Earth Systems Week 2 Notes

Reducing Projection Distortion and Grid Coordinates

• Grid coordinates: Universal Transverse Mercator (UTM) system
  • Designed to reduce distortion for mapping on a constrained zone, useful for smaller-scale maps compared to a global grid
  • Not intuitive like simple lat/long; provides more uniform distance and area relationships within zones
  • Mentioned in relation to replacing or improving broad-scale coordinates for maps

Earth-Sun Relationships

• Open mindset on Earth’s systems; understanding how Earth, Sun, and atmosphere interact
• Earth’s tilt: axis tilt of $23.5^ ext{o}$ informs seasonal geometry
• North orientation: geographic North Pole and Polaris (the North Star) indicate true north in most of the Northern Hemisphere
• Orbital geometry (described):
  • Pluto and other planets aligned in the plane of the ecliptic (conceptual shorthand for planetary alignment in a single plane)
  • Perihelion: the point in Earth’s orbit closest to the Sun; Aphelion: the farthest point
  • Being closer to the Sun in our winter is a consequence of the orbital ellipse, not the distance alone determining energy received
• Tropic/Equator lines define sunlight limits by season:
  • Tropic of Cancer: $+23.5^ ext{o}$N
  • Equator: $0^ ext{o}$
  • Tropic of Capricorn: $-23.5^ ext{o}$S
• Insolation concept: amount of solar energy reaching Earth’s surface; the energy transfer is electromagnetic radiation
• Solar constant (top-of-atmosphere insolation):
  • $S_0 \,\approx\; 1372\ \mathrm{W\,m^{-2}}$
• Energy concepts (definitions in context):
  • Insolation: energy rate from the Sun received per unit area at the top of Earth’s atmosphere
  • Watt (W): power, i.e., energy transfer per unit time
  • Joule (J): unit of energy
  • Energy transfer to Earth’s surface involves electromagnetic radiation from the Sun
• Wien’s displacement law (from the content):
  • The peak wavelength of emitted radiation depends on temperature
  • $\lambda_{\max} = \dfrac{b}{T},\quad b \approx 2.897\times 10^{-3}\ \mathrm{m\,K}$
• Dependency on Sun-Earth radiation: the Sun’s spectral output and Earth’s response depend on wavelength, temperature, and atmospheric filtering

Earth-Sun Interaction and Subsolar Point

• Solar geometry: the subsolar point (the point on Earth where the Sun is directly overhead) migrates with the seasons
• The subsolar latitude moves between $+23.5^ ext{o}$ (summer solstice in NH) and $-23.5^ ext{o}$ (winter solstice in NH)
• Noon sun angle is not always 90°; it varies by latitude and day of year
• Noon sun angle formula (conceptual):
  • At solar noon, the solar elevation angle $h_{noon}$ is
  • $h_{noon} = 90^ ext{o} - |\,\varphi - \delta\,|$
    where $\varphi$ is geographic latitude and $\delta$ is solar declination
• Example calculation (from transcript example):
  • For $\varphi = 40^ ext{o}N$ on December 22 (approx. $\delta = -23.5^ ext{o}$):
  • $h_{noon} = 90^ ext{o} - |40 - (-23.5)| = 90^ ext{o} - 63.5^ ext{o} = 26.5^ ext{o}$
• Subsolar point calculation steps (illustrated in transcript):
  • Determine the distance in degrees between the subsolar latitude and your latitude
  • Example: difference between 23.5° and 40°N ≈ 63.5°
  • Use this to estimate solar elevation and angle at noon
• Solar panel tilt concept (as per transcript): tilt can be adjusted based on incoming solar angle to optimize energy capture

Rotation, Time, and Global Winds

• Earth rotates from West to East
  • Sun rises in the East and sets in the West
  • Time zones arise from this rotation
• Rotational speed varies with latitude: faster at the equator, slower toward the poles
• Coriolis effect:
  • Causes deflection of moving air and water masses due to Earth's rotation
  • Important in shaping global wind patterns and storm rotation
• Atmospheric and oceanic dynamics are influenced by Coriolis forces in large-scale flow
• Tides:
  • Approximately two high tides and two low tides occur each lunar day at most coasts; magnitudes vary by location

Critical Zone

• Conceptual focus: daylight availability and its impact on:
  • Daylight duration and variability
  • Energy use in human systems
  • Biological productivity
  • Weather and plant growth patterns
• The Critical Zone integrates atmosphere, biosphere, pedosphere, and hydrosphere interactions over time

Earth from Outside: High-Altitude Flight Context

• Josef (Joseph) Kittinger example (historical):
  • High-altitude parachute drop test in a pressurized suit
  • Flight around ~31 km above Earth’s surface
  • Demonstrates the lower atmosphere up to the edge of space, including the upper atmosphere
• Education note: illustrates the transition from dense to tenuous air and the challenges of survival in near-space conditions

Fundamental Definitions: Density, Mass, Volume, Pressure, Heat, and Specific Heat

• Density, mass, and volume relations:
  • Mass: $m$
  • Volume: $V$
  • Density: $\rho = \dfrac{m}{V}$
  • Mass is the amount of matter; density links mass to the space it occupies
• Pressure:
  • Pressure is a force applied per unit area: $P = \dfrac{F}{A}$
  • SI unit: Pascal (Pa) where $1\ \text{Pa} = 1\ \text{N}/\text{m}^2$
  • Standard atmospheric pressure at sea level: $P_{\text{atm}} \approx 101{,}325\ \text{Pa}$ or $1013\ \text{hPa}$
• Heat and energy transfer:
  • Heat is the flow of kinetic energy from one substance to another
  • Typically measured in Watts (W) or Joules per second; total energy transfer is measured in Joules (J)
• Specific heat:
  • Amount of energy required to raise the temperature of a substance by $1^ ext{o}C$ per unit mass
  • Definition: $c = \dfrac{q}{m \Delta T}$ per unit mass
• Relationship examples: the amount of heat required to raise a mass by a temperature interval is $Q = m c \Delta T$

Composition and Properties of the Earth's Atmosphere

• Major constituents (approximate):
  • $\text{N}_2\;: \approx 78\%$
  • $\text{O}_2\;: \approx 21\%$
  • $\text{Ar}$ (argon): ≈ 1% (trace amounts elsewhere)
• Notable molecular masses:
  • $\text{N}_2$: molecular weight ≈ $28.013\ \text{amu}$
  • $\text{O}_2$: molecular weight ≈ $31.998\ \text{amu}$
• Heavier molecules and diffusion: $\text{O}<em>2$ is heavier than $\text{N}</em>2$ in the atmosphere on average
• Density and pressure with altitude:
  • Air density decreases with height due to fewer particles per unit volume
  • Atmospheric pressure decreases with height as the weight of the air above decreases

Atmospheric Pressure and Heat Transfer Concepts

• Atmospheric pressure as a force per unit area decreases with altitude
• Heat transfer control factors:
  • Material properties (conductivity, specific heat, etc.)
  • Temperature differences between substances
• Temperature and energy transfer interplay:
  • Heat flows from higher to lower temperature regions
  • Temperature is related to average kinetic energy of particles

Layers of the Atmosphere and Their Roles

• Troposphere (nearest Earth):
  • Contains most weather and clouds
  • Lapse rate: temperature generally decreases with altitude (typical lapse rate ≈ $6.5^ ext{o}C/{\rm km}$)
  • Approximate top: around $8-12\ \text{km}$ depending on latitude and season
• Stratosphere:
  • Altitude range roughly $12-50\ \text{km}$ (up to ~48 km in some descriptions)
  • Contains the ozone layer that absorbs UV radiation
  • Temperature tends to increase with height due to ozone heating
• Mesosphere:
  • Altitude range roughly $50-85\ \text{km}$ (transcribed as ~48-80 km in notes)
  • UV absorption continues; meteors burn up here; temperature declines with height modestly
• Thermosphere:
  • Altitude range roughly $85-600\ \text{km}$ (transcript notes ~80-480 km)
  • Direct absorption of solar radiation; very low density; temperatures can be very high but carry little heat due to sparse air
• Lapse rate and temperature structure: general trend from the surface upward, with layer-specific variations due to composition and solar heating

Early Earth and Differentiation

• Early Earth: molten, partially liquid surface; rapid differentiation led to layered structure (core, mantle, crust)
• Zircon dating concept (from transcript context):
  • Zircon crystals incorporate uranium but exclude lead during formation, enabling radiometric dating by measuring the decay products of uranium to lead
• Differentiation concepts:
  • Separation into distinct compositional layers due to density differences
  • Formation of the metallic core (primarily iron) and silicate mantle/crust
• Core and mantle structure (transcript references):
  • Core: Inner core (solid Fe) surrounded by a liquid outer core (Fe alloy)
  • Mantle: Upper and lower mantle; lithosphere sits atop the asthenosphere
  • Crust: Lithospheric crust (continental and oceanic) overlying mantle
  • Asthenosphere: A plastic, semi-solid layer that allows plate tectonics movement
• Rough interior layout (as per notes):
  • Lithospheric crust thickness: Roughly $10-70\ \text{km}$ (varies for oceanic vs continental)
  • Mantle thickness: Several thousand kilometers (transcript cites values like ~2230 km for certain sections; standard models place the mantle around ~2900 km thick)
  • Outer core thickness: substantial (transcript notes ~2250 km; standard models place outer core thickness around ~2260 km)
  • Inner core radius: ~1220 km in standard models (not explicitly stated in transcript, but commonly cited)

The Rock Cycle and Minerals

• Lithospheric rocks and minerals:
  • Minerals: solid inorganic substances with a repeating, orderly internal structure and fixed chemical composition
  • Rocks: aggregates of minerals bound together
• The rock cycle concept (from the transcript):
  • Rocks form from mineral assemblages; they can be transformed through heating, cooling, weathering, and tectonics into other rock types
• Environment dictates mineral composition and rock type; tectonics drive crustal evolution

Additional Concepts and Terms Included in the Transcript

• “Critical Zone” emphasis on daylight and productivity: connects to energy availability, biology, climate, and weather patterns
• The relationship between energy, light, and biological systems (e.g., photosynthesis, plant growth) is implied through insolation and daylight duration
• The practical link between solar geometry and energy capture (e.g., solar panel tilt) is noted
• Basic geophysical relationships (density, mass, volume) and how they relate to atmospheric conditions
• Historical and experimental context (e.g., high-altitude flight) used to illustrate atmospheric layers and pressures

Key Equations and Quantities (LaTeX-formatted)

• Solar constant (top-of-atmosphere insolation):
  $S_0 \approx 1372\ \mathrm{W\,m^{-2}}$
• Solar wavelength peak (Wien’s law):
  $\lambda_{\max} = \dfrac{b}{T},\quad b \approx 2.897 \times 10^{-3}\ \mathrm{m\,K}$
• Solar noon elevation angle (conceptual):
  $h_{noon} = 90^ ext{o} - |\varphi - \delta|$
  where $\varphi$ = latitude, $\delta$ = solar declination
• Subsolar point declination limits: $\delta \in [-23.5^ ext{o}, +23.5^ ext{o}]$
• Light-energy balance (insolation at surface is less than $S_0$ due to geometry and atmosphere; an explicit surface-insolation model would include albedo and cloud effects)
• Density relation:
  $\rho = \dfrac{m}{V}$
• Pressure definition:
  $P = \dfrac{F}{A},\quad 1\ \text{atm} = 101{,}325\ \text{Pa}$
• Heat and specific heat:
  $Q = m c \Delta T$
• Definition of heat flow (power):
  $\text{Power} = \dfrac{\text{Energy}}{\text{Time}} = \text{W}$

Connections to Foundational Principles and Real-World Relevance

• The tilt of Earth and orbital geometry underpin seasons, day-length variation, and climate zones
• The atmosphere’s composition and layered structure govern weather, climate, UV exposure, and protection from space radiation
• The Coriolis effect and tidal forces shape weather systems and coastal dynamics, with practical implications for navigation, aviation, and coastal engineering
• Radiometric dating (e.g., Zircon) provides methods to understand Earth’s formation timeline and differentiation history
• The rock cycle explains surface and subsurface geology, plate tectonics, mineral resources, and Earth’s geologic history
• Energy concepts (insolation, heat transfer, specific heat) connect solar forcing to climate, ecosystems, and human energy use (e.g., solar panel design)

Practical and Ethical Implications (brief notes)

• Understanding solar energy and climate informs sustainable energy planning and mitigation of climate change
• Knowledge of atmospheric layers and protection from UV radiation highlights the importance of environmental stewardship and public health considerations
• Geological history informs resource management, hazard assessment (earthquakes, volcanism), and infrastructure planning in relation to the dynamic Earth system