Uncertainty Quantification of the Multi-centennial Response of the - PowerPoint PPT Presentation

Uncertainty Quantification of the Multi-centennial Response of the Antarctic Ice Sheet to Climate Change Kevin Bulthuis 1,2 , M. Arnst 1 , S. Sun 2 and F. Pattyn 2 1 Computational and Stochastic Modeling, Universit´ e de Li` ege, Belgium 2 Laboratory of Glaciology, Universit´ e Libre de Bruxelles, Belgium Houston, USA March 11, 2019 SIAM Conference on Mathematical & Computational Issues in the Geosciences

Motivation � Predicting Antarctica’s contribution to future sea-level rise in a warming world ( ∼ 200 million people at risk in coastal regions). � Understanding and identifying the physical processes, feedbacks and instability mechanisms that govern Antarctica’s response to climate change. � Robust policy response strategies to tackle climate changes should rely on integrated risk and uncertainty assessment in climate change projections [IPCC, 2013]. 5 Meter Inundation Inundated Area 0 100 200 300 400 500 Miles 0 150 300 450 600 750 Kilometers Iceberg breakaway, Larsen C Thwaites Glacier Haskell Indian Nations University [Sentinel 1, 2017] [NASA, 2014] Sea-level rise map [CReSIS, 2013] 1 / 21

Motivation: UQ in ice-sheet models � Increased confidence in predictions requires assessment of uncertainties in ice-sheet models. � Challenges: ◮ Wide range of uncertainties: initial conditions, modelling errors, model parameters, climate forcing, basal friction conditions,. . . ◮ Spatially non-homogeneous input and output fields. ◮ Computational cost. � This talk: ◮ Assessment of the AIS response to uncertainties in key processes. ◮ Methods for propagation of uncertainty and sensitivity analysis in ice-sheet models. ◮ Local outputs vs global outputs. ◮ Essential ice-sheet models: Representations of key processes through parameterisations and reduced-order models. 2 / 21

Outline (1) Motivation (2) Ice-sheet modeling (3) UQ with the f.ETISh ice-sheet model: Methodology (4) UQ with the f.ETISh ice-sheet model: Results (5) Conclusion 3 / 21

”Essential” ice-sheet models for UQ of multi-centennial response of AIS ∗ ∗ Sheet (SIA) ∗ Stream (SIA + SSA) Grounding line Shelf (SSA) τ b τ b Shallow flow models ∂ T ∂ t = κ ∆ T − v · ∇ T + σ : ˙ ǫ/ρ c Grounding-line migration + MISI 1 / n − 1 2 A ( T ) − 1 / n � η = 1 1 2 ˙ ǫ : ˙ ǫ Thermomechanical coupling ∗ ∗ ∗ ∗ B n B 1 Sub-shelf melting (PICO model) + calving Isostatic bedrock adjustment fast Elementary Thermomechanical Ice Sheet model (f.ETISh) [Pattyn, 2017]. ”Essential” ice-sheet model amenable to large-scale and long-term simulations and large-ensemble simulations 4 / 21

Ice-sheet model initialisation: Present-day geophysical datasets Atmospheric temperature Geophysical heat flux [Van Wessem et al., 2014] [An et al., 2015] Effective lithosphere thickness Bedrock elevation and ice thickness [Fretwell et al., 2013] [Chen et al., 2018] 5 / 21

Ice-sheet model initialisation: Inversion of basal sliding conditions Basal sliding coefficient c opt Observed ice thickness h obs Model-data misfit | h − h obs | b � The basal sliding coefficient is obtained by solving an inverse problem that seeks to match the observed present-day ice-sheet thickness while assuming that the ice sheet is in steady state. b × 10 f ( h − h obs ) where f is a ”misfit” function that � Fixed-point iteration algorithm: c ( i +1) = c ( i ) b corrects the predicted basal sliding coefficient in order to match simulated steady-state ice thickness h with observations h obs [Pollard et DeConto, 2012]. � Inversion of basal sliding conditions remains a key issue in numerical ice-sheet models. 6 / 21

Outline (1) Motivation (2) Ice-sheet modeling (3) UQ with the f.ETISh ice-sheet model: Methodology (4) UQ with the f.ETISh ice-sheet model: Results (5) Conclusion 7 / 21

Propagation of uncertainty and sensitivity analysis RCP 8.5 (3000) RCP 2.6 (2300) 7 0 . 4 ∆GMSL (m) ∆GMSL (m) 0 . 3 5 0 . 2 3 0 . 1 1 0 − 0 . 1 − 1 1 1 0 . 6 0 . 8 0 . 6 0 . 8 0 . 5 0 . 5 E shelf 0 . 2 E shelf 0 . 2 0 . 1 0 . 1 F melt F melt � Quantity of Interest: Change in Global Mean Sea Level (∆GMSL). � Polynomial chaos expansions as substitutes for the f.ETISh model and the parameters-to-projection relationships (global outputs are expected to be smooth). � For each RCP scenario and sliding law, we built a polynomial chaos expansion using 500 training points (1 forward simulation: ∼ 8h on the C´ ECI clusters (F.R.S.-FNRS & Walloon Region)). � Stochastic sensitivity analysis: Sobol indices evaluated with polynomial chaos expansions. 8 / 21

Random excursion sets and confidence regions � Motivation: Uncertainty in ice-sheet models can trigger significant grounded-ice retreat under MISI ⇒ Need to quantify grounded-ice retreat with uncertainty. � We investigate uncertainty in grounded-ice retreat using confidence regions for random excursion sets. Let the random field BI = { ρ w b ( s ; Ξ ) + ρ i h ( s ; Ξ ) : s ∈ Ω } be the buoyancy imbalance. The grounded ice domain is defined as the following random positive excursion set E 0 + : D Ξ → Ω; ξ �→ E 0 + ( ξ ) = { s ∈ Ω : BI ( s ; ξ ) ≥ 0 } . Let C I 0 + ( α ) be an open set in Ω. Then C I 0 + ( α ) is an inner confidence region for E u + with inclusion probability at least α if C I � 0 + ( α ) ⊆ E 0 + � ≥ α. P Ξ 9 / 21

Computing confidence regions with a one-parameter family of sets Let M I T ( ρ ) = { s ∈ Ω : T ( s ) > ρ } be a one-parameter family of sets indexed by a real number ρ ∈ (0 , 1) and T : Ω → [0 , 1] be a membership function. Then, an approximation for C I 0 + ( α ) is given by ρ ∗ = ρ ∈ ]0 , 1[ ρ s.t. P Ξ ( M I inf T ( ρ ) ⊆ E 0 + ( Ξ )) ≥ α. This problem is equivalent to a quantile problem ρ ∗ = inf { ρ ∈ ]0 , 1[: c Ψ ( ρ ) ≥ α } , with c Ψ the distribution function of the random variable C I 0 + (0 . 95) ∼ M I T (0 . 98) ψ ( Ξ ) = s ∈ ( E 0+ ( Ξ )) c T ( s ) . sup � Example for T ( s ): P Ξ ( BI ( s ; Ξ ) ≥ 0). � Evaluate ρ ∗ with Monte Carlo sampling. 10 / 21

Outline (1) Motivation (2) Ice-sheet modeling (3) UQ with the f.ETISh ice-sheet model: Methodology (4) UQ with the f.ETISh ice-sheet model: Results (5) Conclusion 11 / 21

Problem setting � Goal: Predicting the response of the AIS over the next millenium with quantified uncertainty. 10 � Set of representative scenarios of anthropogenic greenhouse gas ∆ T relative to present (K) RCP2.6 8 emissions (RCP 2.6, RCP 4.5, RCP 6.0, RCP 8.5). RCP4.5 RCP6.0 ⇒ Trajectory for change ∆ T in background atmospheric 6 RCP8.5 temperature. 4 2 � ∆ T acts as a forcing on 0 • Temperature and precipitation − 2 1900 2000 2100 2200 2300 T = T obs − γ ( h − h obs ) + ∆ T , Year RCP scenarios [IPCC, 2013;Golledge et al., 2015] P = P obs × 2 ∆ T /δ T • Surface melting • Ocean temperature and sub-shelf melting To = To obs + F melt ∆ T . B n B 1 � Set of sliding laws defined as characteristic cases of power-law friction v b = − c b � τ b � m − 1 τ b with exponent m = 1 (linear), Sub-shelf melting [Reese et al., 2018] m = 2 (weakly nonlinear) and m = 3 (strongly nonlinear). 12 / 21

Uncertain parameters and characterisation of uncertainty C r = F calv × C # r ( h , v ) To = To obs + F melt ∆ T F calv ∼ U (0 . 5 , 1 . 5) F melt ∼ U (0 . 1 , 0 . 8) Uncertain calving factor Uncertain melt factor � � � σ � F ∂ b ∂ t = − 1 D = E shelf × A τ ( b − b eq + w b ) √ σ 2 τ w ∼ U (1000 , 3500) yrs E shelf ∼ U (0 . 2 , 1) τ e ∼ U (2500 , 5000) yrs Uncertain bedrock relaxation times Uncertain shelf enhancement factor � In essential ice-sheet models, key processes are represented through parameterisations and reduced-order models with free parameters. � These are lumped representations of various sources of uncertainty. E.g. uncertainty in F melt also entails uncertainties in the shifting of ocean currents, ice-ocean interactions, . . . � Ranges of uncertainty are determined from expert assessment. 13 / 21

Nominal projections 7 RCP2.6 6 RCP4.5 F calv = 1 5 RCP6.0 ∆GMSL (m) RCP8.5 4 F melt = 0 . 3 3 E shelf = 0 . 3 2 τ w = τ e = 3000 yrs 1 m = 2 0 2000 2200 2400 2600 2800 3000 Year RCP 2.6 RCP 4.5 RCP 6.0 RCP 8.5 14 / 21

Parameters-to-projection relationship (RCP 2.6, m = 2, t = 3000 yr) ∆ GMSL (m) 0.8 0.6 0.4 0.2 0 0.5 1.0 1.5 0.1 0.3 0.5 0.7 0.25 0.5 0.75 1.0 3000 4000 5000 1000 2000 3000 τ e (yr) τ w (yr) F calv F melt E shelf � Nonlinear response with respect to the calving and shelf enhancement factors. � Linear response with respect to the melt factor. � The bedrock relaxation times do not contribute significantly to the uncertainty in the projections. 15 / 21

Parameters-to-projection relationship (RCP 8.5, m = 2, t = 3000 yr) ∆ GMSL (m) 6 4 2 0 0.5 1.0 1.5 0.1 0.3 0.5 0.7 0.25 0.5 0.75 1.0 3000 4000 5000 1000 2000 3000 F calv F melt E shelf τ e (yr) τ w (yr) � Nonlinear response with respect with respect to the melt factor. Increasing sub-shelf melting leads to the collapse of the West Antarctic ice sheet. Once the WAIS is disintegrated, a plateau in the response function is reached until marine basins in East Antarctica are activated. � In the high emission scenario RCP 8.5, the AIS response is controlled by sub-shelf melting. � The bedrock relaxation times do not contribute significantly to the uncertainty in the projections. 16 / 21