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SUMMARY Paleomagnetic records provide us with information about the extreme geomagnetic events known as excursions and reversals, but the sparsity of available data limits detailed knowledge of the process and timing. To date there are no agreed on criteria for categorizing such events in terms of severity or longevity. In an analogy to categorizing storms in weather systems, we invoke the magnitude of the global (modified) paleosecular variation index $$P_{i_D}$$ to define the severity of the magnetic field state, ranging in level from 0 to 3, and defined by instantaneous values of $$P_{i_D}$$ with level 0 being normal ($$P_{i_D}\lt 0.5$$) to extreme ($$P_{i_D}\ge 15$$). We denote the time of entry to an excursional (or reversal) event by when $$P_{i_D}$$ first exceeds 0.5, and evaluate its duration by the time at which $$P_{i_D}$$ first returns below its median value, termed the end of event threshold. We categorize each excursional event according to the peak level of $$P_{i_D}$$ during the entire event, with a range from Category-1 (Cat-1) to Cat-3. We explore an extended numerical dynamo simulation containing more than 1200 events and find that Cat-1 events are the most frequent (72 per cent), but only rarely lead to actual field reversals where the axial dipole, $$g_1^0$$, has reversed sign at the end of the event. Cat-2 account for about 20 per cent of events, with 34 per cent of those leading to actual reversals, while Cat-3 events arise about 8 per cent of the time but are more likely to produce reversals (43 per cent). Higher category events take as much as 10 times longer than Cat-1 events. Two paleomagnetic field models separately cover the Laschamp excursion and Matuyama–Brunhes (M-B) reversal which are Cat-2 events with respective durations of 3.6 and 27.4 kyr. It seems likely that Cat-2 may be an underestimate for M-B due to limitations in the paleomagnetic records. Our overall results suggest no distinction between excursions and reversals other than a reversal having the ending polarity state opposite to that at the start. 

Abstract We synthesize knowledge from numerical weather prediction, inverse theory, and statistics to address the problem of estimating a high‐dimensional covariance matrix from a small number of samples. This problem is fundamental in statistics, machine learning/artificial intelligence, and in modern Earth science. We create several new adaptive methods for high‐dimensional covariance estimation, but one method, which we call Noise‐Informed Covariance Estimation (NICE), stands out because it has three important properties: (a) NICE is conceptually simple and computationally efficient; (b) NICE guarantees symmetric positive semi‐definite covariance estimates; and (c) NICE is largely tuning‐free. We illustrate the use of NICE on a large set of Earth science–inspired numerical examples, including cycling data assimilation, inversion of geophysical field data, and training of feed‐forward neural networks with time‐averaged data from a chaotic dynamical system. Our theory, heuristics and numerical tests suggest that NICE may indeed be a viable option for high‐dimensional covariance estimation in many Earth science problems. 

We consider a stochastic differential equation model for Earth's axial magnetic dipole field. The model's parameters are estimated using diverse and independent data sources that had previously been treated separately. The result is a numerical model that is informed by the full paleomagnetic record on kyr to Myr time scales and whose outputs match data of Earth's dipole in a precisely defined feature-based sense. Specifically, we compute model parameters and associated uncertainties that lead to model outputs that match spectral data of Earth's axial magnetic dipole field but our approach also reveals difficulties with simultaneously matching spectral data and reversal rates. This could be due to model deficiencies or inaccuracies in the limited amount of data. More generally, the approach we describe can be seen as an example of an effective strategy for combining diverse data sets that is particularly useful when the amount of data is limited. 

Abstract The assumptions of paleointensity experiments are violated in many natural and archeological materials, leading to Arai plots which do not appear linear and yield inaccurate paleointensity estimates, leading to bias in the result. Recently, paleomagnetists have adopted sets of “selection criteria” that exclude specimens with nonlinear Arai plots from the analysis, but there is little consensus in the paleomagnetic community on which set to use. In this study, we present a statistical method we call Bias Corrected Estimation of Paleointensity (BiCEP), which assumes that the paleointensity recorded by each specimen is biased away from a true answer by an amount that is dependent a single metric of nonlinearity (the curvature parameter) on the Arai plot. We can use this empirical relationship to estimate the recorded paleointensity for a specimen where, that is, a perfectly straight line. We apply the BiCEP method to a collection of 30 sites for which the true value of the original field is well constrained. Our method returns accurate estimates of paleointensity, with similar levels of accuracy and precision to restrictive sets of paleointensity criteria, but accepting as many sites as permissive criteria. The BiCEP method has a significant advantage over using these selection criteria because it achieves these accurate results without excluding large numbers of specimens from the analysis. It yields accurate, albeit imprecise estimates from sites whose specimens all fail traditional criteria. BiCEP combines the accuracy of the strictest selection criteria with the low failure rates of the less reliable “loose” criteria. 

Abstract. We consider a stochastic differential equation modelfor Earth's axial magnetic dipole field.Our goal is to estimate the model's parametersusing diverse and independent data sources that had previously been treated separately,so that the model is a valid representation of an expanded paleomagnetic recordon kyr to Myr timescales.We formulate the estimation problem within the Bayesian frameworkand define a feature-based posterior distributionthat describes probabilities of model parameters givena set of features derived from the data.Numerically, we use Markov chain Monte Carlo (MCMC)to obtain a sample-based representation of the posterior distribution.The Bayesian problem formulation and its MCMC solutionallow us to study the model's limitations and remaining posterior uncertainties.Another important aspect of our overall approach is thatit reveals inconsistencies between model and data or within the various data sets.Identifying these shortcomings is a first and necessary step towards building more sophisticated models or towards resolving inconsistencies within the data.The stochastic model we derive representsselected aspects of the long-term behavior of the geomagnetic dipole fieldwith limitations and errors that are well defined.We believe that such a model is useful (besides its limitations) for hypothesis testing and give a few examples of how the model can be used in this context. 

Abstract Simulations of the Argentine Basin have large uncertainties associated with quantities such as air‐sea exchanges of heat and carbon in current generation climate models and ocean reanalysis products. This is due to the complex topography, profound undersampling until recent years, and strong currents and mixing of subpolar and subtropical water masses in the basin. Because mixing of water masses is important here, model resolution is hypothesized to play an important role in estimating ocean quantities and determining overall budgets. We construct three regional ocean models with biogeochemistry at 1/3°, 1/6°, and 1/12° resolutions for the year 2017 to investigate heat and carbon dynamics in the region and determine the effect of model resolution on these dynamics. Initial conditions and boundary forcing from BSOSE (the Biogeochemical Southern Ocean State Estimate (Verdy & Mazloff, 2017),https://doi.org/10.1002/2016JC012650) and atmospheric forcing from ERA5 are used. The models are evaluated for accuracy by comparing output to Argo and BGC‐Argo float profiles, BSOSE, and other reanalyses and mapped products. We then quantify the effect of resolution on model upper ocean heat and carbon transport and the associated air‐sea exchanges. We determine that increasing the resolution from 1/3° to 1/12° enhances the upward vertical transport and surface exchanges of heat but causes no significant effect on surface carbon fluxes despite enhancing downward transport of anomalous DIC.