Comparison of numerical solution strategies for gravity field recovery from GOCE SGG observations implemented on a parallel platform

International audienceThe recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing the Earth?s gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies, i.e. two iterative methods (preconditioned conjugate gradient method, semi-analytic approach) and a strict solver (Distributed Non-approximative Adjustment), which are operational on a parallel platform (?Graz Beowulf Cluster?), are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation, regarding the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the coloured noise characteristics of the gradiometer. The numerical simulations show that there are no significant discrepancies among the solutions of the three methods. The newly proposed Distributed Nonapproximative Adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns out to be a feasible method for practical applications.Key words. Spherical harmonics ? satellite gravity gradiometry ? GOCE ? parallel computing ? Beowulf cluste

Cognitive and behavioral predictors of light therapy use

Objective: Although light therapy is effective in the treatment of seasonal affective disorder (SAD) and other mood disorders, only 53-79% of individuals with SAD meet remission criteria after light therapy. Perhaps more importantly, only 12-41% of individuals with SAD continue to use the treatment even after a previous winter of successful treatment. Method: Participants completed surveys regarding (1) social, cognitive, and behavioral variables used to evaluate treatment adherence for other health-related issues, expectations and credibility of light therapy, (2) a depression symptoms scale, and (3) self-reported light therapy use. Results: Individuals age 18 or older responded (n = 40), all reporting having been diagnosed with a mood disorder for which light therapy is indicated. Social support and self-efficacy scores were predictive of light therapy use (p's<.05). Conclusion: The findings suggest that testing social support and self-efficacy in a diagnosed patient population may identify factors related to the decision to use light therapy. Treatments that impact social support and self-efficacy may improve treatment response to light therapy in SAD. © 2012 Roecklein et al

Constraints from orbital motions around the Earth of the environmental fifth-force hypothesis for the OPERA superluminal neutrino phenomenology

It has been recently suggested by Dvali and Vikman that the superluminal neutrino phenomenology of the OPERA experiment may be due to an environmental feature of the Earth, naturally yielding a long-range fifth force of gravitational origin whose coupling with the neutrino is set by the scale M_*, in units of reduced Planck mass. Its characteristic length lambda should not be smaller than one Earth's radius R_e, while its upper bound is expected to be slightly smaller than the Earth-Moon distance (60 R_e). We analytically work out some orbital effects of a Yukawa-type fifth force for a test particle moving in the modified field of a central body. Our results are quite general since they are not restricted to any particular size of lambda; moreover, they are valid for an arbitrary orbital configuration of the particle, i.e. for any value of its eccentricity $e$. We find that the dimensionless strength coupling parameter alpha is constrained to |alpha| <= 1 10^-10-4 10^-9 for 1 R_e <= lambda <= 10 R_e by the laser data of the Earth's artificial satellite LAGEOS II, corresponding to M_* >= 4 10^9 -1.6 10^10. The Moon perigee allows to obtain |alpha| <= 3 10^-11 for the Earth-Moon pair in the range 15 R_e <= lambda = 3 10^10 - 4.5 10^10. Our results are neither necessarily limited to the superluminal OPERA scenario nor to the Dvali-Vikman model, in which it is M_* = 10^-6 at lambda = 1 R_e, in contrast with our bounds: they generally extend to any theoretical scenario implying a fifth-force of Yukawa-type.Comment: LaTex2e, 18 pages, 4 figures, 1 table, 81 reference

Mass-change And Geosciences International Constellation (MAGIC) expected impact on science and applications

Summary The joint ESA/NASA Mass-change And Geosciences International Constellation (MAGIC) has the objective to extend time series from previous gravity missions, including an improvement of accuracy and spatio-temporal resolution. The long-term monitoring of Earth’s gravity field carries information on mass-change induced by water cycle, climate change, and mass transport processes between atmosphere, cryosphere, oceans and solid Earth. MAGIC will be composed of two satellite pairs flying in different orbit planes. The NASA/DLR–led first pair (P1) is expected to be in a near-polar orbit around 500 km of altitude; while the second ESA–led pair (P2) is expected to be in an inclined orbit of 65–70 degrees at approximately 400 km altitude. The ESA–led pair P2 Next Generation Gravity Mission (NGGM) shall be launched after P1 in a staggered manner to form the MAGIC constellation. The addition of an inclined pair shall lead to reduction of temporal aliasing effects and consequently of reliance on de-aliasing models and post-processing. The main novelty of the MAGIC constellation is the delivery of mass-change products at higher spatial resolution, temporal (i.e. sub–weekly) resolution, shorter latency, and higher accuracy than GRACE and GRACE-FO. This will pave the way to new science applications and operational services. In this article, an overview of various fields of science and service applications for hydrology, cryosphere, oceanography, solid Earth, climate change and geodesy is provided. These thematic fields and newly enabled applications and services were analysed in the frame of the initial ESA Science Support activities for MAGIC. The analyses of MAGIC scenarios for different application areas in the field of geosciences confirmed that the double-pair configuration will significantly enlarge the number of observable mass-change phenomena by resolving smaller spatial scales with an uncertainty that satisfies evolved user requirements expressed by international bodies such as IUGG. The required uncertainty levels of dedicated thematic fields met by MAGIC unfiltered Level-2 products will benefit hydrological applications by recovering more than 90% of the major river basins worldwide at 260 km spatial resolution, cryosphere applications by enabling mass change signal separation in the interior of Greenland from those in the coastal zones and by resolving small-scale mass variability in challenging regions such as the Antarctic Peninsula, oceanography applications by monitoring meridional overturning circulation changes on time scales of years and decades, climate applications by detecting amplitude and phase changes of Terrestrial Water Storage (TWS) after 30 years in 64% and 56% of the global land areas and solid Earth applications by lowering the Earthquake detection threshold from magnitude 8.8 to magnitude 7.4 with spatial resolution increased to 333 km.</jats:p

Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics

In March 2013 the fourth generation of ESA’s (European Space Agency) global gravity field models, DIR4 (Bruinsma et al, 2010b) and TIM4 (Pail et al, 2010), generated from the GOCE (Gravity field and steady-state Ocean Circulation Explorer) gravity observation satellite were released. We evaluate the models using an independent ground truth data set of gravity anomalies over Australia. Combined with GRACE (Gravity Recovery and Climate Experiment) satellite gravity, a new gravity model is obtained that is used to perform comparisons with GOCE models in spherical harmonics. Over Australia, the new gravity model proves to have significantly higher accuracy in the degrees below 120 as compared to EGM2008 and seems to be at least comparable to the accuracy of this model between degree 150 and degree 260. Comparisons in terms of residual quasi-geoid heights, gravity disturbances, and radial gravity gradients evaluated on the ellipsoid and at approximate GOCE mean satellite altitude (h=250 km) show both fourth generation models to improve significantly w.r.t. their predecessors.Relatively, we find a root-mean-square improvement of 39 % for the DIR4 and 23 % for TIM4 over the respective third release models at a spatial scale of 100 km (degree 200). In terms of absolute errors TIM4 is found to perform slightly better in the bands from degree 120 up to degree 160 and DIR4 is found to perform slightly better than TIM4 from degree 170 up to degree 250. Our analyses cannot confirm the DIR4 formal error of 1 cm geoid height (0.35 mGal in terms of gravity) at degree 200. The formal errors of TIM4, with 3.2 cm geoid height (0.9 mGal in terms of gravity) at degree 200, seem to be realistic. Due to combination with GRACE and SLR data, the DIR models, at satellite altitude, clearly show lower RMS values compared to TIM models in the long wavelength part of the spectrum (below degree and order 120). Our study shows different spectral sensitivity of different functionals at ground level and at GOCE satellite altitude and establishes the link among these findings and the Meissl scheme (Rummel and van Gelderen in Manuscripta Geodaetica 20:379–385, 1995)

Development of a Synthetic Earth Gravity Model by 3D mass optimisation based on forward modelling

Several previous Synthetic Earth Gravity Model (SEGM) simulations are based on existing information about the Earth’s internal mass distribution. However, currently available information is insufficient to model the Earth’s anomalous gravity field on a global scale. The low-frequency information is missing when modelling only topography, bathymetry and crust (including the Mohorovičić discontinuity), but the inclusion of information on the mantle and core does not seem to significantly improve this situation. This paper presents a method to determine a more realistic SEGM by considering simulated 3D mass distributions within the upper mantle as a proxy for all unmodelled masses within the Earth.The aim is to improve an initial SEGM based on forward gravity modelling of the topography, bathymetry and crust such that the missing low-frequency information is now included. The simulated 3D mass distribution has been derived through an interactive and iterative mass model optimisation algorithm, which minimises geoid height differences with respect to a degree-360 spherical harmonic expansion of the EGM2008 global external gravity field model. We present the developed optimisation algorithm by applying it to the development of a global SEGM that gives a reasonably close fit to EGM2008, and certainly closer than a SEGM based only on the topography, bathymetry and crust

Observational Requirements for Long-Term Monitoring of the Global Mean Sea Level and Its Components Over the Altimetry Era

Present-day global mean sea level rise is caused by ocean thermal expansion, ice mass loss from glaciers and ice sheets, as well as changes in terrestrial water storage. For that reason, sea level is one of the best indicators of climate change as it integrates the response of several components of the climate system to internal and external forcing factors. Monitoring the global mean sea level allows detecting changes (e.g., in trend or acceleration) in one or more components. Besides, assessing closure of the sea level budget allows us to check whether observed sea level change is indeed explained by the sum of changes affecting each component. If not, this would reflect errors in some of the components or missing contributions not accounted for in the budget. Since the launch of TOPEX/Poseidon in 1992, a precise 27-year continuous record of sea level change is available. It has allowed major advances in our understanding of how the Earth is responding to climate change. The last two decades are also marked by the launch of the GRACE satellite gravity mission and the development of the Argo network of profiling floats. GRACE space gravimetry allows the monitoring of mass redistributions inside the Earth system, in particular land ice mass variations as well as changes in terrestrial water storage and in ocean mass, while Argo floats allow monitoring sea water thermal expansion due to the warming of the oceans. Together, satellite altimetry, space gravity, and Argo measurements provide unprecedented insight into the magnitude, spatial variability, and causes of present-day sea level change. With this observational network, we are now in a position to address many outstanding questions that are important to planning for future sea level rise. Here, we detail the network for observing sea level and its components, underscore the importance of these observations, and emphasize the need to maintain current systems, improve their sensors, and supplement the observational network where gaps in our knowledge remain

DETERMINISTICALLY-MODIFIED INTEGRAL ESTIMATORS OF GRAVITATIONAL TENSOR

The Earth's global gravity field modelling is an important subject in Physical Geodesy. For this purpose different satellite gravimetry missions have been designed and launched. Satellite gravity gradiometry (SGG) is a technique to measure the second-order derivatives of the gravity field. The gravity field and steady state ocean circulation explorer (GOCE) is the first satellite mission which uses this technique and is dedicated to recover Earth's gravity models (EGMs) up to medium wavelengths. The existing terrestrial gravimetric data and EGM scan be used for validation of the GOCE data prior to their use. In this research, the tensor of gravitation in the local north-oriented frame is generated using deterministically-modified integral estimators involving terrestrial data and EGMs. The paper presents that the SGG data is assessable with an accuracy of 1-2 mE in Fennoscandia using a modified integral estimatorby the Molodensky method. A degree of modification of 100 and an integration cap size of for integrating terrestrial data are proper parameters for the estimator

Bright light therapy in pregnant women with major depressive disorder: Study protocol for a randomized, double-blind, controlled clinical trial

Background: Depression during pregnancy is a common and high impact disease. Generally, 5-10 % of pregnant women suffer from depression. Children who have been exposed to maternal depression during pregnancy have a higher risk of adverse birth outcomes and more often show cognitive, emotional and behavioural problems. Therefore, early detection and treatment of antepartum depression is necessary. Both psychotherapy and antidepressant medication, first choice treatments in a non-pregnant population, have limitations in treating depression during pregnancy. Therefore, it is urgent and relevant to investigate alternative treatments for antepartum depression. Bright light therapy (BLT) is a promising treatment for pregnant women with depressive disorder, for it combines direct availability, sufficient efficacy, low costs and high safety, taking the safety for the unborn child into account as well. Methods: In this study, 150 pregnant women (12-18 weeks pregnant) with a DSM-V diagnosis of depressive disorder will be randomly allocated in a 1:1 ratio to one of the two treatment arms: treatment with BLT (9.000 lux) or treatment with dim red light therapy (100 lux). Both groups will be treated for 6 weeks at home on a daily basis for 30 min, within 30 min of habitual wake-up time. Follow-up will take place after 6 weeks of therapy, 3 and 10 weeks after end of therapy, at birth and 2, 6 and 18 months postpartum. Primary outcome will be the average change in depressive symptoms between the two groups, as measured by the Structured Interview Guide for the Hamilton Depression Scale - Seasonal Affective Disorder version and the Edinburg Postnatal Depression Scale. Changes in rating scale scores of these questionnaires over time will be analysed using generalized linear mixed models. Secondary outcomes will be the changes in maternal cortisol and melatonin levels, in maternal sleep quality and gestational age, birth weight, infant behaviour, infant cortisol exposure and infant cortisol stress response. Discussion: If BLT reduces depressive symptoms in pregnant women, it will provide a safe, cheap, non-pharmacological and efficacious alternative treatment for psychotherapy and antidepressant medication in treating antepartum depression, without any expected adverse reactions for the unborn child. Trial registration: Netherlands Trial Register NTR5476. Registered 5 November 2015