1. 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 Sorooshian University of California, Irvine Celebrate Northwest A & F University’s 80 th Anniversary

2. 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).

3. 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

4. Center for Hydrometeorology and Remote Sensing, University of California, Irvine Data Mining 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)

5. 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. EOFs (Spatial Patterns) PCs (Time Series) Space-time Separation Simplification Noise Reduction Physical Meanings

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

7. Center for Hydrometeorology and Remote Sensing, University of California, Irvine The Second EOF-NMD Components e2(x)·s 2 (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.

8. 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

9. Center for Hydrometeorology and Remote Sensing, University of California, Irvine Comparison of the Original and Simplified Precipitation Fields

10. Center for Hydrometeorology and Remote Sensing, University of California, Irvine Teleconnection of Western Precipitation to Climate Oscillations [period =1 year] f=1.5~2.5 drought PC1 and Pacific Decadal Oscillation IndexPC4 and Oceanic Nino 4/Nino 3.4 Index

11. 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.