Tropospheric Warming and Stratospheric Cooling as a Modelled Fingerprint of Anthropogenic Climate Change
The simultaneous warming of the troposphere and cooling of the stratosphere is an important fingerprint of anthropogenic climate forcing. Different causes of climate change produce different vertical, geographical and temporal patterns of atmospheric temperature change.
Manabe and Wetherald predicted this response in 1967 using a one-dimensional radiative–convective model. Increasing CO₂ warmed the surface and troposphere while cooling the stratosphere. Modern climate science now examines this response using line-by-line radiative-transfer models, radiative–convective models, general circulation models, chemistry–climate models and statistical detection-and-attribution methods.
Radiative-transfer modelling
Thermal infrared radiation is described by the radiative-transfer equation:
μ ∂Iν/∂τν = Iν − Bν(T)
where:
- Iν is spectral radiance;
- τν is optical depth;
- Bν(T) is the Planck function;
- μ describes the direction of radiation.
Optical depth depends on absorber concentration, pressure, temperature and spectral absorption coefficients:
dτν = Σᵢ kν,ᵢ qᵢρ dz
CO₂ absorbs and emits strongly in the infrared band centred near 15 μm. Increasing CO₂ raises atmospheric optical depth, including in the less-saturated wings of this band.
The radiative temperature tendency of an atmospheric layer is determined by the divergence of the net radiative flux:
∂T/∂t |rad = g/cₚ · ∂Fnet/∂p
A layer warms when it absorbs more radiation than it emits and cools when its net radiative energy loss increases.
This is more accurate than describing CO₂ as simply absorbing a photon and reradiating it randomly. Climate models calculate the complete upward and downward spectral fluxes through every atmospheric layer.
Tropospheric warming
Increasing CO₂ initially reduces outgoing longwave radiation at the top of the atmosphere. At wavelengths affected by CO₂, radiation escaping to space originates from a higher effective emission level.
Because temperature normally decreases with altitude in the troposphere, this higher level is colder and emits less infrared radiation. The planetary energy imbalance can be written as
N = ASR − OLR
where:
- ASR is absorbed solar radiation;
- OLR is outgoing longwave radiation;
- N is the net energy gain.
After CO₂ increases,
OLR initially falls while absorbed solar radiation changes little, so
N becomes positive. The surface and troposphere then warm until increased infrared emission restores approximate balance.
A simplified global response is
N = F − λΔT
where
F is the imposed forcing,
λ is the climate-feedback parameter and
ΔT is the temperature response.
The greenhouse effect is therefore not permanent heat storage. It is a change in atmospheric opacity that requires the surface–troposphere system to warm before outgoing radiation again balances absorbed sunlight.
Stratospheric cooling
The stratosphere behaves differently because it is much more strongly controlled by radiation and much less by convection.
Its temperature equation may be represented schematically as
∂T/∂t = QSW/cₚ + QLW/cₚ + Qdyn/cₚ
where:
- QSW is solar heating, principally from ozone absorption of ultraviolet radiation;
- QLW is longwave infrared heating or cooling;
- Qdyn includes circulation, wave and adiabatic effects.
The infrared contribution can be written conceptually as
QIR = Qabs − Qemit
Increasing CO₂ increases both infrared absorption and emission. The important quantity is their difference.
Much of the infrared radiation entering the stratosphere from below originates from the relatively cold upper troposphere and tropopause. Additional stratospheric CO₂ does not therefore receive an unlimited increase in infrared energy from below.
At the same time, CO₂ in the stratosphere can emit radiation upward into space. Because relatively little absorbing atmosphere lies above it, a significant fraction of this radiation escapes.
Over much of the stratosphere, increasing CO₂ enhances infrared emission more than absorption:
ΔQIR < 0
The stratosphere consequently cools until its reduced temperature lowers infrared emission enough to restore radiative equilibrium.
Thus, the same increase in CO₂ produces different responses:
Troposphere: increased opacity reduces outgoing infrared radiation and causes warming.
Stratosphere: increased emissivity strengthens net infrared energy loss and causes cooling.
A greenhouse gas does not necessarily warm every layer containing it. Its effect depends on the local temperature, radiation field, optical depth and probability that emitted radiation can escape to space.
The role of ozone
Not all lower-stratospheric cooling can be attributed directly to CO₂.
Ozone heats the stratosphere by absorbing solar ultraviolet radiation. If ozone decreases, shortwave heating also decreases:
ΔO₃ < 0 ⇒ ΔQSW < 0
Human-produced chlorofluorocarbons and related substances caused substantial ozone depletion during the late twentieth century. Ozone loss was the dominant cause of the strong lower-stratospheric cooling observed from 1979 to approximately the mid-1990s.
Increasing greenhouse gases also contributed, particularly in the middle and upper stratosphere. As ozone depletion slowed and ozone began to recover, lower-stratospheric cooling became less pronounced in some regions and periods.
The observed stratospheric record therefore contains several influences:
- CO₂-induced infrared cooling;
- ozone depletion and recovery;
- volcanic aerosols;
- stratospheric water vapour;
- changes in atmospheric circulation;
- natural variability.
Chemistry–climate models are needed to separate these effects.
General circulation and chemistry–climate models
General circulation models solve discretised forms of the conservation equations for momentum, mass, energy, water and atmospheric tracers.
A schematic atmospheric temperature equation is
DT/Dt − α/cₚ · Dp/Dt
= Qrad/cₚ + Qlatent/cₚ + Qturb/cₚ
Radiative schemes calculate solar and infrared fluxes in multiple spectral bands. Convection, clouds, turbulence and gravity-wave drag are represented through parameterisations where they cannot be explicitly resolved.
Chemistry–climate models additionally calculate or prescribe reactions involving ozone, oxygen, chlorine, bromine, methane and nitrous oxide. They represent ozone destruction, ozone recovery, polar stratospheric clouds and volcanic sulfate aerosols.
The models therefore do not assume that CO₂ alone controls lower-stratospheric temperature. They calculate the combined radiative, chemical and dynamical response.
Controlled model experiments
Attribution is established using ensembles of controlled experiments.
Pre-industrial control runs
External forcing is held approximately constant. These simulations estimate internal climate variability.
Historical all-forcing runs
Models include reconstructed changes in greenhouse gases, aerosols, ozone, solar output, volcanic aerosols and land use.
Natural-only runs
Only solar and volcanic forcings vary.
Greenhouse-gas-only runs
Well-mixed greenhouse gases vary while other major forcings are held fixed.
Ozone and aerosol experiments
These isolate the effects of ozone depletion, ozone recovery and anthropogenic aerosols.
Large ensembles
Simulations are repeated with slightly different initial conditions:
Xᵣ(t) = μforced(t) + εᵣ(t)
where
μforced is the externally forced response and
εᵣ is internal variability.
Averaging many ensemble members suppresses uncorrelated variability and reveals the modelled forced signal.
The greenhouse-gas-only experiments produce tropospheric warming and widespread stratospheric cooling. Ozone-depletion experiments produce particularly strong lower-stratospheric cooling. Natural-only experiments do not reproduce the observed long-term vertical pattern.
Comparison with satellite measurements
Satellites measure microwave or infrared radiance rather than temperature at one exact altitude. Retrieved temperature products represent broad atmospheric layers described by weighting functions:
Tsat = ∫ W(p)T(p)dlnp
A lower-stratospheric satellite channel can contain some upper-tropospheric contribution. Because the upper troposphere is warming while the stratosphere is cooling, this must be included in model–observation comparisons.
Climate scientists therefore apply the same satellite weighting functions to model output:
Tmodel,sat = H[Tmodel]
where
H represents the instrument response and sampling.
Satellite records must also be corrected for orbital drift, calibration changes, satellite replacement and changes in observation time. Results are consequently compared across several independent satellite, radiosonde and reanalysis datasets.
Detection and attribution
Observed temperature changes are statistically compared with modelled fingerprints:
y = βGHG XGHG + βO₃ XO₃ + βnat Xnat + ε
where:
- y is the observed temperature-change pattern;
- Xi is the modelled response to forcing i;
- βi is its fitted scaling factor;
- ε represents internal variability and observational error.
The pattern can include latitude, altitude, season and time.
Internal variability is estimated mainly from long control simulations. A forcing is considered detected when the confidence interval for its scaling factor excludes zero. Attribution also requires that the mechanism is physically plausible and that alternative explanations fail to reproduce the observations.
The anthropogenic vertical fingerprint includes:
- warming through most of the troposphere;
- cooling through most of the stratosphere;
- generally stronger CO₂-induced cooling with increasing stratospheric altitude;
- regional and seasonal structures associated with ozone and circulation changes.
Why solar variability is insufficient
Solar forcing is included explicitly in climate models. Changes in solar output can affect the stratosphere through ultraviolet absorption, ozone chemistry and atmospheric circulation.
However, solar-only and natural-only simulations do not reproduce the sustained observed combination of strong tropospheric warming and widespread stratospheric cooling.
The solar hypothesis is therefore rejected through quantitative model comparison, not merely by stating that all atmospheric layers must move exactly in phase.
Milankovitch cycles are also unsuitable because they redistribute solar radiation by latitude and season over tens to hundreds of thousands of years. Their changes over the satellite era are far too small and slow to explain the observed trends.
Conclusion
The evidence can be expressed as a modelling sequence:
Spectroscopy
Increasing CO₂ changes infrared optical depth.
↓
Radiative transfer
The change alters the vertical divergence of infrared flux.
↓
Radiative–convective modelling
The surface and troposphere warm to restore top-of-atmosphere energy balance.
↓
Stratospheric radiative modelling
Additional CO₂ enhances net infrared emission and cools much of the stratosphere.
↓
Chemistry–climate modelling
Ozone depletion explains much of the earlier lower-stratospheric cooling, while greenhouse gases dominate much of the middle- and upper-stratospheric response.
↓
Controlled model experiments
Greenhouse, ozone, aerosol, solar and volcanic effects are calculated separately.
↓
Detection and attribution
The observed latitude–height–time pattern is compared with modelled fingerprints and estimates of natural variability.
The strength of the evidence does not come merely from observing tropospheric warming and stratospheric cooling. It comes from the prior prediction, physical modelling and statistical detection of a multidimensional temperature pattern that is consistent with anthropogenic greenhouse-gas and ozone forcing but cannot be reproduced by natural variability or natural external forcing alone.
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