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
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