<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:math>model for long-time memory of the ocean surface temperature

Fraedrich, Klaus; Luksch, Ute; Blender, Richard

doi:10.1103/physreve.70.037301

Cited by 65 publications

(52 citation statements)

References 19 publications

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“…Recently, due to the developments in the area of complex systems as well as data measurements and data analysis, one can find many opportunities for examination and interpretation of climate change which exhibit irregular systems [1][2][3][4][5][6][7][8]. It is well shown that the climate system is enforced by the well-defined seasonal periodicity, however the existence of unpredictable perturbation and chaotic functioning lead to extreme climate events.…”

Section: Introductionmentioning

confidence: 99%

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Hajian

Movahed

2010

Physica A: Statistical Mechanics and its Applications

134

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We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, (12 − 24) ≤ s ≤ 130 months, is λ = 1.17 ± 0.04 which is almost similar for all underlying rivers at 1σconfidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are λ ∈ (0.76, 0.85) and γ× ∈ (0.30, 0.48), respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), λ ≈ (hsun + hriver)/2 is confirmed.

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Section: Introductionmentioning

confidence: 99%

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Hajian

Movahed

2010

Physica A: Statistical Mechanics and its Applications

134

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“…Records of the Earth's surface temperature illustrate this interdependence, having a continuum of variability following a power-law scaling [1][2][3][4][5][6][7] . But although specific modes of interannual variability are relatively well understood 8,9 , the general controls on continuum variability are uncertain and usually described as purely stochastic processes [10][11][12][13] . Here we show that power-law relationships of surface temperature variability scale with annual and Milankovitchperiod (23,000-and 41,000-year) cycles.…”

Section: Peter Huybers 1 and William Currymentioning

confidence: 99%

“…Numerous explanations have been advanced regarding the continuum, including stochastic resonance 11 , modified random walks 12 , and diffusion 13 , but all these models are partial descriptions of the variability. Ultimately, one seeks a physics of climate from which the temperature spectrum can be deduced, something analogous to oceanography's theories for tides 16 and internal waves 17 .…”

Section: Peter Huybers 1 and William Currymentioning

confidence: 99%

Links between annual, Milankovitch and continuum temperature variability

Huybers

Curry

2006

Nature

313

327

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“…We can additionally bring theoretical considerations to bear. Very different process modelling approaches have each suggested that the PDO specifically, or ocean temperature in general (note the PDO is a feature of North Pacific sea surface temperature), show a fundamental 1/f α spectrum (Fraedrich et al 2003, Huybers and Curry 2006, Newman 2007. On balance, then, it seems reasonable to conclude that the PDO likely has a true power-law spectrum.…”

Section: Resultsmentioning

confidence: 99%

A non-uniqueness problem in the identification of power-law spectral scaling for hydroclimatic time series

Fleming¹

2013

Hydrological Sciences Journal

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Power-law spectral scaling violates assumptions of standard analyses such as statistical change detection. However, hydroclimatic data sets may be too short to differentiate the spectra of 1/f α vs low-order linear memory processes, an ambiguity exacerbated by the ubiquity of both process types. We explore this non-uniqueness problem by applying a heuristic tool to four examples from each of four hydroclimatic data types: circulation indices, station climate, river and aquifer conditions, and glacier mass balance. This selection spans much of the globe and includes some of the longest instrumental data sets available. The most common outcome is that power-law scaling is apparent, but the record is insufficiently long to discriminate between underlying mechanisms. The use of palaeoclimatic data to extend the instrumental record was investigated, but produced mixed results. Conversely, a balance-of-evidence approach, additionally incorporating physical process considerations, may help us recognize variate classes for which 1/f α scaling can be concluded. Practical recommendations are offered.Key words spectrum; persistence; streamflow; groundwater; glacier; palaeoclimate Un problème de non-unicité dans l'identification de la scalance spectrale des lois de puissance pour des séries chronologiques hydroclimatiques Résumé La scalance spectrale d'une loi de puissance ne satisfait pas les hypothèses des analyses classiques telles que la détection des changements statistiques. Les ensembles de données hydroclimatiques peuvent cependant être trop courts pour différencier les processus de spectres en 1/fα des processus linéaires à mémoire courte, ambiguïté exacerbée par l'omniprésence de ces deux types de processus. Nous avons exploré ce problème de non-unicité en appliquant un outil heuristique à quatre exemples de chacun de quatre types de données hydroclimatiques suivants: indices de circulation, climat d'une station, caractéristiques d'une rivière et d'un aquifère et bilan de masse d'un glacier. Cette sélection est répartie sur une grande partie du globe et comprend certaines des plus longues séries disponibles de données instrumentales. Le premier résultat est que la scalance selon une loi de puissance est évidente, mais que les séries ne sont pas suffisamment longues pour distinguer entre les mécanismes sous-jacents. L'utilisation des données paléoclimatiques pour étendre la durée des séries instrumentales a été étudiée, mais n'a fourni que des résultats mitigés. Inversement, une approche par bilan des informations, intégrant en outre des considérations de processus physiques, peut nous aider à reconnaître les classes de variables pour lesquelles on peut conclure à une scalance en 1/fα. Des recommandations pratiques sont proposées.

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1∕fmodel for long-time memory of the ocean surface temperature

Cited by 65 publications

References 19 publications

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Links between annual, Milankovitch and continuum temperature variability

A non-uniqueness problem in the identification of power-law spectral scaling for hydroclimatic time series

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