On the Power Spectrum of “Red Noise”

By D. L. Gilman, F. J. Fuglister, J. M. Mitchell. 1963

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Citations in the corpus

Trend analysis of climate time series: A review of methods (2019, methodology): “For climate variables, the AR(1) model has been found useful empirically (Gilman et al., 1963) and theoretically (Hasselmann, 1976) for describing the autocorrelation structure.”
TAUEST: a computer program for estimating persistence in unevenly spaced weather/climate time series (2002, background): “The simplest yet successful persistence model is a first-order autoregressive (AR(1)) process where a fluctuation depends only on its own immediate past plus a random component (Gilman et al., 1963; Mann and Lees, 1996).”
Spectral signatures of characteristic spatial scales and nonfractal structure in landscapes (2008, background): “The spectral power corresponding to a confidence level a is [Gilman et al., 1963; Percival and Walden, 1993; Torrence and Compo, 1998] Pa fð Þ ¼ 1 2 c22 1 að Þ P fð Þ; ð9Þ where c2 2(1 a) is the value at which the c2 cumulative distribution function with 2 degrees of freedom equals 1 a.”
Comment on ''Heat capacity, time constant, and sensitivity of Earth's climate system'' by S. E. Schwartz (2008, background): “…are linearly additive, the latter component alone might be considered, as a null hypothesis, to conform approximately to an AR(1) process [Gilman et al., 1963; Hasselmann, 1976] in the asymptotic limit where complicating processes such as advective and diffusive exchanges of heat with…”
Statistical analysis of hydroclimatic time series: Uncertainty and insights (2007, background): “[4] On the other hand, the Markovian postulate (dating back to 1960s [Gilman et al., 1963] and still in use today [e.”
Variability of El Niño/Southern Oscillation activity at millennial timescales during the Holocene epoch (2002, background): “Red noise characterizes the spectrum found in many climatic time series, and can be represented as a first-order autoregressive proces”
The Tropical Cyclone Diurnal Cycle of Mature Hurricanes (2014, unknown): “The spectral analyses were tested for signiﬁcance against a Markov red noise continuum (Gilman et al. 1963).”
ADVANCED SPECTRAL METHODS FOR CLIMATIC TIME SERIES (2002, background): “This realization of the possibility of deterministic aperiodicity or “chaos” [Gleick, 1987] created quite a stir. [14] The purpose of this review is to describe briefly some of the implications of this change in outlook for time series analysis, with a special emphasis on climatic time series. Many ”
A quick gap filling of missing hydrometeorological data (2014, background): “For example, several studies have asserted that daily precipitation [Gilman, 1963], sea surface temperature anomalies [Frankignoul and Hasselmann, 1977], Arctic sea ice (Blanchard-Wrigglesworth et al.”
Long memory of rivers from spatial aggregation (2007, unknown): “[3] Many meteorological variables have noise components that can be described as simple first-order autoregressive (AR(1)) processes [Gilman et al., 1963], where a value depends only on its own immediate past plus a random component.”
Geophysical Applications of Partial Wavelet Coherence and Multiple Wavelet Coherence (2012, methodology): “Those phenomena of red-noise characteristics, like our example, can be well modeled by the lag-1 autoregressive process (Gilman et al. 1963; Allen and Smith 1996).”
REDFIT: estimating red-noise spectra directly from unevenly spaced paleoclimatic time series (2002, methodology): “Accordingly, the AR1 model is often used as null hypothesis to assess whether or not the variability recorded in a time series is consistent with a stochastic origin of this type (Gilman et al., 1963).”