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Outgoing longwave radiation

Outgoing longwave (OLR) is the thermal infrared emitted to space from the top of Earth's atmosphere, primarily in wavelengths from 4 to 100 μm, serving as the dominant mechanism by which the planet dissipates absorbed . The annual mean OLR flux is approximately 239 W/m², which in a steady-state budget equals the absorbed shortwave after accounting for planetary of about 0.3. Measured via satellite instruments such as NASA's Clouds and the Earth's System () and NOAA's polar-orbiting platforms, OLR provides empirical data on atmospheric composition effects, including by greenhouse gases and clouds that reduce the flux relative to blackbody emission from the surface. Variations in OLR, driven by factors like , feedback, and cloud dynamics, are key diagnostics for phenomena such as El Niño-Southern Oscillation and long-term trends in Earth's imbalance.

Fundamentals

Definition and Physical Principles

Outgoing longwave radiation (OLR) refers to the emitted by 's surface, atmosphere, and clouds that reaches the top of the atmosphere (TOA) and escapes to , primarily in the portion of the . This outward flux balances the absorbed shortwave solar in 's global energy budget, with a planetary average of approximately 240 W/m². Over 99% of OLR occurs within wavelengths of 4 to 100 μm, peaking near 10 μm for typical temperatures due to the blackbody . The physical basis of OLR emission derives from quantum mechanical principles of , where molecules and surfaces at temperature T emit photons according to for : B(\lambda, T) = \frac{2hc^2}{\lambda^5} \frac{1}{e^{hc/\lambda kT} - 1}, with h as Planck's constant, c as the , k as Boltzmann's constant, and \lambda as wavelength. Integrating over all wavelengths and hemisphere yields the total hemispherical emissive power via the Stefan-Boltzmann law for a blackbody: M = \sigma T^4, where \sigma = 5.6704 \times 10^{-8} W m⁻² K⁻⁴ is the Stefan-Boltzmann constant. For non-ideal emitters like Earth's components, an factor \epsilon (0 < \epsilon ≤ 1, often near 1 in the infrared for water and land surfaces) modifies this to M = \epsilon \sigma T^4. Earth's effective emitting temperature, derived from observed global-mean OLR assuming \epsilon \approx 1, is about 255 K, cooler than the surface average of 288 K due to partial absorption and re-emission by greenhouse gases in the atmosphere. This effective temperature reflects the planet's radiative equilibrium, where OLR equals absorbed solar input minus reflected shortwave. Actual OLR spectra deviate from a pure blackbody curve owing to selective emission, absorption lines (e.g., from H₂O, CO₂), and cloud opacity, resulting in a sensitivity to surface temperature closer to 2.2 W m⁻² K⁻¹ rather than the blackbody 5.5 W m⁻² K⁻¹. Measurements from satellites like CERES confirm these principles, with OLR derived from broadband or spectrally resolved infrared radiances calibrated against radiative transfer models.

Role in Earth's Energy Budget

Outgoing longwave radiation (OLR) constitutes the dominant mechanism by which Earth dissipates absorbed solar energy to space, ensuring balance in the planetary energy budget. The global average OLR, measured at the top of the atmosphere, approximates 239 W/m² based on satellite observations from instruments like NASA's (CERES). This value aligns with the absorbed shortwave radiation (ASR) of roughly 240 W/m² under equilibrium conditions, where incoming solar flux, after accounting for planetary of about 0.30, yields equivalent absorption. Any sustained deviation—where ASR exceeds OLR—results in net energy gain, manifested as rising global temperatures and ocean heat uptake. The Earth's energy imbalance (EEI), quantified as EEI = ASR - OLR, has been positive since at least the late 20th century, reflecting anthropogenic influences such as greenhouse gas increases that initially suppress OLR relative to ASR. CERES data indicate an average EEI of 0.87 ± 0.15 W/m² from 2006 to 2018, with trends showing further intensification to around 1.0 W/m² or higher in recent years due to both enhanced ASR from reduced aerosols and subdued OLR response from water vapor feedbacks. This imbalance equates to approximately 460 terawatts of excess energy trapped annually, primarily stored in the oceans, underscoring OLR's pivotal role in modulating climate sensitivity and long-term stability. Variations in OLR directly influence EEI dynamics; for instance, cloud cover reductions can enhance OLR, partially offsetting ASR increases, while tropospheric warming boosts emission per the Stefan-Boltzmann law, though greenhouse trapping limits the net escape. Peer-reviewed analyses confirm that observed OLR trends, including a slight decline in clear-sky components amid overall stability, align with radiative forcing estimates rather than contradicting them. Monitoring OLR thus provides a critical diagnostic for validating energy budget closures and projecting future warming trajectories.

Emission Mechanisms

Surface Emission Processes

The Earth's surface emits longwave radiation predominantly through thermal emission processes, arising from the acceleration of charged particles within surface materials due to their temperature, resulting in electromagnetic radiation in the infrared spectrum (approximately 3–100 μm). This emission follows the principles of , approximated for real surfaces by the adjusted for emissivity: the total upward radiative flux M = \epsilon \sigma T^4, where T is the surface skin temperature in Kelvin, \sigma = 5.6704 \times 10^{-8} W m⁻² K⁻⁴ is the , and \epsilon is the broadband surface emissivity (typically 0.95–0.99 for natural Earth surfaces in the thermal infrared). Globally averaged, the surface temperature is approximately 288 K, yielding a blackbody emission of about 390 W m⁻², with the actual upward longwave flux estimated at 396 W m⁻² accounting for typical emissivities and spatial variations. Emissivity varies by surface type: oceans (covering ~71% of Earth's surface) exhibit \epsilon \approx 0.97 in the longwave due to water's molecular properties, while vegetated land surfaces approach 0.98, bare soils and sands range 0.92–0.97, and snow/ice near 0.99, influencing local emission intensities but averaging high globally to minimize deviation from blackbody behavior. These values derive from spectral measurements showing near-unity emissivity in key infrared bands (e.g., 8–12 μm), though lower in far-infrared for some arid regions. Emission spectra approximate Planck's law for the local surface temperature, peaking near 10 μm for typical conditions, with negligible contributions from non-thermal processes like chemiluminescence or solar reflection in the longwave domain. Surface heterogeneity—such as diurnal temperature swings or land-ocean contrasts—modulates local fluxes, but the process remains fundamentally temperature-driven, with emissivity corrections ensuring accurate flux estimates in energy budget models.

Atmospheric Emission Contributions


The outgoing longwave radiation (OLR) at the top of the atmosphere comprises emissions from both the Earth's surface and the atmosphere, with the latter dominating due to the high opacity of the atmosphere to in most spectral bands. In global mean conditions, radiative transfer calculations indicate that atmospheric emissions contribute approximately 83% (about 201 W m⁻²) to the total OLR of 243 W m⁻², while direct transmission from the surface accounts for roughly 17% (41 W m⁻²), primarily in the mid-infrared (MIR) window regions where transmittance is higher. This decomposition follows from solving the , where the surface term is the upward surface emission weighted by the atmospheric transmittance to space, and the atmospheric term integrates layer-wise emissions weighted by transmittance from each altitude. Atmospheric contributions arise mainly from thermal emissions by greenhouse gases such as water vapor, carbon dioxide (CO₂), and ozone (O₃), as well as blackbody-like emissions from clouds and aerosols. Water vapor, the most abundant greenhouse gas, emits strongly in the far-infrared (FIR) spectrum (>15 μm), contributing about 45% of global mean OLR (110 W m⁻²), with peak emission from the upper around 500 hPa where allows escape to . CO₂ emissions occur in narrow bands around 15 μm and contribute significantly in the mid-, while O₃ emits in the 9-10 μm region from the . These gaseous emissions are temperature-dependent, following the Planck function modulated by local and the to , resulting in effective radiating levels cooler than the surface and thus lower flux than potential surface emission. Clouds enhance atmospheric contributions by acting as near-blackbody emitters in the infrared, with low-level clouds (e.g., stratus) emitting at cooler temperatures (~270 K) and reducing OLR relative to clear-sky conditions, while high cirrus clouds (~220 K) emit less but can trap surface radiation. All-sky estimates of direct surface transmission drop to about 20 W m⁻² globally, implying net atmospheric (gaseous plus cloud) contributions exceeding 220 W m⁻² for a typical OLR of 240 W m⁻², as clouds absorb nearly all underlying surface and lower-atmosphere radiation before re-emitting upward. Layer-wise analysis shows minimal contributions near the tropopause (~100 hPa) due to low temperatures and specific spectroscopic gaps, with emissions peaking in the lower and mid-troposphere for MIR and FIR, respectively. Regional variations amplify this dominance; in polar areas, FIR fractions rise to 60% owing to drier atmospheres and colder surface emissions favoring longer wavelengths.

Atmospheric Propagation and Absorption

Gaseous Absorption Spectra

The of outgoing longwave radiation (OLR) by atmospheric gases occurs primarily in the thermal infrared from approximately 5 to 50 micrometers (2000 to 200 cm⁻¹), where Earth's surface and atmosphere emit as approximate blackbodies at temperatures of 250–300 . This is governed by molecular vibrational-rotational transitions, resulting in discrete spectral lines that broaden under atmospheric conditions into bands. Comprehensive line-by-line parameters for these spectra are compiled in the HITRAN database, enabling precise calculations. Water vapor (H₂O), the most abundant , exhibits strong across much of the thermal infrared due to its asymmetric (ν₃ at ~2.7 μm, weaker for OLR), (ν₂ at 6.3 μm or 1595 cm⁻¹), and symmetric (ν₁ at ~2.7 μm) modes, coupled with rotational levels. Significant opacity arises in the 5–8 μm region and the pure rotational band beyond 20 μm (below 500 cm⁻¹), including a that extends effective opacity into adjacent "windows." These features account for roughly 50% of the total clear-sky , with strength varying nonlinearly with humidity profiles. Carbon dioxide (CO₂) primarily absorbs in the 15 μm fundamental bending mode (ν₂ at 667 cm⁻¹, spanning 550–750 cm⁻¹ with P- and R-branch structure), rendering the atmosphere nearly opaque at surface levels in this band and contributing about 20% to the . Weaker bands exist at 4.3 μm (asymmetric stretch, ν₃) and 2.7 μm, but the 15 μm region dominates OLR attenuation, with saturation in the band core shifting sensitivity to band wings and upper atmospheric layers as concentrations increase. Ozone (O₃), concentrated in the , absorbs strongly in the 9.6 μm asymmetric stretching band (ν₃ at 1042 cm⁻¹, 8–10 μm range), influencing OLR primarily from higher altitudes and contributing to stratospheric cooling via emission. Minor trace gases like methane (CH₄, 7.7 μm ν₄ band) and nitrous oxide (N₂O, 7.8 and 16.9 μm) add finer absorption in specific sub-bands, but their effects are smaller due to lower concentrations. Overlaps between these spectra, such as H₂O and CO₂ in the 12–18 μm region, enhance overall opacity and complicate .
GasKey Absorption Bands (μm)Wavenumber (cm⁻¹)Notes
H₂O5–8, >201250–2000, <500Includes continuum; dominant absorber.
CO₂15~667Near-total opacity at line centers.
O₃9.6~1042Stratospheric influence on OLR.
CH₄7.7~1300Minor, trace gas contribution.
These spectra define atmospheric "windows" like 8–12 μm, where transmission is higher but still modulated by weak H₂O and O₃ lines, allowing partial escape of surface emission directly to space. Empirical spectra from satellite instruments confirm these features, with absorption strengths validated against laboratory measurements.

Cloud Effects on Transmission

Clouds substantially attenuate the transmission of surface-emitted longwave radiation to space due to their strong absorption in the infrared spectrum, where liquid water droplets and ice crystals exhibit high opacity, particularly in wavelengths beyond 5 μm. Optically thick clouds can absorb up to 90% of incident longwave radiation, effectively blocking direct propagation from the warmer surface through atmospheric windows such as the 8–12 μm band. This absorption is governed by the volume absorption coefficient of cloud particles, with mass absorption coefficients for stratocumulus clouds averaging around 765 g⁻¹ cm² in the infrared. Rather than transmitting radiation, clouds re-emit absorbed energy both upward and downward according to their emissivity (near unity for most cloud types in the longwave) and blackbody temperature, which is typically 20–50 K cooler than the underlying surface. This re-emission reduces the net (OLR), as the upward flux originates from a colder source; for an opaque cloud, a 1 K decrease in cloud temperature can diminish the longwave cloud radiative effect by approximately 2 W m⁻². Direct surface-to-space transmission, estimated at higher values in clear skies, drops to about 22 W m⁻² when clouds are included, reflecting the dominant role of cloud opacity in limiting transmittance. The effect varies by cloud type and altitude: low, thick clouds (e.g., stratus) impose greater reductions in OLR due to their proximity to the surface and high optical depth, blocking warm surface emission while radiating from relatively low temperatures, whereas high, thin cirrus clouds allow partial transmission but still trap some radiation, with their colder tops yielding smaller net OLR compared to low clouds. Additionally, longwave scattering within clouds—more pronounced in ice clouds—further decreases OLR by redirecting photons inward, contributing a global annual mean reduction of 2.7 W m⁻². These processes enhance the atmospheric greenhouse effect, with clouds collectively reducing global OLR relative to clear-sky conditions, though the precise magnitude depends on cloud microphysics and vertical distribution.

Radiative Windows and Spectral Details

The primary radiative window for outgoing longwave radiation (OLR) in Earth's atmosphere is the mid-infrared band spanning approximately 8 to 13 micrometers (wavenumbers 770–1250 cm⁻¹), where absorption by major greenhouse gases such as water vapor and carbon dioxide is comparatively low, permitting direct transmission of surface-emitted thermal radiation to the top of the atmosphere (TOA). This window accounts for a global average of about 40 W m⁻² of OLR directly from the surface, representing a significant fraction of the total clear-sky OLR escaping without substantial reabsorption. Within this band, however, ozone exhibits a notable absorption feature centered at 9.6 micrometers (1040 cm⁻¹), partially attenuating transmission, particularly in the stratosphere where ozone concentrations peak. Spectral details of OLR reveal a blackbody-like modulated by discrete bands from atmospheric constituents, with the surface peaking near 10 micrometers under typical Earth surface of around 288 K. Strong occurs in the carbon dioxide band at 15 micrometers (667 cm⁻¹), where nearly complete opacity limits OLR to emissions from upper atmospheric layers, and in bands around 6.3 micrometers (1590 cm⁻¹) and a rotational beyond 18 micrometers, enhancing the greenhouse effect by trapping radiation. In the far-infrared region (>20 micrometers or <500 cm⁻¹), dominates, yet this spectral range contributes approximately 45% to global-mean OLR, primarily from low-level atmospheric emissions rather than surface transmission. Outside these windows, OLR spectra show reduced intensity relative to a pure blackbody due to the altitude of effective rising to colder air masses, as quantified in radiative kernel analyses that decompose sensitivity to , , and trace gases across bands like the CO₂ (620–750 cm⁻¹) and (1080–1180 cm⁻¹) regions. These radiative windows and absorption features determine the vertical structure of OLR emission: in transparent bands, OLR closely mirrors surface temperatures, whereas in opaque bands, it reflects cooler effective emitting levels, with global OLR integrating to about 240 W m⁻² under present conditions, balanced against absorbed solar radiation. Spectral measurements from instruments like the Infrared Atmospheric Sounding Interferometer confirm linear trends in band-specific OLR over 2008–2017, highlighting water vapor's role in modulating window transmission via its variable concentration.

Temporal and Spatial Variations

Diurnal and Nocturnal Differences

The diurnal cycle of outgoing longwave radiation (OLR) arises primarily from the periodic solar forcing, which heats the 's surface during daylight hours, elevating surface temperatures and thereby increasing blackbody emission in the infrared spectrum according to the Stefan-Boltzmann law. observations from the Earth Radiation Budget Experiment (ERBE) reveal that global OLR typically peaks near local noon, with amplitudes varying by surface type and geography; over most domains, daytime OLR exceeds nighttime values by 10–50 W m⁻², reflecting the direct response to surface warming before significant cloud feedback intervenes. At night, without insolation, the surface cools rapidly, reducing emission, and OLR stabilizes at lower levels, often flat or minimally varying until dawn. Over , the diurnal is pronounced, reaching up to 70 W m⁻² in arid regions like deserts due to land's low thermal , which permits swift heating and nocturnal cooling; empirical orthogonal function (EOF) analysis of ERBE data shows the dominant mode (73–85% variance) as a half-sine wave peaking ~50 W m⁻² around noon and flattening to ~–10 W m⁻² at night. In contrast, oceans exhibit damped cycles with amplitudes of ~25 W m⁻² or less (EOF variance 16–20%), featuring a primary peak and subtle secondary maximum (~1 W m⁻²), attributable to water's high that buffers temperature swings and sustains steadier emission. This land-ocean contrast underscores how surface properties dictate the phase and magnitude of OLR's daily oscillation. Clouds modulate these patterns by absorbing surface-emitted radiation and re-emitting downward, often attenuating the daytime OLR peak; for instance, afternoon convective cloud development over land and can impose a secondary minimum in late afternoon, lagging surface heating by 3–5 hours as moistening builds in the upper . Nocturnal clear-sky conditions enhance OLR escape relative to cloudy nights but remain subordinate to the cooler surface temperatures, yielding net lower values than daytime maxima in clear conditions. Regional EOF decompositions confirm geography and circulation regimes amplify these effects, with subtropical deserts showing maximal amplitudes (~75 W m⁻²) from unhindered surface-driven emission.

Seasonal, Latitudinal, and ENSO-Related Patterns

Outgoing longwave radiation (OLR) displays pronounced gradients, with zonal-mean values peaking in subtropical regions around 20°–30° (approximately 260–280 W/m²) where clear skies and warm surfaces facilitate efficient emission, before declining toward the equator due to convective cloud suppression (zonal means near 210–220 W/m² over the ) and sharply toward the poles (100–150 W/m²) from colder emission and persistent low-level clouds or ice cover. This poleward decrease reflects the thermodynamic control of blackbody emission scaling with the of , compounded by -dependent atmospheric opacity from and clouds. Seasonal patterns in OLR arise primarily from the annual of forcing, surface cycles, and associated shifts in and distributions, yielding hemispheric asymmetries amplified by land-ocean contrasts. In the , boreal summer OLR rises by 10–20 W/m² over mid-latitude continents relative to winter, driven by elevated skin temperatures and convective drying aloft, while values follow an inverted cycle with minimal land modulation. satellite composites from 2000 onward confirm these shifts in top-of-atmosphere OLR, with global-mean amplitudes of ~2–4 W/m² tied to cross-equatorial energy transport, though tropical regions exhibit "OLR loops" where lags seasonally, partially offsetting enhancements. ENSO introduces interannual modulations to these patterns, with El Niño phases featuring negative tropical OLR anomalies (typically 2–5 W/m² in zonal means, regionally up to -20 W/m² over the central Pacific) from equatorward-shifted , high anvil clouds, and reduced that trap infrared radiation. La Niña events reverse this, yielding positive anomalies through strengthened , drier mid-tropospheric conditions, and enhanced outgoing flux in the eastern Pacific. These signals, evident in NOAA interpolated OLR datasets since 1974, serve as diagnostic proxies for ENSO strength, with daytime OLR declining more rapidly than nighttime during warm phases due to amplified feedbacks.

Observational Methods

Satellite-Based Measurements

Satellite-based measurements of outgoing longwave radiation (OLR) originated with the Infrared Interferometer Spectrometer () on NASA's Nimbus-4 satellite, which captured the first spectral radiance data from Earth's atmosphere between 400 and 1600 cm⁻¹ (wavenumbers) during its operational period starting in April 1970. These observations provided early insights into the vertical distribution of infrared emissions but were constrained by the instrument's limited scanning capability and short mission duration of about one year. Broadband OLR datasets emerged in the through non-scanning radiometers on Nimbus-6 (launched 1975) and Nimbus-7 (launched 1978), yielding monthly global averages over a decade with resolutions of 2.5° latitude-longitude grids and uncertainties around 10-15 W/m². These measurements relied on wide-field-of-view detectors calibrated against onboard blackbodies to estimate total flux emitted to space, enabling initial assessments of interannual variability. The Earth Radiation Budget Experiment (ERBE), operational from 1984 to 1990 across three satellites (ERBS, NOAA-9, NOAA-10), advanced precision using both scanning narrow-field-of-view and non-scanning wide-field-of-view radiometers to measure radiance in the 0.5-50 µm range, achieving OLR accuracy of about 1% through in-flight and angular distribution modeling. ERBE data products included time-averaged fluxes at 2.5° , facilitating detection of regional imbalances in . Contemporary measurements are dominated by the Clouds and the Earth's Radiant Energy System (), with instruments launched since 1997 on platforms including (1999), Aqua (2002), and (2011), featuring three broadband channels: shortwave (0.3-5 µm), total (0.3-200 µm), and window (8-12 µm) for deriving full-spectrum OLR via differencing and scene-dependent corrections. Edition 4.2 Energy Balanced and Filled () products provide monthly top-of-atmosphere OLR at 1° , with absolute accuracy better than 0.5% after validation against ERBE and ground references, supporting long-term trend analysis from 2000 onward. Supplementary datasets from the High-resolution Infrared Radiation Sounder (HIRS) on NOAA polar-orbiters, spanning 1979 to present, estimate OLR using regression coefficients applied to multispectral infrared channels, forming a continuous data record with daily 2.5° gridded products and root-mean-square errors of 5-7 W/m² relative to . These systems collectively offer near-global, continuous monitoring essential for quantifying radiative feedbacks, though challenges persist in contamination and diurnal sampling biases addressed via geostationary synergies.

Ground-Based and In-Situ Observations

Ground-based observations of outgoing longwave radiation (OLR) primarily involve indirect estimation through measurements of surface and near-surface radiative es combined with atmospheric profile data input into models, as direct top-of-atmosphere (TOA) flux measurements from the ground are obstructed by the intervening atmosphere. Broadband pyrgeometers, such as those deployed in the U.S. Department of Energy's Atmospheric Radiation Measurement () program, quantify longwave radiation from the surface (typically 300–400 W/m² under clear skies) and longwave radiation (around 300 W/m² globally averaged), alongside surface via thermometry. These data, augmented by profiles of temperature and launched twice daily at ARM sites, enable computation of clear-sky OLR using models like the Rapid Radiative Transfer Model (RRTM), yielding estimates within 5–10 W/m² of observations at sites like the Southern Great Plains. Spectral ground-based instruments enhance accuracy by resolving atmospheric emission features for profile retrievals that inform OLR calculations. The Atmospheric Emitted Radiance Interferometer (AERI), operational since the 1990s at multiple facilities, measures from 520–5600 cm⁻¹ with 1 cm⁻¹ resolution every 8 minutes, achieving radiometric accuracy better than 1%. Retrieved thermodynamic profiles from AERI data, validated against coincident radiosondes (root-mean-square errors of ~1 K for temperature below 2 km), feed into line-by-line or banded codes to simulate TOA OLR spectra, particularly useful for validating absorption in the 15 µm CO₂ band and continuum. Such approaches have demonstrated OLR model-satellite discrepancies of less than 2 W/m² for clear skies over extended periods at sites. In-situ observations, typically from or platforms, provide more direct approximations of OLR by elevating sensors above much of the emitting atmosphere. High-altitude , such as NASA's WB-57 or ER-2 during campaigns like the 2006 Midlatitude experiment, deploy nadir-viewing broadband radiometers (e.g., 4–50 µm channels) to measure upward longwave fluxes at 15–20 km altitudes, where residual atmospheric emission is minimal (<5% of total OLR), yielding values comparable to TOA satellite data within 3–5 W/m² after corrections for altitude and viewing geometry. -borne spectrometers, including instruments from the of , profile spectral radiances up to ~30 km, validating longwave spectroscopy databases used in global OLR models with uncertainties under 1% in key bands. These in-situ datasets, though spatially limited and campaign-specific, offer empirical anchors for satellite calibration and reveal local variability, such as enhanced OLR under subsiding anticyclonic conditions.

Key Datasets and Long-Term Trends

The primary datasets for outgoing longwave radiation (OLR) at the top of the atmosphere derive from observations, providing coverage with varying spatial and temporal resolutions. The NOAA Outgoing Longwave Radiation Climate Data Record (CDR), based on High-resolution Radiation Sounder (HIRS) measurements from polar-orbiting satellites, offers daily and monthly means on a 1° × 1° from 1979 to the present, with to fill observational gaps and achieve . This dataset emphasizes and long-term variability, though absolute fluxes carry higher uncertainty (±4–5 W/m²) compared to systems. Complementing this, NASA's Clouds and the Earth's Radiant Energy System () provides broadband OLR measurements since March 2000, using instruments on , Aqua, and other platforms, with Energy Balanced and Filled (EBAF) products adjusted for angular distribution models and calibrated to achieve stability of 0.1 W/m² per decade and absolute accuracy near 1 W/m². data integrate scanner, imager, and spectral radiometer observations for all-sky and clear-sky OLR, enabling precise top-of-atmosphere flux estimates. For pre-2000 continuity, the Earth Radiation Budget Experiment (ERBE, 1984–1999) serves as a , with HIRS and OLR showing consistency within 1–2 W/m² after bias corrections. Long-term global-mean OLR trends from these datasets reveal small positive changes, consistent with radiative responses to tropospheric warming amid varying and feedbacks. EBAF records indicate an OLR increase of approximately 0.13 to 0.26 W/m² per decade over the 2000–2020 period, with uncertainties reflecting sampling and property adjustments. This trend aligns with ERBE- continuity analyses, showing no significant discontinuity and attributing variations to internal modes like ENSO rather than instrumental drift. Over the longer NOAA HIRS record (1979–2020), the global trend is subdued at around 0.1 W/m² per decade, primarily capturing interdecadal fluctuations tied to and patterns, though with larger due to narrowerband retrievals. These trends imply that OLR has not decreased as might be expected from forcing alone, highlighting offsetting influences from reduced low- cover and upper-tropospheric moistening.

Theoretical and Numerical Modeling

Radiative Transfer Fundamentals

Outgoing longwave radiation originates primarily from thermal emission by the Earth's surface and atmosphere in the spectrum. The surface, with temperatures typically around 288 globally averaged, emits radiation approximating blackbody behavior, quantified by the Stefan-Boltzmann law: the total hemispheric emissive power M = \epsilon \sigma T^4, where \sigma = 5.670 \times 10^{-8} W m^{-2} ^{-4} is the Stefan-Boltzmann constant, T is the absolute temperature, and \epsilon is the surface , often 0.95–0.99 for land and under typical conditions. This emission is spectrally distributed according to , B_\nu(T) = \frac{2 h \nu^3}{c^2} \frac{1}{e^{h\nu / kT} - 1}, peaking near 10 \mum for terrestrial temperatures, with significant overlap in bands of atmospheric gases like H_2O, CO_2, and O_3. The propagation of this radiation through the atmosphere is described by the radiative transfer equation (RTE) in a plane-parallel, non-scattering medium: \mu \frac{dI_\nu}{d\tau_\nu} = I_\nu - S_\nu, where I_\nu(\tau_\nu, \mu) is the monochromatic intensity at \tau_\nu = \int \kappa_\nu \rho \, dz (with \kappa_\nu the coefficient and \rho density), \mu = \cos \theta the cosine of the angle, and S_\nu the source function. Under local thermodynamic equilibrium (LTE), valid throughout the troposphere and lower stratosphere for longwave radiation, S_\nu = B_\nu(T), reducing the RTE to Schwarzschild's equation in differential form: \frac{dI_\nu}{ds} = -\kappa_\nu (I_\nu - B_\nu(T)), where s is path length. Integrating upward from the surface at optical depth \tau_s to the top of atmosphere (\tau = 0) yields I_\nu(0, +\mu) = I_{\nu,s} e^{-\tau_s / \mu} + \int_0^{\tau_s} B_\nu(t) e^{-t / \mu} \frac{dt}{\mu}, capturing attenuation of surface emission by atmospheric opacity and addition of thermal emission from intervening layers. Optical depths \tau_\nu in strong absorption bands exceed unity, rendering the atmosphere opaque and reducing OLR relative to surface emission, while atmospheric windows (e.g., 8–12 \mum) allow partial direct escape. The total OLR is obtained by integrating the upward flux F^\uparrow = \int_0^\infty \int_0^1 2\pi \mu I_\nu(0, \mu) d\mu d\nu over and , typically averaging ~240 W m^{-2} globally to balance absorbed solar radiation in . In clear-sky conditions, dominates opacity variability, with CO_2 providing baseline absorption; clouds introduce additional broadband opacity when present. These fundamentals underpin numerical solutions in or band models, essential for accurate OLR computation.

Simulations in Global Climate Models

Global climate models simulate outgoing longwave radiation (OLR) by integrating parameterizations into their atmospheric dynamics and physics components, solving the time-independent radiative transfer equation for thermal infrared wavelengths from approximately 4 to 1000 μm. These schemes compute upward and downward fluxes at multiple atmospheric levels, incorporating gaseous and primarily from , , , , and , using spectroscopic databases like HITRAN. Cloud and effects are treated via optical property parameterizations, with or correlated-k approximations to manage computational demands while resolving key spectral features. The Model for Models (RRTMG), a widely adopted longwave scheme, employs the correlated-k distribution method to group absorption coefficients across spectral bands, enabling efficient Independent Column Approximation (McICA) sampling of subgrid variability. In models such as NCAR's Community Atmosphere Model version 5 (CAM5) and Community Earth System Model version 1 (CESM1), RRTMG replaced earlier schemes, reducing biases in simulated OLR through better handling of overlapping absorption lines and two-stream multiple approximations. Clear-sky OLR simulations in these models exhibit residual biases of several W/m², often linked to inaccuracies in vertical profiles of and rather than radiative transfer deficiencies. Incorporation of longwave scattering by clouds and water vapor droplets remains a refinement focus, as neglecting it in broadband schemes overestimates global-mean OLR by 1.5–8 /, depending on the approximation used, due to unaccounted downward scattering of upward . Updated parameterizations, such as those adding radiance adjustments for in the Atmosphere Model, improve flux convergence and heating rates without excessive computational cost, aligning simulated OLR more closely with line-by-line benchmarks. GCMs like those in CMIP5 and CMIP6 output variables such as rlut (TOA OLR) for intermodel comparison, revealing robust simulation of OLR's quasi-linear response to surface perturbations, with global-mean longwave clear-sky feedbacks around 1.9 // emerging from balanced increases in blackbody emission and greenhouse trapping by moistened air.

Links to Climate Forcing and Feedbacks

Greenhouse Effect Through OLR Modulation

The modulates outgoing longwave radiation (OLR) by reducing the flux escaping to space through absorption and re-emission processes in the atmosphere. Greenhouse gases (GHGs) such as CO₂, H₂O, and CH₄ absorb radiation emitted upward from the surface in characteristic wavelength bands, thermalizing the energy and elevating the effective emission altitude to colder atmospheric layers. From these altitudes, the re-emitted longwave radiation follows the Stefan-Boltzmann law with lower temperatures, yielding less OLR than the surface emission σT_s^4, where σ is the Stefan-Boltzmann constant and T_s the surface temperature. This spectral-selective absorption prevents direct radiative escape, trapping heat and requiring surface warming to balance incoming absorption. Quantitatively, the natural raises Earth's surface from the of approximately 255 —derived from global mean OLR of about 240 W/—to an observed mean of 288 , a difference of 33 . Without atmospheric absorption, OLR would equal surface emission directly, but GHGs impose an that shifts the emitting level upward, reducing OLR for fixed T_s and driving the lapse to achieve . Increased GHG concentrations amplify this modulation, further suppressing OLR and contributing to positive on the order of 2-3 W/ for post-industrial CO₂ doubling in simple models. Observationally, this effect is evident in spectral measurements showing OLR deficits in GHG windows, such as the 15 μm CO₂ , where data from 2003-2021 confirm decreases tied to rising concentrations. calculations corroborate that GHG forcing predominantly acts to diminish OLR, with feedbacks like enhancing the response, though empirical spectra isolate the direct GHG signal from broader adjustments. This OLR modulation forms the causal basis for GHG-induced warming, distinct from shortwave alterations.

Expected Responses to Rising Greenhouse Gases

Increasing concentrations of well-mixed greenhouse gases, such as (CO₂) and (CH₄), are expected to reduce outgoing longwave radiation (OLR) at the top of the atmosphere by enhancing of upwelling radiation from the Earth's surface and lower atmosphere. This occurs primarily in specific bands: CO₂ around 15 μm and its isotopes, and CH₄ near 7.7 μm, where molecular lines trap outgoing photons, re-emitting them downward or horizontally rather than allowing escape to space. The instantaneous from a doubling of pre-industrial CO₂ (from 280 ppm to 560 ppm) is calculated at approximately 3.7 W/m², manifesting as a reduction in OLR for fixed temperatures, creating an energy imbalance that drives planetary warming. To restore , where absorbed shortwave radiation equals OLR, surface and tropospheric temperatures must rise, increasing blackbody emission proportional to T⁴ per the Stefan-Boltzmann law (σ ≈ 5.67 × 10⁻⁸ W/m²K⁻⁴). However, es diminish the sensitivity of OLR to temperature changes by elevating the effective emission altitude to colder upper-tropospheric layers in absorbing bands, necessitating greater warming—typically 1.0–1.2°C per W/m² of forcing without feedbacks—to compensate. In spectral terms, this results in reduced OLR flux within absorption windows but increased flux in atmospheric windows (e.g., 8–12 μm) due to higher temperatures, with the net global OLR rising only after sustained warming offsets the initial forcing. Climate models incorporating equations predict that feedback amplifies this response, as warming increases atmospheric humidity, further suppressing OLR in overlapping H₂O bands and requiring additional temperature rise. For observed CO₂ increases since (from ~280 to over by ), models simulate an initial OLR reduction of ~0.5–1 W/m² globally, followed by partial recovery through ~0.2–0.5 W/m²K⁻¹ OLR increase from tropospheric warming, though feedbacks introduce by potentially enhancing or reducing net OLR. These expectations derive from line-by-line calculations validated against laboratory , emphasizing causal mechanisms over empirical correlations.

Empirical Observations of OLR Changes

Satellite measurements from the Earth Radiation Budget Experiment (ERBE, 1985–1999) and Clouds and the Earth's Radiant Energy System (, 2000–present) form the primary empirical record of global (OLR) variations. These datasets reveal a modest positive trend in global mean total-sky OLR over recent decades, consistent with surface increases but tempered by atmospheric feedbacks. For the period 1985–2018, combining High-resolution Radiation Sounder (HIRS), ERBE, and CERES observations, global OLR rose in correlation with warming, yielding a of 2.93 ± 0.3 W/m² per K. This falls below the blackbody expectation of approximately 3.3–4 W/m² per K for Earth's , suggesting partial compensation by and cloud effects that enhance and re-emission. CERES data specifically indicate a global total-sky OLR increase of 0.26 ± 0.19 W/m² per decade from March 2000 to December 2022. Sub-period analyses highlight variability: near-zero trends during the 2000–2010 warming , accelerations exceeding 1 W/m² per decade in the 2010–2016 transition to strong El Niño, and subdued changes post-2016. Hemispheric asymmetries appear, with OLR exhibiting slightly stronger increases linked to clear-sky thermal emission and high- alterations, while trends are marginally lower. These patterns align with ENSO-driven variability, where La Niña phases post-2000 have contributed to tropical OLR reductions via enhanced cloudiness. Regionally, OLR has increased more markedly in the , including Arctic amplification effects from reduced low- cover (a "longwave cloud thinning" mechanism) between 2001–2017 compared to 1985–2000. Clear-sky OLR components show distinct latitudinal differences over 1979–2021, with mid-to-high latitudes experiencing greater upward trends attributable to tropospheric warming outpacing feedback in drier conditions. Spectral observations further delineate forcing influences: within CO2, CH4, and N2O absorption bands, OLR has declined due to rising concentrations trapping more infrared radiation, as quantified in attribution studies using spectra. Broadband window regions, however, exhibit OLR gains from surface and tropospheric warming, yielding a net positive total OLR trend despite forcing. Interannual fluctuations, such as those tied to El Niño, amplify these spectral shifts through convective adjustments. Overall, the empirical record underscores OLR's sensitivity to both and dynamic feedbacks, with total changes remaining small relative to absorbed shortwave radiation gains, contributing to an observed doubling of Earth's imbalance since 2000.

Controversies and Empirical Discrepancies

Surface Budget Fallacy and Misinterpretations

The surface budget fallacy refers to the misconception that the surface temperature is primarily determined by local balancing of radiative and non-radiative fluxes at the Earth's surface, rather than by the top-of-atmosphere (TOA) energy imbalance between absorbed solar (ASR) and outgoing (OLR). This error arises when analyses overemphasize surface —such as upward from the surface (approximately 396 W/m² under current conditions), from the atmosphere (around 333 W/m²), and turbulent fluxes like latent and —while neglecting that the TOA budget sets the effective radiating temperature of the planet, which the surface must achieve through vertical heat transport and structure. In reality, perturbations like increased greenhouse gases initially reduce OLR at fixed temperatures, creating a TOA imbalance that drives warming until OLR restores , with surface fluxes adjusting secondarily via and . This fallacy often manifests in misinterpretations of OLR's role in the , where critics argue that enhanced back-radiation to merely increases local without necessitating rise, as appears self-balancing (e.g., higher offset by higher ). However, such views overlook that OLR originates not solely from but from atmospheric layers where to space is near unity, typically at effective emission heights of 5-6 km with temperatures around 255 , far cooler than 's 288 . For OLR to match ASR (about 240 W/m² on average), these emission levels must warm in response to forcings, requiring surface temperatures to rise proportionally due to the tropospheric (approximately 6.5 /km moist adiabat), thus linking surface and TOA causally. Empirical calculations confirm that doubling CO₂ reduces OLR by 3.7 W/m² at fixed temperatures, with surface warming of 1-4°C needed to restore , depending on feedbacks, independent of surface flux details. In climate debates, the has fueled erroneous claims denying greenhouse forcing, such as assertions that observed increases (e.g., 1-2 W/ per decade at some sites) do not imply trapped because surface rises commensurately, ignoring TOA measurements showing OLR or slight declines amid rising temperatures post-2000s. datasets like indicate Earth's imbalance (EEI = ASR - OLR) at 0.5-1 W/ since 2005, consistent with uptake rather than surface-only balances. Proponents of the , often from non-specialist critiques, fail to account for how atmospheric redistributes vertically, making OLR sensitive to upper-tropospheric temperatures rather than surface es alone. Correct analysis prioritizes TOA closure, as validated by line-by-line radiative codes showing OLR's logarithmic dependence on CO₂ concentration, with surface budgets serving mainly to constrain vertical profiles. This distinction underscores why discrepancies in surface observations (e.g., from flux towers) do not invalidate TOA-derived forcings, as local heterogeneities average out globally via atmospheric dynamics.

Model-Predicted vs. Observed OLR Trends

Climate models, such as those in the CMIP6 ensemble, predict that the net trend in global outgoing longwave radiation (OLR) under forcing should be positive over recent s, as the Planck response from surface warming and increases OLR, outweighing the direct reduction from rising concentrations. For the period 2001–2020, these models estimate an OLR response component of approximately 0.39 W m⁻² ⁻¹ driven by increases, partially offsetting a forcing-induced decline of about -0.26 W m⁻² ⁻¹, yielding a net positive trend consistent with observed ranges. Satellite observations from NASA's instrument, spanning 2001–2020, record a global OLR trend of 0.28 ± 0.22 W m⁻² ⁻¹, reflecting a small positive increase attributable to radiative response dominating over forcing effects. This aligns with model expectations from the GFDL AM4 atmosphere-only simulation (0.13 ± 0.02 W m⁻² ⁻¹) and CMIP6 historical runs, which fall within the 95% of CERES data, supporting the attribution of the trend to influences rather than internal variability alone (probability <1%). However, finer-scale analyses reveal potential discrepancies, with some CERES-derived OLR trends (e.g., 0.26 ± 0.15 W m⁻² decade⁻¹) exceeding certain model or reanalysis estimates (0.13 ± 0.13 W m⁻² decade⁻¹), possibly due to sampling differences, unmodeled adjustments, or stronger negative feedbacks in observations. Low models struggle to replicate the observed Earth energy imbalance trends, including OLR components, as they imply insufficient response to match CERES-inferred accumulation. These mismatches highlight ongoing uncertainties in and feedbacks, where models may overestimate positive contributions, though mainstream assessments maintain overall consistency within error bounds.

Debates on Feedbacks and Recent Variability

![Earth's heating rate since 2005 from CERES observations][float-right] Debates on the role of feedbacks in modulating (OLR) center on responses, which can either amplify or dampen the radiative effects of surface warming. observations, particularly from NASA's instrument, provide empirical constraints on these s by measuring changes in OLR associated with variations. Studies using CERES data have inferred a net positive , with (LW) components showing clouds trapping more heat as temperatures rise, contributing to estimates of (ECS) exceeding 2°C per CO₂ doubling. However, analyses of tropical intraseasonal variability reveal potential negative feedbacks, where decreases lead OLR increases that precede surface rises, suggesting clouds may drive rather than respond to warming, implying lower ECS. A key contention involves in cloud-temperature relationships. Mainstream interpretations, such as those reconciling CERES OLR anomalies with surface data, attribute OLR-temperature correlations to feedback processes where warming reduces high-cloud cover, increasing OLR less than expected from the Planck response alone. Critics, including satellite-based analyses, argue that conventional methods bias feedbacks positively by ignoring cloud-induced forcings, with phase-lagged responses in OLR indicating stabilizing negative cloud feedbacks on timescales relevant to . This persists, as energy budget approaches incorporating CERES-derived OLR trends yield ECS estimates around 1.5–2.5°C, lower than many model-derived values assuming stronger positive feedbacks. Recent OLR variability from (2000–2020) shows a modest increase of approximately 0.2 W m⁻² per decade, consistent with surface warming but within the range of internal variability for most months, except notable anomalies in . This trend contributes to an accelerating Earth energy imbalance (EEI), where absorbed shortwave radiation rises faster than OLR, but debates arise over attribution: aerosol reductions may enhance shortwave absorption, while OLR responses reflect competing (positive) and /cloud (potentially negative) effects. Models often overestimate tropical LW cloud feedbacks compared to observations, particularly during ENSO events, highlighting systematic biases that inflate projected . Interannual fluctuations, such as OLR increases during El Niño due to suppressed , further complicate inference, with some analyses suggesting these patterns support lower than consensus model ensembles. Empirical discrepancies underscore the need for refined causal diagnostics beyond linear regressions to resolve whether observed OLR patterns indicate stabilizing mechanisms overlooked in forcings-dominated frameworks.