EOF-Based Linear Prediction Algorithm: Examples

Kwang-Y. Kim Climate System Research Program, Department of Meteorology, Texas A&M University, College Station, Texas

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Gerald R. North Climate System Research Program, Department of Meteorology, Texas A&M University, College Station, Texas

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Abstract

Considered here are examples of statistical prediction based on the algorithm developed by Kim and North. The predictor is constructed in terms of space–time EOFs of data and prediction domains. These EOFs are essentially a different representation of the covariance matrix, which is derived from past observational data. The two sets of EOFs contain information on how to extend the data domain into prediction domain (i.e., statistical prediction) with minimum error variance. The performance of the predictor is similar to that of an optimal autoregressive model since both methods are based on the minimization of prediction error variance. Four different prediction techniques—canonical correlation analysis (CCA), maximum covariance analysis (MCA), principal component regression (PCR), and principal oscillation pattern (POP)—have been compared with the present method. A comparison shows that oscillation patterns in a dataset can faithfully be extended in terms of temporal EOFs, resulting in a slightly better performance of the present method than that of the predictors based on the maximum pattern correlations (CCA, MCA, and PCR) or the POP predictor. One-dimensional applications demonstrate the usefulness of the predictor. The NINO3 and the NINO3.4 sea surface temperature time series (3-month moving average) were forecasted reasonably up to the lead time of about 6 months. The prediction skill seems to be comparable to other more elaborate statistical methods. Two-dimensional prediction examples also demonstrate the utility of the new algorithm. The spatial patterns of SST anomaly field (3-month moving average) were forecasted reasonably up to about 6 months ahead. All these examples illustrate that the prediction algorithm is useful and computationally efficient for routine prediction practices.

Corresponding author address: Dr. Kwang-Y. Kim, Climate System Research Program, Department of Meteorology, Texas A&M University, College Station, TX 77843-3150.

Email: kykim@csrp.tamu.edu

Abstract

Considered here are examples of statistical prediction based on the algorithm developed by Kim and North. The predictor is constructed in terms of space–time EOFs of data and prediction domains. These EOFs are essentially a different representation of the covariance matrix, which is derived from past observational data. The two sets of EOFs contain information on how to extend the data domain into prediction domain (i.e., statistical prediction) with minimum error variance. The performance of the predictor is similar to that of an optimal autoregressive model since both methods are based on the minimization of prediction error variance. Four different prediction techniques—canonical correlation analysis (CCA), maximum covariance analysis (MCA), principal component regression (PCR), and principal oscillation pattern (POP)—have been compared with the present method. A comparison shows that oscillation patterns in a dataset can faithfully be extended in terms of temporal EOFs, resulting in a slightly better performance of the present method than that of the predictors based on the maximum pattern correlations (CCA, MCA, and PCR) or the POP predictor. One-dimensional applications demonstrate the usefulness of the predictor. The NINO3 and the NINO3.4 sea surface temperature time series (3-month moving average) were forecasted reasonably up to the lead time of about 6 months. The prediction skill seems to be comparable to other more elaborate statistical methods. Two-dimensional prediction examples also demonstrate the utility of the new algorithm. The spatial patterns of SST anomaly field (3-month moving average) were forecasted reasonably up to about 6 months ahead. All these examples illustrate that the prediction algorithm is useful and computationally efficient for routine prediction practices.

Corresponding author address: Dr. Kwang-Y. Kim, Climate System Research Program, Department of Meteorology, Texas A&M University, College Station, TX 77843-3150.

Email: kykim@csrp.tamu.edu

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