Statistical downscaling of rainfall Statistical downscaling of rainfall extremes for the Hawaiian Islandsextremes for the Hawaiian Islands

•Oliver Elison Timm1

•Henry F. Diaz2

•Thomas Giambelluca3

•Mami Takahashi3

•1 International Pacific Research Center, University of Hawaii at Manoa , Honolulu, Hawaii•2 Earth System Research Laboratory, CIRES, NOAA, Boulder, Colorado

•3 Department of Geography, University of Hawaii at Manoa , Honolulu, Hawaii

•In collaboration with John Marra, EWC Ocean Science Meeting, Portland, Feburary 26th 2010 IT51C-04

Outline of the presentation

Defining our goal: From IPCC scenarios to local extreme rainfall changes

Data and methods: The statistical challenge of dealing with rare events The downscaling-scheme for daily mean rainfall extremes

Results: Synoptic classifications Linkage between large-scale circulation and local rainfall Downscaling of IPCC AR4 scenario runs

IPCC's Fourth Assessment Report, 2007 precipitation change: likely to decrease

but for Hawaii, no robust signals

Models show a drier climate

Models results inconsistentMost models: drier climate Most models: wetter climate

No significant change Models show a wetter climate

Extreme events: Changes in the tail of distribution

-6 -4 -2 0 2 4 6

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Column C

Column D

Column E

Gaussian distribution

-2 0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

1.2

Column C

Column D

Column E

Gamma distribution

present2046-20652081-2100

present2046-20652081-2100

Hawaii's rainfall is controlled by large-scale modes in synoptic circulation

Trade Wind RegimeKona Wind Regime

700hPa geopotential height and wind anomalies for days with precipitation above 90% quantile

( during wet season)

Left: Station from southern part of Big Island

Right: Hilo Airport

Southern Big Island Eastern Big Island

Na'ālehu(“the volcanic

ashes”)

Na'ālehu(“the volcanic

ashes”)

HiloHilo

Hawaii's rainfall is controlled by large-scale circulation pattern

‘Kona wind’ regime:

Favourable condition

for moisture-rich air

masses from tropics

From large-scale circulation toextreme event 'hindcast'

We use the circulation anomalies that occur on days with extreme eventsto form a 'template pattern'.

-

+

Projection pattern:typical circulation anomalies during extreme rain events

⟶P

-

+

⟶X(t)circulation anomaly:

for a given day t

⟶X(t)

⟶P< , >i(t) =

time t

i(t) extreme event (?)

'Prediction' of extreme events:

Tasks:

•Find the subspace associated with extreme events

in a high-dimensional large-scale climate space X P

•Estimate the transfer-function f(X1,X2,...)

X1(X2) :daily projection index for large-scale projection pattern 1(2)

X1

X2

precipitation

PDF

f(X1,X2)

Large-scale climate

information

Localrainfall

we use logistic regression

to hindcast events

From large-scale circulation tolocal extreme events ('hindcast')

Specific humidity anomalies and wind anomalies 700 hPa

Projection pattern: typical circulation anomalies during extreme rain eventsat Naalehu (southern Big Island)

⟶P

⟶X(t)

⟶X(t)

⟶P< , >i(t) =

Resulting projection indexand observed precipitation

projection index(non-dimensional)rainfall (inches/day)

Measuring the skill of downscaled extreme events:contingency table

hits false alarms

missed events

correct rejections

88/73/105

81/69/105

41/40/4

3572/3447/3415

sum= 122/109/109

81/69/105

sum= 3660/3520/3520

sum= 129/113/109

sum= 3653/3516/3520

sum= 3782/3629/3629

e = yes e = no

h=no

h=yes

e: observed extreme event h: hindcasted event

NCEP reanalysis – Station Naalehu1958-1983/1984-2008/random guess

Measuring the skill in2-d joint probability distribution p(e,h)

hits false alarms

missed events correct rejections

2%/2%/3%

81/69/105

1%/1%/0.1%

95%/95%94%

p(e=1)= 3%/3%/3%

2%/2%2.9%

p(e=0)=97%/97%/97%

p(h=1)=3%/3%/3.1%

p(h=0)=97%/97%/96.9%

100%/100%/100%

e = yes e = no

h=no

h=yes

e: observed extreme event h: hindcasted event

NCEP reanalysis – Station Naalehu1958-1983/1984-2008/random guess

Measuring the skill interms of conditional probabilities p(e|h)

p(e|h)=p(e,h)/p(e)

p(e=yes|h=yes) : 33% / 33% / 3%p(e=yes|h=no) : 2% / 2%/ 3%

p(e=no|h=yes) : 66% / 66% / 97%p(e=no|h=no) : 98% / 98% / 97%

Probability of Detection

Probability of False Alarm

calibration/validation/random guess with p(h=1)=p(e=1)

33% chance of extreme rain given the specific humidity field

specific humidity anomalies 700 hPa (contours)

Projection pattern: typical circulation anomalies during extreme rain eventsat Naalehu (southern Big Island)

⟶P

⟶X(t)

⟶X(t)

⟶P< , >i(t) =

Resulting projection indexand observed precipitation

projection index(non-dimensional)rainfall (inches/day)

ECHAM 4 MPI SRESA1B scenario simulation

Probability Density Function

700-hPa specific humidity

projection Index

NCEP 1958-1983ECHAM 20th cent.ECHAM 2046-2065ECHAM 2081-2100

Projected changes:present / 2046-2065 / 2081-2100

(based on one AR4 model (MPI_ECHAM5 SRESA1B scenario)

hits false alarms

missed events correct rejections

41/40/4 2%/4%/6%

81/69/105

1%/2%/3%

95%/92%89%

p(e=yes)= 3%/4%/5%

2%/2%/2%

p(e=no)=97%/97%/97%

p(h=yes)=3%/6%/9%

p(h=no)=97%/94%/91%

100%/100%/100%

e = yes e = no

h=no

h=yes

Projected changes:expected changes in the contingency table for an

average winter seasonpresent / 2046-2065 / 2081-2100

hits false alarms

missed events correct rejections

41/40/4 4/8/10

81/69/105

2/4/5

170/165/162

p(e=yes)= 6/7/8

4/3/3

p(e=no)=174/173/172

p(h=yes) 6/12/15

p(h=no) 174/168/165

days 180/180/180

e = yes e = no

h=no

h=yes

Conclusions Large-scale circulation provides informationto downscale individual extreme rain events!

Projection-pattern method and logistic regression applicable for Hawaii's rainfall

Model scenarios: downscaled onto the large-scale climate pattern,

they provide quantitative estimates of the expected changes in number of extreme events

Future improvements: – incorporate more large-scale information– multi-model scenario analysis