Radiative feedbacks from stochastic variability in temperature and - PowerPoint PPT Presentation

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

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 obvious upon on inspection of the appropriate time series “ K. Hasselmann 2018 A lot more time series, still no simple explanation.

Energy Budget TOA Energy Balance: Q = F + R ( T ) = F R ( T ) = = F Q k T Hansen 1985, Soden and Held 2006, Roe 2008

Linear Feedbacks TOA Energy Balance: Q = F + R ( T ) = F R ( T ) = λ T = F Q k T Linear feedbacks: R ( T ) = − λ Planck T + λ wv T + λ clouds T + . . . Q = λ · T + F Linear feedbacks: R ( T ) = − λ T

Net feedback determines equilibrium Climate Sensitivity TOA Energy Balance: Q = F + R ( T ) = F R ( T ) = λ T = F Q k T Linear feedbacks: R ( T ) = − λ T Q = λ · T + F Equilibrium Sensitivity: Q = 0 T eq = F λ Hansen 1985, Soden and Held 2006, Roe 2008

Observations of Energy Budget TOA = F R ( T ) = λ T T (K) = F Q k T GISTEMP Q = λ · T + F TOA (W/m 2 ) CERES Donohoe et al 2013

Energy fluxes in the coupled system TOA + F rad − λ T T (K) + F ocn GISTEMP TOA (W/m 2 ) Q = − λ T + F rad + F ocn TOA •Two possible sources of stochastic forcing CERES •Ocean forcing only impacts TOA through changing T

Assuming oceanic forcing… TOA + F rad − λ T T (K) + F ocn GISTEMP TOA (W/m 2 ) Q = − λ T + F rad + F ocn TOA ENSO assumption CERES Oceanic forcing dominates TOA = − λ T

Assuming oceanic forcing… feedback can be regressed 2 (Forster 2016) T (K) TOA (W/m 2 ) 1 0 GISTEMP -1 TOA (W/m 2 ) λ = 1 . 2 (W/m 2 /K ) λ = 1 . 2 (W/m 2 /K ) -2 -0.4 -0.2 0 0.2 0.4 T (K) CERES TOA = − λ T (Forster & Gregory 2006, Murphy 2009, Trenberth et al 2010, Dessler 2010, Stevens & Schwartz 2012, Tsushima & Manabe 2013, Zhou et al 2015)

Choices, choices, choices…. Monthly Sensitive to • averaging T (K) • lag • record length Annual TOA (W/m 2 ) GISTEMP TOA (W/m 2 ) Monthly, lag 4 TOA CERES T (K) (Forster 2016)

Lagged Regression Monthly Sensitive to • averaging • lag • record length Annual TOA (W/m 2 ) Monthly, lag 4 TOA T (K) (Forster 2016)

#GOALS TOA + F rad − λ T Sensitive to + F ocn • averaging • lag • record length Q = − λ T + F rad + F ocn TOA 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)

CESM1 Reproduces salient feature

CESM1 Reproduces salient feature

Physics is separated by frequency, not lag -Carl Wunsch

We need a dynamical model TOA − λ T + F rad + F ocn Q = − λ T + F rad + F ocn TOA

Hasselmann Model TOA − λ T + F rad + F ocn C dT dt = − λ T + F rad + F ocn TOA white noise

Phase fingerprints forcing: ocean forcing TOA − λ T + F rad + F ocn C dT dt = − λ T + F rad + F ocn TOA ( in phase ) TOA = − λ T

Phase fingerprints forcing: radiative forcing TOA − λ T + F rad + F ocn C dT dt = − λ T + F rad + F ocn TOA TOA = C dT ( quadrature ) dt

Physics is separated by frequency, not lag -Carl Wunsch Physics is separated by model hierarchy - Isaac Held (paraphrased)

CESM1 model hierarchy Unforced, pre-industrial control runs • Energy Balance Model • OCN: CESM1 (CAM5) Atmosphere( Y ), Slab( Y ), ENSO( Y ) • SOM: CAM5 + slab ocean model Atmosphere( Y ), Slab( Y ), ENSO( N ) • fSST: CAM5 + fixed SSTs Atmosphere( Y ), Slab( N ), ENSO( N )

Fixed SST simulation TOA − λ T + F rad + F ocn C dT 1 dt = − λ 1 T 1 + F rad + F ocn TOA 1

Fixed SST simulation: ocean forced TOA − λ T + F rad + F ocn C dT 1 dt = − λ 1 T 1 + F rad + F ocn TOA 1 ( in phase ) TOA 1 = − λ 1 T 1

Slab Ocean Model TOA − λ T + F rad + F ocn C dT 2 dt = − λ 2 T 2 + F rad + F ocn TOA 2

Slab Ocean Model: radiatively forced slow mode TOA − λ T + F rad + F ocn Q C dT 2 dt = − λ 2 T 2 + F rad + F ocn TOA 2 dT 2 ( in quadrature ) TOA 2 = − C 2 dt

On fast time scales Air-Sea fluxes provide both forcing and damping TOA Ocean-atmosphere exchanges − λ T + F rad H ∝ U ( T o − T ) Can be separated into Q H H ∝ U ( T o − T ) 0 + U 0 ( T o − T )

On fast time scales Air-Sea fluxes provide both forcing and damping TOA Ocean-atmosphere exchanges − λ T + F rad H ∝ U ( T o − T ) Can be separated into + F ocn = λ ao T + H ∝ U ( T o − T ) 0 + U 0 ( T o − T ) Wind-driven term acts as forcing. Temperature driven term acts as damping term (feedback) H = λ ao T + F ocn

Coupled atmosphere-ocean model dT a (1) dt = − λ rad,a T a + F rad,l − λ ao ( T a − T o ) + F ocn C a TOA + F rad − λ T dT o dt = − λ rad,o T o + F rad,o + λ ao ( T a − T o ) − F ocn C o (2) + F ocn TOA SHF = λ ao T •Atmosphere & land warming may excite different radiative feedbacks vs mixed layer warming (Proistosescu & Huybers 2017) •The system evolves along two eigenmodes, each equivalent to a Hasselmann model (Barsugli and Battisti 1998, Cronin and Emanuel, 2013)

Fast time-scales equivalent to fixed SST dT a (1) dt = − λ rad,a T a + F rad,l − λ ao ( T a − T o ) + F ocn C a TOA + F rad − λ T dT o dt = − λ rad,o T o + F rad,o + λ ao ( T a − T o ) − F ocn C o (2) + F ocn TOA SHF = λ ao T λ rad,o ε = λ rad,o + λ ao dT 1 •On fast time-scales mixed-layer ε C a dt = − λ rad,a T 1 + ε F ocn variability is small •(1) is a good approximation for TOA 1 = − λ rad,a T 1 the first eigenmode (Cronin and Emanuel, 2013)

Fast time-scales equivalent to fixed SST dT a dt = − λ rad,a T a + F rad,l − λ ao ( T a − T o ) + F ocn (1) C a dT o dt = − λ rad,o T o + F rad,o + λ ao ( T a − T o ) − F ocn C o (2) TOA SHF λ rad,o ε = λ rad,o + λ ao dT 1 C 1 dt = − λ 1 T 1 + ε F ocn (Cronin and Emanuel, 2013)

Spectral structures of SHF and TOA support ocean driver fSST ε F ocn SHF PSD TOA + F rad Frequency [1/yr] dT 1 C 1 dt = − λ 1 T 1 + ε F ocn TOA 1 = − λ 1 T 1 + F rad SHF 1 = − λ ao T 1 + F ocn

Filter to high frequencies fSST ε F ocn SHF PSD TOA + F rad Frequency [1/yr] dT 1 C 1 dt = − λ 1 T 1 + ε F ocn TOA 1 = − λ 1 T 1 + F rad SHF 1 = − λ ao T 1 + F ocn

High Frequency heat fluxes (fSST) F surf ≈ cU 0 ( T a − T o )

Slow time scales, ocean and atmosphere are in near equilibrium TOA + F rad dT a − λ T (1) dt = − λ rad,a T a + F rad,l − λ ao ( T a − T o ) + F ocn C a dT o + F ocn dt = − λ rad,o T o + F rad,o + λ ao ( T a − T o ) − F ocn C o (2) = λ ao T TOA SHF •On slow time-scales atmosphere and ocean are equilibrated T a ≈ T o ≈ T 2 (Cronin and Emanuel, 2013)

Slow time scales, the system coevolves TOA + F rad dT a − λ T dt = − λ rad,a T a + F rad,l − λ ao ( T a − T o ) + F ocn (1) C a dT o + F ocn dt = − λ rad,o T o + F rad,o + λ ao ( T a − T o ) − F ocn C o (2) = λ ao T TOA SHF dT 1 dt = − ( λ rad,a + λ ao ) T 1 + F ocn C a ( C a + C o ) dT 2 dt = λ 2 T 2 + F rad (Cronin and Emanuel, 2013)

Slow time scales, the system coevolves TOA + F rad − λ T + F ocn = λ ao T dT 1 dt = − ( λ rad,a + λ ao ) T 1 + F ocn C a ( C a + C o ) dT 2 dt = λ 2 T 2 + F rad (Cronin and Emanuel, 2013)

T 1 , T 2 are eigenmodes of a coupled atmosphere-slab model TOA + F rad − λ T + F ocn = λ ao T 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

Additional ENSO mode TOA + F rad − λ T + F ocn = λ ao T •Damped linear oscillator dT 2 dt 2 + 2 τ dT f E dt + λ T = η ocn •TOA and T constant phase lag TOA ( t ) = − λ T ( t − θ )

We can model the lagged regression We have an analytical stochastic linear model Spectral solution Cross Spectrum Wiener-Khinchin Theorem Lagged Covariance Lagged Regression

Fixed SST — CESM 1 — EBM Slope (W/m 2 /K) TOA 1 = − λ 1 T 1 + F rad T 1 TOA 1 Lag (years)

Slab Ocean Model — CESM 1 — EBM Slope (W/m 2 /K) TOA 1 = − λ 1 T 1 + F rad TOA 2 = − λ 2 T + F rad ∝ dT 2 dt T 1 + T 2 + TOA 1 + TOA 2 Lag (years)

Regression dillution (timescale) ✓ σ T i — CESM 1 ◆ X r (lag) = acf(lag) λ i — EBM σ total Slope (W/m 2 /K) •Net feedback ✦ average of distinct feedbacks, ✦ weighted by relative variance & ✦ weighted by lag T 1 + T 2 + TOA 1 + TOA 2 Lag (years)

Regression dilution (timescale) ✓ σ T i ◆ X r (lag) = acf(lag) λ i σ total