Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Data Mining Tools-Empirical Orthogonal Functions and Nonlinear Mode Decomposition for Spatiotemporal Variability Analyses of

California's Precipitation

Sep. 12-14, 2014 Xian, China

Xiaogang Gao, Hao Liu, Soroosh SorooshianUniversity of California, Irvine

Celebrate Northwest A & F University’s 80th Anniversary

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Motivation (Data-Information)

• Support water planning and management over California (western US).

• Characterize the spatiotemporal variability of seasonal precipitation from historical observation data.

• Explore the relevance between the regional precipitation and climate oscillations.

• Analyze the predictability of seasonal precipitation for the region.

California precipitation variations control the state’s water resources availability.The water storages in Lake Oroville, California’s largest reservoir in 2011 (wet year) and 2014 (drought year).

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Data Mining Tools: Empirical Orthogonal Functions (EOFs) and Nonlinear

Mode Decomposition (NMD)

• The EOF analysis decomposes the data set of a dynamic field into spatial patterns (EOFs) and time series (principal components PCs)– Each EOF maximizes its explained variance, the first EOF explains the largest variance in

the dynamic field– m-leading EOFs can approximate field with high Signal-to-Noise Ratio (SNR)

• The NMD method decomposes the time series into oscillatory modes (waveforms), trend, and noise

• Combine EOF and NMD

1

( , ) ( ) ( )m

i ii

P x t e x s t

1

( , ) ( ) ( ) cos ( )pm n

i ij ijh ijh ijhi j h

P x t e x A t a h t

( , )P x t

( )ie x

( )is t

( , )P x t

( )is t

( ) ( ) ( ( )) ( ) cos( ( ) )ij ij ij ij ijh ijh ijhh

c t A t v t A t a h t

( ) ( ) ( )i ij ij

s t c t t

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Data Mining

1

( , ) ( ) ( ) cos ( )pm n

i ij ijh ijh ijhi j h

P x t e x A t a h t

Applying the EOF-NMD process

CPC Unified Gauge-Based Analysis of Precipitation over CONUS

0.25° × 0.25° and Monthly

Jan. 1971-Dec. 2013, 43 years (516 months)

Western US (focus on California)

To the dataset of Monthly Precipitation in Western US:

(http://www.esrl.noaa.gov/psd/data/gridded/data.unified.daily.conus.html)

( , )P x t

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

EOF Results for Western US Precipitation Data

Four Leading EOFs & PCs explain 90% variance with noise reduction.4

1

( , ) ( ) ( )i ii

P x t e x s t

1( )e x

2 ( )e x

3( )e x

4 ( )e x

1( )s t

2 ( )s t

3( )s t

4 ( )s t

EOFs (Spatial Patterns) PCs (Time Series)

Space-time Separation

Simplification

Noise Reduction

Physical Meanings

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

The First EOF-NMD Components e1(x)·s1(t)

residual

Curve #1

Curve #2

Curve #3

Compare reconstructed (blue) vs. original (red)

3

1( ) ( ) cos ( )p

ij ijh ijh ijhj h

S t A t a h t

Dominant precipitations locate in coast and Sierra Mountains during Nov-Dec-Jan-Feb.

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

The Second EOF-NMD Components e2(x)·s2(t)

residual

Curve #1

Curve #2

Curve #3

Compare reconstructed (blue) vs. original (red)

Oregon and Washington obtain much more precipitation than California,With Atmospheric Rivers in MJJ and Winter Season NDJ precipitation.

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

The Third EOF-NMD Components e3(x)·s3(t)

residual

Curve #1

Curve #2

Curve #3

Compare reconstructed (blue) vs. original (red)

Pacific-induced coastal Precipitations

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Comparison of the Original and Simplified Precipitation Fields

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Teleconnection of Western Precipitation to Climate Oscillations

[period =1 year] [period =1 year]

f=1.5~2.5

drought

PC1 and Pacific Decadal Oscillation Index PC4 and Oceanic Nino 4/Nino 3.4 Index

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Conclusions

• The combined EOF and NMD analysis method can extract the essential spatiotemporal variability from the data set of precipitation in western US.

• The method ranks the leading spatial patterns (EOFs) and the leading oscillatory waveforms (NMD components) to approximate the original field with high accuracy and Signal-to-Noise Ratio.

• The decomposed components demonstrate teleconnection between western US precipitation and large-scale climate oscillations.

• The mathematic representation extracted from given observed data can be applied for empirical forecasts of seasonal precipitation in western US with spatial and temporal details.