Spectral analysis of residual GRACE and GRACE-FO range accelerations

GRACE and GRACE-FO K-band range-rate post-fit residuals obtained after a common estimation of monthly gravity field coefficients and ancillary satellite parameters represent a complex superposition of different effects. In this contribution, we analyze the component of the residuals that is related to geophysical effects. We low pass filter and differentiate range-rate post-fit residuals to obtain residual range-accelerations. A spectral analysis of globaly gridded residual range-accelerations reveals unmodeled signal related to (ocean) tides and hydrology. The time series with approximately 100 millions of data records allows us to identify main periodic contributors in different bands. Diurnal and semi-diurnal signal can be resolved on a 5x5 degree grid, while periods of 5 and 3 hours can be resolved on a 7.5x7.5 and 10x10 degree grid

Influence of accelerometer parametrizations on GRACE post-fit residuals

Accelerometers onboard of satellites can be regarded as a key improvement in gravity field recovery. These instruments are located in the center of mass of the satellite and are precisely measuring non-gravitational forces acting on the satellite surfaces. Accelerometer measurements are distorted in their magnitude and amplitude, so an accelerometer calibration has to be carried out. Usually, in orbit determination and gravity field parameter estimation, a priori values are introduced and corresponding numeric corrections are estimated iteratively. Within the gravity field recovery community various accelerometer calibration parametrizations are applied. We have tested several parametrization scenarios within our in-house developed GRACE-SIGMA gravity field recovery software. In this contribution, we present the impact of these scenarios on post- fit KBRR residuals

GRACE-FO monthly solutions using the GRACE-SIGMA software

In this contribution we present gravity field monthly solutions from GRACE Follow-On (GRACE-FO) Level-1B sensor data. The monthly solutions are computed with the GRACE-SIGMA software developed at the Institute of Geodesy, Leibniz University Hannover. The solutions are obtained using a two-step approach. In a first step, the orbits of the two satellites are pre-adjusted by estimating local arc parameters. In a second step, the monthly gravity field potential in terms of normalized spherical harmonic coefficients is recovered. Several parametrization scenarios are tested and the obtained solutions are compared with solutions of other processing centers. Furthermore, K-band range-rate (KBRR) post-fit residuals are analyzed in time, frequency and space domain and are compared to the typical post-fit residuals of the GRACE mission

Residual ocean tide signal in GRACE(-FO) range-rate post-fit residuals

Ocean tide model imperfections are one of the major uncertainty factors in gravity field recovery. Unmodeled signal can alias into level-2 gravity field products and be interpreted as real signal, e.g. as ice mass loss. An accurate understanding of the ocean tide model imperfections (on spectral and spatial level) is therefore not only important for current, but also for future gravity field missions. For this contribution, we analyzed 20+ years of GRACE(-FO) K-band range-rate post-fit residuals for residual ocean tide signal. The post-fit residuals are obtained as part of the gravity field estimation of monthly solutions. We low pass filter and differentiate range-rate post-fit residuals to obtain residual range-accelerations. Obtained residual range-accelerations are assigned to 5x5 degree grid cells and Lomb-Scargle periodograms for each cell are computed. An analysis of the periodograms reveals peaks at frequencies of ocean tide constituents. The peaks with the largest spectral amplitude can be found at frequencies of the major constituents (O1, M2, K1). In total around 30 constituents are detectable, among them also compound tides and degree-3 tides

Global regularity for the Maxwell-Klein-Gordon equation with small critical Sobolev norm in high dimensions

We show that in dimensions $n \geq 6$ that one has global regularity for the Maxwell-Klein-Gordon equations in the Coulomb gauge provided that the critical Sobolev norm $\dot H^{n/2-1} \times \dot H^{n/2-2}$ of the initial data is sufficiently small. These results are analogous to those recently obtained for the high-dimensional wave map equation but unlike the wave map equation, the Coulomb gauge non-linearity cannot be iterated away directly. We shall use a different approach, proving Strichartz estimates for the covariant wave equation. This in turn will be achieved by use of Littlewood-Paley multipliers, and a global parametrix for the covariant wave equation constructed using a truncated, microlocalized Cronstrom gauge.Comment: 49 pages, no pictures, to appear, CMP. A minor problem with a Fourier angular projection causing a certain phase function to no longer be real has now been fixe

GRACE-FO processing at IfE/LUH

Processing strategy of the LUH-GRACE-FO-2020 monthly gravity field time series is presented. The spectral noise, spatial noise and signal content of the time series (2018-06 - 2020-08) is evaluated

GRACE and GRACE-FO processing at IfE/LUH

Updates on gravity field recovery from GRACE and GRACE Follow-On data at IfE/LUH

Signals of Geophysical Nature in GRACE and GRACE-FO Post-Fit Range-Rate Residuals

Post-fit residuals of satellite-to-satellite tracking measurements of the GRACE and GRACE-FO missions obtained after a common estimation of orbit and gravity field parameters should ideally contain measurement noise with a behavior that meets expectations for the involved sensors. In reality, obtained GRACE and GRACE-FO post-fit range-rate residuals represent a complex superposition of different effects, e.g. of instrumental, environmental and geophysical nature. In this contribution, we focus on the geophysical signals in the post-fit residuals of the LUH GRACE and GRACE-FO time series. We apply band-pass filtering to extract the geophysical signal buried in the residuals and analyze the most distinctive signatures for their spatial and temporal behavior

Oaks retained in production spruce forests help maintain saproxylic beetle diversity in southern Scandinavian landscapes

In Northern Europe, human activities have caused a substantial decrease in the number of old deciduous trees over the last two centuries, leading to a decline in species populations associated with this habitat. One way to mitigate this trend is to increase the abundance of mature and old deciduous trees in commercial forests, such as by tree retention at final harvest. We analysed the biodiversity value of retained mature oaks in the production forests of Norway spruce in southern Sweden, using oaks in pastures as reference. The forest oaks were grown in two different levels of shade. We analysed two categories of saproxylic (i.e. dead wood-dependent) beetles: those utilizing oaks (Group I) and those utilizing oak but not spruce (Group II, which was, therefore, a subcategory of Group I). We found that forest oaks sustained high beetle diversity, in particular, Group I beetles, which were significantly more abundant in forest oaks in heavily thinned patches, as compared with pasture oaks and oaks in moderately thinned patches. For both beetle groups, the composition differed between the forest oaks and pasture oaks, indicating that the forest oaks can be a complementary habitat to that of pasture oaks. There was a positive relationship between oak dead branch diameter and beetle biodiversity, but only for older oaks (∼200 years old). We conclude that retaining oaks in production spruce forests can increase the diversity of oak-associated beetles at the landscape scale. Since many oak associated species depend on relatively high levels of insolation, management of retained oaks in production forests should include periodic removal of encroaching trees

Thinning around old oaks in spruce production forests: current practices show no positive effect on oak growth rates and need fine tuning

The expansion of spruce-dominated forestry in Southern Sweden during the twentieth century has led to a considerable amount of oak (Quercus robur L.) woodlands being converted into stands dominated by planted spruce. The thinning of spruces around oak trees is currently done in Sweden to improve local diversity of insects, oak growing conditions and eventually decrease their mortality. To evaluate the effect of these treatments, we dendrochronologically studied growth of old (100–200 years old) oaks subjected to thinning of different intensity at nine locations in southern Sweden, and compared them to oaks located in nearby pastures. The overall pattern suggests that commonly adopted thinning intensities do not significantly affect oak growth. Oak growth was positively related to oak age and negatively to the amount of dead oak crown. Analyses of correlations between oak growth and summer drought conditions, as reflected by location-specific chronologies of the Monthly Drought Code (MDC), indicated that older trees exhibited generally negative correlations, whereas the correlation remained generally positive for the younger trees, both inside and outside forest stands. We propose that removal of spruces should be primarily done around older and healthier-looking trees