Historical groundwater heads at a confined aquifer in southwest Florida show a nonstationary long-term (multi-year) fluctuation. Stochastic modeling of these data is a main topic here. Ahn and Salas (Ahn, H., Salas, J.D., 1997. Groundwater head sampling based on stochastic analysis. Water Resour. Res. 33(12), 2769-2780) introduced an approach to build time series models of nonstationary data at different time intervals based on an observed time series sampled at a reference interval. The model utilized in their study was a first-order difference autoregressive integrated moving average model. However, some groundwater head data may also be fitted adequately by a second-order difference time series model. Thus, this study derived variance and autocovariance equations for the second-order difference time series model at various time intervals as a function of the parameters of the referenced model. The derived equations are useful for building a time series model at arbitrary time intervals. Unlike the first-order difference models, the variance and auto-covariance equations here are fully derivable, making the second-order difference models more convenient than the first-order difference models. The modeling procedure with the derived equations was tested through example problems of: (1) filling in gaps in time series; and (2) sampling frequency design. The results showed that the second-order difference model in some cases produces lower interpolation error than that of the first-order difference model. (C) Published by Elsevier Science B.V.
