Deterministic And Stochastic Analyses Of Groundwater Level Fluctuations In Homogeneous And Heterogeneous Aquifers

Groundwter system is a complex dynamic system.Groundwater recharge and discharge are two of the main processes in the basin-scale water cycle.These processes vary over space and time and their temporal and spatial variations strongly affect quantity and quality of groundwater resources.Effective management of groundwater resources requires a deeper understanding of these processes,especially their temporal and spatial variations.It is difficult,if not impossible,to measure precisely groundwater recharge and discharge,due to complexity of these variables.However,it is relatively easy to measure groundwater level or hydraulic head in monitoring wells.Extensive data of groundwater levels measured at various time intervals over periods of years or decades are often available.The fluctuations of groundwater level are dynamic responses of the groundwater system to its recharge and discharge,and thus contain significant amount of information about the nature of the recharge and discharge.It is necessary to inverstigate the temporal and spatial variability of groundwater level fluctuations in order to obtain valuable information about groundwater recharge and discharge.In this dissertation transient groundwater flow along a transect of an unconfined aquifer from a divide to a nearby surface water body,e.g.,a river or lake,was investigated in both deterministic and stochastic framework.Several analytical solutions for the groundwater level and lateral discharge without and with a source term and close-form expresions for the variance,covariance,and spectrum of h were derived in homogeneous and heterogeneous auqifers.The results show that the effect of initial condition lasts longer in a less permeable or longer aquifer than in a more permeable or short aquifer.The solution derived was applied to estimate daily recharge and evapotranspiration as well as lateral discharge.We demonstrated that the recharge was reasonably estimated with the commonly-used water-table fluctuation(WTF)method using the water table data away from a fixed-head boundary but the evapotranspiration was overestimated and the net recharge was underestimated because of the lack of consideration of lateral drainage and aquifer storage change in the WTF method.We also derived the analytical solutions for the water level and lateral discharge in a heterogeneous unconfined aquifer under time-dependent sources and boundary conditions.The heterogeneity is characterized with a number of sections of different hydraulic conductivity values.It is shown that the heterogeneity significantly affects water level but not lateral discharge.The lateral discharge varies linearly with the distance from a divide to a river over most part of the aquifer in both homogeneous and heterogeneous aquifer no matter the source is constant or time-dependent as long as it is spatially uniform.Under time-dependent but spatially uniform recharge,the lateral discharge Q may change linearly with the distance from a divide to a river over most part of a one-dimensionally homogeneous or heterogeneous aquifer away from the river and that the recharge affects only Q near the river.The effect of boundary on the groundwater level is limited nearbyt the boundary,and the amplitude of groundwater level fluctuations depends on hydraulic conductivity.We then studied the groundwater level fluctuations due to a white noise random source,flux boundary,and head boundary in a homogeneous aquifer with non-stationary spectral analyses.Close-form expressions for the variance,covariance,and spectrum of groundwater level were derived.The results show that due to affects of deterministic initial condition,groundwater level fluctuations are temporally nonstationary in early time and gradually become temporally stationary while t →∞.Groundwater levels fluctuate as a Brownian motion(Hurst coefficient H=0.5,power law index of spectrum α = 2)or temporal scaling of h(t)exists while they are temporally nonstationary under white noise sources term,and gradually become a weakly or not correlated processes,pink noise or white noise due to H ≤ 0(i.e.,0<a<1)while they become temporally stationary.The time at which h(t)becomes stationary under the white noise flux boundary is shorter than that under the white noise source term,and is shortest under the white noise head boundary for the same aquifer parameters.The temporal correlation of fluctuations increases with the distance away from the random boundary and temporal uncertainties of groundwater level fluctuations are mainly caused by the random sources term except the region near the random boundary.We also have studied the groundwater level fluctuations under a white noise source in a heterogeneous unconfined aquifer.Using nonstationary spectral analyses and superposition principle,the closed-form expressions for the spatiotemporal variance and covariance of stochastic processes h(x,t)were derived.The results show that h(x,t)is temporally nonstationary due to a deterministic initial condition and random sources term,and is spatially nonstationary due to the deterministic boundary condition and space-dependent gradient.The temporal head variance is proportional to time at early time,gradually increases as time progresses.The larger variance of log transmissivity,leading to the larger spatial variability of head,and larger temporal variability of groundwater fluctuations.The temporal correlation of groundwater levels decreases with the distance between two points.