M. A. Pais

Ensemble inversion of time‐dependent core flow models

Quasi-geostrophic core flow models are built from two secular variation models spanning the periods 1960–2002 and 1997–2008. We rely on an ensemble method to account for the contributions of the unresolved small-scale magnetic field interacting with core surface flows to the observed magnetic field changes. The different core flow members of the ensemble solution agree up to spherical harmonic degree l ≃ 10, and this resolved component varies only weakly with regularization. Taking into account the finite correlation time of the small-scale concealed magnetic field, we find that the time variations of the magnetic field occurring over short time scales, such as the geomagnetic jerks, can be accounted for by the resolved (large-scale) part of the flow to a large extent. Residuals from our flow models are 30% smaller for recent epochs, after 1995. This result is attributed to an improvement in the quality of geomagnetic data. The magnetic field models show little frozen flux violation for the most recent epochs, within our estimate of the apparent magnetic flux changes at the core-mantle boundary arising from spatial resolution errors. We associate the more important flux changes detected at earlier epochs with uncertainties in the field models at large harmonic degrees. Our core flow models show, at all epochs, an eccentric and planetary-scale anticyclonic gyre circling around the cylindrical surface tangent to the inner core, at approximately 30 and 60 latitude under the Indian and Pacific oceans, respectively. They account well for the changes in core angular momentum for the most recent epochs.

Variability modes in core flows inverted from geomagnetic field models

The flow of liquid metal inside the Earths core produces the geomagnetic field and its time variations. Understanding the variability of those deep currents is crucial to improve the forecast of geomagnetic field variations, which affect human spacial and aeronautic activities. Moreover, it may provide relevant information on the core dynamics. The main goal of this study is to extract and characterize the leading variability modes of core flows over centennial periods, and to assess their statistical robustness. To this end, we use flows that we invert from two geomagnetic field models (gufm1 and COV-OBS), and apply Principal Component Analysis and Singular Value Decomposition of coupled fields. The quasi geostrophic (QG) flows inverted from both geomagnetic field models show similar features. However, COV-OBS has a less energetic mean and larger time variability. The statistical significance of flow components is tested from analyses performed on subareas of the whole domain. Bootstrapping methods are also used to extract significant flow features required by both gufm1 and COV-OBS. Three main empirical circulation modes emerge, simultaneously constrained by both geomagnetic field models and expected to be robust against the particular a priori used to build them (large scale QG dynamics). Mode 1 exhibits three large vortices at medium/high latitudes, with opposite circulation under the Atlantic and the Pacific hemispheres. Mode 2 interestingly accounts for most of the variations of the Earths core angular momentum. In this mode, the regions close to the tangent cylinder and to the equator are correlated, and oscillate with a period between 80 and 90 years. Each of these two modes is energetic enough to alter the mean flow, sometimes reinforcing the eccentric gyre, and other times breaking it up into smaller circulations. The three main circulation modes added together to the mean flow account for about 70% of the flows variability, 90% of the root mean square total velocities, and 95% of the secular variation induced by the total flows. Direct physical interpretation of the computed modes is not straightforward. Nonethe-less, similarities found between the two first modes and time/spatial features identified in different studies of core dynamics, suggest that our approach can help to pinpoint the relevant physical processes inside the core on centennial timescales.

A modified Equivalent Source Dipole method to model partially distributed magnetic field measurements, with application to Mercury

Hermean magnetic field measurements acquired over the northern hemisphere by the MErcury Surface Space ENvironment GEochemistry, and Ranging (MESSENGER) spacecraft provide crucial information on the magnetic field of the planet. We develop a new method, the Time Dependent Equivalent Source Dipole, to model a planetary magnetic field and its secular variation over a limited spatial region. Tests with synthetic data distributed on regular grids as well as at spacecraft positions show that our modeled magnetic field can be upward or downward continued in an altitude range of −300 to 1460 km for regular grids and in a narrower range of 10 to 970 km for spacecraft positions. They also show that the method is not sensitive to a very weak secular variation along MESSENGER orbits. We then model the magnetic field of Mercury during the first four individual sidereal days as measured by MESSENGER using the modified Equivalent Source Dipoles scheme and excluding the secular variation terms. We find a dominantly zonal field with small-scale nonaxisymmetric features corotating with the Sun in the Mercury Body Fixed system and repeating under similar local time, suggestive of external origin. When modeling the field during one complete solar day, these small-scale features decrease and the field becomes more axisymmetric. The lack of any coherent nonaxisymmetric feature recovered by our method, which was designed to allow for such small-scale structures, provides strong evidence for the large-scale and close-to-axisymmetry structure of the internal magnetic field of Mercury.

Can core flows inferred from geomagnetic field models explain the Earth's dynamo?

We test the ability of velocity fields inferred from geomagnetic secular variation data to produce the global magnetic field of the Earth. Our kinematic dynamo calculations use quasi-geostrophic (QG) flows inverted from geomagnetic field models which, as such, incorporate flow structures that are Earth-like and may be important for the geodynamo. Furthermore, the QG hypothesis allows straightforward prolongation of the flow from the core surface to the bulk. As expected from previous studies, we check that a simple quasi-geostrophic flow is not able to sustain the magnetic field against ohmic decay. Additional complexity is then introduced in the flow, inspired by the action of the Lorentz force. Indeed, on centenial timescales , the Lorentz force can balance the Coriolis force and strict quasi-geostrophy may not be the best ansatz. When the columnar flow is modified to account for the action of the Lorentz force, magnetic field is generated for Elsasser numbers larger than 0.25 and magnetic Reynolds numbers larger than 100. Near the threshold, the resulting magnetic field is dominated by an axial dipole, with some reversed flux patches. Time-dependence is also considered, derived from principal component analysis applied to the inverted flows. We find that time periods from 120 to 50 years do not affect the mean growth rate of the kinematic dynamos. Finally we notice the footprint of the inner-core in the magnetic field generated deep in the bulk of the shell, although we did not include one in our computations.

Temporal Evolution of Sunspot Areas and Estimation of Related Plasma Flows

The increased amount of information provided by ongoing missions such as the Solar Dynamics Observatory (SDO) represents a great challenge for the understanding of basic questions such as the internal structure of sunspots and how they evolve with time. Here, we contribute with the exploitation of new data, to provide a better understanding of the separate growth and decay of sunspots, umbra, and penumbra. Using fuzzy sets to compute separately the areas of sunspot umbra and penumbra, the growth and decay rates for active regions NOAA 11117, NOAA 11428, NOAA 11429, and NOAA 11430 are computed from the analysis of intensitygrams obtained by the Helioseismic and Magnetic Imager onboard SDO. A simplified numerical model is proposed for the decay phase, whereby an empirical irrotational and uniformly convergent horizontal velocity field interacting with an axially symmetric and height-invariant magnetic field reproduces the large-scale features of the much more complex convection observed inside sunspots.

Time‐correlated patterns from spherical harmonic expansions: Application to geomagnetism

We use empirical orthogonal function analysis (EOFA) directly on sets of Schmidt spherical harmonic (SH) coefficients modeling the internal geomagnetic field or its time derivatives at different epochs. We show how to properly use the method such that the application of EOFA to either spatial or spectral domains leads to the same results, bypassing the need to work on snapshots of field charts synthesized from SHs. In case a spatial grid is required, we point out which is the best grid to use. We apply the method to the CM4 geomagnetic field model to illustrate the differences in EOFA modes obtained with and without corrections. Once the corrected main modes of secular acceleration (SA) have been singled out, we retrieve previous results showing that the 1969, 1978, and 1991 geomagnetic field acceleration jumps have the same spatial pattern. A new finding in this study is that the same spatial pattern is present in principal modes of secular variation which, once inverted, may provide the flow responsible for the jerk sequence. Another finding is the unveiling of a different spatial structure common to a second group of jerks with SA pulses around 1985 and 1996, displaying a localization very similar to SA pulses identified in 2006 and 2009 using recent satellite data. Finally, if properly handled, the EOFA can be directly applied to a grid of data values of the geomagnetic field in order to produce SH models of decorrelated modes which may help to separate different sources of the field.