radiation, energy, and power

Global Albedo and Radiation Budget

• Albedo definition: the percentage of incoming radiation that is reflected instead of absorbed or transmitted. Expressed as a fraction or percent:
  • Global mean albedo (LPO) ~ 0.29, i.e., about 29% of incoming radiation is reflected before interacting with Earth’s surface or atmosphere.
• What albedo affects: regulates Earth’s temperature and warming rates by determining how much solar energy remains in the system.
• Regional variability: albedo changes regionally (e.g., ice, snow, vegetation, clouds) even if the global average remains relatively constant locally.
• Conceptual examples discussed: what if the Arctic were greener, what if there were fewer clouds, or if upper-atmosphere particles were introduced? Lower albedo tends to warm the Earth; higher albedo tends to cool it.
• Time series perspective: global albedo anomaly (departure from a reference) over about eleven years shows large year-to-year variation, largely driven by clouds, rather than a clear long-term trend. In the early 21st century, albedo appeared relatively flat on the global scale despite regional changes.
• Cloud influence on albedo:
  • Clouds can dramatically alter albedo because bright clouds over dark open ocean create large reflectivity contrasts.
  • Year-to-year variability in albedo is mainly due to cloud changes rather than a steady trend.
  • El Niño tends to lower albedo (more absorbed solar radiation) while La Niña tends to raise albedo (more reflection) due to shifts in cloud cover.
• El Niño/La Niña examples:
  • Classic El Niño years include 1998 and 2016; La Niña generally associated with higher albedo.
• Absorbed solar radiation vs albedo:
  • Absorbed solar radiation is inversely related to albedo: lower albedo means higher absorption.
• Long-term perspective (2000–2023):
  • Time series comparing absorbed solar radiation shows a flat baseline with a sharp recent rise, suggesting a potential shift in the warming regime if the cloud cover dynamics continue.
  • Low-cloud cover (a key regulator of albedo over the ocean) shows a similar flat trend with a notable decline in the last few years.
• Interpretation and caution:
  • A drop in low cloud cover could drive a dip in global albedo and contribute to record-hot years (e.g., 2023–2024).
  • Correlation vs causation: the observed relationships do not prove causality; other ocean or atmospheric changes could also influence albedo and warming.
  • Short observational records (e.g., ~23 years for cloud cover) limit confidence in trends; long-term satellite data are needed to distinguish natural variability from genuine climate change signals.
• Takeaway: while albedo can influence warming, the interpretation of recent trends requires careful consideration of natural variability, cloud dynamics, and multiple lines of evidence.

Radiative Transfers: Irradiance, Luminosity, and Spectral Quantities

• Key definitions:
  • Luminosity ($L$): the total power emitted by a source across all wavelengths. Distance-independent; intrinsic property of the source.
  • Irradiance ($E$): power received per unit area from a source across all wavelengths. Distance-dependent due to the inverse-square law.
  • Spectral irradiance ($E_
    u$ or $E_ ext{λ}$): irradiance per unit wavelength, i.e., the power per area per unit wavelength.
• Fundamental relationships:
  • Luminosity measures the total energy output:
    L = ext{total power emitted across all wavelengths}.
  • Irradiance falls off with distance due to geometric spreading; exemplified by the inverse-square law: if distance doubles, irradiance drops by a factor of four.
  • Spectral irradiance is similar to irradiance but resolved by wavelength:
    E_ ext{λ} = rac{dP}{dA \, d ext{λ}}.
• Practical point: irradiance depends on distance to the source, while luminosity does not.
• Example distinctions:
  • On a classroom lantern, those closer to the lamp receive higher irradiance than those farther away, even though the lamp’s luminosity is fixed.
  • In the solar system, a planet’s received irradiance per unit area is not simply proportional to planet size but also to distance from the Sun; irradiance is evaluated per unit surface area.
• Important note on distance scaling:
  • Power falls off as the inverse square of distance: power ∝ 1/$r^2$ in a three-dimensional space.
• Practical concept: spectral irradiance versus total irradiance is useful for understanding wavelength-specific heating and color/texture effects on surfaces.

Blackbody Radiation, Stefan–Boltzmann Law, and Real-World Spectra

• Black body and absorptivity/reflectivity/transmittance:
  • Absorptivity (α) = fraction of incident energy absorbed by the surface.
  • Reflectivity (albedo, ρ) = fraction reflected.
  • Transmittance (τ) = fraction transmitted through the material.
  • Energy conservation requires: α + ρ + τ = 1 for any given incident radiation.
• Absorbed energy leads to emission: objects emit thermal radiation as a function of temperature; absorbed energy is re-emitted according to the object's temperature.
• Black body idealization:
  • A black body has absorptivity α = 1, albedo ρ = 0, transmittance τ = 0, and emits radiation according to its temperature as the maximum possible at that temperature.
  • A black body emits a continuous spectrum with peak intensity determined by its temperature; the emitted spectrum is given by Planck’s law (not fully derived here).
• Real objects vs black body:
  • Real objects are not perfect black bodies; their spectra deviate from the ideal blackbody curve, but the blackbody provides a useful approximation for understanding radiative processes and energy budgets.
• Stefan–Boltzmann law (total emitted irradiance for a black body):
  E = C2 T^4
  where $E$ is the irradiance (W m$^{-2}$) and $T$ is the absolute temperature (K); $C$ is the Stefan–Boltzmann constant:
  C = 5.670 374 419 imes 10^{-8} \, ext{W m}^{-2} \, ext{K}^{-4}.
• Sun and blackbody comparison:
  • The Sun’s photosphere is often approximated as a ~5777 K blackbody; its spectrum is close in shape to a blackbody, with visible peak around the solar spectrum.
  • Absorption in the solar atmosphere (e.g., hydrogen absorption in the ultraviolet) removes parts of the spectrum before it reaches Earth.
  • The actual solar spectrum is a composite of emissions from various solar layers with different temperatures, not a single-temperature blackbody.
• Visible peak for Earth-facing radiation:
  • From Earth’s perspective, the peak of the Sun’s radiation falls in the visible band, making the Sun the dominant source of energy for climate in the visible spectrum.
• Human thermal emission:
  • Humans (core temperature ~ 310 K) emit primarily in the infrared; peak emission lies in the infrared region, far from visible light.
  • The human body radiative output is much smaller than the Sun’s; most of what we perceive is reflected sunlight rather than emitted infrared radiation.
• Key takeaway:
  • Blackbody radiation provides a critical baseline for understanding the radiation budget, even though real objects deviate; many remote sensing and climate analyses rely on this framework.

Earth's Energy Budget: Interactions at the Surface and Atmosphere

• Incoming vs outgoing balance:
  • Incoming solar radiation is partially reflected (albedo), partially transmitted, and partially absorbed.
  • Absorbed energy is re-radiated (emitted) by the Earth–atmosphere system, contributing to the planetary energy budget.
• Interaction outcomes when a wave hits a surface:
  • Reflection: direction changes; energy is conserved; no exchange of energy with the surface.
  • Transmission: wave passes through with little or no interaction; energy passes through the medium.
  • Absorption: energy is absorbed and converted to internal energy (temperature rise); the wave no longer propagates in the original form.
• Real-world notes:
  • No surface is a perfect reflector, absorber, or transmitter; all surfaces exhibit some combination of these interactions.
  • The absorptivity (α) and absorptance are related to absorptive processes; the absorptivity is essentially the fraction absorbed.
• The greenhouse gas context:
  • Even in a mixed atmosphere, the energy budget is affected by how much energy is absorbed versus reflected or transmitted in the optical and infrared bands.
  • The spectral composition of incident and emitted radiation matters for determining temperature responses and climate feedbacks.

Greenhouse Gases Beyond CO2: What to Know

• Why look beyond CO2?
  • CO2 is the dominant long-lived greenhouse gas due to its abundance and atmospheric lifetime, but many other gases have large radiative forcing per molecule and shorter/longer lifetimes.
• Methane (CH₄): the second-largest contributor to climate forcing among well-minned gases in the near term
  • Radiative efficiency: CH₄ is about
    $$ ext{CH}_4 ext{ lifetime and forcing} \