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Open Access
July 19, 2012
Abstract
Analysis of water level variations in Brazilian basins using GRACE A comparison between daily in-situ water level time series measured at ground-based hydrometric stations (HS - 1,899 stations located in twelve Brazilian basins) of the Agência Nacional de Águas (ANA) with vertically-integrated water height anomaly deduced from the Gravity Recovery and Climate Experiment (GRACE) geoid is carried out in Brazil. The equivalent water height (EWH) of 10-day intervals of GRACE models were computed by GRGS/CNES. It is a 6-year analysis (July-2002 to May-2008). The coefficient of determination is computed between the ANA water level and GRACE EWH. Values higher than 0.6 were detected in the following basins: Amazon, north of Paraguay, Tocantins-Araguaia, Western North-East Atlantic and north of the Parnaíba. In the Uruguay (Pampas region) and the west of São Francisco basins, the coefficient of determination is around 0.5 and 0.6. These results were adjusted with a linear transfer function and two second degree polynomials (flood and ebb period) between GRACE EWH and ANA water level. The behavior of these two polynomials is related to the phase difference of the two time series and yielded four different types of responses. This paper shows seven ANA stations that represent these responses and relates them with their hydro-geological domain.
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Open Access
July 19, 2012
Abstract
Validation of recent GOCE/GRACE geopotential models over Khartoum state - Sudan This paper evaluates a number of latest releases of GOCE/GRACE global geopotential models (GGMs) using the GPS-levelling geometric geoid heights, terrestrial gravity data and existing local gravimetric models. We investigate each global model at every 5 degree of spherical harmonics. Our analysis shows that the satellite-only models derived by space-wise and time-wise approaches (SPW_R1, SPW_R2 TIM_R1 and TIM_R2), GOCO01S together with EGM08 (combined model) are very distinct and consistent to the local data, which guarantees one of them to be selected as the best of candidate models and then to be utilized in our further geoid studies. One of Satellite-only models will be employed for acquiring the long wavelength geoid component which is one of major steps in the geoid determination. EGM08 will be used to compensate and restore the missing gravity data points in the un-surveyed parts within the target area. We expect further improvements in geoid studies in Sudan due to the improved medium wavelength part of the gravity field from GOCE mission.
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Modifying Cadzow's algorithm to generate the optimal TLS-solution for the structured EIV-Model of a similarity transformation In 2005, Felus and Schaffrin discussed the problem of a Structured Errors-in-Variables (EIV) Model in the context of a parameter adjustment for a classical similarity transformation. Their proposal, however, to perform a Total Least-Squares (TLS) adjustment, followed by a Cadzow step to imprint the proper structure, would not always guarantee the identity of this solution with the optimal Structured TLS solution, particularly in view of the residuals. Here, an attempt will be made to modify the Cadzow step in order to generate the optimal solution with the desired structure as it would, for instance, also result from a traditional LS-adjustment within an iteratively linearized Gauss-Helmert Model (GHM). Incidentally, this solution coincides with the (properly) Weighted TLS solution which does not need a Cadzow step.
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Polyaxial figures of the Moon from the lunar reconnaissance orbiter laser altimetry and multi-mission synthesis of the lunar shape Last decade witnessed a plethora of missions to the Moon by China (Chang'E-1 and Chang-E-2), Japan (SELenological and ENgineering Explorer, SELENE), India (Chandrayaan-1) and USA (Lunar Reconnaissance Orbiter), all carried out laser altimetry measurements. This study is a follow up to a series of earlier investigations that produced a number of new models to represent the gross geometric shape of the Moon using Unified Lunar Control 2005, Chang'E-1, and SELENE laser altimetry data using the Lunar Reconnaissance Orbiter laser altimetry measurements. The symmetric and asymmetric polyaxial geometric models derived from Lunar Reconnaissance Orbiter laser altimetry data, namely, three, four and six-axial lunar figure parameters, are compared and contrasted with the corresponding model parameters estimated from the Chang'E-1 and SELENE laser altimetry. All solutions produced geometric shape, orientation parameters, and the parameters of the geometric center of lunar figure with respect to the center of mass of the Moon showing remarkable agreement with each other within 100 m. A combined solution by the fusion of uniformly sampled laser altimetry data from all three missions produced the best estimates for the lunar shape, orientation, and lunar center of figure parameters, and their realistic error estimates.
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Open Access
August 13, 2012
Abstract
Weighted total least squares formulated by standard least squares theory This contribution presents a simple, attractive, and flexible formulation for the weighted total least squares (WTLS) problem. It is simple because it is based on the well-known standard least squares theory; it is attractive because it allows one to directly use the existing body of knowledge of the least squares theory; and it is flexible because it can be used to a broad field of applications in the error-invariable (EIV) models. Two empirical examples using real and simulated data are presented. The first example, a linear regression model, takes the covariance matrix of the coefficient matrix as Q A = Q n ⊗ Q m , while the second example, a 2-D affine transformation, takes a general structure of the covariance matrix Q A . The estimates for the unknown parameters along with their standard deviations of the estimates are obtained for the two examples. The results are shown to be identical to those obtained based on the nonlinear Gauss-Helmert model (GHM). We aim to have an impartial evaluation of WTLS and GHM. We further explore the high potential capability of the presented formulation. One can simply obtain the covariance matrix of the WTLS estimates. In addition, one can generalize the orthogonal projectors of the standard least squares from which estimates for the residuals and observations (along with their covariance matrix), and the variance of the unit weight can directly be derived. Also, the constrained WTLS, variance component estimation for an EIV model, and the theory of reliability and data snooping can easily be established, which are in progress for future publications.
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Regional sea level change and variability in the Caribbean sea since 1950 We investigate the regional variability in sea level in the Caribbean Sea region over the past 60 years (1950-2009) using an Empirical Orthogonal Function (EOF)-based 2-dimensional past sea level reconstruction (a mean of 3 reconstructions based on few long tide gauge records and different sea level grids from satellite altimetry and ocean circulation models) and satellite altimetry data for the last two decades. We find that over the past 60 years, the mean rate of sea level rise in the region was similar to the global mean rise (~1.8 mm/yr). The interannual mean sea level of the placeCaribbean region appears highly correlated with El Nino-Southern Oscillation (ENSO) indices. Interpolation of the sea level reconstruction grid at different sites, in particular at the Caribbean Islands where tide gauge records are either very short or inexistent, shows that locally, the sea level trend is on the order of 2 mm/yr, i.e. only slightly larger than the mean trend over the region. Besides, correlation with ENSO is in general good, especially since the mid-1980s. We also find a significant correlation between the interannual variability in sea level and hurricane activity, especially over the past decade during which hurricane intensity and sea level interannual variability have both increased.
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Validation of GOCE global gravity field models using terrestrial gravity data in Norway The GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite gravity gradiometry mission maps the Earth's gravity field. Harmonic analysis of GOCE observations provides a global gravity field model (GGFM). Three theoretical strategies, namely the direct, the space-wise and the time-wise approach, have been proposed for GOCE harmonic analysis. Based on these three methods, several GGFMs have been provided to the user community by ESA. Thereby different releases are derived from different periods of GOCE observations and some of the models are based on combinations with other sources of gravity field information. Due to the multitude of GOCE GGFMs, validation against independent data is a crucial task for the quality description of the different models. In this study, GOCE GGFMs from three releases are validated with respect to terrestrial free-air gravity anomalies in Norway. The spectral enhancement method is applied to avoid spectral inconsistency between the terrestrial and the GOCE free-air gravity anomalies. The results indicate that the time-wise approach is a reliable harmonic analysis procedure in all three releases of GOCE models. The space-wise approach, available in two releases, provides similar results as the time-wise approach. The direct approach seems to be highly affected by a-priori information.
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Open Access
August 13, 2012
Abstract
An evaluation of recent GOCE geopotential models in Brazil Several global geopotential models based on Gravity field and steady-state Ocean Circulation Explorer (GOCE) data have been published in the last two years. Some of these models use combinations of different satellite missions, while others use only GOCE data. This paper presents the evaluation and analysis of each approach using GOCE data in the Southeast of Brazil. Two assessments have been made. We compared the geoid heights derived from GOCE-based models with the geoidal heights from 176 GPS stations on leveling benchmarks. The findings show an improvement in GOCE-based models TIM_R3 (0.40 m) and DIR_R3 (0.39 m) for degree and order 210 in relation to EGM2008 (0.44 m) in terms of RMS. For the other models the results did not exceed 0.44 m. The second evaluation reports the comparison in terms of gravity disturbances between terrestrial gravity data and the models. The results, in terms of RMS and up to degree and order 210, indicate slightly low GOCO 02S values (10.34 mGal), TIM_R2 (10.37 mGal) and TIM_R3 (10.47 mGal) compared to EGM2008 (10.66 mGal). We also applied the residual terrain model and, as a result, the RMS errors were reduced by ~35% (~6.0 mGal) in the entire area and by ~45% in the mountain region.
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Mass balance and mass loss acceleration of the Greenland ice sheet (2002 - 2011) from GRACE gravity data We examine the magnitude and acceleration of the Greenland ice sheet mass loss between 2002 and 2011. We use monthly observations of time-variable gravity from the Gravity Recovery and Climate Experiment (GRACE) satellite gravity mission. The Greenland mass loss during this time period is not a constant, but accelerating with time. We have used a quadratic trend in addition to a linear trend, which is usually applied to the GRACE monthly time series of ice mass changes, to show that it better represents GRACE observations. Results of computations provide a mass decrease of -166±20 Gigatonne per year (Gt/yr) by using a linear trend and -111±21 Gt/yr by fitting a quadratic trend to the monthly time series. Quadratic fitting shows that the mass loss increases from -121 Gt/yr in 2002 - 2003 to -210 Gt/yr in 2006 - 2007 and -271 Gt/yr in 2010 - 2011 with an acceleration of -32±6 Gt/yr 2 in 2002 - 2011. This implies that the Greenland ice sheet contribution to sea level rise becomes larger with time. Contrary to recent studies, we use a non-isotropic filter whose degree of smoothing corresponds to a Gaussian filter with a radius of 340 km. Stripping effects in the GRACE data, C 20 effect, and leakage effects are applied.
