We provide here fortran source codes and required subroutines+makefiles for the MTM-SVD multivariate signal analysis procedure of Mann and Park (C) 1994.The method and its applications to various climatic/atmospheric/oceanographic data sets are described in: Mann, M.E., Park, J., Global scale modes of surface temperature variability on interannual to century time scales, Journal of Geophysical Research, 99, 25819-25833, 1994. 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. Mann, M.E. and Park, J., Multivariate Signal Detection in Climate Studies, Advances in Geophysics, in press, 1999. Tourre, Y., Rajagopalan, B., and Kushnir, Y., Dominant patterns of climate variability in the Atlantic over the last 136 years, Journal of Climate, in press, 1999. 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, in press, 1999.The authors take no responsibility for possible bugs, compliler incompatibitiles, etc. If you believe that such problems have beenencountered, please contact us at:[email protected]. CODESThe following (3) fortran codes are provided(1) mtm-svd-spec.f(2) mtm-svd-recon.f(3) mtm-svd-conf.falong with the required fortran subroutinesmtm-rout.frealft.feispk.fzlinpk.fand the corresponding makefiles: Makefile1, Makefile2, Makefile3(1) Provides the MTM-SVD multivariate spectrum decompositionof the data. It requires the dataseries to be analyzedas input (in appropriate format) and returns the output files:evals-1.out Principle eigenvalue spectrum (the "LFV spectrum" of the dataset)evals-2.out 2nd eigenvalue spectrum--generally not of interestevals-3.out 3rd eigenvalue spectrum--generally not of interest[Also produced are the files: svd-means.out (the means for each gridpoint data series) svd-sigmas.out (the standard deviations " ) ](2) Allows for the reconstruction of a narrowband spatiotemporal signal corresponding to a peak with center at frequency f0 as detected in the LFV spectrum from (1). A variety of options are allowed including "evolutive" signal reconstruction (see below). The code requires the properly formated dataseries to be analyzed and for certain options (see below-note 1) the additional input file "frequency.dat" Upon output, the following files are produced:recon-data.out various information about the signal reconstructionsrecon-spat.eof[k] spatial EOFrecon-spat.pat[k] the spatial pattern of the signal (see note 2 below)recon-spec.eof[k] spectral EOF or "principle modulation" of Kth moderecon-stats.out means and standard deviations of the dataseriesrecon-status.out progress updaterecon-time.site[j] time reconstruction for site "j" indicated. (this may include one or more several files depending on the number of sites indicated) 1st y column = reconstucted signal 2nd y column = reference series ("raw" or lowpassed dataseries depending on what user indicates) 3rd y column = raw dataseriesdifferent boundary constraints are possible (see note 3 below)."X" indicates the mode (eg, principle "1" or 2ndary "2" for example)to be reconstructed. Almost always, the principle mode "1" correspondingto the peak in the LFV spectrum is of interest.(3) Allows for non-parametric estimation of the null distributionand signficance levels (median, 90%,95%,99%) for coloured noise withthe same spatial correlation structure as the actual dataseries.The following files are produced:evals-permute1.out median(50% level of null distribution), and 90%,95%,99% levels for signficance of the LFV spectrum calculated in (1)evals-permute2.out same, for 2ndary eigenvalue spectrum (generally not of interest)B. SYNTHETIC TEST CASEA synthetic dataset of 25 gridpoints with a (1) secular trend, (2)low-frequency amplitude/phase modulated oscillation and a (3)high-frequency frequency and amplitude/phase modulated oscillation,immersed in equal variance spatially correlated red noise isprovided in the data files: synth1.dat, synth2.dat, synth3.dat,synth4.dat, synth5.dat for comparison with the analysisperformed by Rajagopalan, B., Mann, M.E., and Lall, U., A Multivariate Frequency-Domain Approach to Long Lead Climatic Forecasting, Weather and Forecasting, submitted, 1997.(preprint available over the web: ftp://love.geology.yale.edu/pub/Climate/Forecasting/ )The additional required file "frequency.dat"for the frequency-modulated the signal reconstruction of (3) isalso provided.The correct LFV spectrum (based on K=3 and bandwidth parameter p =2)evals-synth-1.outand the corresponding 2ndary and 3rd eigenvalue spectra evals-synth-2.outevals-synth-3.outare also provided for the synthetic dataset, as is the evolutiveLFV spectrum evals-synth-40yrwin-1.outbased on 40 year (480 month) moving window.The correct bootstrap signficance levels are provided inevals-permute1-synth.outevals-permute2-synth.outbased on 2000 bootstrap resamples.Postscript figures of the correct results (taken fromRajagopalan et al 1997 cited above) are also providedlfvspec.ps