Spatial and temporal spectra of the geomagnetic field and their scaling properties

Santis, Angelo De; Barraclough, D. R.; Tozzi, Roberta

doi:10.1016/s0031-9201(02)00211-x

Cited by 35 publications

(35 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Barraclough and De Santis, 1997;De Santis et al, 2002), thus confirming the present state of a chaotic geomagnetic field with no reliable prediction after around 6 years. The empirical evidence for the ergodicity of the geomagnetic field given by the present work indicates a strong spatio-temporal coupling among the unknown components of the dynamical system behind the geomagnetic field generation, as it was already found independently by analysing the spatial and temporal spectra of global models and geomagnetic observatory time series, respectively (De Santis et al, 2003). The disclosed ergodicity implies that we can simplify many geomagnetic field analyses for estimating some ergodic measures, such as the information content or various kinds of entropies.…”

Section: Discussionsupporting

confidence: 82%

“…Hongre et al, 1999), would be more easily made in the conventional time domain . In addition, ergodicity would be a further evidence for the strong spatio-temporal coupling among the contributions composing the dynamical system that produces and sustains the geomagnetic field (Hongre et al, 1999;De Santis et al, 2003). The strong coupling is typical of many spatio-temporal chaotic phenomena (e.g.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Ergodicity of the recent geomagnetic field

Santis

Qamili

Cianchini

2011

Physics of the Earth and Planetary Interiors

Self Cite

View full text Add to dashboard Cite

Please cite this article as: De Santis, A., Qamili, E., Cianchini, G., Ergodicity of the recent geomagnetic field, Physics of the Earth and Planetary Interiors (2011), doi: 10.1016/j.pepi.2011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractThe geomagnetic field is a fundamental property of our planet: its study would allow us to understand those processes of Earth's interior, which act in its outer core and produce the main field. Knowledge of whether the field is ergodic, i.e., whether time averages correspond to phase space averages, is an important question since, if this were true, it would point out a strong spatiotemporal coupling among the components of the dynamical system behind the present geomagnetic field generation. Another consequence would be that many computations, usually undertaken with many difficulties in the phase space, can be made in the conventional time domain. We analyse the temporal behaviour of the deviation between predictive and definitive geomagnetic global models for successive intervals from 1965 to 2010, finding a similar exponential growth with time. Also going back in time (at around 1600 and 1900 by using the GUFM1 model) confirms the same findings. This result corroborates previous chaotic analyses made in a reconstructed phase space from geomagnetic observatory time series, confirming the chaotic character of the recent geomagnetic field with no reliable prediction after around 6 years from definitive values, and disclosing the potentiality of estimating important entropic quantities of the field by time averages.Although more tests will be necessary, some of our analyses confirm the efforts to improve the representation of the geomagnetic field with more detailed secular variation and acceleration.

show abstract

Section: Discussionsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Ergodicity of the recent geomagnetic field

Santis

Qamili

Cianchini

2011

Physics of the Earth and Planetary Interiors

Self Cite

View full text Add to dashboard Cite

show abstract

“…This description is chosen since it is consistent with the slope close to −4 found for the power spectrum density (PSD) of observatory series at periods from 5 to 70 years (De Santis et al 2003). The continuation of such a slope for the PSD of the internal field at periods shorter than a few years is unsure given the domination of the external signal towards high frequencies (see Figure two in Ou et al 2015), but there is no need either for a steeper slope given the current estimate of the mantle conductivity (Velímský and Finlay 2011).…”

Section: Cov-obsx1 Modelmentioning

confidence: 94%

“…We consider the simplest stationary, stochastic model compatible with the −4 slope obtained for the temporal PSD of geomagnetic field series at ground-based observatories for periods 5 ≤ T ≤ 70 years (De Santis et al 2003).…”

Section: Stochastic Core Flow Modelingmentioning

confidence: 99%

Stochastic forecasting of the geomagnetic field from the COV-OBS.x1 geomagnetic field model, and candidate models for IGRF-12

2015

View full text Add to dashboard Cite

We present the geomagnetic field model COV-OBS.x1, covering 1840 to 2020, from which have been derived candidate models for the IGRF-12. Towards the most recent epochs, it is primarily constrained by first differences of observatory annual means and measurements from the Oersted, Champ, and Swarm satellite missions. Stochastic information derived from the temporal spectra of geomagnetic series is used to construct the a priori model covariance matrix that complements the constraint brought by the data. This approach makes it possible the use of a posteriori model errors, for instance, to measure the 'observations' uncertainties in data assimilation schemes for the study of the outer core dynamics. We also present and illustrate a stochastic algorithm designed to forecast the geomagnetic field. The radial field at the outer core surface is advected by core motions governed by an auto-regressive process of order 1. This particular choice is motivated by the slope observed for the power spectral density of geomagnetic series. Accounting for time-correlated model errors (subgrid processes associated with the unresolved magnetic field) is made possible thanks to the use of an augmented state ensemble Kalman filter algorithm. We show that the envelope of forecasts includes the observed secular variation of the geomagnetic field over 5-year intervals, even in the case of rapid changes. In a purpose of testing hypotheses about the core dynamics, this prototype method could be implemented to build the 'state zero' of the ability to forecast the geomagnetic field, by measuring what can be predicted when no deterministic physics is incorporated into the dynamical model.

show abstract

“…The auto-covariance function of a series defines its power spectrum S( f ), where f is the frequency. As illustrated in Figure 2, that of observatory records evolves approximately as S( f ) ∝ f −4 at periods longer than 5 years (Currie 1968;De Santis et al 2003). As highlighted by Gillet et al (2013), it is convenient to model such series in the framework of stochastic differential equations (SDEs), for which a −4 slope spectrum at high frequencies corresponds to an SDE of order 2.…”

Section: Local Stochastic Regression Of the Main Fieldmentioning

confidence: 99%

Geomagnetic observatory monthly series, 1930 to 2010: empirical analysis and unmodeled signal estimation

Gillet

2015

Earth Planet Sp

View full text Add to dashboard Cite

Ground-based magnetic observatory series are the main source of information for constructing time-dependent spherical harmonic geomagnetic field models from sub-annual to pluri-decadal time scales. Assessing the reliability of such models requires accurate estimation of the data errors. We propose an analysis of observatory monthly means over the period 1930 to 2010, where we sequentially isolate (i) a stochastic regression for the main field at every site, performed in the framework of Gaussian processes, (ii) a local fit to annual and semiannual signals, (iii) a month by month estimate of global, large length-scale external and induced fields. We then estimate the unmodeled signal level (UMSL, which refers to the instrumental noise plus extra signals not captured by the above data treatment) from the standard deviation of the residuals to the sequential analysis. This may be used to estimate data error covariances in future field modeling studies. Mainly a function of the geomagnetic latitude, the UMSL is larger towards auroral regions and carries the temporal signature of solar activity. While the UMSL shows rather similar magnitudes in all three components in recent epochs (typically a few nT), a significant decrease is found in the downward component of the field around 1960, which correlates with the introduction of proton magnetometers. We detail the geographic distribution of the periodic signals and confirm the variation of their amplitude at pluri-decadal time scales. From the spherical harmonic description of horizontal and vertical fields, we isolate the main patterns of the inducing field in Z. These are dominated by a zonal structure of degree 1 (and to a lesser extent, of degree 3) in dipole coordinates. We nevertheless isolate secondary, non-zonal sources that are most active during the 1960s and around 1990, periods of particularly large solar activity, denoting an unusual morphology of the inducing field.

show abstract

Spatial and temporal spectra of the geomagnetic field and their scaling properties

Cited by 35 publications

References 13 publications

Ergodicity of the recent geomagnetic field

Ergodicity of the recent geomagnetic field

Stochastic forecasting of the geomagnetic field from the COV-OBS.x1 geomagnetic field model, and candidate models for IGRF-12

Geomagnetic observatory monthly series, 1930 to 2010: empirical analysis and unmodeled signal estimation

Contact Info

Product

Resources

About