Estimating hydraulic diffusivity in coastal confined aquifer under tidal fluctuation using a frequency domain model

Abstract

Oceanic tidal propagation into the coastal aquifers is a cost-effective method for estimating hydraulic parameters in coastal aquifers, and identifying the most suitable parameter estimation method for coastal aquifers based on the observations has become an intensively studied subject. In this study, the frequency domain model, LPMLE3 (combination of a local polynomial (LP) signal processing technique with a maximum likelihood estimator (MLE)), was applied to estimate the hydraulic diffusivity (λ) of the coastal aquifer by adjusting the mathematical model in LPMLE3. The mathematical model in LPMLE3 has been adjusted by removing the convective term from the convective diffusion equation within LPMLE3, and a newly developed frequency-domain analytical solution that describes the head changes due to tidal fluctuations in coastal confined aquifers was used to replace the diffusion term. For comparison, an analytical solution in the time domain was also derived by Green’s functions method. After that, the particle swarm optimization algorithm and Markov Chain Monte Carlo method were used to estimate λ. Results show that LPMLE3 performed well in estimating homogeneous or heterogeneous aquifers with complicated boundary conditions. The estimated error of λ is within 10 % in a heterogeneous aquifer when the variance of the natural logarithm of the aquifer hydraulic conductivity is less than 0.05 (σlnK2≤0.05). If the coastal aquifer has a sloping beach, the estimated λ by LPMLE3 method accurately when the sloping beach angle is greater than 65°. As for an inclined coastal aquifer, the dip angle has a greater influence on the offshore areas than the nearshore areas and the estimation errors are relatively small (less than 15 %) when the dip angle is within a range of 0- 15°.