Post-processing climate model output toobtain accurate high-resolution climateprojections

Thordis ThorarinsdottirNorwegian Computing Centerwww.nr.no/~thordis

Bern

November 9, 2018

Joint with Q Yuan, W K Wong, S Beldring, S Huang and C-Y Xu

Post-processing climate model output toobtain accurate high-resolution climateprojections & why uncertainty matterseven if the answer is just a number

Thordis ThorarinsdottirNorwegian Computing Centerwww.nr.no/~thordis

Bern

November 9, 2018

Joint with Q Yuan, W K Wong, S Beldring, S Huang, C-Y Xu and

Peter Guttorp

(IPCC, 2013)

Objective

Data set Resolution Historical Futureperiod period

seNorge 1× 1 km X ?EURO-CORDEX RCM 12× 12 km X X

I Bias-correction: Correct errors in RCM output

I Downscaling: Recover spatial and temporal variability at thefine scale

I Get results within a feasible computation time

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Methods for bias-correction/downscaling

I Model output statistics: Apply a statistical transfer functionbetween model and observed data

I Perfect prognosis: Link large-scale predictors and local-scalepredictands in a regression framework

I Weather generators: Stochastic models that explicitelymodel marginal and higher order structures

(Maraun and Widmann, 2018)

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seNorge_hist

RCM_hist

Our general framework

seNorge_up

seNorge_hist

RCM_hist

upscale

Our general framework

seNorge_up

seNorge_hist

RCM_hist_corr

RCM_hist

correct bias

upscale

Our general framework

RCM_future_corr

seNorge_up

seNorge_hist

RCM_hist_corr

RCM_histkeep climate change signal

correct bias

upscale

Our general framework

RCM_future_corr

seNorge_up

seNorge_hist

RCM_hist_corr

Variability at 1x1

RCM_histkeep climate change signal

simulate

correct bias

upscale

Our general framework

RCM_future_corr

seNorge_up

seNorge_hist

RCM_hist_corr

Variability at 1x1

RCM_hist

Final outputat 1x1

keep climate change signal

downscale

simulate

correct bias

upscale

Our general framework

Study region and data

I Daily temperature data

I Training set: 1957-1986

I Test set: 1987-2005

I 9 catchments, 150-3000 km2

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Bias-correction

Yst ∼ N(µst , σ2st)

where

µst = f µ1 (xs) + f µ2 (t) + f µ3 (t)

log(σst) = f σ1 (xs) + f σ2 (t)

with

f1: baseline

f2: seasonality

f3: trend

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Modelling fine scale variability

We simulate fine scale variability from a separable space-timemodel estimated using historical residuals at 1× 1 km:

Zst =Yst − µstσst

= ηt + νst

ηt ∼ autoregressive process

Wst = Zst − ηt ∼ N(0,Σt)

Cov(Wst ,Ws′t) = θ0t1{‖s − s ′‖ = 0}+ θ1t exp(−‖s − s ′‖/θ2t)

Simulating 19 years of daily fields for 5000 grid points: 4.5 hours

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Z·t does not have Gaussian marginals

Z·t ∼ TPN(µt , σ1t , σ2t), Ut = Φ−1(FTPN(Z·t)) ∼ AR(p)

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Predictive marginal performance per catchment1987-2005

Full distribution Middle part

Gaulfo

ss

Aamot

Krinsv

atn

Oeyun

gen

Trang

en

Vera

vatn

Dillfos

s

Hoegg

aas_

Bru

Kjelds

tad_

i_Gar

berg

elva

Gaulfo

ss

Aamot

Krinsv

atn

Oeyun

gen

Trang

en

Vera

vatn

Dillfos

s

Hoegg

aas_

Bru

Kjelds

tad_

i_Gar

berg

elva

0.00

0.01

0.02

0.03

0.04

IQD

dsMethod eqm Xstar XshiftTrd XshiftTrdSigma rcm CNRM−CM5_CCLM MPI_CCLM

IQD(F ,G ) =

∫(F (x)− G (x))2ω(x)dx

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Predictive marginal performance per catchment1987-2005

Lower part Upper part

Gaulfo

ss

Aamot

Krinsv

atn

Oeyun

gen

Trang

en

Vera

vatn

Dillfos

s

Hoegg

aas_

Bru

Kjelds

tad_

i_Gar

berg

elva

Gaulfo

ss

Aamot

Krinsv

atn

Oeyun

gen

Trang

en

Vera

vatn

Dillfos

s

Hoegg

aas_

Bru

Kjelds

tad_

i_Gar

berg

elva

0.000

0.003

0.006

0.009

IQD

dsMethod eqm Xstar XshiftTrd XshiftTrdSigma rcm CNRM−CM5_CCLM MPI_CCLM

IQD(F ,G ) =

∫(F (x)− G (x))2ω(x)dx

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Autocorrelation functions per catchment 1987-2005

0.7

0.8

0.9

1.0

0 5 10 15

rawRCM

obs

eqm

sdm

0.7

0.8

0.9

1.0

0 5 10 15

rawRCM

obs

eqm

sdm

0.7

0.8

0.9

1.0

0 5 10 15

rawRCM

obs

eqm

sdm

0.7

0.8

0.9

1.0

0 5 10 15

rawRCM

obs

eqm

sdm

0.7

0.8

0.9

1.0

0 5 10 15

rawRCM

obs

eqm

sdm

0.7

0.8

0.9

1.0

0 5 10 15

rawRCM

obs

eqm

sdm

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Spatial correlation per catchment 1987-2005

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Spatial correlation per catchment 1987-2005

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Why uncertainty matters even if theanswer is just a number

Sea level will rise in Bergen on Norway’s west coast

1950 2000 2050 2100

−20

020

4060

8010

012

0

RCP 8.5

Year

Ano

mal

y (c

m)

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Previous report assessed feasibility, consequencesand costs of several adaptation options

1. Outer barrierI > 30 billion NOKI Large

environmental andeconomicconsequences

2. Inner barrier atVagenI 500 million NOKI Limited benefits

3. Inner barrier atDamgardssundetI 500 million NOKI Limited benefits

Regional Havstigning Prosjektrapport

Bergen, 2009-3-26

Grieg Foundation Visjon Vest G. C. Rieber Fondene

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Our questions

I Are these adaptation options appealing from a cost/benefitperspective?

I If we should adapt, when would be the best time?

I What are the effects of the associated uncertainties on thecost/benefit analysis?I Sea level rise is uncertainI Total yearly damage in each year is uncertainI Change in the total yearly damage due to sea level rise is

uncertain

https://github.com/eSACP/SeaLevelDecisions

(T. et al., Water Resources Research, 2017)

(Guttorp and T., Significance, 2018)

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Our questions

I Are these adaptation options appealing from a cost/benefitperspective?

I If we should adapt, when would be the best time?

I What are the effects of the associated uncertainties on thecost/benefit analysis?I Sea level rise is uncertainI Total yearly damage in each year is uncertainI Change in the total yearly damage due to sea level rise is

uncertain

https://github.com/eSACP/SeaLevelDecisions

(T. et al., Water Resources Research, 2017)

(Guttorp and T., Significance, 2018)

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Our questions

I Are these adaptation options appealing from a cost/benefitperspective?

I If we should adapt, when would be the best time?

I What are the effects of the associated uncertainties on thecost/benefit analysis?I Sea level rise is uncertainI Total yearly damage in each year is uncertainI Change in the total yearly damage due to sea level rise is

uncertain

https://github.com/eSACP/SeaLevelDecisions

(T. et al., Water Resources Research, 2017)

(Guttorp and T., Significance, 2018)

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Local sea level projections

We relate git-corrected Bergen sea level to global sea levelseries of Church and White (2011), then use the method of Bolinet al. (2014) to model the relationship between global annualmean temperature and global annual mean sea level rise.

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Local sea level projections

1950 2000 2050 2100

−20

020

4060

8010

012

0

RCP 8.5

Year

Ano

mal

y (c

m)

1950 2000 2050 21000

5010

0

RCP 8.5

Year

Ano

mal

y (c

m)

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Changes in damage costs due to sea level rise

●●

●

Sea level anomaly (cm)

Rel

ativ

e m

ean

annu

al d

amag

e

0 10 20 30 40

15

100

150

200

●●

●

●

●

●

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Sea level anomaly (cm)

Rel

ativ

e m

ean

annu

al d

amag

e

−100 −50 0 50 100

0.00

51

200

400

600

800

1000

● ● ●●●

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Hallegatte et al. (2013) investigate global changes in damagecosts under 20 and 40 cm sea level rise. We extrapolate theirresults for 15 European cities and use the results as an ensembleprediction for the changes in damage costs in Bergen.

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Annual damage costs

Cost (million NOK)

Dens

ity

0 5 10 15 20 25

0.0

0.5

1.0

1.5

2.0

2.5

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

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●

●

● ●

●

●

Estimated quantiles

Obs

erve

d qu

antile

s

0 5 10 15 20 25

05

1015

2025

The Norwegian Natural Perils Pool publishes annual damage costsdue to storm surges on county level. We fit a Burr distribution tothe 1980-2015 data from Hordaland and Rogaland counties.

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Optimal adaptation timing depends on thedecision-maker’s loss function/risk aversion

2020 2040 2060 2080 2100

01

23

4

Year of adaptation measure

Tota

l cos

t 201

6−21

00 (

billi

on N

OK

)

Adaptation option: Build two inner barriers

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Including the uncertainty is vital; uncertainty in thedamage costs has the largest effect

Total cost 2016−2100 (million NOK)

10 20 50 150 500 1500 5000

RCP 8.5

RCP 4.5

RCP 2.6 No uncertaintyDamage uncertaintyEffect uncertaintySLR uncertaintyFull uncertainty

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Excluding uncertainty in sea level rise projectionsdelays the assessed timing for adaptation by adecade

2020 2040 2060 2080 2100

01

23

4

Year of adaptation measure

Tota

l cos

t 201

6−21

00 (

billi

on N

OK

)

Adaptation option: Build two inner barriers

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Conclusions

I Statisticians have a lot to contribute in climate science andclimate-related decision-making (Benestad et al., NCC, 2017)I Stochastic models are needed to realistically describe fine scale

variability in statistical downscalingI Uncertainty assessments and propagation of uncertainty are

vital

I Communication and messaging are key components

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