Data assimilation for a visco-elastic Earth deformation model

We present a data assimilation algorithm for the time-domain spectral-finite element code VILMA. We consider a 1D earth structure and a prescribed glaciation history ICE5G for the external mass load forcing. We use the Parallel Data Assimilation Framework (PDAF) to assimilate sea level data into the model in order to obtain better estimates of the viscosity structure of mantle and lithosphere. For this purpose, we apply a particle filter in which an ensemble of models is propagated in time, starting shortly before the last glacial maximum. At epochs when observations are available, each particle's performance is estimated and they are resampled based on their performance to form a new ensemble that better resembles the true viscosity distribution. In a proof of concept we show that with this method it is possible to reconstruct a synthetic viscosity distribution from which synthetic data were constructed. In a second step, paleo sea level data are used to infer an optimised 1D viscosity distribution

An approach for constraining mantle viscosities through assimilation of palaeo sea level data into a glacial isostatic adjustment model

Glacial isostatic adjustment is largely governed by the rheological properties of the Earth's mantle. Large mass redistributions in the ocean–cryosphere system and the subsequent response of the viscoelastic Earth have led to dramatic sea level changes in the past. This process is ongoing, and in order to understand and predict current and future sea level changes, the knowledge of mantle properties such as viscosity is essential. In this study, we present a method to obtain estimates of mantle viscosities by the assimilation of relative sea level rates of change into a viscoelastic model of the lithosphere and mantle. We set up a particle filter with probabilistic resampling. In an identical twin experiment, we show that mantle viscosities can be recovered in a glacial isostatic adjustment model of a simple three-layer Earth structure consisting of an elastic lithosphere and two mantle layers of different viscosity. We investigate the ensemble behaviour on different parameters in the following three set-ups: (1) global observations data set since last glacial maximum with different ensemble initialisations and observation uncertainties, (2) regional observations from Fennoscandia or Laurentide/Greenland only, and (3) limiting the observation period to 10 ka until the present. We show that the recovery is successful in all cases if the target parameter values are properly sampled by the initial ensemble probability distribution. This even includes cases in which the target viscosity values are located far in the tail of the initial ensemble probability distribution. Experiments show that the method is successful if enough near-field observations are available. This makes it work best for a period after substantial deglaciation until the present when the number of sea level indicators is relatively high

An approach for constraining mantle viscosities through assimilation of palaeo sea level data into a glacial isostatic adjustment model

Glacial isostatic adjustment is largely governed by the rheological properties of the Earth's mantle. Large mass redistributions in the ocean–cryosphere system and the subsequent response of the viscoelastic Earth have led to dramatic sea level changes in the past. This process is ongoing, and in order to understand and predict current and future sea level changes, the knowledge of mantle properties such as viscosity is essential. In this study, we present a method to obtain estimates of mantle viscosities by the assimilation of relative sea level rates of change into a viscoelastic model of the lithosphere and mantle. We set up a particle filter with probabilistic resampling. In an identical twin experiment, we show that mantle viscosities can be recovered in a glacial isostatic adjustment model of a simple three-layer Earth structure consisting of an elastic lithosphere and two mantle layers of different viscosity. We investigate the ensemble behaviour on different parameters in the following three set-ups: (1) global observations data set since last glacial maximum with different ensemble initialisations and observation uncertainties, (2) regional observations from Fennoscandia or Laurentide/Greenland only, and (3) limiting the observation period to 10 ka until the present. We show that the recovery is successful in all cases if the target parameter values are properly sampled by the initial ensemble probability distribution. This even includes cases in which the target viscosity values are located far in the tail of the initial ensemble probability distribution. Experiments show that the method is successful if enough near-field observations are available. This makes it work best for a period after substantial deglaciation until the present when the number of sea level indicators is relatively high

Evaluation of candidate geomagnetic field models for IGRF-12

Background: The 12th revision of the International Geomagnetic Reference Field (IGRF) was issued in December 2014 by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD (http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html). This revision comprises new spherical harmonic main field models for epochs 2010.0 (DGRF-2010) and 2015.0 (IGRF-2015) and predictive linear secular variation for the interval 2015.0-2020.0 (SV-2010-2015). Findings: The models were derived from weighted averages of candidate models submitted by ten international teams. Teams were led by the British Geological Survey (UK), DTU Space (Denmark), ISTerre (France), IZMIRAN (Russia), NOAA/NGDC (USA), GFZ Potsdam (Germany), NASA/GSFC (USA), IPGP (France), LPG Nantes (France), and ETH Zurich (Switzerland). Each candidate model was carefully evaluated and compared to all other models and a mean model using well-defined statistical criteria in the spectral domain and maps in the physical space. These analyses were made to pinpoint both troublesome coefficients and the geographical regions where the candidate models most significantly differ. Some models showed clear deviation from other candidate models. However, a majority of the task force members appointed by IAGA thought that the differences were not sufficient to exclude models that were well documented and based on different techniques. Conclusions: The task force thus voted for and applied an iterative robust estimation scheme in space. In this paper, we report on the evaluations of the candidate models and provide details of the algorithm that was used to derive the IGRF-12 produc

International Geomagnetic Reference Field: the 12th generation

The 12th generation of the International Geomagnetic Reference Field (IGRF) was adopted in December 2014 by the Working Group V-MOD appointed by the International Association of Geomagnetism and Aeronomy (IAGA). It updates the previous IGRF generation with a definitive main field model for epoch 2010.0, a main field model for epoch 2015.0, and a linear annual predictive secular variation model for 2015.0-2020.0. Here, we present the equations defining the IGRF model, provide the spherical harmonic coefficients, and provide maps of the magnetic declination, inclination, and total intensity for epoch 2015.0 and their predicted rates of change for 2015.0-2020.0. We also update the magnetic pole positions and discuss briefly the latest changes and possible future trends of the Earth’s magnetic fiel

Inferring mantle viscosity through data assimilation of relative sea level observations in a glacial isostatic adjustment model

We suggest to apply data assimilation in glacial isostatic adjustment (GIA) to constrain the mantle viscosity structure based on sea level observations. We apply the Parallel Data Assimilation Framework (PDAF) to assimilate sea level data into the time-domain spectral-finite element code VILMA in order to obtain better estimates of the mantle viscosity structure. In a first step, we reduce to a spherically symmetric earth structure and prescribe the glaciation history. A particle filter is used to propagate an ensemble of models in time. At epochs when observations are available, each particle's performance is estimated and the particles are resampled based on their performance to form a new ensemble that better resembles the true viscosity distribution. Using this algorithm, we show the ability to recover mantle viscosities from a set of synthetic relative sea level observations. Those synthetic observations are obtained from a reference run with a given viscosity structure that defines the target viscosity values in our experiments. The viscosity estimation is applied to a three-layer model with an elastic lithosphere and two mantle layers, and to a multi-layer model with a smoother viscosity profile. We use various subsets of realistic observation locations (e.g. only observations from Fennoscandia) and show that it is possible to obtain the target viscosity values in those cases. We also vary the time from which observations are available to evolve the test cases towards a realistic scenario for the availability of relative sea level observations. The most relevant cases start at 26.5ka BP and at 10ka BP as they mark the beginning of the maximum glaciation and the end of deglaciation with a larger amount of observations following, respectively, and end at present day

Parent magnetic field models for the IGRF-12 GFZ-candidates

International audienceWe propose candidate models for IGRF-12. These models were derived from parent models built from 10 months of Swarm satellite data and 1.5 years of magnetic observatory data. Using the same parameterisation, a magnetic field model was built from a slightly extended satellite data set. As a result of discrepancies between magnetic field intensity measured by the absolute scalar instrument and that calculated from the vector instrument, we re-calibrated the satellite data. For the calibration, we assumed that the discrepancies resulted from a small perturbing magnetic field carried by the satellite, with a strength and orientation dependent on the Sun's position relative to the satellite. Scalar and vector data were reconciled using only a limited number of calibration parameters. The data selection process, followed by the joint modelling of the magnetic field and Euler angles, leads to accurate models of the main field and its secular variation around 2014.0. The obtained secular variation model is compared with models based on CHAMP satellite data. The comparison suggests that pulses of magnetic field acceleration that were observed on short time scales average-out over a decade

Round robin comparison study on the form measurement of optical freeform surfaces

A round robin comparison of freeform form measurements was carried out by the project partners and stakeholders of a European metrology research project. Altogether six measuring instruments were considered: five different (pointwise and areal) optical devices and one tactile device. Three optical freeform surfaces were used for the comparison measurements, where two specimens were measured by five instruments and one specimen by four instruments. In this paper, the evaluation methods and results of this round robin are presented for the three freeform surfaces made from a temperature-stable material, Super Invar ®. The freeforms had diameters of 40 mm, 50 mm and 100 mm and best-fit radii of 39.75 mm (convex), 40.9 mm (convex) and 423.5 mm (concave). For comparison, the bilateral pointwise differences between the available measurements were calculated. The root-mean-square values of these differences ranged from 15 nm to 110 nm (neglecting spherical contributions) and provided an insight into the status of typical freeform measurement capabilities for optical surfaces

The Swarm Satellite Constellation Application and Research Facility (SCARF) and Swarm data products

International audiencewith the Earth system, is expected to be launched in late 2013. The objective of the Swarm mission is to providethe best ever survey of the geomagnetic field and its temporal evolution, in order to gain new insights into theEarth system by improving our understanding of the Earth’s interior and environment. In order to derive advancedmodels of the geomagnetic field (and other higher-level data products) it is necessary to take explicit advantageof the constellation aspect of Swarm. The Swarm SCARF (Satellite Constellation Application and ResearchFacility) has been established with the goal of deriving Level-2 products by combination of data from the threesatellites, and of the various instruments. The present paper describes the Swarm input data products (Level-1band auxiliary data) used by SCARF, the various processing chains of SCARF, and the Level-2 output data productsdetermined by SCARF