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

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)

Issues with bias correction

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 2070-2100 minus 1976-2005 Ensemble averaged across 21 GCMs

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:10.1029/2009JD012882.

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

Precipitation Difference between original model-predicted change and change after bias correction in percentage points 2070-2100 minus 1976-2005 Ensemble averaged across 21 GCMs

“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

“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

Correction factor Correction factors necessary to preserve model-predicted changes (2070-2099 vs. 1976-2005) in mean precipitation Averaged across 21 GCMs

Precipitation Difference between original model-predicted change and change after bias correction in percentage points 2070-2100 minus 1976-2005 Ensemble averaged across 21 GCMs

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

Log-RMSE metrics

How much does frequency-dependent bias correction change values?

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

Issues with spatial downscaling

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

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

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

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

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

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

3. Drizzle problem from downscaling

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

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

4. Run out of analogs for extreme days? Existing methods: 1950-99……………………………………………………………………………….2070-99 Anomaly w.r.t. historical period (Tmin, Tmax) LOCA: 1950-99……2000-2009….…2010-2039…..2040-2069……….2070-99 Anomaly w.r.t. 30-year climatology Use LOCA to downscale changes in climatology

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

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

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

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

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

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

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

Goal: Preserve model-predicted changes (Precipitation, CCSM4, rcp 8 Goal: Preserve model-predicted changes (Precipitation, CCSM4, rcp 8.5, 2070-2100 minus 1950-1999) Winter, % Summer, %

Goal: Preserve model-predicted changes (Tmax, CCSM4, rcp 8 Goal: Preserve model-predicted changes (Tmax, CCSM4, rcp 8.5, 2070-2100 minus 1950-1999) Winter, C Summer, C

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

Summary of Production Runs 32 CMIP5 models Historical: 1950-2005. RCP 4.5 and RCP 8.5: 2006-2100 (2099 some models) Climatological period: 1950-99 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

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 2558-2585 Analysis plots: loca.ucsd.edu

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