Atmospheric Microwave Radiometry and Vertical Thermal Sounding

Atmospheric Microwave Radiometry and Orbital Dynamics

• Thermal Emission Across All Wavelengths:

  • Every physical object at a finite temperature emits photons across essentially the entire electromagnetic spectrum, rather than exclusively within the visible or primary infrared bands.
  • Bean's law defines the peak emission wavelength for an emitting body based on temperature; however, thermal emission continues into spectral regions located far from this peak.
  • At wavelengths situated far from the peak wavelength, the photon emission rate drops to very low values, making the emission curve appear to hit zero on standard linear spectrum diagrams.
  • The Earth and its atmosphere continuously emit photons in the microwave regime, which corresponds to the centimeter light scale ($\sim\text{cm}$).
  • Because the rate of microwave emission is exceedingly small, atmospheric microwaves pose no danger, meaning there is no need to wear protective tinfoil hats.
  • Detection of these low-flux microwave emissions requires highly sensitive specialized satellite sensors.

• Satellite Orbits and Coverage Patterns:

  • Microwave measurements of atmospheric emissions are conducted by satellite platforms such as polar-orbiting weather satellites equipped with instruments like the ANSU sensor.
  • Polar orbits follow trajectories passing sequentially from pole to pole (North Pole to South Pole and South Pole to North Pole), granting extensive global observational coverage.
  • As the satellite completes its orbital loops, the Earth rotates eastward beneath it, causing the instrument to observe the atmosphere in adjacent geographical strips.
  • A polar-orbiting satellite achieves complete coverage of the entire planetary surface once every approximately $8\,\text{days}$.
  • While satellite sounding does not match the daily temporal resolution of fixed surface thermometers, it provides completely global spatial coverage.
  • The satellites operate in sun-synchronous orbits, designed so that the spacecraft crosses over specific latitudes (such as the Equator) at the exact same local solar time on every orbit, typically at $1\,\text{PM}$ and $1\,\text{AM}$.

Radiative Transfer and Vertical Sounding Principles

• The Physics of Atmospheric Sounding:

  • Satellites cannot dangle in-situ thermometers into the atmosphere from orbit; instead, they determine atmospheric temperatures remotely through the principles of radiative transfer.
  • The differential change in optical depth ($\Delta \tau$) as radiation travels through an atmospheric path is expressed as:         $\Delta \tau = k \cdot \rho \cdot \Delta z$         where $k$ is the absorption coefficient, $\rho$ is the density of the gas, and $\Delta z$ is the vertical distance measured from space downward into the atmospheric column.
  • The coefficient $k$ is a function of the specific gas species, the gas velocity/temperature distribution, and the precise wavelength of radiation being observed.

• Optical Depth and the Unity Emission Level:

  • Photons escaping to space and detected by a satellite sensor originate predominantly from an atmospheric layer located around an optical depth of unity ($\tau = 1$) for that particular gas and wavelength.
  • Because $\Delta z$ represents the downward path distance from space into the atmosphere, a large value of $k$ causes the optical depth to accumulate rapidly, reaching $\tau = 1$ high up in the atmosphere.
  • Conversely, a small value of $k$ allows radiation to travel deeper into the atmosphere before accumulating sufficient optical depth, placing the $\tau = 1$ emission layer low down in the atmosphere near the surface.
  • By selecting and tuning instrument channels across wavelengths with varying values of $k$, a sensor samples emissions emerging from different altitude levels in the atmosphere.

Oxygen Absorption Channels and Temperature Retrieval

• The $60\,\text{GHz}$ Oxygen Resonance Peak:

  • The ANSU/Amsterdam instrument monitors microwave channels clustered together along the flank of a prominent oxygen absorption feature located between $4\,\text{mm}$ and $8\,\text{mm}$, referred to as the $60\,\text{GHz}$ oxygen resonance.
  • Oxygen is chosen because it is well-mixed and uniformly distributed throughout the atmosphere, making variations in radiation purely dependent on temperature and optical depth rather than changing gas concentrations.
  • Instrument channels are clustered specifically on the steep slope of the resonance peak because the absorption coefficient $k$ changes rapidly across small wavelength intervals along the edge.

• Vertical Atmospheric Profiling:

  • A channel tuned to a wavelength where $k$ is low receives microwave photons from the $\tau = 1$ level situated low in the atmosphere, sampling temperatures close to the planetary surface.
  • A channel tuned to a wavelength where $k$ is high receives photons from the $\tau = 1$ level located high in the atmosphere.
  • The radiant flux of microwave photons detected by the antenna is directly related to the local temperature of that specific atmospheric layer via the Stefan-Boltzmann law.
  • Weighting functions—characterized graphically as smooth vertical distributions or "blobby bumps" centered at the $\tau = 1$ height—describe the exact vertical extent and relative contribution of the atmospheric layer sampled by each channel.
  • By resolving the emitted microwave power across multiple channels with distinct weighting functions, the satellite reconstructs temperature as a function of height through the atmospheric column.

Atmospheric Structure and Observed Temperature Trends

• Historical Satellite Temperature Trends:

  • Microwave sounding satellites have been deployed operationally since approximately $1980$ (or slightly earlier), offering a shorter historical baseline than surface thermometers, which extend back into the late $1800\text{s}$.
  • The lowest atmospheric sounding channels measure a pronounced warming trend of approximately $0.185\,\text{K}$ per decade ($0.185\,\text{K}\,\text{decade}^{-1}$).
  • Over three to four decades ($3$ to $4\,\text{decades}$) of continuous records, this rate accounts for an accumulated temperature increase of over a half-Kelvin ($0.5\,\text{K}$).
  • Mid-altitude channels initially display warming, but the trend progressively flattens with increasing altitude and transitions into unambiguous, persistent cooling in the upper atmosphere.

• Vertical Thermal Structure of the Atmosphere:

  • Troposphere: The lowest atmospheric layer where human life and surface weather exist, defined by an average environmental lapse rate of $6.5\,\text{K}\,\text{km}^{-1}$ (six and a kelp per kilometer).
  • Stratosphere: Sits immediately above the troposphere, exhibiting a temperature inversion where temperatures increase with altitude.
  • Stratopause: The boundary transition zone between the stratosphere and the mesosphere, manifested as a distinct local temperature maximum ("bump").
  • Mesosphere: Layer situated above the stratopause where temperatures decrease with height.
  • Thermosphere: Extends above the mesosphere up to approximately $100\,\text{km}$, which serves as an artificial demarcation for the outer boundary where space begins.

• Radiative Energetics of the Stratopause:

  • The temperature peak at the stratopause results from intense absorption of incoming solar ultraviolet (UV) radiation by atmospheric ozone.
  • Under steady-state equilibrium, the energy absorbed from ultraviolet light must be precisely balanced by longwave infrared emission from greenhouse gases.
  • Because thermal emission scales with temperature to the fourth power according to the Stefan-Boltzmann law ($T^4$), the stratopause must sustain a high temperature to generate the large longwave emission flux necessary to balance UV heating.

Greenhouse Gas Fingerprinting and Upper-Atmosphere Cooling

• Mechanisms of Greenhouse Forcing by Atmospheric Layer:

  • Troposphere: Increasing greenhouse gases elevates the effective $\tau = 1$ emission altitude to a colder layer, reducing outgoing longwave radiation to space and creating a top-of-atmosphere energy imbalance that warms the lower atmosphere.
  • Stratosphere and Mesosphere: The absorption of incoming solar ultraviolet radiation by ozone remains largely constant over decadal warming timescales.
  • An increase in carbon dioxide ($\text{CO}_2$) concentration elevates the radiative emissivity of upper atmospheric layers, allowing them to emit longwave radiation to space far more efficiently.
  • Because the rate of UV energy absorption remains unchanged while longwave cooling efficiency increases, the stratosphere and mesosphere must cool to a lower steady-state temperature to restore radiative balance.

• Attribution and Empirical Evidence for Climate Change:

  • Simultaneous warming in the lower atmosphere (troposphere) and cooling in the upper atmosphere (stratosphere and mesosphere) represents a unique vertical fingerprint of $\text{CO}_2$-induced radiative forcing.
  • External climate drivers such as variations in solar irradiance would heat or cool the entire vertical column uniformly, rather than producing opposing vertical temperature trends.
  • Additional empirical lines of evidence supporting greenhouse-driven climate warming include:
    • High-resolution historical temperature and greenhouse gas records preserved within ice cores.
    • Detailed spatial warming patterns distributed across latitude and longitude.
    • Comprehensive multi-channel vertical temperature profiles across the global atmosphere.