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Anthony DeAngelis

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[http://www-pcmdi.llnl.gov/ipcc/about_ipcc.php] [http://www.hydro.com.au/handson/links/images/rain.gif]. Anthony DeAngelis. Evaluation of Daily precipitation from Coupled Model Intercomparison Project Phase III (CMIP3) Models. Outline. Introduction Data, Models, and Methodology Results - PowerPoint PPT Presentation
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Page 1: Anthony DeAngelis

Anthony DeAngelis

[http://www-pcmdi.llnl.gov/ipcc/about_ipcc.php][http://www.hydro.com.au/handson/links/images/rain.gif]

Page 2: Anthony DeAngelis

Outline

Introduction Data, Models, and Methodology Results

Spatial Comparisons over United States Analysis of Resolution Ranking of Model Performance

Conclusions Future Directions

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Importance of Precipitation Agriculture, water resources, power, etc. Extreme Precipitation

Flooding takes 140 lives in the United States each year (USGS 2006).

Observational evidence of increases in the frequency and intensity of extreme precipitation throughout the world over 20th century (e.g., Groisman et al. 2005)

Model projections of future increases in heavy precipitation in response to increasing greenhouse gases (e.g., Pall et al. 2007)

Quantification of future changes in precipitation relies on model simulations

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How well do models simulate precipitation? IPCC AR4 –Fairly realistic mean precipitation

by ensemble of PCMDI coupled models

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Mean Precipitation 1980-1999

[IPCC AR4, Ch 8, Fig. 8.5]

CMAP Observations

Multi-model mean of

AOGCMs

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How well do models simulate precipitation? IPCC AR4 –Fairly realistic mean precipitation

by ensemble of PCMDI coupled models Sun et al. 2007 –Overestimation of light

precipitation and underestimation of heavy precipitation by CMIP3 models

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observations

Sun et al. (2007) Figure 1

model average

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How well do models simulate precipitation? IPCC AR4 –Fairly realistic mean precipitation by

ensemble of PCMDI coupled models Sun et al. (2007) –Overestimation of light precipitation

and underestimation of heavy precipitation by CMIP3 models

Kiktev et al. 2003 – HadAM3 has little skill in simulating precipitation trends over 1950-1995

Higher resolution models perform better Iorio et al. 2004 – NCAR CCM3 – mean and extreme

precipitation Kimoto et al. 2005 – MIROC 3.0 – extreme precipitation

Models with embedded cloud resolving models or certain convective parameterizations perform better for extreme precipitation (Iorio et al. 2004, Emori et al. 2005)

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What did I do?

Compared 20th century simulations from CMIP3 models with observations over the contiguous United States Looked at differences in spatial pattern of

precipitation characteristics for individual models

Used a longer and consistent time period for comparison (1961-1998) than previous studies

Compared two gridded observational datasets Assessed the role of resolution on model

performance for all models collectively

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Observational Data and Climate Models Observations

Climate Prediction Center’s Daily United States Unified Precipitation (CPC) -0.25° x 0.25° lon-lat (1948-1998) [Higgins et al. 2007]

David Robinson’s daily gridded precipitation (DAVR) - 1.0° x 1.0° lon-lat (1900-2003) [Dyer and Mote 2006]

Climate Models 20th century simulations – forced with observed

atmospheric composition 18 CMIP3 models with daily precipitation from

1961-2000 and a standard (non 360 day) calendar One ensemble member for each model Meehl et al. (2007)

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Model # Modeling Group Country Model ID Spatial Resolution(approximate - lon x lat)

1 Bjerknes Centre for Climate Research Norway BCCR BCM 2.0 2.81° x 2.81°

2 Canadian Centre for Climate Modelling & Analysis Canada CCCMA CGCM 3.1 T47 3.75° x 3.75°

3 Canadian Centre for Climate Modelling & Analysis Canada CCCMA CGCM 3.1 T63 2.81° x 2.81°

4 Centre National de Recherches Météorologiques France CNRM CM 3 2.81° x 2.81°

5 CSIRO Atmospheric Research Australia CSIRO MK 3.0 1.88° x 1.88°

6 CSIRO Atmospheric Research Australia CSIRO MK 3.5 1.88° x 1.88°

7 Geophysical Fluid Dynamics Laboratory USA GFDL CM 2.0 2.50° x 2.00°

8 Geophysical Fluid Dynamics Laboratory USA GFDL CM 2.1 2.50° x 2.00°

9 Goddard Institute for Space Studies USA GISS AOM 4.00° x 3.00°

10 Goddard Institute for Space Studies USA GISS E H 5.00° x 3.91°

11 Goddard Institute for Space Studies USA GISS E R 5.00° x 3.91°

12 Institute of Atmospheric Physics China IAP FGOALS 1.0 G 2.81° x 3.00°

13 Institute for Numerical Mathematics Russia INM CM 3.0 5.00° x 4.00°

14 Center for Climate System Research, National Institute for Environmental Studies, and Frontier Research Center for Global Change

Japan MIROC 3.2 MEDRES 2.81° x 2.81°

15 Max Planck Institute for Meteorology Germany MPI ECHAM 5 1.88° x 1.88°

16 Meteorological Research Institute Japan MRI CGCM 2.3.2 2.81° x 2.81°

17 National Center for Atmospheric Research USA NCAR CCSM 3.0 1.41° x 1.41°

18 National Center for Atmospheric Research USA NCAR PCM 1 2.81° x 2.81°

CMIP3 Models Used

More information: http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php

Page 12: Anthony DeAngelis

Spatial Comparisons

Linear re-gridding to 2.5° x 2.5° lon-lat Typical model resolution that is fine enough

to resolve the coastlines Precipitation Quantities for 1961-1998

Mean Frequency of wet days (precip. ≥ 0.254

mm/day) Standard deviation for wet days divided by

mean for wet days – precipitation variability 99th percentile for all days Generalized extreme value normalized scale

parameter for yearly maximum daily precipitation distribution – extreme precipitation variability

Page 13: Anthony DeAngelis

Mean Precipitation 1961-1998 (mm/day)

Convective parameterizations?[Iorio et al. 2004]

Improper terrain representation?

Agreement with IPCC AR4

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Frequency of Wet Days 1961-1998 (days/year)

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Normalized Standard Deviation for Wet Days 1961-1998

(dimensionless)

Could be related to too many wet days

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99th Percentile for All Days 1961-1998 (mm/day)

Convective parameterizations again?

Page 17: Anthony DeAngelis

Example Generalized Extreme Value (GEV) Distribution

Representative of New Jersey in Observations

location parameter- center of distribution(45 mm/day)

scale parameter- spread of distribution(9 mm/day)

I plot scale/locati

on(0.2 in this

case)

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GEV Normalized Scale Parameter for Yearly Maximum 1961-1998 (dimensionless)

Not enough variability of precipitation extremes

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GEV Normalized Scale Parameter for Yearly Maximum 1961-1998 (dimensionless)

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Does Spatial Resolution Make a Difference? Linear re-gridding to 5.0° x 4.0° lon-lat

Error- root mean square of absolute difference between each model and observations average (Iorio et al. 2004)

Plot error against finite grid equivalent resolution (# of global grid cells)

Fit least squares linear regression to error vs. resolution plot

Page 21: Anthony DeAngelis

Error vs. Resolution Results Statistically significant improvement

in the frequency of wet days with higher resolution

Page 22: Anthony DeAngelis

= model average

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Model # Modeling Group Country Model ID Spatial Resolution(approximate - lon x lat)

1 Bjerknes Centre for Climate Research Norway BCCR BCM 2.0 2.81° x 2.81°

2 Canadian Centre for Climate Modelling & Analysis Canada CCCMA CGCM 3.1 T47 3.75° x 3.75°

3 Canadian Centre for Climate Modelling & Analysis Canada CCCMA CGCM 3.1 T63 2.81° x 2.81°

4 Centre National de Recherches Météorologiques France CNRM CM 3 2.81° x 2.81°

5 CSIRO Atmospheric Research Australia CSIRO MK 3.0 1.88° x 1.88°

6 CSIRO Atmospheric Research Australia CSIRO MK 3.5 1.88° x 1.88°

7 Geophysical Fluid Dynamics Laboratory USA GFDL CM 2.0 2.50° x 2.00°

8 Geophysical Fluid Dynamics Laboratory USA GFDL CM 2.1 2.50° x 2.00°

9 Goddard Institute for Space Studies USA GISS AOM 4.00° x 3.00°

10 Goddard Institute for Space Studies USA GISS E H 5.00° x 3.91°

11 Goddard Institute for Space Studies USA GISS E R 5.00° x 3.91°

12 Institute of Atmospheric Physics China IAP FGOALS 1.0 G 2.81° x 3.00°

13 Institute for Numerical Mathematics Russia INM CM 3.0 5.00° x 4.00°

14 Center for Climate System Research, National Institute for Environmental Studies, and Frontier Research Center for Global Change

Japan MIROC 3.2 MEDRES 2.81° x 2.81°

15 Max Planck Institute for Meteorology Germany MPI ECHAM 5 1.88° x 1.88°

16 Meteorological Research Institute Japan MRI CGCM 2.3.2 2.81° x 2.81°

17 National Center for Atmospheric Research USA NCAR CCSM 3.0 1.41° x 1.41°

18 National Center for Atmospheric Research USA NCAR PCM 1 2.81° x 2.81°

CMIP3 Models Used

More information: http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php

Page 24: Anthony DeAngelis

Error vs. Resolution Results Statistically significant improvement

in the frequency of wet days with higher resolution

All other quantities showed decreasing error with higher resolution, but the linear fit was not statistically significant

All quantities showed low percentage of model error variability explained by the linear fit (r2)

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Other potential reasons for variability in model error Different vertical resolutions Different grid types (e.g., spectral

resolution vs. finite grid) Different cloud and convective

parameterizations Different microphysics schemes Different ocean components Different radiation schemes

Page 26: Anthony DeAngelis

Ranking of Model Performance Ratio: Root mean square error for

each model divided by the average root mean square error for all models for each precipitation quantity Eliminates biases from quantities with

different units (e.g., mean precipitation, frequency of wet days)

Take average of ratio over precipitation quantities for each model and rank them

Page 27: Anthony DeAngelis

CMIP3 Model Ranking

All Precipitation Quantities Mean, Frequency of Wet Days, and Normalized Standard Deviation for Wet Days

99th Percentile and GEV Normalized Scale

Model Rank Average Error Model Rank Average Error Model Rank Average Error

1. MPI ECHAM 5 0.6408 1. MPI ECHAM 5 0.5783 1. GFDL CM 2.1 0.65352. CSIRO MK 3.5 0.7559 2. CSIRO MK 3.5 0.6974 2. GFDL CM 2.0 0.68723. MRI CGCM 2.3.2 0.7666 3. MRI CGCM 2.3.2 0.7251 3. MPI ECHAM 5 0.73464. GFDL CM 2.1 0.7954 4. NCAR CCSM 3.0 0.7448 4. CCCMA CGCM 3.1 T63 0.74125. NCAR CCSM 3.0 0.7987 5. Model Average 0.8621 5. Model Average 0.74576. Model Average 0.8155 6. MIROC 3.2 MEDRES 0.8895 6. CNRM CM 3 0.77627. CCCMA CGCM 3.1 T63 0.8457 7. GFDL CM 2.1 0.8901 7. CCCMA CGCM 3.1 T47 0.79998. MIROC 3.2 MEDRES 0.8647 8. CCCMA CGCM 3.1 T63 0.9154 8. MIROC 3.2 MEDRES 0.82759. CCCMA CGCM 3.1 T47 0.8886 9. CSIRO MK 3.0 0.932 9. MRI CGCM 2.3.2 0.828810. GFDL CM 2.0 0.8982 10. CCCMA CGCM 3.1 T47 0.9477 10. CSIRO MK 3.5 0.843611. INM CM 3.0 0.9161 11. INM CM 3.0 0.9489 11. INM CM 3.0 0.867012. CSIRO MK 3.0 0.9222 12. BCCR BCM 2.0 1.0024 12. NCAR CCSM 3.0 0.879713. BCCR BCM 2.0 0.9712 13. GFDL CM 2.0 1.0388 13. CSIRO MK 3.0 0.907514. CNRM CM 3 1.0737 14. GISS E R 1.0968 14. NCAR PCM 1 0.9147

15. NCAR PCM 1 1.1117 15. IAP FGOALS 1.0 G 1.215 15. BCCR BCM 2.0 0.924316. IAP FGOALS 1.0 G 1.1613 16. NCAR PCM 1 1.243 16. IAP FGOALS 1.0 G 1.080717. GISS E H 1.3447 17. CNRM CM 3 1.272 17. GISS AOM 1.167118. GISS AOM 1.3743 18. GISS E H 1.3503 18. GISS E H 1.336419. GISS E R 1.8701 19. GISS AOM 1.5125 19. GISS E R 3.0301

More information: http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php

Page 28: Anthony DeAngelis

CMIP3 Model Ranking

All Precipitation Quantities Mean, Frequency of Wet Days, and Normalized Standard Deviation for Wet Days

99th Percentile and GEV Normalized Scale

Model Rank Average Error Model Rank Average Error Model Rank Average Error

1. MPI ECHAM 5 0.6408 1. MPI ECHAM 5 0.5783 1. GFDL CM 2.1 0.65352. CSIRO MK 3.5 0.7559 2. CSIRO MK 3.5 0.6974 2. GFDL CM 2.0 0.68723. MRI CGCM 2.3.2 0.7666 3. MRI CGCM 2.3.2 0.7251 3. MPI ECHAM 5 0.73464. GFDL CM 2.1 0.7954 4. NCAR CCSM 3.0 0.7448 4. CCCMA CGCM 3.1 T63 0.74125. NCAR CCSM 3.0 0.7987 5. Model Average 0.8621 5. Model Average 0.74576. Model Average 0.8155 6. MIROC 3.2 MEDRES 0.8895 6. CNRM CM 3 0.77627. CCCMA CGCM 3.1 T63 0.8457 7. GFDL CM 2.1 0.8901 7. CCCMA CGCM 3.1 T47 0.79998. MIROC 3.2 MEDRES 0.8647 8. CCCMA CGCM 3.1 T63 0.9154 8. MIROC 3.2 MEDRES 0.82759. CCCMA CGCM 3.1 T47 0.8886 9. CSIRO MK 3.0 0.932 9. MRI CGCM 2.3.2 0.828810. GFDL CM 2.0 0.8982 10. CCCMA CGCM 3.1 T47 0.9477 10. CSIRO MK 3.5 0.843611. INM CM 3.0 0.9161 11. INM CM 3.0 0.9489 11. INM CM 3.0 0.867012. CSIRO MK 3.0 0.9222 12. BCCR BCM 2.0 1.0024 12. NCAR CCSM 3.0 0.879713. BCCR BCM 2.0 0.9712 13. GFDL CM 2.0 1.0388 13. CSIRO MK 3.0 0.907514. CNRM CM 3 1.0737 14. GISS E R 1.0968 14. NCAR PCM 1 0.9147

15. NCAR PCM 1 1.1117 15. IAP FGOALS 1.0 G 1.215 15. BCCR BCM 2.0 0.924316. IAP FGOALS 1.0 G 1.1613 16. NCAR PCM 1 1.243 16. IAP FGOALS 1.0 G 1.080717. GISS E H 1.3447 17. CNRM CM 3 1.272 17. GISS AOM 1.167118. GISS AOM 1.3743 18. GISS E H 1.3503 18. GISS E H 1.336419. GISS E R 1.8701 19. GISS AOM 1.5125 19. GISS E R 3.0301

More information: http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php

Page 29: Anthony DeAngelis

CMIP3 Model Ranking

All Precipitation Quantities Mean, Frequency of Wet Days, and Normalized Standard Deviation for Wet Days

99th Percentile and GEV Normalized Scale

Model Rank Average Error Model Rank Average Error Model Rank Average Error

1. MPI ECHAM 5 0.6408 1. MPI ECHAM 5 0.5783 1. GFDL CM 2.1 0.65352. CSIRO MK 3.5 0.7559 2. CSIRO MK 3.5 0.6974 2. GFDL CM 2.0 0.68723. MRI CGCM 2.3.2 0.7666 3. MRI CGCM 2.3.2 0.7251 3. MPI ECHAM 5 0.73464. GFDL CM 2.1 0.7954 4. NCAR CCSM 3.0 0.7448 4. CCCMA CGCM 3.1 T63 0.74125. NCAR CCSM 3.0 0.7987 5. Model Average 0.8621 5. Model Average 0.74576. Model Average 0.8155 6. MIROC 3.2 MEDRES 0.8895 6. CNRM CM 3 0.77627. CCCMA CGCM 3.1 T63 0.8457 7. GFDL CM 2.1 0.8901 7. CCCMA CGCM 3.1 T47 0.79998. MIROC 3.2 MEDRES 0.8647 8. CCCMA CGCM 3.1 T63 0.9154 8. MIROC 3.2 MEDRES 0.82759. CCCMA CGCM 3.1 T47 0.8886 9. CSIRO MK 3.0 0.932 9. MRI CGCM 2.3.2 0.828810. GFDL CM 2.0 0.8982 10. CCCMA CGCM 3.1 T47 0.9477 10. CSIRO MK 3.5 0.843611. INM CM 3.0 0.9161 11. INM CM 3.0 0.9489 11. INM CM 3.0 0.867012. CSIRO MK 3.0 0.9222 12. BCCR BCM 2.0 1.0024 12. NCAR CCSM 3.0 0.879713. BCCR BCM 2.0 0.9712 13. GFDL CM 2.0 1.0388 13. CSIRO MK 3.0 0.907514. CNRM CM 3 1.0737 14. GISS E R 1.0968 14. NCAR PCM 1 0.9147

15. NCAR PCM 1 1.1117 15. IAP FGOALS 1.0 G 1.215 15. BCCR BCM 2.0 0.924316. IAP FGOALS 1.0 G 1.1613 16. NCAR PCM 1 1.243 16. IAP FGOALS 1.0 G 1.080717. GISS E H 1.3447 17. CNRM CM 3 1.272 17. GISS AOM 1.167118. GISS AOM 1.3743 18. GISS E H 1.3503 18. GISS E H 1.336419. GISS E R 1.8701 19. GISS AOM 1.5125 19. GISS E R 3.0301

More information: http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php

Page 30: Anthony DeAngelis

CMIP3 Model Ranking

All Precipitation Quantities Mean, Frequency of Wet Days, and Normalized Standard Deviation for Wet Days

99th Percentile and GEV Normalized Scale

Model Rank Average Error Model Rank Average Error Model Rank Average Error

1. MPI ECHAM 5 0.6408 1. MPI ECHAM 5 0.5783 1. GFDL CM 2.1 0.65352. CSIRO MK 3.5 0.7559 2. CSIRO MK 3.5 0.6974 2. GFDL CM 2.0 0.68723. MRI CGCM 2.3.2 0.7666 3. MRI CGCM 2.3.2 0.7251 3. MPI ECHAM 5 0.73464. GFDL CM 2.1 0.7954 4. NCAR CCSM 3.0 0.7448 4. CCCMA CGCM 3.1 T63 0.74125. NCAR CCSM 3.0 0.7987 5. Model Average 0.8621 5. Model Average 0.74576. Model Average 0.8155 6. MIROC 3.2 MEDRES 0.8895 6. CNRM CM 3 0.77627. CCCMA CGCM 3.1 T63 0.8457 7. GFDL CM 2.1 0.8901 7. CCCMA CGCM 3.1 T47 0.79998. MIROC 3.2 MEDRES 0.8647 8. CCCMA CGCM 3.1 T63 0.9154 8. MIROC 3.2 MEDRES 0.82759. CCCMA CGCM 3.1 T47 0.8886 9. CSIRO MK 3.0 0.932 9. MRI CGCM 2.3.2 0.828810. GFDL CM 2.0 0.8982 10. CCCMA CGCM 3.1 T47 0.9477 10. CSIRO MK 3.5 0.843611. INM CM 3.0 0.9161 11. INM CM 3.0 0.9489 11. INM CM 3.0 0.867012. CSIRO MK 3.0 0.9222 12. BCCR BCM 2.0 1.0024 12. NCAR CCSM 3.0 0.879713. BCCR BCM 2.0 0.9712 13. GFDL CM 2.0 1.0388 13. CSIRO MK 3.0 0.907514. CNRM CM 3 1.0737 14. GISS E R 1.0968 14. NCAR PCM 1 0.9147

15. NCAR PCM 1 1.1117 15. IAP FGOALS 1.0 G 1.215 15. BCCR BCM 2.0 0.924316. IAP FGOALS 1.0 G 1.1613 16. NCAR PCM 1 1.243 16. IAP FGOALS 1.0 G 1.080717. GISS E H 1.3447 17. CNRM CM 3 1.272 17. GISS AOM 1.167118. GISS AOM 1.3743 18. GISS E H 1.3503 18. GISS E H 1.336419. GISS E R 1.8701 19. GISS AOM 1.5125 19. GISS E R 3.0301

More information: http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php

Page 31: Anthony DeAngelis

Conclusions

CMIP3 models underestimate mean and extreme precipitation amounts near the Gulf Coast Convective parameterizations (Iorio et al. 2004)

CMIP3 models produce precipitation days too frequently, especially in the north and west Higher resolution models perform much better

CMIP3 models have too little variability in all precipitation and extreme precipitation in the northern interior west

The MPI ECHAM5 is the best, the model average is better than the majority of individual models, and the GISS models are the worst with 20th century precipitation characteristics over the US

Page 32: Anthony DeAngelis

Future Directions

Understand the reasons for differences in model performance What makes the MPI ECHAM5 so good?

Evaluate the ability of CMIP3 models to simulate precipitation changes Time period used here is too short for a

reliable analysis Expand the evaluation of CMIP3

precipitation to other regions

Page 33: Anthony DeAngelis

References

Dyer, J. L., and T. L. Mote, 2006: Spatial variability and patterns of snow depth over North America, Geophys. Res. Lett., 33, L16503, doi:10.1029/2006GL027258.

Emori, S., A. Hasegawa, T. Suzuki, and K. Dairaku, 2005: Validation, parameterization dependence and future projection of daily precipitation simulated with an atmospheric GCM, Geophys. Res. Lett., 32, L06708, doi:10.1029/2004GL022306.

Groisman, P. Y., R. W. Knight, D. R. Easterling, T. R. Karl, G. C. Hegerl, and V. N. Razuvaev, 2005: Trends in intense precipitation in the climate record, J. Clim., 18, 1326-1350.

Higgins, R. W., W. Shi, E. Yarosh, and R. Joyce, 2000: Improved United States precipitationquality control system and analysis. NCEP/Climate Prediction Center Atlas No. 7, published online at http://www.cpc.ncep.noaa.gov/research_papers/ncep_cpc_atlas/7/.

Iorio, J. P., P. B. Duffy, B. Govindasamy, S. L. Thompson, M. Khairoutdinov, and D. Randall, 2004: Effects of model resolution and subgrid scale physics on the simulation of precipitation in the continental United State, Clim. Dyn., 23, 243–258, doi:10.1007/s00382-004-0440-y.

Kiktev, D., D. M. H. Sexton, L. Alexander, and C. K. Folland, 2003: Comparison of modeled and observed trends in indices of daily climate extremes, J. Clim., 16, 3560–3571.

Kimoto, M., N. Yasutomi, C. Yokoyama, and S. Emori, 2005: Projected changes in precipitation characteristics near Japan under the global warming, Scientific Online Letters on the Atmosphere, 1, 85–88, doi:10.2151/sola.2005-023.

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References Continued

Meehl, G. A., C. Covey, T. Delworth, M. Latif, B. McAvaney, J. F. B. Mitchell, R. J. Stouffer, and K. E. Taylor, 2007: The WCRP CMIP3 multi-model dataset: A new era in climate change research, Bull. Amer. Meteor. Soc., 88, 1383-1394.

Pall, P., M. R. Allen, and D. A. Stone, 2007: Testing the Clausius-Clapeyron constraint on changes in extreme precipitation under CO2 warming, Clim. Dyn., 28, 351-363.

Randall, D. A. and Coauthors, 2007: Climate Models and Their Evaluation. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor and H. L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

Sun, Y., S. Solomon, A. Dai, and R. W. Portmann, 2007: How often will it rain? J. Clim., 20, 4801-4818.

United States Department of the Interior, United States Geological Survey, 2006: Fact Sheet: Flood Hazards- A National Threat. Available at http://pubs.usgs.gov/fs/2006/3026/.

For more plots, see http://envsci.rutgers.edu/~toine379/extremeprecip/home


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