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Dimension reduction for integrating data series in Bayesian inversion of geostatistical models
(2019)
This study explores methods with which multidimensional data, e.g. time series, can be effectively incorporated into a Bayesian framework for inferring geostatistical parameters. Such series are difficult to use directly in the likelihood estimation procedure due to their high dimensionality; thus, a dimension reduction approach is taken to utilize these measurements in the inference. Two synthetic scenarios from hydrology are explored in which pumping drawdown and concentration breakthrough curves are used to infer the global mean of a log-normally distributed hydraulic conductivity field. Both cases pursue the use of a parametric model to represent the shape of the observed time series with physically-interpretable parameters (e.g. the time and magnitude of a concentration peak), which is compared to subsets of the observations with similar dimensionality. The results from both scenarios highlight the effectiveness for the shape-matching models to reduce dimensionality from 100+ dimensions down to less than five. The models outperform the alternative subset method, especially when the observations are noisy. This approach to incorporating time series observations in the Bayesian framework for inferring geostatistical parameters allows for high-dimensional observations to be faithfully represented in lower-dimensional space for the non-parametric likelihood estimation procedure, which increases the applicability of the framework to more observation types. Although the scenarios are both from hydrogeology, the methodology is general in that no assumptions are made about the subject domain. Any application that requires the inference of geostatistical parameters using series in either time of space can use the approach described in this paper.
Soil moisture dynamics are affected by complex interactions among several factors. Understanding the relative importance of these factors is still an important challenge in the study of water fluxes and solute transport in unsaturated media. In this study, the spatio-temporal variability of surface soil moisture was investigated in a 10 ha flat cropped field located in northern Italy. Soil moisture was measured on a regular 50 x 50 m grid on seven dates during the growing season. For each measurement campaign, the spatial variability of the soil moisture was compared with the spatial variability of the soil texture and crop properties. In particular, to better understand the role of the vegetation, the spatio-temporal variability of two different parameters - leaf area index and crop height - was monitored on eight dates at different crop development stages. Statistical and geostatistical analysis was then applied to explore the interactions between these variables. In agreement with other studies, the results show that the soil moisture variability changes according to the average value within the field, with the standard deviation reaching a maximum value under intermediate mean soil moisture conditions and the coefficient of variation decreasing exponentially with increasing mean soil moisture. The controls of soil moisture variability change according to the average soil moisture within the field. Under wet conditions, the spatial distribution of the soil moisture reflects the variability of the soil texture. Under dry conditions, the spatial distribution of the soil moisture is affected mostly by the spatial variability of the vegetation. The interaction between these two factors is more important under intermediate soil moisture conditions. These results confirm the importance of considering the average soil moisture conditions within a field when investigating the controls affecting the spatial variability of soil moisture. This study highlights the importance of considering the spatio-temporal variability of the vegetation in investigating soil moisture dynamics, especially under intermediate and dry soil moisture conditions. The results of this study have important implications in different hydrological applications, such as for sampling design, ranking stability application, indirect measurements of soil properties and model parameterisation.