1. Statistical downscaling using Localized Constructed Analogs (LOCA)
David Pierce and Dan Cayan
Scripps Institution of Oceanography
Bridget Thrasher, Edwin Maurer, John Abatzoglou, Katherine Hegewisch
SLOW
Why yet another statistical downscaling scheme?
Motivated by our D&A studies of western runoff, temperature, and snowpack
Emphasize hydrological and D&A implications
Development sponsored by
The California Energy Commission
Department of Interior/US Geological Survey  via the Southwest Climate Science Center
NOAA RISA Program through the California Nevada Applications Program
Production runs sponsored by
U.S. Army Core of Engineers/USBR
NASA via computing resources

2. Downscaling system Global Regridding Bias Spatial
Models Correction Downscaling
Quantile Mapping
(QM)
Constructed Analogs
(CA; Hidalgo et al. 2008)
Bias Correction and Constructed Analogs (BCCA; Maurer et al. 2010)
Multivariate Adapted Constructed analogs (MACA; Abatzoglou & Brown 2012)
Bias Correction with Spatial Disaggregation (BCSD; Wood et al. 2004)

3. Issues with bias correction

4. 1. QM does not preserve model-predicted changes
(Maurer and Pierce, HESS, 2014)
deg-C
Tmax
Difference between original model-predicted change and change after bias correction
minus
Ensemble averaged across 21 GCMs

5. EDCDFm reference:
Li, H., J. Sheffield, and E. F. Wood, 2010: Bias correction of monthly precipitation and temperature fields from Intergovernmental Panel on Climate Change AR4 models using equidistant quantile matching. J. Geophys. Res. Atmos., 115 (D10101), doi: /2009JD

6. What about precipitation?
Evaluate temperature changes as a difference (degrees C)
Evaluate precipitation changes as a ratio (percent)
Positive definite
Wide dynamic range
Rain shadow regions

7. Precipitation
Difference between original model-predicted change and change after bias correction in percentage points
minus
Ensemble averaged across 21 GCMs

8. “PresRat” scheme Like EDCDFm (Li et al. 2010) except:
Preserves the ratio of model-predicted changes (not the difference)
Zero-precipitation threshold (preserve observed number of dry days in historical period)
Final correction factor to preserve mean change

9. “PresRat” scheme Like EDCDFm (Li et al. 2010) except:
Preserves the ratio of model-predicted changes (not the difference)
Zero-precipitation threshold (preserve observed number of dry days in historical period)
Final correction factor to preserve mean change

10. Correction factor
Correction factors necessary to preserve model-predicted changes ( vs ) in mean precipitation
Averaged across 21 GCMs

11. Precipitation
Difference between original model-predicted change and change after bias correction in percentage points
minus
Ensemble averaged across 21 GCMs

12. 2. Model Errors can be a Function of Frequency
If log-RMSE is f, then models are off by factor of (1 + f), on average

13. Log-RMSE metrics

14. How much does frequency-dependent bias correction change values?

15. 3. Standard QM not multivariate
Temperature on precipitating days affects snow cover (Abatzoglou et al.)
Bias correct temperature conditional on precipitation > 0 or not

16. Issues with spatial downscaling

17. Spatial Downscaling with constructed analogs
Hidalgo, H.G., Dettinger, M.D., and Cayan, D.R., 2008
Slide from Mike Dettinger, USGS (tenaya.ucsd.edu)

18. Spatial Downscaling with constructed analogs
Hidalgo, H.G., Dettinger, M.D., and Cayan, D.R., 2008
Slide from Mike Dettinger, USGS (tenaya.ucsd.edu)

19. Spatial Downscaling with constructed analogs
Hidalgo, H.G., Dettinger, M.D., and Cayan, D.R., 2008
Slide from Mike Dettinger, USGS (tenaya.ucsd.edu)

20. Spatial Downscaling with constructed analogs
Hidalgo, H.G., Dettinger, M.D., and Cayan, D.R., 2008
Slide from Mike Dettinger, USGS (tenaya.ucsd.edu)

21. Issues with current downscaling (BCCA)
“BCCA” = “Bias correction with Constructed Analogs”
Averaging step reduces temporal variance (i.e., mute extremes)

22. 2. Frequency of occurrence -> percent of amount
Take an extreme example for illustration:
60% of the time
40% of the time
Changing from frequency of occurrence to percent of amount ALSO changes extreme values
Contributes to reduction in extremes

23. 3. Drizzle problem from downscaling

24. New downscaling (LOCA) (Step 1 of 2)
BCCA uses 30 best matching analog days over entire domain
LOCA starts with 30 best matching analog days over the region around the point
Region: everywhere correlation with point being downscaled is > 0 (in obs)
Regions are calculated by season (DJF, MAM, JJA, SON) and variable (pr, tasmax, tasmin, etc.)
Gives a natural domain independence to LOCA (extending domain past region does not affect results at the point)
Example shown for precipitation

25. New downscaling (LOCA) (Step 2 of 2)
Example for precip, 1 Jan 1940
(P=0)
Once 30 regional analog days are selected:
Find best one (of the 30) matching days in a small localized region (~1 degree) around each point
This two step process means each point:
Is consistent with what’s happening regionally
Is the best match locally
Points whose selected analog day is different from a neighbor’s (“edge points”) use a weighted average of the relevant analog days
~30% of points are edge points
Greatly reduced averaging means:
Better extremes
Better spatial coherence
Far less “drizzle” problem

26. 4. Run out of analogs for extreme days?
Existing methods:
………………………………………………………………………………
Anomaly w.r.t. historical period (Tmin, Tmax)
LOCA:
…… ….… … ………
Anomaly w.r.t. 30-year climatology
Use LOCA to downscale changes in climatology

27. 5. Averaging increases spatial coherence
precip (red = more coherent)
Project in association with Keith Dixon, GFDL

28. Evaluation: Seasonal mean of daily precipitation (mm/day) in CCSM4
Error in %

29. Evaluation:
Seasonal mean of daily Tmax (degC) in CCSM4
Error in degC

30. Evaluation:
Standard deviation of daily precip (mm/day), averaged by season
CCSM4
Error in %

31. Evaluation:
Standard deviation of daily Tmax (degC), averaged by season
CCSM4
Error in degC

32. Goal: Realistic daily extremes (Precip)
Winter, mm/day
Summer, mm/day

33. Goal: Realistic daily extremes (Temp)
Winter, C
Summer, C

34. Goal: Preserve model-predicted changes (Precipitation, CCSM4, rcp 8
Goal: Preserve model-predicted changes (Precipitation, CCSM4, rcp 8.5, minus )
Winter, %
Summer, %

35. Goal: Preserve model-predicted changes (Tmax, CCSM4, rcp 8
Goal: Preserve model-predicted changes (Tmax, CCSM4, rcp 8.5, minus )
Winter, C
Summer, C

36. Example VIC output (water yr avgs)
Available variables:
Evapotranspiration
Snowpack
Humidity
Total runoff
Soil moisture
Black = with obs forcing
Green = 10 models
Red = model average

37. Summary of Production Runs
32 CMIP5 models
Historical: RCP 4.5 and RCP 8.5: (2099 some models)
Climatological period:
Interpolated model calendars to standard calendar w/leap days
North America 24.5 N to 52.8 N at 1/16th degree resolution
Daily Tmin, Tmax, Precip (specific humidity? 23 models).
ACCESS1-0
ACCESS1-3
CCSM4
CESM1-BGC
CESM1-CAM5
CMCC-CM
CMCC-CMS
CNRM-CM5
CSIRO-Mk3-6-0
CanESM2
EC-EARTH
FGOALS-g2
GFDL-CM3
GFDL-ESM2G
GFDL-ESM2M
GISS-E2-H
GISS-E2-R
HadGEM2-AO
HadGEM2-CC
HadGEM2-ES
IPSL-CM5A-LR
IPSL-CM5A-MR
MIROC-ESM
MIROC-ESM-CHEM
MIROC5
MPI-ESM-LR
MPI-ESM-MR
MRI-CGCM3
NorESM1-M
bcc-csm1-1
bcc-csm1-1-m
inmcm4

38. Summary Many bias correction & downscaling schemes…
Quantile mapping, BCCA:
Muted extremes
Different biases at different frequencies
Too much spatial coherence
Drizzle problems
Wrong temperature of precipitation
New bias correction and LOCA downscaling
Extremes preserved pretty well, along with seasonal means and std deviations
Reasonable preservation of original model-predicted changes
Frequency dependent bias correction
Spatial coherence not degraded as much
Greatly reduces drizzle problem
Bias correct temperature conditional on precipitation
Pierce, D. W., D. R. Cayan, and B. L. Thrasher, 2014: Statistical downscaling using Localized Constructed Analogs (LOCA). Journal of Hydrometeorology, v. 15, page
Analysis plots: loca.ucsd.edu

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