The Independent Variable in Geoscience Modelling: Why the Dew-Point Anchor Hypothesis Matters

Version 2.0 (10 April 2026) – Added new Section 5: A Simple Pedagogical Illustration of Forward vs Inverse Modelling. The original Pedagogical Conclusion has been moved to Section 6.

This short pedagogical note examines the fundamental importance of correctly identifying the independent variable in geoscience modelling. Drawing on the author’s early training in mathematics and his professional experience in inverse modelling, the paper argues that atmospheric structure is best approached as an inverse problem anchored at a physically fixed boundary condition.

The note introduces the Dew-Point Anchor Hypothesis, which proposes that the Lifting Condensation Level (or its planetary equivalent, the frost point) of the dominant condensing volatile provides the primary, observable thermodynamic boundary condition for tropospheric structure. Once this phase-equilibrium level is fixed by the Clausius–Clapeyron relation, surface temperature and surface pressure become dependent variables constrained by the adiabatic lapse rate and hydrostatic balance.

The hypothesis is shown to apply universally across planetary atmospheres (Earth H₂O, Venus H₂SO₄–H₂O, Mars CO₂, Titan CH₄) and offers a more robust, less tunable foundation for modelling than conventional top-of-atmosphere radiative balance approaches.

The paper includes a personal dedication to the author’s late father, Henry (Harry) Mulholland, whose teaching on the independent variable first inspired this line of thinking.