What question did this study set out to answer?

The research aims to develop a cloud energetic classification system within the Thermodynamic Manifold Framework using empirical atmospheric data.

April 16, 2026Open Access

Cloud Energetic Classification and Edge Dynamics within the Thermodynamic Manifold Framework — Supplementary Note S1 with Software (v3.0)

Key Points

The research aims to develop a cloud energetic classification system within the Thermodynamic Manifold Framework using empirical atmospheric data.
Introduced dimensionless cloud energy ratio R = F_dyn / F_rad.
Analyzed ERA5 atmospheric observations from 1980 to 2025 as data points.
Characterized edge dynamics at the physical boundary ρ = R / R_max = 1.
Parametric envelope fit achieved R² = 0.937 indicating strong model performance.
Observed asymmetry index AI of +0.111 pointing to slow build-up and fast collapse in cloud events.
Identified a spontaneous organization threshold at approximately ρ = 0.75.

Abstract

This deposit contains the Supplementary Note S1 and accompanying open-source software (cloudₘanifoldᵥ3₀. py) for the cloud energetic classification module of the Thermodynamic Manifold Framework (TMF). The note introduces a dimensionless cloud energy ratio R = Fdyn / Fᵣad, shows that ERA5 atmospheric observations are constrained to a curved surface Rₘax (T, C) in (T, C, R) state space, and characterises the edge dynamics at the physical boundary ρ = R / Rₘax = 1. Key empirical results from ERA5 (1980–2025, n = 16. 3M): - Parametric envelope fit R² = 0. 937 - Asymmetry index AI = +0. 111 (slow build-up, fast collapse), n = 700, 269 events - Spontaneous organisation threshold at ρ ≈ 0. 75 - Probabilistic state estimator P (regime | ρ, T, C, k) Related TMF paper: https: //doi. org/10. 5281/zenodo. 19430594

Cloud Energetic Classification and Edge Dynamics within the Thermodynamic Manifold Framework — Supplementary Note S1 with Software (v3.0)

Key Points

Abstract

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