Radiative Forcing and Climate Sensitivity
Radiative Forcing and Climate Sensitivity Prof. Dr. K. Pfeilsticker Institut für Umweltphysik Universität Heidelberg INF 229 69120 Heidelberg (Feb. 3, 2011)
Outline: 1.) Introduction 2.) Radiative forcing, climate sensitivity, heat capacity and response times 3.) Distribution of additional forcing 4.) Climate sensitivity for CO2 doubling 5.) The IPCC 2007 consensus 6.) Summary&conclusions
Klaus Pfeilsticker
RF and climate sensitivity: Adjustment to a new climate state The concept of RF, feedbacks and climate sensitivity (S = 1/λs). (a) A change in a radiatively active agent causes an instantaneous (RF). (b) The standard definition of RF includes the relatively fast stratospheric adjustments, with the troposphere kept fixed. (c) Non-radiative effects in the troposphere (for example of CO2 heating rates on clouds and aerosol semidirect and indirect effects) occurring on similar time scales can be considered as fast feedbacks or as a forcing.
Instantaneous forcing
feedbacks
feedbacks
(d–f) During the transient climate change phase (d), the forcing is balanced by ocean heat uptake and increased long-wave radiation emitted from a warmer surface, with feedbacks determining the Ts until equilibrium is reached with a constant forcing (e, f). The equilibrium depends on whether additional slow feedbacks (for example ice sheets or vegetation) with their own intrinsic timescale are kept fixed (e) or are allowed to change (f). (Knutti&Hegerl; Nature Geoscience , 735, 1, 2008.) Klaus Pfeilsticker
RF and climate sensitivity We first define the climate sensitivity λ:
λ=
ΔTsurface
ΔEtropopause
=
S
−1
Climate modelling indicate that for a variety of radiative forcings the climate sensitivity λs = 0.76±0.3 K/(W/m2 (IPCC 2007, see next transparency). We recall that in radiative equilibrium the incoming solar radiation should equal outgoing longwave radiation, i.e. 4 S o ⋅ (1 − A) = σ ⋅ T ⋅ (1 − B ) s 4
If this equilibrium is disturbed an amount RF, then we need to inspect the equation 4 S o ⋅ (1 − A) − σ ⋅ T ⋅ (1 − B ) = RF s 4
for λo = ∂Ts/∂E. We obtain for climate sensitivity λo without feedbacks, i.e (A≠A(Ts) and B≠B(Ts)): Ts ∂Ts 1
λo =
∂E
=
4 ⋅ S o ⋅ (1 − A)
=
4 ⋅ σ ⋅ Ts (1 − B) 3
= 0 .3
K
(W m2)
By comparing λo with λ, we see that the gain (G) in climate sensitivity due to feedbacks is:
G≡ Klaus Pfeilsticker
λs
λo (= 2.5)
RF, climate sensitivity, heat capacity&climate response times In the lecture radiative transfer, we defined the climate sensitivity as λ = ∂Ts/ ∂E. Now we are interested on how disturbance of size E affect the RT equilibrium.. We note that the disturbance E may become visible by a change in heat content ΔH (stored in the oceans, land masses, ice shields, ...) of the climate system, i.e. 4 ∂T ∂H S o ⋅ (1 − A(t )) = − σ ⋅ T ⋅ (1 − B (t )) = C ⋅ s s ∂t 4 ∂t
(1)
where C is the heat capacity and ∂Ts/∂t the rate of Ts within the climate system. The heat capacity C of the climate system can be inferred from either inspecting
C=
∂H ∂t
∂Ts ∂t
or
C=
∂H ∂Ts
The climate system‘s heat capacity C = (0.1 - 2.05) GJ/K·m2, mean 0.53±0.22 GJ/K·m2, (e.g. Levitus et al, 2005) is due to the heating of 1. 2. 3. 4.
the upper layer of the ocean, 86% the continental land masses, 5%; melting of continental glaciers, 5%, and heating of the atmosphere, 4% Klaus Pfeilsticker
Time series of global ocean ΔH, and ΔTs. ΔH (L300, L700, and L3000) are from Levitus et al. [2005] for ocean depths from the surface to 300, 700, and 3000 m, respectively (Schwartz, JGR, 2008).
The oceanic heat content The oceanic heat contents has been measured/inferred from (1) bathythermographs (XBTs) dropped from ships along their tracks since the early 40th past century (2) ARGO floats since 2003 see http://www.argo.ucsd.edu/ (3) from the contribution of the thermal expansion to the observed sea level rise since 1992, e.g., see http://www.ipcc.ch/ipccreports/tar/wg1/412.htm Latest research (Lyman et al., Nature, 465, 334, 2010) indicate that a statistically significant linear warming trend for 1993–2008 of 0.64 W/m2 (or 1022 J/yr calculated for the Earth’s entire surface area), with a 90 % confidence interval of 0.53–0.75 W/m2 (Trenberth et al., Nature, 465, 304, 2010). This is roughly double the amount, than suggested by RT calculations (see next transparency)
RF and climate sensitivity: Where is the RF energy gone since 1950?
Cumulative energy budget for the Earth since 1950. (a) Mostly positive and mostly longlived forcing agents from 1950 through 2004. (b) The positive forcings have been balanced by stratospheric aerosols, direct and indirect aerosol forcing, increased outgoing radiation from a warming Earth and the amount remaining to heat the Earth. The aerosol direct and indirect effects portion is a residual after computing all other terms (Murphy et al., 114, D17107, 2009). Klaus Pfeilsticker
RF, climate sensitivity, heat capacity&climate response times A disturbance E = Δ(So· (1 - A) /4 - σ · Ts4 ·(1 - B)) may finally lead the climate to relax into a new state or temperature Ts, which in the linear (causeÆ response) regime is:
ΔTs (∞) = λs ⋅ E For a step-like disturbance (Heaviside function) we readly obtain
ΔTs (t ) = ΔTs (∞) ⋅ [1 − exp(− t )] = λs ⋅ E ⋅ [1 − exp(− t )]
τ
τ
where the time constant τ is related to the heat capacity C and climate sensitivity λs by
ΔTs =
τ ⋅E C
⇒
τ = λs ⋅ C
Assuming an autocorrelation process for climate adaption due to an RF – which itself is problematic (Knutti et al., 2008; Scafetta, 2008; Foster et al. 2008) - by which the climate system eventually reacts on a disturbance RF, Schwartz (2008) arrived at τ = 8.5 ± 2.5 yrs. This would imply a λs = 0.51 ± 0.26 K/W/m2, which is at the lower end λs as compiled by the IPCC report 2007. Recalling that the climate sensitivity without feedbacks (A≠A(Ts) and B≠B(Ts)) is λo = 0.3 K/(W/m2) or including feedbacks (A=A(Ts) and B=B(Ts)) λs = 0.76±0.3 K/(W/m2), we arrive at τ = 12.77 ± 3.8 yrs or G = end λs/ λo =2.5. However, a closer inspection casts doubts as to whether the climate system has a unique time constant τ to adapt to a disturbance RF. In fact climate models indicate time constances ranging from days (stratospheric radiation balance), months to years (atmospheric temperature lapse rate), over decades (oceanic heat balance, and adaption of the biosphere) to thousands of years (change in thermohaline circulation to the ice coverage) (see next slide). In fact for an horizan relevant for our civilization, AOGCMs reveals a time constant on the order of τ ~50 yrs, or even larger(e.g., Hansen, 2005). Klaus Pfeilsticker
RF and climate sensitivity: Adjustment to a new climate state The concept of RF, feedbacks and climate sensitivity (S = 1/λs). (a) A change in a radiatively active agent causes an instantaneous (RF). (b) The standard definition of RF includes the relatively fast stratospheric adjustments, with the troposphere kept fixed. (c) Non-radiative effects in the troposphere (for example of CO2 heating rates on clouds and aerosol semidirect and indirect effects) occurring on similar time scales can be considered as fast feedbacks or as a forcing.
Instantaneous forcing
feedbacks
feedbacks
(d–f) During the transient climate change phase (d), the forcing is balanced by ocean heat uptake and increased long-wave radiation emitted from a warmer surface, with feedbacks determining the Ts until equilibrium is reached with a constant forcing (e, f). The equilibrium depends on whether additional slow feedbacks (for example ice sheets or vegetation) with their own intrinsic timescale are kept fixed (e) or are allowed to change (f). (Knutti&Hegerl; Nature Geoscience , 735, 1, 2008.) Klaus Pfeilsticker
RF, climate sensitivity, heat capacity&climate response times Next we may ask ourself, whether we can further get some insights into the gain factor, G = λs/ λo. Starting with the definition of the climate sensitivity
λ=
dTs dE
and allowing the albedos A and B to feedback with Ts, i.e. A=A(Ts) and B=B(Ts)), we get
Ts = Ts ( E , E[ A(Ts )], E[ B(Ts )]) For simplicity we consider the inverse function E(Ts) and the identity dTs/dE = (dE/dTs)-1:
E = (Ts , Ts ( A), Ts ( B)) ∂T ∂T dT ∂E ∂E ∂Ts ∂E ∂Ts −1 λs = s = ( + ⋅ + ⋅ ) = λo ⋅ (1 + s + s ) −1 dE ∂Ts ∂Ts ∂A ∂Ts ∂B ∂A ∂B
Accordingly the gain factor G is
G=
λs ∂T ∂T = 1 (1 + s + s ) ∂A ∂B λo
or by using the energy equilibrium equation (1) for A(Ts) and B(Ts), we obtain
G= Klaus Pfeilsticker
λs 1 ∂ ln A 1 ∂ ln B = 1 (1 + ⋅ − ⋅ ) 4 ∂ ln Ts 4 ∂ ln Ts λo
Climate sensitivity for a doubling of CO2 (280 ppm to 560 ppm) A doubling of CO2 causes an instantaneous radiative forcing of 3.7 W/m2. It translates into ΔTs =2.8 K warming depending on the study (see Figure). Hence λs = 2.8K/4.36 (W/m2) = 0.76±0.3 K/(W/m2) and G = 2.5.
Left figure: Cumulative distributions of climate sensitivity derived from observed 20th century warming (red), model climatology (blue), proxy evidence (cyan) and from AOGCMs (green) Right figure: Estimates of equilibrium global climate sensitivity and associated uncertainty from major national and international assessments [Charney et al., 1979; IPCC, 2007; for citations to earlier IPCC reports see IPCC, 2007]. Klaus Pfeilsticker
RF components as compiled by the recent IPCC report (2007)
AR4: www.ipcc.ch Applying λ (= 0.76±0.3 K/(W/m2) inferred from paleo-climate data or recent observational and modelling studies) to the present RF of 1.6 ±1 W/m2 leads to a warming of ΔTs (∞) = 1 ± 0.76 K. This compared well with the presently observed ΔTs = 0.7 K, when keeping in mind the time constant (τ) for the climate to adapt to a changed RF ! Klaus Pfeilsticker
Climate sensitivity on geological time scales (past 420 Ma) One may ask how atmospheric CO2 forced the climate in the past, and how sensitive the climate reacted on the CO2 forcing. For the modern Earth, Svante Arrhenius (1859 -1927) already predicted an equilibrium ΔTs =1.5 - 5 oC for 2·CO2. This result is well confirmed by recent climate models (most likely value + 2.8 oC) for the modern Earth. For the past Earth (past 420 Ma) a similar sensitivity (1.6 – 5.5 oC best estimate ΔTs =2.8 oC) can be inferred from paleo-proxis (18O, 13C, ....) even though many factors may have changed past 420 Ma (e.g., land/sea distribution, TSI, biosphere, Ca and Mg silicate weathering, ....) Comparison of CO2 calculated by the model GEOCARBSULF for varying Δ T(2*) to an independent CO2 record from proxies. For the GEOCARBSULF calculations (red, blue and green lines), standard parameters from GEOCARB11 and EOCARBSULF12 were used except for an activation energy for Ca and Mg silicate weathering of 42 kJ/mol. The proxy record (dashed white line) was compiled from 47 published studies using five independent methods (n = 490 data points). All curves are displayed in 10 Myr time-steps. The proxy error envelope (black)represents ±1 s.d. of each time-step. The GEOCARBSULF error envelope (yellow) is based on a combined sensitivity analysis (10% and 90% percentile levels) of four factors (weathering, δ13C river run-off used in the model (Royer et al., Nature, 446, 2007). Klaus Pfeilsticker
Climate sensitivity for CO2 doubling Distributions and ranges for climate sensitivity from different lines of evidence. (a) The most likely values (circles), likely (bars, more than 66% probability) and very likely (lines, more than 90% probability) ranges are subjective estimates by the authors based on the available distributions and uncertainty estimates from individual studies, taking into account the model structure, observations and statistical methods used. Values are typically uncertain by 0.5 °C. Dashed lines indicate no robust constraint on an upper bound. Distributions are truncated in the range 0–10 °C; most studies use uniform priors in climate sensitivity. Single extreme estimates or outliers (some not credible) are marked with crosses. The IPCC likely range and most likely value are indicated by the vertical grey bar and black line, respectively. (b) A partly subjective classification of the different lines of evidence for some important criteria. The overall level of scientific understanding (LOSU) indicates the confidence, understanding and robustness of an uncertainty estimate towards assumptions, data and models. Expert elicitation and combined constraints are difficult to assess; both should have a higher LOSU than single lines of evidence, but experts tend to be overconfident and the assumptions are often not clear. (Knutti&Hegerl; Nature Geoscience , 735, 1, 2008.)
Klaus Pfeilsticker
Intrinsic uncertainty of the climate sensitivity We saw that an increase/decrease in A with Ts causes a +/- feedback in the climate system. Conversely, an increase/decrease in B with Ts cause a -/+ feedback. These changes in A and B may happen e.g., due to a cloud feedback (simultaneous change in A and B) and/or water vapor feedback (change in B)….. Thus climate modeling must concentrate to understand well the changes in A and B by Ts, i.e. ∂A/∂Ts and ∂B/∂Ts . Next, we are interested how well climate can be predicted. We know that the instantaneous climate sensitivity is λo = 0.3 to 0.32 K/(W/m2) and λ = 0.76±0.3 K/(W/m2). In the linear regime (where the strengths of feedbacks are linear with respect to applied forcing), we define a feedback factor f as λ 1 ∂ ln A 1 ∂ ln B ) ≡ 1 G = s = 1 (1 + ⋅ − ⋅ 1− f 4 ∂ ln Ts 4 ∂ ln Ts λo 1 ∂ ln A 1 ∂ ln B ) f = (− ⋅ + ⋅ 4 ∂ ln Ts 4 ∂ ln Ts Climate modeling shows that for the CO2 doubling 0.41 ≤ f ≤ 0.73, or 1.7 ≤ G ≤ 3.7 (λ = 0.75±0.3 K/(W/m2)) or 2oC ≤ ΔT ≤ 4.5oC. Uncertainty in climate prediction (δG) can then best be expressed as δG ≈ 1 ⋅ σ (1 − f )
2
f
with f bar being the mean feedback factor and σf its standard deviation. Klaus Pfeilsticker
Intrinsic uncertainty of the climate sensitivity Uncertainty propagation can easily be demonstratated assuming a positive (+) feedback (ΔT=ΔT0/(1-f)) >0 and pdfs for f (hf(f)) and ΔT (hT(ΔT)). ΔT0 is the sensitivity in the absence of feedbacks. If the mean estimate of the total feedbacks is substantially +, any distribution in hf(f) will lead to a highly skewed distribution in ΔT. For the purposes of illustration, a normal distribution in hf(f) is shown with a mean of 0.65 and a σf = 0.13, typical to that obtained from feedback studies of GCMs. The dot-dashed lines represent 95% confidence intervals on the distributions. Note that values of f ≥ 1 imply an unphysical, catastrophic runaway feedback (Roe&Baker, Science, 318, 2007). Klaus Pfeilsticker
Intrinsic uncertainty of climate sensitivity Assuming that the errors in the feedback factors f are normaly distributed 2
h
f
(f)=
σ
1 (f−f) ⋅ exp(−0.5[ ) ] σf ⋅ 2π f
then because hT(ΔT)) is a function hf(f)), a Tayler expansion yields
ΔT ΔT0 df 0) Δ = Δ ⋅ = T f T ( ) ( ( )) ⋅ ( 1 − hf hf dΔT (ΔT ) 2 ⋅h f ΔT to the first approximation and hT(ΔT)) is
h
Klaus Pfeilsticker
f
(ΔT ) =
σ
ΔT ΔT 0 1 1 − f − 0 ⋅ ⋅ exp(−0.5 ⋅ ΔT ]2 ) 2 [ Δ T 2 π ⋅ f
σf
Intrinsic uncertainty of climate sensitivity Climate sensitivity distributions: (A) from Soden&Held, 2007 which calculated (f, σf) of (0.62, 0.13) from a suite of GCM simulations; (B) from Colman (2003), which found (f, σf) of (0.7, 0.14) from a different suite of models; and (C) from the ~5700-member multi ensemble climate prediction net (Stainforth et al., 2005 and Sanderson et al., 2007) for different choices of cloud processes. (D) Fit hT(ΔT)) to the result of Sanderson et al., (2007) which was found by estimating the mode of the probability density and its accompanying ΔT and solving for (f, σf ) from previous equations, which yielded values of (0.67, 0.12) (Roe&Baker, Science, 318, 2007). Klaus Pfeilsticker
Climate sensitivity distributions
Climate sensitivity estimates Climate sensitivity distributions from various studies with the use of a wide variety of methods (black lines) and overlain with a fits of hT(ΔT)) (green lines): (A) from Hegerl et al., (2006) (f, σf) = (0.58, 0.17) and (0.63, 0.21); (B) from Murphy et al., (2004) (f, σf) = (0.67, 0.10) and (0.60, 0.14); (C) Forest et al., (2002) (f, σf) = (0.64, 0.20) and (0.56, 0.16); (D) Andronova et al., (2001) (f, σf) = (0.82, 0.11), (0.65, 0.14), and (0.15, 0.28); (E) Gregory et al., (2002) (f, σf) = (0.86, 0.35) and (F) Royer et al., (2007) = (f, σf) (0.72, 0.17), (0.75, 0.19), and (0.77, 0.21).
Detailed studies show that, f and σf are in the range of (0.11, 0.06) vs (0.09, 0.02) for the albedo feedback (0.17, 0.11) vs (0.22, 0.12) for the cloud feedback and (0.42, 0.06) vs (0.31, 0.04) for the water vapor and lapse rate feedbacks combined (Colman, 2003) vs Soden&Held (2006). Accordingly, for the present climate G = 2.63±1.6, f = 0.62 ± 0.3, and λ = 0.789 ± 0.3 K/(W/m2. This compares well with λ = 0.76±0.3 K/(W/m2). Note that the largest uncertainty arise due to the cloud feedback (G = 1.3±0.19 and f = 0.22 ± 0.12). Klaus Pfeilsticker
Relative sensitivity of surface temperatures to changes in green house gases per unit atmospheric mass Ozone increase (absolute)
H2O increase (absolute)
Pressure (hPa)
Methane increase (absolute)
~25 km
Tropopause
~ 5 km
Radiative Forcing
Figure: Illustration of how the surface impact depends on altitude and latitude where the methane, ozone and water vapour changes take place. Shading show relative surface impact, measured as radiative forcing from a fixed mass increase applied to different altitudes. Red shows where the increase in gas led to maximum surface warming (courtesy P. Foster). 19
Conclusion: Take-home messages 1. 2.
3. 4. 5.
We have seen that the climate sensitivity, heat capacity of the climate system and relaxation time to disturbances are intimately tied. While the climate sensitivity for instantaneous forcing λo can straightforwardly be calculated (i.e. λo =0.3 K/(W/m2), the climate sensitivity including feedbacks (λs) is largely - and probably inherently - uncertain and largely dependent on the considered time scale. For political decision making, most important is the climate sensitivity acting on time scale of decades, i.e. λs = 0.76±0.3 K/(W/m2 (IPCC2007). This implies an expected temperature increase for CO2 doubling (E = 3.9 W/m2) of 3K with a 1 σ range of 1.79 - 4.2 K. Using the heat capacity of the climate system (C = 0.53±0.22 GJ/K·m2) accessible within decades, i.e. mixing of the upper oceanic layers, but excluding the deep oceanic turn-over or melting of the large ice shields, results in a relaxation time of 12.5 years (at least). ⇒ for more info see the lecturer notes under: http://www.iup.uni-heidelberg.de/institut/studium/
Klaus Pfeilsticker
Outline: 1.) Introduction 2.) Radiative forcing, climate sensitivity, heat capacity and response times 3.) Distribution of additional forcing 4.) Climate sensitivity for CO2 doubling 5.) The IPCC 2007 consensus 6.) Summary&conclusions
Klaus Pfeilsticker
RF and climate sensitivity: Adjustment to a new climate state The concept of RF, feedbacks and climate sensitivity (S = 1/λs). (a) A change in a radiatively active agent causes an instantaneous (RF). (b) The standard definition of RF includes the relatively fast stratospheric adjustments, with the troposphere kept fixed. (c) Non-radiative effects in the troposphere (for example of CO2 heating rates on clouds and aerosol semidirect and indirect effects) occurring on similar time scales can be considered as fast feedbacks or as a forcing.
Instantaneous forcing
feedbacks
feedbacks
(d–f) During the transient climate change phase (d), the forcing is balanced by ocean heat uptake and increased long-wave radiation emitted from a warmer surface, with feedbacks determining the Ts until equilibrium is reached with a constant forcing (e, f). The equilibrium depends on whether additional slow feedbacks (for example ice sheets or vegetation) with their own intrinsic timescale are kept fixed (e) or are allowed to change (f). (Knutti&Hegerl; Nature Geoscience , 735, 1, 2008.) Klaus Pfeilsticker
RF and climate sensitivity We first define the climate sensitivity λ:
λ=
ΔTsurface
ΔEtropopause
=
S
−1
Climate modelling indicate that for a variety of radiative forcings the climate sensitivity λs = 0.76±0.3 K/(W/m2 (IPCC 2007, see next transparency). We recall that in radiative equilibrium the incoming solar radiation should equal outgoing longwave radiation, i.e. 4 S o ⋅ (1 − A) = σ ⋅ T ⋅ (1 − B ) s 4
If this equilibrium is disturbed an amount RF, then we need to inspect the equation 4 S o ⋅ (1 − A) − σ ⋅ T ⋅ (1 − B ) = RF s 4
for λo = ∂Ts/∂E. We obtain for climate sensitivity λo without feedbacks, i.e (A≠A(Ts) and B≠B(Ts)): Ts ∂Ts 1
λo =
∂E
=
4 ⋅ S o ⋅ (1 − A)
=
4 ⋅ σ ⋅ Ts (1 − B) 3
= 0 .3
K
(W m2)
By comparing λo with λ, we see that the gain (G) in climate sensitivity due to feedbacks is:
G≡ Klaus Pfeilsticker
λs
λo (= 2.5)
RF, climate sensitivity, heat capacity&climate response times In the lecture radiative transfer, we defined the climate sensitivity as λ = ∂Ts/ ∂E. Now we are interested on how disturbance of size E affect the RT equilibrium.. We note that the disturbance E may become visible by a change in heat content ΔH (stored in the oceans, land masses, ice shields, ...) of the climate system, i.e. 4 ∂T ∂H S o ⋅ (1 − A(t )) = − σ ⋅ T ⋅ (1 − B (t )) = C ⋅ s s ∂t 4 ∂t
(1)
where C is the heat capacity and ∂Ts/∂t the rate of Ts within the climate system. The heat capacity C of the climate system can be inferred from either inspecting
C=
∂H ∂t
∂Ts ∂t
or
C=
∂H ∂Ts
The climate system‘s heat capacity C = (0.1 - 2.05) GJ/K·m2, mean 0.53±0.22 GJ/K·m2, (e.g. Levitus et al, 2005) is due to the heating of 1. 2. 3. 4.
the upper layer of the ocean, 86% the continental land masses, 5%; melting of continental glaciers, 5%, and heating of the atmosphere, 4% Klaus Pfeilsticker
Time series of global ocean ΔH, and ΔTs. ΔH (L300, L700, and L3000) are from Levitus et al. [2005] for ocean depths from the surface to 300, 700, and 3000 m, respectively (Schwartz, JGR, 2008).
The oceanic heat content The oceanic heat contents has been measured/inferred from (1) bathythermographs (XBTs) dropped from ships along their tracks since the early 40th past century (2) ARGO floats since 2003 see http://www.argo.ucsd.edu/ (3) from the contribution of the thermal expansion to the observed sea level rise since 1992, e.g., see http://www.ipcc.ch/ipccreports/tar/wg1/412.htm Latest research (Lyman et al., Nature, 465, 334, 2010) indicate that a statistically significant linear warming trend for 1993–2008 of 0.64 W/m2 (or 1022 J/yr calculated for the Earth’s entire surface area), with a 90 % confidence interval of 0.53–0.75 W/m2 (Trenberth et al., Nature, 465, 304, 2010). This is roughly double the amount, than suggested by RT calculations (see next transparency)
RF and climate sensitivity: Where is the RF energy gone since 1950?
Cumulative energy budget for the Earth since 1950. (a) Mostly positive and mostly longlived forcing agents from 1950 through 2004. (b) The positive forcings have been balanced by stratospheric aerosols, direct and indirect aerosol forcing, increased outgoing radiation from a warming Earth and the amount remaining to heat the Earth. The aerosol direct and indirect effects portion is a residual after computing all other terms (Murphy et al., 114, D17107, 2009). Klaus Pfeilsticker
RF, climate sensitivity, heat capacity&climate response times A disturbance E = Δ(So· (1 - A) /4 - σ · Ts4 ·(1 - B)) may finally lead the climate to relax into a new state or temperature Ts, which in the linear (causeÆ response) regime is:
ΔTs (∞) = λs ⋅ E For a step-like disturbance (Heaviside function) we readly obtain
ΔTs (t ) = ΔTs (∞) ⋅ [1 − exp(− t )] = λs ⋅ E ⋅ [1 − exp(− t )]
τ
τ
where the time constant τ is related to the heat capacity C and climate sensitivity λs by
ΔTs =
τ ⋅E C
⇒
τ = λs ⋅ C
Assuming an autocorrelation process for climate adaption due to an RF – which itself is problematic (Knutti et al., 2008; Scafetta, 2008; Foster et al. 2008) - by which the climate system eventually reacts on a disturbance RF, Schwartz (2008) arrived at τ = 8.5 ± 2.5 yrs. This would imply a λs = 0.51 ± 0.26 K/W/m2, which is at the lower end λs as compiled by the IPCC report 2007. Recalling that the climate sensitivity without feedbacks (A≠A(Ts) and B≠B(Ts)) is λo = 0.3 K/(W/m2) or including feedbacks (A=A(Ts) and B=B(Ts)) λs = 0.76±0.3 K/(W/m2), we arrive at τ = 12.77 ± 3.8 yrs or G = end λs/ λo =2.5. However, a closer inspection casts doubts as to whether the climate system has a unique time constant τ to adapt to a disturbance RF. In fact climate models indicate time constances ranging from days (stratospheric radiation balance), months to years (atmospheric temperature lapse rate), over decades (oceanic heat balance, and adaption of the biosphere) to thousands of years (change in thermohaline circulation to the ice coverage) (see next slide). In fact for an horizan relevant for our civilization, AOGCMs reveals a time constant on the order of τ ~50 yrs, or even larger(e.g., Hansen, 2005). Klaus Pfeilsticker
RF and climate sensitivity: Adjustment to a new climate state The concept of RF, feedbacks and climate sensitivity (S = 1/λs). (a) A change in a radiatively active agent causes an instantaneous (RF). (b) The standard definition of RF includes the relatively fast stratospheric adjustments, with the troposphere kept fixed. (c) Non-radiative effects in the troposphere (for example of CO2 heating rates on clouds and aerosol semidirect and indirect effects) occurring on similar time scales can be considered as fast feedbacks or as a forcing.
Instantaneous forcing
feedbacks
feedbacks
(d–f) During the transient climate change phase (d), the forcing is balanced by ocean heat uptake and increased long-wave radiation emitted from a warmer surface, with feedbacks determining the Ts until equilibrium is reached with a constant forcing (e, f). The equilibrium depends on whether additional slow feedbacks (for example ice sheets or vegetation) with their own intrinsic timescale are kept fixed (e) or are allowed to change (f). (Knutti&Hegerl; Nature Geoscience , 735, 1, 2008.) Klaus Pfeilsticker
RF, climate sensitivity, heat capacity&climate response times Next we may ask ourself, whether we can further get some insights into the gain factor, G = λs/ λo. Starting with the definition of the climate sensitivity
λ=
dTs dE
and allowing the albedos A and B to feedback with Ts, i.e. A=A(Ts) and B=B(Ts)), we get
Ts = Ts ( E , E[ A(Ts )], E[ B(Ts )]) For simplicity we consider the inverse function E(Ts) and the identity dTs/dE = (dE/dTs)-1:
E = (Ts , Ts ( A), Ts ( B)) ∂T ∂T dT ∂E ∂E ∂Ts ∂E ∂Ts −1 λs = s = ( + ⋅ + ⋅ ) = λo ⋅ (1 + s + s ) −1 dE ∂Ts ∂Ts ∂A ∂Ts ∂B ∂A ∂B
Accordingly the gain factor G is
G=
λs ∂T ∂T = 1 (1 + s + s ) ∂A ∂B λo
or by using the energy equilibrium equation (1) for A(Ts) and B(Ts), we obtain
G= Klaus Pfeilsticker
λs 1 ∂ ln A 1 ∂ ln B = 1 (1 + ⋅ − ⋅ ) 4 ∂ ln Ts 4 ∂ ln Ts λo
Climate sensitivity for a doubling of CO2 (280 ppm to 560 ppm) A doubling of CO2 causes an instantaneous radiative forcing of 3.7 W/m2. It translates into ΔTs =2.8 K warming depending on the study (see Figure). Hence λs = 2.8K/4.36 (W/m2) = 0.76±0.3 K/(W/m2) and G = 2.5.
Left figure: Cumulative distributions of climate sensitivity derived from observed 20th century warming (red), model climatology (blue), proxy evidence (cyan) and from AOGCMs (green) Right figure: Estimates of equilibrium global climate sensitivity and associated uncertainty from major national and international assessments [Charney et al., 1979; IPCC, 2007; for citations to earlier IPCC reports see IPCC, 2007]. Klaus Pfeilsticker
RF components as compiled by the recent IPCC report (2007)
AR4: www.ipcc.ch Applying λ (= 0.76±0.3 K/(W/m2) inferred from paleo-climate data or recent observational and modelling studies) to the present RF of 1.6 ±1 W/m2 leads to a warming of ΔTs (∞) = 1 ± 0.76 K. This compared well with the presently observed ΔTs = 0.7 K, when keeping in mind the time constant (τ) for the climate to adapt to a changed RF ! Klaus Pfeilsticker
Climate sensitivity on geological time scales (past 420 Ma) One may ask how atmospheric CO2 forced the climate in the past, and how sensitive the climate reacted on the CO2 forcing. For the modern Earth, Svante Arrhenius (1859 -1927) already predicted an equilibrium ΔTs =1.5 - 5 oC for 2·CO2. This result is well confirmed by recent climate models (most likely value + 2.8 oC) for the modern Earth. For the past Earth (past 420 Ma) a similar sensitivity (1.6 – 5.5 oC best estimate ΔTs =2.8 oC) can be inferred from paleo-proxis (18O, 13C, ....) even though many factors may have changed past 420 Ma (e.g., land/sea distribution, TSI, biosphere, Ca and Mg silicate weathering, ....) Comparison of CO2 calculated by the model GEOCARBSULF for varying Δ T(2*) to an independent CO2 record from proxies. For the GEOCARBSULF calculations (red, blue and green lines), standard parameters from GEOCARB11 and EOCARBSULF12 were used except for an activation energy for Ca and Mg silicate weathering of 42 kJ/mol. The proxy record (dashed white line) was compiled from 47 published studies using five independent methods (n = 490 data points). All curves are displayed in 10 Myr time-steps. The proxy error envelope (black)represents ±1 s.d. of each time-step. The GEOCARBSULF error envelope (yellow) is based on a combined sensitivity analysis (10% and 90% percentile levels) of four factors (weathering, δ13C river run-off used in the model (Royer et al., Nature, 446, 2007). Klaus Pfeilsticker
Climate sensitivity for CO2 doubling Distributions and ranges for climate sensitivity from different lines of evidence. (a) The most likely values (circles), likely (bars, more than 66% probability) and very likely (lines, more than 90% probability) ranges are subjective estimates by the authors based on the available distributions and uncertainty estimates from individual studies, taking into account the model structure, observations and statistical methods used. Values are typically uncertain by 0.5 °C. Dashed lines indicate no robust constraint on an upper bound. Distributions are truncated in the range 0–10 °C; most studies use uniform priors in climate sensitivity. Single extreme estimates or outliers (some not credible) are marked with crosses. The IPCC likely range and most likely value are indicated by the vertical grey bar and black line, respectively. (b) A partly subjective classification of the different lines of evidence for some important criteria. The overall level of scientific understanding (LOSU) indicates the confidence, understanding and robustness of an uncertainty estimate towards assumptions, data and models. Expert elicitation and combined constraints are difficult to assess; both should have a higher LOSU than single lines of evidence, but experts tend to be overconfident and the assumptions are often not clear. (Knutti&Hegerl; Nature Geoscience , 735, 1, 2008.)
Klaus Pfeilsticker
Intrinsic uncertainty of the climate sensitivity We saw that an increase/decrease in A with Ts causes a +/- feedback in the climate system. Conversely, an increase/decrease in B with Ts cause a -/+ feedback. These changes in A and B may happen e.g., due to a cloud feedback (simultaneous change in A and B) and/or water vapor feedback (change in B)….. Thus climate modeling must concentrate to understand well the changes in A and B by Ts, i.e. ∂A/∂Ts and ∂B/∂Ts . Next, we are interested how well climate can be predicted. We know that the instantaneous climate sensitivity is λo = 0.3 to 0.32 K/(W/m2) and λ = 0.76±0.3 K/(W/m2). In the linear regime (where the strengths of feedbacks are linear with respect to applied forcing), we define a feedback factor f as λ 1 ∂ ln A 1 ∂ ln B ) ≡ 1 G = s = 1 (1 + ⋅ − ⋅ 1− f 4 ∂ ln Ts 4 ∂ ln Ts λo 1 ∂ ln A 1 ∂ ln B ) f = (− ⋅ + ⋅ 4 ∂ ln Ts 4 ∂ ln Ts Climate modeling shows that for the CO2 doubling 0.41 ≤ f ≤ 0.73, or 1.7 ≤ G ≤ 3.7 (λ = 0.75±0.3 K/(W/m2)) or 2oC ≤ ΔT ≤ 4.5oC. Uncertainty in climate prediction (δG) can then best be expressed as δG ≈ 1 ⋅ σ (1 − f )
2
f
with f bar being the mean feedback factor and σf its standard deviation. Klaus Pfeilsticker
Intrinsic uncertainty of the climate sensitivity Uncertainty propagation can easily be demonstratated assuming a positive (+) feedback (ΔT=ΔT0/(1-f)) >0 and pdfs for f (hf(f)) and ΔT (hT(ΔT)). ΔT0 is the sensitivity in the absence of feedbacks. If the mean estimate of the total feedbacks is substantially +, any distribution in hf(f) will lead to a highly skewed distribution in ΔT. For the purposes of illustration, a normal distribution in hf(f) is shown with a mean of 0.65 and a σf = 0.13, typical to that obtained from feedback studies of GCMs. The dot-dashed lines represent 95% confidence intervals on the distributions. Note that values of f ≥ 1 imply an unphysical, catastrophic runaway feedback (Roe&Baker, Science, 318, 2007). Klaus Pfeilsticker
Intrinsic uncertainty of climate sensitivity Assuming that the errors in the feedback factors f are normaly distributed 2
h
f
(f)=
σ
1 (f−f) ⋅ exp(−0.5[ ) ] σf ⋅ 2π f
then because hT(ΔT)) is a function hf(f)), a Tayler expansion yields
ΔT ΔT0 df 0) Δ = Δ ⋅ = T f T ( ) ( ( )) ⋅ ( 1 − hf hf dΔT (ΔT ) 2 ⋅h f ΔT to the first approximation and hT(ΔT)) is
h
Klaus Pfeilsticker
f
(ΔT ) =
σ
ΔT ΔT 0 1 1 − f − 0 ⋅ ⋅ exp(−0.5 ⋅ ΔT ]2 ) 2 [ Δ T 2 π ⋅ f
σf
Intrinsic uncertainty of climate sensitivity Climate sensitivity distributions: (A) from Soden&Held, 2007 which calculated (f, σf) of (0.62, 0.13) from a suite of GCM simulations; (B) from Colman (2003), which found (f, σf) of (0.7, 0.14) from a different suite of models; and (C) from the ~5700-member multi ensemble climate prediction net (Stainforth et al., 2005 and Sanderson et al., 2007) for different choices of cloud processes. (D) Fit hT(ΔT)) to the result of Sanderson et al., (2007) which was found by estimating the mode of the probability density and its accompanying ΔT and solving for (f, σf ) from previous equations, which yielded values of (0.67, 0.12) (Roe&Baker, Science, 318, 2007). Klaus Pfeilsticker
Climate sensitivity distributions
Climate sensitivity estimates Climate sensitivity distributions from various studies with the use of a wide variety of methods (black lines) and overlain with a fits of hT(ΔT)) (green lines): (A) from Hegerl et al., (2006) (f, σf) = (0.58, 0.17) and (0.63, 0.21); (B) from Murphy et al., (2004) (f, σf) = (0.67, 0.10) and (0.60, 0.14); (C) Forest et al., (2002) (f, σf) = (0.64, 0.20) and (0.56, 0.16); (D) Andronova et al., (2001) (f, σf) = (0.82, 0.11), (0.65, 0.14), and (0.15, 0.28); (E) Gregory et al., (2002) (f, σf) = (0.86, 0.35) and (F) Royer et al., (2007) = (f, σf) (0.72, 0.17), (0.75, 0.19), and (0.77, 0.21).
Detailed studies show that, f and σf are in the range of (0.11, 0.06) vs (0.09, 0.02) for the albedo feedback (0.17, 0.11) vs (0.22, 0.12) for the cloud feedback and (0.42, 0.06) vs (0.31, 0.04) for the water vapor and lapse rate feedbacks combined (Colman, 2003) vs Soden&Held (2006). Accordingly, for the present climate G = 2.63±1.6, f = 0.62 ± 0.3, and λ = 0.789 ± 0.3 K/(W/m2. This compares well with λ = 0.76±0.3 K/(W/m2). Note that the largest uncertainty arise due to the cloud feedback (G = 1.3±0.19 and f = 0.22 ± 0.12). Klaus Pfeilsticker
Relative sensitivity of surface temperatures to changes in green house gases per unit atmospheric mass Ozone increase (absolute)
H2O increase (absolute)
Pressure (hPa)
Methane increase (absolute)
~25 km
Tropopause
~ 5 km
Radiative Forcing
Figure: Illustration of how the surface impact depends on altitude and latitude where the methane, ozone and water vapour changes take place. Shading show relative surface impact, measured as radiative forcing from a fixed mass increase applied to different altitudes. Red shows where the increase in gas led to maximum surface warming (courtesy P. Foster). 19
Conclusion: Take-home messages 1. 2.
3. 4. 5.
We have seen that the climate sensitivity, heat capacity of the climate system and relaxation time to disturbances are intimately tied. While the climate sensitivity for instantaneous forcing λo can straightforwardly be calculated (i.e. λo =0.3 K/(W/m2), the climate sensitivity including feedbacks (λs) is largely - and probably inherently - uncertain and largely dependent on the considered time scale. For political decision making, most important is the climate sensitivity acting on time scale of decades, i.e. λs = 0.76±0.3 K/(W/m2 (IPCC2007). This implies an expected temperature increase for CO2 doubling (E = 3.9 W/m2) of 3K with a 1 σ range of 1.79 - 4.2 K. Using the heat capacity of the climate system (C = 0.53±0.22 GJ/K·m2) accessible within decades, i.e. mixing of the upper oceanic layers, but excluding the deep oceanic turn-over or melting of the large ice shields, results in a relaxation time of 12.5 years (at least). ⇒ for more info see the lecturer notes under: http://www.iup.uni-heidelberg.de/institut/studium/
Klaus Pfeilsticker
