Temporal Signatures of Observations and Model Outputs: Do Time Series Decomposition Methods Capture Relevant Time Scales?

Time series decomposition methods were applied to meteorological and air quality data and their numerical model estimates. Decomposition techniques express a time series as the sum of a small number of independent modes which hypothetically represent identifiable forcings, thereby helping to untangle complex processes. Mode-to-mode comparison of observed and modeled data provides a mechanism for model evaluation. The decomposition methods included empirical orthogonal functions (EOF), empirical mode decomposition (EMD), and wavelet filters (WF). EOF, a linear method designed for stationary time series, is principal component analysis (PCA) applied to time-lagged copies of a given time series. EMD is a relatively new nonlinear method that operates locally in time and is suitable for nonstationary and nonlinear processes; it is not, in theory, band-width limited, and the number of modes is automatically determined. Wavelet filters are band-width guided with the number of modes set by the analyst. The purpose of this paper is to compare the performance of decomposition techniques in characterizing time scales in meteorological and air quality variables. The time series for this study, modeled and observed temperature and PM2.5, were chosen because they represent relatively easy and difficult tests,