Browsing by Author "Lorenz, Christof"

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Open Access
Applying stochastic constraints on time-variable GRACE data
(2009) Lorenz, Christof
Since its launch in the year 2002, the space satellite mission GRACE provides spherical harmonic coefficients, which can be used to observe the time-variable part of the Earth's gravity field. It was initially assumed that the derived gravitational quantities from these coefficients are of high accuracy and would thus deliver reliable large scale mass estimates. However, the provided coefficients of higher harmonic degree and order turned out to be seriously contaminated with noise, yielding an unrealistic signal of mass variations in form of massive north-south stripes. In this work, two methods are investigated, which add stochastic constraints to time variable GRACE coefficients. It is assumed that these techniques are able to reduce the noise level in the monthly datasets by assimilating the GRACE coefficients with more reliable data. Both approaches need prior estimates of a signal and error covariances. Hence, the signal covariance of the time-variable gravity field is assumed to be of isotropic nature and is thus computed as a Kaula-type power law, which is fit into the part where the signal degree variances of the GRACE solutions linearly attenuate. The error covariance is estimated according to the energy balance approach which allows the simulation of a fully populated GRACE covariance matrix. Stochastic constraining in the spectral domain combines both signal and error covariance estimates in a Bayesian type regularization procedure, which constrains the monthly GRACE solutions with the modelled signal covariance. It is shown that Bayesian type regularization can be used to build a spectral filter kernel. Furthermore, the weight between both GRACE coefficients and the regularization term is estimated by a variance component estimation. Tests with a full, block diagonal and diagonal covariance matrix are performed, as it is widely believed that full covariance information can be sufficiently approximated by a block diagonal matrix. Furthermore, the Bayesian type regularization filter is tested with three different monthly GRACE solutions and compared with other widely used filtering techniques. The second approach constrains the time-variable GRACE coefficients with hydrological observations, which are provided as monthly precipitation and run-off values on basin scale. Both the GRACE and hydrological observation group are assimilated in one linear model, which is solved by sequential least squares estimation, yielding an agreement between mass estimates from GRACE and observed hydrology.
Open Access
Interrelations of vegetation growth and water scarcity in Iran revealed by satellite time series
(2022) Behling, Robert; Roessner, Sigrid; Foerster, Saskia; Saemian, Peyman; Tourian, Mohammad J.; Portele, Tanja C.; Lorenz, Christof
Iran has experienced a drastic increase in water scarcity in the last decades. The main driver has been the substantial unsustainable water consumption of the agricultural sector. This study quantifies the spatiotemporal dynamics of Iran’s hydrometeorological water availability, land cover, and vegetation growth and evaluates their interrelations with a special focus on agricultural vegetation developments. It analyzes globally available reanalysis climate data and satellite time series data and products, allowing a country-wide investigation of recent 20+ years at detailed spatial and temporal scales. The results reveal a wide-spread agricultural expansion (27,000 km 2) and a significant cultivation intensification (48,000 km 2). At the same time, we observe a substantial decline in total water storage that is not represented by a decrease of meteorological water input, confirming an unsustainable use of groundwater mainly for agricultural irrigation. As consequence of water scarcity, we identify agricultural areas with a loss or reduction of vegetation growth (10,000 km 2), especially in irrigated agricultural areas under (hyper-)arid conditions. In Iran’s natural biomes, the results show declining trends in vegetation growth and land cover degradation from sparse vegetation to barren land in 40,000 km 2, mainly along the western plains and foothills of the Zagros Mountains, and at the same time wide-spread greening trends, particularly in regions of higher altitudes. Overall, the findings provide detailed insights in vegetation-related causes and consequences of Iran’s anthropogenic drought and can support sustainable management plans for Iran or other semi-arid regions worldwide, often facing similar conditions.
Open Access
Photography-aided gravity modeling of solid bodies
(2010) Lorenz, Christof
Not all secrets of the The Great Pyramid of Giza were revealed, even after centuries of observation and research. One of the main questions concerns the construction of the pyramid. The most popular and reasonable theory assumes the old Egyptians to use an exterior ramp in the lower third and an interior ramp in the upper two thirds of the pyramid on which the stones were carried upstairs. However, there is no evidence that this is really true. Microgravimetry-measuring techniques are able to give information about the inner mass distribution of the pyramid and hence reveal yet unknown facts about the inner structure. Therefore, a reference gravity signal must be computed in order to detect mass deviations in the inside. In this work, an approach is discussed which uses photographs to construct a three-dimensional model of a body. It is shown that the information gained from three-dimensional reconstruction can be used to construct a solid body. For the computation of the gravity signal of this solid body an algorithm is applied which transforms the volume integral in Newton's law of gravity into line integrals, which allows the computation of gravitational quantities for arbitrary polyhedra. With the help of a small section of the Great Pyramid it is shown that detecting inner mass deviations from a reference body requires detailed knowledge about the surface. As the errors in the measured gravity signal caused by a mis-modeled body might have a high magnitude, the signal from inner mass deviations might completely vanish. However, if the surface of an object is well known it is indeed possible to make a statement about the inner structure of a body based on close-mesh measurements on its surface.