Environmental Controls on Water Vapor Deuterium Excess in the Coastal Boundary Layer: An Information Theory Perspective

Abstract We use information theory to quantify the environmental controls on water vapor deuterium excess (D‐excess) in coastal Southern California from June 2023 through February 2024. Using Shannon entropy, mutual information (MI), and joint mutual information, metrics that capture both linear and nonlinear relationships, we identify the most informative variables and variable combinations governing D‐excess across contrasting marine and continental regimes. Relative humidity with respect to sea surface temperature (RHS) is consistently the strongest individual predictor, explaining up to 27% of D‐excess variability during marine conditions but only 10% in continental air masses. The Relative humidity(RHS) + sea surface temperature (SST) combination demonstrates synergistic effects, where their joint influence (explaining up to 36% of D‐excess variability) exceeds what either variable achieves individually, confirming their coupled influence on deuterium excess. Wind direction complements RHS most effectively during continental conditions. The best three‐variable combination (RHS + SST + Planetary Boundary Layer height) explains 38% of D‐excess variability in marine air, while no combination exceeds 20% explanatory power during continental periods. Information theory shows that heteroscedasticity in D‐excess relationships indicates regime shifts in controlling processes and quantifies fundamental constraints on predictor variables: some environmental factors like surface pressure or water vapor flux contain insufficient information content to explain D‐excess variability regardless of their physical relevance. These results highlight the different predictability limits between marine and continental regimes, challenging the adequacy of linear models and providing a rigorous framework for quantifying the information content of isotope‐climate relationships with implications for both modern and paleoclimate applications.