Statistical downscaling of rainfall extremes for the Hawaiian Islands Oliver Elison Timm 1 Henry F. Diaz 2 Thomas Giambelluca 3 Mami Takahashi 3 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 26 th 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 climateMost models: wetter climate No significant changeModels show a wetter climate

Extreme events: Changes in the tail of distribution Gaussian distribution Gamma distribution present present

Hawaii's rainfall is controlled by large-scale modes in synoptic circulation Trade Wind Regime Kona 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”) Hilo

Hawaii's rainfall is controlled by large-scale circulation pattern ‘Kona wind’ regime: Favourable condition for moisture-rich air masses from tropics

Horizontal anomalies linked to anomalies in vertical structure upward moisture flux downward moisture flux <30% of mean rainfall % of mean rainfall % of mean rainfall >220% of mean rainfall Island-wide station index for rainfall percentages relative to long-term climatological mean (134 stations) 95% percentile = 220% mean precipitation

Task: discriminate extreme events within the information from large-scale circulation Example illustration of the detection of extreme rainfall events using specific humidity and vertical velocity (omega) at 700hPa level. Red dots: Island-wide extreme rain events (daily data) (>95% percentile) find climate variables and pattern that provide best information for ‘hindcasting’ extreme events

From large-scale circulation to extreme event 'hindcast' We use the circulation anomalies that occur on days with extreme events to 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 Local rainfall we use logistic regression to hindcast events

From large-scale circulation to local extreme events ('hindcast') Specific humidity anomalies and wind anomalies 700 hPa Projection pattern: typical circulation anomalies during extreme rain events at Naalehu (southern Big Island) P X(t) P i(t) = Resulting projection index and 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 Naalehu / /random guess

Measuring the skill in 2-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 Naalehu / /random guess

Measuring the skill in terms 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 events at Naalehu (southern Big Island) P X(t) P i(t) = Resulting projection index and 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 ECHAM 20 th cent. ECHAM ECHAM

Projected changes: present / / (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 season present / / 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 information to 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

What is the limit of the prediction skill? TRMM satellite rainfall estimates 11-Dec-1999 NCEP Reanalysis rainfall estimates 11-Dec-1999 Reanalysis products have their own uncertainty State of large-scale circulation and projection indices contain errors ERA40 Reanalysis data and TRMM rainfall estimates 11-Dec-1999

Extreme events are local features: spatial correlation is low TRMM GPCP GOES ERA40 NCEP different rainfall estimates for Hawaii wet season Nov 1999 – Apr 2000 data source: Asia-Pacific Data-Research Center (APDRC)

How to update the contingency table information? Contingency table equivalent to joint distribution p(e,h) Conditional p(e|h)=p(e,h)/p(h) Assumption: p(e|h) does not change under changing climate p(e,h)=p(e|h)*p(h) → p(e) can be obtained by marginalization Moreover we can use p(e,h) to estimate the estimated hit rate, missed events and false alarm rate.