The Bayesian detection of discontinuities in a polynomial regression and its application to the cycle-slip problem

This paper deals with the problem of detecting and correcting cycle-slips in Global Navigation Satellite System (GNSS) phase data by exploiting the Bayesian theory. The method is here applied to undifferenced observations, because repairing cycle-slips already at this stage could be a useful pre-processing tool, especially for a network of permanent GNSS stations. If a dual frequency receiver is available, the cycle-slips can be easily detected by combining two phase observations or phase and range observations from a single satellite to a single receiver. These combinations, expressed in a distance unit form, are completely free from the geometry and depend only on the ionospheric effect, on the electronic biases and on the initial integer ambiguities; since these terms are expected to be smooth in time, at least in a short period, a cycle-slip in one or both the two carriers can be modelled as a discontinuity in a polynomial regression. The proposed method consists in applying the Bayesian theory to compute the marginal posterior distribution of the discontinuity epoch and to detect it as a maximum a posteriori (MAP) in a very accurate way. Concerning the cycle-slip correction, a couple of simultaneous integer slips in the two carriers is chosen by maximazing the conditional posterior distribution of the discontinuity amplitude given the detected epoch. Numerical experiments on simulated and real data show that the discontinuities with an amplitude 2 or 3 times larger than the noise standard deviation are successfully identified. This means that the Bayesian approach is able to detect and correct cycle-slips using undifferenced GNSS observations even if the slip occurs by one cycle. A comparison with the scientific software BERNESE 5.0 confirms the good performance of the proposed method, especially when data sampled at high frequency (e.g. every 1 s or every 5 s) are available.     

Instability in spatial error models: an application to the hypothesis of convergence in the European case

This paper focuses on the hypothesis of stability in the mechanisms of spatial dependence that are usually employed in spatial econometric models. We propose a specification strategy for which the first step is to solve a local estimation algorithm, called the Zoom estimation. The aim of this stage is to detect problems of heterogeneity in the parameters and to identify the regimes. Then we resort to a battery of formal Lagrange Multipliers to test the assumption of stability in the processes of spatial dependence. The alternative hypothesis consists of the existence of several regimes in these parameters. A small Monte Carlo serves to confirm the behaviour of this strategy in a context of finite size samples. As an illustration, we solve an application to the case of the hypothesis of convergence for the per capita income in the European regions. Our results reveal the existence of a strong Centre-Periphery dichotomy in which instability extends to all the elements (coefficients of regression as well as parameters of spatial dependence) that intervene in a classical conditional β-convergence model.     

Biomass expansion factor and root-to-shoot ratio for Pinus in Brazil

The Biomass Expansion Factor (BEF) and the Root-to-Shoot Ratio (R) are variables used to quantify carbon stock in forests. They are often considered as constant or species/area specific values in most studies. This study aimed at showing tree size and age dependence upon BEF and R and proposed equations to improve forest biomass and carbon stock. Data from 70 sample Pinus spp. grown in southern Brazil trees in different diameter classes and ages were used to demonstrate the correlation between BEF and R, and forest inventory data, such as DBH, tree height and age. Total dry biomass, carbon stock and CO₂ equivalent were simulated using the IPCC default values of BEF and R, corresponding average calculated from data used in this study, as well as the values estimated by regression equations. The mean values of BEF and R calculated in this study were 1.47 and 0.17, respectively. The relationship between BEF and R and the tree measurement variables were inversely related with negative exponential behavior. Simulations indicated that use of fixed values of BEF and R, either IPCC default or current average data, may lead to unreliable estimates of carbon stock inventories and CDM projects. It was concluded that accounting for the variations in BEF and R and using regression equations to relate them to DBH, tree height and age, is fundamental in obtaining reliable estimates of forest tree biomass, carbon sink and CO₂ equivalent.     

A New Combined Assessment of Mixed Uncertainty in Spatial Models: Conceptualization and Implementation

Uncertainty quantification is not often performed in spatial modeling applications, especially when there is a mixture of probabilistic and non‐probabilistic uncertainties. Furthermore, the effect of positional uncertainty is often not assessed, despite its relevance to geographical applications. Although there has been much work in investigating the aforementioned types of uncertainty in isolation, combined approaches have not been much researched. This has resulted in a lack of tools for conducting mixed uncertainty analyses that include positional uncertainty. This research addresses the issue by first presenting a new, flexible, simulation‐oriented conceptualization of positional uncertainty in geographic objects called F‐Objects. F‐Objects accommodates various representations of uncertainty, while remaining conceptually simple. Second, a new Python‐based framework is introduced, termed Wiggly and capable of conducting mixed uncertainty propagation using fuzzy Monte Carlo simulation (FMCS). FMCS combines both traditional Monte Carlo with fuzzy analysis in a so‐called hybrid approach. F‐Objects is implemented within the Wiggly framework, resulting in a tool capable of considering any combination of: (1) probabilistic variables; (2) fuzzy variables; and (3) positional uncertainty of objects (probabilistic/fuzzy). Finally, a realistic GIS‐based groundwater contamination problem demonstrates how F‐Objects and Wiggly can be used to assess the effect of positional uncertainty.     

Adaptive capacity in Tanzanian Maasailand: Changing strategies to cope with drought in fragmented landscapes

This study examines the ways in which the adaptive capacity of households to climatic events varies within communities and is mediated by institutional and landscape changes. We present qualitative and quantitative data from two Maasai communities differentially exposed to the devastating drought of 2009 in Northern Tanzania. We show how rangeland fragmentation combined with the decoupling of institutions and landscapes are affecting pastoralists’ ability to cope with drought. Our data highlight that mobility remains a key coping mechanism for pastoralists to avoid cattle loss during a drought. However, mobility is now happening in new ways that require not only large amounts of money but new forms of knowledge and connections outside of customary reciprocity networks. Those least affected by the drought, in terms of cattle lost, were those with large herds who were able to sell some of their cattle and to pay for private access to pastures outside of Maasai areas. Drawing on an entitlements framework, we argue that the new coping mechanisms are not available to all, could be making some households more vulnerable to climate change, and reduce the adaptive capacity of the overall system as reciprocity networks and customary institutions are weakened. As such, we posit that adaptive capacity to climate change is uneven within and across communities, is scale-dependent, and is intimately tied to institutional and landscape changes.     

Using time‐domain reflectometry to characterize shallow solute transport in an oak woodland hillslope in northern California,USA

The natural heterogeneity of water and solute movement in hillslope soils makes it difficult to accurately characterize the transport of surface‐applied pollutants without first gathering spatially distributed hydrological data. This study examined the application of time‐domain reflectometry (TDR) to measure solute transport in hillslopes. Three different plot designs were used to examine the transport of a conservative tracer in the first 50 cm of a moderately sloping soil. In the first plot, which was designed to examine spatial variability in vertical transport in a 1·2 m² plot, a single probe per meter was found to adequately characterize vertical solute travel times. In addition, a dye and excavation study in this plot revealed lateral preferential flow in small macropores and a transport pattern where solute is focused vertically into preferential flow pathways. The bypass flow delivers solute deeper in the soil, where lateral flow occurs. The second plot, designed to capture both vertical and lateral flow, provided additional evidence confirming the flow patterns identified in the excavation of the first plot. The third plot was designed to examine lateral flow and once again preferential flow of the tracer was observed. In one instance rapid solute transport in this plot was estimated to occur in as little as 3% of the available pore space. Finally, it was demonstrated that the soil anisotropy, although partially responsible for lateral subsurface transport, may also homogenize the transport response across the hillslope by decreasing vertical solute spreading. Copyright © 2002 John Wiley & Sons, Ltd.     

Zinc and sulfur isotope variation in sphalerite from carbonate-hosted zinc deposits,Cantabria, Spain

We studied zinc and sulfur isotopes and the chemical composition of sphalerite samples from Picos de Europa (Aliva mine) and sphalerite and hydrozincite samples from La Florida mine, two carbonate-hosted Mississippi Valley-type (MVT) deposits located in northern Spain; despite being close, they are hosted in carbonatic rocks of different ages, Lower Carboniferous and Lower Cretaceous, respectively. The two generations of sphalerite at Picos de Europa show different δ⁶⁶Zn values (stage 1 sphalerite +0.24 per mil and stage 2 sphalerite from ?0.75 to +0.08 per mil). Both generations also differ in the sulfur isotope composition (stage 1 has δ³⁴S?=?+6.6 and stage 2 has δ³⁴S?=??0.9 to +2.9 per mil) and the chemical composition (stage 1 sphalerite, compared to stage 2 sphalerite, is significantly enriched in Pb, As, Mn, Sb, slightly enriched in Ag, Ni, and Cu and depleted in Co, Ga, Tl, Te, Ge, and Sn). We suggest that Zn isotope fractionation was controlled predominantly by pH and T changes. High Zn isotope values reflect rapid precipitation of sphalerite from higher-temperature acidic fluids that carried Zn mostly as chloride species after interaction with carbonate rocks while lower Zn isotope values most likely resulted from a longer precipitation process from fluid at higher pH and decreasing T that carried dominantly Zn sulfide species. At La Florida, sphalerite samples show light ⁶⁶Zn-depleted signatures with δ⁶⁶Zn values from ?0.80 to ?0.01 per mil (mostly between ?0.80 and ?0.24 per mil) and δ³⁴S values from +10.7 to +15.7 per mil without any relationship between the δ⁶⁶Zn and δ³⁴S values. Here, the variation in Zn isotope values is interpreted as related to mixing of fluids from two reservoirs. The Zn was carried by a single deep-seated and higher T (~250–320 °C) fluid, and precipitation took place after mixing with a connate S-rich fluid in a system with mH₂S?>?mZn²⁺ as a result of change in pH, T, and Zn predominant species. The light δ⁶⁶Zn accompanied by heavy δ³⁴S values resulted from fractionation of Zn aqueous sulfides at near-neutral pH and decreasing T. Hydrozincite samples show much heavier δ⁶⁶Zn values (+0.21 to +0.33 per mil), consistent with fractionation during supergene processes.