RisserMR StoneDA IMSC2016
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
´ ı Stone, Christopher Paciorek, Mark Risser, Daith´ ´ Michael Wehner, Oliver Angelil
Mark Risser ([email protected])
1
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
The computational challenge of event attribution • We need climate models to accurately characterise the counterfactual scenario • We need large ensembles to resolve the probabilities of rare events • We need high spatial resolution to resolve extreme weather • Ocean-atmosphere models have large biases which may severely distort physical and statistical representation of extremes
Mark Risser ([email protected])
2
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
“Pall2011” solution: forget the ocean!
Mark Risser ([email protected])
3
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
But there are important assumptions... Invariance to ocean state: Anthropogenic response same for all ocean states, e.g. ˜ and La Nina ˜ events same risk ratios for El Nino No change in ocean variability: The nature of ocean variability, e.g. frequency of ˜ El Ninos Unimportance of ocean-atmosphere interaction: Short-time scale interactions, e.g. under tropical cyclones
Here we examine the appropriateness of the first assumption
Mark Risser ([email protected])
4
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
CAM5.1-1degree simulations in the C20C+ D&A Project Scenario
Number of simulations
“All-Hist/est1”
50 for 1982-2013, 50 for 1997-2013, 300 for 2011-2013
“Nat-Hist/CMIP5-est1”
50 for 1982-2013, 50 for 1997-2013, 300 for 2011-2013
• Details on simulations at http://portal.nersc.gov/c20c • Also see poster #5 tomorrow!
Estimate Risk Ratio:
Mark Risser ([email protected])
RRt =
pAt pN t
t = 1, . . . , T
5
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Hierarchical statistical model for ALL and NAT probabilities • A hierarchical statistical modelling framework to borrow information over time. • First level: – The number of ALL or NAT simulations in month j of year t in which the event occurred:
ZAtj and ZN tj .
– Modelled as arising from a binomial experiment with nt total trials and success probabilities pAtj and pN tj . – Conditional on probabilities pAtj and pN tj , Zktj and ZN tj are independent.
Mark Risser ([email protected])
6
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
• Second level: – A mixed effects logistic regression –
logit pktj ≡ log
pktj 1−pktj
= x⊤ kt β k + αt + δt 1{k=A} + γj
∗ k ∈ {A, N }, t = 1, . . . , T , j = 1, . . . , 12 ∗ xkt = (1, xkt1 , . . . , xktr ) is a vector of r covariates ∗ β k = (βk0 , . . . , βkr ) is a vector of unknown regression coefficients • Third level: – Tie together year-specific effects (αt , δt ) and month-specific effects (γj ) to allow borrowing of information (“partial pooling”) – Specify
iid
2
αt ∼ N (0, τ ),
Mark Risser ([email protected])
iid
2
δt ∼ N (0, σ ),
iid
γt ∼ N (0, ω 2 )
7
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Bayesian analysis • Set θ = (α, δ, γ, β A , β N , τ 2 , σ 2 ) • Rewrite likelihood in terms of parameters: p(Z|θ) • Use Bayes’ Theorem to update the prior with observed data (Z) to determine posterior:
p(θ|Z) =
R p(Z|θ)p(θ) θ p(Z|θ)p(θ)dθ
• Posterior not available in closed form, so use Markov chain Monte Carlo methods to obtain joint samples from the posterior of θ
Mark Risser ([email protected])
8
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
And finally to the Risk Ratio... • RRt ≈= RR0 × exp{βA1 xAt1 − βN 1 xN t1 } × exp{δt } • So we can interpret σ 2 = Var(δt ) ≈ Var(log RRt ) as the effect of oceanic internal variability
Mark Risser ([email protected])
9
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Applying it to monthly hot, cold, wet months over
∼ 2Mm2 regions Regions
Mark Risser ([email protected])
Covariate
10
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Hot months, Krasnoyarsk, Russia
Mark Risser ([email protected])
11
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Wet months, S. Andean Community (Peru, Bolivia)
Mark Risser ([email protected])
12
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
The quantitative effect of ocean variability:
Mark Risser ([email protected])
σ
13
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Anti-correlation of quantitative and qualitative effects! Hot
Mark Risser ([email protected])
Cold
14
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Wet
Mark Risser ([email protected])
15
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
For more information: Mark Risser: [email protected] C20C+ D&A Project: http://portal.nersc.gov/c20c/
Mark Risser ([email protected])
16
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
´ ı Stone, Christopher Paciorek, Mark Risser, Daith´ ´ Michael Wehner, Oliver Angelil
Mark Risser ([email protected])
1
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
The computational challenge of event attribution • We need climate models to accurately characterise the counterfactual scenario • We need large ensembles to resolve the probabilities of rare events • We need high spatial resolution to resolve extreme weather • Ocean-atmosphere models have large biases which may severely distort physical and statistical representation of extremes
Mark Risser ([email protected])
2
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
“Pall2011” solution: forget the ocean!
Mark Risser ([email protected])
3
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
But there are important assumptions... Invariance to ocean state: Anthropogenic response same for all ocean states, e.g. ˜ and La Nina ˜ events same risk ratios for El Nino No change in ocean variability: The nature of ocean variability, e.g. frequency of ˜ El Ninos Unimportance of ocean-atmosphere interaction: Short-time scale interactions, e.g. under tropical cyclones
Here we examine the appropriateness of the first assumption
Mark Risser ([email protected])
4
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
CAM5.1-1degree simulations in the C20C+ D&A Project Scenario
Number of simulations
“All-Hist/est1”
50 for 1982-2013, 50 for 1997-2013, 300 for 2011-2013
“Nat-Hist/CMIP5-est1”
50 for 1982-2013, 50 for 1997-2013, 300 for 2011-2013
• Details on simulations at http://portal.nersc.gov/c20c • Also see poster #5 tomorrow!
Estimate Risk Ratio:
Mark Risser ([email protected])
RRt =
pAt pN t
t = 1, . . . , T
5
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Hierarchical statistical model for ALL and NAT probabilities • A hierarchical statistical modelling framework to borrow information over time. • First level: – The number of ALL or NAT simulations in month j of year t in which the event occurred:
ZAtj and ZN tj .
– Modelled as arising from a binomial experiment with nt total trials and success probabilities pAtj and pN tj . – Conditional on probabilities pAtj and pN tj , Zktj and ZN tj are independent.
Mark Risser ([email protected])
6
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
• Second level: – A mixed effects logistic regression –
logit pktj ≡ log
pktj 1−pktj
= x⊤ kt β k + αt + δt 1{k=A} + γj
∗ k ∈ {A, N }, t = 1, . . . , T , j = 1, . . . , 12 ∗ xkt = (1, xkt1 , . . . , xktr ) is a vector of r covariates ∗ β k = (βk0 , . . . , βkr ) is a vector of unknown regression coefficients • Third level: – Tie together year-specific effects (αt , δt ) and month-specific effects (γj ) to allow borrowing of information (“partial pooling”) – Specify
iid
2
αt ∼ N (0, τ ),
Mark Risser ([email protected])
iid
2
δt ∼ N (0, σ ),
iid
γt ∼ N (0, ω 2 )
7
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Bayesian analysis • Set θ = (α, δ, γ, β A , β N , τ 2 , σ 2 ) • Rewrite likelihood in terms of parameters: p(Z|θ) • Use Bayes’ Theorem to update the prior with observed data (Z) to determine posterior:
p(θ|Z) =
R p(Z|θ)p(θ) θ p(Z|θ)p(θ)dθ
• Posterior not available in closed form, so use Markov chain Monte Carlo methods to obtain joint samples from the posterior of θ
Mark Risser ([email protected])
8
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
And finally to the Risk Ratio... • RRt ≈= RR0 × exp{βA1 xAt1 − βN 1 xN t1 } × exp{δt } • So we can interpret σ 2 = Var(δt ) ≈ Var(log RRt ) as the effect of oceanic internal variability
Mark Risser ([email protected])
9
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Applying it to monthly hot, cold, wet months over
∼ 2Mm2 regions Regions
Mark Risser ([email protected])
Covariate
10
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Hot months, Krasnoyarsk, Russia
Mark Risser ([email protected])
11
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Wet months, S. Andean Community (Peru, Bolivia)
Mark Risser ([email protected])
12
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
The quantitative effect of ocean variability:
Mark Risser ([email protected])
σ
13
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Anti-correlation of quantitative and qualitative effects! Hot
Mark Risser ([email protected])
Cold
14
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
Wet
Mark Risser ([email protected])
15
Quantifying the effect of ocean variability on the attribution of extreme climate events to human influence
For more information: Mark Risser: [email protected] C20C+ D&A Project: http://portal.nersc.gov/c20c/
Mark Risser ([email protected])
16
