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The operational phase of landfills may last for 20 years or more. Significant changes in leachate quality and generation rate may occur during this operational period. A mathematical model has been developed to simulate the landfill leachate behaviour and distributions of moisture and leachate constituents through the landfill, taking into consideration the effects of time-dependent landfill development on the hydraulic characteristics of waste and composition of leachate. The model incorporates governing equations that describe processes influencing the leachate production and biochemical processes taking place during the stabilization of wastes, including leachate flow, dissolution, acidogenesis and methanogenesis. To model the hydraulic property changes occurring during the development stage of the landfills, a conceptual modelling approach was proposed. This approach considers the landfill to consist of cells or columns of cells, which are constructed at different times, and considers each cell in the landfill to consist of several layers. Each layer is assumed to be a completely mixed reactor containing uniformly distributed solid waste, moisture, gases and micro-organisms. The use of the proposed conceptual model enables the incorporation of the spatial changes in hydraulic properties of the landfill into the model and also makes it possible to predict the spatial and temporal distributions of moisture and leachate constituents. The model was calibrated and partially verified using leachate data from Keele Valley Landfill in Ontario, Canada and data obtained from the literature. Ranges of values were proposed for model parameters applicable for real landfill conditions.

The knowledge of the statistical parameters of the variance, σ2, and the correlation scale, λ, characterizing the spatial structures of the log of the saturated hydraulic conductivity, lnKs, pore size distribution parameter α, and the specific water capacity, C, is required in stochastic modeling in order to understand the overall response of large‐scale heterogeneous unsaturated flow systems. These parameters are estimated assuming second‐order stationarity and an exponential semivariogram model with nugget effect. Methods of ordinary least squares (OLS), maximum likelihood (ML), and restricted maximum likelihood (RML) are used for estimating σ2 and λ, while methods of cross‐validation (kriging) and uncorrelated residuals are used to validate the semivariogram model with estimated σ2 and λ. The objectives of this study were to evaluate the sensitivity of σ2 and λ to the estimation methods and to discuss the implications of the analysis in view of the stochastic modeling. The significance of the results of parameter estimation and model validation in relation to the stochastic modeling of large‐scale transient unsaturated flow is demonstrated with two examples involving the variance of soil‐water pressure head, σ2h, and the vertical component of effective hydraulic conductivity, K*11. Results show that the estimated values of σ2 and λ are highly dependent on the estimation method. Although the majority of the estimated parameters pass the validation tests, the RML estimates of σ2 and λ used in estimating σ2h and K*11 significantly reduce the prediction uncertainties.

Summary Pollution of ground water caused by excessive and uncontrolled use of nitrogen fertilizer is worrying. A recent example of such pollution has been observed in an agricultural basin in the province of Nevsehir, Turkey, where up to 900 kg ha−1 nitrogen fertilizer is used for growing potatoes in sandy soils under irrigation. Using nitrogen fertilizer in amounts that guarantee large yields without polluting ground water is essential. We present results of field experiments and numerical simulations involving 15N‐labelled nitrogen fertilizer leaching. In the field, we monitored the movement of water and the distributions of nitrogen species within the soil–water–plant continuum. The detailed dynamics of the nitrogen cycle within the system were simulated. Simulations included calibration and validation of the nitrogen version of the LEACHM model (LEACHN, version 3) and long‐term applications of the model. The model’s predictions of nitrogen fluxes under long‐term use of fertilizer and irrigation were analysed. Nearly half of the applied ammonium‐N was converted to nitrate‐N during the growing season. With increasing additions of N the rate of plant uptake declined, while leaching increased significantly, and the fraction of nitrogen remaining in the soil profile increased only moderately. In long‐term applications, a significant fraction of the applied fertilizer tended to accumulate after the first year in soil as the residual nitrogen not taken up by the crop. Accumulated residual nitrogen is converted to nitrate‐N and leached rapidly from the soil profile during the wet season following the harvest. To reduce leaching of the residual nitrate, the rates, frequencies and timings of fertilizer application and irrigation must be scheduled in accordance with the plant growth periods and the hydraulic regime of the soil.

A numerical experiment was designed to study the stochastic behavior of one‐dimensional transient unsaturated flow in a Monte Carlo setting. Soil hydraulic properties, log‐saturated hydraulic conductivity ln Ks, pore size distribution parameter α, and the specific water capacity C are assumed to be statistically homogeneous random fields described by exponential correlation functions with identical correlation lengths. Fifty realizations of each soil hydraulic property, with statistical properties obtained from a field experiment, are generated by using a nearest‐neighbor model. Numerical solutions of the one‐dimensional flow equation are used repeatedly to obtain realizations of soil water pressure head ψ and flux q corresponding to the realizations of In Ks, α, and C. The dependence of ψ and q on the statistical properties of ln Ks, α, and C and the magnitude of the hydraulic head gradient G prevailing at the lower boundary are investigated. In addition, results of Monte Carlo analysis and spectral perturbation analyses are compared with field observations. The greatest variability of ψ and q are observed when soil hydraulic properties are uncorrelated and have large variances and integral scales and when G at the lower boundary is unity. The Monte Carlo and spectral perturbation analyses tend to agree reasonably well for the flow domains in which ergodicity of local soil hydraulic properties is assured. Results of the Monte Carlo and spectral perturbation analyses are also supported by field observations.