Modelling decadal secular variation with only magnetic diffusion

Secular variation (SV) of Earth’s internal magnetic field is the sum of two contributions, one resulting from core fluid flow and the other from magnetic diffusion. Based on the millenial diffusive timescale of global-scale structures, magnetic diffusion is widely perceived to be too weak to significantly contribute to decadal SV, and indeed is entirely neglected in the commonly adopted end-member of frozen-flux. Such an argument however lacks consideration of radially fine-scaled magnetic structures in the outermost part of the liquid core, whose diffusive timescale is much shorter. Here we consider the opposite end-member model to frozen flux, that of purely diffusive evolution associated with the total absence of fluid flow. Our work is based on a variational formulation, where we seek an optimised full-sphere initial magnetic field structure whose diffusive evolution best fits, over various time windows, a time-dependent magnetic field model. We present models which are regularised based on their magnetic energy, and consider how well they can fit the COV-OBS.x1 ensemble mean using a global error bound based on the standard deviation of the ensemble. within the core. For With the se regularised models, over time periods of up to 30 years, it is possible to fit COV-OBS.x1 within one standard deviation at all times. For time windows up to 102 years we show that our models can fit COV-OBS.x1 when adopting a time-averaged global uncertainty. Our modelling is sensitive only to magnetic structures in approximately the top 10% of the liquid core, and show an increased surface area of reversed flux at depth. The diffusive models recover fundamental characteristics of field evolution including the historical westward drift, the recent acceleration of the North Magnetic Pole and reversed-flux emergence. Based on a global time-averaged residual, our diffusive models fit the evolution of the geomagnetic field comparably, and sometimes better than, frozen-flux models within short time windows

On the Considerations of Using Near Real Time Data for Space Weather Hazard Forecasting

Space weather represents a severe threat to ground-based infrastructure, satellites and communications. Accurately forecasting when such threats are likely (e.g., when we may see large induced currents) will help to mitigate the societal and financial costs. In recent years computational models have been created that can forecast hazardous intervals, however they generally use post-processed “science” solar wind data from upstream of the Earth. In this work we investigate the quality and continuity of the data that are available in Near-Real-Time (NRT) from the Advanced Composition Explorer and Deep Space Climate Observatory (DSCOVR) spacecraft. In general, the data available in NRT corresponds well with post-processed data, however there are three main areas of concern: greater short-term variability in the NRT data, occasional anomalous values and frequent data gaps. Some space weather models are able to compensate for these issues if they are also present in the data used to fit (or train) the model, while others will require extra checks to be implemented in order to produce high quality forecasts. We find that the DSCOVR NRT data are generally more continuous, though they have been available for small fraction of a solar cycle and therefore DSCOVR has experienced a limited range of solar wind conditions. We find that short gaps are the most common, and are most frequently found in the plasma data. To maximize forecast availability we suggest the implementation of limited interpolation if possible, for example, for gaps of 5 min or less, which could increase the fraction of valid input data considerably

Forecasting yearly geomagnetic variation through sequential estimation of core low and magnetic diffusion

Earth’s internal magnetic field is generated through motion of the electrically conductive iron-alloy fluid comprising its outer core. Temporal variability of this magnetic field, termed secular variation (SV), results from two processes: one is the interaction between core fluid motion and the magnetic field, the other is magnetic diffusion. As diffusion is widely thought to take place over relatively long, millennial time scales, it is common to disregard it when considering yearly to decadal field changes; in this frozen-flux approximation, core fluid motion may be inferred on the core–mantle boundary (CMB) using observations of SV at Earth’s surface. Such flow models have been used to forecast variation in the magnetic field. However, recent work suggests that diffusion may also contribute significantly to SV on short time scales provided that the radial length scale of the magnetic field structure within the core is sufficiently short. In this work, we introduce a hybrid method to forecast field evolution that considers a model based on both a steady flow and diffusion, in which we adopt a two-step process: first fitting the SV to a steady flow, and then fitting the residual by magnetic diffusion. We assess this approach by hindcasting the evolution for 2010–2015, based on fitting the models to CHAOS-6 using time windows prior to 2010. We find that including diffusion yields a reduction of up to 25% in the global hindcast error at Earth’s surface; at the CMB this error reduction can be in excess of 77%. We show that fitting the model over the shortest window that we consider, 2009–2010, yields the lowest hindcast error. Based on our hindcast tests, we present a candidate model for the SV over 2020–2025 for IGRF-13, fit over the time window 2018.3–2019.3. Our forecasts indicate that over the next decade the axial dipole will continue to decay, reversed-flux patches will increase in both area and intensity, and the north magnetic (dip) pole will continue to migrate towards Siberia

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Investigation of regional variation in core flow models using spherical Slepian functions

Abstract By assuming that changes in the magnetic field in the Earth’s outer core are advection-dominated on short timescales, models of the core surface flow can be deduced from secular variation. Such models are known to be under-determined and thus require other assumptions to produce feasible flows. There are regions where poor knowledge of the core flow dynamics gives rise to further uncertainty, such as within the tangent cylinder, and assumptions about the nature of the flow may lead to ambiguous patches, such as if it is assumed to be strongly tangentially geostrophic. We use spherical Slepian functions to spatially and spectrally separate core flow models, confining the flow to either inside or outside these regions of interest. In each region we examine the properties of the flow and analyze its contribution to the overall model. We use three forms of flow model: (a) synthetic models from randomly generated coefficients with blue, red and white energy spectra, (b) a snapshot of a numerical geodynamo simulation and (c) a model inverted from satellite magnetic field measurements. We find that the Slepian decomposition generates unwanted spatial leakage which partially obscures flow in the region of interest, particularly along the boundaries. Possible reasons for this include the use of spherical Slepian functions to decompose a scalar quantity that is then differentiated to give the vector function of interest, and the spectral frequency content of the models. These results will guide subsequent investigation of flow within localized regions, including applying vector Slepian decomposition methods

Evaluation of candidate models for the 13th generation International Geomagnetic Reference Field

In December 2019, the 13th revision of the International Geomagnetic Reference Field (IGRF) was released by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD. This revision comprises two new spherical harmonic main field models for epochs 2015.0 (DGRF-2015) and 2020.0 (IGRF-2020) and a model of the predicted secular variation for the interval 2020.0 to 2025.0 (SV-2020-2025). The models were produced from candidates submitted by fifteen international teams. These teams were led by the British Geological Survey (UK), China Earthquake Administration (China), Universidad Complutense de Madrid (Spain), University of Colorado Boulder (USA), Technical University of Denmark (Denmark), GFZ German Research Centre for Geosciences (Germany), Institut de physique du globe de Paris (France), Institut des Sciences de la Terre (France), Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (Russia), Kyoto University (Japan), University of Leeds (UK), Max Planck Institute for Solar System Research (Germany), NASA Goddard Space Flight Center (USA), University of Potsdam (Germany), and Université de Strasbourg (France). The candidate models were evaluated individually and compared to all other candidates as well to the mean, median and a robust Huber-weighted model of all candidates. These analyses were used to identify, for example, the variation between the Gauss coefficients or the geographical regions where the candidate models strongly differed. The majority of candidates were sufficiently close that the differences can be explained primarily by individual modeling methodologies and data selection strategies. None of the candidates were so different as to warrant their exclusion from the final IGRF-13. The IAGA V-MOD task force thus voted for two approaches: the median of the Gauss coefficients of the candidates for the DGRF-2015 and IGRF-2020 models and the robust Huber-weighted model for the predictive SV-2020-2025. In this paper, we document the evaluation of the candidate models and provide details of the approach used to derive the final IGRF-13 products. We also perform a retrospective analysis of the IGRF-12 SV candidates over their performance period (2015–2020). Our findings suggest that forecasting secular variation can benefit from combining physics-based core modeling with satellite observations

International Geomagnetic Reference Field: the thirteenth generation

In December 2019, the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group (V-MOD) adopted the thirteenth generation of the International Geomagnetic Reference Field (IGRF). This IGRF updates the previous generation with a definitive main field model for epoch 2015.0, a main field model for epoch 2020.0, and a predictive linear secular variation for 2020.0 to 2025.0. This letter provides the equations defining the IGRF, the spherical harmonic coefficients for this thirteenth generation model, maps of magnetic declination, inclination and total field intensity for the epoch 2020.0, and maps of their predicted rate of change for the 2020.0 to 2025.0 time period

Climatology of the Harmonic Frequency Separation of Ionospheric Alfvén Resonances at Eskdalemuir Observatory, UK

We extracted the harmonic frequency separation (Δf) of Ionospheric Alfvén Resonances (IAR) observed in the Eskdalemuir induction coil magnetometer data for the 9 year data set of 2013–2021. To obtain Δf values, we used a machine learning technique that identifies the harmonics and from this we calculated the average separation. To investigate the climatology of the IAR, we have modeled the Δf of the IAR for the data set using a time of flight calculation with model Alfvén velocity profiles. When analyzing Δf from the model and data, we found that in general they follow the same trends. The modeled Δf and Δf from the data both show an inverse correlation with foF2, which confirms that the frequencies of the IAR are controlled by electron density. It follows that Δf is greater around midnight and during the winter months, due to the decrease in plasma mass density. Variability is also reflected when comparing yearly trends in Δf with the sunspot number; higher frequencies are observed and modeled at low sunspot number. It is difficult to examine trends with instantaneous geomagnetic activity as IAR are not visible in spectrograms when geomagnetic activity is high. We find cases where the difference in measured and modeled Δf is significant, suggesting that the model does not capture short term variations in plasma mass density that influence the IAR during these days. We plan to undertake further modeling of Δf on shorter timescales.</p