What is the Source of Uncertainty Regarding Global Warming?

Transcription

1 What is the Source of Uncertainty Regarding Global Warming? AKA Quan)fying the Sources of Inter- model Spread in Equilibrium Climate Sensi)vity ; in review at JCli Peter Caldwell, Mark Zelinka, Karl Taylor, and Kate Marvel CFMIP Mee)ng, June 10, 2015 Prepared by LLL under Contract DE- AC52-07A UCRL: LLL- PRES

2 What is the Source of Uncertainty Regarding Global Warming? Mathema'cally, this ques'on is ~equivalent to asking which terms induce the most inter- model spread in the ECS equa'on: Equilibrium Climate Sensi)vity = global- ave equilibrium temperature response to CO 2 doubling ECS = F Forcing is taken here to be the fast response to doubling CO 2 λ Pl + λ WV + λ LR + λ Alb + λ SW Cld + λ LW Cld Planck feedback Water Vapor feedback Lapse Rate feedback Albedo feedback Shortwave Cloud Feedback Longwave Cloud Feedback Prepared by LLL under Contract DE- AC52-07A UCRL: LLL- PRES

3 What is the Source of Uncertainty Regarding Global Warming? Mathema'cally, this ques'on is ~equivalent to asking which terms induce the most inter- model spread in the ECS equa'on: ECS = F λ Pl + λ WV + λ LR + λ Alb + λ SW Cld + λ LW Cld Isola)ng the impact of individual terms is hard when those terms are in the denominator! Prepared by LLL under Contract DE- AC52-07A UCRL: LLL- PRES

4 Breaking ECS into a Sum of Terms: Dufresne + Bony (2008, JCli; hereaeer DB08) provide a way to write ECS as a sum of terms: ECS = F F- F λ net feedback, λ=σλ i = F ' λ F λ Mul)- model mean forcing = F ' λ F λ Pl Planck feedback λ λ Pl $ ' = F ' λ F & λ λ i ) % i Pl ( λ λ Pl = F ' λ F λ + i λ Pl i Pl λ Pl F λ 4

5 Breaking ECS into a Sum of Terms: Dufresne + Bony (2008, JCli; hereaeer DB08) provide a way to write ECS as a sum of terms: Good: ECS = F λ = F ' λ F λ = F ' λ F λ Pl λ λ Pl $ = F ' λ F & λ % λ i Pl λ Pl λ i = F ' λ F λ + i λ Pl i Pl λ Pl ' ) ( F λ Breaks ECS exactly into terms associated with each F and λ i Makes physical sense: λ Pl summand is ΔT if Planck was the only feedback opera)ng Other summands are the Planck response needed to balance a given λ i Bad: on- unique: why mul)ply by λ Pl /λ Pl? The variance assigned to λ i is not zero even if var(λ i )=0 for i Pl 5

6 An Alterna)ve Decomposi)on: ECS = ( F + F ') ( ) 1 = F + F ' = F λ + F ' λ + F λ 2 1 λ + λ ' Taylor expansion about λ =0 " λ + λ ' % + higher order terms 2 # $ λ & ' i=1 λ i ' + higher order terms 6

7 An Alterna)ve Decomposi)on: ECS = ( F + F ') ( ) 1 = F + F ' = F λ + F ' λ + F λ 2 1 λ + λ ' " λ + λ ' % + higher order terms 2 # $ λ & ' i=1 λ i ' + higher order terms Bad: Lineariza)on is inexact Constant and higher- order are unrelated to a specific process (so can t be used to analyze contribu)ons to mul)- model mean response) Good: var(λ i )=0 term i has no contribu)on to var(ecs) Error due to lineariza)on can be rigorously quan)fied Lineariza+on error is rela+vely small. See the paper or ask for details... 7

8 So ECS is Decomposed... ow what? DB08 use the inter- model standard devia)on of each summand as a measure of that term s importance to var(ecs) (see Fig), but formally Fig: ormalized inter- model standard devia'on of ECS par''oning. Reprinted from DB08. var( T i ) = i=1 i=1 j=1 cov( T i,t ) j ( ) = var T i + 2 cov T i,t j i=1 i=1 j>i ( ) so covariances between feedbacks must also be considered! 8

9 Viewing Contribu)ons to ECS Spread var( T i ) = i=1 i=1 j=1 cov( T i,t ) j matrix... so plot that matrix! is a sum over a covariance Fig: ormalized covariance matrix for DB08 decomposi'on using CMIP5 data. Colors indicate magnitude All elements are normalized by var(ecs) so they sum to 1 Variances are on the diagonal cov(t i,t j ) = cov(t j, T i ), so omit and mul)ply by 2 9

10 Enough Theory, Let s Look at Data! Use Gregory et al (2004) approach to get feedback and forcing components as the slope and y- intercept (respec)vely) of model response to abrupt quadrupling of CO 2 RadiaJve kernels used to compute radia)ve response to Pl, WV, LR, and Alb changes adjusted cloud radiajve effect used for SW and LW Cld ECS is the ra)o of net forcing and feedback terms calculated above Analysis are based on 17 CMIP5 models with SW, LW, and net clear sky kernel errors of < 10% 10

11 Results: Fig: ormalized covariance matrices for DB08 and the new approach using CMIP5 data. Covariance terms are very important Par))oning approach makes a huge difference 11

12 Beter WV + LR Defini)ons WV and LR terms have lots of covariance (see Fig) This is expected because RH remains ~constant as the climate changes Held and Shell advocate redefining WV feedbacks based on changes in RELATIVE rather than SPECIFIC humidity This requires adding the effect of WV change at fixed RH to LR and Pl (for height dependent and independent effects, respec)vely) Fig: Cov matrices for new decomposi'on using tradi'onal and HS12 feedback defini'ons (in lev and right panels, respec'vely) Using HS12 defini'ons makes sense and reduces the magnitude of covariance terms! 12

13 Which Terms are Important? var(λ SW Cld ) dominates (as expected) Fig: Cov matrix for new decomposi'on using HS12 defini'ons (from last slide) 13

14 Which Terms are Important? var(λ SW Cld ) dominates (as expected) var(λ LW Cld ) and var(f) are also important Fig: Cov matrix for new decomposi'on using HS12 defini'ons (from last slide) 14

15 Which Terms are Important? var(λ SW Cld ) dominates (as expected) var(λ LW Cld ) and var(f) are also important cov(λ SW Cld, F) and cov(λ LW Cld, F) are big but compensate (see also Ringer et al, 2014 GRL) Fig: Cov matrix for new decomposi'on using HS12 defini'ons (from last slide) 15

16 Which Terms are Important? var(λ SW Cld ) dominates (as expected) var(λ LW Cld ) and var(f) are also important cov(λ SW Cld, F) and cov(λ LW Cld, F) are big but compensate (see also Ringer et al, 2014 GRL) cov(λ SW Cld, λ Alb ) and cov(λ LR, λ LW Cld) are important sinks of ECS variance (see also Huybers, 2010 JCli and Mauritsen et al, 2013 ClimDyn) Fig: Cov matrix for new decomposi'on using HS12 defini'ons (from last slide) 16

17 Which Terms are Important? var(λ SW Cld ) dominates (as expected) var(λ LW Cld ) and var(f) are also important cov(λ SW Cld, F) and cov(λ LW Cld, F) are big but compensate (see also Ringer et al, 2014 GRL) cov(λ SW Cld, λ Alb ) and cov(λ LR, λ LW Cld) are important sinks of ECS variance (see also Huybers, 2010 JCli and Mauritsen et al, 2013 ClimDyn) cov(λ SW Cld, λ LW Cld ) is large but spurious the correla)on between these quan))es is 0 Fig: scazer plot of λ SW Cld, λ LW Cld 17

18 Conclusions: 1. Asking What causes global warming uncertainty? asking which quan))es in the ECS equa)on dominate var(ecs)? 2. Isola)ng the impact of individual terms is hard when those terms are in the denominator! 3. The DB08 par))oning is a. non- unique and b. does not isolate variance from individual processes 4. Our new par))oning solves these problems; comparing methods shows that subjec)ve par))oning choices have a big impact 5. Covariances are important! 6. Held and Shell (2012, JCli) defini)ons are useful 7. λ SW Cld is s)ll the dominant source of ECS spread, but other terms play an important role 18

19 Extra Slides contact:

20 ECS Decomposi)on for Emergent Constraints corr(ecs, X) = corr( T i, X) λ i=1 i=1 = corr(t i, X) F λ WV λ LR λ Alb λ SW λ LW Real constraints should be associated with a single physical mechanism (or an explainable set of mechanisms). Par))oning uncovers what those are.

21 Why isn t λ Cld Dominant in DB08? Because WV+LR are an)- correlated and SW+LW Cld are posi)vely correlated Fig: Cov matrices for CMIP5 with Cld and WV +LR terms combined 21

22 But Vial et al (2013) says Forcing isn t (a) Important! " X Since Vial doesn t separate forcing variability from λ variability: Vial eq 24: ¼ " # DT e s;dsst ¼ 1 k p F þ F adj þ X x6¼p! k x þ Re k!dt e s;dsst Divides by λ Pl instead of λ Uses F instead of F DB08: ECS = F ' λ F λ + i λ Pl i Pl λ Pl F λ Fig: AVer par''oning ECS into components listed on x- axis, Vial computes Inter- model standard devia'ons and normalizes by the standard devia'on of ECS. This is Fig. 6 from Vial et al. (2013)

23 Linearizing 1/λ is ok ECS predicted from the linearized equa)on looks very similar to that from the full model with fixed F (compare red and green lines on lee) The importance of individual summands is largely unaffected by linearizing (right panel). Fig: Panel A= actual model ECS (blue), ECS neglec'ng F (red), and linearized 1/λ + neglected F (green). Each triangle in Panel B denotes var(ecs) neglec'ng perturba'ons in all terms except the one listed on the x axis. Red triangles use lineariza'on, blue triangles do not. HS12 par''oning is used for this plot. 23

24 Which Terms are Important? 24