6 Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 7.7 Hydrogen Storage and Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 7.8 Solar Energy Home . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 7.9 Solar Energy and Desalination Plants . . . . . . . . . . . . . . . . . . . . . . . . . . 261 7.10 Future Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 A A Simple Explanation of Beta Distribution . . . . . . . . . . . . . . . . . . . . . . . . 267 B A Simple Power Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Chapter 1 Energy and Climate Change 1.1 General Energy and fresh water are the two major commodities that furnish the fundamen- tals of every human activity for a reasonable and sustainable quality of life. Energy is the fuel for growth, an essential requirement for economic and social develop- ment. Solar energy is the most ancient source and the root for almost all fossil and renewable types. Special devices have been used for benefiting from the solar and other renewable energy types since time immemorial. During the early civilizations water and wind power have been employed as the major energy sources for naviga- tion, trade, and information dissemination. For instance, Ebul-İz Al-Jazari (1136– 1206), as mentioned by Şen (2005), was the first scientist who developed various instruments for efficient energy use. Al-Jazari described the first reciprocating pis- ton engine, suction pump, and valve, when he invented a two-cylinder reciprocating suction piston pump, which seems to have had a direct significance in the develop- ment of modern engineering. This pump is driven by a water wheel (water energy) that drives, through a system of gears, an oscillating slot-rod to which the rods of two pistons are attached. The pistons work in horizontally opposed cylinders, each provided with valve-operated suction and delivery pipes. His original drawing in Fig. 1.1a shows the haulage of water by using pistons, cylinders, and a crank moved by panels subject to wind power. In Fig. 1.1b the equivalent instrument design is achieved by Hill (1974). Ebul-İz Al-Jazari’s original robotic drawing is presented in Fig. 1.2. It works with water power through right and left nozzles, as in the figure, and accordingly the right and left hands of the human figure on the elephant move up and down. In recent centuries the types and magnitudes of the energy requirements have increased in an unprecedented manner and mankind seeks for additional energy sources. Today, energy is a continuous driving power for future social and tech- nological developments. Energy sources are vital and essential ingredients for all human transactions and without them human activity of all kinds and aspects can- not be progressive. Population growth at the present average rate of 2% also exerts extra pressure on limited energy sources. Zekai Sen, Solar Energy Fundamentals and Modeling Techniques 1 DOI: 10.1007/978-1-84800-134-3, ©Springer 2008 4 1 Energy and Climate Change havior giving rise to unusual local heat and cold. Such events will also affect the world food production rates. In addition, global temperatures could rise by a further 1 – 3.5 °C by the end of the twenty-first century, which may lead potentially to dis- ruptive climate change in many places. By starting to manage the CO2 emissions through renewable energy sources now, it may be possible to limit the effects of climate change to adaptable levels. This will require adapting the world’s energy systems. Energy policy must help guarantee the future supply of energy and drive the necessary transition. International cooperation on the climate issue is a prereq- uisite for achieving cost-effective, fair, and sustainable solutions. At present, the global energy challenge is to tackle the threat of climate change, to meet the rising demand for energy, and to safeguard security of energy supplies. Renewable energy and especially solar radiation are effective energy technologies that are ready for global deployment today on a scale that can help tackle climate change problems. Increase in the use of renewable energy reduces CO2 emissions, cuts local air pollution, creates high-value jobs, curbs growing dependence of one country on imports of fossil energy (which often come from politically unstable regions), and prevents society a being hostage to finite energy resources. In addition to demand-side impacts, energy production is also likely to be af- fected by climate change. Except for the impacts of extreme weather events, re- search evidence is more limited than for energy consumption, but climate change could affect energy production and supply as a result of the following (Wilbanks et al., 2007): 1. If extreme weather events become more intense 2. If regions dependent on water supplies for hydropower and/or thermal power plant cooling face reductions in water supplies 3. If changed conditions affect facility siting decisions 4. If conditions change (positively or negatively) for biomass, wind power, or solar energyproductions Climate change is likely to affect both energy use and energy production in many parts of the world. Some of the possible impacts are rather obvious. Where the climate warms due to climate change, less heating will be needed for indus- trial increase (Cartalis et al., 2001), with changes varying by region and by season. Net energy demand on a national scale, however, will be influenced by the struc- ture of energy supply. The main source of energy for cooling is electricity, while coal, oil, gas, biomass, and electricity are used for space heating. Regions with sub- stantial requirements for both cooling and heating could find that net annual elec- tricity demands increase while demands for other heating energy sources decline (Hadley et al., 2006). Seasonal variation in total energy demand is also important. In some cases, due to infrastructure limitations, peak energy demand could go be- yond the maximum capacity of the transmission systems. Tol (2002a,b) estimated the effects of climate change on the demand for global energy, extrapolating from a simple country-specific (UK) model that relates the energy used for heating or cooling to degree days, per capita income, and energy efficiency. According to Tol, by 2100 benefits (reduced heating) will be about 0.75% of gross domestic product 1.3 Energy and Society 5 (GDP) and damages (increased cooling) will be approximately 0.45%, although it is possible that migration from heating-intensive to cooling-intensive regions could affect such comparisons in some areas (Wilbanks et al., 2007). Energy and climate are related concerning cooling during hot weather. Energy use has been and will continue to be affected by climate change, in part because air-conditioning, which is a major energy use particularly in developed countries, is climate-dependent. However, the extent to which temperature rise has affected en- ergy use for space heating/cooling in buildings is uncertain. It is likely that certain adaptation strategies (e.g., tighter building energy standards) have been (or would be) taken in response to climate change. The energy sector can adapt to climate- change vulnerabilities and impacts by anticipating possible impacts and taking steps to increase its resilience, e.g., by diversifying energy supply sources, expanding its linkages with other regions, and investing in technological change to further ex- pand its portfolio of options (Hewer 2006). Many energy sector strategies involve high capital costs, and social acceptance of climate-change response alternatives that might imply higher energy prices. Climate change could have a negative impact on thermal power production since the availability of cooling water may be reduced at some locations because of climate-related decreases (Arnell et al., 2005) or seasonal shifts in river runoff (Zierl and Bugmann 2005). The distribution of energy is also vulnerable to climate change. There is a small increase in line resistance with increasing mean temperatures cou- pled with negative effects on line sag and gas pipeline compressor efficiency due to higher maximum temperatures. All these combined effects add to the overall uncer- tainty of climate change impacts on power grids. 1.3 Energy and Society Since the energy crisis in 1973 air pollution from combustion processes has caused serious damage and danger to forests, monuments, and human health in many coun- tries, as has been documented by official studies and yearly statistics. Many environ- mental damages, including acid rain and their forest-damaging consequences, have incurred economic losses in the short term and especially in the long term. Hence, seemingly cheap energy may inflict comparatively very high expenses on society. Figure 1.3 shows three partners in such a social problem including material benefi- ciary, heat beneficiary, and, in between, the third party who has nothing to do with these two major players. On the other hand, the climate change due to CO2 emission into the atmosphere is another example of possible social costs from the use of energy, which is handed over to future generations by today’s energy consumers. Again the major source of climate change is the combustion of unsuitable quality fossil fuels. Today, the scale of development of any society is measured by a few parameters among which the used or the per capita energy amount holds the most significant rank. In fact, most industrialized countries require reliable, efficient, and readily 6 1 Energy and Climate Change Fig. 1.3 Energy usage part- ners available energy for their transportation, industrial, domestic, and military systems. This is particularly true for developing countries, especially those that do not possess reliable and sufficient energy sources. Although an adequate supply of energy is a prerequisite of any modern society for economic growth, energy is also the main source of environmental and atmo- spheric pollution (Sect. 1.6). On the global scale, increasing emissions of air pol- lution are the main causes of greenhouse gases and climate change. If the trend of increasing CO2 continues at the present rate, then major climatic disruptions and local imbalances in the hydrological as well as atmospheric cycles will be the con- sequences, which may lead to excessive rainfall or drought, in addition to excessive heat and cold. Such changes are already experienced and will also affect the world’s potential for food production. The continued use of conventional energy resources in the future will adversely affect the natural environmental conditions and, conse- quently, social energy-related problems are expected to increase in the future. A new factor, however, which may alleviate the environmental and social problems of fu- ture energy policies, or even solve them, is the emerging new forms of renewable sources such as solar, wind, biomass, small hydro, wave, and geothermal energies, as well as the possibility of solar hydrogen energy. The two major reasons for the increase in the energy consumption at all times are the steady population increase and the strive for better development and comfort. The world population is expected to almost double in the next 50 years, and such an increase in the population will take place mostly in the developing countries, because the developed countries are not expected to show any significant population increase. By 2050, energy demand could double or triple as population rises and developing countries expand their economies and overcome poverty. The energy demand growth is partially linked to population growth, but may also result from larger per capita energy consumptions. The demand for and pro- duction of energy on a world scale are certain to increase in the foreseeable future. Of course, growth will definitely be greater in the developing countries than in the industrialized ones. Figure 1.4 shows the world population increase for a 100-year period with predictions up to 2050. It indicates an exponential growth trend with in- creasing rates in recent years such that values double with every passage of a fixed amount of time, which is the doubling time. The recent rise in population is even more dramatic when one realizes that per capita consumption of energy is also rising thus compounding the effects. Economic growth and the population increase are the two major forces that will continue to 1.3 Energy and Society 9 Prior to the discovery of fossil fuels, coal and water played a vital role in such a search. For instance, transportation means such as the oceangoing vessels and early trains ran on steam power, which was the combination of coal and water va- por. After the discovery of oil reserves, steam power became outmoded. Hence, it seemed in the first instance that an unparalleled energy alternative had emerged for the service of mankind. Initially, it was considered an unlimited resource but with the passage of time, limitations in this alternative were understood not only in the quantitative sense but also in the environmental and atmospheric pollution senses. Society is affected by climate and hence energy in one of the three major ways: 1. Economic sectors that support a settlement are affected because of changes in productive capacity or changes in market demand for the goods and services produced there (energy demand). The importance of this impact depends in part on whether the settlement is rural (which generally means that it is dependent on one or two resource-based industries with much less energy consumption) or urban, in which case there usually is a broader array of alternative resources including energy resources consumption centers. 2. Some aspects of physical infrastructure (including energy transmission and dis- tribution systems), buildings, urban services (including transportation systems), and specific industries (such as agro-industry and construction) may be directly affected. For example, buildings and infrastructure in deltaic areas may be af- fected by coastal and river flooding; urban energy demand may increase or de- crease as a result of changed balances in space heating and space cooling (addi- tional energy consumption); and coastal and mountain tourism may be affected by changes in seasonal temperature and precipitation patterns and sea-level rise. Concentration of population and infrastructure in urban areas can mean higher numbers of people and a higher value of physical capital at risk, although there also are many economies of scale and proximity in ensuring a well-managed infrastructure and service provision. 3. As a result of climate change society may be affected directly through extreme weather conditions leading to changes in health status and migration. Extreme weather episodes may lead to changes in deaths, injuries, or illness. Population movements caused by climate changes may affect the size and characteristics of settlement populations, which in turn changes the demand for urban services (including energy demand). The problems are somewhat different in the largest population centers (e.g., those of more than 1 million people) and mid-sized to small-sized regional centers. The former are more likely to be destinations for migrants from rural areas and smaller settlements and cross-border areas, but larger settlements generally have much greater command over national re- sources. Thus, smaller settlements actually may be more vulnerable. Informal settlements surrounding large and medium-size cities in the developing world remain a cause for concern because they exhibit several current health and envi- ronmental hazards that could be exacerbated by global warming and have lim- ited command over resources. 10 1 Energy and Climate Change 1.4 Energy and Industry Industry is defined as including manufacturing, transport, energy supply and de- mand, mining, construction, and related informal production activities. Other sec- tors sometimes included in industrial classifications, such as wholesale and retail trade, communications, real estate and business activities are included in the cate- gories of services and infrastructure. An example of an industrial sector particularly sensitive to climate change is energy (Hewer 2006). After the industrial revolution in the mid-eighteenth century human beings started to require more energy for con- sumption. Hence, non-renewable energy sources in the form of coal, oil, and wood began to deplete with time. As a result, in addition to the limited extent and en- vironmental pollution potential, these energy sources will need to be replaced by renewable alternatives. Global net energy demand is very likely to change (Tol 2002b) as demand for air-conditioning is highly likely to increase, whereas demand for heating is highly likely to decrease. The literature is not clear on what temperature is associated with minimum global energy demand, so it is uncertain whether warming will initially increase or decrease net global demand for energy relative to some projected base- line. However, as temperatures rise, net global demand for energy will eventually rise as well (Scheinder et al., 2007). Millennium goals were set solely by indicators of changes in energy use per unit of GDP and/or by total or per capita emissions of CO2. Tracking indicators of protected areas for biological diversity, changes in forests, and access to water all appear in the goals, but they are not linked to climate-change impacts or adaptation; nor are they identified as part of a country’s capacity to adapt to climate change (Yohe et al., 2007). With the unprecedented increase in the population, the industrial products, and the development of technology, human beings started to search for new and alterna- tive ways of using more and more energy without harming or, perhaps, even destroy- ing the natural environment. This is one of the greatest unsolved problems facing mankind in the near future. There is an unending debate that the key atmospheric energy source, solar radiation, should be harnessed more effectively and turned di- rectly into heat energy to meet the growing demand for cheaper power supplies. The net return from industrial material produced in a country is the reflection of energy consumption of the society in an efficient way. Otherwise, burning fossil fuels without economic industrial return may damage any society in the long run, especially with the appearance of renewable energy resources that are expected to be more economical, and therefore, exploitable in the long run. The extensive fossil fuel reservoirs available today are decreasing at an unprecedented rate and, hence, there are future non-sustainability alarms on this energy source. It is, therefore, necessary to diminish their exploitation rate, even starting from today, by partial replacements, especially through the sustainable alternatives such as solar energy. The fossil fuel quantities that are consumed today are so great that even minor imbalances between supply and demand cause considerable societal disruptions. In order to get rid of such disruptions, at least for the time being, each country 1.4 Energy and Industry 11 imports coal, and especially oil to cover the energy imbalances. The oil embargo by the Organization of Petroleum Exporting Countries (OPEC) in 1973, gave the first serious warning and alarm to industrialized countries that energy self-sufficiency is an essential part of any country concerned for its economic, social, and even cultural survival. In fact, the technological and industrial developments in the last 150 years rendered many countries to energy-dependent status. Worldwide use of energy for several decades, especially in the industrial sectors, appeared to be increasing dramatically, but in the last decade, it has leveled off, and even dropped to a certain extent as shown in Fig. 1.6. In this graph, all forms of energy uses are represented in terms of the amount of coal that would provide the equivalent energy. Around the 1970s most of the predictions foresaw that energy demand would continue to accelerate causing expected severe energy shortages. However, just the opposite situation has developed, and today, there is a surplus of energy on the worldwide market that has resulted from economic downturn coupled with many-fold increases in the oil price during the last 20 years. Fossil fuel reserves in the form of oil and natural gas are still adequate at present consumption rates for the next 50 years. However, with increasing amounts of re- newable energy and discoveries of new reservoirs this span of time is expected to extend for almost a century from now onward. Linkage systems, such as transportation and transmission for industry and settle- ments (e.g., water, food supply, energy, information systems, and waste disposal), are important in delivering the ecosystem and other services needed to support hu- man well-being, and can be subject to climate-related extreme events such as floods, landslides, fire, and severe storms. Fig. 1.6 Changes in annual energy consumption in the world (Dunn 1986) 14 1 Energy and Climate Change For success in these areas, it is necessary to have sound scientific basic research with its proper applications. The basic data for these activities can be obtained from extensive climatic, meteorological, hydrological, and hydro-geological observation network establishments with spatial and temporal monitoring of the uncontrollable variables. Ever greater cooperation is needed in detecting and predicting atmo- spheric changes, and assessing consequential environmental and socio-economic impacts, identifying dangerous pollution levels and greenhouse gases. New and es- pecially renewable energy sources are required for controlling emissions of green- house gases. Consumption of fossil fuels in industry as well as transportation gives rise to significant atmospheric emissions. The major points in energy use are the protection of the environment, human health, and the hydrosphere. Any undesir- able changes in the atmospheric conditions may endanger forests, hydrosphere ecosystems, and economic activities such as agriculture. The ozone layer within the stratosphere is being depleted by reactive chlorine and bromine from human- made chlorofluorocarbons (CFCs) and related substances. Unfortunately, levels of these substances in the atmosphere increase continuously signaling future dangers if necessary precautions are not taken into consideration. It has been stated by Dunn (1986) that several problems have arisen from the in- creased use of energy, e.g., oil spillages resulting from accidents during tanker trans- portation. Burning of various energy resources, especially fossil fuels, has caused a global-scale CO2 rise. If the necessary precautions are not considered in the long run, this gas in the atmosphere could exceed the natural levels and may lead to cli- matic change. Another problem is large-scale air pollution in large cities especially during cold seasons. The use of fossil fuels in automobiles produces exhaust gases that also give rise to air pollution as well as increasing the surface ozone concentra- tion which is dangerous for human health and the environment. Air pollution leads to acid rain that causes pollution of surface and groundwater resources which are the major water supply reservoirs for big cities. In order to reduce all these unwanted and damaging effects, it is consciously desirable to shift toward the use of environmentally friendly and clean renewable energy resources, and especially, the solar energy alternatives. It seems that for the next few decades, the use of conventional energy resources such as oil, coal, and natural gas will continue, perhaps at reduced rates because of some replacement by renewable sources. It is essential to take the necessary measures and developments toward more exploitation of solar and other renewable energy alternatives by the advancement in research and technology. Efforts will also be needed in conversion and moving toward a less energy demanding way of life. The use of energy is not without penalty, in that energy exploitation gives rise to many undesirable degradation effects in the surrounding environment and in life. It is, therefore, necessary to reduce the environmental impacts down to a minimum level with the optimum energy saving and management. If the energy consumption continues at the current level with the present energy sources, which are mainly of fossil types, then the prospects for the future cannot be expected to be sustainable or without negative impacts. It has been understood by all the nations since the 1970s that the energy usage and types must be changed toward more clean and environ- 1.6 Energy and the Atmospheric Environment 15 mentally friendly sources so as to reduce both environmental and atmospheric pollu- tions. Sustainable future development depends largely on the pollution potential of the energy sources. The criterion of sustainable development can be defined as the development that meets the needs of the present without compromising the ability of future generations to meet their own needs. Sustainable development within a soci- ety demands a sustainable supply of energy and an effective and efficient utilization of energy resources. In this regard, solar energy provides a potential alternative for future prospective development. The major areas of environmental problems have been classified by Dincer (2000) as follows: 1. Major environmental accidents 2. Water pollution 3. Maritime pollution 4. Land use and siting impact 5. Radiation and radioactivity 6. Solid waste disposal 7. Hazardous air pollution 8. Ambient air quality 9. Acid rain 10. Stratospheric ozone depletion 11. Global climate change leading to greenhouse effect The last three items are the most widely discussed issues all over the world. The main gaseous pollutants and their impacts on the environment are presented in Table 1.2. Unfortunately, energy is the main source of pollution in any country on its way to development. It is now well known that the sulfur dioxide (SO2) emission from fossil fuels is the main cause of acid rain as a result of which more than half the forests in the Northern Europe have already been damaged. In order to decrease degradation effects on the environment and the atmosphere, technological develop- ments have been sought since the 1973 oil crisis. It has been recently realized that Table 1.2 Main gaseous pollutants Gaseous pollutants Greenhouse Stratospheric Acid effect ozone depletion precipitation Carbon monoxide (CO) + ± Carbon dioxide (CO2) + ± Methane (CH4) + ± Nitric oxide (NO) and nitrogen dioxide (NO2) ± + + Nitrous oxide (N2O) + ± Sulfur dioxide (SO2) − + Chlorofluorocarbon(CFCs) + + Ozone (O3) + + Plus and minus signs indicate proportional and inversely proportional effects whereas ± implies either effect depending on circumstances 16 1 Energy and Climate Change renewable energy sources and systems can have a beneficial impact on the following essential technical, environmental, and political issues of the world. These are: 1. Major environmental problems such as acid rain, stratospheric ozone depletion, greenhouse effect, and smog 2. Environmental degradation 3. Depletion of the world’s non-renewable conventional sources such as coal, oil, and natural gas 4. Increasing energy use in the developing countries 5. World population increase In most regions, climate change would alter the probability of certain weather conditions. The only effect for which average change would be important is sea- level rise, under which there could be increased risk of inundation in coastal settle- ments from average (higher) sea levels. Human settlements for the most part would have to adapt to more or less frequent or intense rain conditions or more or less frequent mild winters and hot summers, although individual day weather may be well within the range of current weather variability and thus not require exception- ally costly adaptation measures. The larger, more costly impacts of climate change on human settlements would occur through increased (or decreased) probability of extreme weather events that overwhelm the designed resiliency of human systems. Much of the urban center managements as well as the governance structures that direct and oversee them are related to reducing environmental hazards, including those posed by extreme weather events and other natural hazards. Most regulations and management practices related to buildings, land use, waste management, and transportation have important environmental aspects. Local capacity to limit envi- ronmental hazards or their health consequences in any settlement generally implies local capacity to adapt to climate change, unless adaptation implies particularly ex- pensive infrastructure investment. An increasing number of urban centers are developing more comprehensive plans to manage the environmental implications of urban development. Many techniques can contribute to better environmental planning and management including market- based tools for pollution control, demand management and waste reduction, mixed- use zoning and transport planning (with appropriate provision for pedestrians and cyclists), environmental impact assessments, capacity studies, strategic environ- mental plans, environmental audit procedures, and state-of-the-environment reports (Haughton 1999). Many cities have used a combination of these techniques in de- veloping “Local Agenda 21s,” which deal with a list of urban problems that could closely interact with climate change and energy consumption in the future. Exam- ples of these problems include the following points (WRI 1996): 1. Transport and road infrastructure systems that are inappropriate to the settle- ment’s topography (could be damaged by landslides or flooding with climate change) 2. 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Stockholm Environment Institute, Boston Rosenzweig C, Casassa G, Karoly DJ, Imeson A, Liu C, Menzel A, Rawlins S, Root TL, Seguin B, Tryjanowski P (2007) Assessment of observed changes and responses in natural and managed systems. In: Parry ML, Canziani OF, Palutikof JP, van der Linden PJ, Hanson CE (eds) Climate change 2007: impacts, adaptation and vulnerability. Cambridge University Press, Cambridge, UK, pp 79–131 Sachs JD (2005) The end of poverty: economic possibilities for our time. Penguin, New York Schneider S, Semenov H, Patwardhan S, Burton A, Magadza I, Oppenheimer CHD, Pittock M, Rahman A, Smith JB, Suarez A, Yamin F (2007) Assessing key vulnerabilities and the risk from climate change. In: Parry ML, Canziani OF, Palutikof JP, van der Linden PJ, Hanson CE (eds) Climate change 2007: impacts, adaptation and vulnerability. Cambridge University Press, Cambridge, UK, pp 779–810 Şen Z (2005) Batmayan güneºlerimiz. Our suns without sunset (in Turkish). Bilim Serisi. 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Water Resour Res 41:W02028 Chapter 2 Atmospheric Environment and Renewable Energy 2.1 General Human beings, animals, and plants alike are dependent on some gases, nutrients, and solids that are available rather abundantly and almost freely in nature for their survival. Among these the most precious ones are the air in the atmosphere that living organisms breathe and the water that is available in the hydrosphere either in the troposphere as a vapor (humidity) or in the lithosphere as a liquid (rainfall, runoff, groundwater, seas, lakes) or a solid (glaciers, snow, ice, hail). The atmo- sphere has evolved over geological time and the development of life on the earth has been closely related to the composition of the atmosphere. From the geological records, it seems that about 1.5 billion years ago free oxygen first appeared in the at- mosphere in appreciable quantities (Harvey 1982). The appearance of life was very dependent on the availability of oxygen but once a sufficient amount had accumu- lated for green plants to develop, photosynthesis was able to liberate more into the atmosphere. During all these developments solar radiation provided the sole energy source. In general, there are six different heat and mass exchanges within the atmosphere. These exchanges play the main role in the energy distribution throughout the whole system. The major energy source is solar radiation between the atmosphere and space. This energy source initiates the movement of heat and mass energy from the oceans (seas) into the air and over the land surfaces. The next important heat energy transfer occurs between the free surface bodies (oceans, seas, rivers, reservoirs) and the atmosphere. Thus water vapor, as a result of evaporation, is carried at heights toward the land by the kinetic energy of the wind. Such a rise gives the water va- por potential energy. After condensation by cooling, the water vapor appears in the form of precipitation and falls at high elevations forming the surface runoff which due to gravity flows toward the seas. During its travel toward the earth’s surface, a raindrop loses its potential energy while its kinetic energy increases. Water va- por is the inter-mediator in such a dynamic system. Finally, the water is returned to the seas via streams and rivers, because gravity ultimately takes over the movement of masses. The natural energy cycle appears as an integral part of the hydrological Zekai Sen, Solar Energy Fundamentals and Modeling Techniques 21 DOI: 10.1007/978-1-84800-134-3, ©Springer 2008 24 2 Atmospheric Environment and Renewable Energy Table 2.1 Albedo values Surface Albedo (%) New snow 85 Old snow 75 Clayey desert 29–31 Green grass 8–27 Pine forest 6–19 Calm sea surface 2–4 Granite 12–18 Water (depending on angle of incidence) 2–78 High-level cloud 21 Middle-level cloud (between 3 and 6 km) 48 Low-level cloud sheets 69 Cumulus clouds 70 surfaces and deserts have high albedo values. On the other hand, the surface albedo is also a function of the spectral reflectivity of the surface. The planetary radiation is dominated by emission from the lower troposphere. It shows a decrease with latitude and such a decrease is at a slower rate than the de- crease in the absorbed solar radiation energy. At latitudes less than 30° the planetary albedo is relatively constant at 25% and, consequently, there are large amounts of solar radiation for solar energy activities and benefits in these regions of the earth. However, the solar absorption exceeds the planetary emission between 40° N and 40° S latitudes, and therefore, there is a net excess in low latitudes and a net deficit in high latitudes. Consequently, such an imbalance in the solar radiation energy implies heat transfer from low to high latitudes by the circulations within the atmo- sphere. Accordingly, the solar energy facilities decrease steadily from the equatorial region toward the polar regions. It is possible to state that the natural atmospheric circulations at planetary scales are due to solar energy input into the planetary at- mosphere. In order to appreciate the heat transfer by the atmosphere, the difference between the absorbed and emitted planetary solar radiation amounts can be inte- grated from one pole to other, which gives rise to radiation change as in Fig. 2.1. It can be noted that the maximum transfer of heat occurs between 30° and 40° of latitude and it is equal to 4 ×1015 W. The regional change of net solar radiation budget is shown in Fig. 2.2, which indicates substantial seasonal variation. Increased cloudiness can reduce solar energy production. For many reasons, clouds are critical ingredients of climate and affect the availability of many re- newable energy resources at a location (Monteith 1962). About half of the earth is covered by clouds at any instant. The clouds are highly dynamic in relation to atmospheric circulation. Especially, the irradiative properties of clouds make them a key component of the earth’s energy budget and hence solar energy. 2.2 Weather, Climate, and Climate Change 25 Fig. 2.1 a,b. Zonal solar radiation changes Fig. 2.2 Seasonal solar radiation changes 26 2 Atmospheric Environment and Renewable Energy 2.3 Atmosphere and Its Natural Composition Foreign materials that man releases into the atmosphere at least temporarily and locally change its composition. The most significant man-made atmospheric ad- ditions (carbon monoxide, sulfur oxides, hydrocarbons, liquids such as water va- por, and solid particles) are gases and aerosol particles that are toxic to animal and plant life when concentrated by local weather conditions, such as inversion layer development, orographic boundaries, and low pressure areas. The principal pollution sources of toxic materials are automotive exhausts and sulfur-rich coal and petroleum burned for power and heating. Fortunately, most toxic pollutants are rather quickly removed from the atmosphere by natural weather processes depend- ing on the meteorological conditions, which do not have long-term effects as ex- plained in the previous section. In a pollutant intact atmosphere naturally available gases namely, nitrogen, oxy- gen, and carbon dioxide are replenished through cycles lasting many years due to the natural phenomena that take place between various spheres. Figure 2.3 shows the interaction between the atmosphere, biosphere, lithosphere, and hydrosphere for the nitrogen cycle that is the main constituent in the atmosphere and it completes its renewal process about once every 100 million years. Nitrogen is the dominant ele- ment in the lower atmosphere (about 78%) but it is among the rarer elements both in the hydrosphere and the lithosphere. It is a major constituent not only of the atmo- sphere, but also of the animals and plants of the living world where it is a principal element in proteins, the basic structural compounds of all living organisms. Certain microscopic bacteria convert the tremendous nitrogen supply of the atmosphere into water-soluble nitrate atom groups that can then be used by plants and animals for protein manufacturing. The nitrogen re-enters the atmosphere as dead animals and plants are decomposed by other nitrogen-releasing bacteria. The second major constituent of the lower atmosphere is oxygen (about 21%), which is the most abundant element in the hydrosphere and lithosphere. Most of the uncombined gaseous oxygen of the atmosphere is in neither the hydrosphere nor the lithosphere but as a result of photosynthesis by green plants. In the photo- synthesis process sunlight breaks down water into hydrogen and oxygen. The free oxygen is utilized by animals as an energy source being ultimately released into the atmosphere combined with carbon as CO2, which is taken up by plants to begin the cycle again, as shown in Fig. 2.4. Such a cycle recycles all the oxygen available in the atmosphere in only 3000 years. Thus the free oxygen like nitrogen is closely interrelated with the life processes of organisms. Although CO2 is one of the minor constituents of the lower atmosphere, it plays a fundamental role in the atmospheric heat balance, like ozone within the strato- sphere, and is a major controlling factor in the earth’s patterns of weather and cli- mate. The CO2 cycle is shown schematically in Fig. 2.5. Green plants directly use atmospheric CO2 to synthesize more complex carbon compounds which, in turn, are the basic food for animals and non-green plants. The carbon is ultimately returned into the atmosphere as a waste product of animal and plant respiration or decomposition just as free oxygen is contributed by green plant 2.4 Anthropogenic Composition of the Atmosphere 29 There is an increase in CO2 in the atmosphere due to the increased use of fossil fuels and many scientists say that this results in global warming. The same thing is now said about global warming as was said about the ozone problem. It is not quite possible to reduce the production of CO2, because of economics and the science for CO2 and global warming is not completely certain. 2.4.1 Carbon Dioxide (CO2) The consumption of the fossil fuels is responsible for the increase of the CO2 in the atmosphere by approximately 3 ×1012 kg/year (IPCC 2007). CO2 is a greenhouse gas and causes an increase in the average temperature on earth. The major problem is the fact that a large amount, approximately 98% of CO2 on earth, is dissolved in the water of the oceans (7.5 ×1014 kg in the atmosphere, 4.1 ×1016 kg in the ocean). The solubility of CO2 decreases with the increasing temperature of water by approximately 3%/degree Kelvin. If the average temperature of the oceans increases the CO2 solubility equilibrium between the atmosphere and the oceans shifts toward the atmosphere and then leads to an additional increase in the greenhouse gas in the atmosphere. The world eco-system is suffering from air pollution and global warming. The issue is a central problem now for every evolving technology to be accepted by the global community. It is therefore necessary to develop new and eco- friendly technologies. The global system is being disturbed such that it is no longer tolerant of further dirty technologies. As a result of burning coal and oil as fuel, the level of CO2 has risen significantly in the last 100 years. It is estimated that CO2 accounts for about 60% of the anthro- pogenic (or human-caused) greenhouse change, known as the enhanced greenhouse effect. If carbon fuels are of biological origin, then sometime in the earth’s distant past there must have been far more CO2 in the atmosphere than there is today. There are two naturally different sources for this gas, as emissions from animal life and de- caying plant matter, etc. (Fig. 2.5), which constitute about 95% of the CO2, and the rest comes from human activity (anthropogenic) sources, including the burning of carbon-based (especially fossil) fuels. It is known that although the anthropogenic share is a comparatively small portion of the total, it contributes in an accumulative manner over time. Since CO2 is one of the large gas molecules that traps long-wave radiation to warm the lower atmosphere by the so-called greenhouse effect, atmospheric scien- tists and meteorologists alike suggested that increase in the CO2 might be causing a general warming of the earth’s climate (IPCC 2007). Worries about the effect of CO2 on the climate have given rise to further detailed studies and investigations to focus attention on the complex interactions between man’s activities and the atmo- sphere that surrounds them and thus may prevent still more serious problems from arising in the future. Although pollutants may originate from natural or man-made activities, the term pollution is often restricted to considerations of air quality as modified by human 30 2 Atmospheric Environment and Renewable Energy actions, particularly when pollutants are emitted from industrial, urban, commer- cial, and nuclear sites at rates in excess of the natural diluting and self-purifying processes currently prevailing in the lower atmosphere. Air pollution seems to be a local problem with three distinctive geographic factors: 1. All the wealth of human beings is defined by the distribution of housing, in- dustry, commercial centers, and motor vehicle transportation between various centers. Such a system forms the major source of man-made pollution. 2. A natural phenomenon in the atmosphere, which controls the local and temporal climatic weather variations as a result of which the pollutants introduced into the atmosphere are either scattered in various directions or carried away by air movements in the form of winds. 3. The interaction between the pollution emissions and the atmosphere may well be modified by local relief factors, especially when pollution is trapped by rela- tively stagnant air within a valley. Over millions of years, much of the CO2 was removed by sea and land flora (plants). Most was returned to the air when the plant material decayed, but some of the carbon was locked up in the form of wood, peat, coal, petroleum, and natural gas (Fig. 2.5). Now that these fuels are burnt, the carbon is being released into the atmo- sphere once again. CO2 is less soluble in warmer water than in cold, and as ocean surface layers warm, CO2 could be driven out of solution and into the atmosphere, thus exacerbating the problem. There are benefits to increased CO2 concentrations as well as potential problems. Plants need CO2 and the optimal concentration for most plants it is estimated to be between 800 and 1200 ppm. Some plants do best at even higher concentrations and for instance the optimal range for rice is 1500 to 2000 ppm. As the atmosphere becomes richer in CO2, crops and other plants will grow more quickly and profusely. A doubling of CO2 concentrations can be ex- pected to increase global crop yields by 30% or more. Higher levels of CO2 increase the efficiency of photosynthesis, and raise plants’ water-use efficiency by closing the pores (stomata) through which they lose moisture. The CO2 effect is twice that for plants that receive inadequate water than for well-watered plants. In addition, higher CO2 levels cause plants to increase their fine root mass, which improves their ability to take in water from the soil (Bradley and Fulmer 2004). 2.4.2 Methane (CH4) While it is 25 times more powerful a warming agent than CO2, methane has a much shorter life span and its atmospheric concentration is only about 17 ppm. Concentra- tions have more than doubled since 1850, though for reasons that are still unclear, they have leveled off since the 1980s. Human activity accounts for about 60% of CH4 emissions, while the rest comes from natural sources such as wetlands. Hu- man sources include leakage from pipelines, evaporation from petroleum recovery and refining operations, rice fields, coal mines, sanitary landfills, and waste from domestic animals. About 20% of the total human greenhouse impact is due to CH4. 2.4 Anthropogenic Composition of the Atmosphere 31 2.4.3 Nitrous Oxide (N2O) Its warming potential is some 300 times that of CO2. It has an atmospheric concen- tration of about 0.32 ppm, up from 0.28 ppm in 1850. In the United States, 70% of man-made nitrous oxide emissions come from the use of nitrogen-containing agri- cultural fertilizers and automobile exhaust. Globally, fertilizers alone account for 70% of all emissions. The Environmental Protection Agency (EPA) has calculated that production of nitrous oxide from vehicles rose by nearly 50% between 1990 and 1996 as older cars without converters were replaced with newer, converter-equipped models. Critics argue that the EPA’s numbers are greatly exaggerated. In addition, they point out that converters reduce emissions of another greenhouse gas, ozone, as well as carbon monoxide and NOx (which leads to smog). 2.4.4 Chlorofluorocarbons (CFCs) These are powerful global warming gases that do not exist in nature but are produced by humans. In the upper atmosphere or stratosphere, CFCs are broken down by sunlight. The chlorine that is released by this decomposition acts as a catalyst to break naturally occurring ozone (O3) molecules into oxygen (O2) molecules. Ozone helps block the sun’s ultraviolet radiation, which can cause skin cancer after long- term exposure. Worldwide CFC emissions have been steadily dropping, and it is expected that ozone depletion (the ozone hole), which reached its peak in the last decade, will drop to zero later this century. The fact that CFCs are chemically inert (that is, they do not react with other chemicals) makes them very useful in a wide variety of applications, but it also means that they last for a very long time in the atmosphere, about 50,000 years. These gases affect the climate in different ways depending upon their location in the atmosphere. At lower altitudes, they trap heat like other greenhouse gases and have a much stronger warming effect than CO2. In fact, some can trap as much as 10,000 times more heat per molecule than CO2. While CO2 is measured in atmo- spheric concentrations of parts per million, CFCs are measured in parts per trillion. Despite their low concentrations, it is believed that these gases account for about 15% of the human greenhouse change (Bradley and Fulmer 2004). 2.4.5 Water Vapor (H2O) Almost 70% of the earth’s surface is covered by water bodies which are referred to collectively as the hydrosphere. Although there is not extensive human activity in the hydrosphere itself, the intensive activities on the land threaten the biological richness of oceans and especially the coastal areas where about 60% of the world’s population live. Although legislative measures are taken, their application cannot be 34 2 Atmospheric Environment and Renewable Energy Concentrations of air pollutants in general and fine particulate matter in partic- ular may change in response to climate change because their formation depends, in part, on temperature and humidity. Air-pollution concentrations are the result of interactions between variations in the physical and dynamic properties of the atmo- sphere on time scales from hours to days, atmospheric circulation features, wind, topography, and energy use. Some air pollutants demonstrate weather-related sea- sonal cycles (Confalonieri et al., 2007). 2.5 Energy Dynamics in the Atmosphere With the unprecedented increase in the population and industrial products and the development of technology, human beings search for ways of using more and more energy without harming or, perhaps, even destroying the natural environment. This is one of the greatest unsolved problems facing humankind in the near future. There is an unending debate that key atmospheric energy sources such as solar and wind power should be harnessed more effectively and turned directly into heat energy to meet the growing demand for cheaper power supplies. All types of energy can be traced back to either atmospheric activities in the past or related to the present and future activities within the atmosphere. The renewable or primary energy sources are regarded as the ones that are related to present at- mospheric movements, however, secondary energy sources are non-renewable and have been deposited in the depths of the earth typically in the form of oil and coal. They are also referred to as the fossil fuels. So, burning the fossil fuels, the stored energy of past atmospheric activities, is added to the present energy demand. Con- sequently, their burning leads to the altering of the weather in the short term and climate in the long term in an unusual manner. The renewable energy sources are primary energy alternatives that are part of the everyday weather elements such as sunshine and the wind. External sources of energy to the atmosphere are the sun’s radiation (insolation) and the sun and moon’s gravitation in the form of tides. Additionally, the internal sources are the earth’s heat through conduction and earth’s gravitation and rotation. These internal and external sources are constant energy supplies to the atmosphere. Apart from balancing each other they both contain thermal and mechanical forms depending on heat and mass, respectively. The sun’s radiation (insolation) is the main source of heat energy and earth’s motion and gravitation exert most influence on the masses. The atmosphere is fed by a continuous flux of radiation from the sun and gravitation remains a constant force internally. Briefly, radiation is the transfer of energy through matter or space by electric or magnetic fields suitably called electromagnetic waves. High-energy waves are emitted from the tiniest particles in the nucleus of an atom, whereas low energy is associated with larger whole atoms and molecules. The highest energy waves are known as radioactivity since they are generated by the splitting (fission) or joining (fusion) of particles, and low energy waves result from vibration and collision of 2.6 Renewable Energy Alternatives and Climate Change 35 molecules. The sun can be regarded as a huge furnace in which hydrogen atoms fuse into helium at immensely high temperatures (Chapter 3). The solar radiation is partially absorbed by matter of increasing size, first by exciting electrons as in ionization and then by simulating molecular activity at lower energy levels. The latter is sensed as heat. Hence, radiation is continuously degraded or dissipated from tiny nuclear particles to bigger molecules of matter. 2.6 Renewable Energy Alternatives and Climate Change Renewable energy sources are expected to become economically competitive as their costs already have fallen significantly compared with conventional energy sources in the medium term, especially if the massive subsidies to nuclear and fossil forms of energy are phased out. Finally, new renewable energy sources offer huge benefits to developing countries, especially in the provision of energy services to the people who currently lack them. Up to now, the renewable sources have been com- pletely discriminated against for economic reasons. However, the trend in recent years favors the renewable sources in many cases over conventional sources. The advantages of renewable energy are that they are sustainable (non-depletable), ubiquitous (found everywhere across the world in contrast to fossil fuels and min- erals), and essentially clean and environmentally friendly. The disadvantages of re- newable energy are its variability, low density, and generally higher initial cost. For different forms of renewable energy, other disadvantages or perceived problems are pollution, odor from biomass, avian with wind plants, and brine from geothermal. In contrast, fossil fuels are stored solar energy from past geological ages. Even though the quantities of oil, natural gas, and coal are large, they are finite and for the long term of hundreds of years they are not sustainable. The world energy de- mand depends, mainly, on fossil fuels with respective shares of petroleum, coal, and natural gas at 38%, 30%, and 20%, respectively. The remaining 12% is filled by the non-conventional energy alternatives of hydropower (7%) and nuclear energy (5%). It is expected that the world oil and natural gas reserves will last for several decades, but the coal reserves will sustain the energy requirements for a few centuries. This means that the fossil fuel amount is currently limited and even though new reserves might be found in the future, they will still remain limited and the rate of energy demand increase in the world will require exploitation of other renewable alterna- tives at ever increasing rates. The desire to use renewable energy sources is not only due to their availability in many parts of the world, but also, more empathetically, as a result of the fossil fuel damage to environmental and atmospheric cleanness issues. The search for new alternative energy systems has increased greatly in the last few decades for the following reasons: 1. The extra demand on energy within the next five decades will continue to in- crease in such a manner that the use of fossil fuels will not be sufficient, and therefore, the deficit in the energy supply will be covered by additional energy production and discoveries. 36 2 Atmospheric Environment and Renewable Energy 2. Fossil fuels are not available in every country because they are unevenly dis- tributed over the world, but renewable energies, and especially solar radiation, are more evenly distributed and, consequently, each country will do its best to research and develop their own national energy harvest. 3. Fossil fuel combustion leads to some undesirable effects such as atmospheric pollution because of the CO2 emissions and environmental problems including air pollution, acid rain, greenhouse effect, climate changes, oil spills, etc. It is understood by now that even with refined precautions and technology, these undesirable effects can never be avoided completely but can be minimized. One way of such minimization is to substitute at least a significant part of the fossil fuel usage by solar energy. In fact, the worldwide environmental problems resulting from the use of fossil fuels are the most compelling reasons for the present vigorous search for future alter- native energy options that are renewable and environmentally friendly. The renew- able sources have also some disadvantages, such as being available intermittently as in the case of solar and wind sources or fixed to certain locations including hy- dropower, geothermal, and biomass alternatives. Another shortcoming, for the time being, is their transportation directly as a fuel. These shortcomings point to the need for intermediary energy systems to form the link between their production site and the consumer location, as already mentioned above. If, for example, heat and elec- tricity from solar power plants are to be made available at all times to meet the demand profile for useful energy, then an energy carrier is necessary with storage capabilities over long periods of time for use when solar radiation is not available (Veziroğlu 1995). The use of conventional energy resources will not be able to offset the energy demand in the next decades but steady increase will continue with undesirable en- vironmental consequences. However, newly emerging renewable alternative energy resources are expected to take an increasing role in the energy scenarios of the future energy consumptions. 2.6.1 Solar Energy Almost all the renewable energy sources originate entirely from the sun. The sun’s rays that reach the outer atmosphere are subjected to absorption, reflection, and transmission processes through the atmosphere before reaching the earth’s surface (Chap. 3). On the other hand, depending on the earth’s surface topography, as ex- plained by Neuwirth (1980), the solar radiation shows different appearances. The emergence of interest in solar energy utilization has taken place since 1970, principally due to the then rising cost of energy from conventional sources. Solar radiation is the world’s most abundant and permanent energy source. The amount of solar energy received by the surface of the earth per minute is greater than the energy utilization by the entire population in one year. For the time being, solar energy, being available everywhere, is attractive for stand-alone systems particularly 2.6 Renewable Energy Alternatives and Climate Change 39 As a result of climate change by the 2070s, hydropower potential for the whole of Europe is expected to decline by 6%, translated into a 20 – 50% decrease around the Mediterranean, a 15 – 30% increase in northern and eastern Europe, and a stable hydropower pattern for western and central Europe (Lehner et al., 2001). Another possible conflict between adaptation and mitigation might arise over water resources. One obvious mitigation option is to shift to energy sources with low greenhouse gas emissions such as small hydropower. In regions, where hy- dropower potentials are still available, and also depending on the current and future water balance, this would increase the competition for water, especially if irrigation might be a feasible strategy to cope with climate change impacts on agriculture and the demand for cooling water by the power sector is also significant. This recon- firms the importance of integrated land and water management strategies to ensure the optimal allocation of scarce natural resources (land, water) and economic in- vestments in climate change adaptation and mitigation and in fostering sustainable development. Hydropower leads to the key area of mitigation, energy sources and supply, and energy use in various economic sectors beyond land use, agriculture, and forestry. The largest amount of construction work to counterbalance climate change im- pacts will be in water management and in coastal zones. The former involves hard measures in flood protection (dykes, dams, flood control reservoirs) and in coping with seasonal variations (storage reservoirs and inter-basin diversions), while the latter comprises coastal defense systems (embankment, dams, storm surge barriers). Adaptation to changing hydrological regimes and water availability will also require continuous additional energy input. In water-scarce regions, the increas- ing reuse of waste water and the associated treatment, deep-well pumping, and especially large-scale desalination, would increase energy use in the water sector (Boutkan and Stikker 2004). 2.6.4 Biomass Energy Overall 14% of the world’s energy comes from biomass, primarily wood and char- coal, but also crop residue and even animal dung for cooking and some heating. This contributes to deforestation and the loss of topsoil in developing countries. Biofuel production is largely determined by the supply of moisture and the length of the growing season (Olesen and Bindi 2002). By the twenty-second century, land area devoted to biofuels may increase by a factor of two to three in all parts of Europe (Metzger et al., 2004). Especially, in developing countries biomass is the major com- ponent of the national energy supply. Although biomass sources are widely avail- able, they have low conversion efficiencies. This energy source is used especially for cooking and comfort and by burning it provides heat. The sun’s radiation that conveys energy is exploited by the plants through photosynthesis, and consequently, even the remnants of plants are potential energy sources because they conserve his- toric solar energy until they perish either naturally after very long time spans or 40 2 Atmospheric Environment and Renewable Energy artificially by human beings or occasionally by forest fires. Only 0.1% of the so- lar incident energy is used by the photosynthesis process, but even this amount is ten times greater than the present day world energy consumption. Currently, living plants or remnants from the past are reservoirs of biomass that are a major source of energy for humanity in the future. However, biomass energy returns its energy to the atmosphere partly by respiration of the living plants and partly by oxidation of the carbon fixed by photosynthesis that is used to form fossil sediments which eventually transform to the fossil fuel types such as coal, oil, and natural gas. This argument shows that the living plants are the recipient media of incident solar radi- ation and they give rise to various types of fossil fuels. Biofuel crops, increasingly an important source of energy, are being assessed for their critical role in adaptation to climatic change and mitigation of carbon emis- sions (Easterling et al., 2007). 2.6.5 Wave Energy Water covers almost two thirds of the earth, and thus, a large part of the sun’s radiant energy that is not reflected back into space is absorbed by the water of the oceans. This absorbed energy warms the water, which, in turn, warms the air above and forms air currents caused by the differences in air temperature. These currents blow across the water, returning some energy to the water by generating wind waves, which travel across the oceans until they reach land where their remaining energy is expended on the shore. The possibility of extracting energy from ocean waves has intrigued people for centuries. Although there are a few concepts over 100 years old, it is only in the past two decades that viable schemes have been proposed. Wave power generation is not a widely employed technology, and no commercial wave farm has yet been estab- lished. In the basic studies as well as in the design stages of a wave energy plant, the knowledge of the statistical characteristics of the local wave climate is essential, no matter whether physical or theoretical/numerical modeling methods are to be employed. This information may result from wave measurements, more or less so- phisticated forecast models, or a combination of both, and usually takes the form of a set of representative sea states, each characterized by its frequency of occurrence and by a spectral distribution. Assessment of how turbo-generator design and the production of electrical energy are affected by the wave climate is very important. However, this may have a major economic impact, since if the equipment design is very much dependent on the wave climate, a new design has to be developed for each new site. This introduces extra costs and significantly limits the use of serial construction and fabrication methods. Waves have an important effect in the planning and design of harbors, waterways, shore protection measures, coastal structures, and the other coastal works. Surface waves generally derive their energy from the wind. Waves in the ocean often have irregular shapes and variable propagation directions because they are under the in- 2.6 Renewable Energy Alternatives and Climate Change 41 fluence of the wind. For operational studies, it is desired to forecast wave parameters in advance. Özger and Şen (2005) derived a modified average wave power formula by using perturbation methodology and a stochastic approach. 2.6.6 Hydrogen Energy Hydrogen is the most abundant element on earth, however, less than 1% is present as molecular hydrogen gas H2; the overwhelming part is chemically bound as H2O in water and some is bound to liquid or gaseous hydrocarbons. It is thought that the heavy elements were, and still are, being built from hydrogen and helium. It has been estimated that hydrogen makes up more than 90% of all the atoms or 75% of the mass of the universe (Weast 1976). Combined with oxygen it generates water, and with carbon it makes different compounds such as methane, coal, and petroleum. Hydrogen exhibits the highest heating value of all chemical fuels. Furthermore, it is regenerative and environment friendly. Solar radiation is abundant and its use is becoming more economic, but it is not harvested on large scale. This is due to the fact that it is difficult to store and move energy from ephemeral and intermittent sources such as the sun. In contrast, fossil fuels can be transported easily from remote areas to the exploitation sites. For the transportation of electric power, it is necessary to invest and currently spend money in large amounts. Under these circumstances of economic limitations, it is more rational to convert solar power to a gaseous form that is far cheaper to transport and easy to store. For this purpose, hydrogen is an almost completely clean-burning gas that can be used in place of petroleum, coal, or natural gas. Hydrogen does not release the carbon compounds that lead to global warming. In order to produce hy- drogen, it is possible to run an electric current through water and this conversion process is known as electrolysis. After the production of hydrogen, it can be trans- ported for any distance with virtually no energy loss. Transportation of gases such as hydrogen is less risky than any other form of energy, for instance, oil which is frequently spilled in tanker accidents, or during routine handling (Scott and Hafele 1990). The ideal intermediary energy carrier should be storable, transportable, pollution- free, independent of primary resources, renewable, and applicable in many ways. These properties may be met by hydrogen when produced electrolytically using solar radiation, and hence, such a combination is referred to as the solar-hydrogen process. This is to say that transformation to hydrogen is one of the most promising methods of storing and transporting solar energy in large quantities and over long distances. Among the many renewable energy alternatives, solar-hydrogen energy is re- garded as the most ideal energy resource that can be exploited in the foreseeable fu- ture in large quantities. On the other hand, where conventional fuel sources are not available, especially in rural areas, solar energy can be used directly or indirectly by the transformation into hydrogen gas. The most important property of hydrogen 44 2 Atmospheric Environment and Renewable Energy References Anderson M (1992) Current status of wind farms in the UK. 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The solar radiation is absorbed, reflected, or diffused by solid particles in any location of space and especially by the earth, which depends on its arrival for many activities such as weather, climate, agriculture, and socio-economic movement. Depending on the geometry of the earth, its distance from the sun, geographical location of any point on the earth, astronomical coordinates, and the composition of the atmosphere, the incoming irradiation at any given point takes different shapes. A significant fraction of the solar radiation is absorbed and reflected back into space through atmospheric events and consequently the solar energy balance of the earth remains the same. This chapter provides the basic astronomical variables and their definitions and uses in the calculation of solar radiation (energy) assessment. These basic concepts, definitions, and derived astronomical equations furnish the foundations of solar en- ergy evaluation at any given location. They are deterministic in the sense that there is no uncertainty about the effect of weather events, which will be taken into con- sideration in the next three chapters. 3.2 The Sun The sun has played a dominant role since time immemorial for different natural activities in the universe at large and in the earth in particular for the formation of fossil and renewable energy sources. It will continue to do so until the end of the earth’s remaining life, which is predicted to be about 5×109 years. Deposited fossil fuels, in the form of coal, that are used through combustion are expected to last for approximately the next 300 years at the most, and from then onward human beings will be left with renewable energy resources only. Zekai Sen, Solar Energy Fundamentals and Modeling Techniques 47 DOI: 10.1007/978-1-84800-134-3, ©Springer 2008 50 3 Solar Radiation Deterministic Models the unlimited source of solar energy. The source of almost all renewable energy is the enormous fusion reactor in the sun which converts H into He at the rate of 4 ×106 tonnes per second. The theoretical predictions show that the conversion of four H atoms (i. e., four protons) into He using carbon nuclei as a catalyst will last about 1011 years before the H is exhausted. The energy generated in the core of the sun must be transferred toward its surface for radiation into the space. Protons are converted into He nuclei and because the mass of the He nucleus is less than the mass of the four protons, the difference in mass (around 5 ×109 kg/second) is converted into energy, which is transferred to the surface where electromagnetic radiation and some particles are emitted into space; this is known as the solar wind. It is well known by now that the planets, dust, and gases of the solar system that orbit around the enormous central sun contain 99.9% of the mass of the system and provide the gravitational attraction that holds it together. The average density of the sun is slightly greater than of water at 1.4 g/cm3. One of the reasons for sun’s low density is that it is composed predominantly of H, which is the light- est element. Its massive interior is made up of matter held in a gaseous state by enormously high temperatures. Consequently, in smaller quantities, gases at such extreme temperatures would rapidly expand and dissipate. The emitted energy of the sun is 3.8 ×1026 W and it arises from the thermonuclear fusion of H into He at temperatures around 1.5 ×106 K in the core of the sun, which is given by the following chemical equation (Şen 2004) and it is comparable with Fig. 3.2: 411H →43 He+ 2β + energy(26.7 MeV) In the core of the sun, the dominant element is He (65% by mass) and the H content is reduced to 35% by mass as a direct result of consumption in the fusion reactions. It is estimated that the remaining H in the sun’s core is sufficient to main- tain the sun at its present luminosity and size for another 4 ×109 years. There is a high-pressure gradient between the core of the sun and its perimeter and this is balanced by the gravitational attraction of the sun’s mass. The energy released by the thermonuclear reaction is transported by energetic photons, but, because of the strong adsorption by the peripheral gases, most of these photons do not penetrate the surface. In all regions of the electromagnetic spectrum, the outer layers of the sun continuously lose energy by radiation emission into space in all directions. Con- sequently, a large temperature gradient exists between the core and the outer parts of the sun. The sun radiates electromagnetic energy in terms of photons which are light par- ticles. Almost one third of this incident energy on the earth is reflected back, but rest is absorbed and is, eventually, retransmitted to deep space in terms of long-wave in- frared radiation. Today, the earth radiates just as much energy as it receives and sits in a stable energy balance at a temperature suitable for life on the earth. In fact, solar radiation is in the form of white light and it spreads over a wider spectrum of wave- lengths from the short-wave infrared to ultraviolet. The wavelength distribution is directly dependent on the temperature of the sun’s surface. The total power that is incident on the earth’s surface from the sun every year is 1.73 ×1014 kW and this is equivalent to 1.5 ×1018 kWh annually, which is equiv- 3.3 Electromagnetic (EM) Spectrum 51 alent to 1.9 ×1014 coal equivalent tons (cet). Compared to the annual world con- sumption of almost 1010 cet, this is a very huge and unappreciable amount. It is approximately 10,000 times greater than that which is consumed on the earth an- nually. In engineering terms, this energy is considered to be uniformly spread all over the world’s surface and, hence, the amount that falls on one square meter at noon time is about 1 kW in the tropical regions. The amount of solar power avail- able per unit area is known as irradiance or radiant-flux density. This solar power density varies with latitude, elevation, and season of the year in addition to time in a particular day (see Sect. 3.7). Most of the developing countries lie within the trop- ical belt of the world where there are high solar power densities and, consequently, they want to exploit this source in the most beneficial ways. On the other hand, about 80% of the world’s population lives between latitudes 35° N and 35° S. These regions receive the sun’s radiation for almost 3000 – 4000 h/year. In solar power density terms, this is equivalent to around 2000 kWh/year, which is 0.25 cet/year. Additionally, in these low latitude regions, seasonal sunlight hour changes are not significant. This means that these areas receive the sun’s radiation almost uniformly throughout the whole year. Apart from the solar radiation, the sunlight also carries energy. It is possible to split the light into three overlapping groups: 1. Photovoltaic (PV) group: produces electricity directly from the sun’s light 2. Photochemical (PC) group: produces electricity or light and gaseous fuels by means of non-living chemical processes 3. Photobiological (PB) group: produces food (animal and human fuel) and gaseous fuels by means of living organisms or plants The last two groups also share the term “photosynthesis”, which means literally the building (synthesizing) by light. 3.3 Electromagnetic (EM) Spectrum All solid, liquid, and gaseous matter is no more than a vibrating cosmic dance of en- ergy. Matter is perceived by human beings in a three-dimensional form with struc- ture, density, color, and sound. Density makes the matter solid, liquid or gaseous and, in addition, the movement of its atoms and molecules gives rise to the sensa- tions of heat and cold. The interaction of matter with the area of the electromagnetic (EM) spectrum that is known as light gives it color, perceived through the eyes. However, if one takes a step inward, it can be observed that matter is composed of large and small molecules. Each atom, until the advent of modern physics, was considered to consist of a nucleus of positively charged protons and zero-charged neutrons, with a number of “shells” of orbiting, negatively charged electrons. With these particles, the H and He atoms are shown in Fig. 3.3. In modern physics, the subatomic particles are considered as wave packets, as electromagnetic force fields, and as energy relationships. They have “spin” and they rotate about the axis of their movement. They have no “oscillation,” like an ultra-high-speed pendulum. By spinning and oscillating, they 52 3 Solar Radiation Deterministic Models Fig. 3.3 a H atom. b He atom move around relative to each other in three dimensions. They also have an “electrical charge” and a “magnetic moment” and, therefore, an EM field. Radiation consists of atomic or subatomic particles, such as electrons, and/or EM energy waves, such as heat, light, radio and television signals, infrared, X-rays, gamma rays, etc. Particle and wave are two forms of light and EM radiation. The former has lo- calized mass in space and can have charge in addition to other properties. Two par- ticles cannot occupy the same space at the same time. On the other hand, wave has no mass, is spread out over space at the speed of light, and obeys the superposition principle which means two or more waves can occupy the same space at the same time. For instance, EM waves consist of electric and magnetic fields, which are per- pendicular to each other and perpendicular to the direction of travel as shown in Fig. 3.4. The oscillating field planes of electric and magnetic waves are perpendicular to each other, i. e., when the electric field E and magnetic field Hm are in the yz-plane, respectively, the propagation direction is along the x axis. Solar radiation EM waves travel with the speed of light and cover the distance between the sun and the earth in about 8 min. EM radiation from the sun is described by its wavelength, λ (distance from peak to peak of the wave), and frequency, f (number of cycles per second). As the wave moves past a location, the frequency is also expressed as the number Fig. 3.4 EM waves 3.4 Energy Balance of the Earth 55 Fig. 3.7 EM spectrum 3.4 Energy Balance of the Earth The earth radiates the same amount of energy into space as the amount of EM en- ergy absorbed from the sun (Fig. 3.8). Hence, in the long term the energy balance of the earth is essentially zero, except for the small amount of geothermal energy generated by radioactive decay. If the in and out energies are not balanced then the earth is expected to increase or to decrease in temperature and radiate more or less energy into space to establish another balance level. At this point, it is useful to remember the present day global warming and climate change phenomena. Clear- sky shortwave solar radiation varies in response to altitude and elevation, surface gradient (slope), and orientation (aspect), as well as position relative to neighboring surfaces. The sun’s radiation (solar) energy first interacts with the atmosphere and then reaches to the earth’s surface (Fig. 3.9). Incoming solar radiation of 100 units (100%) is shared by cloud and surface reflections and the rest is absorbed by the atmosphere and the earth’s surface. The atmospheric absorption accounts for about two thirds of the incoming ir- radiation and it is primarily due to water vapor and to a lesser degree by CO2 that exist in the atmospheric composition (Chap. 2). Absorbed EM radiation is converted into thermal energy at absorption locations. The earth’s surface has a comparatively lower temperature, typically between 270 K and 320 K, and hence radiates at longer 56 3 Solar Radiation Deterministic Models Fig. 3.8 Long-term earth energy balance Fig. 3.9 Terrestrial solar radiation according to (Şen 2004) wavelengths that do not appear appreciably in the spectrum of Fig. 3.7. This energy drives weather events in terms of evaporation and transportation of heat from the equator to the poles (Hadley cell) and additionally provides energy for wind and currents in the ocean with some absorption and storage in plants as photosynthesis. Some of this energy is radiated back to space (clear skies) as infrared radiation and the rest is absorbed in the atmosphere. Some of the infrared radiation goes back into space and the rest is re-radiated back to earth. Hence, clear nights are cooler than cloudy nights because the nighttime radiation into space has a temperature of 3 K. As the solar radiation reaches the upper boundary of earth’s atmosphere, the light starts to scatter depending on the cloud cover and the atmospheric com- position (Hay 1984). A proportion of the scattered light comes to earth as diffuse radiation. The term “sunshine” implies not the diffuse but the direct solar radiation 3.5 Earth Motion 57 Fig. 3.10 Visible and radio waves reach the surface (solar beam) that comes straight from the sun. On a clear day, direct radiation can approach a power density of 1000 W/m2, which is known as solar power density for solar collector testing purposes. The atmosphere is largely transparent to visible and radio wavelengths, but absorbs radiation at other wavelengths (Fig. 3.10). This figure shows the EM wave recipient change by altitude. It is obvious that of all the EM waves radio waves are receivable at the lowest altitude. 3.5 Earth Motion Earth’s orbital movement around the sun affects the climate, solar radiation, and temporal variations. The total amount of solar radiation reaching the earth’s surface can vary due to changes in the sun’s output, such as those associated with earth’s axis tilt, wobble, and orbital trace. Orbital oscillations can also result in different parts of the earth getting more or less sunlight even when the total amount reaching the planet remains constant, which is similar to the way the tilt in the earth’s axis produces the hemispheric seasons. Due to the variations in the earth’s orbital move- ments around the sun there are very slow climate cycles. The earth’s rotation about its own axis and revolution around the sun is very involved and has the combination of three movements at any time. These are as follows: 1. Tilt (Fig. 3.11): Due to the axis tilt the sun’s motion across the sky changes during each year. The tilt of the earth changes cyclically between 21°45’ and 24°15’ with a cyclic period of 42,000 years. A large tilt warms the poles, which means more solar radiation input and causes smaller temperature differences in the summer hemisphere. The tilt of the earth’s rotational axis with respect to the sun is called obliquity, which is defined as the angle between the earth’s orbit and the plane of the 60 3 Solar Radiation Deterministic Models Fig. 3.15 Earth’s axis tilt affect on incident radiation per area In this figure, it is summer at the south pole and there is sunlight 24 h a day, while at the north pole there is no sunlight (see Sect. 3.12.3). In the northern hemisphere it is winter, because the same amount of incident radiation is spread over a larger area. Notice the parallel solar radiation lines on the plane at the top and at the equator, which has the same length as the parallel lines between rays. Of course, the same solar energy will impinge on both plates, but the one at the top will have more surface area and hence its solar energy absorption will be comparatively smaller than the other plate at the equator. This implies that the more the angle (zenith angle) between the normal of the plate and the solar beam, the less is the solar energy generation (see Sect. 3.12). This tremendous amount of solar energy radiates into space from the surface of the sun with a power of 3.8 ×1023 kW. Solar energy is referred to as renew- able and/or sustainable energy because it will be available as long as the sun con- tinues to shine. The energy from the sunshine, EM radiation, is referred to as in- solation. The earth intercepts only a very small portion of this power, since the projected area of the earth as seen from the sun is very small. At the top of the at- mosphere, the power intercepted by the earth is 173×109 W, which is equivalent to 1360 W/m2. On a clear day, at the surface of the earth, the solar radiation is about 1000 – 1200 W/m2, on a plane perpendicular to the sun’s beam depending on the elevation and the amount of haze in the atmosphere. In order to appreciate the arrival of solar radiation on the earth’s surface, it is very helpful to simplify the situation as shown in Fig. 3.15 where the earth is repre- sented as a sphere. This implies that at the equator a horizontal surface at that point immediately under the sun would receive 1360 W/m2. Along the same longitude but at different latitudes, the horizontal surface receives less solar radiation from the equator toward the polar region. If the earth rotates around the vertical axis to the earth–sun plane, then any point on the earth’s surface receives the same amount of radiation throughout the year. However, the earth rotates around an axis which is inclined to the earth–sun plane, and therefore, the same point receives different amounts of solar radiation on different days and times in a day throughout the year. Hence, the seasons start to play a role in the incident solar radiation variation. 3.6 Solar Radiation 61 3.6 Solar Radiation Solar radiation from the sun after traveling in space enters the atmosphere at the space–atmosphere interface, where the ionization layer of the atmosphere ends. Af- terwards, a certain amount of solar radiation or photons are absorbed by the atmo- sphere, clouds, and particles in the atmosphere, a certain amount is reflected back into the space, and a certain amount is absorbed by the earth’s surface. The earth’s surface also reflects a certain amount of energy by radiation at different wavelengths due to the earth’s surface temperature. About 50% of the total solar radiation re- mains in the atmosphere and earth’s surface. The detailed percentages can be seen in Fig. 3.9. The earth’s rotation around its axis produces hourly variations in power intensities at a given location on the ground during the daytime and results in com- plete shading during the nighttime. The presence of the atmosphere and associated climate effects both attenuate and change the nature of the solar energy resource. The combination of reflection, absorption (filtering), refraction, and scattering result in highly dynamic radiation levels at any given location on the earth. As a result of the cloud cover and scattering sunlight, the radiation received at any point is both direct (or beam) and diffuse (or scattered). After the solar radiation enters the earth’s atmosphere, it is partially scattered and partially absorbed. The scattered radiation is called diffuse radiation. Again, a por- tion of this diffuse radiation goes back to space and a portion reaches the ground. Solar radiation reaches the earth’s surface in three different ways as direct, diffuse, and reflected irradiations as in Fig. 3.16. The quantity of solar radiation reaching any particular part of the earth’s surface is determined by the position of the point, time of year, atmospheric diffusion, cloud cover, shape of the surface, and reflectivity of the surface. However, in hilly and mountainous terrains, the distribution of slopes has ma- jor effects on surface climate and radiation amounts. Surface radiation may change widely according to the frequency and optical thickness of clouds, and modeling these cloud properties successfully is important for treatment of the surface energy balance (Chap. 4). Direct solar radiation is that which travels in a straight line from the sun to the earth’s surface. Clear-sky day values are measured at many localities in the world. To model this would require knowledge of intensities and direction at different times of the day. Direct radiation as the name implies is the amount of solar radiation received at any place on the earth directly from the sun without any disturbances. In practical terms, this is the radiation which creates sharp shadows of the subjects. There is no interference by dust, gas, and cloud or any other intermediate material on the direct solar radiation. Direct radiation is practically adsorbed by some inter- mediator and then this inter-mediator itself radiates EM waves similar to the main source which is the sun. Direct solar radiation can be further reflected and dispersed across the surface of the earth or back into the atmosphere. On the other hand, the radiation arriving on the ground directly in line from the sun is called direct or beam radiation (Fig. 3.16a). Beam radiation is the solar radiation received from the sun 62 3 Solar Radiation Deterministic Models Fig. 3.16 a–c. Solar radiation paths. a Direct. b Diffuse. c Reflected without scatter by the atmosphere. It is referred to as direct solar radiation. This is actually the photon stream in space and has a speed of 3,000,000 km/s. Passing through the atmosphere, the solar beam undergoes wavelength- and direction-dependent adsorption and scattering by atmospheric gases, aerosols, and cloud droplets. The scattered radiation reaching the earth’s surface is referred to as diffuse radiation (Fig. 3.16b). Diffuse radiation is first intercepted by the con- stituents of the air such as water vapor, CO2, dust, aerosols, clouds, etc., and then released as scattered radiation in many directions. This is the main reason why dif- fuse radiation scattering in all directions and being close to the earth’s surface as a source does not give rise to sharp shadows. When the solar radiation in the form of an electromagnetic wave hits a particle, a part of the incident energy is scattered in all directions and it is called diffuse radiation. All small or large particles in na- ture scatter radiation. Diffuse radiation is scattered out of the solar beam by gases (Rayleigh scattering) and by aerosols (which include dust particles, as well as sul- fate particles, soot, sea salt particles, pollen, etc.). Reflected radiation is mainly re- flected from the terrain and is therefore more important in mountainous areas. Direct shortwave radiation is the most important component of global radiation because it contributes the most to the energy balance and also the other components depend 3.6 Solar Radiation 65 This is referred to as the relative optical air mass. On the basis of the assumptions that the earth does not have any eccentricity and the troposphere is completely ho- mogeneous and free of any aerosol or water vapor, then the relative optical mass, m, in any direction with an angle of θz from the zenith can be written simply as m = ma secθz = ma cosθz . (3.7) If the assumptions are applied to an actual case, this expression yields errors of up to 25% at θz = 60°, which decrease to 10% at θz = 85° (Iqbal 1986). At sea level, m = 1 when the sun is at the zenith and m = 2 for θz = 60°. Air mass as defined in Eq. 3.7 is a useful quantity in dealing with atmospheric ef- fects. It indicates the relative distance that light must travel through the atmosphere to a given location. There is no attenuation effect in the space outside the atmo- sphere, the air mass is regarded as equal to zero and as equal to one when the sun is directly overhead. However, an air mass value of 1.5 is considered more repre- sentative of average terrestrial conditions and it is commonly used as a reference condition in rating photovoltaic modules and arrays (Fig. 3.18). The two main factors affecting the air mass ratio are the direction of the path and the local altitude. The path’s direction is described in terms of its zenith angle, θz , which is the angle between the path and the zenith position directly overhead. The adjustment in air mass for local altitude is made in terms of the local atmospheric pressure, p, and is defined as m = p p0 m0 , (3.8) where p is the local pressure and m0 and p0 are the corresponding air mass and pres- sure at sea level. Equation 3.7 is valid only for zenith angles less than 70° (Kreith Fig. 3.18 Sun’s angle and distance through atmosphere 66 3 Solar Radiation Deterministic Models and Kreider 1978). Otherwise, the secant approximation under-estimates solar en- ergy because atmospheric refraction and the curvature of the earth have not been accounted for. Frouin et al. (1989) have suggested the use of the following: m = [ cosθz + 0.15 (93.885 − θz)−1.253 ]−1 . (3.9) Kreith and Kreider (1978) and Cartwright (1993) have suggested the use of the following relationship, where the model requires the calculation of air mass ratio as m = [ 1229 + (614sinα)2 ]1/2 − 614sinα . (3.10) It is obvious then that the relative proportion of direct to diffuse radiation depends on the location, season of the year, elevation from the mean sea level, and time of day. On a clear day, the diffuse component will be about 10 – 20% of the total radia- tion but during an overcast day it may reach up to 100%. This point implies, practi- cally, that in the solar radiation and energy calculations, weather and meteorological conditions in addition to the astronomical implications must be taken into consider- ation. On the other hand, throughout the year the diffuse solar radiation amount is smaller in the equatorial and tropical regions than the sub-polar and polar regions of the world. The instantaneous total radiation can vary considerably through the day depending on the cloud cover, dust concentration, humidity, etc. 3.7 Solar Constant The sun’s radiation is subject to many absorbing, diffusing, and reflecting effects within the earth’s atmosphere which is about 10 km average thick and, therefore, it is necessary to know the power density, i. e., watts per meter per minute on the earth’s outer atmosphere and at right angles to the incident radiation. The density defined in this manner is referred to as the solar constant. The solar constant and the associated spectrum immediately outside the earth’s atmosphere are determined solely by the nature of the radiating sun and the distance between the earth and the sun. Earth receives virtually all of its energy from space in the form of solar EM radiation. Its total heat content does not change significantly with time, indicat- ing a close overall balance between absorbed solar radiation and the diffuse stream of low-temperature, thermal radiation emitted by the planet. The radiance at the mean solar distance – the solar constant – is about 1360 W/m2 (Monteith 1962). At the mean earth–sun distance the sun subtends an angle of 32’. The radiation emitted by the sun and its spatial relationship to the earth result in a nearly fixed intensity of solar radiation outside the earth’s atmosphere. The solar constant, I0 (W/m2), is the energy from the sun per unit time per unit area of surface per- pendicular to the direction of the propagation of the radiation. The measurements made with a variety of instruments in separate experimental programs resulted as I0 = 1353 W/m2 with an estimated error of ±1.5%. The World Radiation Center 3.8 Solar Radiation Calculation 67 Fig. 3.19 Monthly variation of extraterrestrial solar radiation has adopted a value of 1367 W/m2 with an uncertainty of 1%. The most updated solar constant is I0 = 1367 W/m2, which is equivalent to I0 = 1.960 cal/cm2 min or 432 Btu/ft2h or 4.921 MJ/m2h. Iqbal (1986) gives more detailed information on the solar constant. As the dis- tance between the sun and the earth changes during the whole year the value of the solar constant changes also during the year as in Fig. 3.19. The best value of the solar constant available at present is I0 = 1360 W/m2 (Frochlich and Werhli 1981). Whereas the solar constant is a measure of solar power density outside the earth’s atmosphere, terrestrial applications of photovoltaic (Chap. 7) devices are complicated by the following two variables that must be taken into consideration: 1. Atmospheric effects (Chap. 2) 2. Geometric effects, including the earth’s rotation about its tilted axis and its or- bital revolution around the sun (Sect. 3.11) 3.8 Solar Radiation Calculation Solar irradiance, I (W/m2), is the rate at which radiant energy is incident on a unit surface. The incident energy per unit surface is found by integration of irradiance over a specified time, usually an hour or a day. Insolation is a term specifically for solar energy irradiation on surfaces of any orientation. 70 3 Solar Radiation Deterministic Models 1 January to 365 on 31 December. On the other hand, solar radiation is attenuated as it passes through the atmosphere and, in a simplified case, may be estimated accord- ing to an exponential decrease by using Bouger’s Law (Kreith and Kreider 1978) as I = I0 e−km (3.16) where it is assumed that the sky is clear, I and I0 are the terrestrial and extraterrestrial intensities of beam radiation, k is an absorption constant, and m is the air mass ratio. 3.8.1 Estimation of Clear-Sky Radiation As the solar radiation passes through the earth’s atmosphere it is modified due to the following reasons: 1. Absorption by different gases in the atmosphere 2. Molecular (or Rayleigh) scattering by the permanent gases 3. Aerosol (Mie) scattering due to particulates Absorption by atmospheric molecules is a selective process that converts incom- ing energy to heat, and is mainly due to water, oxygen, ozone, and carbon dioxide. Equations describing the absorption effects are given by Spencer (1972). A number of other gases absorb radiation but their effects are relatively minor and for most practical purposes can be ignored (Forster 1984). Atmospheric scattering can be either due to molecules of atmospheric gases or due to smoke, haze, and fumes (Richards 1993). Molecular scattering is considered to have a dependence inversely proportional to the fourth power of the wavelength of radiation, i. e., λ−4. Thus the molecular scattering at 0.5 mm (visible blue) will be 16 times greater than at 1.0 mm (near-infrared). As the primary constituents of the atmosphere and the thickness of the atmosphere remain essentially constant un- der clear-sky conditions, molecular scattering can be considered constant for a par- ticular wavelength. Aerosol scattering, on the other hand, is not constant and de- pends on the size and vertical distribution of the particulates. It has been suggested (Monteith and Unsworth 1990) that a λ−1.3 dependence can be used for continen- tal regions. In an ideal clear atmosphere Rayleigh scattering is the only mechanism present (Richards 1993) and it accounts for the blueness of the sky. The effects of the atmosphere in absorbing and scattering solar radiation are variable with time as atmospheric conditions and the air mass ratio change. Atmospheric transmittance, τ , values vary with location and elevation between 0 and 1. According to Gates (1980) at very high elevations with extremely clear air τ may be as high as 0.8, while for a clear sky with high turbidity it may be as low as 0.4. As shown in Figs. 3.16 and 3.20, the solar radiation during its travel through the atmosphere toward the earth surface meets various phenomena, including scat- ter, absorption, reflection, diffusion, meteorological conditions, and air mass, which change with time. It is useful to define a standard atmosphere “clear” sky and cal- 3.8 Solar Radiation Calculation 71 culate the hourly and daily radiation that would be received on a horizontal surface under these standard conditions. Hottel (1976) has presented a method of estimating the beam radiation transmitted through a clear atmosphere and he introduced four climate types as in Table 3.1. The atmospheric transmittance for beam radiation, τ , is given in an exponentially decreasing form depending on the altitude, A, and zenith angle as τ = a + b exp ( − c cosθz ) , (3.17) where the estimations of constants a, b, and c for the standard atmosphere with 23 km visibility are given for altitudes less then 2.5 km by (Kreith and Kreider 1978) a = 0.4237 − 0.00821 (6 − A)2 , (3.18) b = 0.5055 − 0.005958 (6.5 − A)2 , (3.19) and c = 0.2711 − 0.01858 (2.5 − A)2 , (3.20) where A is the altitude of the observer in kilometers. The correction factors (ra , rb and rc) are given for four climate types (Table 3.1). Kreith and Kreider (1978) have described the atmospheric transmittance for beam radiation by the empirical relationship τ = 0.56 ( e−0.65 m + e−0.095 m ) . (3.21) The constants account for attenuation of radiation by the different factors discussed above. Since scattering is wavelength dependent, the coefficients represent an aver- age scattering over all wavelengths. This relationship gives the atmospheric trans- mittance for clear skies to within 3% accuracy (Kreith and Kreider 1978) and the relationship has also been used by Cartwright (1993). The atmospheric transmit- tance in Eq. 3.21 can be replaced by site-specific values, if they are available, and hence the solar radiation on a horizontal plane can be estimated as I = I0τ . (3.22) Table 3.1 Correction factors Climate type ra rb rc Tropical 0.95 0.98 1.02 Mid-latitude summer 0.97 0.99 1.02 Sub-artic summer 0.99 0.99 1.01 Mid-latitude winter 1.03 1.01 1.00 72 3 Solar Radiation Deterministic Models 3.9 Solar Parameters Solar radiation and energy calculations require some geometric and time quantities concerning the sun position relative to the earth and any point on the earth. It is also necessary to know the relation between the local standard time and the solar time. 3.9.1 Earth’s Eccentricity It is desirable to have the distance and the earth’s eccentricity in mathematical forms for simple calculations. Although a number of such forms are available of varying complexities, it is better to have simple and manageable expressions such as the one suggested by Spencer (1972), who gave the eccentricity, ε, correction factor of the earth’s orbit as ε =1.00011 + 0.034221cos + 0.001280sin + 0.000719cos2 + 0.000077sin2 , (3.23) where day angle, , in radians is given as = 2π(Nd − 1) 365 . (3.24) On the other hand, in terms of degrees one can write the day angle as = 360 (Nd − 1) 365.242 . (3.25) Duffie and Backman (1991) suggested a simple approximation for ε as follows: ε = 1 + 0.033cos ( 2π Nd 365 ) . (3.26) The use of this last expression instead of Eq. 3.23 does not make an appreciable difference. The average distance between the sun and the earth is R = 150×106 km. Due to the eccentricity of the earth’s orbit, the distance varies by 1.7%. 3.9.2 Solar Time Solar time is based not only on the rotation of the earth about its axis but also on the earth’s revolution around the sun during which the earth does not sweep equal areas on the ecliptic plane (see Fig. 3.21). 3.9 Solar Parameters 75 angular distance measured from the prime (solar noon) meridian through Green- wich, UK, west or east to a point on the earth’s surface. Any location west (east) of the prime meridian is positive (negative) location (see Fig. 3.22). The two significant positions of the sun are height above the horizon, which is referred to as the solar altitude at noon and it changes by 47° from 21 June to 21 December. At the equinoxes on 21 March and 21 September, at noon the sun is directly overhead with 90° at the equator and sunrise (sunset) is due east (west) for all locations on the earth. The winter (summer) solstice corresponds to dates that the sun reaches it highest (lowest) positions at solar noon in each hemisphere. On 21 December the sun is directly overhead at 23°30’ south latitude and on 21 June it is directly overhead at the same degree north latitude. These two latitudes are called the “tropic of Capricorn” and “tropic of Cancer,” respectively. The position of the sun can be calculated for any location and any time as shown in Fig. 3.23. The position of the sun is given by two angles, which are altitude, αA , and azimuth angle, γ . The altitude (or elevation) is the angle of the sun above the horizon and azimuth (or bearing) is the angle from north to the projection on the earth of the line to the sun. The solar position is symmetrical about solar noon (which is different than 12 noon local time). Irradiation fluctuates according to the weather and the sun’s location in the sky. This location constantly changes through- out the day due to changes in both the sun’s altitude (or elevation) angle and its azimuth angle. Figure 3.23 shows the two angles used to specify the sun’s location in the sky. Fig. 3.22 Useful angles 76 3 Solar Radiation Deterministic Models Fig. 3.23 Position of the sun by altitude and azimuth The zenith angle, θz , is the angle between the vertical and the line connecting to the sun (the angle of incidence of beam radiation on a horizontal surface). Likewise, the angle between the horizontal and the line to the sun is the solar altitude angle, (the complement angle of the zenith angle), hence αA + θz = 90°. The angle between the earth–sun line and the equatorial plane is called the dec- lination angle, δ, which changes with the date and it is independent of the location (see Fig. 3.22). The declination is maximum 23°45’ on the summer/winter solstice and 0° on the equinoxes (Fig. 3.24). The following accurate expression is considered for declination angle, δ, in ra- dians and the eccentricity correction factor of the earth’s orbit as defined above Fig. 3.24 The declination angles 3.10 Solar Geometry 77 (Spencer 1972): δ = 0.006918 − 0.399912cos + 0.07257sin − 0.006758cos2 + 0.000907sin − 0.002697cos3 + 0.00148sin3 . (3.31) It is also possible to consider the following expressions for the approximate cal- culations of δ and E0 (Iqbal 1986) as δ = 23.45sin [ 360 (284 + Nd) 365 ] . (3.32) As stated by Jain (1988) this expression estimates δ with a maximum error of 3’ and Eq. 3.23 estimates ε with a maximum error of 0.0001. Declination angle is considered to be positive when the earth–sun vector lies northward of the equatorial plane. Declination angle may also be defined as the angular position of the sun at noon with respect to the equatorial plane. It may be obtained as sinδ = 0.39795cos[0.98563 (Nd − 1)] , (3.33) where the cosine term is to be expressed in degrees and hence the arc sine term will be returned in radians (Kreider and Kreith 1981). The hour angle, ω, is the angular distance that the earth rotates in a day, which is equal to 15° multiplied by the number of hours (15×24 = 360°) from local solar noon (see Fig. 3.22). This is based on the nominal time, 24 h, required for the earth to rotate once i. e., 360°. Values east (west) of due south (north), morning (evening) are positive (negative). Hence, the ω can be defined by ω = 15 (12 − h) , (3.34) where h is the current hour of the day. The solar altitude is the vertical angle between the horizontal and the line con- necting to the sun. At sunset (sunrise) altitude is 0° and 90° when the sun is at the zenith. The altitude relates to the latitude of the site, the declination angle, and the hour angle. 3.10 Solar Geometry The geometric relationship between the sun and the earth can be described by the latitude of the site, the time of the year, the time of the day, the angle between the sun and the earth, and the altitude and azimuth angles of the sun. Geometric fundamen- tals, which are needed in solar radiation calculations, are presented in Fig. 3.25, in- cluding the beam of direct solar irradiance I reaching a point A on horizontal terrain. The solar declination, δ, latitude, θ , hour angle (longitude), φ, and the earth’s an- gular rotational velocity, ω, are the essential geometry and variables involved in the determination of the duration of daily irradiation, and energy input by solar radia- tion. O is the earth’s center, and I is the vector of direct solar radiation reaching the 80 3 Solar Radiation Deterministic Models toward the north (south) with positive (negative) angle values. Its unit vector is uθ as shown in Fig. 3.26. The completion of the spherical coordinate system requires the third axis perpendicular to the previous two axes and it is tangential at the same earth point to the latitude circle and its unit vector is uφ . On the other hand, there is another coordinate system in the form of Cartesian axes that go through the earth’s center with the z axis directed toward the north along the earth’s rotational axis with unit vector k. The x axis with its unit vector i, goes through the earth’s center and it constitutes the intersection line between the equator plane and the solar noon half meridian plane. The third Cartesian coordinate axis is perpendicular to these two axes and has unit vector j. The change of the geographic point on the earth changes the spherical system accordingly, but the Cartesian system remains as it is. In solar energy calculations, it is necessary to refer to the constant coordinate system, which is the defined as the Cartesian system and hence all the directions must be expressed in terms of (i, j, k) unit vectors. The unit vector ur is radial outward at point A and is perpendicular to the hori- zontal plane tangential at point A where uθ is in the direction of increasing absolute value of the latitude and it is tangential to the meridian containing point A and uφ has the direction of increasing hour angle and in the mean time it is perpendicular to both uθ and ur . Hence, these unit vectors can be related to a Cartesian coordinate system unit direction vectors i, j, and k by considering the earth’s center point O. In Fig. 3.25, N indicates the north pole, and I is the direct solar radiation vector. The k axis coincides with the direction of the line segment O-N, which is part of the earth’s rotation axis, and the other two unit vectors, i and j, fall on the equatorial plane. The ur , uθ , and u unit vectors can be expressed in terms of the latitude, hour angle, and the Cartesian unit vectors i, j, and k, by considering from Fig. 3.26 the projections of spherical coordinates on the Cartesian coordinate system as follows: ur = (cosθ cosφ)i+ (cosθ sinφ)j + (sinθ)k , (3.35) uθ = (−sinθ cosφ)i+ (−sinθ sinφ)j+ (cosθ)k , (3.36) and uφ = (−sinφ)i+ (cosφ)j . (3.37) These equations are valid for horizontal planes with its normal vector that falls on to the ur direction. Hence, there is no need for further calculation in order to define the position of the horizontal plane. It is convenient to remember at this point that, in the solar radiation and energy calculations, so far as the planes are concerned their positions are depicted with the normal vectors. For the sake of argument, let us define a plane with its three dimensions as the thickness, Tr , length, Lφ , and width, Wθ , where each subscript indicates the direction of each quantity. In other words, any horizontal plane is defined by its latitudinal width, longitudinal length, and radial thickness, as shown in Fig. 3.27. This plane is horizontal in the sense that its normal direction coincides with the radial axis of the spherical coordinate system (Fig. 3.26). Hence, the rotation of this plane around the radial axis causes the plane to remain horizontal whatever the 3.10 Solar Geometry 81 Fig. 3.27 Solar horizontal plane rotation angle. On the other hand, the horizontal plane becomes inclined in one of the three rotations: 1. Rotation around the φ axis: It gives the plane a tilt angle, hence the new axis as r ′, θ ′, and φ′ have the configuration in Fig. 3.28. On the other hand, in the case of a sloping surface a view perpendicular to the great circle containing the solar noon meridian appears as in Fig. 3.29. Such a two-dimensional view shows several of the geometric factors governing the solar radiation of a sloping surface where solar irradiance, I , falls at the base of a slope, which can be downward or upward from the horizontal plane tangen- tial at A’. Herein, a positive (negative) sign to a downward (upward) slope is considered. The downward slope in this figure is rotated α°, which is the critical angle, and if exceeded, would result in a shaded slope during solar noon. If the view in Fig. 3.25 represents the northern hemisphere summer solstice then the solar declination would be δ = 23.45°, and day-long irradiation would be experi- enced at latitudes 66.55° ≤ θ° ≤ 90°. On the other hand, Fig. 3.30 is a graphical Fig. 3.28 φ axis rotation 82 3 Solar Radiation Deterministic Models Fig. 3.29 View perpendicular to the plane of a great circle summary of a rotation of the coordinate vectors ur , uθ , and uφ exerted to achieve a downward (positive) slope. The third unit vector uφ = u′φ is perpendicular onto the plane and serves as the axis of rotation in this instance. An upward (negative) slope would be achieved by making the rotation in a clockwise direction. Here, α is the tilt angle or the slope angle, which is counted as positive toward the north as upward slope. The new position of the plane has u′r as the new normal and u′θ axis perpendicular to it. This rotation will leave the unit vector of the φ axis the same, hence, uφ = u′φ . The relationship between (u′r and u′θ ) and the original axes unit vectors can be written as u′r = (cosα)ur − (sinα)uθ , (3.38) u′θ = (sinα)ur + (cosα)uθ , (3.39) and u′φ = uφ . (3.40) Hence, the substitution of Eqs. 3.35 and 3.36 conveniently into the first two equations gives the inclined plane expressions with respect to longitude and latitude as follows: u′r = (cosα cosθ + sinα sinθ)cosφi + (cosα cosθ + sinα sinθ)sinφj − (cosα sin−sinα cosθ)k , (3.41) 3.11 Zenith Angle Calculation 85 Fig. 3.33 Rotation of the spherical coordinate system to achieve a desired aspect  u′′′θ = [−sinα cosθ cosφ − cosα cossinθ cosφ + sinα sinsinφ] i+ − [sinα cosθ sinφ + cosα cossinθ sinφ + cosα sincosφ] j+ ,(3.51) [−sinα sinθ + cosα coscosθ ]k and u′′′φ = − [−cossinφ + sinsinθ cosφ] i+ [coscosφ − sinsinθ sinφ] j+ (3.52) [sincosθ ]k . In the case of α =  = 0 the unit vectors in Eqs. 3.50–3.52 revert to those in Eqs. 3.35–3.37, respectively. 3.11 Zenith Angle Calculation It is possible to calculate the angle by considering the scalar vector multiplication between the solar beam and the normal to the plane directions (Figs. 3.26, 3.33; 86 3 Solar Radiation Deterministic Models Eq. 3.50), which can be expressed as I• u′′′r = |I| · ∣∣u′′′r ∣∣cosθz , (3.53) where • indicates scalar multiplication. Equation 3.53 can be re-written as cosθz = I • u ′′′ r |I| · ∣∣u′′′r ∣∣ . (3.54) The absolute values on the right hand side are intensity of the vectors. From Fig. 3.26 one can express the solar radiation direction vector as follows: I = (−cosδ)i+ (−sinδ)k . (3.55) The scalar multiplication in the numerator of Eq. 3.54 is equal to the multiplication of the corresponding components of the two vectors. By considering that i • i = j • j = k• k = 1 and i• j = i• k = j • k = 0. The substitution of Eqs. 3.54 and 3.55 into Eq. 3.47 yields cosθz = (cosδ sinα cossinθ − cosδ cosα cosθ)cosφ − cosδ sinα sinsinθ − sinδ cosα sinθ − sinδ sinα coscosθ . (3.56) This is the general expression and it is possible to deduce special case solutions. For instance, in the case of the horizontal plane α =  = 0 and the resulting equation is cosθz = −cosδ cosθ cosφ − sinδ sinθ . (3.57) The same expression can be reached by the scalar multiplication of the sun beam and ur vectors from Eqs. 3.33 and 3.55. This implies that the solar radiation direction is in the opposite of r (zenith) direction, and therefore, one can write actually that cosθz = cosδ cosθ cosφ + sinδ sinθ . (3.58) On the other hand, if the plane is tilted then only scalar multiplication of Eqs. 3.40 and 3.55 yields cosθz = −cosδ cosα cosθ cosφ + cosδ sinα sinθ cosφ − sinδ cosα sinθ − sinδ sinα cosθ . (3.59) By considering the basic trigonometric relationships this expression can be rewritten succinctly as follows: cosθz = − [cosδ cosφ cos(θ +α)+ sinδ sin(θ −α)] , (3.60) which reduces to Eq. 3.55 when α = 0. 3.12 Solar Energy Calculations 87 3.12 Solar Energy Calculations Once the solar irradiance, I , on the ground is known then the solar radiation per- pendicular to a horizontal surface IH can be calculated similar to Eq. 3.11 as IH = I cosθz , (3.61) where θz is the zenith angle (see Fig. 3.20). Hourly direct radiation is obtained by integrating this quantity over a 1-h period: Ih = 1h∫ 0 I cosθz (3.62) In the measurement of direct irradiation, Id, two pyranometer readings are neces- sary, one with and the other without an occulting device. The hourly beam radiation on a horizontal surface is deduced from the difference between the these readings, thus, IH = I − Id. (3.63) Hence, the diffuse radiation can be obtained as Id = I − IH . (3.64) The daily global radiation, IDg, on a horizontal surface can be calculated by integra- tion as IDg = day∫ I dt . (3.65) Similarly, daily diffuse radiation, IDd, on a horizontal surface is IDd = day∫ Id dt . (3.66) Hence, daily direct radiation is the difference between these two quantities and can be written as ID = IDg − IDd. (3.67) It is possible to calculate the daily solar energy input incident on a sloping terrain. Considerations from Fig. 3.20 lead to the following expression for the daily solar radiation energy input, IDay, onto a sloping surface as IDay = φss∫ φsr I cosθz dφ , (3.68)
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