Stochastic models in agricultural watersheds

A stochastic time-series approach using spectral analysis theory is developed and applied to drainage analysis of an agricultural watershed, Rio Grande Valley, New Mexico, U.S.A. The spectral theory demonstrates that a linear reservoir model is a suitable approximation to the Dupuit aquifer over a wide range of frequencies. A first-order perturbation of the variables allows the system parameters to be evaluated from both the stochastic solution of the fluctuating or zero-mean process, and the temporal-mean or steady-state solution. Deep percolation is estimated by first assuming a "no storage" situation in which recharge is a constant fraction (leaching fraction) of applied water. A second approach to deep percolation incorporates a soil-moisture reservoir to simulate storage in the soil zone. The equations developed are useful for characterizing drainage systems which exhibit a statistically stationary response to rainfall and/or irrigation.