Mann (2004) Time Series Smoothing Routine
Provides smoothed time series and measure of misfit with option of boundary conditions useful in series with long-term trends or non-stationary behavior
The Smoothing Routine is Described in:
Mann, M.E., On Smoothing Potentially Non-Stationary Climate Time Series,
Geophysical Research Letters, 31, L07214, doi: 10.1029/2004GL019569, 2004.
Matlab Smoothing Routine Code
Updated Version yields a smoothed series based on combination of boundary constraints that minimizes MSE relative to raw time series
Mann & Lees Multi-Taper Method (MTM)
Multitaper spectral analysis which
provides an optimally low-variance, high-resolution spectral estimate.
Assumptions regarding signal (narrowband, but not strictly periodic) and noise ("red") that are most appropriate in the context of climate studies.
A "robust" method for accurate
determination of the noise component of the spectrum.
The MTM Method is Described in:
Mann, M.E., Lees. J., Robust
Estimation of Background Noise and Signal Detection in Climatic Time Series,
Climatic Change, 33, 409-445, 1996.
The MTM Method is Used in the SSA-MTM Toolkit
MTM Fortran code
Includes required subroutines and sample data for comparison wih results shown in the above paper.
An enhanced version
with "evolutive" spectral analysis and spectral coherence estimation is also now
available.
A separate package for performing complex demodulation
of a time series as used in,
Mann, M.E., Park. J., Greenhouse
Warming and Changes in the Seasonal Cycle of Temperature: Model Versus
Observation, Geophysical Research Letters, 23, 1111-1114,
1996.
Mann & Park MTM-SVD Multivariate Signal Analysis
Detection of irregular spatiotemporal oscillatory signals immersed in spatially-correlated coloured noise with optimal signal detection properties
"Evolutive'' approach to detecting intermittent and/or frequency-modulated spatiotemporal oscillations.
Reconstruction of spatial and temporal patterns of oscillatory climate signals
MTM-SVD Fortran codes, synthetic test dataset, and analysis results
Codes Include:
- "LFV" multivariate spectrum estimation
- Spatiotemporal signal reconstruction
- Bootstrap confidence level estimation procedure, along with
required subroutines, makefiles, and the synthetic test input and output.
MTM-SVD References
- Mann, M.E., Park, J., Spatial
Correlations of Interdecadal Variation in Global Surface Temperatures,Geophysical Research Letters, 20, 1055-1058, 1993.
- Mann, M.E., Lall, U., Saltzman, B., Decadal-to-century scale climate variability: Insights into the Rise and Fall of the Great Salt Lake, Geophysical Research Letters, 22, 937-940, 1995.
- Mann, M.E., Park, J., Bradley, R.S., Global Interdecadal and Century-Scale Climate Oscillations During the Past Five Centuries, Nature, 378, 266-270, 1995.
- Mann, M.E., Park, J., Greenhouse Warming and Changes in the Seasonal Cycle of Temperature: Model Versus Observations, Geophysical Research Letters, 23, 1111-1114, 1996.
- Koch, D., Mann, M.E., Spatial and Temporal Variability of 7Be Surface Concentrations, Tellus, 48B, 387-396, 1996.
- Mann, M.E., Park, J., Joint Spatio-Temporal Modes of Surface Temperature and Sea Level Pressure Variability in the Northern Hemisphere During the Last Century, Journal of Climate, 9, 2137-2162, 1996.
- Rajagopalan, B., Mann, M.E., and Lall, U., A Multivariate Frequency-Domain Approach to Long-Lead Climatic Forecasting, Weather and Forecasting,, 13, 58-74, 1998.
- Tourre, Y., Rajagopalan, B., and Kushnir, Y., Dominant patterns of climate variability in the Atlantic over the last 136 years, Journal of Climate, 12, 2285-2299, 1998.
- Mann, M.E., Park, J, Oscillatory Spatiotemporal Signal Detection in Climate Studies: A Multiple-Taper Spectral Domain Approach , Advances in Geophysics, 41, 1-131, 1999. (click here for version w/ color figures)
- Delworth, T.L., and Mann, M.E., Observed and Simulated Multidecadal Variability in the Northern Hemisphere, Climate Dynamics, 16, 661-676, 2000.
- Mann, M.E., Bradley, R.S., Hughes, M.K., Long-term variability in the El Nino Southern Oscillation and associated teleconnections, , Diaz, H.F. and Markgraf, V. (eds) El Nino and the Southern Oscillation: Multiscale Variability and its Impacts on Natural Ecosystems and Society, Cambridge University Press, Cambridge, UK, 357-412, 2000.
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