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Uncertainty Analysis and Inverse Modeling of Seawater Intrusion in Coastal Aquifers

Rajabi, Mohammad Mahdi | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47131 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Ataei Ashtiani, Behzad
  7. Abstract:
  8. Groundwater is the primary source of freshwater in many coastal areas and small islands around the world. The most important hazard to groundwater quality in coastal aquifers is seawater intrusion (SWI) resulting from over pumping, prolonged drought conditions and sea level rise due to climate change impacts. Numerical models of SWI are an important tool in the management of coastal aquifers. However, numerical modeling of SWI is one of the most challenging problems in groundwater hydrology. One of the reasons for the challenging nature of SWI numerical modeling is the relatively large level of uncertainty associated with the estimation of the model input parameters. This study focused on three key aspects of handling model input uncertainty in SWI studies which we review in the following: 1. Uncertainty analysis which involved quantifying the impact of model input uncertainties on the uncertainty in model outputs. A review of literature illustrates that Monte Carlo simulations are the most widely used method of uncertainty analysis in almost every field of engineering, including SWI numerical modeling. However, Monte Carlo simulations are computationally expensive and this has prevented their wide-spread use in real world SWI modeling studies. This study focuses on two approaches for solving the computational problem of Monte Carlo simulations:The use of optimized Latin hypercube sampling (OLHS) methods for efficient sampling from the probability distribution of model inputs. This study shows that different OLHS strategies improve the sampling efficiency with a factor between 2.4 to 6.4 compared to simple random sampling, and 1.5 to 3.9 compared to Latin hypercube sampling. The study also includes a comprehensive comparison of various OLHS methods, and concludes that the CLD-ESE strategy is the most efficient among the evaluated strategies. The study then proposes a novel approach for improving the efficiency of OLHS strategies. The proposed approach is based on the use of midpoints in the hypercube intervals as the initial design that is fed into the optimization algorithm of OLHS strategies. The study shows that this approach can improve the space-filling characteristics of OLHS by as much as 27 percent. The use of non-intrusive polynomial chaos expansions (PCEs) as a meta-model which replaces the original full model in Monte Carlo simulations. The study shows that despite the highly non-linear and non-smooth input/output relationship that exists in SWI models, non-intrusive PCEs of order 3 and 4 provide a reliable and yet computationally efficient surrogate of the original numerical model. 2. Sensitivity analysis which focuses on how the uncertainty in the outputs of the model can be allocated to different sources of uncertainty in the model inputs. Previous studies involving sensitivity analysis of groundwater numerical models have mostly relied on local methods, and a few more recent studies have employed derivative-based and variance-based global methods. However, for several reasons reviewed in this study, none of these methods has the necessary characteristics to be an ideal method for sensitive analysis of SWI models. The only method that has all the necessary characteristics is the moment-independent global method. However, the moment-independent method has extremely high computational demands, and this has been the major obstacle in the path of using this method for sensitivity analysis of SWI models. In this study, we have employed PCE meta-models to significantly accelerate the computational algorithm of the moment-independent method. Our study shows that this strategy also results in reliable estimates of the moment-independent sensitivity indices. As an example, the computational cost of estimating the delta indices for permeability and recharge rate in the Henry problem test case, reduces by a factor of 0,02 when the numerical model is replaced with the PCE meta-models.3. Stochastic inverse modeling which aims at providing quantitative estimates of model input uncertainties in the process of model calibration. In this study, the stochastic inverse modeling problem is formulated within the framework of Bayesian inference, and the proposed algorithm is subsequently extended to the fuzzy case. The resulting fuzzy Bayesian inference strategy allows for the incorporation of soft data (such as expert knowledge) into the estimation of model input parameters. The methodology also permits the use of imprecise field data in model calibration. To solve the computational problems associated with fuzzy Bayesian inference we have employed a two stage Markov Chain Monte Carlo method with involves a combined use of meta-modeling and numerical modeling, and the study shows that this approach can effectively reduce the computational cost of the proposed fuzzy Bayesian inference algorithm
  9. Keywords:
  10. Coastal Aquifer ; Sea Water Intrusion ; Numerical Modeling ; Sensitivity Analysis ; Uncertainty Analysis ; Inverse Modelling

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