Analysis Tools

Turn-key routines for the RegEM EIV Climate Reconstruction Routine
Turn-key routines for the RegEM EIV code (written in R programming language) can be found here.
This code was featured in Schmidt et al. (2011):
Schmidt, G.A., Mann, M.E., Rutherford, S.D., A comment on “A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?” by McShane and WynerAnn. Appl. Stat., 5, 65 70, 2011.

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.
Matlab Smoothing Routine Code can be found here.
The Smoothing Routine is Described in:
Mann, M.E., On Smoothing Potentially Non-Stationary Climate Time SeriesGeophysical Research Letters, 31, L07214, doi: 10.1029/2004GL019569, 2004.
An updated version yields a smoothed series based on combination of boundary constraints that minimizes MSE relative to raw time series.
Updated routines from Mann (2008) can be found here.
Download a PDF of Mann (2008) here.

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 SeriesClimatic 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 with results shown in the above Mann & Lees 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 ObservationGeophysical 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 codes, synthetic test dataset, and analysis results:
NOTE: an issue was brought to our attention about averaging angles in the code: mtm-svd-recon.f.; more details and a potential fix can be found here. The FORTRAN 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.

A MATLAB version of the code can be found HERE. MATLAB code generously provided by Marco Correa-Ramirez and Samuel Hormazabal See their paper here.
Python version of the code can be found HERE and is derived from the MATLAB code developed by Marco Correa-Ramirez and Samuel Hormazabal. Python code generously provided by Mathilde Jutras, a doctoral student at McGill University as of July 2020.

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.


Analysis Tools

Turn-key Routines 

Link to R code here

Papers go here

Time Series Smoothing Routine 

Multi-Taper Method

MTM-SVD Multivariate Signal Analysis