Stability and convergence of general multistep and multivalue methods with variable step size.

Thesis--University of Illinois.

Methods of mathematical analysis and computation.

Mode of access: Internet.

Development of a Conceptual Site Model for Evaluating Seawater Intrusion under Sea Level Rise Scenarios Using Analytical Methods

Island County is located in the Puget Sound of Washington State and includes several islands, the largest of which is Whidbey Island. Central Whidbey Island was chosen as the project site, as residents use groundwater for their water supply and seawater intrusion near the coast is known to contaminate this resource. In 1989, Island County adopted a Saltwater Intrusion Policy and used chloride concentrations in existing wells in order to define and map “risk zones.” In 2005, this method of defining vulnerability was updated with the use of water level elevations in conjunction with chloride concentrations. The result of this work was a revised map of seawater intrusion vulnerability that is currently in use by Island County. This groundwater management strategy is defined as trigger-level management and is largely a reactive tool. In order to evaluate trends in the hydrogeologic processes at the site, including seawater intrusion under sea level rise scenarios, this report presents a workflow where groundwater flow and discharge to the sea are quantified using a revised conceptual site model. The revised conceptual site model used several simplifying assumptions that allow for first-order quantitative predictions of seawater intrusion using analytical methods. Data from water well reports included lithologic and well construction information, static water levels, and aquifer tests for specific capacity. Results from specific capacity tests define the relationship between discharge and drawdown and were input for a modified Theis equation to solve for transmissivity (Arihood, 2009). Components of the conceptual site model were created in ArcGIS and included interpolation of water level elevation, creation of groundwater basins, and the calculation of net recharge and groundwater discharge for each basin. The revised conceptual site model was then used to hypothesize regarding hydrogeologic processes based on observed trends in groundwater flow. Hypotheses used to explain a reduction in aquifer thickness and hydraulic gradient were: (1) A large increase in transmissivity occurring near the coast. (2) The reduced aquifer thickness and hydraulic gradient were the result of seawater intrusion. (3) Data used to create the conceptual site model were insufficient to resolve trends in groundwater flow. For Hypothesis 2, analytical solutions for groundwater flow under Dupuit assumptions were applied in order to evaluate seawater intrusion under projected sea level rise scenarios. Results indicated that a rise in sea level has little impact on the position of a saltwater wedge; however, a reduction in recharge has significant consequences. Future work should evaluate groundwater flow using an expanded monitoring well network and aquifer recharge should be promoted by reducing surface water runoff.

Supporting interoperable interpolation: the INTAMAP approach

In many Environmental Information Systems the actual observations arise from a discrete monitoring network which might be rather heterogeneous in both location and types of measurements made. In this paper we describe the architecture and infrastructure for a system, developed as part of the EU FP6 funded INTAMAP project, to provide a service oriented solution that allows the construction of an interoperable, automatic, interpolation system. This system will be based on the Open Geospatial Consortium’s Web Feature Service (WFS) standard. The essence of our approach is to extend the GML3.1 observation feature to include information about the sensor using SensorML, and to further extend this to incorporate observation error characteristics. Our extended WFS will accept observations, and will store them in a database. The observations will be passed to our R-based interpolation server, which will use a range of methods, including a novel sparse, sequential kriging method (only briefly described here) to produce an internal representation of the interpolated field resulting from the observations currently uploaded to the system. The extended WFS will then accept queries, such as ‘What is the probability distribution of the desired variable at a given point’, ‘What is the mean value over a given region’, or ‘What is the probability of exceeding a certain threshold at a given location’. To support information-rich transfer of complex and uncertain predictions we are developing schema to represent probabilistic results in a GML3.1 (object-property) style. The system will also offer more easily accessible Web Map Service and Web Coverage Service interfaces to allow users to access the system at the level of complexity they require for their specific application. Such a system will offer a very valuable contribution to the next generation of Environmental Information Systems in the context of real time mapping for monitoring and security, particularly for systems that employ a service oriented architecture.

Testing term structure estimation methods:evidence from the UK STRIPs market

Prices and yields of UK government zero-coupon bonds are used to test alternative yield curve estimation models. Zero-coupon bonds permit a more pure comparison, as the models are providing only the interpolation service and also not making estimation feasible. It is found that better yield curves estimates are obtained by fitting to the yield curve directly rather than fitting first to the discount function. A simple procedure to set the smoothness of the fitted curves is developed, and a positive relationship between oversmoothness and the fitting error is identified. A cubic spline function fitted directly to the yield curve provides the best overall balance of fitting error and smoothness, both along the yield curve and within local maturity regions.

Projected sequential Gaussian processes: flexible interpolation for large data sets

Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential framework for inference in such projected processes is presented, where the observations are considered one at a time. We introduce a C++ library for carrying out such projected, sequential estimation which adds several novel features. In particular we have incorporated the ability to use a generic observation operator, or sensor model, to permit data fusion. We can also cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the variogram parameters is based on maximum likelihood estimation. We illustrate the projected sequential method in application to synthetic and real data sets. We discuss the software implementation and suggest possible future extensions.

Projected sequential Gaussian processes:a C++ tool for interpolation of large datasets with heterogeneous noise

Heterogeneous datasets arise naturally in most applications due to the use of a variety of sensors and measuring platforms. Such datasets can be heterogeneous in terms of the error characteristics and sensor models. Treating such data is most naturally accomplished using a Bayesian or model-based geostatistical approach; however, such methods generally scale rather badly with the size of dataset, and require computationally expensive Monte Carlo based inference. Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential Bayesian framework for inference in such projected processes is presented. The observations are considered one at a time which avoids the need for high dimensional integrals typically required in a Bayesian approach. A C++ library, gptk, which is part of the INTAMAP web service, is introduced which implements projected, sequential estimation and adds several novel features. In particular the library includes the ability to use a generic observation operator, or sensor model, to permit data fusion. It is also possible to cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the covariance parameters is explored, including the impact of the projected process approximation on likelihood profiles. We illustrate the projected sequential method in application to synthetic and real datasets. Limitations and extensions are discussed. © 2010 Elsevier Ltd.

Transfer function-noise modeling and spatial interpolation to evaluate the risk of extreme (shallow) water-table levels in the Brazilian Cerrados

Water regimes in the Brazilian Cerrados are sensitive to climatological disturbances and human intervention. The risk that critical water-table levels are exceeded over long periods of time can be estimated by applying stochastic methods in modeling the dynamic relationship between water levels and driving forces such as precipitation and evapotranspiration. In this study, a transfer function-noise model, the so called PIRFICT-model, is applied to estimate the dynamic relationship between water-table depth and precipitation surplus/deficit in a watershed with a groundwater monitoring scheme in the Brazilian Cerrados. Critical limits were defined for a period in the Cerrados agricultural calendar, the end of the rainy season, when extremely shallow levels (< 0.5-m depth) can pose a risk to plant health and machinery before harvesting. By simulating time-series models, the risk of exceeding critical thresholds during a continuous period of time (e.g. 10 days) is described by probability levels. These simulated probabilities were interpolated spatially using universal kriging, incorporating information related to the drainage basin from a digital elevation model. The resulting map reduced model uncertainty. Three areas were defined as presenting potential risk at the end of the rainy season. These areas deserve attention with respect to water-management and land-use planning.