Estimating Feedbacks from Natural Variability in the Global Energy - - PowerPoint PPT Presentation
Estimating Feedbacks from Natural Variability in the Global Energy Budget Cristian Proistosescu, Aaron Donohoe, Kyle Armour Malte Stuecker, Gerard Roe, Cecilia Bitz University of Washington Energy budget at TOA T (K) Q = T + F
Cristian Proistosescu, Aaron Donohoe, Kyle Armour Malte Stuecker, Gerard Roe, Cecilia Bitz
University of Washington
CERES GISTEMP
TOA (W/m2) T (K)
Energy budget at TOA
CERES GISTEMP
TOA (W/m2) T (K)
Zero forcing at TOA
Temperature driven by internal variability such as ENSO
(Forster & Gregory 2006, Murphy 2009, Trenberth et al 2010, Dessler 2010, Stevens & Schwartz 2012, Tsushima & Manabe 2013, Donohoe et al 2014)
2 1
0.4 0.2
Q (W/m2) T (K)
Regressed Feedbacks
structure of regression-based feedback (Forster 2016)
λ = 1.2 (W/m2/K)
CERES v GISTEMP
Q lags Q leads
Temporal Structure
CERES v GISTEMP
Q lags Q leads
Sampling rate
CERES v GISTEMP
Q lags Q leads
#goals
variability?
CESM 1
Q lags Q leads
CERES v GISTEMP
Q lags Q leads
CESM 1 control run
CESM 1
Q lags Q leads
Model Hierarchy
T1: Surface air temperature variability atop fixed SSTs
C dT dt = λ · T + F
Fixed SSTs
Frequency (1/year) Spectral Energy (K2/s)
T1 +
— CAM5 - FSST — EBM (stochastic atmospheric variability)
Global Hasselmann Model:
Slab ocean model
— CAM5 - SOM — EBM
Frequency (1/year) Spectral Energy (K2/s)
T1 +
T1: Surface air temperature variability atop fixed SSTs Good fit at high frequencies
Slab ocean model
— CAM5 - SOM — EBM
Frequency (1/year) Spectral Energy (K2/s)
T1 + T2
T1: Surface air temperature variability atop fixed SSTs T2: Mixed-layer variability
T1 + T2
Fully Coupled
— CESM 1 — EBM
Frequency (1/year) Spectral Energy (K2/s)
T1 + T2
Good fit except for ENSO band T1: Surface air temperature variability atop fixed SSTs T2: Mixed-layer variability
Fully Coupled
Frequency (1/year) Spectral Energy (K2/s)
T1 + T2 + T3
— CESM 1 — EBM
T3: ENSO variability as damped oscillator (AR2) T1: Surface air temperature variability atop fixed SSTs T2: Mixed-layer variability
= λ · T | Focn TOA TOA Frad = λ · T |
(Murphy & Forster 2010, Dessler 2011) (Spencer & Braswell 2010,2011)
Q = C dT dt Q = λT
(in phase) (in quadrature)
Forcing and Phase
Frequency (1/year) Phase Zero phase lag indicates Oceanic source of forcing
F ∝ U 0(Ta − To)
Forcing provided by air-sea fluxes
Fixed SST
= Q1 T1 +
— CESM 1 — EBM
Q1 = λ1 · T1
Quadrature: Radiative forcing
= Q1 + Q2 + T1 + T2
Slab Ocean
— CESM 1 — EBM
Q2 = λ2 · T2 + Frad
Frequency (1/year) Phase
Lag in the ENSO band
= Q1 + Q2 + Q3 T1 + T2 + T3
Fully Coupled
— CESM 1 — EBM
Q3(t) = λ3 · T3(t + τ)
Frequency (1/year) Phase
Analytical spectral solution Cross Spectrum Wiener-Khinchin Theorem Lagged Covariance Lagged Regression
Lagged Regression
Lag (years) Slope (W/m2/K)
= Q1 T1
Fixed SST
— CESM 1 — EBM
Lag (years) Slope (W/m2/K)
= Q1 + Q2 T1 + T2 +
Slab Ocean
— CESM 1 — EBM
= Q1 + Q2 + Q3 T1 + T2 + T3
Lag (years) Slope (W/m2/K)
Fully Coupled
— CESM 1 — EBM
Each mode has been fit individually to a level in the CAM5 hierarchy. Their linear superposition reproduces the full lagged regression structure of the coupled model
= Q1 + Q2 + Q3 T1 + T2 + T3
Lag (years) Slope (W/m2/K)
Regression Coefficient
— CESM 1 — EBM
r(lag) = X λi ✓ σTi σtotal ◆ acf(lag)
(timescale)
= Q1 + Q2 + Q3 T1 + T2 + T3
Lag (years) Slope (W/m2/K) — CESM 1 — EBM
Annual Averages
Annual averaging preferentially eliminates fast, air-sea forced mode
r(lag) = X λi ✓ σTi σtotal ◆ acf(lag)
(timescale)
So what does it mean?
Each GCM will have different
Zero-lag feedback coincidentally similar to long term feedback. Going forward: how to connect mode feedbacks with long term warming
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 Global-warming
r(lag) = X λi ✓ σTi σtotal ◆ acf(lag)
Feedback structure: Average of individual feedbacks, weighted by relative variance and timescale Sampling rate Averaging preferentially smooths out fast modes of variability Forcing Radiative and Oceanic Oceanic dominates but composed of two independent sources Previously unidentified unforced air - sea fluxes important
Summary
Ongoing: Spatio-temporal: Do any of the 3 modes constrain long-term sensitivity? Constraining parameters from the short observational record
Cloud feedback in response to GHG forcing (W/m2) Cloud feedback from natural variability (W/m2)
GCMs
Emergent Constraints
(Zhou et al. 2015)
engender different feedbacks
Surface fluxes dominate on fast timescales
(fixed SST)
Hsurf = cU(T − To) Hsurf ≈ cU 0(Ta − To) + cU(T 0 − To0) Hsurf ≈ Fsurf + λsurfT 0
Energy is extracted by wind from the ocean thermostat
Fsurf ≈ cU 0(Ta − To)
Spectra consistent with dominant surface forcing
λ/C ⌧ ω ω ⌧ λ/C
We need to account for aliasing and averaging
T obs(t) = III∆t · (W∆t ? T(t))
Using averages over bins of width Δt is equivalent to (a) smoothing the continuous signal with a moving average (b) sampling the smoothed process every Δt (here taken as equal to the smoothing window, although this is not required) We can represent this by convolution with a rectangular window and multiplication by a Dirac Comb
Need to account for aliasing and averaging
˜ SXY,N =
N
X
k=−N
SXY (f + k/∆t) · sinc2(f∆t + k)
We need to account for aliasing and averaging Accounting for sampling issues explains bias in transfer function
ST T |θ(f) = θ = {σ, λ, τ}
Consider the spectrum of temperature in the SOM-EBM: Parameters Spectrum Whittle likelihood l(Sobs
T T |θ) = −
X
fj
log ST T |θ(fj) + Sobs
T T (fj)
ST T,θ(fj)
We need to account for aliasing and averaging Whittle Likelihood
ST T |θ(f) = (σ/λ)2 1 + f 2τ 2 θ = {σ, λ, τ}
Consider the spectrum of temperature in the SOM-EBM: Parameters Spectrum de-biased Whittle likelihood Use a truncated version of the sampled spectrum ˜ ST T,N =
N
X
k=−N
ST T (f + k/∆t) · sinc2(f∆t + k) l(Sobs
T T |θ) = −
X
fj
log ˜ ST T,N|θ(fj) + Sobs
T T (fj)
˜ ST T,N|θ(fj)
We need to account for aliasing and averaging De-biassing the Whittle Likelihood
We need to account for aliasing and averaging Posterior distributions
100 years 30 years
We need to account for aliasing and averaging Dependence on record length