MINQUE for block diagonal bordered systems such as those encountered in VLBI data analysis

A sparse matrix method is developed for computing variance factors for block-diagonal, bordered systems of equations using MINQUE (Minimum Norm Quadratic Unbiased Estimation). This method greatly reduces the computational effort required to apply MINQUE, thus making it practical to compute variance factors for some very large systems of equations. The computer implementation of the method is described and applied to the computation of variance factors for a combination of 1609 VLBI (Very Long Baseline Interferometry) observing sessions. The purpose of this test was to compute a variance factor for each of the data sets and, perhaps, to obtain more realistic variance estimates to replace those in common use for the analysis of VLBI data. It was found that the method is satisfactory for use with such large problems, and the test served to verify that the variances in current use in VLBI data adjustments are adequate. Received: 26 November 1996 / Accepted: 12 December 1997     

An assessment of chlorophyll-a concentration spatio-temporal variation using Landsat satellite data,in a small tropical reservoir

Traditional approaches to monitoring aquatic systems are often limited by the need for data collection which often is time-consuming, expensive and non-continuous. The aim of the study was to map the spatio-temporal chlorophyll-a concentration changes in Malilangwe Reservoir, Zimbabwe as an indicator of phytoplankton biomass and trophic state when the reservoir was full (year 2000) and at its lowest capacity (year 2011), using readily available Landsat multispectral images. Medium-spatial resolution (30 m) Landsat multispectral Thematic Mapper TM 5 and ETM+ images for May to December 1999–2000 and 2010–2011 were used to derive chlorophyll-a concentrations. In situ measured chlorophyll-a and total suspended solids (TSS) concentrations for 2011 were employed to validate the Landsat chlorophyll-a and TSS estimates. The study results indicate that Landsat-derived chlorophyll-a and TSS estimates were comparable with field measurements. There was a considerable wet vs. dry season differences in total chlorophyll-a concentration, Secchi disc depth, TSS and turbidity within the reservoir. Using Permutational multivariate analyses of variance (PERMANOVA) analysis, there were significant differences (p < 0.0001) for chlorophyll-a concentration among sites, months and years whereas TSS was significant during the study months (p < 0.05). A strong positive significant correlation among both predicted TSS vs. chlorophyll-a and measured vs. predicted chlorophyll-a and TSS concentrations as well as an inverse relationship between reservoir chlorophyll-a concentrations and water level were found (p < 0.001 in all cases). In conclusion, total chlorophyll-a concentration in Malilangwe Reservoir was successfully derived from Landsat remote sensing data suggesting that the Landsat sensor is suitable for real-time monitoring over relatively short timescales and for small reservoirs. Satellite data can allow for surveying of chlorophyll-a concentration in aquatic ecosystems, thus, providing invaluable data in data scarce (limited on site ground measurements) environments.     

Non-stationary covariance function modelling in 2D least-squares collocation

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC.     

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.     

Mapping of aggregated floodplain plant communities using image fusion of CASI and LiDAR data

Combined optical and laser altimeter data offer the potential to map and monitor plant communities based on their spectral and structural characteristics. A problem unresolved is, however, that narrowly defined plant communities, i.e. plant communities at a low hierarchical level of classification in the Braun-Blanquet system, often cannot be linked directly to remote sensing data for vegetation mapping. We studied whether and how a floristic dataset can be aggregated into a few major discrete, mappable classes without substantial loss of ecological meaning. Multi-source airborne data (CASI and LiDAR) and floristic field data were collected for a floodplain along the river Waal in the Netherlands. Mapping results based on floristic similarity alone did not achieve highest levels of accuracy. Ordination of floristic data showed that terrain elevation and soil moisture were the main underlying environmental drivers shaping the floodplain vegetation, but grouping of plant communities based on their position in the ordination space is not always obvious. Combined ordination-based grouping with floristic similarity clustering led to syntaxonomically relevant aggregated plant assemblages and yielded highest mapping accuracies.     

Applications of AnnAGNPS model for soil loss estimation and nutrient loading for Malaysian conditions

The study evaluated the performance and suitability of AnnAGNPS model in assessing runoff, sediment loading and nutrient loading under Malaysian conditions. The watershed of River Kuala Tasik in Malaysia, a combination of two sub-watersheds, was selected as the area of study. The data for the year 2004 was used to calibrate the model and the data for the year 2005 was used for validation purposes. Several input parameters were computed using methods suggested by other researchers and studies carried out in Malaysia. The study shows that runoff was predicted well with an overall R² value of 0.90 and E value of 0.70. Sediment loading was able to produce a moderate result of R² = 0.66 and E = 0.49, nitrogen loading predictions were slightly better with R² = 0.68 and E = 0.53, and phosphorus loading performance was slightly poor with an R² = 0.63 and E = 0.33. The erosion map developed was in agreement with the erosion risk map produced by the Department of Agriculture, Malaysia. Rubber estates and urban areas were found to be the main contributors to soil erosion. The simulation results showed that AnnAGNPS has the potential to be used as a valuable tool for planning and management of watersheds under Malaysian conditions.     

Using spectral information from the NIR water absorption features for the retrieval of canopy water content

Canopy water content (CWC) is important for mapping and monitoring the condition of the terrestrial ecosystem. Spectral information related to the water absorption features at 970 nm and 1200 nm offers possibilities for deriving information on CWC. In this study, we compare the use of derivative spectra, spectral indices and continuum removal techniques for these regions. Hyperspectral reflectance data representing a range of canopies were simulated using the combined PROSPECT + SAILH model. Best results in estimating CWC were obtained by using spectral derivatives at the slopes of the 970 nm and 1200 nm water absorption features. Real data from two different test sites were analysed. Spectral information at both test sites was obtained with an ASD FieldSpec spectrometer, whereas at the second site HyMap airborne imaging spectrometer data were also acquired. Best results were obtained for the derivative spectra. In order to avoid the potential influence of atmospheric water vapour absorption bands the derivative of the reflectance on the right slope of the canopy water absorption feature at 970 nm can best be used for estimating CWC.     

Evaluation of the geometric stability and the accuracy potential of digital cameras — Comparing mechanical stabilisation versus parameterisation

Recent tests on the geometric stability of several digital cameras that were not designed for photogrammetric applications have shown that the accomplished accuracies in object space are either limited or that the accuracy potential is not exploited to the fullest extent. A total of 72 calibrations were calculated with four different software products for eleven digital camera models with different hardware setups, some with mechanical fixation of one or more parts. The calibration procedure was chosen in accord to a German guideline for evaluation of optical 3D measuring systems [VDI/VDE, VDI/VDE 2634 Part 1, 2002. Optical 3D Measuring Systems–Imaging Systems with Point-by-point Probing. Beuth Verlag, Berlin]. All images were taken with ringflashes which was considered a standard method for close-range photogrammetry. In cases where the flash was mounted to the lens, the force exerted on the lens tube and the camera mount greatly reduced the accomplished accuracy. Mounting the ringflash to the camera instead resulted in a large improvement of accuracy in object space. For standard calibration best accuracies in object space were accomplished with a Canon EOS 5D and a 35 mm Canon lens where the focusing tube was fixed with epoxy (47  μm maximum absolute length measurement error in object space). The fixation of the Canon lens was fairly easy and inexpensive resulting in a sevenfold increase in accuracy compared with the same lens type without modification. A similar accuracy was accomplished with a Nikon D3 when mounting the ringflash to the camera instead of the lens (52  μm maximum absolute length measurement error in object space). Parameterisation of geometric instabilities by introduction of an image variant interior orientation in the calibration process improved results for most cameras. In this case, a modified Alpa 12 WA yielded the best results (29  μm maximum absolute length measurement error in object space). Extending the parameter model with FiBun software to model not only an image variant interior orientation, but also deformations in the sensor domain of the cameras, showed significant improvements only for a small group of cameras. The Nikon D3 camera yielded the best overall accuracy (25  μm maximum absolute length measurement error in object space) with this calibration procedure indicating at the same time the presence of image invariant error in the sensor domain. Overall, calibration results showed that digital cameras can be applied for an accurate photogrammetric survey and that only a little effort was sufficient to greatly improve the accuracy potential of digital cameras.