D. L. Gilman

Bio: D. L. Gilman is an academic researcher. The author has contributed to research in topics: Colors of noise & Noise spectral density. The author has an hindex of 1, co-authored 1 publications receiving 398 citations.

A Practical Guide to Wavelet Analysis.

Abstract: A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmoller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of change...

Advanced spectral methods for climatic time series

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.

Variability of El Niño/Southern Oscillation activity at millennial timescales during the Holocene epoch

Abstract: The variability of El Nino/Southern Oscillation (ENSO) during the Holocene epoch, in particular on millennial timescales, is poorly understood. Palaeoclimate studies have documented ENSO variability for selected intervals in the Holocene, but most records are either too short or insufficiently resolved to investigate variability on millennial scales1,2,3. Here we present a record of sedimentation in Laguna Pallcacocha, southern Ecuador, which is strongly influenced by ENSO variability, and covers the past 12,000 years continuously. We find that changes on a timescale of 2–8 years, which we attribute to warm ENSO events, become more frequent over the Holocene until about 1,200 years ago, and then decline towards the present. Periods of relatively high and low ENSO activity, alternating at a timescale of about 2,000 years, are superimposed on this long-term trend. We attribute the long-term trend to orbitally induced changes in insolation, and suggest internal ENSO dynamics as a possible cause of the millennial variability. However, the millennial oscillation will need to be confirmed in other ENSO proxy records.

Robust estimation of background noise and signal detection in climatic time series

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.

Drought Reconstructions for the Continental United States

Abstract: The development of a 2° lat × 3° long grid of summer drought reconstructions for the continental United States estimated from a dense network of annual tree-ring chronologies is described. The drought metric used is the Palmer Drought Severity Index (PDSI). The number of grid points is 154 and the reconstructions cover the common period 1700–1978. In producing this grid, an automated gridpoint regression method called “point-by-point regression” was developed and tested. In so doing, a near-optimal global solution was found for its implementation. The reconstructions have been thoroughly tested for validity using PDSI data not used in regression modeling. In general, most of the gridpoint estimates of drought pass the verification tests used. In addition, the spatial features of drought in the United States have been faithfully recorded in the reconstructions even though the method of reconstruction is not explicitly spatial in its design. The drought reconstructions show that the 1930s “Dust Bow...