Bayesian data assimilation for stochastic multiscale models of transport in porous media.

We investigate Bayesian techniques that can be used to reconstruct field variables from partial observations. In particular, we target fields that exhibit spatial structures with a large spectrum of lengthscales. Contemporary methods typically describe the field on a grid and estimate structures which can be resolved by it. In contrast, we address the reconstruction of grid-resolved structures as well as estimation of statistical summaries of subgrid structures, which are smaller than the grid resolution. We perform this in two different ways (a) via a physical (phenomenological), parameterized subgrid model that summarizes the impact of the unresolved scales at the coarse level and (b) via multiscale finite elements, where specially designed prolongation and restriction operators establish the interscale link between the same problem defined on a coarse and fine mesh. The estimation problem is posed as a Bayesian inverse problem. Dimensionality reduction is performed by projecting the field to be inferred on a suitable orthogonal basis set, viz. the Karhunen-Loeve expansion of a multiGaussian. We first demonstrate our techniques on the reconstruction of a binary medium consisting of a matrix with embedded inclusions, which are too small to be grid-resolved. The reconstruction is performed using an adaptive Markov chain Monte Carlo method. We find that the posterior distributions of the inferred parameters are approximately Gaussian. We exploit this finding to reconstruct a permeability field with long, but narrow embedded fractures (which are too fine to be grid-resolved) using scalable ensemble Kalman filters; this also allows us to address larger grids. Ensemble Kalman filtering is then used to estimate the values of hydraulic conductivity and specific yield in a model of the High Plains Aquifer in Kansas. Strong conditioning of the spatial structure of the parameters and the non-linear aspects of the water table aquifer create difficulty for the ensemble Kalman filter. We conclude with a demonstration of the use of multiscale stochastic finite elements to reconstruct permeability fields. This method, though computationally intensive, is general and can be used for multiscale inference in cases where a subgrid model cannot be constructed

Bayesian data assimilation for stochastic multiscale models of transport in porous media.

We investigate Bayesian techniques that can be used to reconstruct field variables from partial observations. In particular, we target fields that exhibit spatial structures with a large spectrum of lengthscales. Contemporary methods typically describe the field on a grid and estimate structures which can be resolved by it. In contrast, we address the reconstruction of grid-resolved structures as well as estimation of statistical summaries of subgrid structures, which are smaller than the grid resolution. We perform this in two different ways (a) via a physical (phenomenological), parameterized subgrid model that summarizes the impact of the unresolved scales at the coarse level and (b) via multiscale finite elements, where specially designed prolongation and restriction operators establish the interscale link between the same problem defined on a coarse and fine mesh. The estimation problem is posed as a Bayesian inverse problem. Dimensionality reduction is performed by projecting the field to be inferred on a suitable orthogonal basis set, viz. the Karhunen-Loeve expansion of a multiGaussian. We first demonstrate our techniques on the reconstruction of a binary medium consisting of a matrix with embedded inclusions, which are too small to be grid-resolved. The reconstruction is performed using an adaptive Markov chain Monte Carlo method. We find that the posterior distributions of the inferred parameters are approximately Gaussian. We exploit this finding to reconstruct a permeability field with long, but narrow embedded fractures (which are too fine to be grid-resolved) using scalable ensemble Kalman filters; this also allows us to address larger grids. Ensemble Kalman filtering is then used to estimate the values of hydraulic conductivity and specific yield in a model of the High Plains Aquifer in Kansas. Strong conditioning of the spatial structure of the parameters and the non-linear aspects of the water table aquifer create difficulty for the ensemble Kalman filter. We conclude with a demonstration of the use of multiscale stochastic finite elements to reconstruct permeability fields. This method, though computationally intensive, is general and can be used for multiscale inference in cases where a subgrid model cannot be constructed

Retinal Effects of 6 Months of Daily Use of Tadalafil or Sildenafil

Objective: To assess changes in electroretinography (ERG) and other retinal function parameters during 6 months of daily use of tadalafil, sildenafil citrate, or placebo

Climate uncertainty and implications for U.S. state-level risk assessment through 2050.

Decisions for climate policy will need to take place in advance of climate science resolving all relevant uncertainties. Further, if the concern of policy is to reduce risk, then the best-estimate of climate change impacts may not be so important as the currently understood uncertainty associated with realizable conditions having high consequence. This study focuses on one of the most uncertain aspects of future climate change - precipitation - to understand the implications of uncertainty on risk and the near-term justification for interventions to mitigate the course of climate change. We show that the mean risk of damage to the economy from climate change, at the national level, is on the order of one trillion dollars over the next 40 years, with employment impacts of nearly 7 million labor-years. At a 1% exceedance-probability, the impact is over twice the mean-risk value. Impacts at the level of individual U.S. states are then typically in the multiple tens of billions dollar range with employment losses exceeding hundreds of thousands of labor-years. We used results of the Intergovernmental Panel on Climate Change's (IPCC) Fourth Assessment Report 4 (AR4) climate-model ensemble as the referent for climate uncertainty over the next 40 years, mapped the simulated weather hydrologically to the county level for determining the physical consequence to economic activity at the state level, and then performed a detailed, seventy-industry, analysis of economic impact among the interacting lower-48 states. We determined industry GDP and employment impacts at the state level, as well as interstate population migration, effect on personal income, and the consequences for the U.S. trade balance

Climate uncertainty and implications for U.S. state-level risk assessment through 2050.

Decisions for climate policy will need to take place in advance of climate science resolving all relevant uncertainties. Further, if the concern of policy is to reduce risk, then the best-estimate of climate change impacts may not be so important as the currently understood uncertainty associated with realizable conditions having high consequence. This study focuses on one of the most uncertain aspects of future climate change - precipitation - to understand the implications of uncertainty on risk and the near-term justification for interventions to mitigate the course of climate change. We show that the mean risk of damage to the economy from climate change, at the national level, is on the order of one trillion dollars over the next 40 years, with employment impacts of nearly 7 million labor-years. At a 1% exceedance-probability, the impact is over twice the mean-risk value. Impacts at the level of individual U.S. states are then typically in the multiple tens of billions dollar range with employment losses exceeding hundreds of thousands of labor-years. We used results of the Intergovernmental Panel on Climate Change's (IPCC) Fourth Assessment Report 4 (AR4) climate-model ensemble as the referent for climate uncertainty over the next 40 years, mapped the simulated weather hydrologically to the county level for determining the physical consequence to economic activity at the state level, and then performed a detailed, seventy-industry, analysis of economic impact among the interacting lower-48 states. We determined industry GDP and employment impacts at the state level, as well as interstate population migration, effect on personal income, and the consequences for the U.S. trade balance

Executive summary for assessing the near-term risk of climate uncertainty : interdependencies among the U.S. states.

Policy makers will most likely need to make decisions about climate policy before climate scientists have resolved all relevant uncertainties about the impacts of climate change. This study demonstrates a risk-assessment methodology for evaluating uncertain future climatic conditions. We estimate the impacts of climate change on U.S. state- and national-level economic activity from 2010 to 2050. To understand the implications of uncertainty on risk and to provide a near-term rationale for policy interventions to mitigate the course of climate change, we focus on precipitation, one of the most uncertain aspects of future climate change. We use results of the climate-model ensemble from the Intergovernmental Panel on Climate Change's (IPCC) Fourth Assessment Report 4 (AR4) as a proxy for representing climate uncertainty over the next 40 years, map the simulated weather from the climate models hydrologically to the county level to determine the physical consequences on economic activity at the state level, and perform a detailed 70-industry analysis of economic impacts among the interacting lower-48 states. We determine the industry-level contribution to the gross domestic product and employment impacts at the state level, as well as interstate population migration, effects on personal income, and consequences for the U.S. trade balance. We show that the mean or average risk of damage to the U.S. economy from climate change, at the national level, is on the order of $1 trillion over the next 40 years, with losses in employment equivalent to nearly 7 million full-time jobs