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EN
The impact of continental hydrological loading from land water, snow and ice on polar motion excitation, calculated as hydrological angular momentum (HAM), is difficult to estimate, and not as much is known about it as about atmospheric angular momentum (AAM) and oceanic angular momentum (OAM). In this paper, regional hydrological excitations to polar motion are investigated using monthly terrestrial water storage data derived from the Gravity Recovery and Climate Experiment (GRACE) mission and from the five models of land hydrology. The results show that the areas where the variance shows large variability are similar for the different models of land hydrology and for the GRACE data. Areas which have a small amplitude on the maps make an important contribution to the global hydrological excitation function of polar motion. The comparison of geodetic residuals and global hydrological excitation functions of polar motion shows that none of the hydrological excitation has enough energy to significantly improve the agreement between the observed geodetic excitation and geophysical ones.
EN
Since the launch of the GRACE (Gravity Recovery And Climate Experiment) satellite mission in 2002, significant progress in the knowledge regarding the temporal variations of the Earth’s gravity field has been achieved. The main objectives of this contribution are to define a suitable filter to reduce the noise contained in the latest release, i.e. RL05, of GRACE-based GGMs as well as to select the most suitable GRACE-based GGM time series for estimating mass variations in the Earth system over Poland. The performance of the Gaussian filter with different radii and the de-correlation filters (DDK1–DDK5) applied to reduce the noise contained in those GGMs was examined. First, they were investigated globally. Then, they were examined over the area of Poland, in particular, over two basins, i.e. the Vistula river basin and the Odra river basin. Moreover, both the internal and external accuracy of RL05 GRACE-based GGMs were assessed. Error degree variances of geoid heights were calculated on the basis of these models. Equivalent water thickness variations obtained from GRACE-based GGMs were compared with the corresponding ones obtained from the hydrology model. The obtained results were analysed and discussed. Finally the filtering method and the GGM time series most suitable for estimating mass variations in the Earth system over Poland were selected.
PL
Satelitarna misja GRACE (Gravity Recovery And Climate Experiment zapoczątkowana w 2002 roku znacząco przyczyniła się do rozwoju wiedzy o zmianach w czasie pola siły ciężkości Ziemi. Głównym celem niniejszego opracowania jest zdefiniowanie odpowiedniego filtru do redukcji szumu zawartego w ostatniej wersji, tj. wersji 5. globalnych modeli geopotencjału opracowanych na podstawie danych z misji GRACE, jak również wybór najbardziej odpowiedniego szeregu czasowego globalnych modeli geopotencjału wyznaczonych na podstawie danych z misji GRACE, do określenia zmian rozkładu mas w systemie Ziemia dla obszaru Polski. W szczególności badano wpływ filtrów Gaussa o różnych promieniach oraz filtrów dekorelacyjnych (DDK1–DDK5) na redukcję szumu zawartego w globalnych modelach geopotencjału. Na początku wpływ użycia filtru był badany w ujęciu globalnym. Następnie wpływ ten został zbadany dla obszaru Polski – oddzielnie dla dorzeczy Wisły i Odry. Ponadto, została oszacowana zarówno wewnętrzna, jak i zewnętrzna dokładność wersji 5. globalnych modeli geopotencjału opracowanych na podstawie danych z misji GRACE. Obliczono wariancje błędów wysokości geoidy dla poszczególnych stopni badanych modeli. Zmiany ekwiwalentnej warstwy wody wyznaczone z globalnych modeli geopotencjału opracowanych na podstawie danych z misji GRACE zostały porównane z odpowiednimi zmianami otrzymanymi z modelu hydrologicznego. Wyniki poddano analizie i dyskusji. Ostatecznie wybrano metodę filtracji oraz szereg czasowy globalnych modeli geopotencjału najbardziej odpowiednie do oszacowania zmian rozkładu mas w systemie Ziemia dla obszaru Polski.
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Content available remote Climate-driven Seasonal Geocenter Motion during the GRACE Period
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EN
Annual cycles in the geocenter motion time series are primarily driven by mass changes in the Earth’s hydrologic system, which includes land hydrology, atmosphere, and oceans. Seasonal variations of the geocenter motion have been reliably determined according to Sun et al. (J Geophys Res Solid Earth 121(11):8352-8370, 2016) by combining the Gravity Recovery And Climate Experiment (GRACE) data with an ocean model output. In this study, we reconstructed the observed seasonal geocenter motion with geophysical model predictions of mass variations in the polar ice sheets, continental glaciers, terrestrial water storage (TWS), and atmosphere and dynamic ocean (AO). The reconstructed geocenter motion time series is shown to be in close agreement with the solution based on GRACE data supporting with an ocean bottom pressure model. Over 85% of the observed geocenter motion time series, variance can be explained by the reconstructed solution, which allows a further investigation of the driving mechanisms. We then demonstrated that AO component accounts for 54, 62, and 25% of the observed geocenter motion variances in the X, Y, and Z directions, respectively. The TWS component alone explains 42, 32, and 39% of the observed variances. The net mass changes over oceans together with self-attraction and loading effects also contribute significantly (about 30%) to the seasonal geocenter motion in the X and Z directions. Other contributing sources, on the other hand, have marginal (less than 10%) impact on the seasonal variations but introduce a linear trend in the time series.
EN
The Level-2 monthly GRACE gravity field models issued by Center for Space Research (CSR), GeoForschungs Zentrum (GFZ), and Jet Propulsion Laboratory (JPL) are treated as observations used to extract the equivalent water height (EWH) with the robust independent component analysis (RICA). The smoothing radii of 300, 400, and 500 km are tested, respectively, in the Gaussian smoothing kernel function to reduce the observation Gaussianity. Three independent components are obtained by RICA in the spatial domain; the first component matches the geophysical signal, and the other two match the north-south strip and the other noises. The first mode is used to estimate EWHs of CSR, JPL, and GFZ, and compared with the classical empirical decorrelation method (EDM). The EWH STDs for 12 months in 2010 extracted by RICA and EDM show the obvious fluctuation. The results indicate that the sharp EWH changes in some areas have an important global effect, like in Amazon, Mekong, and Zambezi basins.
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Content available remote Terrestrial water storage variations and their effect on polar motion
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EN
The role of continental water in polar motion excitation can be illustrated by determining Hydrological Angular Momentum calculated from terrestrial water storage (TWS). In this paper we compare global and regional changes in TWS computed using Coupled Model Intercomparison Project Phase 5 climate models, Global Land Data Assimilation System (GLDAS) land hydrology models and observations from the Gravity Recovery and Climate Experiment (GRACE) satellite mission. We also compare hydrological excitation functions derived from models with those obtained from the GRACE mission and the hydrological signal in observed polar motion excitation (the so-called geodetic residuals). The results confirm that GLDAS models of seasonal and non-seasonal TWS change are more consistent with GRACE data than climate models; on the other hand, none of the considered models are fully consistent with GRACE data or geodetic residuals. In turn, GRACE observations are most consistent with the non-seasonal hydrological signal in observed excitation. A detailed study of the contribution of different TWS components to the hydrological excitation function shows that soil moisture dominates.
EN
The main aim of this study is to evaluate the usefulness of Institute of Geodesy at Graz University of Technology (ITSG) daily gravity field models in the determination of hydrological angular momentum (HAM) at nonseasonal time scales. We compared the equatorial components (χ1 and χ2) of HAM calculated with the ITSG daily gravity field models (ITSG-Gravity Recovery and Climate Experiment [ITSG-GRACE] 2016 and ITSG-GRACE 2018) with HAM and sea-level angular momentum (SLAM) from hydrological land surface discharge model (LSDM) and the hydrological signal in the polar motion excitation (known as geodetic residuals [GAO]). Data from ITSG have a daily temporal resolution and allow us to determine oscillations with higher frequencies than the more commonly used monthly data. We limited our study to the period between 2004 and 2011 because of the gaps in GRACE observations before and after this period. We evaluated HAM obtained from ITSG GRACE models in spectral and time domains and determined the amplitude spectra of the analyzed series in the spectral range from 2 to 120 days. Our analyses confirm the existence of a sub-monthly signal in the HAM series determined from ITSG daily data. We observed a similar signal in LSDM-based HAM, but with notably weaker amplitudes. We also observed common peaks around 14 days in the amplitude spectra for the GAO- and ITSG-based series, which may be related to the Earth’s tides. ITSG daily gravity field models can be useful to determine the equatorial components of HAM at nonseasonal time scales.
EN
The aim of this study was to examine the relationship between vertical movements of the Earth’s crust and variation in geoid height. Data from the Gravity Recovery and Climate Experiment (GRACE), precise levelling, tidal gauge observations and Global Navigation Satellite Systems (GNSS) stations for the Sudetes area were used. The GRACE data provided the possibility of the analysis of geopotential changes. The geoid heights were calculated for the period from April 2002 to March 2016, using data from GeoForschungsZentrum (GFZ) GRACE Level-2 Product Release 05 in the form of spherical harmonic coefficients, truncated at degree and order (d/o) 60. Different filters were used. The calculated geoid change over time has the approximate value of 0.16 mm/y. This value was compared to the expected change in geoid height, determined on the basis of the Earth’s crustal movements.
8
Content available remote Milost, lidské úsilí a Boží předvědění podle Jeronýma
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EN
The paper focuses on the theme of divine grace, human agency and divine foreknowledge in Jerome. In his ascetic writings, Jerome praises virginity as a special gift having two aspects: it demands a special effort exceeding ordinary duties and it promises a special reward. People are not given the same measure of divine grace. There is no injustice because effort of one's will is more relevant than human deeds. Divine foreknowledge does not restrain human freedom because God does not determine what will happen but only foreknows it. Human nature is weak and fragile, unable to avoid sinning continuously. However, free will is indispensable for any morally good agency; necessity excludes merit. In every morally good action, one has to will and strive, and God strengthens the effort and brings it to completion. What is not quite clear is how to reconcile Jerome's claim about inability of human will to avoid sinning with his optimistic view of initium voluntatis.
EN
Global satellite gravity measurements provide unique information regarding gravity field distribution and its variability on the Earth. The main cause of gravity changes is the mass transportation within the Earth, appearing as, e.g. dynamic fluctuations in hydrology, glaciology, oceanology, meteorology and the lithosphere. This phenomenon has become more comprehensible thanks to the dedicated gravimetric missions such as Gravity Recovery and Climate Experiment (GRACE), Challenging Minisatellite Payload (CHAMP) and Gravity Field and Steady-State Ocean Circulation Explorer (GOCE). From among these missions, GRACE seems to be the most dominating source of gravity data, sharing a unique set of observations from over 15 years. The results of this experiment are often of interest to geodesists and geophysicists due to its high compatibility with the other methods of gravity measurements, especially absolute gravimetry. Direct validation of gravity field solutions is crucial as it can provide conclusions concerning forecasts of subsurface water changes. The aim of this work is to present the issue of selection of filtration parameters for monthly gravity field solutions in RL06 and RL05 releases and then to compare them to a time series of absolute gravimetric data conducted in quasi-monthly measurements in Astro-Geodetic Observatory in Józefosław (Poland). The other purpose of this study is to estimate the accuracy of GRACE temporal solutions in comparison with absolute terrestrial gravimetry data and making an attempt to indicate the significance of differences between solutions using various types of filtration (DDK, Gaussian) from selected research centres.
PL
Analiza zmian pola ciężkości Ziemi należy do głównych zadań geodezji fizycznej, a znajomość wybranych charakterystyk tego pola stanowi m.in. podstawowy element wyznaczenia kształtu Ziemi i uwiarygodnienia wiedzy na temat redystrybucji jej masy. Od 2002 roku do tego celu wydatnie przyczynia się satelitarna misja grawimetryczna GRACE (ang. Gravity Recovery and Climate Experiment) oraz jej misja kontynuacyjna GRACE-FO (ang. GRACE Follow-On). Wyniki opracowanych obserwacji uzyskanych z misji GRACE/GRACE-FO prezentowane są m.in. w postaci maskonów, które dostarczane są przez trzy centra przetwarzania: 1) CSR (Center for Space Research, Austin, Stany Zjednoczone), 2) JPL (Jet Propulsion Laboratory, Pasadena, Stany Zjednoczone) oraz 3) GSFC (Goddard Space Flight Center, Maryland, Stany Zjednoczone). W pracy wykorzystano dane udostępniane przez centrum przetwarzania GSFC w postaci globalnego rozkładu zmian całkowitej zawartości wody w kontynentach (ang. Total Water Storage, TWS), wyrażonego w postaci wysokości słupa wody (ang. Equivalent Water Height, EWH). W badaniach skupiono się na zidentyfikowaniu obszarów o wyraźnych zmianach TWS. Fluktuacje TWS przeanalizowano pod kątem zmian krótkookresowych, tj. amplitudy oscylacji rocznej (najbardziej wyraźnej oscylacji w hydrosferze), oraz zmian długookresowych, tj. trendu (kluczowego parametru dla badań klimatycznych), wyznaczonych z wykorzystaniem metody najmniejszych kwadratów. W rezultacie wyselekcjonowano piętnaście obszarów charakteryzujących się ekstremalnymi zmianami, tj. jedenaście obszarów dla parametru amplitudy oscylacji rocznej i cztery obszary dla trendu. Otrzymano zmiany sezonowe większe niż 140 mm na obszarach w obrębie równika (głównie dorzecza rzek - Amazonka, Niger, Ganges, Brahmaputra) oraz obszarach pokrytych ogromnymi masami lodowymi (Alaska, Grenlandia). Największe tempo zmian zasobów wodnych na poziomie ±70 mm/rok obserwowane jest w okolicach Antarktydy Zachodniej, Patagonii czy Morza Kaspijskiego. Wyniki podkreślają również zauważalny wpływ człowieka na zmiany wód kontynentalnych (np. region Meksyku oraz dorzecza rzek Indus, Ganges).
EN
The analysis of Earth’s gravity field changes is the one of essential task of physical geodesy. So the knowledge about selected characteristics of gravity field is the basic element of the Earth shape determining process and help to find information about mass redistribution in the Earth system. Since 2002, the gravity field changes have been successfully observed by the Gravity Recovery and Climate Experiment (GRACE) satellite gravity mission and its continued GRACE-FO (GRACE Follow-On) mission. The results obtained from GRACE/GRACE-FO observations are presented, among other, in form of mascons and they are provid-ed by three processing centers: (1) Center for Space Research (CSR; Austin, United States), (2) Jet Propulsion Laboratory (JPL; Pasadena, United States), and (3) Goddard Space Flight Center (GSFC; Maryland, United States). In the following study, we used data provided by GSFC in form of the global distribution of Total Water Storage (TWS), which are expressed in terms of Equivalent Water Height (EWH). In our study, we focused on identifying areas with significant changes in TWS. We analysed TWS fluctuations in seasonal short-term changes, i.e., amplitude of annual oscillation (the most pronounced oscillation in the land hydro-sphere) and long-term changes, i.e., trend (a key parameter for climate studies) determined using the Least Squares Method. As a result, we selected 15 areas characterised by extreme TWS changes, i.e., 11 areas for annual amplitude and 4 areas for trend parameter. We obtained seasonal changes greater than 140 mm in areas within the equator (mainly Amazon, Niger, Ganges, Brahmaputra river basin regions) and areas covered by huge ice masses (Alaska, Greenland). The greatest rate of change in water storage at ±70 is observed around West Antarctica, Patagonia or the Caspian Sea. The results also emphasize the significant human impact in continental water masses (e.g. Mexico, Indus and Ganges river basins).
EN
Temporal mass variations in the Earth system, which can be detected from the Gravity Recovery and Climate Experiment (GRACE) mission data, cause temporal variations of geoid heights. The main objective of this contribution is to analyze temporal variations of geoid heights over the area of Poland using global geopotential models (GGMs) developed on the basis of GRACE mission data. Time series of geoid height variations were calculated for the chosen subareas of the aforementioned area using those GGMs. Thereafter, these variations were analyzed using two different methods. On the basis of the analysis results, models of temporal geoid height variations were developed and discussed. The possibility of prediction of geoid height variations using GRACE mission data over the area of Poland was also investigated. The main findings reveal that the geoid height over the area of Poland vary within 1.1 cm which should be considered when defining the geoid model of 1 cm accuracy for this area.
EN
In this study, a scheme to estimate oceanic and hydrological effects in the GRACE (Gravity Recovery and Climate Experiment) data is presented. The aim is to reveal tectonic signals for the case of the Sumatra earthquake on 26 December 2004. The variations of hydrological and oceanic effects are estimated with the aid of data set of GRACE, altimetry, World Ocean Atlas, and the GLDAS model for a period of January 2003 to December 2006. The time series of computed gravity changes over Sumatra region show some correlations to the deformation resulting from the earthquake occurred in December 2004. The maximum and minimum impacts of hydrological and oceanic effects on gravity changes are about 3 μGal in radial direction and –5 μGal in northward direction. The maximum and minimum amounts of gravitational gradient changes after the correction are 0.2 and –0.25 mE, which indicates the significant influences of hydrological and oceanic sources on the desired signal.
EN
We can estimate the Equivalent Water Thickness (EWT) from results of observations of the Earth gravity field from the Gravity Recovery and Climate Experiment (GRACE) gravimetric mission. However the maps of EWT obtained from raw gravimetric data contain typical stripes. To eliminate these disturbances we need to filter the raw data to improve the signal to noise ratio. The distribution of EWT obtained from the GRACE mission can be used to determine the gravimetric excitation function. In this paper it was investigated the filter influence on the EWT distribution and the amplitude of the gravimetric excitation functions. We use the EWT data sets derived from Stokes coefficients made accessible and filtered by the International Centre for Global Earth Models (ICGEM). The data sets available on ICGEM website were imported from three research centers GFZ, JPL and CSR. The anisotropic filter, with three degrees of smoothing DDK3, DDK2 and DDK1 is described in (Kusche et al., 2009).
14
Content available remote Water Storage Changes over the Tibetan Plateau Revealed by GRACE Mission
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EN
We use GRACE gravity data released by the Center for Space Research (CSR) and the Groupe de Recherches en Geodesie Spatiale (GRGS) to detect the water storage changes over the Tibetan Plateau (TP). A combined filter strategy is put forward to process CSR RL05 data to remove the effect of striping errors. After the correction for GRACE by GLDAS and ICE-5G, we find that TP has been overall experiencing the water storage increase during 2003-2012. During the same time, the glacier over the Himalayas was sharply retreating. Interms of linear trends, CSR’s results derived by the combined filter are close to GRGS RL03 with the Gaussian filter of 300-km window. The water storage increasing rates determined from CSR’s RL05 products in the interior TP, Karakoram Mountain, Qaidam Basin, Hengduan Mountain, and middle Himalayas are 9.7, 6.2, 9.1, –18.6, and –20.2 mm/yr, respectively. These rates from GRGS’s RL03 products are 8.6, 5.8, 10.5, –19.3 and –21.4 mm/yr, respectively.
PL
Obserwacje zmian mas w skali globalnej przy użyciu satelitów odgrywają kluczową rolę w badaniach dotyczących zmian klimatu, cyrkulacji oceanów, wnętrza Ziemi oraz aktywności ludzkości. Dane te są pozyskiwane dzięki misjom satelitarnym, które skupiają się na badaniu zmian pola grawitacyjnego Ziemi, a co za tym idzie – zmian wysokości geoidy. Dzięki postępowi w dziedzinie geodezji satelitarnej, zwłaszcza systemów nawigacyjnych, misje te mogą dokonywać precyzyjnych pomiarów na skalę globalną, oferując wysoką rozdzielczość przestrzenną i czasową. W niniejszym artykule skupiamy się na przedstawieniu technik obserwacji potencjału grawitacyjnego oraz omówieniu informacji, które można dzięki nim uzyskać. Szczególny nacisk położony jest na misję GRACE i jej następcę, GRACE Follow-On oraz planowanej misji MAGIC.
EN
Observations of mass changes on a global scale using satellites play a crucial role in research related to climate change, ocean circulation, Earth's interior, and human activities. Data is acquired through satellite missions that focus on studying changes in Earth's gravity field, that is changes in geoid height. Thanks to advancements in satellite geodesy, especially in navigational systems, these missions can conduct precise measurements on a global scale, offering high spatial and temporal resolution. In this article, we focus on time-variable Earth’s gravity field observation techniques and discuss the information that can be obtained through them. Special emphasis is placed on the GRACE mission and its successor, GRACE Follow-On and future planned MAGIC mission.
EN
Satellite altimetry provides high-accuracy geometrical measurements of sea level changes. We analyze altimetry time series representing sea surface height anomalies over the mean sea surface provided by the TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3 satellite missions to estimate the annual rate of sea level rise. Then, we compare the results with satellite gravimetric data from GRACE and GRACE Follow-On missions and surface water temperature data, employing statistical analyses to examine the interrelationships and correlations between them. We carry out the main analyses for the period 2001–2021 with a division into 5-year periods for six different areas of the Baltic Sea. The altimetric results show that between 2001 and 2021, the water level of the Baltic Sea rose by 5.8 mm/year on average. About 72% of the changes detected by altimetry missions can be explained by satellite gravimetry from GRACE and GRACE Follow-On, which means that the mass component is responsible for most of the observed sea level change, whereas the remaining 28% can be greatly explained by thermal expansion due to the water temperature rise.
EN
The study presents a compatibility analysis of gravimetric observations with passive microwave observations. Monitoring the variability of soil water content is one of the essential issues in climate-related research. Total water storage changes (∆TWS) observed by Gravity Recovery and Climate Experiment (GRACE), enables the creation of many applications in hydrological monitoring. Soil moisture (SM) is a critical variable in hydrological studies. Advanced Microwave Scanning Radiometer (AMSR-E) satellite products provided unique observations on this variable in near-daily time resolutions. The study used maximum covariance analysis (MCA) to extract principal components for ∆TWS and SM signals. The analysis was carried out for the global area, dividing the discussion into individual continents. The amplitudes of gravimetric and microwave signals were computed via the complex empirical orthogonal function (EOF) and the complex conjugate EOF* to determine the regions for detailed comparison. Similarities and differences in signal convergence results were compared with land cover data describing soil conditions, vegetation cover, urbanization status, and cultivated land. Convergence was determined using Pearson correlation coefficients and cross-correlation. In order to compare ∆TWS and SM in individual seasons, ∆TWS observations were normalized. Results show that naturally forested areas and large open spaces used for agriculture support the compatibility between GRACE and AMSRE observations and are characterized by a good Pearson correlation coefficient >0.8. Subpolar regions with permafrost present constraints for AMSR-E observations and have little convergence with GRACE observations.
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Content available remote Vůle a milost u Jana Cassiana
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The article deals with John Cassian's view of the divine grace and the human will. Cassian stresses the necessity and primacy of the divine help, our human will is weakened by sin but not totally corrupted. With regard to the salvation, one's own effort alone is not sufficient, but God who wants all men to be saved, never ceases to come to one's aid. On the basis of the Scriptures, Cassian sees the co-operation of grace and will interwoven so enigmatically that it is not always clear which comes into operation first: sometimes it is God who takes the initiative, in other instances the initiative is ascribed to man. Cassian's views on grace and will were interpreted as anti-augustinian and called 'semipelagian'. Recent scholarly discussion has rejected this interpretation as ill-founded and the term is now regarded as misleading.
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