Understanding the Spatial Variability of Chlorophyll a and Total Suspended Matter Distribution Along the Southwest Bay of Bengal Using In-Situ and OCM-2 & MODIS-Aqua Measurements

Spatial and temporal distribution of chlorophyll a (chl a) and Total Suspended Matter (TSM) and inter comparison of Ocean Color Monitor-2 (OCM-2) and Moderate Resolution Imaging Spectro-radiometer (MODIS-Aqua) derived chlorophyll a and TSM was made along the southwest Bay of Bengal (BoB). The in-situ chl a and TSM concentration measured during different seasons were ranged from 0.09 to 10.63 μgl^?1 and 11.04–43.75 mgl^?1 respectively. OCM-2 and MODIS derived chl a showed the maximum (6–8 μgl^?1) at nearshore waters and the minimum (0–1 μgl^?1) along the offshore waters. OCM-2 derived TSM imageries showed the maximum (50–60 mgl^?1) along the nearshore waters of Palk Strait and the moderate concentration (2–5 mgl^?1) was observed in the offshore waters. MODIS derived minimum TSM concentration (13.244 mgl^?1) was recorded along the offshore waters, while the maximum concentration of 15.78 mgl^?1 was found along the Kodiakarai region. The inter-comparison of OCM-2 and MODIS chl a data (R ² ?=?0.549, n?=?49, p?<?0.001, SEE?=?±0.117) indicate that MODIS data overestimates chl a concentration in the nearshore waters of the southern BoB compared to the OCM-2. The correlation between OCM-2 and MODIS-Aqua TSM data (R ² ?=?0.508, N?=?53, P?<?0.001 and SEE?=?±0.024) confirms that variation in the range of values measured by OCM-2 (2–60 mgl^?1) and the MODIS (13–16 mgl^?1) derived TSM values. Despite problems in range of measurements, persistent cloud cover etc., the launch of satellites like OCM-2 with relatively high spatial resolutions makes job easier and possible to monitor chl a distribution and sediment discharges on day to day basis in the southwest BoB.     

3-D Radargrammetric Modeling of RADARSAT-2 Ultrafine Mode: Preliminary Results of the Geometric Calibration

The geometry and the accuracy of the 3-D cartographic localization of RADARSAT-2 images are being evaluated as part of the Canadian Space Agency's Science and Operational Applications Research program. In a first step, the Toutin's 3-D physical model, previously developed for RADARSAT-1, was adapted to RADARSAT-2 sensor and applied to two ultrafine mode images (U2 and U25) acquired over an area in Beauport, Quebec. Both the 3-D modeling computed with only 12 ground control points and its geometric localization were evaluated with different check data: 1) independent check points; 2) the two quasi-epipolar images; 3) the two orthoimages; and 4) 1-m accurate orthophotos. All four results and validations are in agreement and confirm that the 3-D geometric localization and restitution accuracy are 1 m in planimetry and 2 m in elevation. The checked data error being included in these evaluations and the relative error computed from the quasi-epipolar comparison provided a high level of confidence that the precision of Toutin's 3-D radargrammetric model is better than 0.25 m.     

Singular value decomposition and cluster analysis as regression diagnostics tools for geodetic applications

It is well known that high-leverage observations significantly affect the estimation of parameters. In geodetic literature, mainly redundancy numbers are used for the detection of single high-leverage observations or of single redundant observations. In this paper a further objective method for the detection of groups of important and less important (and thus redundant) observations is developed. In addition, the parameters which are predominantly affected by these groups of observations are identified. This method thus complements other diagnostics tools, such as, e.g., multiple row diagnostics methods as described in statistical literature (see, e.g., Belsley et al. in Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York, 1980). The method proposed in this paper is based on geometric aspects of adjustment theory and uses the singular value decomposition of the design matrix of an adjustment problem together with cluster analysis methods for regression diagnostics. It can be applied to any geodetic adjustment problem and can be used for the detection of (groups of) observations that significantly affect the estimated parameters or that are of negligible impact. One of the advantages of the proposed method is the improvement of the reliability of observation plans and thus the reduction of the impact of individual observations (and outliers) on the estimated parameters. This is of particular importance for the very long baseline interferometry technique which serves as an application example of the regression diagnostics tool.     

The determination of potential difference by the joint application of measured and synthetical gravity data: a case study in Hungary

In an elementary approach every geometrical height difference between the staff points of a levelling line should have a corresponding average g value for the determination of potential difference in the Earth’s gravity field. In practice this condition requires as many gravity data as the number of staff points if linear variation of g is assumed between them. Because of the expensive fieldwork, the necessary data should be supplied from different sources. This study proposes an alternative solution, which is proved at a test bed located in the Mecsek Mountains, Southwest Hungary, where a detailed gravity survey, as dense as the staff point density (~1 point/34 m), is available along a 4.3-km-long levelling line. In the first part of the paper the effect of point density of gravity data on the accuracy of potential difference is investigated. The average g value is simply derived from two neighbouring g measurements along the levelling line, which are incrementally decimated in the consecutive turns of processing. The results show that the error of the potential difference between the endpoints of the line exceeds 0.1 mm in terms of length unit if the sampling distance is greater than 2 km. Thereafter, a suitable method for the densification of the decimated g measurements is provided. It is based on forward gravity modelling utilising a high-resolution digital terrain model, the normal gravity and the complete Bouguer anomalies. The test shows that the error is only in the order of 10⁻³mm even if the sampling distance of g measurements is 4 km. As a component of the error sources of levelling, the ambiguity of the levelled height difference which is the Euclidean distance between the inclined equipotential surfaces is also investigated. Although its effect accumulated along the test line is almost zero, it reaches 0.15 mm in a 1-km-long intermediate section of the line.     

Preprocessing of gravity gradients at the GOCE high-level processing facility

One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally below the gravity gradient error level, which is predicted to show a 1/f behaviour for low frequencies. In the outlier detection, the 1/f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate for the 1/f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow to estimate gravity gradient scale factors down to the 10⁻³ level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10⁻² level with this method.     

Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.     

Efficient propagation of error covariance matrices of gravitational models: application to GRACE and GOCE

We have applied efficient methods for computing variances and covariances of functions of a global gravity field model expanded in spherical harmonics, using the full variance–covariance matrix of the coefficients. Examples are given with recent models derived from GRACE (up to degree and order 150), and with simulated GOCE derived solutions (up to degree and order 200).     

Classical globally reflected gravity field determination in modern locally oriented multiscale framework

The purpose of this paper is the canonical connection of classical global gravity field determination following the concept of Stokes (Trans Camb Philos Soc 8:672–712, 1849), Bruns (Die Figur der Erde, Publikation Königl. Preussisch. Geodätisches Institut, P. Stankiewicz Buchdruckerei, Berlin, 1878), and Neumann (Vorlesungen über die Theorie des Potentials und der Kugelfunktionen. Teubner, Leipzig, pp 135–154, 1887) on the one hand and modern locally oriented multiscale computation by use of adaptive locally supported wavelets on the other hand. The essential tools are regularization methods of the Green, Neumann, and Stokes integral representations. The multiscale approximation is guaranteed simply as linear difference scheme by use of Green, Neumann, and Stokes wavelets. As an application, gravity anomalies caused by plumes are investigated for the Hawaiian and Iceland areas.