ESDEarth System DynamicsESDEarth Syst. Dynam.2190-4987Copernicus GmbHGöttingen, Germany10.5194/esd-6-525-2015Metrics for linking emissions of gases and aerosols to global precipitation changesShineK. P.k.p.shine@reading.ac.ukhttps://orcid.org/0000-0003-2672-9978AllanR. P.https://orcid.org/0000-0003-0264-9447CollinsW. J.https://orcid.org/0000-0002-7419-0850FuglestvedtJ. S.Department of Meteorology, University of Reading, Reading, UKCenter for International Climate and Environmental Research – Oslo, Oslo, NorwayK. P. Shine (k.p.shine@reading.ac.uk)31August20156252554013March20152April201521July201513August2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://esd.copernicus.org/articles/6/525/2015/esd-6-525-2015.htmlThe full text article is available as a PDF file from https://esd.copernicus.org/articles/6/525/2015/esd-6-525-2015.pdf
Recent advances in understanding have made it possible to relate global
precipitation changes directly to emissions of particular gases and aerosols
that influence climate. Using these advances, new indices are developed here
called the Global Precipitation-change Potential for pulse (GPPP) and
sustained (GPPS) emissions, which measure the precipitation change per
unit mass of emissions.
The GPP can be used as a metric to compare the effects of different
emissions. This is akin to the global warming potential (GWP) and the global
temperature-change potential (GTP) which are used to place emissions on a
common scale. Hence the GPP provides an additional perspective of the
relative or absolute effects of emissions. It is however recognised that
precipitation changes are predicted to be highly variable in size and sign
between different regions and this limits the usefulness of a purely global metric.
The GPPP and GPPS formulation consists of two terms, one
dependent on the surface temperature change and the other dependent on the
atmospheric component of the radiative forcing. For some forcing agents, and
notably for CO2, these two terms oppose each other – as the forcing
and temperature perturbations have different timescales, even the sign of
the absolute GPPP and GPPS varies with time, and the
opposing terms can make values sensitive to uncertainties in input
parameters. This makes the choice of CO2 as a reference gas
problematic, especially for the GPPS at time horizons less than about
60 years. In addition, few studies have presented results for the
surface/atmosphere partitioning of different forcings, leading to more
uncertainty in quantifying the GPP than the GWP or GTP.
Values of the GPPP and GPPS for five long- and short-lived forcing
agents (CO2, CH4, N2O, sulphate and black carbon – BC) are
presented, using illustrative values of required parameters. The resulting
precipitation changes are given as the change at a specific time horizon
(and hence they are end-point metrics) but it is noted that the GPPS
can also be interpreted as the time-integrated effect of a pulse emission.
Using CO2 as a references gas, the GPPP and GPPS for the
non-CO2 species are larger than the corresponding GTP values. For BC
emissions, the atmospheric forcing is sufficiently strong that the GPPS
is opposite in sign to the GTPS. The sensitivity of these values to a
number of input parameters is explored.
The GPP can also be used to evaluate the contribution of different emissions
to precipitation change during or after a period of emissions. As an
illustration, the precipitation changes resulting from emissions in 2008
(using the GPPP) and emissions sustained at 2008 levels (using the
GPPS) are presented. These indicate that for periods of 20 years (after
the 2008 emissions) and 50 years (for sustained emissions at 2008 levels)
methane is the dominant driver of positive precipitation changes due to
those emissions. For sustained emissions, the sum of the effect of the five
species included here does not become positive until after 50 years, by
which time the global surface temperature increase exceeds 1 K.
Introduction
A broad range of emissions of gases and aerosols influence climate, either
directly or indirectly. That influence depends on the characteristics of the
gases and aerosols, such as their lifetime, and their ability to influence
the radiation budget. The conventional cause-and-effect chain links
emissions to changes in concentrations, which then cause a radiative forcing
with subsequent downstream effects on, for example, temperature,
precipitation and sea level. By exploiting understanding of the
characteristics of the gases and aerosols, in concert with simplified
descriptions of the climate system, it is possible to develop simple
methodologies that relate emissions directly to climate impacts, rather than
having to explicitly account for the intermediate steps. Such methodologies
have pedagogic value in making clearer the link between emissions (rather
than, for example, concentration changes) and climate response and they also
have potential applications. The purpose of this paper is to present a
methodology that links global-mean precipitation directly to emissions of
different gases and aerosols. This exploits recent advances in the understanding
of how radiative forcing (RF) and temperature change influence precipitation
change. The methodology presented here yields what we call the Global
Precipitation-change Potential (GPP), which is the global-mean precipitation
change per unit mass of emission. The GPP is presented for both pulse and
sustained emissions.
The impact of climate change depends on more than just global temperature
change. Hence the development of a methodology linking emissions directly to
precipitation is attractive. However, projections from ensembles of climate
model simulations show that precipitation change is much less amenable to a
global representation than temperature change. The projections indicate that
the average surface temperature response to increased concentrations of
greenhouse gases later in this century is largely the same sign over the
whole planet, the temperature changes are coherent on large spatial scales,
and climate models largely agree on the pattern of temperature change, if
not the absolute size (e.g., Knutti and Sendláček, 2013). By contrast,
projected precipitation changes vary regionally in sign, are spatially much
more variable and there is much less agreement between climate models on the
patterns of response (e.g., Knutti and Sendláček, 2013). One part of
the spatial pattern of precipitation change can be understood in quite
simple terms, as being due to the enhanced convergence and divergence of
moisture in a warmer and more moist atmosphere, assuming no change in the
atmospheric flow that transports the moisture (Held and Soden, 2006). Other
parts stem from changes in atmospheric circulation and surface water
availability in response to forcing, and from internal variability; the
response and variability differ between climate models, leading to the
diverse model projections of precipitation change. Nevertheless, the
global-mean precipitation response is coherent amongst these climate models
such as that over the 21st century, precipitation is projected to increase
by about 1 to 3 % per degree C of global-mean warming (e.g., M. Collins et al.,
2013). This paper addresses the dependence of this global-mean component of
precipitation change on the emitted species, as global-mean precipitation
changes can be taken as being a useful indicator of the size of disturbance
of the global hydrological cycle.
Section 2 presents a brief overview of emission metrics which are used to
place emissions of different gases on some common (usually
CO2-equivalent) scale, as this is one potential application of the GPP.
Section 3 presents the simple conceptual model that is used to relate
precipitation change to RF and temperature change, which are themselves
related to emissions. Section 4 presents some illustrative examples of the
GPP drawing values of key parameters from the literature. Section 5 then
uses the methodology in the context of climate metrics, and compares it with
more conventional metrics (the Global Warming Potential – GWP – and Global
Temperature-change Potential – GTP). Section 6 presents an illustration of
the use of the methodology for understanding the effects of emissions in an
individual year (or sustained emissions from that year) on precipitation
changes in or after that year – this illustrates the principal drivers of
the precipitation change, given present-day emissions. Section 7 explores
some aspects of the uncertainty in characterising the GPP and Sect. 8
discusses prospects for further developing the GPP, including possibilities
for including more regional-scale information on precipitation response.
It is noted that Shindell et al. (2012) have demonstrated a link between
radiative forcing (due to a variety of forcing mechanisms) in specific
latitude bands to precipitation change in a number of selected regions;
their precipitation change per unit radiative forcing was called a
“Regional Precipitation Potential”, which is distinct from the GPP
framework presented here, where the precipitation change is directly related
to emissions.
The utility of emission metrics
One potential application of the GPP is to place emissions of different
species on a common scale, in a similar way to the GWP. The 100-year
time-horizon GWP (GWP(100)) is used by the Kyoto Protocol to the United
Nations' Framework Convention on Climate Change to place emissions of many
relatively well-mixed non-CO2 greenhouse gases on a so-called
“CO2-equivalent scale”; this is necessary for the type of multi-gas
treaty that the Kyoto Protocol represents. Metrics such as the GWP can also
be used in life-cycle assessment and carbon footprint studies, for assessing
possible mitigation strategies, for example in particular economic sectors,
and can extend beyond the gases included in the Kyoto Protocol (see
e.g., Fuglestvedt et al., 2010; Deuber et al., 2014).
The GWP characterises the RF in response to a pulse emission of a substance,
integrated over some specified time horizon. It is normally expressed
relative to the same quantity for an equal-mass emission of CO2. The
GWP has enabled the multi-gas operation of the Kyoto Protocol but has also
been the subject of criticism for some applications (e.g., Myhre et al. (2013),
Pierrehumbert (2014) and references therein). This is partly because
the use of time-integrated RF does not unambiguously relate to an impact of
climate change (such as temperature change) and also because it contains
value judgements (particularly the choice of time horizon) that cannot be
rigorously justified for any particular application (Myhre et al., 2013).
Metrics that extend beyond time-integrated forcing have also been proposed.
The GTP (e.g., Shine et al., 2007; Myhre et al., 2013) characterises the
global-mean surface temperature change at some time after an emission. It
may be more applicable to policies that aim to restrict temperature change
below a given target level. The GTP is also subject to criticism and the
need for value judgements when choosing time horizons (Myhre et al., 2013).
Nevertheless the GTP (and its variants, such as the mean global
temperature-change potential – e.g., Gillett and Matthews, 2010; Deuber et al.,
2014 – and integrated temperature potential – e.g., Peters et al., 2011; Azar
and Johansson, 2012) do at least extend to a parameter (temperature change)
more obviously related to a climate change impact. Sterner et al. (2014)
recently presented a metric for sea-level rise. Metrics can also be derived
numerically on the basis of the contribution of an emission of a component
at a given time, to temperature change (or other parameters) during some
future period, as simulated by a simple climate model driven by a specific
emissions scenario (e.g., Tanaka et al., 2009).
Metrics can also be extended to the economic effects of an emission (for
example the Global Cost Potential and Global Damage Potential), by relating
the metrics to costs and damages (e.g., Johansson, 2012) and in certain
restrictive cases these can be shown to have equivalence to physically based
metrics such as the GWP and GTP (e.g., Tol et al., 2012). One difficulty in
such approaches is that the economic damage has to be represented in a
highly-idealised form, as some simple function of, for example, global-mean
temperature change. Conventional physical metrics can also be judged in an
economic context (e.g., Reisinger et al., 2013; Strefler et al., 2014).
The GPP enables an additional and complementary methodology to existing
methods for intercomparing the impacts of emissions of different species,
and the impact of actual or proposed changes in those emissions.
Simple conceptual modelRelationships between radiative forcing and changes in temperature and precipitation
The simple conceptual model presented here originates from the analysis of
simulated precipitation changes in response to increases in CO2
presented by Mitchell et al. (1987). This analysis was based around the
fundamental controls on the energy balance of the troposphere, in which, to
first order, the latent heating resulting from the net rate of condensation
of water vapour (and hence precipitation) is balanced by net radiative
cooling. The conceptual model has been further developed more recently, and
extended to both multi-model assessments and other climate forcing (and
feedback) mechanisms (e.g., Allen and Ingram, 2002; Takahashi, 2009; Andrews
et al., 2010; Kvalevåg et al., 2013; Allan et al., 2014).
The framework starts with an expression of the global-mean atmospheric
energy budget, whereby the net emission of radiation by the atmosphere
(i.e., the atmospheric radiative divergence (Rd), which is the sum of the
emission of longwave radiation by the atmosphere minus the atmospheric
absorption of longwave and shortwave radiation) is balanced by the input of
surface sensible (SH) and latent (LH) heat fluxes so that
Rd=LH+SH.
LH is directly related to the precipitation as, at the global-mean level,
evaporation (and hence LH fluxes) and precipitation approximately balance.
In response to the imposition of an RF and subsequent changes in
temperature, humidity and clouds, Rd will change. The latent heat change
ΔLH can then be written
ΔLH=ΔRd-ΔSH.ΔLH in W m-2 can be converted to precipitation units of
mm day-1 by multiplication by 0.034 (86 400 s in a day divided by the
latent heat of vaporisation, L (2.5 × 106 J kg-1 at 273.15 K)).
There is some level of approximation in this conversion, as L is temperature
dependent and some precipitation falls as snow rather than rain, and hence
the latent heat of sublimation would be more appropriate. The precipitation
change could also be quoted in % of global-mean precipitation (about
2.68 mm day-1 – e.g., Huffman et al., 2009).
ΔRd has two components. The first component is due directly to
the RF mechanism which can change the absorption of shortwave radiation
and/or the emission and absorption of longwave radiation. The conventional
top-of-atmosphere radiative forcing (RF) can be written as the sum of a surface
component (RFs) and an atmospheric component (RFa), and it is
RFa that directly influences ΔRd. Because values of RF are
more readily available than RFa for a wide range of constituents, it
is convenient to relate RFa to RF and so, following Allan et al. (2014), we
define a parameter f such that RFa=f RF. The parameter f could be estimated
directly from RF calculations using a radiative transfer code. However, here
results from fixed-sea-surface-temperature climate model simulations
(e.g., Andrews et al., 2010; Kvalevåg et al., 2013) are used; these have the
advantage that they include the impact on f of rapid adjustments of, for
example, clouds. A disadvantage is that the results of such experiments are
noisier, because of model internal variability, which can be particularly
important for small forcings. Note that a fully consistent approach would
adopt effective radiative forcings (ERF – see Myhre et al., 2013) rather
than RF, and values of f derived using ERFs. However, assessed values of ERFs
are not available for many species and so, in common with Myhre et al., (2013),
the metric values calculated here use RFs, but include a number of
indirect chemical effects and some cloud effects, as noted in Sect. 4. The
values of fare based on one method of deriving ERFs and a possible reason for
differences between f values in Andrews et al. (2010) and Kvalevåg et al. (2013)
(see Sect. 7) is that the fast tropospheric responses that
distinguish RF from ERF differ between the models used in their studies.
The second component of ΔRd is due to the temperature change
resulting from the RF, which leads to changes in emission of longwave
radiation. This change is modified by feedbacks involving other
radiatively important components such as water vapour and clouds
(e.g., Takahashi, 2009; Previdi, 2010) which can also influence ΔRd via
the absorption of shortwave radiation. Climate model simulations indicate
that this component of ΔRd varies approximately linearly with
changes in global-mean surface temperature ΔTs (e.g., Lambert
and Webb, 2008; Previdi, 2010; O'Gorman et al., 2012).
ΔSH in Eq. (2) is less well constrained. It also has two components,
one due to the fast response to RF, which is independent of surface
temperature change, and one due to surface temperature change. The fast
response has been shown to be small for greenhouse gas forcings; Andrews et
al. (2010) and Kvalevåg et al. (2013) show it to be typically less than
10 % of ΔLH for a doubling of CO2, although the size and sign
can vary amongst models (Andrews et al., 2009). However, it can be
much larger for other forcings (of order 50 % of ΔLH in the case of
black carbon; Andrews et al., 2010; Kvalevåg et al., 2013). As noted
by Takahashi (2009) and O'Gorman et al. (2012), an improved conceptual model
could distinguish between ΔRd for the whole atmosphere and
ΔRd for the atmosphere above the surface boundary layer;
changes in ΔRd within the boundary layer seem more effective at
changing SH (e.g., Ming et al., 2010) and hence less effective at changing
LH. Here, following Thorpe and Andrews (2014), we assume the fast component
ΔSH to be small and neglect it, but more work in this area is clearly needed.
Lambert and Webb (2008), Previdi (2010), O'Gorman et al. (2012) and others
show that while generally a smaller term, the surface temperature dependent
part of ΔSH has a similar dependency on ΔTs (at least in
the multi-model mean) as ΔRd. Hence it is convenient to combine
the ΔTs -related changes in Rd and this component of SH in
Eq. (2) into a single term dependent on ΔTs and separate out the RF
term. Equation (2) then becomes, in precipitation units of mm day-1,
ΔP=0.034kΔTs-fRF.
Despite its apparent simplicity, Eq. (3) has been shown by Thorpe and
Andrews (2014) to reasonably well simulate future projections of global-mean
precipitation change from a range of atmosphere–ocean general circulation
models, albeit with a tendency to underestimate the multi-model mean.
Uncertainty in the value of f for all forcing agents (and possible
inter-model variations in f – see Sect. 7) inhibit a full assessment.
We refer to the kΔTs term as the “T term” and the -fRF term as the
“RF term” although they could also be termed the “slow” and “fast”
responses, respectively, which relates to the contrasting heat capacities
and associated response timescales of the ocean and atmosphere. The balance
between these two terms varies between climate forcing agents; as will be
shown, they can act to either reinforce or oppose each other. Hence the same
ΔTs from two different forcing agents can result in a different ΔP.
Note the sign convention here. For the case of a positive RF, since k is
positive, the effect of the T term is to increase Rd as temperature
increases – the increased radiative divergence then leads to a requirement
for a greater latent heat flux (and hence an increase in precipitation) to
maintain the tropospheric energy balance; this term provides the direct link
between surface temperature change and precipitation change. If in this same
case f (and hence RFa) is positive, then the RF term would oppose the
T term (as it would decrease rather than increase the radiative divergence)
and act to suppress precipitation. Physically, in this case, there is less
“demand” for latent heating to balance the tropospheric energy budget.
Illustration for doubling of CO2
As a simple example of the processes, consider the equilibrium response to a
doubling of carbon dioxide, and take k= 2.2 W m-2 K-1 (consistent
with the multi-model means in Previdi, 2010 and Thorpe and Andrews, 2014),
RF2×CO2= 3.7 W m-2 (Myhre et al. (2013) who give the
same value for the ERF) and f= 0.8 (Andrews et al., 2010). The equilibrium
precipitation change ΔP2×CO2 (in %, assuming a
global-mean precipitation of 2.68 mm day-1), can then be written in
terms of the equilibrium surface temperature change ΔT2×CO2 as
ΔP2×CO2=2.79ΔT2×CO2-1.35.
This equation shows that if ΔT2×CO2= 1.35 K,
which, via ΔT2×CO2=λRF2×CO2,
corresponds to a climate sensitivity λ of 0.36 K (W m-2)-1,
ΔP2×CO2 would be zero. The
slope of the line is 2.79 % K-1. Such an expression fits well with the
intercept and slope of the linear fit to equilibrium double-CO2
experiments from a range of climate models found by Allen and Ingram (2002 – their
Fig. 2). Hence Eq. (4) acts as a further validation of the utility
of Eq. (3) for simulating global-mean precipitation change across climate
models with varying parameterisations of, for example, convection, with
climate sensitivities varying across the range from about 0.4 to 1.3 K
(W m-2)-1. The departures of individual models from this best fit
could originate from differences in any of the values of k, f,
RF2×CO2 assumed here, or in inter-model differences in
the importance of the fast component of ΔSH which is not accounted for
here. The slope of the line also corresponds to hydrological sensitivity due
only to the T term, and is in good agreement with the multi-model mean
derived by Thorpe and Andrews (2014).
Since more generally, ΔTeq=λRFeq, Eq. (3) can
also be written in a more general form for any ΔTeq (and hence
RFeq), so that the equilibrium change in precipitation
ΔPeq (in %) is given by
ΔPeq=1.3ΔTeqk-f/λ.
This emphasizes that the offset between the T and RF terms depends strongly
on λ. Using a mid-range climate sensitivity of 0.8 K (W m-2)-1,
the RF term for CO2 offsets about 50 % of the
precipitation change that would result from the T term alone. Considering
the IPCC (2013) “likely” range for λ, which is 0.4 to 1.2 K (W m-2)-1,
the RF term offsets the T term by about 90 % for low
λ and by 30 % at high λ. The overall global-mean
equilibrium hydrological sensitivity (ΔPeq/ΔTeq) to
CO2 forcing can be derived from Eq. (5) and varies from about 0.25 % K-1
to 2 % K-1 over this range of λ, which can be
compared with the value of 2.79 % K-1 due solely to the T term.
Application to emissions of a gas or aerosol
To relate the understanding encapsulated in Eq. (3) to an emission of a
gas or aerosol, we consider first the GPP for a pulse emission of unit mass
of a gas at time t= 0 and consider the precipitation change at time H
after the emission. Following convention, we label this the Absolute GPP
(AGPPP), which is presented here in units of mm day-1 kg-1.
The T term in Eq. (3) becomes k times the absolute GTPP (AGTPP)
(e.g., Shine et al., 2005). Assuming for small perturbations that RF is linear
in the concentration of the emitted species, x, and that the perturbation
decays exponentially with time constant τx, then for a unit
emission, the RF term is given by -fxAxexp(-H/τx), where
Ax is the specific RF (in W m-2 kg-1) of the emitted
species. Hence the AGPP (in mm day-1 kg-1) is given by
AGPPPx(H)=0.034kAGTPPx(H)-fxAxexp-H/τx.
Since a perturbation of CO2 does not decay following a simple
exponential (see e.g., Joos et al., 2013), the calculation of
AGPPPCO2(H) is slightly more involved – see the Appendix for
more details.
The effect of a sustained emission of a unit mass of gas per year, from time
t= 0 can also be considered yielding a sustained AGPP (AGPPS). In this
case, the AGTPS (see Shine et al., 2005) can be used for the T term and
the RF term is now proportional to the time variation of the perturbation of
the species to a step-perturbation (e.g., Fuglestvedt et al., 2010). The
AGPPS is given by
AGPPSx(H)=0.034kAGTPSx(H)-fxAxτx1-exp-H/τx,
which can also be expressed as a function of both AGTPS and AGWP as
AGPPSx(H)=0.034kAGTPSx(H)-fxAGWPx(H).
The calculation of AGPPSCO2(H) is explained in the Appendix.
Note that when H is long compared to the timescale of the climate response
(several hundred years in this case – see the Appendix) the AGTPSx(H)
can itself be related to the AGWPPx(H) (see e.g., Shine et al.,
2005) which would simplify Eq. (8) further.
Here the AGPPP and AGPPS are used to calculate the GPPP and
GPPS relative to a reference gas, and following common practice for GWP
and GTP, CO2 is used as that reference gas here, although
difficulties with this choice will be noted. The GPPP, relative to an
equal mass emission of CO2, is then given by
GPPPx(H)=AGPPPx(H)AGPPPCO2(H),
with a similar expression for GPPS.
Note we have chosen to present the AGPPP and AGPPS as end-point
metrics, i.e., as the effect at the time horizon H of an emission at (or
starting at) t= 0. For some purposes, a time-integrated metric might give a
useful perspective. Following Peters et al. (2011 – see in particular its
Supplement) we note that time-integrated pulse metrics are
mathematically equivalent to end-point metrics for sustained emissions.
Hence, the AGPPS and GPPS can equally be interpreted as
time-integrated forms of the AGPPP and GPPP.
Illustrative values for the absolute global precipitation-change potential
In this section, illustrative calculations of the AGPP are presented. Values
for gas lifetimes and Ax are taken from Myhre et al. (2013) and are
described in more detail in the Appendix. The AGTP calculation requires a
representation of the surface temperature response, which depends on the
climate sensitivity and rate of ocean heat uptake. We use the simple
impulse response function in Boucher and Reddy (2008) (as used in Myhre et
al. (2013) for GTP calculations). Details are given in the Appendix. Values
of f, which describe the partitioning of the RF between surface and
atmosphere are taken from Andrews et al. (2010) – these will likely be
quite strongly model dependent, but for illustration purposes, they suffice.
Some sensitivity tests to the representation of the impulse response
function and f are presented in Sect. 7. The calculations for CH4 and
N2O emissions include indirect effects, the most prominent being their
impact on ozone. Different values of f should be used for each indirect
component, but in the absence of robust assessments for these, the same
value of f is used for the indirect components as is used for the direct components.
Well-mixed greenhouse gases
Figure 1 shows the AGPPP for CO2, CH4 and N2O, for the
total and the RF and T terms individually, for a period of 100 years after
the pulse emission. In Andrews et al. (2010), f is larger for CO2 (0.8)
than for methane (0.5) because, for present-day concentrations, the lower
opacity of the methane bands means that the surface feels more of the
top-of-the-atmosphere forcing than it does for CO2. Since N2O has
a similar atmospheric opacity to CH4, it is hypothesized that
surface–atmosphere partitioning of the RF also behaves in a similar way to
CH4 and so the value of f for N2O is also taken to be 0.5; further
work is needed to establish this. Hence, from Eq. (3), the degree of offset
between the RF and T terms is larger for CO2 than for CH4 and N2O.
Figure 1a for CO2 illustrates the general behaviour. For a pulse
emission, the size of the RF term is maximised at the time of emission, as
this is when the concentration is largest, and then decays as the
perturbation decays. The T term is dictated by the timescale of the response
of the surface temperature to the forcing. The characteristic temperature
response to a pulse forcing (e.g., Shine et al., 2005) is an initial increase
in T, as the thermal inertia of the surface means it takes time to respond
to the forcing, reaching a maximum, followed by a decrease that is
controlled by the timescales of both the decay of the pulse and the climate
response. For the first 5 years, the CO2 precipitation response is
negative as the RF term dominates, after which the T term dominates, but the
total is approximately 50 % of the T term. The long perturbation
timescales mean that the effect on precipitation persists for more than
100 years after an emission, as does the competition between the T and RF terms.
AGPPP for 1 kg pulse emissions of CO2, N2O and
CH4. The T term and RF term refer to the first and second terms on the
right hand side of Eq. (3) respectively, and the Total is the sum of these.
N2O has a lifetime of the order of a century and its AGPPP
(Fig. 1b) is qualitatively similar to CO2 but the T term dominates, because
f is smaller. As CH4 is much shorter lived, its behaviour is somewhat
different. As the pulse, and the associated RF, has disappeared by about
year 40, after this time the AGPPP is determined by the T term only.
Short-lived species
The AGPP is illustrated for two short-lived species, sulphate and black
carbon (BC) aerosols. For both cases, the radiative efficiency and lifetime
values from Myhre et al. (2013) are used and given in the Appendix; for
these illustration purposes only the sulphate direct effects are included,
and the BC values include some aerosol-cloud interaction and surface albedo
effects. In terms of the surface–atmosphere partitioning of RF, these are
two contrasting cases. For sulphate, the Andrews et al. (2010) model results
indicate an f value less than 0.01 in magnitude and is assumed here to be
zero; this indicates that essentially all of the top-of-the-atmosphere
forcing reaches the surface. By contrast, Andrews et al. (2010) find that
for BC, f is 2.5, so that RFa is much greater than RF; the surface
forcing is of opposite sign to RF and RFa as the surface is deprived
of energy, while the atmosphere gains energy. As will be discussed further
in Sect. 7, there are considerable uncertainties in these values,
especially for BC, where both RF and f depend strongly on the altitude of the
BC. Nevertheless, the values used here suffice to illustrate a number of
important points.
Figure 2 shows the AGPPP for BC and sulphate. As both are very
short-lived (weeks) compared to the greenhouse gases, their RF term decays
to zero within a year (and hence is not visible on Fig. 2), and it is only
the thermal inertia of the climate system that enables them to influence
temperature (and hence precipitation) beyond this time period.
An alternative perspective is provided for the sustained-emissions case. In
this case, because the BC and sulphate perturbations persist, so too does
the influence of the RF term on precipitation. Figure 3 shows the AGPPS
for CO2, BC and sulphate. For CO2, the long timescales of the
CO2 perturbation mean that both the RF term and T term increase
throughout the 100-year period shown. At short time horizons, the RF term
dominates, leading to suppression of global precipitation, but after about
15 years, the T term starts to dominate, and the AGPPS becomes
positive. For BC, the impact of the large RF term is dramatic. It is
strongly negative and constant with time (because of the short lifetime),
while the T term is positive and increases until the temperature is almost
in equilibrium with the RF. This counteracts the impact of the RF term, but
the total nevertheless remains negative throughout. For sulphate, because
f is assumed to be zero, the total remains equal to the T term.
AGPPP for 1 kg pulse emissions of black carbon (BC) and
sulphate. Note that the RF term in Eq. (3) is negligible for such
short-lived gases, except at time horizons less than a few weeks, and only
the total is shown.
AGPPS for 1 kg yr-1 sustained emissions of CO2,
BC and sulphate. The T term and RF term refer to the first and second terms
on the right hand side of Eq. (3) respectively, and the Total is the sum of
these. For sulphate, the RF term is assumed to be zero (see text) and so
only the Total is shown.
GPPP (in bold) and GTPP for 1 kg pulse emissions of
N2O and CH4 relative to a 1 kg pulse emission of CO2.
The GPP relative to CO2
Absolute GPP values were presented in Sect. 4. In this section we
normalize the GPP values to the effects of the reference gas CO2 to
provide a relative measure, using Eq. (9) and its equivalent for sustained emissions.
Well-mixed greenhouse gases
Figure 4 shows the GPPP for N2O and CH4; for comparison, the
GTPP is also shown. Note that the plots start at H= 20 years, as the
time at which the AGPPP crosses the zero axis differs slightly amongst
the gases, and this results in a singularity in Eq. (9). For N2O, the
GPPP is at least 300 times greater than CO2 on all timescales
shown, and, per unit emission, is more than 40 % more effective at
changing precipitation than temperature (as given by the GTPP),
compared to CO2. This is because the RF term is less effective at
muting the T term for N2O's GPPP than is the case for CO2. For
CH4 the difference between the GPPP and GTPP is most marked
in an absolute sense at shorter time horizons, when the GPPP of methane
is affected most by the RF term; the GPPP and the absolute difference
with the GTP decline at longer timescales when it is entirely due to the
difference between the AGTPP and AGPPP for CO2.
Absolute metrics, AGWP, AGTPP, AGTPS, AGPPP and
AGPPS for CO2 at time horizons of 20 and 10 years, which are
chosen for illustrative purposes. The first and second sets of AGPP values
use the CO2f factor from Andrews et al. (2010) and Kvalevåg et al. (2013),
respectively (see Table A1).
The GWP, GTPP and GPPP, relative to CO2, for pulse
emissions of four species at time horizons of 20 and 100 years, which are
chosen for illustrative purposes. The absolute values of metrics for
CO2 are given in Table 1.
Table 1 presents the values of all absolute metrics used here for CO2
and Table 2 presents the values of the GWP, GTPP and GPPP for H of
20 and 100 years; these time horizons are chosen for illustrative purposes,
rather than being indicative that they have special significance, except
insofar as 100 years is used for the GWP within the Kyoto Protocol
(e.g., Myhre et al., 2013). For CH4, the GPPP(20) is 50 % larger
than the GWPP(20) and almost double the GTPP(20) mostly because of
the larger effect of the RF term on the AGPPP for CO2. The
time-integrated nature of the GWP means that it is much higher than the
GTPP and GPPP at 100 years, while the GPPP remains about
double the GTPP. The GPPP for N2O is 25–50 % higher than
the GWP and GTPP at both values of H, again because of the larger
effect of the RF term on the AGPPP for CO2.
GPPP (in bold) and GTPP for 1 kg pulse emissions of BC
and sulphate relative to a 1 kg pulse emission of CO2.
GPPS (in bold) and GTPS for 1 kg yr-1 sustained
emissions of BC and sulphate relative to a 1 kg yr-1 sustained
emission of CO2.
Short-lived species
Figure 5 shows the GPPP and GTPP for BC and sulphate. As noted
in Sect. 4.2, the radical difference in their values of f (2.5 for black
carbon, 0 for sulphate) has no impact on the AGPPP for BC and sulphate
beyond very short timescales. Because of this, in Fig. 5, the only
difference between the GPPP and GTPP comes from the influence of
the RF term on AGPPPCO2, and on an equal emissions basis both
short-lived species are, relative to CO2, more effective at changing
precipitation than temperature – this is also shown in Table 2.
Figure 6 shows the GPPS, comparing it with the GTPS. For sulphate,
the difference between the GPPS and GTPS originates entirely from
the effect of the RF term on AGPPSCO2, because of the assumption
that f is zero. For BC they differ dramatically – whilst both BC and
CO2 cause a warming, so that GTPS is positive, their impact on
precipitation is opposite, and the BC GPPS is negative.
Precipitation change, in µm day-1 (top panel), and
temperature change, in mK, (bottom panel) in the years after 2008, following a
pulse emission in 2008, calculated using the AGPPP and AGTPP and
using estimated emissions of the species in 2008.
Table 3 presents values of the GTPS and GPPS for H= 20 and
100 years, including the values for CH4 and N2O for completeness. The
GPPS values at 20 years are particularly influenced by the fact that
the AGPPS for CO2 is relatively small at this time, due to the
strong cancellation between the T and RF terms. At both values of H,
GPPS values are higher in magnitude than the corresponding GTPS
values for all non-CO2 components considered here.
Precipitation response to realistic emissions
To illustrate a further usage of the AGPPP and AGPPS, Figs. 7
and 8 apply them to 2008 emissions, to examine the consequences of the
emissions of the five example species on precipitation. Figure 8.33 of Myhre et
al. (2013) presents a similar calculation applying the AGTPP and shows
that the five species used here are the dominant emissions for determining
temperature change; hence it was felt useful to also present the total
effect of the five emissions in the figures. Emissions are taken from Table 8.SM.18
of Myhre et al. (2013) and reproduced in Table A1. For reference,
the corresponding values using the AGTPP and AGTPS are also
shown in the figures.
Figure 7 shows the impact of the 2008 emissions, emitted as a single pulse,
on global precipitation and temperature change in subsequent years. While
the emissions of CH4, sulphate and BC are 2 to 4 orders of magnitude
smaller than those of CO2, in the early years after the emission, their
effects are competitive with CO2 because of the size of the GPPP
and GTPP; emissions of N2O are small enough that, despite
its large GPPP, its absolute contribution remains low throughout.
Because of the differing compensations between the T and RF terms for
CO2 and CH4, their relative importance differs quite significantly
between precipitation and temperature. Methane's contribution to
precipitation change is less negative or more positive than that of CO2
until about 20 years; it exceeds the CO2 contribution by a factor of 2
at about 10 years, and remains 25 % of the CO2 effect even at
50 years. For temperature, the contributions are approximately the same until
10 years, after which the CO2 contribution dominates, being about
7 times larger by 50 years. For the two aerosol components, the GPPP is
unaffected by the RF term (because the RF due to a pulse emission of a
short-lived gas declines rapidly – see Sect. 4) but their importance for
precipitation relative to CO2 is enhanced, because the RF term acts to
suppress the effect of CO2 on precipitation change. Thus, for example,
the BC effect on precipitation is larger than CO2 out to year 10,
compared to year 4 for temperature.
The GTPS and GPPS, relative to CO2, for sustained
emissions of four other species at time horizons of 20 and 100 years, which are
chosen for illustrative purposes. The absolute values of metrics for
CO2 are given in Table 1.
Precipitation change, in mm day-1 (top panel), and temperature
change, in K, (bottom panel) in the years after 2008, assuming constant emissions
at 2008 levels, calculated using the AGPPS and AGTPS and using
estimated emissions of the species in 2008.
The GPPP and GPPS, relative to CO2, for pulse
emissions of four other species at time horizons of 20 and 100 years, which are
chosen for illustrative purposes, using the values of surface–atmosphere
partitioning of radiative forcing from Kvalevåg et al. (2013). The two
black carbon values are, respectively, using values of f for a model-derived
vertical profile for present-day emissions and assuming that the present-day
burden is placed entirely at 550 hPa. The absolute values of metrics for
CO2 are given in Table 1.
Figure 8 shows the effect of assuming sustained emissions at 2008 levels.
Although not a plausible future scenario (since, for example, emissions of
greenhouse gases are at present continuing to rise) it provides a useful
baseline experiment to assess the relative roles of current emissions when
their atmospheric burdens are replenished each year. As expected from the
AGPPS values, the role of the short-lived species differs considerably
from the pulse case, as the RF term remains active – in the case of
precipitation, BC's effect is now negative throughout. Until about 30 years,
the net effect of all five emissions is a reduction of precipitation, after
which the warming due to CH4 and CO2 is sufficient for their
T terms to overwhelm the reduction caused by sulphate (due to its T term)
and BC (due to its RF term). This near-term reduction of precipitation is
also seen in the results of Allan et al. (2014), where the precipitation
changes are driven directly by forcings and temperatures (rather than by
emissions, as is the case here). By contrast, the temperature effect is
positive after year 1. Perhaps most marked is the role of CH4. It is
the dominant driver of positive precipitation change until about year 50 and
even after 100 years its effect is about 50 % of that due to CO2.
This differs from temperature, where the CO2 effect is greatest after
15 years and 3 times larger by 100 years. Figure 8 also illustrates the
extent to which the sulphate and BC emissions are opposing the precipitation
increase due to the greenhouse gases, at large values of H; those components
would respond relatively quickly to any changes in emissions.
While these are clearly idealised applications of uncertain metrics, they
nevertheless illustrate their potential utility for assessing the relative
importance over time of different emissions on global precipitation change.
The approach could be extended to past or possible future emission profiles,
by convolving the time-dependent emissions with the GPPP and GPPS values.
Mean and standard deviations of the AGTP, AGPP, GTP and GPP for
both pulse (PUL) and sustained (SUS) emissions for time horizons of 20 and
100 years (which are chosen for illustrative purposes), using 18 different
representations of the impulse response function for temperature change.
(a) AGTP and AGPP for carbon dioxide, for both pulse and sustained emissions,
and then GTPP, GPPP, GTPS and AGPPS for (b) methane,
(c) nitrous oxide, (d) sulphate and (e) black carbon. For CO2 the units are
10-16 K kg-1 for AGTPP, 10-14 K kg-1 yr
for AGTPS, 10-18 mm day-1 kg-1 for AGPPP and
10-16 mm day-1 kg-1 yr for AGPPS. The
AGPPS for all other gases are in 10-15 mm day-1 kg-1 yr.
Sensitivities and uncertainties
There are many uncertainties and sensitivities in the calculation of metrics
such as assumptions about the background state (which can affect Ax and
τx), and the impulse response function for CO2 (see
e.g., Fuglestvedt et al., 2010; Joos et al., 2013; Myhre et al., 2013). Two
sensitivities are explored. First, the impulse response model for surface
temperature change used here (see Sect. 4) is a fit to output from
experiments with one particular climate model with its own particular
climate sensitivity. Olivié et al. (2012) present similar fits derived
from 17 different climate models, or model variants – the fits shown in
Table 5 of Olivié et al. (2012) are used, along with the Boucher and
Reddy (2008) fit used in Sect. 4, and cover a wide range of climate
sensitivities (0.49 to 1.06 K (W m-2)-1) and timescales of climate
response, although we note that model uncertainty range may not fully
straddle the true uncertainty range. Olivié and Peters (2013) used these
fits to explore the sensitivity of the GTP calculations. Figure 9 shows the
mean and standard deviation of the pulse and sustained GTP and GPP derived
using these 18 different representations.
Considering the absolute pulse metrics for CO2, Fig. 9a shows that the
AGTPP is only moderately sensitive (with a coefficient of variation (cv)
of about 20 %) to model choice. By contrast the cv is about 60 and
40 % for the AGPPP(20) and AGPPP(100), respectively. This is
because the T term is highly sensitive to the choice of impulse response
model, whilst the RF term is independent; hence the degree of compensation
between these two terms varies amongst these models. The GTPP is most
sensitive for short-lived species and this uncertainty is amplified for the
GPPP, by up to a factor of 2 for the GPPP(100) for sulphate
(Fig. 9d). By contrast, for the longer-lived species the uncertainty in the
GTPP and GPPP differ greatly – for N2O (Fig. 9c), the cv
for GTPP values is only a percent or so, but is typically 40 % for
the GPPP, as both the numerator and denominator in Eq. (9) are impacted
by compensations in the T and RF terms to different degrees at different times.
The GPPS is more sensitive because even the sign of
the AGPPSCO2 is not well constrained at 20 years (Fig. 9a).
Roughly half of the impulse response models yield positive values and half
negative ones, with two near zero, because of the differing degrees of
compensation between the T and RF terms. The value of H at which
the AGPPSCO2 is zero varies from 11 to 61 years amongst the
models. (For comparison, for the AGPPPCO2, the corresponding
range is 4 to 13 years.) In these circumstances, it becomes difficult to
compare the GPPS values as they vary wildly from model to model
(from -18 000 to 24 000 for the GPPS(20) for N2O) and for this reason the
AGPPS is presented in Fig. 9. Even the AGPPSCO2(100)
values vary by over an order of magnitude across the 18 models. In general,
the uncertainties in the AGPPS exceed those in the AGTPS; this is
most marked in the case of N2O, where the GTPS is almost
insensitive to the choice of impulse response model, as the effect of this
choice on the AGTPS for CO2 and N2O is almost the same.
The second sensitivity explored here is to the assumed values of f by
replacing the Andrews et al. (2010) values by those from Kvalevåg et al. (2013)
(see Table A1). Where available, we use the values of ffrom the larger
forcing perturbations given by Kvalevåg et al. (2013) as these give a
clearer signal. For BC, Kvalevåg et al. (2013) present a range of
values, for perturbations at different altitudes – for example they find a
value of f of 6.2 (for 10 times the model-derived vertical profile of BC in
response to present-day emissions) and 13 (when 10 times the present-day
burden is placed entirely at 550 hPa); these can be compared to the Andrews
et al. (2010) value of 2.5. The difference results mostly from the
semi-direct effect of BC and clouds; when BC is entirely placed at certain
pressures (750 and 650 hPa), Kvalevåg et al.'s (2013) results indicate
that f is particularly poorly constrained, because RF is close to zero, while
RFa is large and positive. This is an example of where casting Eq. (3)
directly in terms of RFa rather than RF would be advantageous (see
Sect. 3). It should be noted that this sensitivity test concerns the
impact of BC altitude on f rather than on τx and Ax.
Table 1 shows the AGPPP and AGPPS for CO2 and Table 4 shows
the GPPP and GPPS; these should be compared with the appropriate
columns in Tables 2 and 3 (the GWP, GTPP and GTPS are unaffected
by f). For the GPPP for CH4 and N2O, the effect of changing
the f values is rather modest (10–20 %) because changes in the numerator
and denominator of Eq. (9) compensate to some extent. For BC and sulphate,
changes are entirely dependent on the change in AGPPPCO2, as the
change in f factor has little influence (see Sect. 4.2) and hence changes
are correspondingly larger (20–30 %).
The AGPPSCO2(20) (Table 1) is rather sensitive to the change in
f because of the degree of compensation between the T and RF terms, and
increases by more than a factor of 2 (Table 1). This is the dominant reason
why the GPPS(20) for N2O and CH4 decrease by about a factor
of 2. The changes at 100 years are much smaller, nearer 10 %. The
AGPPS for the short-lived species are, unlike the AGPPP, now
affected by the change in f. Table 5 shows the effect on the sulphate
GPPS(20) to be about a factor of 2, while the GPPS(100) is little
affected. By contrast, the GPPS for black carbon at both time horizons
depends significantly on the altitude of the black carbon perturbation.
Discussion and conclusions
This paper has used a simple, but demonstrably useful, conceptual model of
the drivers of global-mean precipitation change in response to the
imposition of a radiative forcing, to relate precipitation change directly
to emissions. The GPPP and GPPS metrics illustrate the interplay
between the two drivers (the atmospheric component of the radiative forcing,
and the surface temperature change) for different forcings, at different
time horizons, and for both pulse and sustained emissions. The GPPP
and GPPS are given as the change at a specific time horizon (and
hence are end-point metrics). There may be climate effects related to the
total change in precipitation over time for which an integrated metric would
be appropriate, so it is useful to note that the GPPS can also be
interpreted as the time-integrated GPPP.
It has been shown that relative to CO2, the pulse and sustained GPP
values for the non-CO2 species examined here are larger than the
corresponding GTP values, because the CO2 GPP is the sum of two quite
strongly opposing terms. Further, for black carbon emissions, while they act
to warm the climate system, they also act to reduce global-mean
precipitation; while this has been clear from the modelling literature for
some time, the present work shows how the perspective is different for pulse
and sustained emissions. The reduction of precipitation is driven entirely
by the radiative forcing component and since, for pulse emissions of
short-lived species this falls away on timescales of weeks, it is only
apparent on longer timescales for the sustained perspective. This is an
example of how the perturbation design can have a large impact on the
calculated response.
The evaluation of precipitation metrics assumes that the parameters required
for the simple conceptual model are available, and in particular the
partitioning of radiative forcing between surface and atmosphere. Only a
rather limited number of model studies of this partitioning are currently
available, and there are significant differences amongst these and
particular sensitivity to the altitude of absorbing aerosol (e.g., Ming et
al., 2010; Kvalevåg et al., 2013). In addition, further development of
the simple conceptual model (particularly to account for fast changes in the
sensible heat flux) would be beneficial, once understanding improves, as
would a fully consistent usage of effective radiative forcings. The ongoing
Precipitation Driver Response Model Intercomparison Project (PDRMIP)
(http://cicero.uio.no/PDRMIP/) should provide important information on the
utility of the conceptual model and of the degree of robustness of the
surface–atmosphere partitioning amongst a range of climate models for a
number of radiative forcing mechanisms. Clearly further studies for a wider
range of forcing agents are also needed and indeed casting Eq. (3) directly
in terms of the atmospheric component of radiative forcing RFa (rather
than top-of-atmosphere radiative forcing) would be desirable if values of
RFa become more readily available.
It is not suggested that the new metrics could replace conventional
emissions metrics such as the GWP and GTP in climate policy or emission
trading contexts, but they do provide a useful additional perspective for
assessing the effects of emissions; they particularly help to emphasise
where the impact on precipitation differs significantly from that on
temperature or forcing. One difficulty in its application is that
conventional metrics generally use CO2 as a reference gas. For
precipitation change, the forcing and surface temperature components oppose
each other, which means that the effect of CO2 emissions on
precipitation can be zero (at least in the global-mean) at short time
horizons for both pulse and sustained emissions. This is clearly undesirable
for a reference gas, and it has also been shown that the timing of this zero
point is rather sensitive to the particular parameters used in its
calculation. Hence absolute metrics may be more instructive. By applying the
absolute metrics to a specific illustrative case (emissions in 2008, either
as a pulse, or sustained indefinitely) the importance of methane in
influencing the global-mean precipitation change is highlighted – using the
default model parameters here, in the sustained 2008 emissions case, the
precipitation change from methane exceeds that from CO2 for about
50 years, By contrast, for temperature, the effect of CO2 emissions is
almost immediately at least comparable to, or stronger than, methane.
It has been stressed that use of global-mean precipitation change as a
measure of impact has difficulties, because predicted future changes differ
in sign between regions – the global-mean is a small residual of these
opposing more localised changes and hence it only gives rather general
guidance on the effect of different drivers on the changing hydrological
cycle. Nevertheless, some of the regional pattern of response can be
understood as a generic and coherent response to temperature change.
Increases and decreases in precipitation are largely reflective of an
amplification of precipitation minus evaporation fields, primarily explained
by increasing concentrations of water vapour with warming (as expected from
the Clausius–Clapeyron equation); this leads to systematic increases and
decreases in precipitation depending on the region (e.g., Held and Soden,
2006; Liu and Allan, 2013).
The approach here could be enhanced to a more regional level of response by
either using a simple pattern-scaling approach (whereby the pattern of
predicted precipitation change scales with the global-mean) or, better, to
derive a regional variation that accounts for the different effects of the
forcing and temperature response on precipitation change (Good et al., 2012).
The patterns emerging from such an approach would likely depend
significantly on which climate model was used to derive them. In addition,
such patterns would be needed for all the primary forcing agents. For
short-lived emissions, it is known that even global-mean metrics such as the
GWP and GTP depend on the emission location (e.g., Fuglestvedt et al., 2010) – this
will also be true for the precipitation metrics. Metrics can also be
posed in terms of the regional response to regional emissions. For example,
W. J. Collins et al. (2013) employed the Regional Temperature Potential proposed
by Shindell (2012) whereby a matrix is produced that characterises the
effect of RFs in a set of given regions on the temperature change in a set
of given regions; a similar approach could be taken using the Regional
Precipitation Potential proposed by Shindell et al. (2012).
In spite of the difficulties in quantifying the precipitation metrics given
present knowledge of the driving parameters, the framework presented here
adds a useful extra dimension to simple tools that are currently available
for assessing the impact of emissions of different gases and particulates.
The impulse response function, R(t), for a pulse emission of CO2 is assumed
to be of the form
R(t)=ao+∑j=13ajexp-tαj,
where the parameters used here follow Myhre et al. (2013), with
ao= 0.2173, a1= 0.2240, a2= 0.2824, a3= 0.2763
and α1= 394.4 years, α2= 36.54 years and
α3= 4.304 years.
The impulse response function for global-mean surface temperature in
Sects. 4 to 6 is taken from Boucher and Reddy (2008) and is of the form
R(t)=∑i=12cidiexp-tdi,
with c1= 0.631 K (W m-2)-1, c2= 0.429 K
(W m-2)-1 and d1= 8.4 years and d2= 409.5 years. The
equilibrium climate sensitivity for this function is 1.06 K
(W m-2)-1, equivalent to an equilibrium surface temperature change
for a doubling of CO2 of about 3.9 K. Additional impulse response
functions are used in Sect. 7, with alternative values of ci and di.
To derive the AGPPP in Eq. (6), for species for which the
perturbation decays exponentially with a single time-constant
τx, an expression for AGTPP is required. For a species
with a specific RF Ax and using Eq. (A2) this is given by (see, for
example, Fuglestvedt et al., 2010)
AGTPPx(t)=Axτx∑i=12ciτx-diexp-t/τx-exp-t/di.
This equation does not apply in the case where τx=di;
the appropriate expression is given in Shine et al. (2005) for this
case, which has to be modified for the two-term form of Eq. (A2).
For the case of CO2, where the decay of a pulse is given by Eq. (A1),
the AGTPP is given by (see, for example, Fuglestvedt et al., 2010)
AGTPPCO2(t)=ACO2ao∑i=12ci1-exp-tdi+∑i=12ci∑j=13ajαjαj-diexp(-t/αj)-exp-t/di,
and the exponential in the second term on the right-hand side of Eq. (6) is
replaced by Eq. (A1).
To derive the AGPPS in Eq. (7), the GTPS for non-CO2
species is given by (by rearranging the expression in Shine et al., 2005
following Peters et al., 2011)
AGTPSx(t)=Axτx∑i=12ciτx-diτx1-exp-t/τx-di1-exp-t/di,
and again the case where τx=di is given in Shine
et al. (2005), which has to be modified for the two-term form of Eq. (A2).
The calculation of the AGPPS for CO2 requires the AGTPS and
is given by
AGTPSCO2(t)=∑i=12ACO2ciaot-di1-exp-t/di+∑j=13αjajαj-diαj1-exp-t/αi-di1-exp-t/di,
and also AGWPCO2, for the second term on the right hand side of
Eq. (7) which is
AGWPCO2(t)=ACO2aot+∑j=13ajαj1-exp-tαj.
The parameters used for the five different species employed here are presented in Table A1.
Parameter values used for each species included in calculations.
All values are taken from Myhre et al. (2013), unless otherwise stated, and
the CH4 and N2O values of Ax include the indirect effects
described there.
K. P. Shine conceived the idea of the emissions metrics
for precipitation, through conversations with R. P. Allan, performed the
calculations and led the writing. R. P. Allan, W. J. Collins and J. S. Fuglestvedt provided major critical
input to the drafts, including ideas on adjusting the emphasis of the paper
and on possible applications of the metrics.
Acknowledgements
We acknowledge funding from the European Commission,
under the ECLIPSE (Evaluating the Climate and Air Quality Impacts of
Short-Lived Pollutants) Project (Grant Agreement 282688) and thank other
ECLIPSE partners for their encouragement and input to this work. We are
grateful to Katsumasa Tanaka, an anonymous reviewer and the Editor, Steven Smith,
for their helpful comments, and for suggestions and input from
participants in PDRMIP.
Edited by: S. Smith
ReferencesAllan, R. P., Liu, C. L., Zahn, M., Lavers, D. A., Koukouvagias, E., and
Bodas-Salcedo, A.: Physically consistent responses of the global atmospheric
hydrological cycle in models and observations, Surv. Geophys., 35,
533–552, 10.1007/s10712-012-9213-z, 2014.Allen, M. R. and Ingram, W. J.: Constraints on future changes in climate
and the hydrologic cycle, Nature, 419, 224–232, 10.1038/nature01092, 2002.Andrews, T., Forster, P. M., and Gregory, J. M.: A surface energy perspective
on climate change, J. Climate, 22, 2570–2557, 10.1175/2008JCLI2759.1, 2009.Andrews, T., Forster, P. M., Boucher, O., Bellouin, N., and Jones, A.:
Precipitation, radiative forcing and global temperature change, Geophys.
Res. Lett., 37, L14701, 10.1029/2010gl043991, 2010.Azar, C. and Johansson, D. J. A.: On the relationship between metrics to
compare greenhouse gases – the case of IGTP, GWP and SGTP, Earth Syst. Dynam.,
3, 139–147, 10.5194/esd-3-139-2012, 2012.Boucher, O. and Reddy, M. S.: Climate trade-off between black carbon and
carbon dioxide emissions, Energy Policy, 36, 193–200, 10.1016/j.enpol.2007.08.039, 2008.
Collins, M., Knutti, R., Arblaster, J., Dufresne, J.-L., Fichefet, T.,
Friedlingstein, P., Gao, X., Gutowski, W. J., Johns, T., Krinner, G.,
Shongwe, M., Tebaldi, C., Weaver, A. J., and Wehner, M.: Long-term Climate
Change: Projections, Commitments and Irreversibility, in: Climate Change
2013: The Physical Science Basis, Contribution of Working Group I to the
Fifth Assessment Report of the Intergovernmental Panel on Climate Change,
edited by: Stocker, T. F., Qin, D., Plattner, G. K., Tignor, M., Allen, S.
K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M.,
Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 659–740, 2013.Collins, W. J., Fry, M. M., Yu, H., Fuglestvedt, J. S., Shindell, D. T., and
West, J. J.: Global and regional temperature-change potentials for near-term
climate forcers, Atmos. Chem. Phys., 13, 2471–2485, 10.5194/acp-13-2471-2013, 2013.Deuber, O., Luderer, G., and Sausen, R.: CO2 equivalences for
short-lived climate forcers, Climatic Change, 122, 651–664, 10.1007/s10584-013-1014-y, 2014.Fuglestvedt, J. S., Shine, K. P., Berntsen, T., Cook, J., Lee, D. S.,
Stenke, A., Skeie, R. B., Velders, G. J. M., and Waitz, I. A.: Transport
impacts on atmosphere and climate: Metrics, Atmos. Environ., 44, 4648–4677,
10.1016/j.atmosenv.2009.04.044, 2010.Gillett, N. P. and Matthews, H. D.: Accounting for carbon cycle feedbacks
in a comparison of the global warming effects of greenhouse gases,
Environ. Res. Lett., 5, 034011, 10.1088/1748-9326/5/3/034011, 2010.Good, P., Ingram, W., Lambert, F. H., Lowe, J. A., Gregory, J. M., Webb, M.
J., Ringer, M. A., and Wu, P. L.: A step-response approach for predicting
and understanding non-linear precipitation changes, Clim. Dynam., 39,
2789–2803, 10.1007/s00382-012-1571-1, 2012.Held, I. M. and Soden, B. J.: Robust responses of the hydrological cycle to
global warming, J. Climate, 19, 5686–5699, 10.1175/jcli3990.1, 2006.Huffman, G. J., Adler, R. F., Bolvin, D. T., and Gu, G. J.: Improving the
global precipitation record: GPCP Version 2.1, Geophys. Res. Lett.,
36, L17808, 10.1029/2009gl040000, 2009.
IPCC: Climate Change 2013: The Physical Science Basis, Contribution of
Working Group I to the Fifth Assessment Report of the Intergovernmental
Panel on Climate Change, Cambridge University Press, Cambridge, UK
and New York, NY, USA, 1535 pp., 2013.Johansson, D. J. A.: Economics- and physical-based metrics for comparing
greenhouse gases, Climatic Change, 110, 123–141, 10.1007/s10584-011-0072-2, 2012.Joos, F., Roth, R., Fuglestvedt, J. S., Peters, G. P., Enting, I. G., von
Bloh, W., Brovkin, V., Burke, E. J., Eby, M., Edwards, N. R., Friedrich, T.,
Frölicher, T. L., Halloran, P. R., Holden, P. B., Jones, C., Kleinen,
T., Mackenzie, F. T., Matsumoto, K., Meinshausen, M., Plattner, G.-K.,
Reisinger, A., Segschneider, J., Shaffer, G., Steinacher, M., Strassmann,
K., Tanaka, K., Timmermann, A., and Weaver, A. J.: Carbon dioxide and
climate impulse response functions for the computation of greenhouse gas
metrics: a multi-model analysis, Atmos. Chem. Phys., 13, 2793–2825,
10.5194/acp-13-2793-2013, 2013.Knutti, R. and Sendláček, J.: Robustness and uncertainties in the
new CMIP5 climate model projections, Nat. Clim. Change, 3, 369–373,
10.1038/nclimate1716, 2013.Kvalevåg, M. M., Samset, B. H., and Myhre, G.: Hydrological sensitivity to
greenhouse gases and aerosols in a global climate model, Geophys.
Res. Lett., 40, 1432–1438, 10.1002/grl.50318, 2013.Lambert, F. H. and Webb, M. J.: Dependency of global mean precipitation on
surface temperature, Geophys. Res. Lett., 35, L16706, 10.1029/2008gl034838, 2008.Liu, C. L. and Allan, R. P.: Observed and simulated precipitation responses
in wet and dry regions 1850–2100, Environ. Res. Lett., 8, 034002,
10.1088/1748-9326/8/3/034002, 2013.Ming, Y., Ramaswamy, V., and Persad, G.: Two opposing effects of absorbing
aerosols on global-mean precipitation, Geophys. Res. Lett., 37, L13701,
10.1029/2010gl042895, 2010.Mitchell, J. F. B., Wilson, C. A., and Cunnington, W. M.: On CO2
climate sensitivity and model dependence of results, Q. J.
Roy. Meteorol. Soc., 113, 293–322, 10.1002/qj.49711347517, 1987.
Myhre, G., Shindell, D., Bréon, F.-M., Collins, W., Fuglestvedt, J., Huang,
J., Koch, D., Lamarque, J.-F., Lee, D., Mendoza, B., Nakajima, T., Robock,
A., Stephens, G., Takemura, T., and Zhang, H.: Anthropogenic and Natural
Radiative Forcing, in: Climate Change 2013: The Physical Science Basis,
Contribution of Working Group I to the Fifth Assessment Report of the
Intergovernmental Panel on Climate Change, edited by: Stocker, T. F., Qin,
D., Plattner, G. K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A.,
Xia, Y., Bex, V., and Midgley, P. M., Cambridge University Press, Cambridge,
UK and New York, NY, USA, 659–740, 2013.O'Gorman, P. A., Allan, R. P., Byrne, M. P., and Previdi, M.: Energetic
constraints on precipitation under climate change, Surv. Geophys.,
33, 585–608, 10.1007/s10712-011-9159-6, 2012.Olivié, D. J. L. and Peters, G. P.: Variation in emission metrics due to
variation in CO2 and temperature impulse response functions, Earth
Syst. Dynam., 4, 267–286, 10.5194/esd-4-267-2013, 2013.Olivié, D. J. L., Peters, G. P., and Saint-Martin, D.: Atmosphere response
time scales estimated from AOGCM experiments, J. Climate, 25, 7956–7972,
10.1175/jcli-d-11-00475.1, 2012.Peters, G. P., Aamaas, B., Berntsen, T., and Fuglestvedt, J. S.: The
integrated global temperature change potential (iGTP) and relationships
between emission metrics, Environ. Res. Lett., 6, 044021, 10.1088/1748-9326/6/4/044021, 2011.Pierrehumbert, R. T.: Short-lived climate pollution, Ann. Rev. Earth
Planet. Sci., 42, 341–379, 10.1146/annurev-earth-060313-054843, 2014.Previdi, M.: Radiative feedbacks on global precipitation, Environ.
Res. Lett., 5, 025211, 10.1088/1748-9326/5/2/025211, 2010.Reisinger, A., Havlik, P., Riahi, K., van Vliet, O., Obersteiner, M., and
Herrero, M.: Implications of alternative metrics for global mitigation costs
and greenhouse gas emissions from agriculture, Climatic Change, 117,
677–690, 10.1007/s10584-012-0593-3, 2013.
Shindell, D. T.: Evaluation of the absolute regional temperature potential,
Atmos. Chem. Phys., 12, 7955–7960, 10.5194/acp-12-7955-2012, 2012.Shindell, D. T., Voulgarakis, A., Faluvegi, G., and Milly, G.: Precipitation
response to regional radiative forcing, Atmos. Chem. Phys., 12, 6969–6982,
10.5194/acp-12-6969-2012, 2012.Shine, K. P. Fuglestvedt, J. S., Hailemariam, K., and Stuber, N.:
Alternatives to the global warming potential for comparing climate impacts
of emissions of greenhouse gases, Climatic Change, 68, 281–302,
10.1007/s10584-005-1146-9, 2005.Shine, K. P., Berntsen, T. K., Fuglestvedt, J. S., Skeie, R. B., and Stuber,
N.: Comparing the climate effect of emissions of short- and long-lived
climate agents, Philos. T. Roy. Soc. A, 365, 1903–1914, 10.1098/rsta.2007.2050, 2007.Sterner, E., Johansson, D. A., and Azar, C.: Emission metrics and sea level
rise, Climatic Change, 127, 335–351, 10.1007/s10584-014-1258-1, 2014.Strefler, J., Luderer, G., Aboumahboub, T., and Kriegler, E.: Economic
impacts of alternative greenhouse gas emission metrics: a model-based
assessment, Climatic Change, 125, 319–331, 10.1007/s10584-014-1188-y, 2014.Takahashi, K.: The global hydrological cycle and atmospheric shortwave
absorption in climate models under CO2 forcing, J. Climate, 22, 5667–5675,
10.1175/2009jcli2674.1, 2009.Tanaka, K., O'Neill, B. C., Rokityanskiy, D., Obersteiner, M., and Tol,
R. S. J.: Evaluating global warming potentials with historical temperature,
Climatic Change, 96, 443–466, 10.1007/s10584-009-9566-6, 2009.Thorpe, L. and Andrews, T.: The physical drivers of historical and
21st century global precipitation changes, Environ. Res. Lett., 9, 064024,
10.1088/1748-9326/9/6/064024, 2014.Tol, R. S. J., Berntsen, T. K., O'Neill, B. C., Fuglestvedt, J. S., and
Shine, K. P.: A unifying framework for metrics for aggregating the climate
effect of different emissions, Environ. Res. Lett., 7, 044006, 10.1088/1748-9326/7/4/044006, 2012.