06 Fakultät Luft- und Raumfahrttechnik und Geodäsie
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/7
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Item 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.Item Open Access Application of spaceborne geodetic sensors for hydrology(2013) Tourian, Mohammad J.; 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.