| Subsurface hydrologic processes include a series of water/energy/solute movements in water/energy/mass cycles below the surface of the Earth.In subsurface hydrological modeling the needs to identify controlling processes for model development and improvement have been long recognized,prompting the development of many identification methods.A subsurface hydrological model may consist of multiple process-level sub-models,and each sub-model represents a process that is key to the operation of the simulated system.Global sensitivity analysis methods have been widely used to identify important or influential processes for system model development and improvement.A variety of types of uncertainties sources exist in subsurface hydrologic modeling,including the data uncertainty,parameter uncertainty,and model uncertainty.Many existing methods of global sensitivity analysis only consider parametric uncertainty and are not capable of handling model uncertainty caused by multiple process models that arise from competing hypotheses about one or more processes.To address this problem,this dissertation focuses on addressing uncertainty in process models and parameters,and on identifying the controlling processes.The dissertation research includes the following two parts:proposal of new process sensitivity analysis methods and application of the new methods to subsurface hydrological models.The first part of this dissertation is mainly concentrated on developing two new methods to probe model output sensitivity to competing process models:The first new method is called variance-based process sensitivity analysis method and it is presented in Chapter 2.This method integrates the model averaging methods with traditional Sobol's variance-based global sensitivity analysis method to address uncertainty in process models and parameters.It yields two process sensitivity indices.The first one is called first-order process sensitivity index,which was derived by Dai et al.(2017b)as a single summary measure of relative process importance.The second one is called total-effect process sensitivity index,which is derived as a single summary measure of relative process influence.The total-effect process sensitivity index includes the first-order process sensitivity index and high-order indices that address process interactions.Evaluating the two indices is computationally expensive,because it relies on Monte Carlo sampling scheme that requires tens of thousands and even millions of model executions.To reduce computational cost,this dissertation develops a computationally efficient design and estimator to reduce the computational cost.This is demonstrated by a hypothetical one-dimensional(1-D)groundwater flow modeling that considers recharge process,geological process,and snowmelt process.Each of the three processes has two alternative process models,i.e.,the recharge process can be simulated by either linear or non-linear recharge models,the hydraulic conductivity filed can be either homogenous or heterogenous,and the snowmelt process can be either simulated by the degree-day method and the restricted degree-day radiation balance method,resulting in a total of eight system models by integrating the process models.In addition to the two process-sensitivity indices,this dissertation research develops another new method called multi-model absolute difference-based process sensitivity(MMADS)analysis method,and it is presented in Chapter 3.This method integrates the model averaging methods with traditional Morris screening method to address uncertainty in process models and parameters.The basic ideas of MMADS are to first evaluate the differences of the system model output caused by varying process models and/or parameter values embedded in the process models,and then to calculate the mean and variance of the differences for investigating process influence as in the Morris screening method.The results of this method can be used to screen non-influential system processes and parameters from further investigation.A binning method is also developed to reduce computational cost.The efficiency of this method is also demonstrated using the 1-D groundwater flow model.The second part of this dissertation is mainly focused on application of the two new methods for identifying the controlling processes in hydrologic modeling.We evaluated the performance of the two methods by using two hydrologic models:The first application is a two-dimensional(2-D)arsenic(As)sorption and reactive transport model based a laboratory experiment by Duan et al.(2020).A synthetic heterogeneous aquifer was constructed in a sand tank based on the observed hydrogeological conditions in a high As groundwater field site at Jianghan Plain.Three processes,namely,the physical process,the chemical process,and the sorption process were conceptualized.A total of 12=2×2×3 individual system models were considered,corresponding to the two physical process models(i.e.,heterogenous and homogenous permeability filed),two chemical process models(i.e.,heterogenous and homogenous distribution coefficient filed),and three sorption process models(i.e.,simple linear equilibrium model,dual first-order kinetic sorption model,and coupled linear equilibrium sorption model with a kinetic model for describing the oxidation of Fe(II)-bearing clay minerals).Each of the twelve models contains different number of uncertainty parameters.Using the variance-based process sensitivity analysis method with the computationally efficient schemes presented in Chapter 2,a total number of 216,000=12×(3+2)×3,600PFLOTRAN simulations were conducted on the supercomputer of the Florida State University to consider all possible combinations of model configurations and input parameters.We quantify the relative importance and influence of three processes to arsenic concentrations at the pumping wells under individual system models as well as multiple system models.Results show that the most important and influential process on the As concentration in the pumping well could change over time.At the very beginning of the simulation period after pumping started,the physical process significantly influences the As concentration in the pumping well.At the middle stage,the chemical process significantly influences the As concentration in the pumping well.At the final stage,the three different sorption models significantly influence the arsenic concentration in groundwater.The second application is a biogeochemical model at the groundwater-surface water interface within the Hanford Site's 300 Area.Multiple uncertainty sources across climate,flow,heat,and reaction processes were considered based on our understanding of the complex system.Variance-based process sensitivity analysis presented in Chapter 2 as well as the multi-model absolute difference-based process sensitivity analysis methods presented in Chapter 3 were used to identify the controlling processes with respect to the spatio-temporal distribution of the organic carbon(OC)consumption rate in the aquifer at the Hanford Site.The total number of PFLOTRAN simulations considering all possible combinations of model inputs and model configurations is 12,000=6×5×2×2×100for representing six scenarios,five thicknesses of alluvium layer,heterogeneous/homogeneous formations,with/without heat transport process,and 100reaction rates and permeability fields.Hopper supercomputer at the National Energy Research Scientific Computing Center(NERSC)is employed to perform the simulations.Both the variance-based process sensitivity analysis method and multi-model difference-based process sensitivity analysis method suggests the heat process is non-influential.Thus the biogeochemical model may be simplified without considering the heat process.In other words,the temperature-independent reaction rates may be sufficient to capture the OC consumption rate.The Appendix of this dissertation also presents a new open-source Python package,SAMMPy,for performing process sensitivity analysis under multiple system models.Within this framework,an environmental system is conceptualized as an integration of multiple system processes,each of which is represented by one or more process models with uncertain process model parameters.SAMMPy implements the two new sensitivity analysis methods that enables simultaneous generation of a range of process sensitivity indices with considering both parametric uncertainty and process model uncertainty.This package is publicly available on Git Hub via https://github.com/jyangfsu/SAMMPy.Example workflows of a mathematical test function(Sobol-G~*function)and a 1-D groundwater flow model documented in Jupyter Notebooks are also available in the repository. |
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