ELS SHS Unit 2 Why Life on Earth is Possible Study Guide PDF

Unit 2 Why Life on Earth is Possible Table of Contents Table of Contents 1 Introduction 3 Essential Questions 4 Review...

Unit 2 Why Life on Earth is Possible Table of Contents Table of Contents 1 Introduction 3 Essential Questions 4 Review 4 Lesson 2.1: The Origin of Planet Earth 5 Objectives 5 Warm-Up 5 Learn about It 7 Key Points 12 Web Links 12 Check Your Understanding 13 Challenge Yourself 14 Lesson 2.2: Water: The Medium of Life 15 Objectives 15 Warm-Up 15 Learn about It 17 Key Points 21 Web Links 22 Check Your Understanding 22 Challenge Yourself 24 Lesson 2.3: Sun as the Main Source of Energy 25 Objectives 25 Warm-Up 26 Learn about It 27 Key Points 33 Web Links 33 Check Your Understanding 34 Challenge Yourself 35 Lesson 2.4: Earth’s Atmosphere 36 Objectives 36 Warm-Up 36 Learn about It 40 Key Points 46 Web Links 47 Check Your Understanding 47 Challenge Yourself 49 Laboratory Activity 50 Performance Task 52 Self Check 53 Key Words 54 Wrap Up 55 Photo Credits 55 References 55 Answer Key 57 2 EARTH SCIENCE | GRADE 11/12 Unit 2 Why Life on Earth is Possible Do you have a garden at home? Our moms usually have a green thumb, so they are typically the one in charge of the garden. What if your mom bought a new plant but she will not be around for days, and you were asked to take care of this plant? How are you going to make this plant survive? The first thing that you need to do is to expose it to an area where the plants will receive enough sunlight and air. The next important thing is to water them every day. What if you failed to do these two important things? The result will be a reprimand from your mom because you made her plant wilt. Sunlight, air in the atmosphere, and water are the basic things for a plant to survive. Without plants, animals and other organisms that depend on them will eventually diminish or even die. In the case of humans and other life forms, 3 sunlight, air and water are also needed for survival. Without these three, life is not possible here on Earth. Essential Questions At the end of this unit, you should be able to answer the following questions. What makes sunlight, air, and water essential for life on Earth to exist? Is there an infinite supply of sunlight, air, and water? Can human activities affect the supply of sunlight, air, and water? What can we contribute to conserve these three resources? Review There are different theories on the origin of the universe. These are the big bang theory, oscillating universe theory, nebular theory, and encounter theory. ○ The big bang theory suggests that the universe started as a “singularity”— an area predicted to be in the core of a black hole with very high temperature and density ○ The oscillating universe theory discusses that the universe is expanding and will contract once all the energy after the big bang has been used up, only to expand again once it approaches the point of singularity ○ The nebular theory explains that the solar system originated from a nebula — a cloud made up of dust and ionized particles. ○ The encounter theory proposes that the planets formed from the material ejected from the sun during an encounter with another celestial object. 4  Lesson 2.1: The Origin of Planet Earth Objectives In this lesson, you should be able to: explain how Earth was formed according to accretion hypotheses; and differentiate homogenous and heterogenous accretion hypothesis. Have you ever built a snowman? Whether you tried it yourself or just watched it from a movie, the idea of making one is simple. You just roll a piece of snow on your hand to form a sphere. Then, put it back to the ground and roll it. Since the snow is likely to stick to itself, your small sphere can grow as big as you are by accumulating snow from the ground. This is also the same thing that happens in the formation of planets. Before the solar system is formed, stars and planets exist in a massive cloud of dust and gas. These fragments of dust and gas start to bump into each other forming a huge piece of matter. This collision is the start of the process of accretion. How does accretion forms the planets? Warm-Up Formation of Earth Materials: ball string color coded cards with numbers written on it. ○ black = 6 ○ red = 5 ○ yellow = 3 ○ brown = 1 5  ○ blue = ½ Procedure: 1. Use a string to hang the ball on the ceiling. Make sure that the ball is around 3 feet above the ground. This ball represents the particle with the most density and will draw another particle towards it. 2. Assign one student to take a video of a bird's eye view. The video will be watched by all students after the activity. 3. Each student should receive one color card. Then, students will move at a random position surrounding the ball. Each student represents a particle having its own gravity. The arrangement of the particles from heaviest to lightest is: black - red - yellow - brown - blue. Remember that the ball is the heaviest and densest. It tends to pull the kids towards it and towards each other. 4. Students will now move towards the ball depending on the number of steps written on their card. Make sure that each step will be from heel to toe. If they hit another student while taking steps toward the ball, they will combine to create a larger particle by getting the sum of the number written on their card. For example, a student with a yellow card (3) bumps into a student with a brown card (1), together they will move 3 + 1 = 4 steps. Note: The ball's gravity is so strong that each student representing a particle wants to put one hand on the ball. If a student cannot reach the ball, that student can just put their hand on the shoulder of the person touching the ball. Take note that the students touching the ball directly forms the first layer. The second layer is formed by the students who are touching the shoulders of the person that is touching the ball directly. If the shoulders of the students in the first layer are full, other less massive students can just touch the shoulders of those students in the second layer and so on. 5. Stop when you are attached to the ball already. 6. Watch the video recorded to know what is really happening. Guide Questions: 1. What is the shape formed after the particles, which is represented by students, were pulled towards the ball? 2. What is the composition of the formed inner layer? outer layers? 3. What is the relationship of the particle size and the gravitational pull? 6  4. How can you relate this activity to Earth’s formation? Learn about It In a carnival or fair, there is usually a man with a cotton candy machine. When you have seen them making one, you can observe that sugars tend to stick to itself as it spin in the machine and form a large cotton candy. Planet formation is similar to this. The accumulation of small pieces of dust forming huge lumps of matter is a process known as accretion. Accretion happens when gravity attracts tiny bits of matter towards an object. This results in a gradual increase of the object’s size. In relation to the solar system formation, the objects increase its size until it turns into planets and stars. As the objects grow bigger, it pulls more fragments of matter due to stronger gravitational pull. 7  Fig. 1. Steps in accretion. As shown in Fig. 1, accretion happens in four steps. First, clumps of dust grains collide forming planetesimals and eventually turn into protoplanet as more planetesimals are attracted. A protoplanet is a planetary embryo that consists of collection of matter, from which a planet is formed. There are two hypotheses on how the structure of Earth was formed which both involves accretion: homogeneous and heterogeneous accretion hypotheses. Homogeneous Accretion Hypothesis The homogeneous accretion hypothesis states that the formation of Earth began after the condensation of fine particles of the primitive nebula about 4.6 billion years ago. When these particles accreted, they formed a homogeneous primordial Earth. Thus, early Earth had a uniform solid composition. Its primary components were iron, magnesium, nickel, silicates, and some radioactive elements such as uranium and thorium. Due to gravitational contraction and decay of radioactive elements, the temperature of early Earth increased. Iron and nickel melted, and they sank towards the center because of its high density. On the other hand, less dense silicates were displaced, and moved upwards. In this hypothesis, it took many years for iron and nickel to accumulate and reach the center of about 4000 miles deep. During this time, Earth’s surface experienced turmoil, violent earthquakes, continual volcanic eruptions, and covering of the surface with flowing lava. Eventually, iron and nickel accumulated and formed Earth’s core. After cooling down, a thin layer of solid rock formed the crust including the continental and ocean basins. In between the core and the crust is the mantle, which is made up of semi-molten silicate rocks and other minerals. 8  Fig. 2. Steps in homogeneous accretion. Fig. 2 shows a summary of the homogeneous accretion hypothesis. First, similar elements attached to each other, forming a solid mass. Second, particles were melted due to the heat produced in the process. Lastly, heavier elements descend to the center due to gravity, forming the solid core of Earth. Heterogeneous Accretion Hypothesis The heterogeneous accretion hypothesis states that the core has formed at the same time as Earth. Therefore, early Earth had its basic layered structure with core, mantle, and crust. According to this theory, as the nebula cooled down, its particles have condensed depending on their condensation points. Oxides of aluminum and calcium condensed first, followed by iron and nickel. When the nebula cooled further, the silicates condensed. The condensed particles collided with each other and accreted. The formed particles during the initial stage of condensation accreted first. Following this, aluminum and calcium oxides accreted first then followed by iron and nickel to form Earth’s core. The outermost layer is composed of silicates, as well as volatile particles including water. 9  Fig. 3. Steps in heterogeneous accretion. Fig. 3 shows a summary of the heterogeneous accretion hypothesis. First, particles of metal attach with each other first, forming Earth’s core. As it cools further, lighter elements attached to this core. Evidence and Loopholes of the Two Hypotheses Table 1. Difference of Homogenous and Heterogenous Accretion Hypothesis. Homogeneous Accretion Heterogeneous Accretion Hypothesis Hypothesis Main Point Earth accreted from materials Earth accreted during of the same composition after condensation, forming a condensation. Accretion was differentiated planet as it followed by differentiation. grew in size. Supporting The homogeneous accretion The heterogeneous accretion Statements hypothesis provides a hypothesis qualitatively mechanism that explains the explains the density presence of volatile elements in differences among terrestrial 10  the core. It also provides an planets (Mercury, Venus, explanation of the heat source Earth, and Mars). Also, it can for early mantle melting and explain the abundance of formation of early continents. elements such as osmium, iridium, ruthenium, and rhodium in the mantle. Loopholes The hypothesis cannot explain Accretion must be very fast the abundance of elements (103 to 104 years for such as osmium, iridium, completion). This rate does ruthenium, and rhodium in the not coincide with the mantle. occurrence of large impact craters. Also, the abundances of iron, calcium, titanium, and aluminum do not coincide with what was predicted by the theory. The more commonly accepted postulate is the homogeneous accretion hypothesis. Most materials that formed early Earth homogeneously accreted after their complete condensation. After the formation of early Earth, collisions with meteorites and comets resulted to the presence of volatile elements on the surface. Earth is considered as a dynamic planet. It continuously changes ever since its formation 4.6 billion years ago. Through time, several changes happened in the geographic distribution of continents and composition of the atmosphere. 11  Key Points Accretion happens when gravity attracts tiny bits of matter towards an object. This will result to gradual increase of the object’s size. Homogeneous accretion is when Earth accreted from materials of the same composition after condensation. Differentiation followed accretion in the process. Heterogeneous accretion is when Earth accreted during condensation, forming a differentiated planet as it grew in size. Web Links For further information, you can check the following web links: Watch this video to visualize how the solar system was formed. The Daily Conversation. 2014. ‘The Formation of the Solar System in 4K.’ https://www.youtube.com/watch?v=x1QTc5YeO6w&t=25s To deepen your knowledge on accretion, watch this short video clip. Teach Astronomy. 2010. ‘Teach Astronomy - Accretion.’ https://www.youtube.com/watch?v=ynS3or1-xvM Explore the solar system by clicking this interactive site. Space Science Institute. 2014. Build a Solar System.’ http://www.alienearths.org/online/starandplanetformation/planetfamilies.php 12  Check Your Understanding A. Arrange the following events in order. Write numbers 1 to 5 where 1 indicates the first event that occurs, 2 is the second and so on. Homogeneous accretion _______________ Iron and nickel melted, and they sank towards the center because of their high density. _______________ Condensation of fine particles of the primitive nebula. _______________ Due to gravitational contraction and decay of radioactive elements, the temperature of early Earth increased. _______________ Less dense silicates were displaced, and they moved upwards. _______________ Particles accreted forming a homogeneous primordial Earth. Heterogeneous accretion _______________ The condensed particles collided with each other. _______________ Condensation of oxides of aluminum and calcium followed by iron and nickel. _______________ The nebula cooled further. _______________ Condensation of silicates. _______________ Accretion of aluminum and calcium oxides accreted followed by iron and nickel forming Earth’s center core. B. Write true if the statement is correct. Otherwise, write false if incorrect. 1. Accumulation and attachment of particles to an object is known as condensation. 2. Accretion is a term describing sticking together of huge particles to an object. 3. According to homogeneous accretion hypothesis, early earth had its basic layered structure. 13  4. In homogeneous accretion, the early earth’s temperature increased because of gravity and radioactive decay of elements. 5. Elements with lower density sank towards the center of Earth. 6. According to heterogeneous accretion hypothesis, the core has formed at the same time as Earth. 7. The outermost layer of Earth is composed of iron and nickel. 8. Earth is considered a dynamic planet. 9. The presence of volatile elements in the core is explained by homogeneous accretion hypothesis. 10. As the object increase in size, the gravitational pull decreases. Challenge Yourself Answer the following. Limit your answer in 2 to 3 sentences. 1. Make an analogy showing the process of accretion. 2. Discuss the basic steps in accretion. 3. If you were shown two models of accretion hypothesis, how could you distinguish one from the other? 4. In your own opinion, which accretion hypothesis best explains the formation of Earth? 5. What are the pros and cons of each accretion hypothesis? 14  Lesson 2.2: Water: The Medium of Life Objectives In this lesson, you should be able to: explain why water is considered as the medium of life; discuss the origin of water formation on Earth; and enumerate the uses of water. Have you heard of a fireproof balloon? Most of us know that when an inflated balloon is near a source of heat, it will explode immediately. Therefore, making it fireproof is a nice trick. You don’t need any complicated materials for you to be able to do this trick. Just pour water into the balloon before you inflate it. Then, place the part of the balloon with water on the source of heat. Those who are not familiar with the properties of water will be amazed because the balloon will not explode. What properties of water made this trick possible? Warm-Up Measuring the Heat Capacity of Sand and Water Materials: beaker lamp water thermometer sand weighing scale metal cup graduated cylinder Procedure: 1. Obtain the density of the 50 mL water and 50 mL sand. a. Obtain the mass of an empty graduated cylinder. b. Transfer water until it reaches the 50 mL mark of the graduated cylinder. 15  c. To obtain the mass of water, subtract the mass in 1b from 1a. d. Get the density of water by dividing mass by volume. e. Repeat steps 1a to 1c using sand. 2. Pour the 50 mL water and 50 mL sand into two separate metal cups. 3. Using a thermometer, measure the initial temperature in each cup. Record the measurement on the table provided. 4. Place the two metal cups directly under a lamp. Make sure that each cup receive equal amount of light. 5. Record the temperature of each metal cups every minute for 5 minutes. Record the measurement on the table provided. 6. After 5 minutes, turn off the lamp. Continue recording the temperature every minute for another 5 mins. Record your data. Sample Data Table: Time Temperature (oC) (in minutes) Water Sand Guide Questions: 1. Heat capacity is the amount of heat needed to increase the temperature of a substance by one degree. In the activity, which has higher heat capacity, water or sand? Explain. 2. Recall the obtained density for water and sand. What is the relationship of heat capacity and density? 3. Which material had the highest change in temperature after exposure to heat? 16  4. Which material cools down the fastest? Learn about It Earth is also known as the blue planet because two-thirds of it is covered by water. Even it is abundant, humans should still conserve and not abuse water resources. Conservation of water resources is important because all life forms depend on water in various ways such as drinking, irrigation, food preparation, hygiene, watering plants, and many more. It is undeniable that water plays an important role for all living organisms in the planet. Since the prehistoric stage, human beings depend on water for the development. Therefore, life is not possible on Earth without water. Hydrosphere The water environment on Earth is known as the hydrosphere. At present, all water on Earth (water vapor, liquid water, and ice) comprise the hydrosphere. It includes all bodies of water such as oceans, lakes, rivers, and marshes. Clouds, snow, glacier, and rain are also part of the hydrosphere. Hydrosphere is comprised of 97.5% saltwater and 2.5% freshwater. Fig. 4. World water distribution. 17 Saltwater As the name implies, salt water is composed of certain amount of salt. Saltwater comprises the oceans and seas. The ocean houses many species of marine life and diverse mineral resources. If you are fond of diving, you know how much diversity is there under the sea. A lot of organisms depend on saltwater for survival such as saltwater fishes and other marine invertebrates. Since some people are attracted to the wonder of the sea, some wants to keep saltwater organisms in their aquarium. If you are one of these people, you should know that utmost care is needed since marine animals are sensitive to the quality of water. Freshwater Contrary to the popular belief that the freshwater is devoid of salt, freshwater still has small amount of salts but in very low concentrations. Freshwater can be present in the form of rain and snow, and it can even be found in permanently frozen soil known as permafrost. It is commonly stored in rivers, streams, ponds, lakes, marshes, glaciers, and polar caps. Despite the abundance of water on earth, only a small amount of Earth’s water is accessible as freshwater. It only accounts for 2.5% of the total water on Earth. Out of this total percentage, only 1% of freshwater is potable. This percentage will be constant since water is continually recycled through the atmosphere. However, increasing population yields to growing competition on clean water resource. Properties of Water That Enable Existence of Life Water provided optimum environment for the existence of the first life forms on Earth. Water dissolved early Earth molecules which reacted and formed more complex molecules. Water has the right density, transition temperatures, and heat capacity that enable existence and perpetuation of life in the planet. Density Density is measured as mass per unit of volume (in g/cm³). The density of water changes with several factors such as temperature and salinity. Water is densest at 3.98°C and is least dense at freezing temperature. Ice floats on the surface of liquid water because ice has a lower density. Ice insulates the underlying liquid and prevents the liquid from further freezing. If ice sinks when frozen, then the surface of the liquid water will freeze and sink again until such point that all water will be frozen, making chemical reactions impossible. 18 When the lakes start to freeze during winter, people can skate on that frozen lake. If ice doesn’t have low density which enables it to float, all organisms living in the lake will be dead. Fig. 5. A frozen lake. Transition Temperatures All life forms are composed of cells in which their cell membrane separates them from the environment. The cell membrane is important to selectively take in important substances and prevent toxic products to go in. In this case, the consistency of water in maintaining liquid form at room temperatures is important as it allows flow and transfer of substances from the cell to its environment and vice versa. Heat Capacity When you go to the beach especially on a hot day, you will notice that the sand heats faster than the sea. This is because water needs a higher amount of heat before its temperature is raised by one degree. This high heat capacity of water is also the reason why it is important in vehicle engines. It is an excellent coolant since high amount of heat energy can be absorbed without getting too hot. In addition, this property is the reason why the fireproof balloon trick is possible. Unlike the air in the balloon, the water inside needs higher amount of heat before its temperature is increased causing the explosion of balloon. The water’s high heat capacity is important because, without this property, the atmosphere will be extremely cold during winter and extremely hot during 19 summer. Moreover, fishes will not survive if bodies of water gets hot quickly. Most importantly, cells in our bodies are composed of mostly water that allows the maintenance of constant temperature intracellularly. Therefore, if water doesn’t have a high heat capacity, our temperature can get too high quickly which can be highly detrimental to most organisms. Hypothesis on the Origin of Water on Earth The prevailing hypothesis on the origin of water on Earth suggests that water came from comets that collided with Earth. In 2000, scientists investigating LINEAR S-4 comet had discovered that water from the comet had the same isotopic composition as the water in the seas. (Recall that isotopes are atoms with the same number of protons but different number of neutrons.) Other studies suggest that water was already present within Earth since formation as volatiles trapped in magma, and manifested as liquid water during degassing after the crust had formed. The truth may be a mixture of both theories. Uses of Water in Modern Civilizations In modern civilizations, water has a variety of uses. Water is commonly used in agriculture for the irrigation of crops. About 70% of global freshwater use is for agricultural purposes. For industrial purposes, about 20% of water is used globally. Every product that is manufactured utilizes water throughout the production process such as fabricating, washing, cooling, transporting a product, integrating water into a product, and sanitizing the manufacturing facility. For domestic purposes, about 10% of freshwater is used for drinking water, washing dishes, brushing teeth, and bathing. As shown in Fig. 6, water usage for different purposes varies among countries. 20  Fig. 6. Global water use Key Points Hydrosphere is the water environment on Earth. It is comprised of 97.5% saltwater and 2.5% freshwater. Salt water is composed of certain amount of salt. It comprises the oceans and seas. Freshwater has still amount of salts but in very low concentrations. Freshwater can be present in the form of rain and snow, and it can even be found in permanently frozen soil known as permafrost. It can also be stored in rivers, streams, ponds, lakes, marshes, glaciers, and polar caps. Water has the right density, transition temperatures, and heat capacity that enable existence and perpetuation of life. The prevailing hypothesis on the origin of water on Earth suggests that water came from comets that collided with Earth. Other studies suggest 21  that water was already present within Earth since formation as volatiles trapped in magma, and manifested as liquid water during degassing after the crust had formed. About 70% of global freshwater use is for agriculture. For domestic purposes, about 10% of freshwater is used for drinking water and bathing. For industrial purposes, about 20% of water is used globally. Web Links For further information, you can check the following web links: Play this interactive game to know more on using water wisely. Water Use It Wisely. n.d.. ‘Tip Tank Game.’ https://wateruseitwisely.com/tip-tank-game/ Do you want to know the current status of the Pasig river? Click this link to read an article entitled “The Water Quality of the Pasig River in the City of Manila, Philippines: Current Status, Management and Future Recovery”. Gorme, et al. “The Water Quality of the Pasig River in the City of Manila, Philippines: Current Status, Management and Future Recovery.” Environ. Eng. Res.,15 no. 3 (2010), 173-179 http://eeer.org/journal/view.php?number=114 Watch this short video clip for you to know why should we care about water? National Geographic. 2010. ‘Why Care About Water?”’ https://www.youtube.com/watch?v=Fvkzjt3b-dU Check Your Understanding A. Write F if the statement describes a freshwater and S if it describes a saltwater. 1. It is potable water 2. It comprises the oceans and seas. 3. It has very little amount of dissolved salt. 22  4. It comprises the rivers, streams, ponds, lakes. 5. It may cause dehydration if huge amounts are consumed. 6. It is characterized by huge amounts of salt present. 7. It covers 2.5% of the hydrosphere. 8. It can be present in the form of rain, snow, and permafrost. 9. It houses many species of marine life and diverse mineral resources. 10. It covers 97.5% of the hydrosphere. B. Explain why the following situations are possible. 1. frozen lake fishing 2. different temperature of land and sea 3. fireproof balloon 23  4. frozen lake skating 5. Saltwater fish die when transferred to freshwater. Challenge Yourself Answer the following questions. Limit your answer in 2 to 3 sentences. 1. Why does ice float on water? 2. What do you think will happen if water has low heat capacity? 3. In boiling water using a kettle, why does the kettle becomes hot faster than the water? 4. What theory on the origin of water is more convincing to you? Why? 5. Earth has an abundant supply of water. If this is the case, why do some individuals lack supply of clean drinking water? 24  Lesson 2.3: Sun as the Main Source of Energy Objectives In this lesson, you should be able to: describe the sun as the major source of energy; define what is Earth’s energy budget; and identify the factors affecting Earth’s energy budget. Have you ever tried sunbathing? You might be one of those people who spend summer breaks going to the beach and do sunbathing. It is undeniably a nice way of relaxation and appreciation of nature. If sunbathing is a leisure for people, to plants, sunbathing is an important step to sustain life. In fact, plants have developed variety of ways to maximize the use of sunlight exposure while at the same time, preventing water loss. It is undebatable that the sun provides each living thing with the essential necessities of life on Earth. How do humans obtain this life-sustaining nourishment? That's where photosynthesis, a process that involves the capture and use of the sun’s energy to create biological compounds, comes into place. Everything is related in the process. When the sun shines, plants capture sunlight and obtain carbon dioxide from the atmosphere and water in the soil. In return, plants produce sugar and oxygen that are essential for living organisms. Then, the cycle persists for as long as the sun shines. The important role of the sun in photosynthesis is just one of the countless benefits that we can get from the sun. All life forms depend on the sun's warmth for survival. What would life be without the sun? Will there be life in the first place? 25  Warm-Up Understanding Albedo Materials: black construction paper white construction paper scissors stapler desk lamp with 60 watt bulb 2 thermometers Procedure: 1. Fold the black construction paper twice. The first fold is crosswise while the next is lengthwise. Cut only one square out of the four squares formed. 2. Fold the square into half twice more. Staple the two open edges to form a pocket. 3. Repeat steps 1 to 2 but this time using a white construction paper. 4. The bulb end of each thermometer should be inside the pocket. 5. Place the pockets with thermometer directly under a lamp. Make sure that each pockets receive equal amount of light. 6. Record the initial temperature of both pockets prior to turning on the lamp. Write your observations on the initial temperature column. 7. Record the temperature again five times with a two-minute interval (if there is enough time, record up to ten times). Write your observation on the table below. Data and Results Temperature (degrees Celsius) Surface 10 12 14 16 18 20 Initial 2 mins 4 mins 6 mins 8 mins mins mins mins mins mins mins White Black 26 Guide Questions: 1. Which pocket has the highest temperature after the time duration given? 2. The measurement of the amount of solar energy reflected off a surface is termed as albedo. How is albedo measured in this activity? 3. In relation to activity, which has higher albedo, the black or white pocket? 4. How is the color related to temperature? Why? Learn about It On a hot sunny day, wearing a black clothing adds heat to your body than when you are wearing a light colored clothing. The science behind this is because of albedo. Albedo is the ability of a material to reflect light. Therefore, a high albedo means that a material can reflect light more than a material with low albedo. Black surfaces have low albedo since it absorbs more sunlight and its associated heat than the light colored surfaces. Albedo can be measured on a scale of 0 to 1. Values closer to 0 means that a material absorbs all the light while a value of 1 means that a material reflects all the light. This is why black surfaces such as asphalt have values closer to 0 while light colored surfaces such as white paint or ice has values closer to 1. Fig. 7. Albedo values. 27 It is undeniable that sunlight and its associated heat is essential for organisms to function properly. This is true to most organisms especially to plants since it capture the sun's energy to produce food. However, too much heat is damaging. Therefore, using your knowledge of albedo might help to avoid too much heat exposure. An example is to paint the roof and wall of your house with a white color. This helps in keeping your house cooler since white surfaces reflect more light. Uses of Solar Energy The sun is the primary source of energy on Earth. This energy is required for almost all processes that take place within Earth’s atmosphere, hydrosphere, lithosphere, and biosphere. Fig. 8. Importance of the sun on humans and other life forms. Even before the modern civilization, sun is undeniably an essential part of human lives. Moreover, sun played a role in many mythologies and even systems of worship. Since people consider it as a bringer of light and life, sun has been the central deity of humankind. However, as time goes by, people no longer worship the sun, but its importance did not subside. 28 Without the sun, plants cannot perform photosynthesis. This will have a domino effect since, without plants, herbivores that depend on them will diminish or even die. People who consume herbivores such as cows, will also be affected. In addition, sunlight converts molecule precursors in your skin to produce vitamin D, which is responsible for bone maintenance. Solar energy also warms Earth. It is one of the the driving forces of weather and climate. The sun’s energy is transferred across an empty space or vacuum to Earth’s surface through radiation. Radiation is the transfer of heat through electromagnetic waves. This heat is essential in regulating Earth’s temperature. The abundance of solar energy will be put into waste if we will not take advantage of it. Since it is a renewable resource, supply of solar energy will never run out. As long as the sun shines, solar energy is available for everyone to utilize. Through advancement of technology, people can now harness solar energy by means of solar panels. This is a significant development since utilization of solar energy when compared to fossil fuels is better because it is cleaner and the cost of maintenance of equipment is minimal. 29 Earth’s Energy Budget Planning budget is important especially if you are the bread winner of the family. You need to ensure that your income will tally to the expenses spent and savings kept. This also holds true for Earth's energy budget. It needs to ensure that absorbed solar radiation is balanced to the radiated ones. Keeping Earth’s energy budget ensures that the average temperature on Earth remains stable and that life continues to exist. Earth's albedo is 0.3. Thirty percent of the solar energy that reaches the surface of Earth is reflected back to space by the clouds, atmosphere, and light-colored areas (deserts and areas covered with ice and snow). The remaining 70% of the solar energy is absorbed by the atmosphere, land, and oceans. The absorbed energy drives wind and ocean currents. These currents distribute the heat throughout the planet since more sunlight shines on equatorial region than polar regions. All this solar energy absorbed by the atmosphere, air, land and oceans must be radiated back to space. Therefore, energy in should always equal to energy out. Fig. 10. Earth’s energy budget. Thirty percent of the energy from the sun is reflected and scattered by clouds, atmosphere, and Earth’s light-colored surfaces. 30 Factors Affecting Earth’s Energy Budget There are certain factors that affect Earth’s energy budget such as the amount of light colored surfaces, amount of radiation received, Earth’s axial tilt, and the presence of greenhouse gases. Recall that light-colored areas enable the reflection of solar energy. Therefore, when the size of these areas is altered, then energy balance is also affected. Energy balance can also be affected when the amount of radiation received by Earth from the sun changes. For instance, the changes in Earth’s orbit and axial tilt led to a series of ice ages over the last million years. Earth’s axial tilt also affects the amount of radiation coming from the Sun. Throughout the year, the orientation of Earth toward the sun changes due to the 23.5° vertical tilt of its axis, causing the position of the sun across the sky to wander at about 47°. This change has a direct effect on the intensity of insolation. Insolation is the amount of solar radiation that reaches a given area. Simply put, it is the exposure to the sun’s rays. For instance, if the sun is located directly overhead, then the intensity of insolation is higher as compared when the sun’s altitude across the sky is about 45° wherein the sun’s rays are spread over a larger area. This explains why areas within or near the equator experience higher amounts of solar radiation, making the areas warmer. Lastly, the energy balance is affected by the presence of greenhouse gases such as methane, nitrous oxide, ozone, water vapor, and carbon dioxide in the atmosphere. These gases trap solar energy which should have been reflected back to space. The increase of greenhouse gases would mean that more energy is trapped, and some energy are re-emitted in all directions, thus, heating Earth. This heating phenomenon is known as the greenhouse effect. 31  Fig. 11. Greenhouse effect is one of the factors that affects Earth’s energy budget. The energy of the sun is released through ultraviolet, visible, and infrared radiation. About 44% of the radiant energy emitted by the sun is in the form of visible light; 49% is in the form of near-infrared, far-infrared, microwave, and radio waves; and the remaining 7% accounts for ultraviolet radiation. Fig. 12. The sun’s electromagnetic radiation. 32  Key Points Albedo is the ability of a material to reflect light. Earth’s energy budget ensures that the absorbed solar radiation is balanced to the radiated ones. Keeping Earth’s energy budget ensures that the average temperature on Earth remains stable and that life continues to exist. Thirty percent (30%) of the solar energy that reaches the surface of Earth is reflected back to space while the remaining 70% of the solar energy is absorbed by Earth’s surface. The factors that affect Earth’s energy budget are the amount of light colored surfaces, amount of radiation received, Earth’s axial tilt and the presence of greenhouse gases. Web Links For further information, you can check the following web links: Read this article entitled “On the Effects of Albedo Increase through Reflective Roofing on Philippine Urban Atmospheric Temperature: Real-Time Parameter Inputs” to know more about the effects of increasing the albedo. Caraquil, et al. “On the Effects of Albedo Increase through Reflective Roofing on Philippine Urban Atmospheric Temperature: Real-Time Parameter Inputs.” Journal of Science, Engineering, and Technology. 4 (2016), 21-28. Try this simple interactive scenarios to identify the answer to some “what if” scenarios in earth’s energy balance. University Corporation for Atmospheric Research - Center for Science Education. 2015. ‘Earth’s Energy Balance.’ https://scied.ucar.edu/earths-energy-balance Click this link to know more about the net metering scheme in the Philippines. Fortunato Sibayan. n.d. ‘Net Metering.’ https://www.doe.gov.ph/sites/default/files/pdf/announcements/e-power_03_02_net_ metering.pdf 33  Check Your Understanding A. Answer the following question. Use the illustrations below as a guide. 1. What is the total percentage of solar energy reflected? 2. What type of surfaces reflect incoming solar energy? 3. What is the total percentage of solar energy absorbed? 4. Are all the energy absorbed radiated back to space? 5. How much energy is reflected by the atmosphere? Absorbed? 34  6. What is the role of greenhouse gases? 7. What will happen if we keep on adding the production of greenhouse gases? 8. If greenhouse gases are non-existent, what would be Earth's temperature? 9. What are the possible effects to the environment if Earth's temperature is raised? 10. What can you contribute to reduce the amount of greenhouse gases? B. Write true if the statement is correct. Otherwise, write false. 1. Albedo is the ability of the material to absorb light. 2. High albedo means more light energy is reflected. 3. Black surfaces have an albedo value of 1. 4. Earth’s energy budget ensures that energy in is always balanced to energy out. 5. When the size of the area of light surfaces, energy balance is also affected. 6. Earth's axial tilt affects the amount of sun's radiation. 7. Greenhouse gases help cools Earth. 8. Greenhouse effect is a phenomenon that involves the trapping of solar energy by greenhouse gases. 9. Vitamin E which helps in bone maintenance can be obtained by exposure to the sun. 10. People can harness solar energy by means of solar panels. Challenge Yourself Answer the following questions. Limit your answer in 2 to 3 sentences. 1. Compare the albedo values in Alaska and Sahara. Which do you think has higher albedo? Explain. 2. What will be the effect to the ocean's temperature and ice formation during winter if the ocean's albedo decreases? 3. Without greenhouse gases, earth will be as cold as the moon. Why is this possible? 4. How is the greenhouse effect on Earth similar to the greenhouse where plants are grown? 5. What would life be without the sun? 35  Lesson 2.4: Earth’s Atmosphere Objectives In this lesson, you should be able to: describe the characteristics of Earth’s atmosphere; and identify the importance of the hydrologic cycle. When you do star gazing, you are surely amazed of the wide space of the sky that looks never ending. You will observe not only stars but also airplanes passing by and if you’re lucky enough, shooting stars as well. Most people love to see shooting stars because they say that wishes do come true when you see one. Other people don’t have patience to wait for shooting stars. Instead, they just write their wishes on a piece of paper and tie it on the string of a balloon hoping that when the balloon flew away, it will reach the heaven. All of these objects, the sky, shooting stars, airplanes and balloons reach different portion of the atmosphere. What are the different layers of the atmosphere and where these layers could be found? Warm-Up Atmospheric Gases Materials: printable grid paper (100 × 100 grids) colored pens Procedure: 1. Print out three copies of the 100 × 100 grid paper. 2. Label the first grid paper as "Planet A". The second grid paper as "Planet B" and the third as "Planet C". 36 3. Color the squares on each grid paper based on the legend below: Planet A ○ Red = 96 large blocks and 50 small blocks ○ Blue = 3 large blocks and 50 small blocks Planet B ○ Red = 3 small blocks ○ Blue = 78 large blocks ○ Yellow = 21 large blocks ○ Green = 90 small blocks Planet C ○ Red = 95 large blocks ○ Blue = 2 large blocks and 70 small blocks ○ Yellow = 13 small blocks ○ Green = 1 large block and 60 small blocks 4. Take note of the following before you answer the questions that follow: Each large block is equal to 1% or 1 out of 100 parts. Each small block within the large block is equal to 0.01% or 1 out of 10 000 parts. For example, 50 large colored blocks means 50%, 8 small colored blocks means 0.08 %, and 90 colored small blocks means 0.9%. 37 Sample Grid Paper Template (100 × 100) 38 Guide Questions: 1. Describe the atmospheric conditions of each planet by writing the percent composition of each atmospheric gases present. Write your answer on the table provided. Use the following legend to write the correct answer. Planets Atmospheric Gases Planet A = Venus Red = carbon dioxide Planet B = Earth Blue = nitrogen Planet C = Mars Yellow = oxygen Green = argon Percent Composition of Atmospheric Gases Atmospheric in Three Planets gases Venus Earth Mars carbon dioxide nitrogen oxygen argon 2. How is the atmosphere of Venus and Mars similar? 3. Differentiate the percent composition of atmospheric gases in Venus and Mars to that of Earth. 4. How does the percent composition of the atmospheric gases on Earth makes it habitable? 39  Learn about It As compared to the apple and its skin, Earth is like the apple's flesh while the atmosphere is the thin skin. This thin layer is what protects us from harmful infrared rays and ultraviolet rays from the sun. It is composed of a mixture of gases with their unique physical and chemical properties. The bulk of the atmospheric composition of Earth is nitrogen and oxygen in which together comprises 99%. Only 0.9% is argon and the remaining 0.1% is trace gases. Carbon dioxide and ozone, although available in minute amounts, are very essential to life on Earth. Fig. 13. Atmospheric composition of Earth. Layers of the Atmosphere Despite being thin, atmosphere could still be divided into layers. The layers are troposphere, stratosphere, mesosphere, thermosphere, and exosphere. Troposphere The troposphere is the layer closest to Earth. The term troposphere comes from the Greek word “tropos” which means change. It is called such because of the persistently changing weather in this layer of the atmosphere. Its thickness varies depending on your location on Earth, but the range is between 5 and 9 miles (8 and 14 km). Temperature gets cooler as you go higher in the atmosphere. 40 This lowest layer is where humans live. It also regulates weather and climate. It holds nearly all water vapor in Earth’s atmosphere, and is characterized by relatively high atmospheric pressure which allows high concentrations of oxygen ideal for life. Fig. 14. Layers of the atmosphere. Stratosphere The stratosphere is the next layer which is about 35 km thick. As opposed to the troposphere, the temperature in this layer gets warmer as you go higher. An important feature of this layer is the ozone layer which protects Earth from the sun’s harmful UV radiation. However, insulating foams, air conditioners, refrigerators and other things manufactured by industries that use chlorofluorocarbons (CFCs) which causes ozone depletion. As CFCs reach the stratosphere, it will be broken down by the sun’s UV radiation releasing chlorine. These chlorine atoms react and destroy the ozone. A total of 100 000 ozone molecules can be broken apart by just a single chlorine atom. 41  Fig. 15. Ozone layer depletion. In effect, depleted ozone causes more UV radiation to reach Earth’s surface. This extra radiation causes cataracts and skin cancer in humans. Animals and plants can be harmed as well. The ozone found in the stratosphere is essential to life. However, ozones can be detrimental as well. These harmful ozones are found in the troposphere. When inhaled, ozones can irritate the lungs and breakdown lung tissues. Plants are also affected by this tropospheric ozone. 42  Fig. 16. Good and bad ozone. Mesosphere The mesosphere comes from the word “meso” which means middle. This 35 km thick layer is termed as the coldest layer because it has a minimum temperature of roughly -85 degrees Celsius. The reason behind this low temperature is the lessened solar heat and high cooling due to carbon dioxide. Meteor shower or also known as the shooting stars are meteors burning up in the mesosphere. This layer protects Earth from the impact of those space debris. The debris burns as a result of the frictional force between air and debris molecules. 43 Thermosphere The thermosphere comes from the word “thermo” which means heat. Thermosphere is roughly 600 km thick and can reach a temperature of about 1500 degrees Celsius. Moreover, the thermosphere regulates temperature and filters X-rays and some ultraviolet radiation emitted by the sun. Another interesting fact is that the International Space Station orbits through this layer. Exosphere The exosphere comes from the word “exo” which means outside. This 10,000 km thick outermost layer forms a boundary between Earth and space. Exosphere is very thick so going to space is really too far. This farthest layer absorbs some radiation and protects the layers underneath. It contains hydrogen and helium. The air is almost similar to the vacuum in space because it is so thin. Considering the climate, the most important layer of the atmosphere is the boundary layer composed of troposphere and stratosphere. The boundary layer is just next to Earth’s surface. The energy transferred from Earth’s surface in the form of conduction or even moisture from evapotranspiration stays within this boundary and is not transferred to higher atmosphere. Characteristics of the Atmosphere that Enable Life on Earth The atmosphere is crucial in enabling and maintaining life on Earth. Without the atmosphere, Earth would look like the moon. There would be no life forms existing on Earth. Atmospheric gases, such as carbon dioxide and oxygen, are needed by organisms. Carbon dioxide is used by photosynthetic organisms, such as plants and algae, to convert the energy from the sun to usable energy through the process of photosynthesis. On the other hand, oxygen is required by some living organisms 44 including humans for cellular respiration. The ozone layer in the stratosphere is necessary in enabling life on Earth. Without this layer, harmful rays from the sun would reach the surface of Earth and prevent most organisms from surviving. Together with the oceans, the atmosphere keeps Earth’s temperature within the suitable range for life forms. Atmosphere’s Role in the Hydrologic Cycle Water is a renewable resource because it is continually circulated across Earth through a process known as the hydrologic cycle. Its three main important processes are evaporation, condensation and precipitation. Hydrologic Cycle One important process of this cycle is evaporation. Evaporation is the process of converting liquid to gas. Water from the oceans, lakes, streams, rivers, and other bodies of water undergo this process, and it becomes atmospheric water vapor. In plants, instead of evaporation, the process of evapotranspiration takes place. Fig. 17. Steps in the hydrologic cycle. 45 The water vapor in the atmosphere is stored in the form of clouds and moisture (humidity). Cloud formation happens by converting water vapor to liquid form through a process called condensation. Another part of the cycle is precipitation. It is the process of releasing water from the clouds in the form of rain, snow, sleet, or hail. It is the process of returning water from the atmosphere back to Earth’s surface. Once returned to the surface, liquid water may runoff the surface into streams and reservoirs such as lakes and oceans. Water may then infiltrate the subsurface and be incorporated into the groundwater system. It may be consumed and stored in organisms, or trapped in glaciers. The atmosphere is a crucial part of the water cycle. It serves as the reservoir of large amounts of water. The water cycle or hydrologic cycle describes the movement of water from one area to another by changing states―liquid to vapor to ice and back again. It is a never-ending cycle that has occurred for billions of years. All living things depends on this continuous cycle. Therefore, the atmosphere is an efficient medium to move water around the globe. Key Points The atmosphere is crucial in enabling and maintaining life on Earth. Without the atmosphere, Earth would look like the moon. There would be no life forms existing on Earth. The bulk of the atmospheric composition is nitrogen and oxygen in which together comprises 99%. Only 0.9% is argon and the remaining 0.1% is trace gases. The layers are troposphere, stratosphere, mesosphere, thermosphere, and exosphere. ○ Troposphere is where humans live. It also regulates weather and climate. ○ Stratosphere is where the ozone layer that protects Earth from the sun’s harmful UV radiation is found. ○ Mesosphere protects Earth from the impact of space debris. ○ Thermosphere regulates temperature and filters X-rays and some 46  ultraviolet radiation emitted by the sun. ○ Exosphere absorbs some radiation and protects the layers underneath. The atmosphere is an efficient medium to move water around the globe. Web Links For further information, you can check the following web links: Watch this video clip by National Geographic to know more about Earth’s atmosphere and the gases essential to life. National Geographic. 2008. ‘Reveal Earth’s Atmosphere.’ https://www.youtube.com/watch?v=1YAOT92wuD8 Play this interactive game to test your knowledge on Earth’s atmosphere. Brain Pop. n.d.. ‘Time Zone X: Earth’s Atmosphere.’ https://www.brainpop.com/games/timezonexearthsatmosphere/ Play this interactive game to know more on the hydrologic cycle Field Day. n.d.. ‘Water Cycle Games’ https://www.brainpop.com/games/watercyclegame/ Check Your Understanding A. Identify what layer of the atmosphere could the following objects be found. 1. air balloons 2. meteors 3. satellite 4. airplanes 5. ozone 47 B. Identify the layer of the atmosphere being described in each item. Choose the answer from the box below. Write letters only. A. Troposphere B. Stratosphere C. Mesosphere D. Thermosphere E. Exosphere 1. It is the coldest layer of the atmosphere. 2. It is the layer where bad ozone is found 3. It is a layer that protects us from the sun’s harmful UV radiation. 4. It protects Earth from the impact of space debris. 5. It is the atmospheric layer where humans live. C. Find ten atmospheric gases in the word search below. Then, write the hidden message by using the leftover letters in order from left to right and top to bottom. K R Y P T O N C T H A E M E X S A O H S R P H Y E R R E E H G A G S B A L N W I O E H O C I K A N A N Y N M U M T N E T D D H M E E I I G R I N O R R T O S O O P H E V R H R G X E I T A O I A E I S T H P G E M N D O S T O E U N K E N O W R N E O N N X 48  Challenge Yourself Answer the following. Limit your answer in 2 to 3 sentences. 1. What is the importance of atmosphere in the hydrologic cycle? 2. Cite at least three atmospheric gases and give its importance. 3. What will happen if there will be no more hydrological cycle? 4. Why is the tropospheric ozone considered as bad ozone? 5. Can you survive if you will go to mesosphere for days? Why or why not? 49  Laboratory Activity Activity 2.1 Hydrologic Cycle Model Objectives At the end of this laboratory activity, the students should be able to: build a model of the hydrologic cycle; and appreciate the importance of sun, water and atmosphere in making life possible on Earth. Materials and Equipment warm water blue food coloring small bowl plastic wrap rubber bands lamp or any light source clear container or plastic aquarium ziplock bag filled with ice ziplock bag containing sand, gravel or soil Procedure 1. Pour water in the clear container. The depth should be around 2 to 5 cm. Put some food coloring to make the water easier to see. 2. Put the ziplock bag containing sand, gravel or soil on one end of the aquarium. Make sure that the bag is above the water level. 3. Put a small bowl on top of the bag with sand, gravel or soil. 4. Cover the clear container with a plastic wrap. Use a rubber band to hold the wrap in place. 5. Put the ziplock bag filled with ice on the plastic wrap. Position it on the part where the bag of sand and small bowl is located. 6. Turn on the lamp and focus it through the lid. Refer to the setup shown in the illustration below. 50  7. Observe what happens after few minutes. Record your observation. 8. For the second setup, repeat step 1 to 5. Take note that this setup doesn’t need lamp. 9. For the third setup, repeat step 2 to 6. Take note that this setup doesn’t have water inside the clear container. 10. For the fourth setup, repeat step 1, 2, 3, 6. Take note that this setup doesn’t have a plastic wrap and ice. Data and Results Table 1. Materials in the Experiment and its Counterpart in the Hydrologic Cycle Bag of Plastic Materials Used Water Ice Lamp sand wrap Counterpart in the Hydrologic Cycle Table 2. Observations on the Four Hydrologic Cycle Setups First setup Second setup Third setup Fourth setup Observations 51 Guide Questions 1. Which part of the activity simulated evaporation, condensation and precipitation? 2. Is condensation possible without the ice? Why or why not? 3. Is water considered a renewable or non-renewable resource? Why? 4. What do you think is the importance of sun, water and atmosphere for making the hydrologic cycle possible? 5. What would happen if hydrologic cycle doesn’t occur? Performance Task Life on Earth Goal Your goal is to create a skit, poem, or song regarding the importance of Sun, water and atmosphere in making life possible on Earth. Role You have been asked to be an actor or actress, poet or singer Audience The target audience is a senior high school class. Situation You need to showcase your talent to show appreciation to things that makes Earth habitable. Product, Performance, and Purpose You will create a skit, poem, or song to show the importance of sun, water and atmosphere. Your work should be accurate and entertaining. Standards and Criteria Your performance will be graded by the following rubric. 52  Needs Successful Exemplary Below Expectations, Criteria 0% to 49% Improvement Performance Performance 50% to 74% 75% to 99% 100% Preparedness The group seems The group needs The group is The group is unprepared. more time to well-prepared. well-prepared. prepare. Some Some member Each member member doesn’t doesn’t know their knows their role know their role role and act with a and act without and act with a script on hand. script on hand. script on hand. Roles The group Most members of Some members of Excellent job! All members failed to the group didn’t the group didn’t members of the stay in character seem to take their seem to take their group stayed in and didn’t take roles seriously. roles seriously. character and the roles took the roles seriously. seriously. Overall The presentation The presentation The presentation The presentation is not entertaining is entertaining but is entertaining but is entertaining Performance and informative. fails to give seems to lack and informative. accurate more information. information Self Check Check the box if you agree on the following statements. Check I can… differentiate homogeneous and heterogeneous accretion hypothesis. discuss why sun, water, and atmosphere is essential to make life possible on Earth. enumerate ways on how to harness solar energy efficiently, conserve water wisely and reduction of greenhouse gases effectively. 53  Key Words Accretion It happens when gravity attracts tiny bits of matter towards an object. This will result to gradual increase of the object’s size. Albedo It is the ability of a material to reflect light. Exosphere It absorbs some radiation and protects the layers underneath. Heterogeneous It states that Earth accreted during condensation, accretion forming a differentiated planet as it grew in size. Homogeneous It states that Earth accreted from materials of the same accretion composition after condensation. Accretion was followed by differentiation. Hydrosphere It is the water environment on Earth. Mesosphere It protects Earth from the impact of space debris. Stratosphere It is where the ozone layer that protects Earth from the sun’s harmful UV radiation is found. Thermosphere It regulates temperature and filters X-rays and some ultraviolet radiation emitted by the sun. Troposphere It is the atmospheric layer where humans live. It also regulates weather and climate. 54  Wrap Up Why Life on Earth is Possible Photo Credits Fig. 4. World water distribution via Wikimedia Commons. Fig. 5. Frozen lake by Jeff Pang is licensed under CC BY 2.0 via Flickr References NaotatsuShikazono. 2012. Introduction to Earth and Planetary System Science: New View of Earth, Planets and Humans,Germany:Springer Science & Business Media. RenuAnand. 2016.The Story of Planet Earth,New Delhi: The Energy and Resources 55  Institute (TERI). Ronald Martin. 2012. Earth's Evolving Systems: The History of Planet Earth, Massachusetts: Jones & Bartlett Publishers. Michael Pidwirny. 2016. Chapter 4: Solar Radiation and Earth: Single chapter from the eBook Understanding Physical Geography, Our Planet Earth Publishing. Rubin, Kenneth. 2016. Geochemistry Lecture 33 Accessed March 17, 2017. https://www.soest.hawaii.edu/krubin/GG325/lect33.pdf. 56