S U M M A R YMost applications of the publicly released Gravity Recovery and Climate Experiment monthly gravity field models require the application of a spatial filter to help suppressing noise and other systematic errors present in the data. The most common approach makes use of a simple Gaussian averaging process, which is often combined with a 'destriping' technique in which coefficient correlations within a given degree are removed. As brute force methods, neither of these techniques takes into consideration the statistical information from the gravity solution itself and, while they perform well overall, they can often end up removing more signal than necessary. Other optimal filters have been proposed in the literature; however, none have attempted to make full use of all information available from the monthly solutions. By examining the underlying principles of filter design, a filter has been developed that incorporates the noise and full signal variance-covariance matrix to tailor the filter to the error characteristics of a particular monthly solution. The filter is both anisotropic and nonsymmetric, meaning it can accommodate noise of an arbitrary shape, such as the characteristic stripes. The filter minimizes the mean-square error and, in this sense, can be considered as the most optimal filter possible. Through both simulated and real data scenarios, this improved filter will be shown to preserve the highest amount of gravity signal when compared to other standard techniques, while simultaneously minimizing leakage effects and producing smooth solutions in areas of low signal.
S U M M A R YThe DEOS Mass Transport release 1 (DMT-1) model has been produced on the basis of intersatellite K-band ranging data acquired by the GRACE satellite mission. The functional model exploited in the data processing can be considered as a variant of the acceleration approach. Each element of the data vector is defined as a linear combination of three successive range measurements and can be interpreted as the line-of-sight projection of a weighted average of intersatellite accelerations. As such, the data vector can be directly linked to parameters of the gravitational field. In this way, a series of unconstrained monthly gravity field solutions is produced, each of which is defined as a set of spherical harmonic coefficients complete to degree 120. At the post-processing stage, the unconstrained solutions are filtered with a statistically optimal Wiener-type filter based on full covariance matrices of noise and signal. As such, the DMT-1 model is free from along-track artefacts, which are typical for many other GRACE gravity models. The accuracy of the DMT-1 model has been analysed in different ways. First, the signals observed in areas with minimal mass variations (Sahara, East Antarctica and the middle of the Pacific Ocean) are analysed and interpreted as an upper bound of the noise in the DMT-1 model. It is concluded that the pointwise errors after filtering are of the order of 2-3 cm in terms of equivalent water heights. For the mean mass variations in an area of 10 6 km 2 , the corresponding error reduces to 1.5-2 cm. Second, a time-series of mass variations in the Marie Byrd Land (Antarctica) has been analysed, where the true signal (mostly caused by postglacial rebound) is expected to be close to a linear trend. The rms of the post-fit residuals is found to be 3.3 cm, which is consistent with the error analysis in areas with minimal mass variations. Thirdly, the DMT-1 model has been applied to estimate mass variations in [2003][2004][2005][2006] in Lake Victoria (Africa), where a large drop of water level is observed in recent years. The obtained linear trend (−31 ± 3 cm yr −1 ) is in good agreement with that derived from the satellite altimetry data (−35 ± 1 cm yr −1 ).
When using GRACE as a tool for hydrology, many different gravity field model products are now available to the end user. The traditional spherical harmonics solutions produced from GRACE are typically obtained through an optimization of the gravity field data at the global scale, and are generated by a number of processing centers around the world. Alternatives to this global approach include so-called regional techniques, for which many variants exist, but whose common trait is that they only use the gravity data collected over the area of interest to generate the solution. To determine whether these regional solutions hold any advantage over the global techniques in terms of overall accuracy, a range of comparisons were made using some of the more widely used regional and global methods currently available. The regional techniques tested made use of either spherical radial basis functions or single layer densities (i.e., mascons), with the global solutions having been obtained from the various major processing centers. The solutions were evaluated using a range of computed statistics over a selection of major river basins, which were globally distributed and ranged in size from 1 to 6 million km 2 .For one of the basins tested, the Zambezi, additional validation tests were conducted through comparisons against a custom designed regional hydrology model of the region. We could not prove that current regional models perform better than global ones. Monthly mean water storage variations agree at the level of 0.02 m equivalent water height. The differences in terms of monthly mean water storage variations between regional and global solutions are comparable with the differences among only global or regional solutions. Typically they reach values of 0.02 m equivalent water heights, which seems to be the level of accuracy of current GRACE solutions for river basins above 1 million km 123Surv Geophys (2008) 29:335-359 DOI 10.1007 The amplitudes of the seasonal mass variations agree at the sub-centimetre level. Evident from all of the comparisons shown is the importance that the choice of regularization, or spatial filtering, can have on the solution quality. This was found to be true for global as well as regional techniques.
In general, China is short of water resources and some regions even experience a shortage of daily water supply. This could threaten the stability and economic development of the nation. A study on the water storage variations is especially important for the water management and storage prediction in three largest river basins of China, namely, Yangtze, Yellow, and Zhujiang, where the most dense population and leading economic regions are located. The satellite gravity mission GRACE (Gravity Recovery and Climate Experiment) provides an opportunity to macroscopically identify water (or mass) variations in the Earth's system with a spatial resolution of 300-400 km and a temporal resolution of about one month. We use the first release of the DEOS (Delft Institute of Earth Observation and Space Systems) Mass Transport (DMT-1) model based on GRACE data to analyze water storage changes in the three river basins. The DMT-1 model consists of monthly solutions, which are computed using an innovative methodology. The methodology includes, in particular, the application of a statistically optimal Wiener-type filter based on full variance-covariance matrices of noise and signal. This results in particularly sharp mass variation maps. Taking one monthly solution as an example, we compare the results derived from the DMT-1 model with ones produced with the standard post-processing scheme based on a combination of the de-striping and Gaussian filtering. The comparison shows that the DMT-1 model outperforms the other models and is suitable for the analysis of the mass changes in river basins. A subset of the DMT-1 solutions in the interval between February 2003 and May 2008 is used to estimate the secular trends and seasonal variations for the three river basins. The estimated trends show that the water storage of the Yellow River basin does not have significant changes, while the Zhujiang and Yangtze river basins have a large and statistically significant water storage increase. The estimation of seasonal variations demonstrates that the water storage variations in Yangtze and Zhujiang river basins are almost in the same phase. The amplitude of variations in the Zhujiang River basin is larger than that in Yangtze. No clear annual variations are observed in the Yellow River basin. The observed water storage variations generally coincide with the observations and conclusions presented in the hydrological reports of the Chinese Ministry of Water Resources.GRACE, DMT-1, water storage variation, equivalent water layer thickness, Yangtze-Yellow-Zhujiang river basins, secular and seasonal variation Citation:Zhao Q L, Liu X L, Ditmar P, et al. Water storage variations of the Yangtze, Yellow, and Zhujiang river basins derived from the DEOS Mass Transport (DMT-1) model.
Proper characterization of test setups used in industry for testing and traceable measurement of lighting devices by the substitution method is an important task. According to new standards for testing LED lamps, luminaires and modules, uncertainty budgets are requested because in many cases the properties of the device under test differ from the transfer standard used, which may cause significant errors, for example if a LED-based lamp is tested or calibrated in an integrating sphere which was calibrated with a tungsten lamp. This paper introduces a multiple transfer standard, which was designed not only to transfer a single calibration value (e.g. luminous flux) but also to characterize test setups used for LED measurements with additional provided and calibrated output features to enable the application of the new standards.
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