Measures of Parameter Uncertainty in Geostatistical Estimation and Geostatistical Optimal Design

Studies of site exploration, data assimilation, or geostatistical inversion measure parameter uncertainty in order to assess the optimality of a suggested scheme. This study reviews and discusses measures for parameter uncertainty in spatial estimation. Most measures originate from alphabetic criteria in optimal design and were transferred to geostatistical estimation. Further rather intuitive measures can be found in the geostatistical literature, and some new measures will be suggested in this study. It is shown how these measures relate to the optimality alphabet and to relative entropy. Issues of physical and statistical significance are addressed whenever they arise. Computational feasibility and efficient ways to evaluate the above measures are discussed in this paper, and an illustrative synthetic case study is provided. A major conclusion is that the mean estimation variance and the averaged conditional integral scale are a powerful duo for characterizing conditional parameter uncertainty, with direct correspondence to the well-understood optimality alphabet. This study is based on cokriging generalized to uncertain mean and trends because it is the most general representative of linear spatial estimation within the Bayesian framework. Generalization to kriging and quasi-linear schemes is straightforward. Options for application to non-Gaussian and non-linear problems are discussed.     

Metasomatism and the formation of greisen in Grainsgill,Cumbria, England

A section of hornfelsed Skiddaw Slate adjacent to the margin of the Grainsgill Greisen is described and chemical analyses of the various rock types presented. The results confirm that hydrothermal fluids liberated K and Na from the granite to produce the greisen. This gave rise to K metasomatism of the adjacent hornfels and to retrogressive metamorphism over a radius of 200m from the intrusion. Na leached from the hornfels near the intrusion and that liberated during the formation of the greisen are probably the sources of the Na in the brines recorded in fluid inclusions within the nearby quartz-tungsten veins.     

Recent evolution of Lake Arreo,northern Spain: influences of land use change and climate

We present a high-resolution, multiproxy reconstruction of the depositional history of Lake Arreo, northern Spain, for the last 60 years. We conducted sedimentological, geochemical and diatom analyses in short cores and made a detailed comparison with regional instrumental climate data (1952–2007), limnological monitoring of the lake (1992–2008) and recent land use changes that affect the lake catchment. Chronology is based on “floating” discontinuous varve counts and ¹³⁷Cs and ¹⁴C dates. Four periods were identified in the Lake Arreo recent history: (1) prior to 1963, varved facies intercalated with fine turbidite deposits, and diatom assemblages dominated by Cyclotella taxa indicate predominantly meromictic conditions, (2) from 1964 to 1978, permanent anoxia persisted in bottom waters, as shown by similar facies and diatom assemblages as before, though detrital layers were coarser, (3) from 1979 to 1994, sediment delivery to the lake increased and laminated, clastic facies were deposited, and (4) from 1995 to 2008, dominance of massive facies and an increase in Fragilaria tenera and Achnanthes minutissima reflect relatively lower lake levels, less frequent bottom anoxia with more frequent water column mixing, similar to modern conditions. The period 1952–1979 was a time of meromixis and varved facies deposition, and was characterized by higher rainfall and less intense agricultural pressure in the watershed. There were two short humid periods (1992–1993 and 1996–1998) when monitoring data show more anoxic weeks per year and relatively higher lake levels. Increased cultivation of small landholdings in 1963, and particularly after 1979, caused a large increase in sediment delivery to the lake. The inferred lake evolution is in agreement with monitoring data that suggest a transition from dominantly meromictic conditions prior to 1993–1994 to a predominantly monomictic pattern of circulation since then, particularly after 2000. The synergistic effects of intensive water extraction for irrigation and lower rainfall since 1979, and particularly since 1994, brought the long period of meromictic conditions in Lake Arreo to an end. Water balance and sediment delivery to the lake are dominant factors that control the limnological and mixing conditions in Lake Arreo and they must be considered in management and restoration plans.     

Spectrophotometric Variability of Mira

Data from the Pulkovo spectrophotometric data base on the absolute quasimonochromatic fluxes from oCet in the 320–1080 nm range are used to determine the physical parameters of this star in different phases of its light curve. The continuum emission layer is found to expand between the phases of the cycle corresponding to the rising and falling branches of the light curve. The average expansion velocity is 32 km/s. By the time the star’s brightness has fallen by roughly three magnitudes, its radius has increased by almost a factor of three. Over this same time the temperature of the layer has fallen from 3000 K to 2200 K. For this expansion velocity, the calculated mass rate loss is ⊙ M /year.__________Translated from Astrofizika, Vol. 48, No. 2, pp. 175–189 (May 2005).     

High-precision repeat-groundtrack orbit design and maintenance for Earth observation missions

The focus of this paper is the design and station keeping of repeat-groundtrack orbits for Sun-synchronous satellites. A method to compute the semimajor axis of the orbit is presented together with a station-keeping strategy to compensate for the perturbation due to the atmospheric drag. The results show that the nodal period converges gradually with the increase of the order used in the zonal perturbations up to \(J_{15}\). A differential correction algorithm is performed to obtain the nominal semimajor axis of the reference orbit from the inputs of the desired nodal period, eccentricity, inclination and argument of perigee. To keep the satellite in the proximity of the repeat-groundtrack condition, a practical orbit maintenance strategy is proposed in the presence of errors in the orbital measurements and control, as well as in the estimation of the semimajor axis decay rate. The performance of the maintenance strategy is assessed via the Monte Carlo simulation and the validation in a high fidelity model. Numerical simulations substantiate the validity of proposed mean-elements-based orbit maintenance strategy for repeat-groundtrack orbits.     

Formation Mechanism of Mud Bank Along the Southwest Coast of India

Mud bank formation during the southwest monsoon along the southwest coast of India remains an enigma to the researchers and coastal community in spite of several earlier studies. The present study attempts to unravel the mystery through a high-frequency, season-long time-series observation at Alappuzha, located at the southern part of the west coast of India, a region of frequent occurrence of mud bank. Using 7-month-long weekly time-series observation, we identified strong winds and high waves associated with onset of the southwest monsoon and subsequent three episodic atmospheric low-pressure events (LPEs).With the help of in situ time-series data, we show that the strong winds and high waves associated with southwest monsoon pre-conditions the near shore bottom sediment to bring it into suspension. The high amplitude waves associated with the southwest monsoon, while propagating from the deep water to shallow water region, interact with the bottom initiating bottom-sediment movement and its suspension due to wave refraction and shoaling. The sporadic occurrence of the atmospheric LPEs enhances the process of suspension of bottom sediment in the near shore region leading to the formation of fluid mud. Simulations with a cohesive sediment transport model yielded realistic estimates of sediment transport, in the presence of an onshore current, a pre-requisite for transporting the fluid mud toward the coast. The prevailing onshore upwelling current during the southwest monsoon provides the favorable pre-requisite conditions for transporting the fluid mud through depression channel network towards the coast. Once sufficient quantity and thickness of fluid mud is accumulated in the near shore region, it acts as a wave damper for subsequent high monsoon waves, as indicated by the time-series wave data, leading to the formation of tranquil mud bank region. Depression channel networks extending from the shelf to the coast off Alappuzha, Kochi, Ponnani, Beypore, and Ullal were found in the bathymetric charts, thus explaining why mud banks occur only at few locations in spite of the prevalence of similar monsoon conditions.     

Chemical denudation rates in Kärkevagge, Swedish Lapland

This study examines the spatial and temporal variability of chemical denudation rates in Kärkevagge, northern Sweden. The chemical flux rates within the valley are strongly influenced by the local geology. Chemical denudation rates determined for the study period are more than double those previously reported in the literature for this valley. Rates of greater than 46t km⁻² a⁻¹ were measured at the valley mouth over the course of the melt season. This difference is likely due to differences in measurement technique compared to that used by past researchers. This rate is also much higher than for other arctic and alpine watersheds. Chemical denudation in Kärkevagge is comparable to larger temperate rivers. The rapid chemical denudation in Kärkevagge is likely due to sulfide weathering creating acid solutions.     

The periastron advance in the second post-Newtonian approximation in general relativity

In this paper we present a second order post-Newtonian approximation to the Hamiltonian of theN-body system. Subsequently we improve the well-known Robertson's formula for the perihelion advancement by a correction term of orderc, wherec ^–4 is the velocity of light.