Transformation of amplitudes and frequencies of precession and nutation of the earth’s rotation vector to amplitudes and frequencies of diurnal polar motion

The temporal change of the rotation vector of a rotating body is, in the first order, identical in a space-fixed system and in a body-fixed system. Therefore, if the motion of the rotation axis of the earth relative to a space-fixed system is given as a function of time, it should be possible to compute its motion relative to an earth-fixed system, and vice versa. This paper presents such a transformation. Two models of motion of the rotation axis in the space-fixed system are considered: one consisting only of a regular (i.e., strictly conical) precession and one extended by circular nutation components, which are superimposed upon the regular precession. The Euler angles describing the orientation of the earth-fixed system with respect to the space-fixed system are derived by an analytical solution of the kinematical Eulerian differential equations. In the first case (precession only), this is directly possible, and in the second case (precession and nutation), a solution is achieved by a perturbation approach, where the result of the first case serves as an approximation and nutation is regarded as a small perturbation, which is treated in a linearized form. The transformation by means of these Euler angles shows that the rotation axis performs in the earth-fixed system retrograde conical revolutions with small amplitudes, namely one revolution with a period of one sidereal day corresponding to precession and one revolution with a period which is slightly smaller or larger than one sidereal day corresponding to each (prograde or retrograde) circular nutation component. The peculiar feature of the derivation presented here is the analytical solution of the Eulerian differential equations.     

Application of ray-traced tropospheric slant delays to geodetic VLBI analysis

The correction of tropospheric influences via so-called path delays is critical for the analysis of observations from space geodetic techniques like the very long baseline interferometry (VLBI). In standard VLBI analysis, the a priori slant path delays are determined using the concept of zenith delays, mapping functions and gradients. The a priori use of ray-traced delays, i.e., tropospheric slant path delays determined with the technique of ray-tracing through the meteorological data of numerical weather models (NWM), serves as an alternative way of correcting the influences of the troposphere on the VLBI observations within the analysis. In the presented research, the application of ray-traced delays to the VLBI analysis of sessions in a time span of 16.5 years is investigated. Ray-traced delays have been determined with program RADIATE (see Hofmeister in Ph.D. thesis, Department of Geodesy and Geophysics, Faculty of Mathematics and Geoinformation, Technische Universität Wien. http://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-3444, 2016) utilizing meteorological data provided by NWM of the European Centre for Medium-Range Weather Forecasts (ECMWF). In comparison with a standard VLBI analysis, which includes the tropospheric gradient estimation, the application of the ray-traced delays to an analysis, which uses the same parameterization except for the a priori slant path delay handling and the used wet mapping factors for the zenith wet delay (ZWD) estimation, improves the baseline length repeatability (BLR) at 55.9% of the baselines at sub-mm level. If no tropospheric gradients are estimated within the compared analyses, 90.6% of all baselines benefit from the application of the ray-traced delays, which leads to an average improvement of the BLR of 1 mm. The effects of the ray-traced delays on the terrestrial reference frame are also investigated. A separate assessment of the RADIATE ray-traced delays is carried out by comparison to the ray-traced delays from the National Aeronautics and Space Administration Goddard Space Flight Center (NASA GSFC) (Eriksson and MacMillan in http://lacerta.gsfc.nasa.gov/tropodelays, 2016) with respect to the analysis performances in terms of BLR results. If tropospheric gradient estimation is included in the analysis, 51.3% of the baselines benefit from the RADIATE ray-traced delays at sub-mm difference level. If no tropospheric gradients are estimated within the analysis, the RADIATE ray-traced delays deliver a better BLR at 63% of the baselines compared to the NASA GSFC ray-traced delays.     

State‐Led Innovation at the City Level: Policy Measures to Promote New Energy Vehicles in Shenzhen,China

Unlike many Western countries, the Chinese state has a much more active role in innovation that includes direct involvement with actors in innovation processes and the use of state capacity, money, and power to attain certain goals. With the rise of China, innovation processes that critically depend on state action, often labeled state‐led innovation, have thus received growing scholarly attention. However, only few contributions study the specific sector of new energy vehicles (NEV) and policy measures applied at the city level. This paper examines policy and planning tools used in Shenzhen, China, to assert innovation in the NEV industry, using an evaluation of documents and interviews. The paper finds that a city can play a decisive role in the implementation of innovation policy, and Chinese cities in particular make use of a broad set of innovation support measures ranging from binding quotas, public procurement, and incentives to bans and orders. The findings underline the importance of strong regulatory instruments that do not conform to the Western notion of market‐compliant policy, but nevertheless work effectively in the Chinese context. Moreover, the results highlight how successful policy support for innovation in the NEV can be implemented.     

Fluid–rock interaction in autoliths of agpaitic nepheline syenites in the Ilímaussaq intrusion, South Greenland

Within the 1.16 Ga old Ilímaussaq intrusion, up to 700 m large autoliths occur in one stratigraphic unit of the layered floor series of agpaitic nepheline syenites (kakortokites). These autoliths consist of two different rock types: augite syenite and naujaite (agpaitic nepheline syenite). All three rock types show a number of alteration features related to the entrapment of the autoliths in the kakortokite magma caused by the interaction with a fluid phase.

In the kakortokites, the oxidation of primary arfvedsonite to aegirine and fluorite is restricted to the close proximity to the autoliths. Close to the surrounding kakortokite, the primary mafic phases of the augite syenites (augite, fayalite, Fe–Ti oxides) are completely replaced by arfvedsonite, aenigmatite, biotite, aegirine and fluorite. The decomposition of primary hastingsite to spectacular aegirine–augite–nepheline–aenigmatite symplectites can be observed up to several meters inside the autoliths. Additionally, fluorite formed at grain boundaries of primary nepheline. In the naujaite autoliths, primary arfvedsonite is replaced by aegirine–biotite intergrowths and abundant aenigmatite is occasionally replaced by Ti-rich aegirine and Fe–Ti oxides.

The mineral reactions in the autoliths are used to decipher details of the late to post-magmatic processes in a peralkaline syenitic intrusion. Mineral equilibria record an evolution governed by falling temperature (620 to ca. 500 °C) and increasing relative oxygen fugacity from FMQ + 1 to above FMQ + 4. Quantification of the observed mineral reactions reveals the infiltration of the autoliths with an oxidizing fluid phase rich in Na and F and minor addition of K. Volatiles (H and F) and in some cases also Fe, Ti and Ca (± Mg) released from primary autolith phases were mainly just relocated within the autoliths.     

Uranyl Retention on Quartz—New Experimental Data and Blind Prediction Using an Existing Surface Complexation Model

The adsorption behaviour of uranyl onto seven different samples of quartz was studied in batch experiments. Sea-sand (0.1–0.3 mm), Fil-Pro 12/20 (1–2 mm) and five Min-U-Sil samples with smaller particle sizes (5, 10, 15, 30 and 40 μm) were used. The uptake curves show “pH adsorption edges” in the range of pH 4–5. A good agreement of the new data with literature data was found when plotting surface-normalised distribution coefficients versus pH. Differences in the adsorption behaviour for pre-treated and untreated sea-sand samples were detectable resulting in a shift of the pH edge to higher pH values after treatment. A literature surface complexation model was applied for blind predictions of the experimental results. The simulations described the experimental observations quite well for the Min-U-Sil samples. For the two coarser quartz samples, the calculated over-predictions were explained by the larger-than-expected measured specific surface area and measurable amounts of associated minerals, for Fil-Pro 12/20 and sea-sand, respectively. Dissolution of the samples was studied as a function of pH. After 5 days, the measured Si concentrations were all higher than equilibrium quartz solubilities, but lower than those of amorphous silica. With increasing pH, dissolved silica increased. This strongly suggests that formation of dissolved uranyl–silicato complexes have to be considered based on measured silica concentrations.     

Least squares parameter estimation in chaotic differential equations

A recent least squares algorithm, which is designed to adapt implicit models to given sets of data, especially models given by differential equations or dynamical systems, is reviewed and used to fit the Hénon-Heiles differential equations to chaotic data sets.This numerical approach for estimating parameters in differential equation models, called theboundary value problem approach, is based on discretizing the differential equations like a boundary value problem,e.g. by a multiple shooting or collocation method, and solving the resulting constrained least squares problem with a structure exploiting generalized Gauss-Newton-Method (Bock, 1981).Dynamical systems like the Hénon-Heiles system which can have initial values and parameters that lead to positive Lyapunov exponents or phase space filling Poincaré maps give rise to chaotic time series. Various scenarios representing ideal and noisy data generated from the Hénon-Heiles system in the chaotic region are analyzedw.r.t. initial conditions, parameters and Lyapunov exponents. The original initial conditions and parameters are recovered with a given accuracy. The Lyapunov spectrum is then computed directly from the identified differential equations and compared to the spectrum of the true dynamics.presently at IWR, Universität Heidelberg, Im Neuenheimer Feld 368, D-6900 Heidelberg, Germany     

AN EMPIRICAL STUDY OF THE ELECTRON TEMPERATURE AND HEAVY ION VELOCITIES IN THE SOUTH POLAR CORONAL HOLE

The solar wind ions flowing outward through the solar corona generally have their ionic fractions freeze-in within 5 solar radii. The altitude where the freeze-in occurs depends on the competition between two time scales: the time over which the wind flows through a density scale height, and the time over which the ions achieve ionization equilibrium. Therefore, electron temperature, electron density, and the velocity of the ions are the three main physical quantities which determine the freeze-in process, and thus the solar wind ionic charge states. These physical quantities are determined by the heating and acceleration of the solar wind, as well as the geometry of the expansion. In this work, we present a parametric study of the electron temperature profile and velocities of the heavy ions in the inner solar corona. We use the ionic charge composition data observed by the SWICS experiment on Ulysses during the south polar pass to derive empirically the electron temperature profile in the south polar coronal hole. We find that the electron temperature profile in the solar inner corona is well constrained by the solar wind charge composition data. The data also indicate that the electron temperature profile must have a maximum within 2 solar radii. We also find that the velocities of heavy ions in their freeze-in regions are small (<100 km s^-1) and different elements must flow at different velocities in the inner corona.     

A minimal model for wind- and mixing-driven overturning: threshold behavior for both driving mechanisms

We present a minimal conceptual model for the Atlantic meridional overturning circulation which incorporates the advection of salinity and the basic dynamics of the oceanic pycnocline. Four tracer transport processes following Gnanadesikan in Science 283(5410):2077–2079, (1999) allow for a dynamical adjustment of the oceanic pycnocline which defines the vertical extent of a mid-latitudinal box. At the same time the model captures the salt-advection feedback (Stommel in Tellus 13(2):224–230, (1961)). Due to its simplicity the model can be solved analytically in the purely wind- and purely mixing-driven cases. We find the possibility of abrupt transition in response to surface freshwater forcing in both cases even though the circulations are very different in physics and geometry. This analytical approach also provides expressions for the critical freshwater input marking the change in the dynamics of the system. Our analysis shows that including the pycnocline dynamics in a salt-advection model causes a decrease in the freshwater sensitivity of its northern sinking up to a threshold at which the circulation breaks down. Compared to previous studies the model is restricted to the essential ingredients. Still, it exhibits a rich behavior which reaches beyond the scope of this study and might be used as a paradigm for the qualitative behaviour of the Atlantic overturning in the discussion of driving mechanisms.     

Real-time raster projection for web maps

The virtual globe is the default visualization for Digital Earth applications, but it can only show one half of the Earth. This article introduces user-adjustable, on-the-fly projection of georeferenced raster images for web mapping and web GIS applications. This technique allows users to center a map on arbitrary locations, while still seeing the entire Earth surface. Modern web mapping libraries can apply map projection transformations to vector data in the browser, but they do not currently support the projection of raster images at interactive frame rates. We use the cross-platform WebGL (Web Graphics Library) graphics pipeline for hardware-accelerated projection of raster data in web browsers. Two algorithmic techniques – inverse per-fragment projection, and combined forward per-triangle and inverse per-fragment projection – for georeferenced raster imagery are documented. The resulting raster maps combine the ease of use and flexibility of interactive virtual globes with the ability to show the entire Earth. The adjustable projection of raster imagery allows users to observe global phenomena that are difficult to visualize on virtual globes or traditional maps with static projections.