Projecting the uncertainty of sea level rise using climate models and statistical downscaling!
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1 Projecting the uncertainty of sea level rise using climate models and statistical downscaling! Peter Guttorp! Norsk Regnesentral! University of Washington!
2 Outline! The importance of sea level rise! Measuring sea level! Modeling global sea level! Modeling local sea level! Uncertainty quantification!
3
4 City of Vancouver! $25 billion worth of real estate at risk by end of century! Flooding, storm surge damage, erosion, groundwater levels! BC expects 50cm rise by 2050! Greenest City Action Plan 2011! Climate Change Adaptation Strategy 2012!
5 Measuring tides! Connected to sea in bottom of well. Eliminates wave action and enables measurement under ice. A GPS measures station altitude.!
6 Sea level data!
7 Global mean sea level! Each point in the global mean sea level (GMSL) time series plots is the area-weighted mean of all of the sea surface height anomalies measured either by tide gauges or (from 1995) by the altimeter of the TOPEX and Jason satellites in a single, 10-day satellite track repeat cycle (time for the satellite to begin repeating the same ground track).!
8 Difference between gauges and satellite! Land motion! glacial rebound (millenial scale)! tectonic activity (decadal scale)! Altimeter drift! orbital drift! instrument drift! Sea level anomaly (cm) Year
9 Climate models! Statistically, climate = distribution of weather etc.! A climate model is a deterministic model of atmosphere, ocean etc.! Numerical solution. Coupling.! Very few climate models calculate sea level.! To get projections of sea level, need combination of eustatic (mass added, 1/3-1/2) and steric (same mass, 1/2-2/3) effects.!
10 Scenarios! Climate models from the latest modeling experiment CMIP5! Four scenarios, named after the 2100 radiative forcing!
11 A simple model! Change in! sea level height! Sea level anomaly (cm) dh dt = a(t T 0) + b dt dt (a) Cumulative change! in temperature! (slow response)! Sea Level Difference (cm) (c) Change in! temperature! (quick response)! â = 0.16 (0.07) ˆb = 0.33 (0.53) Error MA(2) Temperature anomaly ( C) (b) Temperature anomaly ( C) (d) (e) Residual (cm) Residual (cm) Innovation (cm)
12 Robustness of fit! C2006" R07 GISS" 0.36 (0.11)" Current GISS" 0.31 (0.10)" HadCRUT4" 0.31 (0.08)" C2006 Res" R07 GISS" 0.46 (0.09)" Current GISS" 0.40 (0.07)" HadCRUT4" 0.40 (0.09)" C2011" R07 GISS" 0.19 (0.08)" Current GISS" 0.16 (0.07)" HadCRUT4" 0.17 (0.07)" C2011 Res" R07 GISS" 0.31 (0.07)" Current GISS" 0.27 (0.07)" HadCRUT4" 0.28 (0.07)" (0.28,0.64) (0.02,0.30)"
13 Sea level projections! Use projected temperatures instead of observed in the formula!! dh! dt = â(t ˆT 0 ) Each climate model/scenario will give a different projected sea level rise.! Uncertainty? Comes from! Estimation uncertainty! Model uncertainty! Scenario uncertainty!
14 Simultaneous confidence set! The idea is to calculate excursion sets above and below a given level (a set such that the process is above at all points with probability 1-α).! A contour set is the intersection of the (interiors of) complements of excursions above and below.! The computations are done sequentially using fast integration methods for mixtures of Gaussian integrals (Bolin & Lindgren, 2014).!
15 Uncertain projection! RCP 4.5 Sea level anomaly (cm) Year 2100 pointwise CI (38-56) AR5 (33-68)"
16 What if we fit models instead of observations?! 32 models have historical runs! Time series models!! dh(t) = â i (T i (t) ˆT 0,i ) + e i (t)! dt Errors are either ARMA(1,1) or MA(2)! Histogram of slope Frequency slope
17 Year Year Model-based vs. data-based! RCP 2.6 RCP 4.5 Sea level anomaly (cm) Sea level anomaly (cm) Year RCP Year RCP 8.5 Sea level anomaly (cm) Sea level anomaly (cm)
18 IPCC AR5!
19 Selection bias?! RCP 4.5 Temperature Anomaly ( C) Year
20 Do the models reproduce historical temperatures?! CCSM4 GISS data Data CMIP5 models Model CCSM4 GISS data Data CMIP5 models Model
21 Downscaling! Use the statistical relationship between global sea level change and local sea level change!! Apply this relationship to global sea levels estimated from projected temperatures!! Uncertainties?!
22 Local stations! 20 km Map data 2015 City of Kamloops, Google Report a map error
23 Vancouver! Sea level anomaly (cm) Year Vancouver sea level anomalies (cm) Innovation Year Global sea level anomalies (cm)
24 ! gl,i H t!!!! Model for sea level t projections for = â(t u i t 0 H t Van = ˆbH t gl,i + ε t Vancouver! ˆT 0 )du + ς t
25 Year Year Uncertainty bands! RCP 2.6 RCP 4.5 Anomaly (cm) Anomaly (cm) Year RCP Year RCP 8.5 Anomaly (cm) Anomaly (cm)
26 Anomaly (cm) Uncertainty! 2050 RCP 4.5 Density
27 Further directions! Full Bayesian approach with model weights based on quality of historical projections! Uncertainty analysis of IPCC model-based estimates! Spatial estimates at sites without measurements! Tipping point analysis!
28 References! Bolin & Lindgren, JRSS B 77 (2015), ! Bolin et al., Statistica Sinica 25 (2015), ! Guttorp, 2014, Ann. Rev. Statist., 1, ! Guttorp et al, 2014, J Appl Meteor Climat, 53, ! Rahmstorf, S et al., 2011, Clim. Dyn. 39, ! Stocker et al., 2013, Climate Change 2013:! The Physical Science Basis. Cambridge University Press. Ch. 13.!
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