Spatial-Temporal Modeling of Active Layer Thickness

The objective of this study is to provide the methodology to model and estimate spatial-temporal variation in the active layer thickness (ALT) at the U1 Barrow site of the Circumpolar Active Layer Monitoring network, and to demonstrate its use in spatial-temporal interpolation. Specifically, we use 18 years of data (1995—2012) collected on 11 by 11 square grid of locations separated by 100 meters to build the model. Then, we use the data collected in 2013 to demonstrate the validity and predictive power of our methodology. In our study, we propose two models that provide a realistic description of space-time variability in ALT. At the same time, these models are feasible to efficiently estimate model parameters from available data. Specifically, we adopt linear modeling approach. The main modeling difficulties lie in defining a deterministic trend that represents the large scale spatial and temporal variation, and a realistic stochastic model that characterizes the space-time dependency of the residuals. Formulations that take into account interactions among spatial and temporal components are also developed. Fitting the space-time geostatistical model can be computationally demanding since the number of observations is large. Hence, we use a composite likelihood approach which is a criterion function based on the likelihood of marginal events. In our data analysis, we demonstrate that our models resemble the empirical patterns. Moreover, we compare our models to the naive one, which does not take the spatial and temporal correlation in residuals into consideration. The root mean squared error is reduced by 27 percent when our approach is taken.