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Regional climate prediction comparisons
via statistical upscaling and downscaling
Peter GuttorpUniversity of Washington
Norwegian Computing Center
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Outline
Regional climate modelsComparing model to dataUpscalingDownscalingResults
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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
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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)
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Data
SMHI synoptic stations in south central Sweden, 1961-2008
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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
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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
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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
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Upscaling
Geostatistics: predicting grid square averages from dataDifficulties:TrendsSeasonal variationLong term memory featuresShort term memory features
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Long term memory models
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A “simple” model
space-time trend
periodic seasonalcomponent
noise
seasonalvariability
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Looking site by site
Naive wavelet-based trend (Craigmile et al. 2004)
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Seasonal part
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Seasonal variability
Modulate noise two term Fourier series
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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
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Estimated SDFs of standardized noise
Clear evidence of both short and long memory parts
FD
FEXP
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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
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Dependence parameters
LTM
Short term
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Trend estimates
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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
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Downscaling
Climatology terms:Dynamic downscalingStochastic downscalingStatistical downscaling
Here we are using the term to allow•data assimilation for RCM•point prediction using RCM
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Downscaling model
smoothed RCM
(0.91,0.95)
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Comparisons
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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
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Predictions and data
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Spatial comparison
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Annual scale
Borlänge
Stockholm
Göteborg
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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