# On the Variability of the Barometric Effect and Its Relation to Cosmic-Ray Neutron Sensing

## TL;DR

This study shows that the barometric coefficient varies by location and sensor type, requiring site-specific corrections for accurate soil moisture measurements using cosmic-ray neutron sensing.

## Contribution

The study introduces a method for deriving site- and sensor-specific barometric coefficients to improve soil moisture estimation.

## Key findings

- Barometric coefficients (β) vary spatially and temporally, with values differing between CRNS and neutron monitor stations.
- Empirical methods for estimating β show stronger agreement with each other than with analytical approaches.
- Sensor type and elevation significantly influence β values, while soil moisture and humidity have negligible effects.

## Abstract

Accurate estimation of the barometric coefficient (β) is important for correcting pressure effects in soil moisture data from cosmic-ray neutron sensing (CRNS) due to the barometric effect. To evaluate estimation strategies for β, we compared analytical and empirical approaches using 71 CRNS and 46 neutron monitor (NM) stations across the United States, Europe, and globally. Our results show spatio-temporal variation in the barometric effect, with β ranging from 0.66 to 0.82 %hPa for NM and from 0.63 to 0.80 %hPa for CRNS. These coefficients exhibit higher variability than previously published semi-analytical models. In addition, we found that the analytically determined β values were systematically lower compared with empirical estimates, with stronger agreement between the two empirical methods (r≈0.67) than between empirical and analytical approaches. Furthermore, NM stations produced higher β values than CRNS, indicating that differences in detector energy sensitivity affected the values of β. Principal Component Analysis (PCA) further showed that the analytical and empirical β estimates clustered together, reflecting shared sensitivity to elevation. In contrast, soil moisture and atmospheric humidity projected nearly orthogonally to the β vectors, indicating negligible influence, while cut-off rigidity contributed to a separate, inverse gradient. Analytical β estimates were fully orthogonal to AH, while empirical methods showed only slight deviations beyond orthogonality. The barometric coefficient (β), therefore, varies with location, altitude, atmospheric conditions, and sensor type, highlighting the necessity of station-specific values for precise correction. Overall, our study emphasizes the need for atmospheric correction in CRNS measurements and introduces a method for deriving site- and sensor-specific β values for accurate soil moisture estimation.