Confronting input, parameter, structural, and measurement uncertainty in multi-site multiple-response watershed modeling using Bayesian inferences

2012 Fall.Includes bibliographical references.Simulation modeling is arguably one of the most powerful scientific tools available to address questions, assess alternatives, and support decision making for environmental management. Watershed models are used to describe and understand hydrologic and water quality responses of land and water systems under prevailing and projected conditions. Since the promulgation of the Clean Water Act of 1972 in the United States, models are increasingly used to evaluate potential impacts of mitigation strategies and support policy instruments for pollution control such as the Total Maximum Daily Load (TMDL) program. Generation, fate, and transport of water and contaminants within watershed systems comprise a highly complex network of interactions. It is difficult, if not impossible, to capture all important processes within a modeling framework. Although critical natural processes and management actions can be resolved at varying spatial and temporal scales, simulation models will always remain an approximation of the real system. As a result, the use of models with limited knowledge of the system and model structure is fraught with uncertainty. Wresting environmental decisions from model applications must consider factors that could conspire against credible model outcomes. The main goal of this study is to develop a novel Bayesian-based computational framework for characterization and incorporation of uncertainties from forcing inputs, model parameters, model structures, and measured responses in the parameter estimation process for multisite multiple-response watershed modeling. Specifically, the following objectives are defined: (i) to evaluate the effectiveness and efficiency of different computational strategies in sampling the model parameter space; (ii) to examine the role of measured responses at various locations in the stream network as well as intra-watershed processes in enhancing the model performance credibility; (iii) to facilitate combining predictions from competing model structures; and (iv) to develop a statistically rigorous procedure for incorporation of errors from input, parameter, structural and measurement sources in the parameter estimation process. The proposed framework was applied for simulating streamflow and total nitrogen at multiple locations within a 248 square kilometer watershed in the Midwestern United States using the Soil and Water Assessment Tool (SWAT). Results underlined the importance of simultaneous treatment of all sources of uncertainty for parameter estimation. In particular, it became evident that incorporation of input uncertainties was critical for determination of model structure for runoff generation and also representation of intra-watershed processes such as denitrification rate and dominant pathways for transport of nitrate within the system. The computational framework developed in this study can be implemented to establish credibility for modeling watershed processes. More importantly, the framework can reveal how collection of data from different responses at different locations within a watershed system of interest would enhance the predictive capability of watershed models by reducing input, parametric, structural, and measurement uncertainties

Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening

This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. Multicomponent persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for chemical and biological problems. Extensive numerical experiments involving more than 4,000 protein-ligand complexes from the PDBBind database and near 100,000 ligands and decoys in the DUD database are performed to test respectively the scoring power and the virtual screening power of the proposed topological approaches. It is demonstrated that the present approaches outperform the modern machine learning based methods in protein-ligand binding affinity predictions and ligand-decoy discrimination

Structural Kinetic Modeling of Metabolic Networks

To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit kinetic modeling based on differential equations is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a detailed and quantitative account of the dynamical capabilities of metabolic systems, without requiring any explicit information about the particular functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible, or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a systematic statistical exploration of the comprehensive parameter space. The method is applied to two paradigmatic examples: The glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.Comment: 14 pages, 8 figures (color