Browsing by Author "Sneeuw, Nico (Prof. Dr.-Ing.)"

Now showing 1 - 12 of 12

Open Access
Analyzing and characterizing spaceborne observation of water storage variation : past, present, future
(2024) Saemian, Peyman; Sneeuw, Nico (Prof. Dr.-Ing.)
Water storage is an indispensable constituent of the intricate water cycle, as it governs the availability and distribution of this precious resource. Any alteration in the water storage can trigger a cascade of consequences, affecting not only our agricultural practices but also the well-being of various ecosystems and the occurrence of natural hazards. Therefore, it is essential to monitor and manage the water storage levels prudently to ensure a sustainable future for our planet. Despite significant advancements in ground-based measurements and modeling techniques, accurately measuring water storage variation remained a major challenge for a long time. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE Follow-On (GRACE-FO) satellites have revolutionized our understanding of the Earth's water cycle. By detecting variations in the Earth's gravity field caused by changes in water distribution, these satellites can precisely measure changes in total water storage (TWS) across the entire globe, providing a truly comprehensive view of the world's water resources. This information has proved invaluable for understanding how water resources are changing over time, and for developing strategies to manage these resources sustainably. However, GRACE and GRACE-FO are subject to various challenges that must be addressed in order to enhance the efficacy of our exploitation of GRACE observations for scientific and practical purposes. This thesis aims to address some of the challenges faced by GRACE and GRACE-FO. Since the inception of the GRACE mission, scholars have commonly extracted mass changes from observations by approximating the Earth's gravity field utilizing mathematical functions termed spherical harmonics. Various institutions have already processed GRACE(-FO) data, known as level-2 data in the GRACE community, considering the constraints, approaches, and models that have been utilized. However, this processed data necessitates post-processing to be used for several applications, such as hydrology and climate research. In this thesis, we evaluate various methods of processing GRACE(-FO) level-2 data and assess the spatio-temporal effect of the post-processing steps. Furthermore, we aim to compare the consistency between GRACE and its successor mission, GRACE-FO, in terms of data quality and measurement accuracy. By analyzing and comparing the data from these two missions, we can identify any potential discrepancies or differences and establish the level of confidence in the accuracy and reliability of the GRACE-FO measurements. Finally, we will compare the processed level-3 products with the level-3 products that are presently accessible online. The relatively short record of the GRACE measurements, compared to other satellite missions and observational records, can limit some studies that require long-term data. This short record makes it challenging to separate long-term signals from short-term variability and validate the data with ground-based measurements or other satellite missions. To address this limitation, this thesis expands the temporal coverage of GRACE(-FO) observations using global hydrological, atmospheric, and reanalysis models. First, we assess these models in estimating the TWS variation at a global scale. We compare the performance of various methods including data-driven and machine learning approaches in incorporating models and reconstruct GRACE TWS change. The results are also validated against Satellite Laser Ranging (SLR) observations over the pre-GRACE period. This thesis develops a hindcasted GRACE, which provides a better understanding of the changes in the Earth's water storage on a longer time scale. The GRACE satellite mission detects changes in the overall water storage in a specific region but cannot distinguish between the different compartments of TWS, such as surface water, groundwater, and soil moisture. Understanding these individual components is crucial for managing water resources and addressing the effects of droughts and floods. This study aims to integrate various data sources to improve our understanding of water storage variations at the continental to basin scale, including water fluxes, lake water level, and lake storage change data. Additionally, the study demonstrates the importance of combining GRACE(-FO) observations with other measurements, such as piezometric wells and rain-gauges, to understand the water scarcity predicament in Iran and other regions facing similar challenges. The GRACE satellite mission provides valuable insights into the Earth's system. However, the GRACE product has a level of uncertainty due to several error sources. While the mission has taken measures to minimize these uncertainties, researchers need to account for them when analyzing the data and communicate them when reporting findings. This thesis proposes a probabilistic approach to incorporate the Total Water Storage Anomaly (TWSA) data from GRACE(-FO). By accounting for the uncertainty in the TWSA data, this approach can provide a more comprehensive understanding of drought conditions, which is essential for decision makers managing water resources and responding to drought events.
Open Access
Analyzing and modeling environmental loading induced displacements with GPS and GRACE
(2015) Chen, Qiang; Sneeuw, Nico (Prof. Dr.-Ing.)
The redistribution of atmospheric, oceanic and hydrological masses on the Earth's surface varies in time and this in turn loads and deforms the surface of the solid Earth. Analyzing such environmental loading signal and modeling its induced elastic displacements are of great importance for explaining geophysical phenomena. Based on the well-established loading theory, this thesis makes use of two different space-borne measurements, i.e. GPS and GRACE, along with other environmental loading data to investigate three different aspects of environmental loading and its induced elastic deformations: Firstly, an increasing concern is observed recently over time variable seasonal signals in geodesy. Several model based approaches were applied to extract amplitude and phase modulated annual and semiannual signals. In view of this phenomenon, this thesis introduces an alternative approach, namely, singular spectrum analysis (SSA). With respect to these model-dependent approaches, the advantage of SSA lies in data-driven and model-independence. Several aspects regarding the application of SSA, e.g. optimal choice of window size, are investigated before showing its abilities. Through applying SSA to the lake level time series of Lake Urmia (Iran) and the basin averaged equivalent water height time series of the Congo basin, the capabilities of SSA in separating time varying seasonal signals are demonstrated. In addition, we find that SSA is also able to extract the non-linear trend as well as long-term oscillations from geodetic time series. Secondly, we look into the comparison between GPS and GRACE with an emphasis on GRACE data filtering. Three types of deterministic filters and two types of stochastic filters are studied and compared over GPS sites from two regions, i.e. the Europe area and the Amazon area. The comparisons indicate that no single filtering scheme could provide consistently better performance over other considered filters. However, we find that the stochastic filters generally show better performance than the deterministic filters. The DDK 1 filter outperforms other filters in the Europe area and the regularization filter of parameter lambda=4, which follows the concept of the DDK filters, shows optimal performance in the Amazon area. The combination of the isotropic Gaussian filter of a low smoothing radius, e.g. around 300 km with the destriping filter is proved to be optimal filter choice if only the deterministic filters are considered. Thirdly, based on an overview of displacements modeling at various spatial scales, we evaluate three methods, i.e. two types of half-space approaches and the classic Green function approach, by using a high spatial resolution local load data along the lower Mississippi river when a severe flood happened in 2011. The equivalence between the two half-space approaches, i.e. point load approach and surface load approach, are demonstrated with the local load data. However, the point load approach is recommended for practical use in terms of computational efficiency. In addition, within such a limited spatial extent, we investigate the differences between the half-space approach and the Green function approach. It is shown that the half-space approach predicts larger displacements than the Green function approach and agrees better with the observed deformations at 11 considered GPS sites. Meanwhile, strong global environmental loading effects are found via two global hydrological models, i.e. GLDAS and MERRA. Thus, a reduction of these far-field loading effects beforehand is suggested before probing the local crustal structure using the half-space approach. Last but not least, based on the local load data, the effects of site-dependent Green functions are studied with two types of site-dependent Green functions, which were generated by modifying the local crustal structure of the REF Earth model using the CRUST 1.0 and CRUST 2.0 models. A relative RMS of differences of more than 5% in vertical component and 25% in horizontal components are found with respect to the PREM Earth model based Green functions. It indicates that the Green functions could contribute more uncertainties in loading induced displacements modeling than reported in the literature.
Open Access
Application of spaceborne geodetic sensors for hydrology
(2013) Tourian, Mohammad Javad; Sneeuw, Nico (Prof. Dr.-Ing.)
How much freshwater do we have on land? How is the freshwater cycle changing with time? Actually, we can not properly answer these questions as our knowledge of the spatial and temporal dynamics of the hydrological cycle is limited. The lack of knowledge is mainly induced by shortage of observational evidence, which motivates the objective of this study: the monitoring of the hydrological cycle using spaceborne geodetic sensors. Among the current space geodetic sensors, GRACE and satellite altimetry are the two active mission concepts, that can capture part of the hydrological cycle. However, monitoring the hydrological cycle using these two sensors is challenging. Satellite altimetry is investigated as an independent spaceborne sensor that provides the water level and discharge time series. An algorithm is developed to improve the quality of water level time series over inland water surfaces. This algorithm particularly deals with the challenges of resolution and uncertainty of altimetry. The obtained altimetric water level time series is validated against in situ measurements showing about 10% improvement in accuracy of the time series. Moreover, this study proposes an algorithm to reduce the random noise from pre-retracked data. The algorithm combines the results of different retrackers and provides water level time series with reduced noise level. The validation shows a significant reduction of noise level and a clear improvement in correlation with in situ measurements. Moreover, this study proposes a statistical approach based on quantile functions to infer a functional relationship between altimetric water level and in situ river discharge without the need for synchronous data sets. This method is based on a scatter diagram of quantile functions, in which the probability-coordinate is eliminated. In contrast, the conventional methods for simultaneous measurements operate directly on time series and eliminate the time-coordinate. The results show that the proposed methodology provides the same range of error as the common conventional empirical method. The good performance of the statistical approach supports the usage of altimetry to salvage pre-satellite altimetry discharge data and turn them into active use for the satellite altimetry time frame. In addition, a stochastic process model is implemented to (i) deal with the data outages in altimetric discharge, (ii) provide a scheme for data assimilation and (iii) smooth the discharge estimation. The model benefits from the cyclostationary behaviour of the discharge and is combined with the estimated discharge from altimetry and available in situ measurements to form a linear dynamic system. The dynamic system is solved using the Kalman filter, that provides an unbiased discharge with minimum variance. The error level of the results is comparable to the empirical approach. In this study, the utility of GRACE data as sensor of hydrological water storage changes is shown to be limited by the following challenges: consistency, resolution, separability and uncertainty. The challenge of inconsistency is addressed by developing two filters for hydrological and hydro-meteorological water storage changes, which lead to a better correlation with GRACE mass storage changes. The challenges of separability and resolution are not specifically investigated in this study, yet their consequences, which appear in different forms of uncertainties is investigated. To deal with the GRACE uncertainties, an algorithm is developed to detect outliers in monthly solutions. The outliers have been corrected by replacing them by an inter-annual monthly mean of the respective month. The results conclude that outlier identification and correction must be performed before further assimilation of GRACE products into hydrological or hydro-meteorological analysis. Further, a longrange correlation has been identified as another source of uncertainty in GRACE monthly solutions. EOF analysis is employed to identify the zonal behaviour of the GRACE C20 errors as the responsible source for the long-range correlation. It is considered as an error source because its residual contains tidal aliasing errors instead of white noise. Therefore, to reduce the uncertainties in GRACE monthly solutions, tidal aliasing errors are also investigated. Primary and secondary tidal aliasing errors of main tidal constituents, S1, S2, P1, K1, K2, M2, O2, O1 and Q1 are identified in GRACE monthly solutions. The effect of tidal aliasing error is estimated using a least squares Fourier analysis indicating errors up to 22mm over the globe. In general, after dealing with GRACE’s challenges and achieving a data set without outliers, long-range correlation and tidal aliasing errors, the noise level of GRACE is quantified. The quantification shows a variation between 2–20mm/month over different parts of the globe, with higher values over tropical and boreal regions. The results specifically confirm that small catchments in the tropics contain more noise contamination. It is also shown that a lower noise level of a catchment does not necessarily lead to a better correlation of GRACE with hydro-meteorological signal. Finally, the joint performance of spaceborne geodetic sensors for estimating the actual evapotranspiration ETa is assessed. There, two approaches are introduced to estimate ETa using the results of GRACE and satellite altimetry. The results of both approaches are compared with different models and their ensemble mean. All in all, given the obtained relative discrepancy, the methods seem to be a viable way for determining ETa for most non-desert catchments containing hot and warm summers.
Open Access
Assessing the statistical relations of terrestrial water mass change with hydrological variables and climate variability
(2019) Zhang, Jinwei; Sneeuw, Nico (Prof. Dr.-Ing.)
Open Access
Assessment of ICESat-2 laser altimetry in hydrological applications
(2024) Wang, Bo; Sneeuw, Nico (Prof. Dr.-Ing.)
Water bodies act as critical components of the hydrological cycle, serving as reservoirs, lakes, wetlands, and aquifers that store and release water over time. Monitoring changes in the extent and volume of these water bodies is crucial for understanding their role in regulating water flow, maintaining baseflow during dry periods, and supporting ecological habitats. Furthermore, the identification of trends and alterations in water body dynamics aids in detecting potential impacts of climate change and human activities on the hydrological cycle. Historically, gauge stations have been employed to monitor the water level of these bodies since the 19th century. However, their numbers have been dwindling since the 1970s due to maintenance challenges. With the development of satellite altimetry missions, more accurate and continuous monitoring of lakes and rivers has become possible. These satellites in recent years offer the capability to provide water level data with different along-track sampling distances. For instance, ICESat-2 offers a sampling distance of 70 cm with a footprint size of ~17 m, while Sentinel-3 provides a sampling distance of 300 m. The temporal resolution ranges from 10 days (Jason-3) to 369 days (Cryosat-2). These advances allow researchers to effectively observe and understand changes in water bodies. The invention of satellite-based laser altimetry has brought a revolutionary advancement in our ability to monitor and study Earth’s water bodies with unprecedented precision and extensive spatial coverage. This doctoral thesis aims to explore the diverse applications of ICESat-2 laser altimetry data over inland water bodies. Through these investigations, the aim is to advance our understanding of global hydrological processes and acquire valuable insights to improve water resource management strategies. It is important to understand the error budget of the altimetric observations, one component of which is radial orbit error. Apart from the altimetric ranging errors, radial orbit errors directly influence the accuracy of the measurement of Earth’s surface heights. These errors can be assessed by analyzing the difference of surface heights at ground track intersections, so-called crossover differences (XO differences). An effective approach is to model the orbit error by minimizing the residual XO difference by the least-squares (LS) method, which is commonly known as XO adjustment. This method was implemented in the Arctic region to examine the performance of the LS adjustment over spherical cap geometry and assess the level of radial orbit error across a large-scale area. This analysis will aid in understanding the accuracy and reliability of ICESat-2 satellite orbit over the Arctic region. The ICESat-2 satellite captures high-resolution observations of Earth’s surface, including land and water, thus enabling dense measurements of heights. The green laser used in ICESat-2 has the capability to penetrate water surfaces, allowing measurements of not only the lake water level but also the nearshore water bottom. This study proposes a novel algorithm that combines ICESat-2 measurements with Landsat imagery to extract lake water level, extent and volume. This algorithm was applied to Lake Mead, resulting in a long-term time series of water level, extent and volume dating back to 1984, only derived from remote sensing data. The ICESat-2 satellite is equipped with three pairs of laser transmitters, which concurrently generate three pairs of ground tracks. This unique characteristic enables us to derive river surface heights for each ground track, thereby calculating the river slope between two tracks, referred to as the across-track river slope. Moreover, when one ground track passes through the river surface, producing dense measurements, it allows us to obtain the small-scale slope for that specific track, termed the along-track based river slope. By using these methods, both types of slopes were estimated for the entire length of the Rhine River and subsequently generated the average slope for each reach along the river.
Open Access
Dynamic water masks from optical satellite imagery
(München : Verlag der Bayerischen Akademie der Wissenschaften, 2019) Elmi, Omid; Sneeuw, Nico (Prof. Dr.-Ing.)
Investigation of the global freshwater system has a vital role in critical issues e.g. sustainable development of water resources, acceleration of the hydrological cycle, variability of global sea level. Measurement of river streamflow is vital for such investigations as it gives a reliable estimate of freshwater fluxes over the continents. Despite such importance, the number of river discharge gauging station has been decreasing. At the same time, information on the global freshwater system has been increasing because of various types of ground observations, water-use information and spaceborne geodetic observations. Nevertheless, we cannot answer properly crucial questions about the amount of freshwater available on a certain river basin, or the spatial and temporal dynamics of freshwater variations and discharge, or the distribution of world’s freshwater resources in the future. The lack of comprehensive measurements of surface water storage and river discharge is a major impediment for a realistic understanding of the hydrological water cycle, which is a must for answering the aforementioned questions. This thesis aims to improve the methods for monitoring the surface extent of inland water bodies using satellite images. Satellite imaging systems capture the Earth surface in a wide variety of spectral and spatial resolution repeatedly. Therefore satellite imagery provides the opportunity to monitor the spatial change in shorelines, which can serve as a way to determine the water extent. Each band of a multispectral image reveals a unique characteristic of the Earth surface features like surface water extent. However selecting the spectral bands which provide the relevant information is a challenging task. In this thesis, we analyse the potential of multispectral transformations like Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) to tackle this issue by condensing the information available in all spectral bands in just a few uncorrelated variables. Moreover, we investigate how the change between multispectral images at different epochs can be highlighted by using the transformations. This study proposes an automatic algorithm for extracting the lake water extent from MODIS images and generating dynamics lake masks. For improving the accuracy of the lake masks and computational efficiency of the algorithm, two masks are defined for limiting the search area. The restricting masks are developed according to DEM of the surrounding area together with a map of the long-term variation of pixel values. Subsequently, an unsupervised pixel-based classification algorithm is applied for defining the lake coastline. The algorithm particularly deals with the challenges of generating long time series of lake masks. We apply the algorithm on five lakes in Africa and Asia, each of which demonstrates a challenge for lake area monitoring. However in the validation section, we demonstrate that the algorithm can generate accurate dynamic lake masks. Rivers show diverse behaviour along their path due to the contribution of different parameters like gradient of the elevation, river slope, tributaries and river bed morphology. Therefore for generating accurate river reach mask, we need to consider additional sources of information apart from pixel intensity. The region-based classification algorithm that we propose in this study takes advantages of all types of available information including pixel intensity and spatial and temporal interactions. Markov Random Fields provide a flexible frame for interaction between different sources of data and constraint. To find the most probable configuration of the field, the Maximum A Posteriori solution for the MRF must be found. To this end, the problem is reshaped as an energy minimization. The energy function is minimized applying graph cuts as a powerful optimization technique. The uncertainty in the graph cuts solution is also measured by calculating the minimum marginal energies. The proposed method is applied to four rivers reaches with different hydrological characteristics. We validate the obtained river area time series by comparing with in situ river discharge and satellite altimetric water level time series. Moreover, in this study, we present river discharge estimation models using the generated river reach masks. Our aim is to find an empirical relationship between the average river reach width and river discharge. The statistics in the validation periods support the idea of using river width-discharge prediction models as a complementary technique to the other spaceborne geodetic river discharge prediction approaches.
Open Access
Die Invariantendarstellung in der Satellitengradiometrie : theoretische Betrachtungen und numerische Realisierung anhand der Fallstudie GOCE
(2007) Baur, Oliver; Sneeuw, Nico (Prof. Dr.-Ing.)
Die Satellitengradiometrie (Satellite Gravity Gradiometry, SGG) ist die derzeit modernste Technik zur Bestimmung und Modellierung hochauflösender Gravitationsfelder. Sie gründet auf der Beobachtung zweiter Ableitungen des Gravitationspotenzials, welche als Gravitationsgradienten (GG) bezeichnet werden und deren Gesamtheit im Gravitationstensor (oder Eötvös-Tensor) zusammen gefasst ist. Letzterer zeichnet sich durch Symmetrie und Spurfreiheit aus. Technisch realisiert wird die Gradiometrie über skalierte Beschleunigungsdifferenzen zwischen frei fallenden Testmassen. Mittels der Kombination aus sechs dreidimensionalen Beschleunigungsmessern lässt sich der volle Gravitationstensor im dreidimensionalen Raum aufstellen. Herkömmlicherweise erfolgt die Gravitationsfeldbestimmung aus SGG Beobachtungen durch die Analyse einzelner GG. Dabei wird für jeden beobachteten GG der (lineare) funktionale Zusammenhang zu den unbekannten Gravitationsfeldparametern hergestellt. Es ergibt sich folglich für jeden GG eine individuelle Beobachtungsgleichung. Dieser Ansatz wird hier als die klassische Vorgehensweise betrachtet. Sie kommt ohne die Orientierung des Gravitationstensors relativ zum Referenzsystem der Gravitationsfeldmodellierung nicht aus, da die einzelnen GG abhängig von der Lage des Gradiometersystems im Raum sind. Alternativ dazu befasst sich der erste Teil dieser Arbeit mit der theoretischen Gravitationsfeldanalyse basierend auf den Rotationsinvarianten des Gravitationstensors. Diese Größen verhalten sich invariant gegenüber orthogonalen Transformationen und lassen sich damit unabhängig von der Orientierung des Gravitationstensors formulieren. Andererseits ist die Invariantendarstellung mit einer Reihe von Erschwernissen verbunden. Die nicht-linearen Funktionale des Gravitationspotenzials verlangen eine entsprechende Linearisierung. Daran gekoppelt ist ein iterativer Lösungsprozess. Dabei ist eine effiziente Linearisierungsstrategie maßgeblich von drei Faktoren abhängig: einem möglichst kleinen Linearisierungsfehler, schnellem Konvergenzverhalten und einem geringen numerischen Aufwand. Es stellt sich heraus, dass die Linearisierung in Form einer Störungsrechnung alle drei Kriterien erfüllt. Darüber hinaus gründet die Invariantendarstellung auf der Volltensorgradiometrie. Dies impliziert, dass sämtliche GG mit möglichst gleicher Genauigkeit verfügbar sein müssen. Eine derartige Annahme kann jedoch nicht grundsätzlich vorausgesetzt werden. Um die Volltensorgradiometrie allgemeingültiger zu gewährleisten, wird deshalb die synthetische Berechnung unbeobachteter GG untersucht. Aktuelles Interesse erfährt die Satellitengradiometrie derzeit vorrangig durch den geplanten Start der Mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) im Frühjahr 2008. Die numerischen Beispiele der Invariantendarstellung basieren auf einer Simulationsrechnung dieses Szenarios. Die Güte der erhaltenen Lösungen wird gegenüber den Ergebnissen unter Anwendung des klassischen Analyseverfahrens von SGG Beobachtungen abgegrenzt. So widmet sich der zweite Teil dieser Arbeit der rechentechnischen Umsetzung der Gravitationsfeldanalyse. Die auftretenden Gleichungssysteme werden nach der Methode der kleinsten Quadrate gelöst. Neben der direkten Lösungsmethode durch Inversion des Normalgleichungssystems nimmt hier das iterative LSQR (Least-Squares unter Verwendung einer QR Zerlegung) Verfahren eine zentrale Rolle ein. Es stellt nur geringe speichertechnische Anforderungen. Des weiteren ist es hinsichtlich der parallelen Implementierung auf Multiprozessor-Plattformen weitaus systemunabhängiger und effizienter als die direkte Lösungsmethode. Das LSQR Verfahren wird für dessen wirtschaftlichen Einsatz in der Gravitationsfeldbestimmung angepasst bzw. erweitert. Zentrale Aspekte sind in diesem Zusammenhang die Regularisierung und Präkonditionierung. Während die Regularisierung Einfluss auf die Güte der Lösung nimmt, zielt die Präkonditionierung auf das beschleunigte Konvergenzverhalten des iterativen Prozesses ab. Weiterhin werden die entsprechenden Konzepte und Ergebnisse der parallelen Implementierung aufgezeigt. Die Umsetzung der Algorithmen erfolgt auf Hochleistungsrechnern des Höchstleistungsrechenzentrums Stuttgart (HLRS) und des Center for Computing and Networking Services in Amsterdam (SARA). Tatsächlich blieben umfassende Simulationsrechnungen der Invariantendarstellung mit Hinblick auf die Satellitengradiometrie bisher aus. Diese Lücke wird mit der vorliegenden Arbeit geschlossen. Die Kombination aus physikalisch-mathematischer Modellbildung und effizienter numerischer Umsetzung demonstriert letztlich die erfolgreiche Handhabung der Invariantendarstellung in der Satellitengradiometrie.
Open Access
Performance evaluation of different satellite radar altimetry missions for monitoring inland water bodies
(2017) Roohi, Shirzad; Sneeuw, Nico (Prof. Dr.-Ing.)
Inland water bodies, e.g. lakes and rivers, play vital roles in society and in nature. Moreover, these water bodies can be considered as integrators of environmental change to study climate effects and hydrological cycle at global and regional scales. Because changes in the water level of lakes and rivers indicate changes in climatic parameters, such as precipitation and evaporation, it is necessary to monitor water level variation of inland water bodies continuously to understand long term changes. Traditional methods, e.g. using in-situ gauges, provide precise water level determination. But they can not monitor these water bodies in a way that today’s human needs are to be satisfied, because in-situ gauge networks do not cover all inland water bodies and their data are not publicly available. Furthermore, they are expensive to install and to maintain, especially in remote areas. In-situ gauge networks follow national policy and there is not a unified data base of their measurements. Satellite altimetry as a space-borne technology helps us to partially solve the issue of water level monitoring. This technique was originally designed to observe ocean water surface. But due to advances in satellite radar systems and in data processing methodologies, the application of satellite altimetry has been extended to monitor small lakes and narrow rivers over the past 20 years. So far, studying water level variations of inland water bodies has been a challenge for satellite altimeters in terms of spatial and temporal resolution as well as accuracy of water level determination. Due to a relatively large radar footprint, the illuminated area inside the footprint can be inhomogeneous, i.e. consisting of water, land and vegetation. Therefore, responses to the radar pulses from such a surface are complex and lead to multi-peak waveforms (corrupted waveforms). Seriously corrupted waveforms need to be analyzed to extract optimal ranges. Retracking is an effective method to improve the accuracy of the range measurement from contaminated waveforms and, consequently, to determine a more accurate water level. The design of an optimal retracking algorithm appropriate for a specific inland water body is very important in this respect. The quality of retracked water level depends on the type of altimeters and on the algorithm that is used in the retracking process. Moreover, the shape and size of the inland water bodies can affect the quality of the water level determination. In this thesis, we analyzed the waveforms in two different ways: full-waveform and sub-waveform retracking. For this purpose, different physical and empirical retracking algorithms have been employed to retrack the waveforms. In full-waveform retracking, for a given waveform one retracked range correction is estimated. But in sub-waveform retracking more than one retracked range correction can be calculated. We analyze all sub-waveforms in a given waveform and select the optimal one to retrack and consequently to determine water level variations. Three different analyses have been performed to select the optimal sub-waveform. In the first analysis we retracked only the first sub-waveform for all of the waveforms. In the second analysis all detected sub-waveforms in a given waveform are retracked to calculate the mean retracked range correction. In the last analysis we retrack the sub-waveform that provides the water level with minimum RMS with respect to model fits. For a given satellite, first we determine the water level according to on-board retrackers. The results of the on-board retrackers have been validated against available in-situ gauge data to find the best on-board retracker. Then, the full and sub-waveforms have been processed by different retracking algorithms to define the retracked water level. The retracked water level derived from different retracking scenarios have been compared with in-situ gauge data to evaluate the accuracy of each scenario. Finally, the results of the best on-board retracker were compared with the results from post-processing the waveforms to find the most accurate water level estimator. Radar characteristics and geometry of the satellite orbit, that affect on the altimeter’s performance, are designed based on main objectives of a given mission. Monitoring inland water bodies have not been the main objectives for the altimetry missions till now. We therefore do our analysis over data from different altimeters and evaluate their performance in water level monitoring of different inland water bodies. To complete our analysis, a comparison between different satellite altimeters has been performed to assess the performance of each altimeter in continental water level determination. We selected challenging objects with different shapes and sizes in different continents. For a given object, two or three satellite altimetry data sets have been analyzed to study water level variations. We used different satellite altimetry missions in our study, divided into pulse-limited and beam-limited altimeters. For the pulse-limited altimeters we selected Envisat, Jason-2, SARAL and CryoSat-2 LRM and for the beam-limited ones we used CryoSat-2 SAR and SARI n modes and I CES at satellite altimeters. GDR and SGDR data of these altimeters have been analyzed over four lakes: Neagh (Northern Ireland), Nasser (Egypt), Urmia (Iran) and Qinghai (China). We also analyzed the same data type of Envisat, Jason-2 and SARAL missions over different sections of the Danube river. We have found that over inland water bodies it is necessary to retrack the waveforms to achieve a qualified water level determination. Comparing the results from the on-board retrackers with those of the post-processed waveforms indicates that there tracked water level is more accurate. Our numerical results of the waveform retracking show that the sub-waveform outperforms the full-waveform especially over small lakes and complex shape (even large) lakes as well as over narrow rivers, e.g. Danube river. Over lakes Neagh and Nasser the beam-limited altimeters show better performance than the pulse-limited altimeters. In the case of Urmia lake, we analyzed only pulse-limited altimeters. Envisat provides the water level more accurately than CryoSat-2 LRM . Over Qinghai lake, covered by beam- and pulse-limited altimeters, both Envisat and CryoSat-2 LRM have the same performance. They show better performance than I CES at. Over Danube river, Envisat and SARAL show the same performance which is better than that of Jason-2. If we compare the results of all retracking scenarios for all missions, we can conclude that the mean sub-waveform retracked with the threshold retracker is the best retracking scenario to monitor small and complex shape inland water bodies. The first sub-waveform retracked with this retracker is an alternative scenario for the inland water bodies.
Open Access
Sampling the earth's time-variable gravity field from satellite orbit : design of future gravity satellite missions
(2013) Iran Pour, Siavash; Sneeuw, Nico (Prof. Dr.-Ing.)
The launch of the GRACE mission has generated a broad interest within the geophysical community in the detection of temporal gravity fields and their applications, e.g. the detection of ice mass loss over Greenland and Antarctica, the hydrological cycle over Amazon and central Africa and the estimation of sea level rise. However the spatio-temporal resolution of GRACE solutions is limited by a restricted sensitivity of the metrology system, the reduced isotropy of the inline leader-follower formation (which mainly manifests itself in a North-South striped error pattern) and the temporal aliasing of high frequency time variable geophysical signals into the long time-interval solutions. When using high quality sensors in future gravity missions, aliasing of the high frequency (short period) geophysical signals to the lower frequency (longer period) signals is one of the most challenging obstacles. Two sampling theorems mainly govern the space-time sampling of a satellite-mission: (i) a Heisenberg-type principle in satellite geodesy which states that the product of spatial resolution and time resolution is constant, and (ii) the Colombo-Nyquist rule (CNR), which requires the number of satellite revolutions in the full repeat-cycle to be equal at least twice the maximum spherical harmonic degree to be detected. The latter rule, therefore, limits the spatial resolution of the solution. This study investigates the quality of sub-Nyquist recoveries, i.e. solutions from time intervals shorter than required by CNR, of different orbit configurations and satellite formations. In particular, the dependence of such quality on the measurement duration and ground-track patterns is investigated. It is shown that (i) the number of observations with specific coverage of the Earth by a satellite configuration (as indicated by a modified Colombo-Nyquist rule), (ii) the mission altitude and (iii) avoidance of large unobserved gaps by satellite ground-track patterns have the most important effect on the quality of the recoveries. The sub-cycle concept apparently does not play an important role in assessing the quality. Moreover, the study investigates the modified Colombo-Nyquist rule for two pairs of satellites, where the number of revolutions by both satellite pairs is taken into account. It is also found that sub-Nyquist recoveries by such double pair scenarios outperform the ones from single inline satellite missions with twice the size of time intervals. It is indeed expected that using an inclined satellite mission, together with a near-polar mission, adds East-West measurement component to the North-South component of the near-polar satellite mission. Furthermore, the short time interval recoveries suffer less from temporal aliasing of certain time-variable gravity field components. Consequently, it means that the recovery also benefits from higher time resolution. The gravity recovery simulations of this study are based on a quick-look tool, developed at the Institute of Geodesy, University of Stuttgart. The closed-loop simulation tool assumes a nominal repeat orbit for a satellite mission. Based on the quality assessment of the recoveries and the technical concerns with the implementation of formation flights, a near-polar moderate pendulum formation with an opening angle of less than 10°, approximately 300 km altitude and almost homogeneous gap evolution is suggested for a next generation of single pair gravity mission. For double pair satellite missions, a combination of a near-polar inline or moderate pendulum and a 72° inclined inline pair is recommended. The suggested optimal scenarios of this study are selected through the quality assessment of sub-Nyquist gravity recoveries of different configurations. It is also shown that the quality of the sub-Nyquist gravity recoveries can be improved by employing post processing tools. The post-processing tools of this research study include a white noise filter, based on EOF+KS-Test analysis and a regularization method which can handle all kinds of noise. The tools are employed to deal with the poorer quality of short-time interval recoveries due to the spatial aliasing, although it is almost impossible to remove all noise without diminishing some of the real signals.
Open Access
Understanding and repairing the signal damage due to filtering of mass change estimates from the GRACE satellite mission
(2017) Vishwakarma, Bramha Dutt; Sneeuw, Nico (Prof. Dr.-Ing.)
Filtering noisy observations to extract meaningful information is an old and necessary exercise for engineers and scientists. Filtering affects both the signal and the noise. While the noise is reduced to a minimum, the filtered observation is a smoothed representation of the true signal. The amount and type of smoothing required depends on the noise level. The geodetic satellite mission, GRACE provides heavily contaminated time variable gravity field of the Earth. Therefore, we have to use a strong smoothing operator before the data can be used. Over the past decade, many types of filters have been developed for treating the noisy GRACE products, which damages the signal. Therefore, along with filters, a number of methods to restore the signal damage have emerged. However, the majority of these methods use hydrological models to compute correction terms, such as leakage, bias, or scale factors, in a setup that lacks a detailed mathematical understanding. We fill this gap by studying the convolution integral on the sphere, with a motivation to revert the signal changes in filtered GRACE products. Since the dominant time varying signal observed by GRACE comes from mass transports in the hydrosphere, we analyze the impact of filtering on catchment scale hydrology. We discuss the convolution integral in the spatial domain, which helps us to break the total impact of filtering into two parts: leakage and attenuation of catchment-confined signal, where leakage is only the contribution of signal from outside the catchment. We find that leakage changes the amplitude as well as the phase of the catchment-confined filtered signal. Previous contributions have addressed only the amplitude change due to filtering, usually with the help of a hydrological model. This practice propagates the error and the uncertainties in models to the corrected GRACE products. Therefore, we advocate avoiding models for computing correction terms. A mathematical dissection of the convolution integral leads us to two methods for approaching the true regional average: the method of scale and the method of deviation. The method of scale uses the uniform layer approximation, while the method of deviation avoids any approximation. In a noise-free closed-loop test, we show that the method of scale is able to approach the truth, while the method of deviation gives us the true value. These methods need accurate knowledge of leakage and the deviation integral, which are estimated in a data-driven framework employing once filtered and twice filtered GRACE fields. In a closed-loop simulation environment with GRACE-type noise, we demonstrate for 32 catchments that we are able to approach the true leakage and the true deviation integral. The efficacy of data-driven method of deviation is found to be superior to three popular model dependent approaches. After being satisfied with data-driven methods for hydrology, we intend to use them for assessing the ice mass loss in ice sheets such as Antarctica and Greenland, but we find that they fail for ice sheets. This is due to the physical difference between the spatial mass change distribution in an ice sheet and in a hydrological catchment: the former suffers from a mass change concentrated near coast, while the later experiences a mass change throughout the catchment. Therefore, we tailor a new approximation for ice sheets giving us the data-driven method for ice sheets. It is tested effective in a noisy closed-loop simulation environment. The data-driven methods are used to correct the filtered GRACE products and to analyze the total water mass loss over Aral sea, lake Urmia, lake Victoria, California, Antarctica, and Greenland. We report and compare our findings with previously reported figures. We find that the long term trend in mass change is suppressed by filtering, and overestimated by model dependent approaches. This thesis explores the signal damage at catchment scale due to filtering of GRACE products, and develops data-driven methods to repair the signal damage. In a realistic closed-loop simulation environment, we demonstrate that the corrected signal is closer to truth. The performance decays with the catchment size, but is still better than model dependent approaches. Furthermore, the data-driven method is less accurate over arid regions (desert), however, the performance is on a par with the model dependent methods. Nevertheless, we extract our confidence from the overall performance of the data-driven methods in closed-loop environments to believe that we get superior mass change estimates from GRACE. This contribution helps us to reduce the filtering induced uncertainty in GRACE products.
Open Access
Understanding filtering on the sphere : experiences from filtering GRACE data
(2015) Devaraju, Balaji; Sneeuw, Nico (Prof. Dr.-Ing.)
Geodesists employ signal processing techniques on the sphere to analyse gravity field data, and the primary mathematical tool of choice has been the spherical harmonics. Harmonic analysis and synthesis were the predominant signal processing techniques that were employed. However, with the launch of the Gravity Recovery And Climate Experiment (GRACE) satellite mission, there was a strong need for low-pass filtering techniques as the grace data is heavily contaminated with noise. Now, after a decade since the launch there is a garden of filters that have been proposed, which has brought with it the problem of filter choice. It is in this context that this study would like to understand the anatomy of low-pass linear filters, their mechanics of filtering, and measure their performance that will enable consistency in the choice of a filter for the problem in hand. When applying filters there is always a question of choice, and from the experiences in filtering GRACE, it can be said that the output is heavily influenced by the chosen filter. Irrespective of the filter chosen, filtering smudges part of the signal in addition to smoothing out noise, and the amount of signal lost depends on the filter. In order to assess the suitability of a filter and to understand its behaviour, a framework has been developed. The framework consists of a set of metrics designed on the basis of the energy of the filters and log-normal of the filter weights. This thesis elucidates a number of attributes of the filters and filtering on the sphere. It makes positive strides in the direction of understanding the mechanics of linear low-pass filtering on the sphere, especially with respect to resolution and leakage. Further, it also puts forth a set of metrics that provide a generic understanding of the filter in hand, enabling appropriate filter choice.
Open Access
Understanding ocean tide aliasing in satellite gravimetry
(2019) Liu, Wei; Sneeuw, Nico (Prof. Dr.-Ing.)