Correlation based snapshot models of the archeomagnetic field

SUMMARY For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective a priori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. A priori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided.

Correlation based snapshot models of the archeomagnetic field

<p>For the global time stationary geomagnetic core field, a new modeling concept for Holocene archeomagnetic data is presented. Major challenges consist of the uneven data distribution, missing vector field components and non-linear relations between observations and the geomagnetic potential. Instead of a truncated spherical harmonics approach, we propose a fully Bayesian, Gaussian process based model. Inherently, the Bayesian approach provides location dependent uncertainties.</p><p>The geomagnetic potential is assumed to be a Gaussian process whose covariance structure is given by an explicit kernel function, including several hyperparameters. For this kind of non-parametric models, the full Bayesian posterior is numerically intractable. Instead, we propose an approximate computation using a Bayesian update system. In a first step, the full vector records are used to obtain, within Laplace approximation, a rough field estimate. This estimate serves as a point of linearization for the non-linear observations. The approximate posterior is then given by a Gaussian mixture. Marginals for all relevant parameters and the field itself can be computed. We are able to quantify the impact of data coverage on uncertainty reduction.</p>

A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes: L95-GRS (v1.0)

Bocquet and Sakov (2013) introduced a low-order model based on the coupling of the chaotic Lorenz-95 (L95) model, which simulates winds along a mid-latitude circle, with the transport of a tracer species advected by this zonal wind field. This model, named L95-T, can serve as a playground for testing data assimilation schemes with an online model. Here, the tracer part of the model is extended to a reduced photochemistry module. This coupled chemistry meteorology model (CCMM), the L95-GRS (generic reaction set) model, mimics continental and transcontinental transport and the photochemistry of ozone, volatile organic compounds and nitrogen oxides. Its numerical implementation is described. The model is shown to reproduce the major physical and chemical processes being considered. L95-T and L95-GRS are specifically designed and useful for testing advanced data assimilation schemes, such as the iterative ensemble Kalman smoother (IEnKS), which combines the best of ensemble and variational methods. These models provide useful insights prior to the implementation of data assimilation methods into larger models. We illustrate their use with data assimilation schemes on preliminary yet instructive numerical experiments. In particular, online and offline data assimilation strategies can be conveniently tested and discussed with this low-order CCMM. The impact of observed chemical species concentrations on the wind field estimate can be quantitatively assessed. The impacts of the wind chaotic dynamics and of the chemical species non-chaotic but highly nonlinear dynamics on the data assimilation strategies are illustrated.

Oceanographic Field Estimates from Remote Sensing and Glider Fleets

This work investigates the merging of temperature observations from a glider fleet and remote sensing, based on a field experiment conducted in an extended coastal region offshore La Spezia, Italy, in August 2010. Functional optimal interpolation and spline formalisms are used to integrate temperature profiles from a fleet of three gliders with remotely sensed sea surface temperature into a volumetric thermal field estimate. Independent measurements from a towed ScanFish vehicle are used for validation. Results indicate that the optimal interpolation approach performs better than the spline model at and above the thermocline depth as long as anisotropic covariances computed from the remote sensing data are used. Below the thermocline, the two merging techniques give similar performance.