Robust estimation of background noise and signal detection in climatic time series
TL;DR: In this paper, the authors present a technique for isolating climate signals in time series with a characteristic "red" noise background which arises from temporal persistence, which is estimated by a robust procedure that is largely unbiased by the presence of signals immersed in the noise.
Abstract: We present a new technique for isolating climate signals in time series with a characteristic ‘red’ noise background which arises from temporal persistence. This background is estimated by a ‘robust’ procedure that, unlike conventional techniques, is largely unbiased by the presence of signals immersed in the noise. Making use of multiple-taper spectral analysis methods, the technique further provides for a distinction between purely harmonic (periodic) signals, and broader-band (‘quasiperiodic’) signals. The effectiveness of our signal detection procedure is demonstrated with synthetic examples that simulate a variety of possible periodic and quasiperiodic signals immersed in red noise. We apply our methodology to historical climate and paleoclimate time series examples. Analysis of a ≈ 3 million year sediment core reveals significant periodic components at known astronomical forcing periodicities and a significant quasiperiodic 100 year peak. Analysis of a roughly 1500 year tree-ring reconstruction of Scandinavian summer temperatures suggests significant quasiperiodic signals on a near-century timescale, an interdecadal 16–18 year timescale, within the interannual El Nino/Southern Oscillation (ENSO) band, and on a quasibiennial timescale. Analysis of the 144 year record of Great Salt Lake monthly volume change reveals a significant broad band of significant interdecadal variability, ENSO-timescale peaks, an annual cycle and its harmonics. Focusing in detail on the historical estimated global-average surface temperature record, we find a highly significant secular trend relative to the estimated red noise background, and weakly significant quasiperiodic signals within the ENSO band. Decadal and quasibiennial signals are marginally significant in this series.
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TL;DR: The connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis are described.
Abstract: [1] The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.
2,116 citations
Cites background from "Robust estimation of background noi..."
..., 1995b; Thomson, 1995], paleoclimate proxy data [Chappellaz et al., 1990; Thomson, 1990a, 1990b; Berger et al., 1991; Mann et al., 1995a; Mann and Lees, 1996; Mommersteeg et al., 1995; Park and Maasch, 1993; Yiou et al., 1991, 1994, 1995, 1997], geochemical tracer data [Koch and Mann, 1996], and seismological data [Park et al....
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...…et al., 1995b; Thomson, 1995], paleoclimate proxy data [Chappellaz et al., 1990; Thomson, 1990a, 1990b; Berger et al., 1991; Mann et al., 1995a; Mann and Lees, 1996; Mommersteeg et al., 1995; Park and Maasch, 1993; Yiou et al., 1991, 1994, 1995, 1997], geochemical tracer data [Koch and Mann,…...
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...[150] Significance levels for harmonic or narrowband spectral features relative to the estimated noise background can be determined from the appropriate quantiles of the chi-square distribution, by assuming that the spectrum is distributed with 2K degrees of freedom [Mann and Lees, 1996]....
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TL;DR: In this article, the authors attempt hemispheric temperature reconstructions with proxy data networks for the past millennium, focusing not just on the reconstructions, but the uncertainties therein, and important caveats.
Abstract: Building on recent studies, we attempt hemispheric temperature reconstructions with proxy data networks for the past millennium. We focus not just on the reconstructions, but the uncertainties therein, and important caveats. Though expanded uncertainties prevent decisive conclusions for the period prior to AD 1400, our results suggest that the latter 20th century is anomalous in the context of at least the past millennium. The 1990s was the warmest decade, and 1998 the warmest year, at moderately high levels of confidence. The 20th century warming counters a millennial-scale cooling trend which is consistent with long-term astronomical forcing.
1,742 citations
Cites background from "Robust estimation of background noi..."
...An indicator of climate variability should exhibit, at a minimum, the red noise spectrum the climate itself is known to exhibit [see Mann and Lees, 1996 and references therein]....
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TL;DR: In this article, a spatially resolved global reconstructions of annual surface temperature patterns over the past six centuries are based on the multivariate calibration of widely distributed high-resolution proxy climate indicators.
Abstract: Spatially resolved global reconstructions of annual surface temperature patterns over the past six centuries are based on the multivariate calibration of widely distributed high-resolution proxy climate indicators. Time-dependent correlations of the reconstructions with time-series records representing changes in greenhouse-gas concentrations, solar irradiance, and volcanic aerosols suggest that each of these factors has contributed to the climate variability of the past 400 years, with greenhouse gases emerging as the dominant forcing during the twentieth century. Northern Hemisphere mean annual temperatures for three of the past eight years are warmer than any other year since (at least) ad 1400.
1,720 citations
Cites result from "Robust estimation of background noi..."
...This latter trend has been shown to be inconsistent with red nois...
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TL;DR: In this paper, a Fortran 90 program (REDFIT) is presented that overcomes this problem by fitting a first-order autoregressive (AR1) process, being characteristic for many climatic processes, directly to unevenly spaced time series.
1,048 citations
Cites background or methods from "Robust estimation of background noi..."
...Although it would be possible to identify and subtract harmonic signal components prior to estimating t (see Mann and Lees, 1996 for evenly spaced time series), this approach may fail if there are quasi-periodic signals (e.g. narrow-band noise), which often occur in climatic time series....
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...The unknown value of t is estimated from an unevenly spaced time series using the least-squares algorithm devised by Mudelsee (2002). The spectrum of an irregularly spaced time series is determined without the need for interpolation by means of the Lomb–Scargle Fourier transform (Lomb, 1976; Scargle, 1982, 1989)....
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TL;DR: The WATCH Forcing Data for 1958-2001 based on the 40-yr ECMWF Re-Analysis (ERA-40) and for 1901-57 based on reordered reanalysis data as mentioned in this paper.
Abstract: The Water and Global Change (WATCH) project evaluation of the terrestrial water cycle involves using land surface models and general hydrological models to assess hydrologically important variables including evaporation, soil moisture, and runoff. Such models require meteorological forcing data, and this paper describes the creation of the WATCH Forcing Data for 1958–2001 based on the 40-yr ECMWF Re-Analysis (ERA-40) and for 1901–57 based on reordered reanalysis data. It also discusses and analyses model-independent estimates of reference crop evaporation. Global average annual cumulative reference crop evaporation was selected as a widely adopted measure of potential evapotranspiration. It exhibits no significant trend from 1979 to 2001 although there are significant long-term increases in global average vapor pressure deficit and concurrent significant decreases in global average net radiation and wind speed. The near-constant global average of annual reference crop evaporation in the late twentieth century masks significant decreases in some regions (e.g., the Murray–Darling basin) with significant increases in others.
797 citations
Cites methods from "Robust estimation of background noi..."
...This parameter was determined using the robust spectralfitting method of Mann and Lees (1996) because largeamplitude regular components such as diurnal and annual Unauthenticated | Downloaded 03/19/22 06:12 PM UTC cycles can cause a positive bias....
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References
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01 Sep 1982
TL;DR: In this article, a local eigenexpansion is proposed to estimate the spectrum of a stationary time series from a finite sample of the process, which is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows to treat both bias and smoothing problems.
Abstract: In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.
3,921 citations
"Robust estimation of background noi..." refers background in this paper
...reshaping procedure (Thomson, 1982; Lees, 1995), providing an estimate of the continuous background spectrum....
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TL;DR: A review of the intergovernmental panel on climate change report on global warming and the greenhouse effect can be found in this paper, where the authors present chemistry of greenhouse gases and mathematical modelling of the climate system.
Abstract: Book review of the intergovernmental panel on climate change report on global warming and the greenhouse effect. Covers the scientific basis for knowledge of the future climate. Presents chemistry of greenhouse gases and mathematical modelling of the climate system. The book is primarily for government policy makers.
3,456 citations
Book•
01 May 1981
TL;DR: This book will be most useful to applied mathematicians, communication engineers, signal processors, statisticians, and time series researchers, both applied and theoretical.
Abstract: This book will be most useful to applied mathematicians, communication engineers, signal processors, statisticians, and time series researchers, both applied and theoretical. Readers should have some background in complex function theory and matrix algebra and should have successfully completed the equivalent of an upper division course in statistics.
3,231 citations
03 Jun 1993
TL;DR: In this article, the authors present a bibliographical reference record created on 2004-09-07, modified on 2016-08-08, and includes references and indexes Reference Record.
Abstract: Note: Includes bibliographical references and indexes Reference Record created on 2004-09-07, modified on 2016-08-08
1,962 citations