Cooperative Institute for Climate and Satellites (CICS)

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Cooperative Research Programs (CoRP)Satellite Climate Studies Branch (SCSB)

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Reconstruction of Near-Global Precipitation Variations Based on

Gauges and Correlations with SST and SLP

Thomas Smith1

Phillip Arkin2

1. NOAA/NESDIS/STAR SCSB and CICS, College Park, Maryland2. CICS/ESSIC/University of Maryland, College Park, Maryland

Cooperative Institute for Climate and Satellites (CICS)Earth System Science Interdisciplinary Center (ESSIC)

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Outline• All analyses are of Precipitation Anomalies

• Base Satellite Data– IR (from 1979), MW (from mid 1980s)– Need global satellite analyses for reconstruction statistics

• Direct Reconstructions: fitting data to Empirical Orthogonal Functions (REOF)– EOF (or PC) analysis, for covariance maps– Fit available gauge-station data to a set of covariance maps– Monthly gauge-based 5-degree analyses available beginning 1900

• Indirect Reconstructions: using Canonical Correlation Analysis (RCCA)– Correlate fields of sea-surface temperature (SST) and sea-level pressure (SLP) with

fields of precipitation– Both SST and SLP analyzed for the 20th century

• Merged Direct & Indirect Reconstructions– Direct Recons for over land and interannual and shorter variations over oceans– Indirect Recons more reliable for multi-decadal variations over oceans

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Satellite-Based Analyses

• Monthly analyses, 1979-Present

• Several analyses available– Global precipitation climatology project (GPCP), multiple

inputs, begins 1979, developed for climate studies– CAMS/OPI, several inputs, begins 1979, developed for

interannual studies– Optimum Interpolation (OI) of MW and ERA-40

reanalysis, begins 1987, data problems over land before 1992

• New OI analyses being tested in an attempt to obtain longer record using OI methods

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Anomaly S.D.

• CAMS/OPI ocean S.D. more concentrated in tropics– OIP best for convective

precipitation

• Both GPCP and OI S.D. have more extra-tropical variations– GPCP uses mix of

satellite estimates + gauges

– OI uses only microwave estimates, stronger variations than GPCP

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Examples of spatial modes: Joint EOFs of OI and GPCP Anomalies

• EOF (PC) analysis jointly of 2 fields

• Shows common variations by mode

• Mode 1: Main ENSO

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Joint EOF 2: Secondary ENSO Mode

• Mostly variance associated with the very strong 1997-1998 episode– Lags mode 1

• Both analyses have similar ocean variations

• Tested using different analyses, use GPCP for final REOF

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Reconstruction Based on EOFs (REOF)

• EOF spatial covariance modes– 3 regions: 80S-20S, 30S-30N, 20N-80N– Separate so tropics do not dominate– Only large-scale modes used

• In each region, fit available gauge anomalies to the set of modes– 3 areas merged with smoothing at boundaries

• Cross-validation testing to find the best set of modes for each region– For S.H. 5 EOFs, for Tropics 15 EOFs, for N.H. 10 EOFs

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Anomaly Distribution

• Relative frequency distribution for common months and locations (1992-2001)

• Both anomalies approximately normal– reconstruction methods

should work

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Gauge Sampling of 5-deg Regions

• Gauge-based analyses, annual averages of monthly % sampling– Global Historical Climate

Network (GHCN)– Global Precipitation

Climatology Center (GPCC)– Climate Research Unit (CRU)

• CRU gives best sampling of 5-deg areas in historical period– Differences due to data

processing & how many stations needed to form a 5-deg area

– Test all & use CRU based analysis

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REOF Methods

• Space points, x, and times, t

• Data: Anomalies, a, minus a first guess– Can sometimes estimate a

first guess; otherwise can use 0 first guess

• Anomaly reconstruction: First guess plus weighted sum of the modes

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mmm twxtxtxA

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Best Fit Weights for the Modes

• Reconstruction fit, F, using modes– Modes function of

space– Weights function of time

• Squared error of the fit over all areas with sampling

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mmm twxtxF

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xx

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txFtxDtE cos),(),()(2

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System of Equations For Weights

• Differentiate error with each weight and set to 0 for system of equations to minimize error

• Equations to minimize error – Weights affected by data and

sampling– System of equations solved

each time for the set of weights

• Note: with complete data and orthogonal modes, computing the weights is simplified

– EOF (or PC) time series

MnforxtxD

xxtw

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xxxn

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m

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,,2,1,cos)(),(

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Sampling and Screening Modes

• Data must be sufficient to sample a mode’s variations– Mode variance proportional to

the square of the mode value

• Compute the fraction of sampled variance of each mode

• Use only modes with a critical fraction of variance sampled– Use cross-validation testing to

find the critical sampling fraction

K

xxm

K

xxmx

v

x

xmf

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2

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Cross Validation

• Simulate historical periods– Modes computed from data excluding the time to be analyzed,

and enough surrounding time to be independent– Data sub-sampled to simulate historical sampling

• Reconstruct using simulated historical conditions and compare to full data to find errors

• Used for tuning the reconstruction and for finding its errors

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Cross-Validation For Tuning and Skill

Evaluation

• Independent modes– Delete base data for each test

analysis year

• Station sampling for 3 periods– Here GHCN sampling used

• Anomaly correlation with base full data– S.H. extra-tropics: low skill– Tropics: highest skill– N.H. extra-tropics some skill over

oceans

Ocean Avgs 1912-21 1952-61 1992-01 0.37 0.40 0.39

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REOF Spatial Statistics

• Global spatial standard deviation (upper)– Similar interannual changes– GHCN low before 1940 (low

sampling)– CRU strong most of record– Filtered GPCP strong at the

end of record

• Global spatial correlation between analyses– High GHCN, CRU for high-

sampling period, lower values before 1940

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Regression Against SOI

• SOI represents ENSO interannual variability (annual averages)

• Shows typical ENSO precipitation patterns

• GHCN-based recon gives slightly weaker regression

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Regression Against NAO

• Dec-March Regression

• Similar patterns, especially in Northern Hemisphere

• GPCC tropical Pacific different from the others

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REOF Conclusions

• Satellite-based analysis are needed for historical reconstruction statistics

• Major interannual variations can be reconstructed for the 20th century

• REOF oceanic multi-decadal variations may be less reliable – Different base data & analysis data change multi-decadal results much

more than interannual results– REOF multi-decadal inconsistent with theoretical modeling results

• Improvements may be obtained from improved satellite base data

• Ocean-area sampling too sparse to use more EOF modes

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Reconstructions Based on CCA (RCCA), and Comparisons to REOFs

• Canonical Correlation Analysis (CCA)– Fields of predictors correlated with a predictand field– Data smoothed and condensed using EOFs before CCA

computed

• Training Data: GPCP, SST, SLP (1979-2004)– Annual average anomalies, GPCP satellite based– SST and SLP give ocean observations correlated with

precipitation on long time scales

• Analysis Data: SST, SLP (1900-2004)– SST & SLP global analyses available

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Canonical Correlation Analysis (CCA)

• Compress anomaly predictor (SST, SLP) and predictand (GPCP) fields using separate EOFs– All fields normalized– One joint predictor EOF, separate predictand EOF

• Predictor CCA equations: to relate compressed predictor fields to compressed predictand field– CCA modes developed– CCA eigenvalue used to weight analysis– For reconstruction, predictor data used to find weights for predictand

field• CCA predicting annual precipitation from annual SST and

SLP– 8 modes used, most oceanic variations from the first 3 modes

CCA is described in detail by Barnett and Preisendorfer (1987, Mon. Wea. Rev., 115, 1825-1850)

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Correlations Between Analyses• Computed for period when all are available (1900-1998)

– Averages over oceans, land, & areas with CRU gauge sampling– Annual-spatial averages correlated

• Each individual reconstruction correlates well with CRU gauges– ENSO and other major modes allow interannual variations to be resolved– REOF(Blend) has the best fit over land, but the nearly-independent RCCA is almost as

good– AR4 ensemble averages out interannual variations, leaving in multi-decadal variations

• RCCA has same oceanic multi-decadal tendency as AR4, REOF has opposite tendency

Correlations between averages over the given areas Oceans Land Gauge-samplingCRU, REOF(Blend) ---- ---- 0.88CRU, RCCA ---- ---- 0.74REOF(Blend), RCCA 0.64 0.81 0.83REOF(Blend), AR4 -0.06 -0.01 -0.07RCCA, AR4 0.32 -0.02 0.00

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Land Comparisons

• RCCA & REOF & CRU data land averages, filtered– REOF(Blend) from REOF(CRU) and REOF(GPCP)

• RCCA & REOF similar for most of period• RCCA & REOF(GPCP) similar for the GPCP period

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Ocean Comparisons

• RCCA & REOF ocean averages, filtered• RCCA & REOF differ before 1980

– 1970s climate shift in RCCA– REOF does not resolve trend in RCCA & in AR4 ensemble

• RCCA & REOF(GPCP) similar– REOF(GPCP) can be used for updates

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Trends• Computed for period when all are available (1900-1998)

– Averages over oceans, land, & land areas with CRU gauge sampling

– Annual and low-pass filtered (as in figures)

• In each individual reconstruction, opposite trends over ocean & land– May be from use of ENSO modes to analyze ENSO-like multi-decadal

– ENSO has opposite land-sea anomalies

– Gauge data make land trends positive for REOF, no gauge data in RCCA

Trends in mm/mon per 100 years for averages over the given areas Oceans Land Gauge-samplingCRU Gauges ---- ---- 1.2REOF(Blend) -0.4 0.4 0.4 RCCA 1.6 -0.5 -1.1 AR4 0.7 -0.1 -0.5

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Spatial Standard Deviation of Recons

• RCCA underestimates interannual signals• REOFs give consistent level of signal over analysis

period• GPCP resolves variations filtered by REOF modes

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RCCA Conclusions

• Multi-decadal variations over oceans can be reconstructed from SST and SLP using RCCA

• Over land, RCCA large-scale multi-decadal & interannual variations are consistent with independent observations over the 20th century

• Over oceans, RCCA large-scale multi-decadal & interannual variations are consistent with model variations 20th century

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Merged Reconstructions

• REOF reliable over land where gauges are available

• Interannual REOF reliable over oceans, but multi-decadal REOF less reliable over oceans

• Multi-decadal RCCA appears to be more reliable over oceans

• Merge by replacing ocean multi-decadal REOF with ocean multi-decadal from RCCA

• For recent period, use REOF(GPCP)

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Merged Recon Averages

• Filtered Recons for All Areas and Ocean Areas• Ocean average changes most• Including land removes the 1970s climate shift and most

interannual variations

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Recon Trends

• Ocean tropical trend greatest• Land trends weaker & tend to be opposite to ocean trends

– Similar to ENSO land-sea differences, suggests ENSO-like processes

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Normalized Joint EOF

• Merged Recon and AR4 Ensemble

• Both annual averaged and filtered before JEOF

• First mode indicates joint trend-like variations– Tropical ENSO-like

increase– Mid-latitude decrease – High-latitude increase– Pattern differences may

reflect model biases

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Possible Uses of Reconstructed Precipitation

• Climate-dynamics studies of global precipitation on interannual to multi-decadal time scales– Developing ocean-land changes over the 20th century can

be better understood and diagnosed– Oceanic influence on dry and wet regimes can be more

clearly shown

• To validate and improve coupled-climate model precipitation– Both improvement of the models and statistical adjustment

of model output possible with global reconstructions

Data available at http://cics.umd.edu/~tsmith/recpr/

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Summary & Conclusions• EOF-based reconstructions resolve oceanic interannual

variations through the 20th century– Direct reconstruction using the available gauge data – Over land REOF does best for all variations

• CCA-based reconstructions resolve oceanic multi-decadal variations through the 20th century– Indirect method using correlations with better sampled variables

• Merged analysis takes advantage of the best qualities of both

• Future improvements possible with new data or refined reconstruction methods– Extended reanalyses may yield independent precipitation

information

Data available at http://cics.umd.edu/~tsmith/recpr/

Cooperative Institute for Climate and Satellites (CICS)

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