Regional climate prediction comparisons

via statistical upscaling and downscaling

Peter GuttorpUniversity of Washington

Norwegian Computing Center

peter@stat.washington.edu

Outline

Regional climate modelsComparing model to dataUpscalingDownscalingResults

Acknowledgements

Joint work with Veronica Berrocal, University of Michigan, and Peter Craigmile, Ohio State University

Temperature data from the Swedish Meteorological and Hydrological Institute web site

Regional model output from Gregory Nikulin, SMHI

Climate and weather

Climate change [is] changes in long-term averages of daily weather.

NASA: Climate and weather web site

Climate is what you expect; weather is what you get.

Heinlein: Notebooks of Lazarus Long (1978)

Climate is the distribution of weather.

AMSTAT News (June 2010)

Data

SMHI synoptic stations in south central Sweden, 1961-2008

Models of climate and weather

Numerical weather prediction:Initial state is criticalDon’t care about entire distribution, just most likely eventNeed not conserve mass and energy

Climate models:Independent of initial stateNeed to get distribution of weather rightCritical to conserve mass and energy

Regional climate models

Not possible to do long runs of global models at fine resolutionRegional models (dynamic downscaling) use global model as boundary conditions and runs on finer resolutionOutput is averaged over land use classes“Weather prediction mode” uses reanalysis as boundary conditions

Comparison of model to data

Model output daily averaged 3hr predictions on (12.5 km)2 gridUse open air predictions onlyRCA3 driven by ERA 40/ERA InterimData daily averages point measurements (actually weighted average of three hourly measurements, min and max)Aggregate model and data to seasonal averages

Upscaling

Geostatistics: predicting grid square averages from dataDifficulties:TrendsSeasonal variationLong term memory featuresShort term memory features

Long term memory models

A “simple” model

space-time trend

periodic seasonalcomponent

noise

seasonalvariability

Looking site by site

Naive wavelet-based trend (Craigmile et al. 2004)

Seasonal part

Seasonal variability

Modulate noise two term Fourier series

Both long and short memory

Consider a stationary Gaussian process with spectral density

Examples:B(f) constant: fractionally differenced process (FD)B(f) exponential: fractional exponential process (FEXP) (log B truncated Fourier series)

Short term memory Long term

memory

Estimated SDFs of standardized noise

Clear evidence of both short and long memory parts

FD

FEXP

Space-time model

Gaussian white measurement errorProcess model in wavelet space

scaling coefficients have mean linear in time and latitude separable space-time covariancetrend occurs on scales ≥ 2j for some jobtained by inverse wavelet transform with scales < j zeroed

Gaussian spatially varying parameters

Dependence parameters

LTM

Short term

Trend estimates

Estimating grid squares

Pick q locations systematically in the grid squareDraw sample from posterior distribution of Y(s,t) for s in the locations and t in the seasonCompute seasonal averageCompute grid square average

Downscaling

Climatology terms:Dynamic downscalingStochastic downscalingStatistical downscaling

Here we are using the term to allow•data assimilation for RCM•point prediction using RCM

Downscaling model

smoothed RCM

(0.91,0.95)

Comparisons

Reserved stations

Borlänge: Airport that has changed ownership, lots of missing dataStockholm: One of the longest temperature series in the world. Located in urban park.Göteborg: Urban site, located just outside the grid of model output

Predictions and data

Spatial comparison

Annual scale

Borlänge

Stockholm

Göteborg

Comments

Nonstationarityin meanin covariance

Uncertainty in model output”Extreme seasons” where down-and upscaling agree with each other but not with the model outputModel correction approaches