Theoretical vs experimental relationship between K-40 counts and gravimetric water content at a well instrumented agricultural research station in Nebraska, USA
Authors: Becker Sophia M. , Franz Trenton E. 
Published: February 2023

Detection of gamma-rays emitted by K-40 decay demonstrates potential for reliable soil moisture estimation for agricultural and hydrological applications. With a circular footprint of roughly 20 m radius, gamma-ray spectroscopy (GRS) provides a continuous, non-invasive average measurement that fills the scale gap between point and satellite data. GRS sensors have also been successfully integrated with Unmanned Aerial Systems opening the potential for soil moisture mapping.&#160; Current theoretical models of gamma-ray spectra and soil moisture have not been extensively tested with empirical data. An existing soil moisture model for NaI gamma-ray spectra includes a method for biomass water content correction and was tested with five sampling campaigns in a tomato field, while another soil moisture model was tested with a single sampling campaign in a sugar beet field using CsI gamma-ray spectra. We hypothesize that testing existing theoretical models with thorough empirical data over a range of soil moisture and vegetative conditions will increase our understanding of the relationship between gamma-ray spectra, soil moisture, and biomass, and will allow us to validate and/or improve the soil moisture calibration function.In this study we conduct a robust calibration of a stationary CsI gamma-ray soil moisture sensor (gSMS, Medusa Radiometrics) against gravimetric water content samples at a long term agricultural experimental field in eastern Nebraska, United States. Additional measurements include an Eddy Covariance tower, a Cosmic-Ray Neutron Sensor, in-situ soil moisture sensors, and destructive vegetation sampling every 10 days during the growing season. In total, 18 sampling campaigns were conducted between June 2021 and October 2022 under bare soil, maize, and soybean conditions. Soil samples were collected in a radial pattern at 0, 2, 5, and 12 m from the sensor, every 60 degrees following the expected spatial sensitivity of the gSMS. Samples from the 19 locations surrounding the sensor were aggregated in 5 cm intervals from 0 to 35 cm depth. Both a depth-weighting function and the arithmetic mean were used to calculate the average gravimetric water content within the sensing volume.We then leverage the relatively large experimental data set of gravimetric water content and K-40 counts to test current theoretical approaches to soil moisture estimation with GRS. Data from both bare soil and vegetated conditions allow us to investigate and potentially remove the biomass water content signal from the soil moisture estimation. Comparison with the existing theoretical calibration functions shows large deviations with the empirical data. &#160;Cosmic-ray Neutron Sensor data recorded at the site shows a high degree of correlation (R > 0.7 for hourly data) between the K-40 counts and neutron counts under changing biomass conditions. Lastly, comparison of the GRS derived soil moisture data with the in-situ soil moisture sensors, rainfall, and evapotranspiration result in good correspondence with soil moisture state and water fluxes at the study site.