Metrics for linking emissions of gases and aerosols to global precipitation changes

. 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 (GPP P ) and sustained (GPP S ) 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 GPP P and GPP S 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 CO 2 , these two terms oppose each other – as the forcing and temperature perturbations have different timescales, even the sign of the absolute GPP P and GPP S varies with time, and the opposing terms can make values sensitive to uncertainties in


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 Precipitationchange 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 CO 2 -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 regionalscale 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-CO 2 greenhouse gases on a so-called "CO 2 -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).
Earth Syst.Dynam., 6, 525-540, 2015 www.earth-syst-dynam.net/6/525/2015/ 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 CO 2 .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.

Relationships 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 CO 2 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 globalmean atmospheric energy budget, whereby the net emission of radiation by the atmosphere (i.e., the atmospheric radiative divergence (R d ), 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 (1) LH is directly related to the precipitation as, at the globalmean 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, R d will change.The latent heat change LH can then be written (2) LH 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 × 10 6 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).
R d 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 (RF s ) and an atmospheric component (RF a ), and it is RF a that directly influences R d .Because values of RF are more readily available than RF a for a wide range of constituents, it is convenient to relate RF a to RF and so, following Allan et al. (2014), we define a parameter f such that RF a = 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 f are 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 R d 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 R d via the absorption of shortwave radiation.Climate model simulations indicate that this component of R d varies approximately linearly with changes in global-mean surface temperature T s (e.g., Lambert and Webb, 2008;Previdi, 2010;O'Gorman et al., 2012).
SH 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 LH for a doubling of CO 2 , 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 LH 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 R d for the whole atmosphere and R d for the atmosphere above the surface boundary layer; changes in R d 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 SH 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 SH has a similar dependency on T s (at least in the multi-model mean) as R d .Hence it is convenient to combine the T s -related changes in R d and this component of SH in Eq. ( 2) into a single term dependent on T s and separate out the RF term.Equation (2) then becomes, in precipitation units of mm day −1 , (3) 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 k T s term as the "T term" and the −f RF 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 T s from two different forcing agents can result in a different P .
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 R d 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 RF a ) 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 CO 2
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 andThorpe andAndrews, 2014), RF 2×CO 2 = 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 P 2×CO 2 (in %, assuming a global-mean precipitation of 2.68 mm day −1 ), can then be written in terms of the equilibrium surface temperature change T 2×CO 2 as This equation shows that if λ of 0.36 K (W m −2 ) −1 , P 2×CO 2 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-CO 2 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 , RF 2×CO 2 assumed here, or in intermodel differences in the importance of the fast component of SH 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).
(3) can also be written in a more general form for any T eq (and hence RF eq ), so that the equilibrium change in precipitation P eq (in %) is given by (5) 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 CO 2 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 ( P eq / T eq ) to CO 2 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 (AGPP P ), which is presented here in units of mm day −1 kg −1 .The T term in Eq. (3) becomes k times the absolute GTP P (AGTP P ) (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 τ x , then for a unit emission, the RF term is given by −f x A x exp(−H /τ x ), where A x 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 Since a perturbation of CO 2 does not decay following a simple exponential (see e.g., Joos et al., 2013), the calculation of AGPP CO 2 P (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 (AGPP S ).In this case, the AGTP S (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 AGPP S is given by which can also be expressed as a function of both AGTP S and AGWP as The calculation of AGPP CO 2 S (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 AGTP x S (H ) can itself be related to the AGWP x P (H ) (see e.g., Shine et al., 2005) which would simplify Eq. ( 8) further.
Here the AGPP P and AGPP S are used to calculate the GPP P and GPP S relative to a reference gas, and following common practice for GWP and GTP, CO 2 is used as that reference gas here, although difficulties with this choice will be noted.The GPP P , relative to an equal mass emission of CO 2 , is then given by with a similar expression for GPP S .
Note we have chosen to present the AGPP P and AGPP S 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 AGPP S and GPP S can equally be interpreted as time-integrated forms of the AGPP P and GPP P .
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 CH 4 and N 2 O 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 AGPP P for CO 2 , CH 4 and N 2 O, 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 CO 2 (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-theatmosphere forcing than it does for CO 2 .Since N 2 O has a similar atmospheric opacity to CH 4 , it is hypothesized that surface-atmosphere partitioning of the RF also behaves in a similar way to CH 4 and so the value of f for N 2 O 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 CO 2 than for CH 4 and N 2 O.
Figure 1a for CO 2 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 CO 2 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.
N 2 O has a lifetime of the order of a century and its AGPP P (Fig. 1b) is qualitatively similar to CO 2 but the T term dominates, because f is smaller.As CH 4 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 AGPP P is determined by the T term only.3) respectively, and the Total is the sum of these.

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-ofthe-atmosphere forcing reaches the surface.By contrast, Andrews et al. ( 2010) find that for BC, f is 2.5, so that RF a is much greater than RF; the surface forcing is of opposite sign to RF and RF a 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 AGPP P 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 sustainedemissions 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 AGPP S for CO 2 , BC and sulphate.For CO 2 , the long timescales of the CO 2 perturbation mean that both the RF term and T term increase through-Earth Syst.Dynam., 6, 525-540, 2015 www.earth-syst-dynam.net/6/525/2015/  3) is negligible for such short-lived gases, except at time horizons less than a few weeks, and only the total is shown.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.
out 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 AGPP S 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.

The GPP relative to CO 2
Absolute GPP values were presented in Sect. 4. In this section we normalize the GPP values to the effects of the reference gas CO 2 to provide a relative measure, using Eq. ( 9) and its equivalent for sustained emissions.

Well-mixed greenhouse gases
Figure 4 shows the GPP P for N 2 O and CH 4 ; for comparison, the GTP P is also shown.Note that the plots start at H = 20 years, as the time at which the AGPP P crosses the zero axis differs slightly amongst the gases, and this results in a singularity in Eq. ( 9).For N 2 O, the GPP P is at least 300 times greater than CO 2 on all timescales shown, and, per unit emission, is more than 40 % more effective at changing precipitation than temperature (as given by the GTP P ), compared to CO 2 .This is because the RF term is less effective at muting the T term for N 2 O's GPP P than is the case for CO 2 .For CH 4 the difference between the GPP P and GTP P is most marked in an absolute sense at shorter time horizons, when the GPP P of methane is affected most by the RF term; the GPP P and the absolute difference with the GTP decline at longer timescales when it is entirely due to the difference between the AGTP P and AGPP P for CO 2 .Table 1 presents the values of all absolute metrics used here for CO 2 and Table 2 presents the values of the GWP, GTP P and GPP P 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 CH 4 , the GPP P (20) is 50 % larger than the GWP P (20) and almost double the GTP P (20) mostly because of the larger effect of the RF term on the AGPP P for CO 2 .The time-integrated nature of the GWP means that it is much higher than the GTP P and GPP P at 100 years, while the GPP P remains about double the GTP P .The GPP P for N 2 O is 25-50 % higher than the GWP and GTP P at both values of H , again because of the larger effect of the RF term on the AGPP P for CO 2 .2010) and Kvalevåg et al. (2013), respectively (see Table A1).
Because of this, in Fig. 5, the only difference between the GPP P and GTP P comes from the influence of the RF term on AGPP CO 2 P , and on an equal emissions basis both shortlived species are, relative to CO 2 , more effective at changing precipitation than temperature -this is also shown in Table 2.
Figure 6 shows the GPP S , comparing it with the GTP S .For sulphate, the difference between the GPP S and GTP S originates entirely from the effect of the RF term on AGPP CO 2 S , because of the assumption that f is zero.For BC they differ dramatically -whilst both BC and CO 2 cause a warming, so that GTP S is positive, their impact on precipitation is opposite, and the BC GPP S is negative.
Table 3 presents values of the GTP S and GPP S for H = 20 and 100 years, including the values for CH 4 and N 2 O for completeness.The GPP S values at 20 years are particularly influenced by the fact that the AGPP S for CO 2 is relatively small at this time, due to the strong cancellation between the T and RF terms.At both values of H , GPP S values are higher in magnitude than the corresponding GTP S values for all non-CO 2 components considered here.

Precipitation response to realistic emissions
To illustrate a further usage of the AGPP P and AGPP S , Figs.A1.For reference, the corresponding values using the AGTP P and AGTP S 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 CH 4 , sulphate and BC are 2 to 4 orders of magnitude smaller than those of CO 2 , in the early years after the emission, their effects are competitive with CO 2 because of the size of the GPP P and GTP P ; emissions of N 2 O are small enough that, despite its large GPP P , its absolute contribution remains low throughout.Because of the differing compensations between the T and RF terms for CO 2 and CH 4 , 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 CO 2 until about 20 years; it exceeds the CO 2 contribution by a factor of 2 at about 10 years, and remains 25 % of the CO 2 effect even at 50 years.For temperature, the contributions are approximately the same until 10 years, after which the CO 2 contribution dominates, being about 7 times larger by 50 years.For the two aerosol components, the GPP P is unaffected by Table 3.The GTP S and GPP S , relative to CO 2 , 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 CO 2 are given in Table 1. 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 CO 2 is enhanced, because the RF term acts to suppress the effect of CO 2 on precipitation change.Thus, for example, the BC effect on precipitation is larger than CO 2 out to year 10, compared to year 4 for temperature.
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 AGPP S values, the role of the shortlived 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 CH 4 and CO 2 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 rewww.earth-syst-dynam.net/6/525/2015/Earth Syst.Dynam., 6, 525-540, 2015 Table 4.The GPP P and GPP S , relative to CO 2 , 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 CO 2 are given in Table 1.
GPP P (20) GPP P (100) GPP S (20) GPP S ( 100 sults 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 CH 4 .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 CO 2 .This differs from temperature, where the CO 2 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 GPP P and GPP S values.

Sensitivities and uncertainties
There are many uncertainties and sensitivities in the calculation of metrics such as assumptions about the background state (which can affect A x and τ x ), and the impulse response function for CO 2 (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 de- (a) AGTP and AGPP for carbon dioxide, for both pulse and sustained emissions, and then GTP P , GPP P , GTP S and AGPP S for (b) methane, (c) nitrous oxide, (d) sulphate and (e) black carbon.For CO 2 the units are 10 −16 K kg −1 for AGTP P , 10 −14 K kg −1 yr for AGTP S , 10 −18 mm day −1 kg −1 for AGPP P and 10 −16 mm day −1 kg −1 yr for AGPP S .The AGPP S for all other gases are in 10 −15 mm day −1 kg −1 yr.viation of the pulse and sustained GTP and GPP derived using these 18 different representations.
Considering the absolute pulse metrics for CO 2 , Fig. 9a shows that the AGTP P 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 AGPP P (20) and AGPP P (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 GTP P is most sensitive for short-lived species and this uncertainty is amplified for the GPP P , by up to a factor of 2 for the GPP P (100) for sulphate (Fig. 9d).By con-Earth Syst.Dynam., 6, 525-540, 2015 www.earth-syst-dynam.net/6/525/2015/trast, for the longer-lived species the uncertainty in the GTP P and GPP P differ greatly -for N 2 O (Fig. 9c), the cv for GTP P values is only a percent or so, but is typically 40 % for the GPP P , 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 GPP S is more sensitive because even the sign of the AGPP CO 2 S 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 AGPP CO 2 S is zero varies from 11 to 61 years amongst the models.(For comparison, for the AGPP CO 2 P , the corresponding range is 4 to 13 years.)In these circumstances, it becomes difficult to compare the GPP S values as they vary wildly from model to model (from −18 000 to 24 000 for the GPP S (20) for N 2 O) and for this reason the AGPP S is presented in Fig. 9.Even the AGPP CO 2 S (100) values vary by over an order of magnitude across the 18 models.In general, the uncertainties in the AGPP S exceed those in the AGTP S ; this is most marked in the case of N 2 O, where the GTP S is almost insensitive to the choice of impulse response model, as the effect of this choice on the AGTP S for CO 2 and N 2 O 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 f from 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 modelderived 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 RF a is large and positive.This is an example of where casting Eq. ( 3) directly in terms of RF a 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 τ x and A x .
Table 1 shows the AGPP P and AGPP S for CO 2 and Table 4 shows the GPP P and GPP S ; these should be compared with the appropriate columns in Tables 2 and 3 (the GWP, GTP P and GTP S are unaffected by f ).For the GPP P for CH 4 and N 2 O, 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 AGPP CO 2 P , as the change in f factor has little influence (see Sect. 4.2) and hence changes are correspondingly larger (20-30 %).The AGPP CO 2 S (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 GPP S (20) for N 2 O and CH 4 decrease by about a factor of 2. The changes at 100 years are much smaller, nearer 10 %.The AGPP S for the short-lived species are, unlike the AGPP P , now affected by the change in f .Table 5 shows the effect on the sulphate GPP S (20) to be about a factor of 2, while the GPP S (100) is little affected.By contrast, the GPP S 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 GPP P and GPP S 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 GPP P and GPP S 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 GPP S can also be interpreted as the time-integrated GPP P .
It has been shown that relative to CO 2 , the pulse and sustained GPP values for the non-CO 2 species examined here are larger than the corresponding GTP values, because the CO 2 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 shortlived 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 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 CO 2 as a reference gas.For precipitation change, the forcing and surface temperature components oppose each other, which means that the effect of CO 2 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 CO 2 for about 50 years, By contrast, for temperature, the effect of CO 2 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 shortlived 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.

Figure 1 .
Figure 1.AGPP P for 1 kg pulse emissions of CO 2 , N 2 O and CH 4 .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.

Figure 2 .
Figure 2. AGPP P 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.

Figure 3 .
Figure 3. AGPP S for 1 kg yr −1 sustained emissions of CO 2 , 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.

Figure 4 .
Figure 4. GPP P (in bold) and GTP P for 1 kg pulse emissions of N 2 O and CH 4 relative to a 1 kg pulse emission of CO 2 .

Figure 5
Figure5shows the GPP P and GTP P for BC and sulphate.As noted in Sect.4.2, the radical difference in their values of f

Figure 5 .
Figure 5. GPP P (in bold) and GTP P for 1 kg pulse emissions of BC and sulphate relative to a 1 kg pulse emission of CO 2 .

Figure 6 .
Figure 6.GPP S (in bold) and GTP S for 1 kg yr −1 sustained emissions of BC and sulphate relative to a 1 kg yr −1 sustained emission of CO 2 .

Figure 7 .
Figure 7. 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 AGPP P and AGTP P and using estimated emissions of the species in 2008.
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 AGTP P 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

GTPFigure 8 .
Figure 8. 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 AGPP S and AGTP S and using estimated emissions of the species in 2008.

Figure 9 .
Figure 9. 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 GTP P , GPP P , GTP S and AGPP S for (b) methane, (c) nitrous oxide, (d) sulphate and (e) black carbon.For CO 2 the units are 10 −16 K kg −1 for AGTP P , 10 −14 K kg −1 yr for AGTP S , 10 −18 mm day −1 kg −1 for AGPP P and 10 −16 mm day −1 kg −1 yr for AGPP S .The AGPP S for all other gases are in 10 −15 mm day −1 kg −1 yr.

Table 2 .
The GWP, GTP P and GPP P , relative to CO 2 , 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 CO 2 are given in Table1.GWP (20) GWP (100) GTP P (20) GTP P (100) GPP P (20) GPP P (100) 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/)shouldprovide 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 RF a (rather than top-of-atmosphere radiative forcing) would be desirable if values of RF a become more readily available.