Estimating uncertainty of mean water table depth in the contiguous United States using highly parameterized linear inverse method

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Because of spatiotemporal observation gaps and prohibitive computational cost, estimating uncertainty of mean water table depth in the continental scale is a challenging problem. Based on the groundwater flow of mean water table, we first analyzed uncertainty of the mean water table depth in the contiguous US using a highly parameterized linear inverse method with unknown boundary condition and source/sink terms. To estimate uncertainty of the mean heads, the total relative errors of temporal heads and mean heads for all observed wells with more than one head instead of the relative error of temporal heads and mean head for each observed well was proposed to obtain t Location-scale and Gaussian distributions of the total relative errors in the synthetic cases. The results indicate that uncertainties of the mean heads by t Location-scale distribution are more accurate than those by Gaussian distribution. Then, we applied the inverse method and t Location-scale distribution of the total relative errors in the contiguous US to estimate uncertainty of the mean water table depth during 1900–2016. The results demonstrate that uncertainty in the K values did not result in large uncertainty of the mean water table depth. Uncertainty of the mean water table depth in the contiguous US was first estimated based on variation of hydraulic conductivity and the observed mean water table, where 100 realizations of the mean water table depth were obtained by t Location-scale distribution. The results demonstrate both the feasibility and high precision of the inverse method.