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.     

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.     

Penetrative convection in rotating fluids: A model for the base of stellar convection zones

Abstract

To model penetrative convection at the base of a stellar convection zone we consider two plane parallel, co-rotating Boussinesq layers coupled at their fluid interface. The system is such that the upper layer is unstable to convection while the lower is stable. Following the method of Kondo and Unno (1982, 1983) we calculate critical Rayleigh numbers R_c for a wide class of parameters. Here, R_c is typically much less than in the case of a single layer, although the scaling R_c～T^2/3 as T → ∞ still holds, where T is the usual Taylor number. With parameters relevant to the Sun the helicity profile is discontinuous at the interface, and dominated by a large peak in a thin boundary layer beneath the convecting region. In reality the distribution is continuous, but the sharp transition associated with a rapid decline in the effective viscosity in the overshoot region is approximated by a discontinuity here. This source of helicity and its relation to an alpha effect in a mean-field dynamo is especially relevant since it is a generally held view that the overshoot region is the location of magnetic field generation in the Sun.     

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.     

Climatic response of thick leaf spruce (Picea crassifolia) tree-ring width at different elevations over Qilian Mountains, northwestern China

Tree-ring cores of thick leaf spruce (Picea crassifolia) taken from four sites at different elevations, in the middle of the Qilian Mountains, in the arid and semi-arid region of northwestern China, were used to develop four tree-ring width chronologies using standard dendrochronological methods. Results indicate that with increasing altitude the chronologies’ year-to-year variations decreased. Hence, the sensitivity of the tree-ring chronologies to climate decreases with altitude. Further analysis showed that the significant limiting factor on tree growth is spring precipitation. Measurements of stomata density and leaf dry weight suggest the species’ ecological adaptation strategy changes with elevation. At high elevation the metabolic rate of thick leaf spruce decreases, thus showing the effect of the climate.     

Possible representation for discovery observations of stellar flares

It is shown that the chronology of flare star discoveries in the Pleiades cluster and the Orion association can be described satisfactorily by various distribution functions (gamma, binomial, decreasing exponential, and delta) for the mean frequencies of stellar flares. However, it has been found that this is due to the uncertainty in the observationally derived distribution function for the mean frequency of stellar flares. The most likely function is that derived by Ambartsumian, which has a physical basis.Translated fromAstrofizika, Vol. 38, No. 1, pp. 25–32, January–March, 1995.     

Effects of early season defoliation ofAnthyllis cytisoides(a Mediterranean browse species) on further herbivore attack

To determine if defoliation of a woody plant affects foraging by folivorous insects, we examined the infection rate (number of leaves damaged per total number of leaves sampled on marked stems) ofAnthyllis cytisoidesunder three experimental treatments: 10, 50 and 90% plant defoliation. Observations were made for three age classes, established by trunk base perimeter (equal to or lower than 11 cm, between 11 and 20 cm, larger than 20 cm). Plants respond positively to artificial defoliation by increasing total vegetative length of the stem and total inflorescence length. This response is most evident in young individuals.Response to herbivory was measured as overall infection rate and also as infection rate by different feeding guilds—chewing, mining, or sucking insects. We found that increased defoliation elicited increased resistance of leaves to insect attack. This was particularly evident in young plants. Different insect guilds respond in different ways. Attack by chewing insects declines with defoliation for all plant age classes; only sucking insects which feed on the oldest plants reduce feeding rate with plant defoliation. Finally, mining insects present the opposite trend in young and senescent plants.     

Microfossils from the Lower Kundelungu (Late Precambrian) of Zambia

Lower Kundelungu black argillites and silty dolomicrites from the Ndola area contain a rich microfossil assemblage, of which several forms can be attributed to the form-genus Fibularix Pflug, 1965. The same assemblage has also been found in fine-grained, mildly metamorphosed sedimentary rocks from Kalengwa and Karibarembi (North-Western Province). These findings support the Kundelungu correlation of the Kalengwa and Karibarembi successions.Three new species of Fibularix are described and illustrated. Seven types of sphaeromorphs are described and illustrated, though treated informally. Some sphaeromorphs are detached parts of Fibularix chains.The Lower Kundelungu microfossils resemble very closely some palynomorphs that occur in the Brioverian (Late Precambrian) of France, in the Libby Formation (Belt) of the northwestern United States, and in other formations of Late Precambrian age.     

Hanford tank residual waste – Contaminant source terms and release models

Residual waste is expected to be left in 177 underground storage tanks after closure at the US Department of Energy’s Hanford Site in Washington State, USA. In the long term, the residual wastes may represent a potential source of contamination to the subsurface environment. Residual materials that cannot be completely removed during the tank closure process are being studied to identify and characterize the solid phases and estimate the release of contaminants from these solids to water that might enter the closed tanks in the future. As of the end of 2009, residual waste from five tanks has been evaluated. Residual wastes from adjacent tanks C-202 and C-203 have high U concentrations of 24 and 59 wt.%, respectively, while residual wastes from nearby tanks C-103 and C-106 have low U concentrations of 0.4 and 0.03 wt.%, respectively. Aluminum concentrations are high (8.2–29.1 wt.%) in some tanks (C-103, C-106, and S-112) and relatively low (<1.5 wt.%) in other tanks (C-202 and C-203). Gibbsite is a common mineral in tanks with high Al concentrations, while non-crystalline U–Na–C–O–P ± H phases are common in the U-rich residual wastes from tanks C-202 and C-203. Iron oxides/hydroxides have been identified in all residual waste samples studied to date. Contaminant release from the residual wastes was studied by conducting batch leach tests using distilled deionized water, a Ca(OH)₂-saturated solution, or a CaCO₃-saturated water. Uranium release concentrations are highly dependent on waste and leachant compositions with dissolved U concentrations one or two orders of magnitude higher in the tests with high U residual wastes, and also higher when leached with the CaCO₃-saturated solution than with the Ca(OH)₂-saturated solution. Technetium leachability is not as strongly dependent on the concentration of Tc in the waste, and it appears to be slightly more leachable by the Ca(OH)₂-saturated solution than by the CaCO₃-saturated solution. In general, Tc is much less leachable (<10 wt.% of the available mass in the waste) than previously predicted. This may be due to the coprecipitation of trace concentrations of Tc in relatively insoluble phases such as Fe oxide/hydroxide solids.