Estimating plant root density distribution using physics-informed neural networks and time series decomposition

Measuring plant root density distribution is important for soil hydraulic properties, biogeochemical processes, and water resource availability, yet current methods face destructive or labor-cost problem. In this paper, we proposed a novel method to estimate plant root density distribution. First, physics-informed neural networks (PINNs) was employed to convert soil matric potential (SMP) at multiple depths into volumetric soil water content (VSWC). Subsequently, a time series decomposition method is utilized to extract periodic fluctuations in VSWC due to water uptake by the plant root system. Subsequently, the peaks of the periodic fluctuations were averaged and normalized across different depths. Noise was added to the data to test the robustness of the method. The correlation coefficients of the estimated results were 0.94, 0.92, 0.95, 0.66, 0.06, 0.16 when the signal-to-noise ratios (SNR) were no noise, 50db, 40db, 30db, 20db, 10db. VSWC and SMP with SNR less than 30db were used to estimate plant root distribution separately. The correlation coefficients of the results based on SMP were −0.18, −0.78, and −0.16, respectively, and the results based on VSWC were 0.91, 0.78, and 0.83, respectively. VSWC sensors maintained robust performance (r = 0.91–0.78) down to 30 dB SNR, while SMP sensors required ≥ 40 dB SNR to avoid error. Finally, laboratory validation using instrumented soil columns with bamboo (Monsteradeliciosa Liebm) demonstrated strong agreement between estimated and gravimetrically-measured root densities (r = 0.89). The method demonstrates optimal robustness when VSWC is employed and can also be utilized when the SNR of the SMP exceeds 30 dB.