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

Multivariate emulation of computer simulators: model selection and diagnostics with application to a humanitarian relief model

We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for multivariate covariance-separable emulators are developed and techniques to improve the adequacy of an emulator are discussed and implemented. A variety of emulators are compared for a humanitarian relief simulator, modelling aid missions to Sicily after a volcanic eruption and earthquake, and a sensitivity analysis is conducted to determine the sensitivity of the simulator output to changes in the input variables. The results from parametric and nonparametric emulators are compared in terms of prediction accuracy, uncertainty quantification and scientific interpretability

Spectral rate theory for projected two-state kinetics

Classical rate theories often fail in cases where the observable(s) or order parameter(s) used are poor reaction coordinates or the observed signal is deteriorated by noise, such that no clear separation between reactants and products is possible. Here, we present a general spectral two-state rate theory for ergodic dynamical systems in thermal equilibrium that explicitly takes into account how the system is observed. The theory allows the systematic estimation errors made by standard rate theories to be understood and quantified. We also elucidate the connection of spectral rate theory with the popular Markov state modeling (MSM) approach for molecular simulation studies. An optimal rate estimator is formulated that gives robust and unbiased results even for poor reaction coordinates and can be applied to both computer simulations and single-molecule experiments. No definition of a dividing surface is required. Another result of the theory is a model-free definition of the reaction coordinate quality (RCQ). The RCQ can be bounded from below by the directly computable observation quality (OQ), thus providing a measure allowing the RCQ to be optimized by tuning the experimental setup. Additionally, the respective partial probability distributions can be obtained for the reactant and product states along the observed order parameter, even when these strongly overlap. The effects of both filtering (averaging) and uncorrelated noise are also examined. The approach is demonstrated on numerical examples and experimental single-molecule force probe data of the p5ab RNA hairpin and the apo-myoglobin protein at low pH, here focusing on the case of two-state kinetics

MODELING AND MANAGEMENT OF WATER QUANTITY AND QUALITY IN COLD-CLIMATE PRAIRIE WATERSHEDS

Saskatchewan’s surface and ground water sources are vital to life in the province, not only as the supply of safe drinking water for the residents, but also as a key driver of economic activity. The Qu'Appelle and Assiniboine River Basins are among the highly valued water resources in the province as they supply water for more than one-third of the population of Saskatchewan and contain a chain of eight lakes that are major recreational and economically valued resources in the region. The health of several watersheds within these highly valued river basins is being degraded by intensive agricultural and other developmental activities. The decision making processes for sustainable water management in these watersheds is stunted by limited observed field data. As a result, for Saskatchewan watersheds in general, and the Qu’Appelle and Assiniboine River Basins in particular, a better understanding is required of the type, extent and sources of pollutant loadings, and effects of potential alternative management practices may have to mitigate water quality problems. Modeling approaches that have the capacity to analyze the quantity and quality of water resources, identify existing and potential watershed stressors, and the relative importance of best management options are therefore needed. With the intention of helping decision makers in the province, this thesis focuses on developing an eco-hydrological model, which is suitable for Canadian prairie watersheds and capable of simulating the long term effects of management practices. Following a review of several models, the Soil and Water Assessment Tool (SWAT) has been selected for this study. In order achieve the objectives, the SWAT model has been modified to suit site specific characteristics of the Canadian prairies. The first such modification was to incorporate the numerous landscape depressions that vary in storage capacity into SWAT. This was done by representing depression storage heterogeneity using a probability distribution using an algorithm called “Probability Distributed Landscape Depressions (PDLD)”. The modified model, called SWAT-PDLD, was tested over two prairie watersheds: the Assiniboine and Moose Jaw watersheds. An improved simulation for streamflow was achieved for both case study watersheds as compared to the original SWAT lumped storage approach. The other modification to SWAT was the incorporation of seasonally varying soil erodibility due to the cold climate conditions. This was done using a sediment module with a time variant soil erodibility factor that allows the value of soil erodibility to vary between seasons. The modified SWAT-PDLD along with seasonally varying soil erodibility was tested for sediment export simulation for the same two case study watersheds: the Assiniboine and Moose Jaw watersheds. Results show an improved sediment simulation for both case study watersheds when seasonally varying soil erodibility factors are considered as compared to the original SWAT model sediment module, which uses annual values of soil erodibility. The modified model was also used to simulate phosphorous and nitrogen export from the Assiniboine watershed and a satisfactorily model performance was obtained. In addition, the developed model was used to assess the impacts of three different management practices on the export of pollutants for the Assiniboine watershed. The scenarios considered were conservation tillage, a cover crop, and filter strips. Model results show that both the filter strips and cover crops decreased sediment, phosphorous, and nitrogen export, while conservation tillage increased phosphorous export in the study watershed. Finally, the study investigated the different sources of modeling uncertainty for the developed model. Parameter as well as precipitation, observed discharge, and model structure uncertainty of the SWAT-PDLD model was evaluated. Parameter uncertainty was quantified using three different techniques that include GLUE, ParaSol, and SUFI-2. Model structure uncertainty was assessed using a framework that combines the Bayesian Model Averaging (BMA) and Shuffled Complex Evolution (SCE). Results suggest that ignoring either input error or model structure uncertainty will lead to unrealistic model simulations and incorrect uncertainty bounds. The study also shows that prediction uncertainty bounds, posterior parameter distribution, and final parameter values vary between methods

Multi-model Ensemble Analysis with Neural Network Gaussian Processes

Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from rescaling low-resolution climate models. We propose a statistical approach, called NN-GPR, using Gaussian process regression (GPR) with an infinitely wide deep neural network based covariance function. NN-GPR requires no assumptions about the relationships between models, no interpolation to a common grid, no stationarity assumptions, and automatically downscales as part of its prediction algorithm. Model experiments show that NN-GPR can be highly skillful at surface temperature and precipitation forecasting by preserving geospatial signals at multiple scales and capturing inter-annual variability. Our projections particularly show improved accuracy and uncertainty quantification skill in regions of high variability, which allows us to cheaply assess tail behavior at a 0.44$^\circ$/50 km spatial resolution without a regional climate model (RCM). Evaluations on reanalysis data and SSP245 forced climate models show that NN-GPR produces similar, overall climatologies to the model ensemble while better capturing fine scale spatial patterns. Finally, we compare NN-GPR's regional predictions against two RCMs and show that NN-GPR can rival the performance of RCMs using only global model data as input.Comment: 12 pages, 9 figure

Multivariate calibration of a water and energy balance model in the spectral domain

The objective of this paper is to explore the possibility of using multiple variables in the calibration of hydrologic models in the spectral domain. A simple water and energy balance model was used, combined with observations of the energy balance and the soil moisture profile. The correlation functions of the model outputs and the observations for the different variables have been calculated after the removal of the diurnal cycle of the energy balance variables. These were transformed to the frequency domain to obtain spectral density functions, which were combined in the calibration algorithm. It has been found that it is best to use the square root of the spectral densities in the parameter estimation. Under these conditions, spectral calibration performs almost equally as well as time domain calibration using least squares differences between observed and simulated time series. Incorporation of the spectral coefficients of the cross-correlation functions did not improve the results of the calibration. Calibration on the correlation functions in the time domain led to worse model performance. When the meteorological forcing and model calibration data are not overlapping in time, spectral calibration has been shown to lead to an acceptable model performance. Overall, the results in this paper suggest that, in case of data scarcity, multivariate spectral calibration can be an attractive tool to estimate model parameters

Ensemble-characterisation of satellite rainfall uncertainty and its impacts on the hydrological modelling of a sparsely gauged basin in Western Africa

Many areas of the planet lack the infrastructure required to make accurate and timely estimations of rainfall. This problem is especially acute in sub-Saharan Africa, where a paucity of rain recording radar and sufficiently dense raingauge networks combine with highly variable rainfall, a reliance on agriculture that is predominantly rain fed and systems that are prone to flooding and drought. Satellite Rainfall Estimates (SRFE) are useful as they can provide additional spatial and temporal information to drive various downstream environmental models and early warning systems (EWS). However, when operating at higher spatial and temporal resolutions SRFE contain large uncertainties which propagate through the downstream models. This thesis uses the TAMSAT1 SRFE algorithm developed by Teo (2006) to estimate the rainfall over a large, data sparse and heterogenous catchment in the Senegal Basin. The uncertainty within the TAMSAT1 SRFE is represented using a set of ensemble estimates, each unique but equiprobable based on the full conditional distribution of the recorded rainfall, produced using the TAMSIM algorithm, also developed by Teo (2006). The ensemble rainfall estimates were then used in turn to drive a Pitman Rainfall-Runoff model of the catchment hydrology. The use of ensemble rainfall estimates was shown to be incompatible with the pre-calibrated parameter values for the hydrological model. A novel approach, the EnsAll method, was developed to calibrate the hydrological model which incorporated each individual ensemble member. The EnsAll calibrated model showed the greatest skill when driven by the ensemble rainfall estimates and little bias. A comparison of the hydrographs produced from TAMSIM ensemble rainfall estimates and that from an ensemble of perturbed TAMSAT1 estimates showed that the full spatio-temporally distributed method used by TAMSIM is superior to a simpler perturbation method for characterizing SRFE uncertainty. Overall, the SRFE used were shown to outperform the rainfall estimates produced from the sparse raingauge network as a hydrological model driver. However, they did demonstrate a lack of ability to represent the large interseasonal variations in rainfall resulting in large systematic biases. These biases were observed propagating directly to the modelled hydrological ouput

Ensemble-characterisation of satellite rainfall uncertainty and its impacts on the hydrological modelling of a sparsely gauged basin in Western Africa

Many areas of the planet lack the infrastructure required to make accurate and timely estimations of rainfall. This problem is especially acute in sub-Saharan Africa, where a paucity of rain recording radar and sufficiently dense raingauge networks combine with highly variable rainfall, a reliance on agriculture that is predominantly rain fed and systems that are prone to flooding and drought. Satellite Rainfall Estimates (SRFE) are useful as they can provide additional spatial and temporal information to drive various downstream environmental models and early warning systems (EWS). However, when operating at higher spatial and temporal resolutions SRFE contain large uncertainties which propagate through the downstream models.This thesis uses the TAMSAT1 SRFE algorithm developed by Teo (2006) to estimate the rainfall over a large, data sparse and heterogenous catchment in the Senegal Basin. The uncertainty within the TAMSAT1 SRFE is represented using a set of ensemble estimates, each unique but equiprobable based on the full conditional distribution of the recorded rainfall, produced using the TAMSIM algorithm, also developed by Teo (2006). The ensemble rainfall estimates were then used in turn to drive a Pitman Rainfall-Runoff model of the catchment hydrology.The use of ensemble rainfall estimates was shown to be incompatible with the pre-calibrated parameter values for the hydrological model. A novel approach, the EnsAll method, was developed to calibrate the hydrological model which incorporated each individual ensemble member. The EnsAll calibrated model showed the greatest skill when driven by the ensemble rainfall estimates and little bias. A comparison of the hydrographs produced from TAMSIM ensemble rainfall estimates and that from an ensemble of perturbed TAMSAT1 estimates showed that the full spatio-temporally distributed method used by TAMSIM is superior to a simpler perturbation method for characterizing SRFE uncertainty.Overall, the SRFE used were shown to outperform the rainfall estimates produced from the sparse raingauge network as a hydrological model driver. However, they did demonstrate a lack of ability to represent the large interseasonal variations in rainfall resulting in large systematic biases. These biases were observed propagating directly to the modelled hydrological ouput