Statistics, Numerical Mdels and Ensembles Duglas Nychka, Reinhard Furrer,, Dan Cley Claudia Tebaldi, Linda Mearns, Jerry Meehl and Richard Smith (UNC). Spatial predictin and data assimilatin Precipitatin extremes Cmbining IPCC climate mdel exp. Supprted by the Natinal Science Fundatin CAS2K5, Annecy, FR, Sep 2005
Anther way f summarizing the talk Part 1: Observatins are in the wrng place! Part 2 Observatins d nt measure what we want! Part 3 Nt sure what we have bserved!
Statistical Science What d yu want t knw? e.g. θ What have yu measured? e.g Y Relate them using a prbability distributin. e.g. Data = parameter errr = θ θ Characterize reasnable values fr θ given the data 0
The statistical methd Fr cmplicated prblems Use Bayesian mdels and Mnte Carl methds t generate a statistical ensemble fr θ. The ensemble mean is a gd estimate fr θ. The spread is a gd measure f uncertainty fr θ.
Part 1: Observatins are in the wrng place! Air quality
Spatial Predictin Predict surface zne where it is nt mnitred. 200 150 Ambient daily zne in PPB June 16, 1987, US Midwestern Regin. 100 50 0
A mdel fr the spatial field The zne surface has a mean and variance that can vary ver space. The crrelatin f zne at tw different lcatins has a knwn frm. Ozne fllws a Gaussian distributin
An ensemble apprach Start with a ensemble f fields that are distributed accrding t nes best guess r frecast withut cnsulting the data. Update each member f the ensemble using the bserved data. The sample mean and cvariances amng the ensemble members culd be used fr the update calculatins. This is the same algrithm used in the ensemble Kalman filter fr numerical weather predictin
Sme ensemble members fr zne
Uncertainty f zne at center f regin Predictins acrss 100 members. Frequency 0 5 10 15 20 25 60 80 100 120 140 160 PPB
Spatial Predictin The ensemble mean A Kriging, Bayes, OI,, BLUE slutin 200 150 100 50 0
A real ensemble frecast. Updates dne as in zne example
Part 2 Observatins d nt measure what we want!
Precipitatin extremes Hw will climate change effect extreme precipitatin? Extremes in precipitatin are used t determine fld ptential fr urban areas, fr dam and radway specificatins and als have extensive eclgical imprtance. Hw des ne estimate extremes where n bservatins are made? Hw des ne determine a pssible 25 year event frm 20 years wrth f data? Typically extremes are described by the return perid: A 25 year event = prbability f seeing this value (r higher) in a given year is 1/25 r 4%
The Western US
Clrad Frnt Range
Observed precipitatin fr Bulder, CO Daily precipitatin amunts mm 0 40 100 1950 1960 1970 1980 1990 2000 years
Observed precipitatin fr Bulder, CO Daily precipitatin amunts threshlded at 2.5 cm mm 0 40 100 1950 1960 1970 1980 1990 2000 years Distributin abve threshld: Density 0.0 0.5 1.0 1.5 2.0 0 1 2 3 4 mm
A spatial mdel fr precipitatin extremes Use extreme value statistical thery t apprximate the distributin f large values three parameters. Assume that the parameters f the distributin vary ver space. (see Part 1.) If yu knw the parameters f the distributin this can easily be cnverted t a 25 year return level.
Distributin fit t the Bulder exceedances... and the estimated 25 year event ( 9cm) Density 0.0 0.2 0.4 0.6 0.8 2 4 6 8 10 12 CM
Six ensemble members fr 25 year event 25 year return level based n all daily met statins in the Frnt Range
Ensemble mean f the 25 year return level
Ensemble mean f the 25 year return level Elevatin and return level (cm)
Part 3 Nt sure what yu have bserved!...
Data and the IPCC What will the climate be like in 2100? Hw much data d we have t answer this questin. The mst recent experiments t supprt the furth reprt f the Internatinal Panel n Climate Change amunt t an archive f apprximately 100 Tb. Mre than 20 different climate mdels/mdeling centers represented. Several different future scenaris. Multiply respnses e.g. temperature, precipitatin,
Sme Data Present winter temperatures, 9 AOGCMs Future - Present really a massive data set? Is this
NCEP Nrthern Hemisphere Winter
Standard IPCC regins
A Statistical Mdel Observatins = truth P errr Mdel Present = truth P mdel/regin bias 1 errr. Mdel Future = truth F mdel/regin bias 2 errr. Climate change = truth F - truth P
Sme ensemble members fr reginal change Future Present DJF temperature (A2)
Western Nrth America temp. change Frequency 0 50 150 250 3.0 3.5 4.0 4.5 5.0 C
Ensemble distributins: AR4 A summary fr the 2 3 4 5 6 7
Summary Statistical ensembles are a useful way t estimate spatial fields and characterize uncertainty. Statistical methds can be used t estimate cmplex indirect features. The size f massive data sets may nt be massive. Statistics can be used t gauge the representativeness f a sample.
Thank yu!