A new theoretical solution of the effect of atmospheric pressure on water level

Abstract

Based on the partial differential equation governing the effect of atmospheric pressure on water level of confined well, deriving the boundary condition and considering the seepage water between well and aquifer, the author obtained the analytical solution of water level change in time domain under the action of an atmospheric pressure history with the Laplace transform method. This solution is composed of two terms:stable and retarded terms. The stable term is the multiplication of barometric efficiency and simultaneous atmospheric pressure, and it implies the value of water level after infinite time when the atmospheric pressure is a constant from the time in question. The retarded term is the transient process due to the time lag of water exchange between well and aquifer. From the solution, it is obtained that the interference of atmospheric pressure on water level is the integral superimposition of the contribution of all atmospheric pressure changes before the time in question. So that, we further found out the response function of pulsive atmospheric pressure history. Calculation shows: (1) The pulsive response function starts from zero and tends to a steady value, which is proportional to the barometric efficiency, when the time tends to infinity; (2) The retarded time depends on the mechanical property of aquifer and the radius of well. The larger the seepage coefficient, the smaller the radius of well and the thicker the aquifer, then the shorter the retarded time gets. This solution can be used as the theoretical basis for further analysis of the atmospheric effect and practical correcting method in the future.