Do ARMA Models Provide Better Gap Filling in Time Series of Soil Temperature and Soil Moisture? The Case of Arable Land in the Kulunda Steppe, Russia

The adoption of climate-smart agriculture requires the comprehensive development of environmental monitoring tools, including online observation of climate and soil settings. They are often designed to measure soil properties automatically at different depths at hour or minute intervals. It is essential to have a complete dataset to use statistical models for the prediction of soil properties and to make short-term decisions regarding soil tillage operations and irrigation during a vegetation period. This is also important in applied hydrological studies. Nevertheless, the time series of soil hydrological measurements often have data gaps for different reasons. The study focused on solving a problem of gap-filling in hourly time series of soil temperature and moisture, measured at the 30 cm depth using a weighted gravitation lysimeter station while meteorological data were recorded simultaneously by a weather station. The equipment was installed in the Kulunda Steppe in the Altai Krai, Russia. Considering that climate conditions affect soil temperature and moisture content directly, we did a comparative analysis of the gap-filling performance using the three imputation methods—linear interpolation, multiple linear regression, and extended ARMA ( p , q ) models with exogenous climatic variables. The results showed that, according to the minimum of the mean absolute error, ARMA ( p , q ) models with optimally selected order parameters, and an adaptive window, had some advantages compared to other single-imputation methods. The ARMA ( p , q ) model produced a good quality of gap-filling in time series with the mean absolute error of 0.19 °C and 0.08 Vol. % for soil temperature and moisture content, respectively. The findings supplemented the methodology of hydrological data processing and the development of digital tools for the online monitoring of climate and soil properties in agriculture.