A PDE Method for Modelling the Soil Temperature of Cropfields with Data from Wireless Sensor Networks

The aim of this work is to model the soil temperature dynamics of a strip of land of a cropfield in which a wireless sensor network has been deployed. Each sensor provides a measurement of the soil temperature every 5 minutes. We wonder whether it would be possible to develop a mathematical model using PDEs reliant on historical data up to a designated temporal threshold, thereafter relying on a diminished subset of sensor data. The solution proposed is using the 1D heat equation with variable Dirichlet conditions provided by the sensor data. To obtain future predictions, the Dirichlet data can be forecasted using the time series Holt-Winters method. To test the methodology, four experiments are carried out with real data. The method shows a good level of accuracy (MAPE \(< 7.5\) %; MABE \(<\) 2 \({}\,^{\circ }\) C) while requiring much less data compared to machine learning methods.