# Presentation: 472397

## Climate Sensitivity:  Linear Perspectives            

- Isaac Held, Jerusalem, Jan 2009

*1*

## Infrared radiation escaping to space -

- - 50km model under development at GFDL

*How can the response of such a complex system be “linear”?*

*2*

## Response of global mean temperature to increasing CO2 seems simple,

*Response of global mean temperature to increasing CO2 seems simple,*
*  **as one might expect from the simplest linear energy balance models *

*3*

## White areas => less than two thirds of the models agree on the sign of the change

*White areas => less than two thirds of the models agree on the sign of the change*

*Percentage change in precipitation by end of 21st century:*
*                           **PCMDI-AR4 archive*

*But we are not interested in global mean temperature, but rather things like *
*the response in local precipitation  *

*4*

## Precipitation and evaporation

*Precipitation and evaporation*
*      “**Aqua_planet” climate model*
*            **(no seasons, no land surface) *

*Instantaneous precip (lat,lon)*

*Time means*

*4a*

## Aqua planet (P – E) response to doubling of CO2

*Aqua planet (P – E) response to doubling of CO**2*

*4b*

## Saturation vapor pressure 

*Saturation vapor pressure** *

*  **7% increase per 1K warming*
*            **20% increase for 3K*

*4c*

## GCMs match observed trend and interannual variations 

*GCMs match observed trend and interannual variations *
*of tropical mean (ocean only) column water vapor *
*when given the observed ocean temperatures *
*as boundary condition*

*Courtesy of Brian Soden*

*4d*

##          Local vertically integrated atmospheric moisture budget:

*precipitation*

*evaporation*

*vertically integrated *
*moisture flux*

*vapor mixing ratio*

*4e*

##                              PCMDI/CMIP3

*                             **PCMDI/CMIP3*
* *

*But response of global mean temperature is correlated (across GCMs)*
*with the response of the poleward moisture flux responsible for the pattern*
*of subtropical decrease and subpolar increase in precipitation*

*Global mean T*

*% increase in*
*poleward*
*moisture flux*
*In midlatitudes*

*4f*

## One can see effects of poleward shift of midlatitude circulation

*One can see effects of poleward shift of midlatitude circulation*
*And increase(!) in strength of Hadley cell*

*4g*

## Temperature change

*Temperature change*

*% Precipitation change *

*PCMDI -AR4 Archive*

*5*

## One often sees the statement that 

*One often sees the statement that *
*“**Global mean is useful because averaging reduces noise”  *
*But one can reduce noise a lot more*
*by projecting temperature change onto a pattern that looks like *
*this (pattern predicted in response to increase in CO2)*
*                                    **or this (observed linear trend)*

*Or one can find the pattern that maximizes*
*the ratio of decadal scale to interannual*
*variability – Schneider and Held 2001*

*6*

## “The global mean surface temperature has an especially simple relationship with the global mean TOA energy balance”  ??

*Seasonal OLR vs Surface T*
*at different latitudes*

*Seasonal OLR vs 500mb T*
*at different latitudes*

*Most general linear OLR-surfaceT relation*

*Relation between global means depends on spatial structure*

*7*

## Efficacy  (Hansen et al, 2005) :

*Different sources of radiative forcing that provide the same*
*net global flux at the top-of-atmosphere can give different*
*global mean surface temperature responses*
*Forcing for doubling CO**2** roughly 3.7 W/m**2*
*If global mean response to doubling CO**2** is T**2X*
*E = efficacy **= (<T> /T**2X**)(3.7/F)*
*One explanation for efficacy:*
*Responses to different forcings have different spatial structures*
*Tropically dominated responses => E <1*
*       **Polar dominated responses => E>1*
*  *

*8*

## Why focus on top of atmosphere energy budget rather than surface?

*Why focus on top of atmosphere energy budget rather than surface?*
*Because surface is strongly coupled to atmosphere by non-radiative fluxes*
*   **(particularly evaporation)*

*Classic example:  adding absorbing aerosol does not change T, *
*but reduces evaporation*

*9*

## If net solar flux does not change, outgoing IR does not change either (in equilibrium),

*  **-- with increased CO2, atmosphere is more opaque to infrared photons*
*=> **average level of emission to space moves upwards, maintaining same T*
*=> warming of surface, given the lapse rate*

*Final response depends on how other absorbers/reflectors *
*(esp. clouds, water vapor, surface snow and ice)*
*change in response to warming due to CO**2**, *
*and on how the mean lapse rate changes *

*10*

## t

*Double the CO**2** and wait for the system to equilibrate*
*But what is the “system”?*
*  **glaciers?  “natural” vegetation? *
* **Why not specify emissions rather than concentrations?*
*Transient climate sensitivity:*
*Increase CO**2** 1%/yr and examine climate at the time of doubling*

*t*

*CO**2** forcing *

*Heat uptake by deep ocean*

*W/m**2*

*~3.7*

*Typical setup – increase till doubling – then hold constant*

*After CO2 stabilized, warming of near surface*
* **can be thought of as due to reduction in heat uptake *

*T response*

*11*

## “Observational constraints” on climate sensitivity (equilibrium or transient)

*“**Observational constraints” on climate sensitivity (equilibrium or transient)*

*Model (a,b,c,...) *

*Simulates some observed phenomenon: *
*comparison with simulation constrains a,b,c ... *

*predicts climate sensitivity;*
*depends on a,b,c,...*

*Model can be GCM – in which case constraint can be rather indirect*
*(constraining processes of special relevance to climate sensitivity)*
*Or it can be simple model in which climate sensitivity *
*is determined by 1 or 2 parameters. *

*12*

## Hall and Xu, 2006

*Hall and Xu, 2006*

*A great example of an observational constraint: looking across GCMs, *
*strength of snow albedo feedback very well correlated with magnitude of*
*mean seasonal cycle of surface albedos over land*
* **=>   observations of seasonal cycle constrain strength of feedback*

*Can we do this for cloud feedbacks?*

*13*

## The simplest linear model

*The left-hand side of this equation (the ocean model)*
* **is easy to criticize, but what about the right hand side?*

*forcing*

*Heat uptake*

*14*

## N/F

*N/F*

*T/T**EQ*

*The simplest linear model*

*If correct, evolution should be along the diagonal*

*15*

## N/F

*N/F*

*T/T**EQ*

*Evolution in a*
*particular GCM*
*(GFDL’s CM2.1)*
*for 1/% till doubling*
*+ stabilization*

*16*

## N/F

*N/F*

*T/T**EQ*

*E**N**=2*

*The efficacy of heat uptake >1 *
*since it primarily affects subpolar*
*latitudes*

*Transient sensitivity affected*
*by efficacy as well as magnitude of heat uptake *

*17*

## N/F

*N/F*

*T/T**EQ*

*Lots of papers, and IPCC, use concept of *
*“**Effective climate sensitivity” to estimate*
*equilibrium sensitivity  -- can’t integrate models*
*long enough to get to accurate new equilibrium,*

*Linearly extrapolating*
*from zero, through*
*time of doubling,*
*to estimate*
*equilibrium sensitivity*

*Result is time-dependent*

*Are some of our difficulties in relating different observational constraints*
*on sensitivity due to inadequate simple models/concepts? *

*18*

## AR4 models

*2*

*4*

*3*

*5*

*1*

*2*

*1.5*

*2.5*

*Equilibrium sensiivity*

*AR4 models*

*Transient*
*sensitivity*

*Not well correlated across models – equiilbrium response brings into play *
*feedbacks/dynamics in subpolar oceans that are surpressed in transient response*

*19*

## Response of global mean temperature in CM2.1 to instantaneous doubling of CO2

*Response of global mean temperature in CM2.1 to instantaneous doubling of CO2*
*Equilibrium sensitivity >3K*
*Transient response ~1.6K*

*Fast response*

*Slow response*
*evident only*
*after ~100 yrs*
*and seems *
*irrelevant for*
*transient *
*sensitivity*

*20*

## feedbacks

*tropopause*

*F*

***T*

***T*

*atmosphere*

*ocean*

*In equilibrium:*

*feedbacks*

*21*

## Wm-2K-1

*base*

*Lapse*
*rate*

*Snow/*
*   **Ice*

*Water*
*vapor*

*clouds*

*  **net*
*“**feedback”*

*total*

*Wm**-2**K**-1*

*Positive*
*feedback*

*Global mean feedback analysis for CM2.1 (in A1B scenario over 21**st** century)*

*Base in isolation would give sensitivity of ~1.2K*
*Feedbacks convert this to ~3K*

*22*

## Knutti+Hegerl, 2008

*Knutti+Hegerl, 2008*

*Assorted estimates of equilibrium sensitivity*

*23*

## 24

*24*

## Roe-Baker

*Roe-Baker*

*Gaussian distribution of f => skewed distribution of 1/(1-f)*

*25*

## Positive

*Cloud feedback *
*as residual*

*Cloud feedback *
*by adjusting cloud forcing*
*for masking effects*

*Positive*
*feedback*

*Rough feedback analysis for AR4 models*

*“**Cloud forcing”*

*Lapse rate cancels water vapor in part*
*and reduces spread*

*26*

## Cloud forcing

*0*

*Cloud forcing*

*Cloud feedback*

*Water vapor feedback*

*Cloud feedback is different from *
*change in cloud forcing*

*27*

## Simple substitution

*but taking clouds from A and water vapor from B decorrelates them*

*Not a perturbation quantity*

*Right answer*

*A = control    B = perturbation*

*Another problem*

*Soden et al, J.Clim, 2008*
*describe alternative ways of*
*Alleviating this problem *

*28*

## Annual, zonal mean water vapor kernel, normalized to correspond to % change in RH

*Annual, zonal mean water vapor kernel, normalized to correspond to % change in RH*

*Total *

*Clear sky*

*Difference between total and clear sky kernels used to adjust for masking effects*
*              **and compute cloud feedback from change in cloud forcing*

*Mostly comes from upper*
*tropical troposphere, so negatively*
*correlated with lapse rate feedback*

*29*

## Courtesy of B. Soden

*Courtesy of B. Soden*

*Net cloud feedback*
*from 1%/ yr  CMIP3/AR4*
*simulations*

*SW **and **LW** cloud feedback*

*LW feedbacks positive  (FAT hypothesis? => Dennis’s lecture)*
*SW feedbacks positive/negative, and correlated with total*

*30*

## Wm-2K-1

*base*

*Lapse*
*rate*

*Snow/*
*   **Ice*

*Water*
*vapor*

*clouds*

*  **net*
*“**feedback”*

*total*

*Wm**-2**K**-1*

*31*

## Choice of “base” = “no feedback”  is arbitrary!

*alternative choices of *
*starting point*
*(not recommended)*

*Weak negative*
*“**lapse rate feedback”*

*Very strong negative*
*“**free tropospheric *
*feedback”*

*Choice of “base” = “no feedback”  is arbitrary!*

*32*

## base

*base*

*rh*

*Water vapor*
*Lapse rate*
*Fixed rh*

*Water vapor*
*uniform T, fixed rh*

*Lapse rate*

*Water vapor*

*What if we choose*
*constant **relative humidity*
*rather than constant **specific humidity *
*as the base*

*33*

## Wm-2K-1

*Fixed rh*
*uniform T*
*base*

*fixed rh*
*lapse*
*rate*

*rh*

*Snow/*
*ice*

*clouds*

*  **Net *
*“**feedback”*

*total*

*Wm**-2**K**-1*

*34*

## 3.3

*3.3*

*1.85*

*clouds*

*Non-dimensional version*

*Clouds look like they have *
*increased in importance*
* **(since water vapor change *
*due to temperature change*
*resulting from cloud change is now *
*charged to the “ cloud” account}*

*Net *
*feedback*

*total*

*35*

## 20th century warming

*20**th** century warming*
*1000yr record *
*Ice ages – LGM*
*Deep time*
*Volcanoes*
*Solar cycle*
*Internal Fluctuations*
*Seasonal cycle etc*

*36*

## Pliocene – could our models be

*Pliocene – could our models be*
*this wrong on the latitudinal*
*structure ?  *

*21**st** century*
*Warming*
*IPCC*

*Pliocene*
*reconstruction*

*37*

## 38

*38*

*www.globalwarmingart.com*

*“**We conclude that a climate sensitivity greater than 1.5 6C has probably been a robust feature of the Earth’s climate system over the past 420 million years ...”*
*             **Royer, Berner, Park;   Nature 2007*

*CO**2** thought to be major driver*
*of deep-time temperature*
*variations*

## 39

*39*

*www.globalwarmingart.com*

## Global mean cooling due to Pinatubo volcanic eruption

*Global mean cooling due to Pinatubo volcanic eruption*

*Range of *
*~10 Model*
*Simulations*
*GFDL CM2.1*

*Courtesy of G Stenchikov*

*Observations*
*with *
*El Nino*
*removed*

*Relaxation time after abrupt cooling contains information on climate sensitivity*

*40*

## Yokohata, et al, 2005

*Yokohata, et al, 2005*

*Low sensitivity model*

*High sensitivity model*

*Pinatubo simulation*

*41*

## Observed total solar irradiance variations in 11yr solar cycle (~ 0.2% peak-to-peak)

*Observed total solar irradiance variations in 11yr solar cycle (~ 0.2% peak-to-peak)*

*42*

## Tung et al => 

*Tung et al => *
*0.2K peak to peak*
*(other studies yield only 0.1K)*
*Seems to imply large transient *
*sensitivity*

*4 yr damping time*

*1.8K (transient) sensitivity*

*Only gives*
* **0.05 peak to peak*

*43*

## www.globalwarmingart.com

*www.globalwarmingart.com*

*44*

## Models can produce very good fits by including aerosol effects, 

*(GFDL CM2.1 -- Includes estimates of volcanic and anthropogenic aerosols,*
*  **as well as estimates of variations in solar irradiance)*

*Models can produce very good fits by including aerosol effects, *
*but models with *
*stronger aerosol forcing and higher climate sensitivity *
*are also viable (and vice-versa)*

*45*

## “It is likely that increases in greenhouse gas concentrations alone 

*“**It is likely that increases in greenhouse gas concentrations alone *
*would have caused more warming than observed because *
*volcanic and anthropogenic aerosols have offset some warming *
*that would otherwise have taken place.” (AR4 WG1 SPM).*

*Observations*
*     **(GISS)*

*GFDL’s CM2.1 with well-mixed greenhouse gases only*

*Global mean *
*temperature *
*change *

*46*

## Observed

*Observed*
*warming*

*47*

## Kiehl, 2008:   In AR4, forcing over 20th century and 

*Kiehl, 2008:   In AR4, forcing over 20**th** century and *
*equilibrium climate sensitivity negatively correlated*
*How would this look for transient climate sensitivity?*

*48*

## http://data.giss.nasa.gov/gistemp/

*Do interhemispheric differences in warming provide a simple test*
*of aerosol forcing changes over time?*

*49*

## Internal variability can create

- temperature anomalies
- (10yr running means)
- averaged around latitude
- circles over 20th century:
- -- Observations (big)
- -- 5 realizations of a model    simulation (small)

- Source:  Delworth and Knutson, Science (2000).

*Internal variability can create*
*Interhemispheric gradients*

*50*

## OLR

*OLR*

*SW down*

*SW up*

*total*

*Forcing computed from differencing TOA fluxes in two runs of a model (B-A)*
*B = fixed SSTs with varying forcing agents; A fixed SSTs and fixed forcing agents*

*51*

## Temperature change averaged over 5 realizations of coupled model

*Temperature change averaged over 5 realizations of coupled model*

*52*

## Fit with

*Fit with*

*53*

## Forcing with no damping

*Forcing with no damping*

*Forcing (with no damping) fits the trend well, if you use *
*transient climate sensitivity, *
*which takes into account *
*magnitude/efficacy of heat uptake*

*54*

## S

*S*

***T*

*N*

*c*

*Spenser-Braswell, 2008*

*Suppose N isTOA  noise, but correlated with T because it forces T*
*Regressing flux with T *

*Why can’t we just look at *
*the TOA fluxes and *
*surface temperatures?*
*TOA record is short,*
*But there are other issues*

*If S and N are uncorrelated*
*and have the same spectrum*
*one can show that*

*(Assuming no forcing)*

*55*

## Wm-2K-1

*Shortwave regression across ensemble, *
*   **following K. Swanson 2008*

*Wm**-2**K**-1*

*All-forcing*
*20th century*

*Following an idea of K. Swanson, *
*take a set of realizations of the 20th century from one model, *
*and correlate global mean TOA with surface temperature across the ensemble*

*56*

## Wm-2K-1

*Shortwave regression across ensemble, *
*   **following K. Swanson 2008*

*All-forcing*
*20th century*

*A1B scenario*

*Wm**-2**K**-1*

*Is this a sign of non-linearity? What is this?*

*57*

## Wm-2K-1

*Shortwave regression across ensemble, *
*   **following K. Swanson 2008*

*All-forcing*
*20th century*

*Wm**-2**K**-1*

*A1B scenario*

*90%*

*Estimate of noise in this statistic from 2000yr control run*

*58*

## Wm-2K-1

*Shortwave regression across ensemble, *
*   **following K. Swanson 2008*

*Wm**-2**K**-1*

*        **Well-mixed*
*greenhouse gases only*

*59*

## Wm-2K-1

*Shortwave regression across ensemble, *
*   **following K. Swanson 2008*

*Wm**-2**K**-1*

*Independent set of 10*
*           **A1B runs*

*60*

## Wm-2K-1

*Longwave regression across ensemble, *
*   **following K. Swanson 2008*

*Wm**-2**K**-1*

*All-forcing*
*20th century*

*61*

## Wm-2K-1

*Longwave regression across ensemble, *
*   **following K. Swanson 2008*

*Wm**-2**K**-1*

*All-forcing*
*20th century*

*A1B scenario*

*62*

## Wm-2K-1

*Longwave regression across ensemble, *
*   **following K. Swanson 2008*

*Wm**-2**K**-1*

*63*

## Wm-2K-1

*Longwave regression across ensemble, *
*   **following K. Swanson 2008*

*Wm**-2**K**-1*

*        **Well-mixed*
*greenhouse gases only*

*64*

## Wm-2K-1

*Longwave regression across ensemble, *
*   **following K. Swanson 2008*

*Wm**-2**K**-1*

*Independent set of 10*
*           **A1B runs*

*But we can fit the models 20**th** century simulations *
*without time-dependence in OLR-temperature relationship!*

*May be telling us that ENSO is changing, but with no obvious*
*connection to global sensitivity*

*65*

## Fluctuation-dissipation   

*                  **(Fluctuation-response)*

*A framework for inferring sensitivity from internal variability:*
*(why wait for a volcano when the climate is always relaxing back from being*
*perturbed naturally *

*Exact for this multi-variate linear system, but also works for some nonlinear*
*systems – ie statistical mechanics *

*66*

## Gritsun and Branstator, 2007

*Gritsun and Branstator, 2007*

*67*

## Final Thoughts:

*The uncertainty in **forcing** over the 20th century is what*
*primarily limits our ability to use 20th century warming*
* **to determine transient sensitivity empirically*
*=> constraining **aerosol** forcing the key*
*2) The difficulty in simulating **clouds** prevents us from developing a *
*satisfying reductive theory/model of climate sensitivity*
*(Can we constrain cloud feedbacks analogously to how *
*Hall and Qu constrain albedo feedbacks? ) *
*3) Is some of the spread in estimates of sensitivity *
*based on different methods due to **inappropriate simple models/concepts*
*(e.g., ignoring the efficacy of heat uptake)?*
*4) Can one use observations of **internal variability*
*(temporal correlations or relationships between TOA fluxes and other fields)*
*to constrain sensitivity*
*  *
*  *

*68*

## Slide 76

## Supplementary figures

## (C. Keeling)

*(C. Keeling)*

## Carbon dioxide

- CFCs: (1975) V. Ramanathan
-            (1974) Molina-Rowland: catalytic destruction of ozone by chlorine;
-            (1985) Farman et al: ozone hole

*Carbon dioxide*

*methane*

*Nitrous oxide*

*CFCs*

## Jouzel, Lorius et al-- Vostok 

*Jouzel, Lorius et al-- Vostok *
* **late 70’s-80’s*

*Etheridge, et al -- Law Dome 1990’s*

*Ice cores** + direct measurements*
*provide a beautiful record of *
*the history of atmospheric*
*carbon dioxide*

*www globalwarmingart.com.*

## Carbon dioxide

*Carbon dioxide*

*methane*

*Nitrous oxide*

*CFCs*

*other*

- http://www.esrl.noaa.gov/gmd/aggi/

##   Was the 20th century warming 

*  **Was the 20th century warming** *
*1) primarily forced by **increasing greenhouse gases**?*
*or,*
*2) primarily forced by **something else**?*
*or,*
*3) primarily an **internal fluctuation** of the climate?*
*Claim:  Our climate theories STRONGLY support 1)*
*A central problem for the IPCC has been to evaluate this claim*
*and communicate our level of confidence appropriately*

## Energy is going into ocean

*Energy is going into ocean*
*=>*
*More energy is entering the *
*atmosphere from space than is*
*going out*

*Almost all parts of the Earth’s*
*surface have warmed over the *
*past 100 years*

-  IPCC 4th Assessment Report.

*www.globalwarmingart.com*

## IPCC AR4 WG1 Summary for Policymakers

*IPCC AR4 WG1 Summary for Policymakers*

## ?

*?*

*?*

## 100kms

*100kms*

*Clouds (especially in the tropics)*
*are influenced by small scales in the *
*atmospheric circulation*

*simulation of *
*a 100km x 100km*
*area of the tropics*

## Courtesy of 

**Change in Low Cloud Amount (%/K) GFDL and NCAR/CAM models**

*Courtesy of *
*Brian Soden*

**Notes:**
GFDL simulates a large reduction in low clouds (positive feedback) and higher sensitivity. NCAR simulates a large increase in low clouds (negative feedback) and low sensitivity.

## Total Column Water Vapor Anomalies (1987-2004)

**Total Column Water Vapor Anomalies (1987-2004)**

- Held and Soden J.Clim. 2006

- We have high confidence in the model projections of increased water vapor.

**Notes:**
Not just simple and robust, but also based on some aspect of model simulation in which we have confidence. 
Doesn’t get simpler or more robust than WV.