IMSC Whitney
What can we learn about temperature extremes from millennial-scale equilibrium climate simulations? Whitney Huang1 Joint work Michael Stein2 , Elisabeth Moyer2 , Shanshan Sun2 , and David McInerney3 Purdue University1 , University of Chicago2 , University of Adelaide3
June 8, 2016, IMSC
Overview Climate Model
Statistical Model
GCM (CCSM3)
EVA (GEV)
1000 yrs equilibrated runs
Annual max/min
CO2: 289 and 700 ppm
Return levels
Changes in temperature extremes Data length on return level estimation
Part 1: Changes in temperature extremes
Model annual extremes as GEV distributions I
Example: annual maxima at Texas grid cell
Daily Tmax (°C)
Texas 30
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20 10 0 1
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9
10
Year
I
Fit generalized extreme value (GEV(µ, σ, ξ)) distribution to annual max/min
I
r -year return level: the value whose probability of exceedance is 1r in any given year
Fit GEV to annual max California
preindustrial 700 ppm
50° N ID ●
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45° N 40° N 35° N
CA ●
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TX
30° N
26
28
30
32
Annual maxima (°C)
34
120° W 110° W 100° W
90° W
80° W
70° W
Compute the r-year return level for 289 ppm climate California
preindustrial 700 ppm
26
28
20−yr RL
30
32
34
Annual maxima (°C)
o σ ˆ0 n ˆ ˆ 20 = µ RL ˆ0 − 1 − (− log (1 − 0.05))−ξ0 ξˆ0
Compute the r-year return level for 700 ppm climate California
preindustrial 700 ppm
26
28
20−yr RL
30
20−yr RL
32
34
Annual maxima (°C)
o σ ˆ1 n ˆ ˆ 20 = µ RL ˆ1 − 1 − (− log (1 − 0.05))−ξ1 ξˆ1
Compute the difference in r-year return level California
preindustrial 700 ppm
26
28
20−yr RL
∆20−yr RL
30
20−yr RL
32
34
Annual maxima (°C)
ˆ 20 − RL ˆ 20 ∆20-yr RL = RL
Warm extremes shift with summer means California percentile 0.5
28
30
32
Annual maxima (°C)
34
0.8
0.9
3
1.0
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2 1 0
26
0.7
4
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Change in summer mean Change in 20−yr return
10 20 100
∆20−yr RL
20−yr RL
2
20−yr RL
∆ return level (°C)
preindustrial 700 ppm
0.6
Return period (years)
ˆ = (2.9 ∗ ∗, 0.02, 0.01) (∆ˆ µ, ∆ˆ σ , ∆ξ)
Fit GEV to annual min Texas preindustrial 700 ppm 50° N ID ●
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45° N 40° N 35° N
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CA ●
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TX
30° N
−25 −20 −15 −10
−5
Annual minima (°C)
0
5
120° W 110° W 100° W
90° W
80° W
70° W
Cold extremes shift more than winter means Texas percentile preindustrial 700 ppm
−5
Annual minima (°C)
0
5
0.2
10 ●
0.3
0.4
0.5
Change in winter mean Change in 20−yr return
8 ●
6 4 2
Return period (years)
ˆ = (4.8 ∗ ∗, −1.1 ∗ ∗, 0.05) (∆ˆ µ, ∆ˆ σ , ∆ξ)
2
−25 −20 −15 −10
0.1
100 20 10
∆ return level (°C)
0
Fit GEV to annual min Idaho preindustrial 700 ppm 50° N ID ●
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45° N 40° N 35° N
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TX
30° N
−60
−50
−40
−30
Annual minima (°C)
−20
−10
120° W 110° W 100° W
90° W
80° W
70° W
Cold extremes shift more than winter means Idaho percentile preindustrial 700 ppm
−50
−40
−30
Annual minima (°C)
−20
−10
0.2
0.3
0.4
0.5
12 10
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8 6 4 ●
2
Change in winter mean Change in 20−yr return
Return period (years)
ˆ = (11.0 ∗ ∗, 0.7 ∗ ∗, 0.03) (∆ˆ µ, ∆ˆ σ , ∆ξ)
2
−60
0.1
100 20 10
∆ return level (°C)
0
Part II: Data length on return level estimation
What if we have shorter runs or data?
Annual minima (°C)
Idaho −20
Est 1 Est 2
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Est 19Est 20
−30 −40 −50 −60
200
400
600
800
Year
To assess the sampling error due to short runs I
divide the time series into segments
I
refit GEV to each segment, compute the changes in return levels
1000
Sampling error is large for short runs
Estimates of change in 50−year RL ∆RL50=8.7
Density
20 years data 50 years data
−3
−1
1
2
3
4
5
6
7
8
9
11
Change in 50−year RL (°C)
13
15
17
Summary Changes in temperature extremes (in our model) I
Warm extremes: mainly due to the summer mean shifts
I
Cold extremes: shifts larger than the winter mean shifts
Data length on return level estimation I
Sampling error is large for extrapolation
Things not addressed I
Is annual block size long enough?
I
Comparison of different estimation methods
Acknowledgments I
RDCEP: Center for Robust Decision Making on Climate and Energy Policy
I
STATMOS: Research Network for Statistical Methods for Atmospheric and Oceanic Sciences
I
Under revision at Advances in Statistical Climatology, Meteorology and Oceanography (ASCMO)
June 8, 2016, IMSC
Overview Climate Model
Statistical Model
GCM (CCSM3)
EVA (GEV)
1000 yrs equilibrated runs
Annual max/min
CO2: 289 and 700 ppm
Return levels
Changes in temperature extremes Data length on return level estimation
Part 1: Changes in temperature extremes
Model annual extremes as GEV distributions I
Example: annual maxima at Texas grid cell
Daily Tmax (°C)
Texas 30
●
● ●
●
●
●
●
●
●
●
20 10 0 1
2
3
4
5
6
7
8
9
10
Year
I
Fit generalized extreme value (GEV(µ, σ, ξ)) distribution to annual max/min
I
r -year return level: the value whose probability of exceedance is 1r in any given year
Fit GEV to annual max California
preindustrial 700 ppm
50° N ID ●
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45° N 40° N 35° N
CA ●
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TX
30° N
26
28
30
32
Annual maxima (°C)
34
120° W 110° W 100° W
90° W
80° W
70° W
Compute the r-year return level for 289 ppm climate California
preindustrial 700 ppm
26
28
20−yr RL
30
32
34
Annual maxima (°C)
o σ ˆ0 n ˆ ˆ 20 = µ RL ˆ0 − 1 − (− log (1 − 0.05))−ξ0 ξˆ0
Compute the r-year return level for 700 ppm climate California
preindustrial 700 ppm
26
28
20−yr RL
30
20−yr RL
32
34
Annual maxima (°C)
o σ ˆ1 n ˆ ˆ 20 = µ RL ˆ1 − 1 − (− log (1 − 0.05))−ξ1 ξˆ1
Compute the difference in r-year return level California
preindustrial 700 ppm
26
28
20−yr RL
∆20−yr RL
30
20−yr RL
32
34
Annual maxima (°C)
ˆ 20 − RL ˆ 20 ∆20-yr RL = RL
Warm extremes shift with summer means California percentile 0.5
28
30
32
Annual maxima (°C)
34
0.8
0.9
3
1.0
●
2 1 0
26
0.7
4
●
Change in summer mean Change in 20−yr return
10 20 100
∆20−yr RL
20−yr RL
2
20−yr RL
∆ return level (°C)
preindustrial 700 ppm
0.6
Return period (years)
ˆ = (2.9 ∗ ∗, 0.02, 0.01) (∆ˆ µ, ∆ˆ σ , ∆ξ)
Fit GEV to annual min Texas preindustrial 700 ppm 50° N ID ●
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45° N 40° N 35° N
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CA ●
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TX
30° N
−25 −20 −15 −10
−5
Annual minima (°C)
0
5
120° W 110° W 100° W
90° W
80° W
70° W
Cold extremes shift more than winter means Texas percentile preindustrial 700 ppm
−5
Annual minima (°C)
0
5
0.2
10 ●
0.3
0.4
0.5
Change in winter mean Change in 20−yr return
8 ●
6 4 2
Return period (years)
ˆ = (4.8 ∗ ∗, −1.1 ∗ ∗, 0.05) (∆ˆ µ, ∆ˆ σ , ∆ξ)
2
−25 −20 −15 −10
0.1
100 20 10
∆ return level (°C)
0
Fit GEV to annual min Idaho preindustrial 700 ppm 50° N ID ●
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45° N 40° N 35° N
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CA ●
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TX
30° N
−60
−50
−40
−30
Annual minima (°C)
−20
−10
120° W 110° W 100° W
90° W
80° W
70° W
Cold extremes shift more than winter means Idaho percentile preindustrial 700 ppm
−50
−40
−30
Annual minima (°C)
−20
−10
0.2
0.3
0.4
0.5
12 10
●
8 6 4 ●
2
Change in winter mean Change in 20−yr return
Return period (years)
ˆ = (11.0 ∗ ∗, 0.7 ∗ ∗, 0.03) (∆ˆ µ, ∆ˆ σ , ∆ξ)
2
−60
0.1
100 20 10
∆ return level (°C)
0
Part II: Data length on return level estimation
What if we have shorter runs or data?
Annual minima (°C)
Idaho −20
Est 1 Est 2
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Est 19Est 20
−30 −40 −50 −60
200
400
600
800
Year
To assess the sampling error due to short runs I
divide the time series into segments
I
refit GEV to each segment, compute the changes in return levels
1000
Sampling error is large for short runs
Estimates of change in 50−year RL ∆RL50=8.7
Density
20 years data 50 years data
−3
−1
1
2
3
4
5
6
7
8
9
11
Change in 50−year RL (°C)
13
15
17
Summary Changes in temperature extremes (in our model) I
Warm extremes: mainly due to the summer mean shifts
I
Cold extremes: shifts larger than the winter mean shifts
Data length on return level estimation I
Sampling error is large for extrapolation
Things not addressed I
Is annual block size long enough?
I
Comparison of different estimation methods
Acknowledgments I
RDCEP: Center for Robust Decision Making on Climate and Energy Policy
I
STATMOS: Research Network for Statistical Methods for Atmospheric and Oceanic Sciences
I
Under revision at Advances in Statistical Climatology, Meteorology and Oceanography (ASCMO)
