Seasonal and Daily Temperatures – Comprehensive Study Notes

Radiative Equilibrium and the Earth’s Energy Budget

• Radiative equilibrium concept: Energy in (shortwave from the Sun) = Energy out (infrared from the Earth).
• In simple terms, the Earth’s temperature at radiative equilibrium is the equilibrium temperature, Te.
• Key numerical reference:
  • Solar constant (top-of-atmosphere): F_s = 1372\ \text{W m}^{-2}
  • Albedo: A (fraction reflected)
  • Absorbed solar energy (global mean) is reduced by albedo and spread over the globe, leading to the effective emission temperature.
  • Effective emission temperature: Te = \left(\frac{(1-A)Fs}{4\sigma}\right)^{1/4} \approx 255\ \text{K}
  • Real global-mean surface temperature: T_s \approx 288\ \text{K} \; (\approx 15^{\circ}\mathrm{C}, 59^{\circ}\mathrm{F})
• Important takeaway: Te ≈ constant implies a balance between incoming and outgoing radiation, but the surface temperature is higher than Te due to atmospheric processes (greenhouse effect).
• What happens if energy input ≠ energy output? A mismatch would imply warming (input > output) or cooling (input < output).

The Greenhouse Effect

• Without greenhouse gases (GHGs): longwave energy emitted by Earth’s surface would go directly to space.
• With GHGs: the atmosphere absorbs a portion of the longwave radiation emitted by the surface and re-emits it both downward (warming the surface) and upward (emission to space).
• This additional downward longwave radiation is what we call the greenhouse effect, and it raises the surface temperature above Te.
• Practical implication: The surface is warmer than the simple radiative balance would predict because of atmospheric absorption and re-emission of infrared radiation.

Distribution of Incoming Solar Radiation: The Global Budget

• Global incoming solar energy at the top of the atmosphere can be broken down into what is reflected, absorbed by the atmosphere, and absorbed at the surface.
• A representative breakdown (from the transcript):
  • Incoming solar radiation: 100 units
  • Reflected and scattered: 30 units (albedo effect)
  • Absorbed into the Earth system: 70 units
  • Absorbed by atmosphere and clouds: 19 units
  • Absorbed at the Earth's surface: 51 units
• The atmosphere and clouds absorb some of the shortwave radiation, while the surface absorbs the remainder.
• This breakdown is part of the broader Earth energy balance: not all incoming solar energy reaches the surface; a portion is reflected, some is absorbed in the atmosphere, and a large portion is absorbed at the surface.

Details of the Earth–Atmosphere Energy Balance (Overview)

• The energy balance numbers indicate the relative contribution of each process to the Earth’s climate system.
• The figure provides a detailed breakdown (70% reference level) to help understand climate sensitivity, but the exact numbers are less critical for qualitative understanding.
• Core concept: The balance involves shortwave input, longwave output, and exchanges between surface, atmosphere, and clouds.

Latitudinal and Temporal Distribution: Heat Transport and Balance

• Since Te is approximately constant, the Earth is in radiative equilibrium on a global scale.
• However, energy input is not uniformly distributed across the globe:
  • Northern latitudes experience a deficit of energy (tending to cool if not compensated by transport).
  • Equatorial regions experience a surplus of energy (tending to warm if not transported away).
• To maintain equilibrium, heat is transported from the equator toward the poles via three primary mechanisms:
  1) Ocean circulation (~40% of heat transport)
  2) Weather transporting sensible heat (~30%)
  3) Weather transporting and generating latent heat (~30%)
• The distribution and transport of heat are essential to understanding seasonal and regional temperature patterns.

Seasonal Variations and Insolation

• Insolation (incoming solar radiation) drives the Earth’s average temperature but is not uniformly distributed in space or time.
• Key idea: Insolation keeps the Earth warm, but its geographic distribution changes with season due to orbital geometry and Sun-Earth angle.
• What controls the amount of incoming radiation at a given point?
  • Orbital geometry and distance to the Sun (elliptical orbit) – the inverse-square law applies, but it is not the dominant control for seasonal patterns.
  • Sun angle (solar elevation angle) – how high the Sun is in the sky at local noon dramatically changes the intensity per unit area.

Sun Angle and Orbit: Geometry of Solar Exposure

• Sun Angle concepts:
  • Solar Elevation Angle: angle between the horizon and the Sun.
  • Zenith Angle: angle between the vertical and the Sun.
• Earth’s tilt: 23.5° relative to its orbital plane.
  • Equinox: roughly equal day and night (12 hours each).
  • Solstice: maximum or minimum daylight hours (longest or shortest day).
• Solar Declination (d): latitude where the Sun is directly overhead at solar noon.
  • At the Tropic of Cancer (~23.5°N) on the NH summer solstice.
  • At the equator on the equinox.
  • At the Tropic of Capricorn (~23.5°S) on the NH winter solstice.
• A common relation used to estimate solar angle at local noon:
  • \text{SA} = 90^{\circ} - f + d
    where f = latitude, d = declination.

Apparent Path of the Sun Across Latitudes (Solstices and Equinox)

• The apparent solar path changes with latitude and season.
• June solstice (NH summer) and December solstice (NH winter) show different solar trajectories.
• Equinoxes (spring and autumn) feature Sun paths that cross the equator, resulting in nearly equal day and night lengths globally.
• Local season variation is visually apparent in how high the Sun climbs and how long daylight lasts at a given latitude.

Daily Insolation During the Solstices

• Daily insolation changes during solstices due to two main factors:
  • Maximum possible insolation (sunlight intensity at local noon) varies with Sun angle.
  • Duration of daylight varies with season.
• Two example locations: Lawrence, KS and Juneau, AK illustrate different latitude effects on insolation and temperature.

Daylight Duration and Regional Implications

• Example: Lawrence, KS (~39°N) experiences a daylight duration difference of about 5.9 hours between winter and summer solstices.
• Implications of sun angle on climate and landscape:
  • Slopes and aspect affect solar heating (e.g., ski slopes facing north receive less direct sun in NH winter).
  • Soil moisture and vegetation differ by slope orientation due to differential insolation.
  • Solar panel placement is influenced by sun elevation and duration of sun exposure.

Annual Temperature Variation in the Northern Hemisphere

• Observed NH temperature patterns often peak in late July, not on the summer solstice (June 21), and reach a minimum in late January, not on the winter solstice (Dec 21).
• This lag is analogous to the diurnal cycle, where peak temperatures occur after solar noon due to cumulative warming and heat storage in the surface and near-surface layer.

Daily Temperature Variation: Diurnal Cycle and Net Radiation

• Daily temperature variation is driven by the diurnal cycle of radiation:
  • Solar radiation (shortwave) dominates daytime heating; surface warms and emits longwave radiation.
  • Terrestrial radiation follows Stefan-Boltzmann’s law: E = \sigma T^4
  • Net radiation controls whether surface warms or cools:
  • Net radiation > 0: surface warms (roughly 6:00–15:00 to 15:00–17:00 depending on location)
  • Net radiation < 0: surface cools (mid-afternoon to dawn)
• The warmest part of the day is not at solar noon but typically in the mid-to-late afternoon (3–5 PM) due to the lag in the response of surface temperature to incoming energy.
• Net radiation at the surface is defined as: Rn = S{abs} - L_{out} where:
  • S_{abs} is absorbed solar shortwave at the surface
  • L_{out} is emitted longwave radiation by the surface (and can include atmospheric back-radiation in detailed budgets)
• The same basic process operates on daily scales but with different magnitudes and time constants compared to seasonal scales.

Processes Governing Daily Temperature Variation: Boundary Layer and Heat Exchange

• The primary mechanism for daily temperature variations is radiative heating of the ground.
• The boundary layer (near-surface air) plays a critical role:
  • Heat is transferred from the ground to the air via conduction (near the surface).
  • Convection then transports heated air upward and cooler air downward, mixing the boundary layer.
  • The boundary layer is where most of the diurnal temperature variation occurs.
• The depth and efficiency of mixing depend on wind speed and stability:
  • Calm winds and clear skies favor stronger surface cooling at night (radiation inversion forms).
  • Wind enhances mixing, distributing heat upward and reducing near-surface temperature swings.

Absorption and Heating of the Surface: Albedo, Materials, and Vegetation

• Surface heating depends on several factors:
  • Albedo (reflectivity): higher albedo means less absorbed energy.
  • Specific heat capacity of the surface material (e.g., water vs. land vs. ice) affects how quickly the surface heats or cools.
  • Land surface type (water, land, glacier) and vegetation cover.
  • Soil type (sand, silt, clay) and soil moisture influence absorption and heat storage.
• Land surface characteristics determine how much solar energy is absorbed and how quickly it heats the near-surface air.

Factors Affecting Daytime Warming: Wind and Mixing

• Wind speed critically affects daytime warming by promoting vertical mixing near the surface:
  • Stronger mixing brings down cooler air and transports warm air upward, which can moderate surface temperatures and warm layers aloft.
  • This results in cooler near-surface temperatures and warmer air higher up, shifting the vertical temperature profile.

Nighttime Cooling and Inversion Formation

• Nighttime cooling occurs because:
  • No solar input to heat the ground, but the ground continues to emit longwave radiation (E = \sigma T^4).
  • Surface cools rapidly, and convection from the surface declines as the surface becomes cooler than the air above (stable conditions).
  • Heat transfer by conduction from the warm air to the cool ground near the surface dominates in a shallow boundary layer.
• Radiation inversion: a shallow layer near the surface where temperature increases with height, opposite to the usual decrease with height in the lower troposphere.
• Factors enhancing radiation inversion formation:
  • Calm wind or very light winds
  • Long night or short night
  • Dry air or humid air (varies with moisture and cloud cover)
  • Clear skies or absence of cloud cover
  • Surface wetness, vegetation type, and surface type can also influence inversion strength.

Frost Damage and Mitigation Strategies

• Frost can damage crops when temperatures drop below freezing or near freezing.
• Mitigation strategies include:
  • Orchard heaters
  • Wind machines to mix air and prevent frost pockets
  • Helicopters to mix air or move warm air downward
  • Covering plants to trap heat
  • Flooding ground to insulate or release latent heat (select cases)

Seasonal and Weather Extremes: Tornado and Severe Weather Context (NOAA SPC examples)

• The transcript includes storm-scale diagnostic plots and indices from the NOAA/NWS Storm Prediction Center (SPC), illustrating concepts such as:
  • Wind speed vs. height (inferred temperature advection)
  • Temperature and dewpoint profiles, lapse rates, CAPE (Convective Available Potential Energy), CINH (Convective Inhibition), LCL (combined cloud base), LFC (level of free convection), EL (equilibrium level)
  • SHER/SRH (shear-related indices), MLCAPE, DCAPE, and storm mode indicators
  • The material underscores how atmospheric instability and shear relate to severe weather potential.
• While technically important for meteorology, these details supplement the broader energy-balance framework by showing how atmospheric thermodynamics and vertical structure influence surface weather (e.g., temperature extremes, convective activity).

Surface Air Temperature Measurements: How and Where to Measure

• Important measurement practices for air temperature:
  • Measurements should be taken in the shade to avoid direct solar heating of the thermometer.
  • Ensure adequate ventilation around the sensor box to avoid artificial warming.
  • Do not place the thermometer right at ground level; standard heights are about 1.5–2 meters above ground.
• Practical note: Surface materials and local heat sources can bias temperature readings if proper placement is not followed.

Human Influence on Temperature Readings and Urban Heat Islands

• The placement and surface materials near measurement sites can significantly bias recorded temperatures.
• For example, introducing blacktop or other heat-absorbing surfaces nearby can raise near-surface air temperatures, illustrating urban heat island effects and measurement biases if not accounted for.

Quick Summary: Key Concepts to Remember

• Radiative equilibrium and Te vs Ts; the greenhouse effect explains why Ts > Te.
• Energy budget components: albedo, atmospheric absorption, surface absorption, and the atmospheric greenhouse effect.
• Heat transport from equatorial to polar regions via oceans and atmosphere (sensible and latent heat).
• Seasonal and diurnal variations driven by Sun-Earth geometry, obliquity, declination, and wind-driven boundary-layer processes.
• Solar angle and duration of daylight significantly modulate insolation and temperatures, with notable regional differences due to latitude and terrain.
• Daily temperature evolution is governed by net radiation and the boundary layer; nighttime cooling and radiation inversions are common in clear, calm conditions.
• Measurement best practices matter for accurate air temperature readings; urban heat effects can bias observations if not properly managed.

Notation and Formulas (Glossary)

• Stefan-Boltzmann law: E = \sigma T^4
• Net radiation (surface; simplified): Rn = S{abs} - L_{out}
• Global mean absorbed solar fraction: \frac{(1-A)F_s}{4}
• Effective emission temperature: Te = \left(\frac{(1-A)Fs}{4\sigma}\right)^{1/4}
• Surface temperature context: T_s \approx 288\ \text{K}
• Solar declination and solar angle relationships: SA = 90° - f + d, where f = latitude and d = declination

Connections to Previous Topics and Real-World Relevance

• The Earth’s energy balance underpins climate change discussions: how increases in atmospheric greenhouse gases shift the balance, raising Ts while Te remains governed by energy in/out.
• Understanding insolation patterns helps explain regional climate differences, agricultural planning, and solar energy potential assessments.
• Boundary layer processes connect physics of radiation to meteorological phenomena such as daily temperature swings, frost risk, and heat accumulation in urban areas.
• Measurement practices matter for climate data integrity and underscores the importance of standardized observation networks.

Philosophical and Practical Implications

• Philosophical: Radiative balance emphasizes the planet as a coupled system where small changes in albedo or greenhouse gas concentration can lead to noticeable climate shifts through feedbacks.
• Practical: Knowledge of solar geometry and daily temperature dynamics informs agriculture, energy planning (heat loads and solar energy capture), and infrastructure design (cooling needs, shading, and insulation).
• Ethical: Accurate temperature records and transparent reporting are essential for informed policy-making and public trust in climate science.

Quick Reference: Key Figures and Tables Mentioned (Conceptual)

• Te ≈ 255 K; Ts ≈ 288 K
• Fractional energy partition at the top of the atmosphere: ~30% reflected, ~70% absorbed (atmosphere/clouds ~19; surface ~51)
• Heat transport shares: Ocean ~40%, Sensible heat ~30%, Latent heat ~30%
• Latitude-longitude related relations: SA ≈ 90° − f + d
• Diurnal cycle: E = σT^4 governs surface radiation; net radiation drives warming/cooling; maximum surface temperature often in mid to late afternoon.

End of Notes