Assessment of bio-inspired metaheuristic optimisation algorithms for estimating soil temperature

Abstract Root zone temperature is one of the most important soil characteristics, controlling many of the physical, chemical and biological processes in the soil. Temperature varies by soil depth, and exerts a profound impact on plant germination and growth. In this study, the accuracy of two artificial intelligence models including support vector regression (SVR) and elman neural network (ENN) and their hybrids with firefly algorithm (SVR-FA and ENN-FA) and krill herd algorithm (SVR-KHA and ENN-KHA) was assessed in estimating soil temperature (Ts) at 5, 10, 20, 30, 50 and 100 cm depths at Maragheh meteorological station in north-western Iran. The results of the models were evaluated under 5 scenarios with various inputs including the main meteorological parameters measured at the station (air temperature, sunshine hours, relative humidity, wind speed and saturation vapour pressure deficit). Daily Ts data recorded from January 1, 2006 to December 30, 2012 and from January 1, 2013 to December 30, 2015 were used for model training and testing, respectively. The results showed that error rates have decreased from 5 to 10 cm soil depth (root mean square error (RMSE) reduced by 2.97, 4.68 and 3.19% for the best scenarios of SVR, SVR-FA and SVR-KHA models, respectively), whereas error rates have been increasing from 10 to 100 cm soil depths (RMSE increased by 62.4, 80.9 and 73.6% for the best scenarios of SVR, SVR-FA and SVR-KHA models, respectively). For the best scenarios of ENN, ENN-FA and ENN-KHA models, RMSE values decreased by 2.1, 1.6 and 3.1% from 5 to 10 cm depth and increased by 61.1, 84.1 and 81.1% from 10 to 100 cm depth, so that all six models reached their best performance at 10 cm soil depth. Examination of the results in terms of under-estimation or over-estimation of Ts indicated that the lowest and highest differences in performance between under- and over-estimation sets were 0.01 °C (SVR-FA at 5 cm depth) and 1.64 °C (SVR at 100 cm depth) for SVR-based models and 0 °C (ENN at 10 cm depth) and 0.56 °C (ENN at 100 cm depth) for ELM-based models, respectively. According to the results from the best scenarios of SVR, SVR-FA and SVR-KHA models in the under-estimation set at 100 cm depth, all the three models have exhibited a poorer performance over the temperature range 15–25 °C (RMSE increased by 56.7, 47 and 61.3% for SVR, SVR-FA and SVR-KHA, respectively) compared to temperature values outside that range. Exactly the same trend was also observed for ELM-based models, where the mentioned increases in RMSE were about 37.7, 59.4 and 55.5% for ELM, ELM-FA and ELM-KHA, respectively. According to the results, bio-inspired metaheuristic optimisation algorithms based on SVR and ENN which use appropriate meteorological parameters as inputs can have a relatively satisfactory performance in estimating Ts under climatic conditions similar to our study area, especially in lower depths, and can be used as an alternative to direct measurement of this important parameter.