Sensitivity analysis is the study of how uncertainty in model predictions is determined by uncertainty in model inputs. A global sensitivity analysis considers the potential effects from the simultaneous variation of model inputs over their finite range of uncertainty. A number of techniques are available to carry out global sensitivity analysis from a set of Monte Carlo simulations; some techniques are more efficient than others, depending on the strategy used to sample the uncertainty of model inputs and on the formulae employed for estimating sensitivity measures. The most common approaches are summarised in this paper by focusing on the limitations of each in the context of a sensitivity analysis of a spatial model. A novel approach for undertaking a spatial sensitivity analysis (based on the method of Sobol' and its related improvements) is proposed and tested. This method makes no assumptions about the model and enables the analysis of spatially distributed, uncertain inputs. The proposed approach is illustrated with a simple test model and a groundwater contaminant model.

Descriptions of soil hydraulic properties, such as the soil moisture retention curve, θ(h), and saturated hydraulic conductivities, K_s, are a prerequisite for hydrological models. Since the measurement of K_s is expensive, it is frequently derived from statistical pedotransfer functions (PTFs). Because it is usually more difficult to describe K_s than θ(h) from pedotransfer functions, Pollacco et al. (2013) developed a physical unimodal model to compute K_s solely from hydraulic parameters derived from the Kosugi θ(h). This unimodal K_s model, which is based on a unimodal Kosugi soil pore-size distribution, was developed by combining the approach of Hagen–Poiseuille with Darcy's law and by introducing three tortuosity parameters. We report here on (1) the suitability of the Pollacco unimodal K_s model to predict K_s for a range of New Zealand soils from the New Zealand soil database (S-map) and (2) further adaptations to this model to adapt it to dual-porosity structured soils by computing the soil water flux through a continuous function of an improved bimodal pore-size distribution. The improved bimodal K_s model was tested with a New Zealand data set derived from historical measurements of K_s and θ(h) for a range of soils derived from sandstone and siltstone. The K_s data were collected using a small core size of 10 cm diameter, causing large uncertainty in replicate measurements. Predictions of K_s were further improved by distinguishing topsoils from subsoil. Nevertheless, as expected, stratifying the data with soil texture only slightly improved the predictions of the physical K_s models because the K_s model is based on pore-size distribution and the calibrated parameters were obtained within the physically feasible range. The improvements made to the unimodal K_s model by using the new bimodal K_s model are modest when compared to the unimodal model, which is explained by the poor accuracy of measured total porosity. Nevertheless, the new bimodal model provides an acceptable fit to the observed data. The study highlights the importance of improving K_s measurements with larger cores.