A procedure for testing the assumption of homoscedasticity in least squares residuals: a case study of GPS carrier-phase observations

Due to increased demands on the quality of the results of Global Positioning System (GPS) evaluations, various authors have studied improvements of the stochastic model of GPS carrier-phase observations. These improvements are based on the reasonable assumption that the commonly used stochastic model with independent and homoscedastic (i.e. equal variance) errors is unrealistic. However, this has not been proved rigorously so far. A statistical test procedure based on uncorrelated least–squares residuals, which allows verification of the hypothesis of a heterogeneous variance, is provided. The statistical test procedure is of interest in its own right, and is independent of the practical problem considered. The presented technique is applied to GPS carrier-phase observations. Results show that the variances of the investigated observations are far from homogeneous. It is indicated that the error variances of the presented data increase with decreasing GPS satellite elevation. These results confirm the assumption that the commonly used stochastic model of GPS observations is inadequate and has to be improved.     

Stratigraphy of the Middle Devonian boundary: Formal definition of the susceptibility magnetostratotype in Germany with comparisons to sections in the Czech Republic, Morocco and Spain

One major difficulty in geology is high-resolution correlation among widely separated sections, especially in the Paleozoic where magnetostratigraphy polarity is not well established because rocks are often remagnetized, where critical biostratigraphic zonation may be poor or lacking, or where structural complexities make correlations very difficult. To address this problem, we have been using magnetostratigraphy susceptibility measurements. Here, we report our work from the Middle Devonian in Europe and North Africa. The Middle Devonian (Emsian–Eifelian) global boundary stratotype section and point (GSSP), located in the Eifel Hills, western Germany, was ratified by the International Subcommission on Stratigraphy in 1985, after careful evaluation of the biostratigraphy for this and many other sections. The boundary interval has been characterized using biostratigraphy, and the beginning of the Eifelian stage has been specifically defined by the first occurrence of the conodont Polygnathus costatus partitus. We have collected the Eifel Hills section for magnetic susceptibility (MS) measurement and here we establish it as the magnetostratotype for the Emsian–Eifelian stage boundary, by formally defining the magnetostratigraphy susceptibility for the section. We then collected, measured and compared the magnetostratotype to four other sections for which conodont biostratigraphy has been studied and where P. costatus partitus is present; two Emsian–Eifelian sections in Morocco and two sections in the Czech Republic (including the Emsian–Eifelian parastratotype). Finally, we have measured the MS for the El Puerto Creek section in the Cantabrian Mountains of Spain and identified the location of the Emsian–Eifelian boundary within the section based on MS comparison to the GSSP in conjunction with excellent biostratigraphic indicators, primarily brachiopods. While the conodont zonation in the El Puerto Creek section is poorly defined, we believe that the correspondence between the MS and biostratigraphy in the section allows the identification of the Emsian–Eifelian boundary. These results indicate that this method can be successfully applied to marine sequences where ambiguities in correlation exist.     

A Procedure for Estimating the Variance Function of Linear Models and for Checking the Appropriateness of Estimated Variances: A Case Study of GPS Carrier-phase Observations

In many applications of linear model theory, homogeneous variances are assumed. In practice, however, the variances are frequently heterogeneous. Therefore, to improve the results, the unknown variances have to be estimated. The appropriateness of the estimated variances has then to be checked by a suitable statistical test procedure. Such a procedure is also useful to study models of global positioning system (GPS) carrier-phase observations. While the functional model of GPS carrier-phase observations is widely accepted, the stochastic model is still under development. As well as the neglected correlations of GPS observations, a homogenous variance function is frequently assumed. In Bischoff et al. (J Geod 78:397–404, 2005), we showed by statistical testing that the assumption of constant variances is not appropriate. In this paper, we give a procedure to estimate an individual variance function for a pair of satellites and a procedure to check the appropriateness of the estimated variances. As an example, the approach is applied to double-differenced carrier-phase GPS observations.     

Dissolution Enthalpies of Magnesian Calcites

A series of synthetic and biogenicmagnesian calcites was dissolved in weak acetic acidsolutions to measure the enthalpies of dissolution at25°C. For the synthetic phases, heat releasedwas 33.5 kJ/mol for calcite, decreasing to 33 kJ/molfor a phase of 2 mol % MgCO3, and increasing to35 kJ/mol for a phase of 15 mol %. Values of excessenthalpies, ΔHxs, calculated using calciteand magnesite end-members, average about -1 kJ/mol forthe synthetic phases. Total entropies of solidsolution formation, ΔSSS, also werecalculated using available data on Gibbs free energiesof formation and these excess enthalpies. Values ofΔSSS range from -2 J/(mol-K) at 2 mol % to-5 J/(mol-K) at 15 mol % MgCO3. These negativevalues of ΔHxs and ΔSSSsuggest that some form of ordering (cation?) isobtained in the synthetic phases, and that vibrationalentropies of the solid solution are diminished incomparison to the end-members. In contrast, biogenic samples generally have positivevalues of ΔHxs, increasing from +1 kJ/molat 5 mol % to +3 kJ/mol at 20 mol % MgCO3. Mostvalues of ΔSSS are equal (within errors)to values expected from configurational enthalpyalone. Thus, in most biogenic materials cationordering probably is not obtained, and most phases aremore typical of equivalent-site solid solutions.     

The critical point and two-phase boundary of seawater, 200–500°C

The two-phase boundary of seawater was determined by isothermal decompression of fully condensed seawater in the range of 200–500°C. The pressure at which phase separation occurred for each isotherm was determined by a comparison of the refractive index of fluid removed from the top and bottom of the reaction vessel. The critical point was determined to be in the range of 403–406°C, 285–302 bar and was located by the inflection in the two-phase boundary and by the relative volume of fluid and vapor as a function of temperature. The two-phase boundary of 3.2% NaCl solution was found to coincide exactly with that of seawater over the range tested in the present study. The boundary for both is described by a single seventh-order polynomial equation. The two-phase boundary defines the maximum temperature of seawater circulating at depth in the oceanic crust. Thus the boundary puts a limit of about 390°C for seawater circulating near the seafloor at active ocean ridges (2.5 km water depth), and about 465°C at the top of a magma chamber occurring at 2 km below the seafloor.     

Testing theories of the vertical stratification of the ACC against observations

Recent theories of the Antarctic Circumpolar Current (ACC) suggest that its lateral and vertical stratification is controlled by its baroclinic instability: eddies in the ACC not only feed-off the available potential energy stored in sloping isopycnals but play a central role is setting up that stratification. Simple theory makes predictions about how the depth of the thermocline in the ACC depends on the surface winds, the air–sea buoyancy flux and transfer by baroclinic eddies. By examining gridded hydrographic data, here we test some of these predictions against observations. We show that, to a remarkable degree, the buoyancy field in the ACC decays exponentially with depth beneath the mixed layer. The e-folding depth increases equatorward, from less than 500 m on the poleward flank of the ACC to greater then 1000 m on its equatorial flank, in a manner that is broadly consistent with the theory.     

Hydrological modelling in the anthroposphere: predicting local runoff in a heavily modified high-alpine catchment

Hydrological models within inflow forecasting systems for high-alpine hydropower reservoirs can provide valuable information as part of a decision support system for the improvement of hydropower production or flood retention. The information, especially concerning runoff, is however rarely available for the calibration of the hydrological models used. Therefore, a method is presented to derive local runoff from secondary information for the calibration of the model parameters of the rainfallrunoff model COSERO. Changes in water levels in reservoirs, reservoir outflows, discharge measurements at water intakes and in transport lines are thereby used to derive the local, “natural” flow for a given sub-catchment. The proposed method is applied within a research study for the ÖBB Infrastructure Railsystem division in the Stubache catchment in the central Austrian Alps. Here, the ÖBB operates the hydropower scheme “Kraftwerksgruppe Stubachtal”, which consists of 7 reservoirs and 4 hydropower stations. The hydrological model has been set up considering this human influences and the high natural heterogeneity in topography and land cover, including glaciers. Overall, the hydrological model performs mostly well for the catchment with highest NSE values of 0.78 for the calibration and 0.79 for the validation period, also considering the use of homogeneous parameter fields and the uncertainty of the derived local discharge values. The derived runoff data proved to be useful information for the model calibration. Further analysis, examining the water balance and its components as well as snow cover, showed satisfactory simulation results. In conclusion, a unique runoff dataset for a small scale high-alpine catchment has been created to establish a hydrological flow prediction model which in a further step can be used for improved and sustainable hydropower management.     

Local effects of blue mussels around turbine foundations in an ecosystem model of Nysted off-shore wind farm, Denmark

The development of off-shore wind farms along the coastline of north-west Europe is rapidly increasing; it is therefore important to study how this will affect the marine environment. The present study modelled the growth and feed-backs of blue mussels in natural beds and on turbine foundations in an off-shore wind farm (OWF) located in a shallow coastal ecosystem by coupling a dynamic energy budget (DEB) model to a small-scale 3D hydrodynamic–biogeochemical model. The model results showed that blue mussels located higher up in the water column on turbine pillars achieved a 7–18 times higher biomass than those located on the scour protection because the former experience an enhanced advective food supply. Secondly, the high biomasses of blue mussels on foundations created local ‘hot spots’ of biological activity and changed ecosystem dynamics due to their feed-backs e.g. ingestion of microplankton and copepods, excretion of ammonium and egestion of faecal pellets. The model results were supported by field measurements around foundations of Chl a concentrations and biomasses of the fauna community. Our study emphasised that OWFs seem to be particularly favourable for blue mussels in the western Baltic Sea and that the functioning of the OWFs as artificial reef ecosystems depends upon how the blue mussels interact with their local pelagic and benthic environment.