SLIDE 1 Radiative feedbacks from stochastic variability in temperature and radiative imbalance in a hierarchy of CESM simulations
Cristian Proistosescu
JISAO, University of Washington NCAR May 10, 2018
Collaborators: Kyle Armour - University of Washington Aaron Donohoe - University of Washington Gerard Roe - University of Washington Malte Stuecker - University of Washington Cecilia Bitz - University of Washington
SLIDE 2 1976 “Understanding the origin of climatic variability in the entire spectral range, from extreme ice age changes to seasonal anomalies, is a primary goal of climate research. Yet [...] there exists today (1976) no generally accepted, simple explanation for the observed structure of climate variance spectra […] A persistent difficulty is that the input response relationships are not
- bvious upon on inspection of the appropriate time series “
- K. Hasselmann
2018 A lot more time series, still no simple explanation.
SLIDE 3 Hansen 1985, Soden and Held 2006, Roe 2008
Energy Balance:
Q = F + R(T)
Energy Budget
kT
= F
TOA
Q
R(T) =
= F
SLIDE 4
Energy Balance:
Q = F + R(T)
R(T) = −λT R(T) = −λPlanckT + λwvT + λcloudsT + . . .
Linear feedbacks: Linear feedbacks:
Linear Feedbacks
Q = λ · T + F
kT
= F
TOA
Q
R(T) = λT
= F
SLIDE 5 Equilibrium Sensitivity:
Teq = F λ
Hansen 1985, Soden and Held 2006, Roe 2008
Energy Balance:
Q = F + R(T)
R(T) = −λT
Linear feedbacks:
Q = 0
Net feedback determines equilibrium Climate Sensitivity
Q = λ · T + F
kT
= F
TOA
Q
R(T) = λT
= F
SLIDE 6 CERES GISTEMP TOA (W/m2) T (K)
Observations of Energy Budget
Donohoe et al 2013
kT
= F
TOA
Q
R(T) = λT
= F
Q = λ · T + F
SLIDE 7 CERES GISTEMP TOA (W/m2) T (K)
- Two possible sources of stochastic forcing
- Ocean forcing only impacts TOA through
changing T
Energy fluxes in the coupled system
Q = −λT + Frad + Focn
TOA
− λT
TOA
+ Frad
+ Focn
SLIDE 8
CERES GISTEMP TOA (W/m2) T (K)
− λT
TOA
+ Frad
+ Focn
ENSO assumption Oceanic forcing dominates
TOA = −λT
Q = −λT + Frad + Focn
TOA
Assuming oceanic forcing…
SLIDE 9 CERES GISTEMP TOA (W/m2) T (K)
Assuming oceanic forcing… feedback can be regressed
2 1
0.4 0.2
TOA (W/m2) T (K)
(Forster 2016)
λ = 1.2 (W/m2/K)
(Forster & Gregory 2006, Murphy 2009, Trenberth et al 2010, Dessler 2010, Stevens & Schwartz 2012, Tsushima & Manabe 2013, Zhou et al 2015)
λ = 1.2 (W/m2/K)
TOA = −λT
SLIDE 10 CERES GISTEMP TOA (W/m2) T (K)
Choices, choices, choices….
TOA (W/m2) T (K)
Monthly Annual Monthly, lag 4 TOA
(Forster 2016)
Sensitive to
- averaging
- lag
- record length
SLIDE 11 Lagged Regression
TOA (W/m2) T (K)
Monthly Annual Monthly, lag 4 TOA
(Forster 2016)
Sensitive to
- averaging
- lag
- record length
SLIDE 12 #GOALS
Sensitive to
- averaging
- lag
- record length
We cannot use feedback estimates from variability until we understand the temporal structure. (Forster 2016) Results are sensitive to assumptions about
- forcing. (Spencer and Braswell, 2010,2011)
Q = −λT + Frad + Focn
TOA
− λT
TOA
+ Frad
+ Focn
SLIDE 13
CESM1
Reproduces salient feature
SLIDE 14
CESM1
Reproduces salient feature
SLIDE 15 Physics is separated by frequency, not lag
SLIDE 16
We need a dynamical model
TOA
− λT
TOA
+ Frad
+ Focn
Q = −λT + Frad + Focn
SLIDE 17
Hasselmann Model
TOA
− λT
TOA
+ Frad
+ Focn
C dT dt = −λT + Frad + Focn
white noise
SLIDE 18 Phase fingerprints forcing: ocean forcing
TOA
− λT
TOA
+ Frad
+ Focn
C dT dt = −λT + Frad + Focn
(in phase)
TOA = −λT
SLIDE 19 TOA
− λT
TOA
+ Frad
+ Focn
C dT dt = −λT + Frad + Focn
TOA = C dT dt
(quadrature)
Phase fingerprints forcing: radiative forcing
SLIDE 20 Physics is separated by frequency, not lag
Physics is separated by model hierarchy
SLIDE 21 CESM1 model hierarchy
- OCN: CESM1 (CAM5)
- SOM: CAM5 + slab ocean model
- fSST: CAM5 + fixed SSTs
Unforced, pre-industrial control runs
Atmosphere(Y), Slab(Y), ENSO(Y) Atmosphere(Y), Slab(Y), ENSO(N) Atmosphere(Y), Slab(N), ENSO(N)
SLIDE 22
Fixed SST simulation
− λT
TOA
+ Frad
+ Focn
C dT1 dt = −λ1T1 + Frad + Focn TOA1
SLIDE 23 Fixed SST simulation: ocean forced
− λT
TOA
+ Frad
+ Focn
(in phase)
C dT1 dt = −λ1T1 + Frad + Focn TOA1 TOA1 = −λ1T1
SLIDE 24
Slab Ocean Model
− λT
TOA
+ Frad
+ Focn
C dT2 dt = −λ2T2 + Frad + Focn TOA2
SLIDE 25 Slab Ocean Model: radiatively forced slow mode
− λT
TOA
+ Frad
+ Focn
Q
C dT2 dt = −λ2T2 + Frad + Focn TOA2
(in quadrature)
TOA2 = −C2 dT2 dt
SLIDE 26
On fast time scales Air-Sea fluxes provide both forcing and damping − λT
TOA
+ Frad Q
H
Ocean-atmosphere exchanges Can be separated into
H ∝ U(To − T) H ∝ U(To − T)0 + U 0(To − T)
SLIDE 27
On fast time scales Air-Sea fluxes provide both forcing and damping
Ocean-atmosphere exchanges Wind-driven term acts as forcing. Temperature driven term acts as damping term (feedback) Can be separated into
− λT
TOA
+ Frad
+ Focn
H ∝ U(To − T) H ∝ U(To − T)0 + U 0(To − T) H = λaoT + Focn = λaoT +
SLIDE 28 Coupled atmosphere-ocean model
− λT
TOA
+ Frad
+ Focn
= λaoT
TOA SHF
(Barsugli and Battisti 1998, Cronin and Emanuel, 2013)
- Atmosphere & land warming may excite different
radiative feedbacks vs mixed layer warming (Proistosescu & Huybers 2017)
Ca dTa dt = −λrad,aTa + Frad,l − λao(Ta − To) + Focn Co dTo dt = −λrad,oTo + Frad,o + λao(Ta − To) − Focn
- The system evolves along two eigenmodes, each
equivalent to a Hasselmann model (1) (2)
SLIDE 29 Fast time-scales equivalent to fixed SST − λT
TOA
+ Frad
+ Focn
= λaoT
TOA SHF
(Cronin and Emanuel, 2013)
Co dTo dt = −λrad,oTo + Frad,o + λao(Ta − To) − Focn Ca dTa dt = −λrad,aTa + Frad,l − λao(Ta − To) + Focn
- On fast time-scales mixed-layer
variability is small
- (1) is a good approximation for
the first eigenmode
εCa dT1 dt = −λrad,aT1 + εFocn
(1) (2)
ε = λrad,o λrad,o + λao TOA1 = −λrad,aT1
SLIDE 30
Fast time-scales equivalent to fixed SST
TOA SHF
(Cronin and Emanuel, 2013)
Co dTo dt = −λrad,oTo + Frad,o + λao(Ta − To) − Focn Ca dTa dt = −λrad,aTa + Frad,l − λao(Ta − To) + Focn (1)
(2)
ε = λrad,o λrad,o + λao C1 dT1 dt = −λ1T1 + εFocn
SLIDE 31
Spectral structures of SHF and TOA support ocean driver
SHF1 = −λaoT1 + Focn + Frad
fSST TOA SHF
C1 dT1 dt = −λ1T1 + εFocn TOA1 = −λ1T1 + Frad
Frequency [1/yr] PSD
εFocn
SLIDE 32
Filter to high frequencies
SHF1 = −λaoT1 + Focn + Frad
fSST TOA SHF
C1 dT1 dt = −λ1T1 + εFocn TOA1 = −λ1T1 + Frad
Frequency [1/yr] PSD
εFocn
SLIDE 33
High Frequency heat fluxes (fSST)
Fsurf ≈ cU 0(Ta − To)
SLIDE 34 Slow time scales, ocean and atmosphere are in near equilibrium
TOA SHF
(Cronin and Emanuel, 2013)
Co dTo dt = −λrad,oTo + Frad,o + λao(Ta − To) − Focn Ca dTa dt = −λrad,aTa + Frad,l − λao(Ta − To) + Focn
- On slow time-scales atmosphere
and ocean are equilibrated (1) (2)
Ta ≈ To ≈ T2
− λT
+ Frad
+ Focn
= λaoT TOA
SLIDE 35
Slow time scales, the system coevolves
TOA SHF
(Cronin and Emanuel, 2013)
Co dTo dt = −λrad,oTo + Frad,o + λao(Ta − To) − Focn Ca dTa dt = −λrad,aTa + Frad,l − λao(Ta − To) + Focn (1)
(2)
(Ca + Co)dT2 dt = λ2T2 + Frad Ca dT1 dt = −(λrad,a + λao)T1 + Focn TOA
− λT
+ Frad
+ Focn
= λaoT
SLIDE 36
Slow time scales, the system coevolves
(Cronin and Emanuel, 2013)
(Ca + Co)dT2 dt = λ2T2 + Frad Ca dT1 dt = −(λrad,a + λao)T1 + Focn
− λT
+ Frad
+ Focn
= λaoT TOA
SLIDE 37 T1, T2 are eigenmodes of a coupled atmosphere-slab model
On fast time scales
- Atmosphere equilibrating with ocean
- Strong forcing, very strong damping
On slow time scales
- Joint system equilibrating with space
- Weak forcing,
- Very weak radiative damping leads to
- large response, slow equilibration
− λT
+ Frad
+ Focn
= λaoT TOA
SLIDE 38 Additional ENSO mode
- TOA and T constant phase lag
fE dT 2 dt2 + 2τ dT dt + λT = ηocn
TOA(t) = −λT(t − θ)
− λT
TOA
+ Frad
+ Focn
= λaoT
SLIDE 39
Spectral solution Cross Spectrum Wiener-Khinchin Theorem Lagged Covariance Lagged Regression
We can model the lagged regression
We have an analytical stochastic linear model
SLIDE 40
Fixed SST
Lag (years) Slope (W/m2/K)
T1
— CESM 1 — EBM
TOA1 TOA1 = −λ1T1 + Frad
SLIDE 41
Slab Ocean Model
TOA1 = −λ1T1 + Frad
Lag (years) Slope (W/m2/K)
T1 + T2 +
— CESM 1 — EBM
TOA1 + TOA2 TOA2 = −λ2T + Frad ∝ dT2 dt
SLIDE 42 Regression dillution
Lag (years) Slope (W/m2/K)
T1 + T2 +
— CESM 1 — EBM
TOA1 + TOA2
r(lag) = X λi ✓ σTi σtotal ◆ acf(lag)
(timescale)
✦average of distinct feedbacks, ✦ weighted by relative variance & ✦ weighted by lag
SLIDE 43
Regression dilution
r(lag) = X λi ✓ σTi σtotal ◆ acf(lag)
(timescale)
SLIDE 44 Fully Coupled model
r(lag) = X λi ✓ σTi σtotal ◆ acf(lag)
(timescale)
T1 + T2 + T3
Lag (years) Slope (W/m2/K) — CESM 1 — EBM
TOA1 + TOA2 + TOA3
Understanding previous results
✦average of distinct feedbacks, ✦ weighted by relative variance & ✦ weighted by lag
- Multiple source of forcing
- Changing fractional variances & acf
explains sensitivity to lag, sampling, & smoothing
SLIDE 45 Variance fraction is dependent on sampling and record length
r(lag) = X λi ✓ σTi σtotal ◆ acf(lag)
Annual averaging preferentially eliminates fast, air-sea forced mode
Understanding previous results
✦average of distinct feedbacks, ✦ weighted by relative variance & ✦ weighted by lag
- Multiple source of forcing
- Changing fractional variances & acf
explains sensitivity to lag, sampling, & smoothing
T1 + T2 + T3
Lag (years) Slope (W/m2/K) — CESM 1 — EBM
TOA1 + TOA2 + TOA3
SLIDE 46 λ1 = 1.2 λ2 = 0.9 λ3 = 2.7 r(0) = 0.8 r(τ) = 1.1 λGHG = 0.9
Air-sea forced Radiatively forced ENSO Zero-lag Peak regression (NOT ENSO) Global-warming
So what does it mean?
r(lag) = X λi ✓ σTi σtotal ◆ acf(lag)
Dynamics are well separated by time-scale. However, variance and covariance (regression) amalgamate across time scales
Understanding previous results
✦average of distinct feedbacks, ✦ weighted by relative variance & ✦ weighted by lag
- Multiple source of forcing
- Changing fractional variances & acf
explains sensitivity to lag, sampling, & smoothing
SLIDE 47 Time scale structure of feedbacks
r(lag) = X λi ✓ σTi σtotal ◆ acf(lag)
Stochastic variations in energy budget Conclusions (a)Mechanistic model for joint variability (b)System can be understood as superposition of linear modes (i) atmosphere & land (ii) Mixed Layer (iii) Coupling to deep ocean (c)We can model and understand interannual feedback Proistosescu et al 2018, in press (GRL) Understanding previous results
✦average of distinct feedbacks, ✦ weighted by relative variance & ✦ weighted by lag
- Multiple source of forcing
- Changing fractional variances & acf
explains sensitivity to lag, sampling, & smoothing
