Jensen's Inequality Quantifies How Temporal Averaging of Moisture Inputs Affects Modeled Soil Respiration Across Continental Scales

Abstract

Understanding how temporal patterns of moisture and temperature variability influence biogeochemical responses remains a central challenge in modeling the Earth system. Jensen's inequality provides a mathematical framework for quantifying when nonlinear processes cause the response to average conditions to differ systematically from the average of responses to actual conditions. We applied this framework to continental‐scale AmeriFlux soil moisture (volumetric water content, ) and temperature data (134.5 million hourly observations from 2,004 sensors) to compare two approaches for modeling soil respiration: one using time‐resolved inputs and one using long‐term averages. Both approaches use identical nonlinear respiration functions; no flux observations are used for validation. Sensors in dry regions show large Jensen's inequality effects (median ) because they experience highly skewed moisture distributions where brief wet periods drive disproportionate simulated respiratory responses. Wet regions show smaller effects (median ) due to more uniform moisture distributions. Data density analysis reveals that sensors at exhibit the largest differences, while sensors at show minimal differences, demonstrating the mechanistic basis for where ecosystems operate on the moisture‐respiration curve. Climate gradient analysis shows transitions from large effects in arid to moderate effects in humid systems. Depth analysis reveals that surface soils show maximum effects, while deeper soils show reduced effects due to environmental buffering. Moisture‐temperature coupling demonstrates systematic negative correlations in water‐limited systems, indicating that co‐variation modulates modeled biogeochemical responses. Jensen's inequality thus serves as a diagnostic tool for identifying where temporal averaging introduces the largest differences in simulated soil respiration.