An Integrated Approach for Estimation and Uncertainty Analysis of Soil Pore Electrical Conductivity

This study proposes an integrated methodology to advance the estimation and uncertainty analysis of soil pore electrical conductivity. Drawing on previous work from Aljoumani et al. (2015), where modifications were made to the Hilhorst model, and subsequent enhancements in Aljoumani et al. (2018), this research unfolds in a systematic manner.

Commencing with a comprehensive examination of critical data from the Aljoumani el al.(2015) study, including bulk electrical conductivity, soil permittivity, and pore water permittivity, we transition into the construction of an improved Hilhorst model. This advanced model convert the deterministic Hilhorst model to stochastic model incorporates linear dynamic modeling and the Kalman filter, enabling precise estimation of soil salinity (pore electrical conductivity) and determination of corresponding offsets.

To address uncertainty comprehensively, we employ a multifaceted strategy. Beginning with the modeling of relationships using the Long Short-Term Memory (LSTM) algorithm, an artificial recurrent neural network, we intricately examine the interplay between the original time series of soil permittivity, pore water permittivity, and bulk electrical conductivity.

Subsequently, we utilize bootstrapping to generate 1000 series for soil permittivity and pore water permittivity. The LSTM model then produces 1000 series of bulk electrical conductivity, using the generated soil and pore water permittivity series as input.

Applying the modified Hilhorst model to the 1000 series obtained from bootstrapping and the LSTM model, we obtain 1000 models, each providing 1000 offsets and predicted pore water electrical conductivity series. Returning to the original data, the modified model is applied to construct predicted series of pore electrical conductivity. Upper and lower bounds are established using the calculated 5th and 95th percentiles of the 1000 offset values from the generated data.

In summary, this integrated methodology not only ensures accurate estimations of soil pore electrical conductivity but also provides a robust framework for quantifying uncertainty comprehensively.