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Data from: Jensen's inequality reveals how moisture variability controls soil respiration across continental scales

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May 22, 2026 version files 2.70 MB

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Abstract

Understanding how temporal patterns of moisture variability influence modeled biogeochemical responses remains a central challenge in Earth system science. 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, θ) and temperature data (134.5 million hourly observations from 2,004 sensors) to compare two approaches for modeling soil respiration: one using time-resolved environmental inputs and one using long-term temporal 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 difference of -63.6% between approaches) because they experience highly skewed moisture distributions where brief wet periods drive disproportionate simulated respiratory responses. Wet regions show smaller effects (median -27.1%) because they have more uniform moisture distributions. Data density analysis reveals that sensors operating at θ ≈ 0.05 exhibit the largest differences between approaches, while sensors at θ ≈ 0.45 show minimal differences, demonstrating the mechanistic basis for where ecosystems operate on the moisture-respiration curve. Climate gradient analysis shows systematic transitions from large effects in arid systems 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 environmental co-variation modulates modeled biogeochemical responses. Jensen's inequality thus serves as a diagnostic tool for identifying where temporal averaging of environmental inputs introduces the largest differences in simulated soil respiration.