Simple climate models can be valuable if they are able to
replicate aspects of complex fully coupled earth system models. Larger
ensembles can be produced, enabling a probabilistic view of future climate
change. A simple emissions-based climate model, FAIR, is presented, which
calculates atmospheric concentrations of greenhouse gases and effective
radiative forcing (ERF) from greenhouse gases, aerosols, ozone and other
agents. Model runs are constrained to observed temperature change from 1880
to 2016 and produce a range of future projections under the Representative
Concentration Pathway (RCP) scenarios. The constrained estimates of
equilibrium climate sensitivity (ECS), transient climate response (TCR) and
transient climate response to cumulative
Most multi-model studies, such as the Coupled Model Intercomparison Project
(CMIP), which produces headline climate projections for the Intergovernmental
Panel on Climate Change (IPCC) assessment reports, compare atmosphere–ocean
general circulation models that are run with prescribed concentrations of
greenhouse gases. Greenhouse gas and aerosol emissions time series are
provided by integrated assessment modelling groups based on socio-economic
narratives
Earth system models in CMIP5 all show a positive carbon cycle feedback,
meaning that as surface temperature increases, land and ocean carbon sinks
become less effective at absorbing
Simple models can be used to emulate radiative forcing and temperature
responses to emissions and atmospheric concentrations and can be tuned to
replicate the behaviour of individual climate and earth system models
FAIR v1.0 is well-calibrated to the temperature and carbon cycle response of
earth system models. FAIR v1.3 is extended to calculate non-
The model philosophy in FAIR is to represent these processes as simply as
possible and to be able to emulate the historical effective
radiative forcing (ERF) time series in AR5
given input emissions. FAIR is written in Python and is open source. The
extension to non-
This paper introduces the FAIR model in Sect.
FAIR v1.3 takes emissions of greenhouse gases and short-lived climate forcers
as its main input. This is an array of size (number of years
The effective radiative forcing (ERF) from 13 different forcing agents
(Table
Emissions time series input used in FAIR, based on the RCP emissions
datasets in
The set of greenhouse gases used in FAIR. With the exception of
methane lifetime, radiative efficiencies and lifetimes are from AR5
The 13 separate forcing groups considered in FAIR v1.3 in the
calculation of effective radiative forcing. The ERF uncertainty represents
the 5–95 % range and is used in the generation of the large ensemble
(Sect.
Simplified overview of the FAIR v1.3 model.
The carbon cycle component in FAIR is described in detail by
The four time constants
A one-box decay model is assumed for other greenhouse gases where the sink is
an exponential decay of the existing gas concentration anomaly. New emissions
are converted to the equivalent increase in molar mixing ratios
For
Natural emissions of methane and nitrous oxide used in the FAIR
model. Future emissions are fixed at their 2011 values. Also shown are the
present-day best estimates of
Natural emissions of
The best estimate of
The oxidation of
Oxidation of CO and NMVOCs to
The ERF from 13 different forcing agent groups are considered:
We use the updated
Finally, a scaling to
For all well-mixed greenhouse gases in Table
Tropospheric ozone is formed from a complex chemical reaction chain from
emissions of
Contribution to tropospheric ozone ERF from each precursor.
Pre-industrial emissions from
The stratospheric ozone ERF is calculated using the functional relationship
borrowed from
In AR5, the ERF from the stratospheric water vapour oxidation of methane was
assumed to be 15 % of the methane ERF. This was based on the methane forcing
relationship of
This gives a coefficient of
Method 2 is similar, based on kerosene fuel supplied
For method 1, the past and future aviation
Aerosols have a lifetime of the order of days
The aerosol ERF contains contributions from aerosol-radiation interactions
(ERFari) and from aerosol–cloud interactions (ERFaci). ERFari includes the
direct radiative effect of aerosols, in addition to rapid adjustments due to
changes in the atmospheric temperature, humidity and cloud profile (formerly
the semi-direct effect;
We use the multi-model results from Aerocom
Contribution to ERFari from each aerosol precursor species and contribution to 2011 ERFari.
ERFaci describes how aerosols affect clouds in the radiation budget; the two
main mechanisms are changes in cloud droplet size, which changes cloud albedo
In FAIR we use an emulation of the global aerosol model of
Informed by the simple aerosol model of
Equation (
The best-estimate ERF of 0.04 W m
Land use forcing is a result of surface albedo change
Deforestation produces land-use-related
The simple relationship in Eq. (
Noting that this simple relationship may not be suitable in all cases, the
user is free to supply their own time series of ERF from land use change. If
gridded land use data are available, the transitions to and from forested land
each year can be convoluted with the marginal contribution to land use
forcing per square kilometre deforestation (e.g. from
The SOLARIS-HEPPA v3.2 solar irradiance dataset prepared
for CMIP6 is used to generate the solar ERF, which includes projections of
the variation in future solar cycles from 1850 to 2300
Historical volcanic forcing is punctuated by several
large eruptions that cause large but short-lived negative forcing episodes,
with several smaller eruptions that cause year-to-year changes in the
volcanic forcing. In order to generate a historical volcanic ERF time series, we first start with gridded volcanic optical depths taken from the Easy
Volcanic Aerosol generator over the 1850–2014 period
In the context of measuring forcing since the pre-industrial, we have to
assume an “average” level of volcanic background aerosol. We therefore
define the 1850–2014 period to have a mean volcanic forcing of zero. To
achieve this we subtract the mean (negative) forcing from the historical
period, resulting in a quiescent year ERF of around
In simple impulse response models, forcing is related to total temperature
change in year
Owing to the use of ERF rather than RF in FAIR v1.3 and its better
correspondence with temperature, efficacies are assumed to be unity for all
forcing agents except black carbon on snow (
There is some evidence that ECS and TCR have not been constant values over
the historical period
To test the model response to a range of forcing pathways, we perform a
100 000-member Monte Carlo simulation using emissions from the RCP datasets
As a wide range of forcing, and thus temperature, scenarios can be generated,
there are a proportion of ensemble members generated that fall outside the
range of plausibility. We constrain the full 100 000-member ensemble
(hereafter FULL) to the observed temperature change from the
The C&W observed warming from 1880 to 2016 is higher
than the UK Met Office Hadley Centre observational dataset (HadCRUT4; Morice et al. 2012) estimate
of
It should be stressed that there are several issues to consider when
attempting to derive plausible parameter sets from observational data. These
include the type of observational constraints to employ
The ECS and TCR from CMIP5 models
We allow
Some uncertainty in the carbon cycle parameters is assumed with samples of
The uncertainty in each of the 13 forcing components is modelled following
the 5–95 % confidence intervals for each forcing from AR5
The FULL and NROY joint and marginal distributions of ECS and TCR are shown
in Fig.
The temperature constraint in NROY results in distributions of ECS and TCR
that are lower than in FULL. Some of the prior sample space in which ECS and
TCR are larger than the likely AR5 ranges has been rejected in the NROY
distribution. While the possibility that ECS
The historical (1765–2005) greenhouse gas concentrations from the RCP
scenarios in
The FAIR model reproduces the historical concentrations of greenhouse gases
(Fig.
The historical
Kyoto Protocol gases have been grouped as HFC134a-eq based on their radiative
efficiency, and ODSs have been similarly grouped as CFC12-eq (Fig.
Comparison of the historical and RCP greenhouse gas concentrations
in FAIR (heavy solid lines) with 5–95 % confidence intervals (shading) for
Figure
For tropospheric ozone, the
BC on snow has a smaller ERF in FAIR than the corresponding RF in MAGICC6,
although the efficacy factor of 3 used in FAIR results in a similar effect on
temperature between the models (Fig.
Figure
Comparison of the radiative forcing from RCP2.6, RCP4.5, RCP6.0 and
RCP8.5 derived from 13 separate components
The distribution of ERF in 2017 for aerosols, greenhouse gases and the
anthropogenic total in both the FULL and the NROY ensembles assuming the
RCP8.5 forcing pathway is shown in Fig.
ERF from aerosols (blue), greenhouse gases (red) and total
anthropogenic (black) for present-day (2017, based on RCP8.5) runs from FAIR
constrained to observed temperature change (NROY; histograms) and from prior
distributions (FULL; curves); compare
Median and 5–95 % credible intervals for effective radiative
forcing from greenhouse gases, aerosols and anthropogenic total from the FULL
and NROY FAIR ensembles in 2017. Anthropogenic total contains contributions
from contrails, BC on snow and land use change and therefore is not equal to
the sum of greenhouse gas and aerosol forcing. Compare Fig.
There are negative correlations between aerosol radiative forcing and
Relationship between
Figure
Differences between the models can arise from many sources. The results of
There is an approximately linear relationship between cumulative
We show both the TCRE assuming
To determine the TCRE we run FAIR in
The NROY ensemble in FAIR shows a TCRE of 0.95 to 2.22 K for a cumulative
carbon emission of 1000 Gt with a best estimate of 1.39 K. We diagnose TCRE
based on the RCP8.5 simulation. The TCRE range from FAIR is within the range
of estimates from AR5 (0.8 to 2.5 K,
Transient climate response to
The top of atmosphere energy imbalance
For most years from 2001 to 2015, the net energy balance from CERES is within
the uncertainty range estimated from the FAIR NROY ensemble. The Argo
estimate of
Sensitivity in the ECS, TCR and TCRE to variations in the underlying assumptions in the FAIR large ensemble. For the sensitivity experiments the section number in the paper describing the change is given. The “accepted” column details the proportion of the 100 000-member FULL ensemble that satisfied the specified temperature constraint.
Sensitivity in the effective radiative forcing to variations in the underlying assumptions in the FAIR large ensemble.
Sensitivity in the 2100 temperature change in RCP scenarios to variations in the underlying assumptions in the FAIR large ensemble.
To determine the robustness of the results of the NROY ensemble, the input
assumptions were varied or the ensemble members subjected to a different
constraint as described in this section. The results are summarised in
Tables
The prior distributions of ECS and TCR have a large influence on the
posterior distributions attained
Comparison of earth's energy imbalance
As the RWF is approximately independent of TCR we use an alternative prior
starting with the distributions of TCR and RWF. Noting the analysis of
The best estimate and credible range of ERF is very similar to NROY with the
alternative prior distributions (Table
The canonical RF value of
It is found that this lower value of
Historical temperatures were also constrained using the HadCRUT4 dataset
without infilling
We also perform analysis on the FULL dataset, where the input assumptions are
guided by CMIP5 models and AR5 uncertainty ranges but no constraint to
historical temperature is performed. We show in
Tables
We present a simple model, FAIR v1.3, that calculates global
temperature change, effective radiative forcing from a variety of drivers and concentrations of greenhouse gases. The emissions-based model is based on
the FAIR v1.0 carbon-cycle–climate model with an extension for emissions of
non-
Within FAIR, the response of the carbon cycle model can be adjusted via the
rate of uptake of carbon by land and ocean processes parameterised as a
function of total temperature change and cumulative carbon emissions
(iIRF
Using a correlated joint log-normal prior distribution of ECS and TCR based on
CMIP5 models, running a 100 000-member ensemble in FAIR, and keeping only
those ensemble members that match the rate of temperature change from
1880–2016 in C&W (the “not ruled out yet” or NROY ensemble), we
find the median and 5–95 % credible ranges of ECS and TCR to be 2.86 (2.01
to 4.22) K and 1.53 (1.05 to 2.41) K respectively. The transient climate
response to
Our estimate of TCR is not as low as the range derived by
Temperature changes projected in the NROY ensemble in 2100 are a little lower
than those from
FAIR is useful for creating large ensembles of future temperature change
based on input uncertainties in the carbon cycle parameters and effective
radiative forcing strengths. This can be used for instance to assess the
impacts of emissions commitment scenarios or committed warming
The source code can be obtained at
The supplement related to this article is available online at:
The authors declare that they have no conflict of interest.
Christopher J. Smith and Piers M. Forster acknowledge financial support from the Natural Environment Research Council under grant NE/N006038/1. The authors are grateful to Zebedee Nicholls (University of Melbourne) and Robert Gieseke (PIK Potsdam) for assistance with repository management and code streamlining. We also thank Steve Ghan (Pacific Northwest University) for providing his original code for calculating global aerosol indirect effects. Edited by: Volker Grewe Reviewed by: Brian O'Neill and William Collins