Mapping an uncertainty zone between interpolated types of a categorical variable

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mapping an uncertainty zone between interpolated types of a categorical variable

Categorical data cannot be interpolated directly because they are outcomes of discrete random variables. Thus, types of categorical variables are transformed into indicator functions that can be handled by interpolation methods. Interpolated indicator values are then backtransformed to the original types of categorical variables. However, aspects such as variability and uncertainty of interpolated values of categorical data have never been considered. In this paper we show that the interpolation variance can be used to map an uncertainty zone around boundaries between types of categorical variables. Moreover, it is shown that the interpolation variance is a component of the total variance of the categorical variables, as measured by the coefficient of unalikeability. (C) 2011 Elsevier Ltd. All rights reserved.

Post-processing of sequential indicator simulation realizations for modeling geologic bodies

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Especulative (sic) attack on exchange rate target zone regime : the uncertainty case

We present a continuous time target zone model of speculative attacks. Contrary to most of the literature that considers the certainty case, i.e., agents know for sure the Central Bank behavior in the future, we build uncertainty into the madel in two different ways. First, we consider the case in whicb the leveI of reserves at which the central bank lets the regime collapse is uncertain. Alternatively, we ana1ize the case in which, with some probability, the government may cbange its policy reducing the initially positive trend in domestic credito In both cases, contrary to the case of a fixed exchange rate regime, speculators face a cost of launching a tentative attack that may not succeed. Such cost induces a delay and may even prevent its occurrence. At the time of the tentative attack, the exchange rate moves either discretely up, if the attack succeeds, or down, if it fails. The remlts are consistent with the fact that, typically, an attack involves substantial profits and losses for the speculators. In particular, if agents believed that the government will control fiscal imbalances in the future, or alternatively, if they believe the trend in domestic credit to be temporary, the attack is postponed even in the presence of a signal of an imminent collapse. Finally, we aIso show that the timing of a speculative attack increases with the width of the target zone.

Robust model predictive control with zone control

Model predictive control (MPC) is usually implemented as a control strategy where the system outputs are controlled within specified zones, instead of fixed set points. One strategy to implement the zone control is by means of the selection of different weights for the output error in the control cost function. A disadvantage of this approach is that closed-loop stability cannot be guaranteed, as a different linear controller may be activated at each time step. A way to implement a stable zone control is by means of the use of an infinite horizon cost in which the set point is an additional variable of the control problem. In this case, the set point is restricted to remain inside the output zone and an appropriate output slack variable is included in the optimisation problem to assure the recursive feasibility of the control optimisation problem. Following this approach, a robust MPC is developed for the case of multi-model uncertainty of open-loop stable systems. The controller is devoted to maintain the outputs within their corresponding feasible zone, while reaching the desired optimal input target. Simulation of a process of the oil re. ning industry illustrates the performance of the proposed strategy.

Model Uncertainty in Panel Vector Autoregressive Models.

We develop methods for Bayesian model averaging (BMA) or selection (BMS) in Panel Vector Autoregressions (PVARs). Our approach allows us to select between or average over all possible combinations of restricted PVARs where the restrictions involve interdependencies between and heterogeneities across cross-sectional units. The resulting BMA framework can find a parsimonious PVAR specification, thus dealing with overparameterization concerns. We use these methods in an application involving the euro area sovereign debt crisis and show that our methods perform better than alternatives. Our findings contradict a simple view of the sovereign debt crisis which divides the euro zone into groups of core and peripheral countries and worries about financial contagion within the latter group.

Model Uncertainty in Panel Vector Autoregressive Models.

We develop methods for Bayesian model averaging (BMA) or selection (BMS) in Panel Vector Autoregressions (PVARs). Our approach allows us to select between or average over all possible combinations of restricted PVARs where the restrictions involve interdependencies between and heterogeneities across cross-sectional units. The resulting BMA framework can find a parsimonious PVAR specification, thus dealing with overparameterization concerns. We use these methods in an application involving the euro area sovereign debt crisis and show that our methods perform better than alternatives. Our findings contradict a simple view of the sovereign debt crisis which divides the euro zone into groups of core and peripheral countries and worries about financial contagion within the latter group.

Numerical modeling of the effect of variation of boundary conditions on vadose zone hydraulic properties

An accurate estimation of hydraulic fluxes in the vadose zone is essential for the prediction of water, nutrient and contaminant transport in natural systems. The objective of this study was to simulate the effect of variation of boundary conditions on the estimation of hydraulic properties (i.e. water content, effective unsaturated hydraulic conductivity and hydraulic flux) in a one-dimensional unsaturated flow model domain. Unsaturated one-dimensional vertical water flow was simulated in a pure phase clay loam profile and in clay loam interlayered with silt loam distributed according to the third iteration of the Cantor Bar fractal object Simulations were performed using the numerical model Hydrus 1D. The upper and lower pressure heads were varied around average values of -55 cm for the near-saturation range. This resulted in combinations for the upper and lower constant head boundary conditions, respectively, of -50 and -60 cm, -40 and -70 cm, -30 and -80 cm, -20 and -90 cm, and -10 and -100 cm. For the drier range the average head between the upper and lower boundary conditions was set to -550 cm, resulting in the combinations -500 and -600 cm, -400 and -700 cm, -300 and -800 cm, -200 and -900 cm, and -100 and -1,000 cm, for upper and lower boundary conditions, respectively. There was an increase in water contents, fluxes and hydraulic conductivities with the increase in head difference between boundary conditions. Variation in boundary conditions in the pure phase and interlayered one-dimensional profiles caused significant deviations in fluxes, water contents and hydraulic conductivities compared to the simplest case (a head difference between the upper and lower constant head boundaries of 10 cm in the wetter range and 100 cm in the drier range).

Estimating vadose zone hydraulic properties using ground penetrating radar: The impact of prior information

A number of geophysical methods, such as ground-penetrating radar (GPR), have the potential to provide valuable information on hydrological properties in the unsaturated zone. In particular, the stochastic inversion of such data within a coupled geophysical-hydrological framework may allow for the effective estimation of vadose zone hydraulic parameters and their corresponding uncertainties. A critical issue in stochastic inversion is choosing prior parameter probability distributions from which potential model configurations are drawn and tested against observed data. A well chosen prior should reflect as honestly as possible the initial state of knowledge regarding the parameters and be neither overly specific nor too conservative. In a Bayesian context, combining the prior with available data yields a posterior state of knowledge about the parameters, which can then be used statistically for predictions and risk assessment. Here we investigate the influence of prior information regarding the van Genuchten-Mualem (VGM) parameters, which describe vadose zone hydraulic properties, on the stochastic inversion of crosshole GPR data collected under steady state, natural-loading conditions. We do this using a Bayesian Markov chain Monte Carlo (MCMC) inversion approach, considering first noninformative uniform prior distributions and then more informative priors derived from soil property databases. For the informative priors, we further explore the effect of including information regarding parameter correlation. Analysis of both synthetic and field data indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when we combine these data with a realistic, informative prior.

Bayesian Markov-chain-Monte-Carlo inversion of time-lapse cross hole ground-penetrating radar data to characterize the vadose zone at the Arrenaes field site, Denmark

The ground-penetrating radar (GPR) geophysical method has the potential to provide valuable information on the hydraulic properties of the vadose zone because of its strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR traveltime data can allow for a significant reduction in uncertainty regarding subsurface van Genuchten-Mualem (VGM) parameters. Much of the previous work on the stochastic estimation of VGM parameters from crosshole GPR data has considered the case of steady-state infiltration conditions, which represent only a small fraction of practically relevant scenarios. We explored in detail the dynamic infiltration case, specifically examining to what extent time-lapse crosshole GPR traveltimes, measured during a forced infiltration experiment at the Arreneas field site in Denmark, could help to quantify VGM parameters and their uncertainties in a layered medium, as well as the corresponding soil hydraulic properties. We used a Bayesian Markov-chain-Monte-Carlo inversion approach. We first explored the advantages and limitations of this approach with regard to a realistic synthetic example before applying it to field measurements. In our analysis, we also considered different degrees of prior information. Our findings indicate that the stochastic inversion of the time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions compared with the corresponding priors, which in turn significantly improves knowledge of soil hydraulic properties. Overall, the results obtained clearly demonstrate the value of the information contained in time-lapse GPR data for characterizing vadose zone dynamics.

Diversité et structure du zooplancton : importance pour la conservation de la biodiversité aquatique en zone urbaine

L'écologie urbaine est un nouveau champ de recherche qui cherche à comprendre les structures et les patrons des communautés et des écosystèmes situés dans des paysages urbains. Les petits plans d’eau sont connus comme des écosystèmes aquatiques qui peuvent contenir une biodiversité considérable pour plusieurs groupes taxonomiques (oiseaux, amphibiens, macroinvertébrés), ce qui en fait des écosystèmes intéressants pour les études de conservation. Cependant, la biodiversité du zooplancton, un élément central des réseaux trophiques aquatiques, n’est pas entièrement connue pour les plans d’eaux urbains et devrait être mieux décrite et comprise. Cette étude a évalué les patrons de biodiversité des communautés zooplanctoniques dans des plans d’eau urbains sur l’Ile de Montréal et leurs sources de variation. Des suggestions pour l’évaluation et la conservation de la biodiversité sont aussi discutées. La biodiversité zooplanctonique des plans d’eaux urbains s’est avérée être assez élevée, avec les cladocères et les rotifères montrant les contributions à la diversité gamma et bêta les plus élevées. Sur l’ensemble des plans d’eau, il y avait une corrélation négative entre les contributions à la bêta diversité des cladocères et des rotifères. Au niveau de chaque plan d'eau, la zone littorale colonisée par des macrophytes s'est avérée être un habitat important pour la biodiversité zooplactonique, contribuant considérablement à la richesse en taxons, souvent avec une différente composition en espèces. Les communautés zooplanctoniques répondaient aux facteurs ascendants et descendants, mais aussi aux pratiques d’entretien, car le fait de vider les plans d’eau en hiver affecte la composition des communautés zooplanctoniques. Les communautés de cladocères dans ces plans d’eau possédaient des quantités variables de diversité phylogénétique, ce qui permet de les classer afin de prioriser les sites à préserver par rapport à la diversité phylogénétique. Le choix des sites à préserver afin de maximiser la diversité phylogénétique devrait être correctement établi, afin d’eviter de faire des choix sous-optimaux. Cependant, pour des taxons tels que les cladocères, pour lesquels les relations phylogénétiques demeurent difficiles à établir, placer une confiance absolue dans un seul arbre est une procédure dangereuse. L’incorporation de l’incertitude phylogénétique a démontré que, lorsqu’elle est prise en compte, plusieurs différences potentielles entre la diversité phylogenétique ne sont plus supportées. Les patrons de composition des communautés différaient entre les plans d’eau, les mois et les zones d’échantillonnage. Etant donné les intéractions sont significatives entres ces facters; ceci indique que tous ces facteurs devraient êtres considérés. L’urbanisation ne semblait pas sélectionner pour un type unique de composition des groupes alimentaires, étant donné que les communautés pouvaient changer entres des assemblages de types alimentaires différents. Les variables environnementales, surtout la couverture du plan d’eau en macrophytes, étaient des facteurs importants pour la biodiversité zooplanctonique, affectant la richesse spécifique de divers groupes taxonomiques et alimentaires. Ces variables affectaient aussi la composition des communautés, mais dans une moindre mesure, étant des variables explicatives modestes, ce qui indiquerait le besoin de considérer d’autres processus.

The intraplate Porto dos Gauchos seismic zone in the Amazon craton - Brazil

The largest earthquake observed in the stable continental interior of the South American plate occurred in Serra do Tombador, Mato Grosso state - Brazil, on January 31,1955 with a magnitude of 6.2 m(b). Since then no other earthquake has been located near the 1955 epicentre. However, in Porto dos Gauchos, 100 km northeast of Serra do Tombador, a recurrent seismicity has been observed since 1959. Both Serra do Tombador and Porto dos Gauchos are located in the Phanerozoic Parecis basin. Two magnitude 5 earthquakes occurred in Porto dos Gauchos, in 1998 and 2005, with intensities up to VI and V, respectively. These two main shocks were followed by aftershock sequences lasting more than three years each. Local seismic stations have been deployed by the Seismological Observatory of the University of Brasilia since 1998 to study the ""Porto dos Gauchos"" seismic zone (PGSZ). A local seismic refraction survey was carried out with two explosions to help define the seismic velocity model. Both the 1998 and 2005 earthquake sequences occurred in the same WSW-ENE oriented fault zone with right-lateral strike-slip mechanisms. The epicentral zone is in the Parecis basin, near its northern border where there are buried grabens, generally trending WNW-ESE, such as the deep Mesoproterozoic Caiabis graben which lies partly beneath the Parecis basin. However, the epicentral distribution indicates that the 1998 and 2005 sequences are related to a N60 degrees E fault which probably crosses the entire Caiabis graben. The 1955 earthquake, despite the uncertainty in its epicentre, does not seem to be directly related to any buried graben either. The seismicity in the Porto dos Gauchos seismic zone, therefore, is not directly related to rifted crust. The probable direction of the maximum horizontal stress near Porto dos Gauchos is roughly E-W, consistent with other focal mechanisms further south in the Pantanal basin and Paraguay. but seems to be different from the NW-SE direction observed further north in the Amazon basin. The recurrent seismicity observed in Porto dos Gauchos, and the large 1955 earthquake nearby, make this area of the Parecis basin one of the most important seismic zones of Brazil. (C) 2009 Elsevier B.V. All rights reserved.

Spatial variability and potential impacts of climate change on flood and debris flow hazard zone mapping and implications for risk management

The main goals of this study were to identifythe alpine torrent catchments that are sensitive to climatic changes and to assess the robustness of the methods for the elaboration of flood and debris flow hazard zone maps to specific effects of climate changes. In this study, a procedure for the identification and localization of torrent catchments in which the climate scenarios will modify the hazard situation was developed. In two case studies, the impacts of a potential increase of precipitation intensities to the delimited hazard zones were studied. The identification and localization of the torrent and river catchments, where unfavourable changes in the hazard situation occur, could eliminate speculative and unnecessary measures against the impacts of climate changes like a general enlargement of hazard zones or a general over dimensioning of protection structures for the whole territory. The results showed a high spatial variability of the sensitivity of catchments to climate changes. In sensitive catchments, the sediment management in alpine torrents will meet future challenges due to a higher rate for sediment removal from retention basins. The case studies showed a remarkable increase of the areas affected by floods and debris flow when considering possible future precipitation intensities in hazard mapping. But, the calculated increase in extent of future hazard zones lay within the uncertainty of the methods used today for the delimitation of the hazard zones. Thus, the consideration of the uncertainties laying in the methods for the elaboration of hazard zone maps in the torrent and river catchments sensitive to climate changes would provide a useful instrument for the consideration of potential future climate conditions. The study demonstrated that weak points in protection structures in future will become more important in risk management activities.

Oxygen variance and meridional oxygen supply in the Tropical North East Atlantic oxygen minimum zone

The distribution of the mean oceanic oxygen concentration results from a balance between ventilation and consumption. In the eastern tropical Pacific and Atlantic, this balance creates extended oxygen minimum zones (OMZ) at intermediate depth. Here, we analyze hydrographic and velocity data from shipboard and moored observations, which were taken along the 23°W meridian cutting through the Tropical North East Atlantic (TNEA) OMZ, to study the distribution and generation of oxygen variability. By applying the extended Osborn-Cox model, the respective role of mesoscale stirring and diapycnal mixing in producing enhanced oxygen variability, found at the southern and upper boundary of the OMZ, is quantified. From the well-ventilated equatorial region toward the OMZ core a northward eddy-driven oxygen flux is observed whose divergence corresponds to an oxygen supply of about 2.4 µmol kg-1 year-1 at the OMZ core depth. Above the OMZ core, mesoscale eddies act to redistribute low- and high-oxygen waters associated with westward and eastward currents, respectively. Here, absolute values of the local oxygen supply >10 mmol kg-1 year-1 are found, likely balanced by mean zonal advection. Combining our results with recent studies, a refined oxygen budget for the TNEA OMZ is derived. Eddy-driven meridional oxygen supply contributes more than 50 % of the supply required to balance the estimated oxygen consumption. The oxygen tendency in the OMZ, as given by the multidecadal oxygen decline, is maximum slightly above the OMZ core and represents a substantial imbalance of the oxygen budget reaching about 20 % of the magnitude of the eddy-driven oxygen supply.