Explicit estimation of aquifer diffusivity from linear stream stage

Different approaches are available for estimation of aquifer hydraulic diffusivity from a linear stream-stage variation and corresponding groundwater heads. These approaches require interpolation from tabulated values or computation of hydraulic gradient at the stream aquifer interface. Certain methods use approximation or interpolation of tabulated values for an infinite series. These methods are prone to errors in the estimated aquifer hydraulic diffusivity. An alternative approach is to use a closed-form solution of the problem and develop an explicit expression for the aquifer hydraulic diffusivity, which is free from errors of using infinite series, interpolation, and computation of hydraulic gradient. Such an alternative method is developed for a linearly varying stream stage. The new method can yield the estimate of hydraulic diffusivity even from a single observation. The proposed method would be applicable to practical hydraulic engineering problems keeping in view that most of a rising part of a stream stage hydrograph can be approximated by a linear rise and certain rivers may show a linearly varying stream stage. Use of the new method is demonstrated on published and field data, which shows that the estimates obtained using the new method are comparable to that obtained using an optimization approach.