Principal Component Analysis

The Karhunen-Lo eve basis functions, more frequently referred to as principal components or empirical orthogonal functions (EOFs), of the noise response of the climate system are an important tool for geophysical studies. Many researchers have used this tool to examine the geophysical and climatological phenomena. Perhaps more frequent use of EOFs in recent studies is in conjunction with the development of the signal detection and estimation methods of the background uctuations of a detection variable serve as an orthogonal basis set and are used to design optimal techniques for detecting and estimating signals. A detection and prediction approach is to design a lter or optimal weights for the signal to be detected. It has been reported that weighted averaging of data over the surface of the Earth improved the detectability of climatic changes (Hasselmann 1979; Stefanick 1981; Bell 1982). Since the signal-to-noise ratio (SNR) varies geographically, there exists an optimal geographical weighting of the signal which maximizes the SNR. The design of an optimal weighting function may require detailed knowledge on the natural uctuation of the climate system. A conceptually similar approach is to employ a particular pattern (or patterns) of climatic change for detection and prediction (e.g., Barnett and Hasselmann 1979; Hasselmann 1979). The patterns of interest (also called the predictors) may include the principal components (empirical orthogonal functions) (e. von Storch 1990) among others. This approach also requires complete knowledge of the natural variability of the climate system. To test and improve the detection and prediction techniques addressed above, a complete cross-spectral covariance matrix, or similarly, a complete set of the principal components of natural uctuations of the climate system for each frequency band of the spectrum is necessary. In reality, a reliable spectrum of observational covariance matrix is not available because observations are not suuciently long and sampling errors contaminate the observational records (Preisendorfer and Barnett 1977; North et al. 1982). Further, inadequate spatial coverage of observations may introduce bias. Therefore, the covariance matrix of the noise response is often estimated from a simple stochastic model. Kim and North (1991, 1992) examined the covariance matrix in terms of various second-moment statistics earlier. Examined here are the principal components of the covariance matrix of the surface temperature uctuations in a simple coupled climate model in comparison with observations. The principal components not only are an

[1]  H. Keller,et al.  Analysis of Numerical Methods , 1967 .

[2]  J. Wallace,et al.  Empirical Orthogonal Representation of Time Series in the Frequency Domain. Part I: Theoretical Considerations , 1972 .

[3]  K. Hasselmann On the signal-to-noise problem in atmospheric response studies , 1979 .

[4]  K. Hasselmann,et al.  Techniques of Linear Prediction, With Application to Oceanic and Atmospheric Fields in the Tropical Pacific (Paper 9R0319) , 1979 .

[5]  M. Stefanick Space and Time Scales of Atmospheric Variability , 1981 .

[6]  B. Weare,et al.  Examples of Extended Empirical Orthogonal Function Analyses , 1982 .

[7]  Robert F. Cahalan,et al.  Sampling Errors in the Estimation of Empirical Orthogonal Functions , 1982 .

[8]  T. Bell Optimal weighting of data to detect climatic change: Application to the carbon dioxide problem , 1982 .

[9]  T. Barnett Interaction of the Monsoon and Pacific Trade Wind System at Interannual Time Scales Part I: The Equatorial Zone , 1983 .

[10]  J. Horel Complex Principal Component Analysis: Theory and Examples , 1984 .

[11]  G. North Empirical Orthogonal Functions and Normal Modes , 1984 .

[12]  T. Barnett Variations in Near-Global Sea Level Pressure , 1985 .

[13]  K. Lau,et al.  Aspects of the 40 50 Day Oscillation during the Northern Summer as Inferred from Outgoing Longwave Radiation , 1985 .

[14]  T. Wigley,et al.  Northern Hemisphere Surface Air Temperature Variations: 1851–1984 , 1986 .

[15]  M. Richman,et al.  Rotation of principal components , 1986 .

[16]  T. Barnett,et al.  An investigation of the El Niño‐Southern Oscillation cycle With statistical models: 2. Model results , 1987 .

[17]  J. Hansen,et al.  Global trends of measured surface air temperature , 1987 .

[18]  A. Barnston,et al.  Classification, seasonality and persistence of low-frequency atmospheric circulation patterns , 1987 .

[19]  K. Hasselmann PIPs and POPs: The reduction of complex dynamical systems using principal interaction and oscillation patterns , 1988 .

[20]  A. Sutera,et al.  The EOFs of the Geopotential Eddies at 500 mb in Winter and Their Probability Density Distributions , 1988 .

[21]  H. Storch,et al.  Predicting the State of the Southern Oscillation Using Principal Oscillation Pattern Analysis , 1990 .

[22]  T. Barnett An Attempt to Detect the Greenhouse-Gas Signal in a Transient GCM Simulation , 1991 .

[23]  B. Goswami,et al.  Predictability of a coupled ocean-atmosphere model , 1991 .

[24]  kwang-yul kim,et al.  Surface temperature fluctuations in a stochastic climate model , 1991 .

[25]  kwang-yul kim,et al.  On the transient response of a sample coupled climate system , 1992 .

[26]  kwang-yul kim,et al.  Seasonal cycle and second‐moment statistics of a simple coupled climate system , 1992 .

[27]  G. North,et al.  Forced and free variations of the surface temperature field in a general circulation model , 1992 .

[28]  A. Hansen,et al.  Structure in the Phase Space of a General Circulation Model Deduced from Empirical Orthogonal Functions. , 1992 .

[29]  E. Maier‐Reimer,et al.  Climate Variability in a Coupled GCM. Part I: The Tropical Pacific , 1993 .

[30]  Kwang Youn Kim,et al.  EOF analysis of surface temperature field in a stochastic climate model , 1993 .

[31]  T. Barnett,et al.  ENSO and ENSO-related Predictability. Part I: Prediction of Equatorial Pacific Sea Surface Temperature with a Hybrid Coupled Ocean–Atmosphere Model , 1993 .

[32]  K. Hasselmann Optimal Fingerprints for the Detection of Time-dependent Climate Change , 1993 .

[33]  B. Santer,et al.  Detecting anthropogenic climate change with an optimal fingerprint method , 1994 .

[34]  G. Plaut,et al.  Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere. , 1994 .

[35]  B. Santer,et al.  Signal-to-noise analysis of time-dependent greenhouse warming experiments , 1994 .

[36]  kwang-yul kim,et al.  Spectral Approach to Optimal Estimation of the Global Average Temperature , 1994 .

[37]  kwang-yul kim,et al.  Detection of Forced Climate Signals. Part 1: Filter Theory , 1995 .

[38]  H. Storch,et al.  Principal oscillation patterns: a review , 1995 .

[39]  kwang-yul kim,et al.  Detection of forced climate signals. Part II: Simulation results , 1995 .

[40]  X. Cheng,et al.  Robustness of Low-Frequency Circulation Patterns Derived from EOF and Rotated EOF Analyses , 1995 .

[41]  kwang-yul kim,et al.  Optimal Estimation of Spherical Harmonic Components from a Sample with Spatially Nonuniform Covarian , 1996 .

[42]  kwang-yul kim,et al.  EOFs of One-Dimensional Cyclostationary Time Series: Computations, Examples, and Stochastic Modeling , 1996 .

[43]  kwang-yul kim,et al.  An optimal method to estimate the spherical harmonic components of the surface air temperature , 1996 .

[44]  G. North,et al.  Comparisons of the second-moment statistics of climate models , 1996 .

[45]  kwang-yul kim,et al.  EOFs of Harmonizable Cyclostationary Processes , 1997 .

[46]  David L. Montroy Linear Relation of Central and Eastern North American Precipitation to Tropical Pacific Sea Surface Temperature Anomalies , 1997 .