Effective aggregation of gappy replicated time series using INLA

Soil CO2 efflux data from automated chambers provide an important constraint for ecosystem and soil respiration. Usually, half-hourly time series of several replicated chambers have to be aggregated to plot-level while gaps in the time series have to be accommodated. Gaps cause jumps and other problems in aggregation of replicated measurement in each half-hour, therefore, lookup tables and machine learning approaches are used to fill gaps beforehand.

Here, we present an alternative fully Bayesian approach for the combined gap-filling and aggregation based on Integrated Nested Laplace Approximation (INLA). This method integrates all information from every measurement across replicates and across time and therefore efficiently estimates the correlation structure among all observations. It provides the full marginal posterior distribution of the aggregated time series at the plot level across the time span of the time series. We compare several aggregation approaches using four years of data from 16 automatic chambers at the eddy-covariance site in Majadas de Tietar in Spain (ES-LM1, ES-LMa).

This approach is applicable for other replicated time series as well. We further explore its usage for analysing time-varying effects across treatments and habitats and its usage for gap-filling net ecosystem exchange (NEE) data based on the full correlation structure in a data-cube of time and environmental conditions.