Elementary mathematics sheds light on the transpiration budget

This contribution aims to present a concise and effective methodology for accurately characterizing transpiration, a crucial component of the hydrological cycle. Rather than delving into intricate derivations of transpiration formulas, we employ simplifications, such as a century-old turbulence model, principles from Lord Kelvin's thermodynamics, and an energy budget overlooking thermal leaf capacity. Despite these simplifications, we assert the general validity of our approach in identifying primary mechanisms underlying transpiration.

Our methodology initiates with a treatment of five equations, including the mass budget, outlining the procedure: Clausius-Clapeyron equation, water vapor transport, turbulence-induced thermal energy transport, and stationary energy budget with radiative feedback. Initially, we introduce a simplified approach excluding the water budget, followed by its inclusion to demonstrate that adhering to the water budget is sufficient without imposing artificial constraints. Utilizing a linearized form of the Clausius-Clapeyron equation, we establish the Penman Formula, a well-regarded solution for estimating temperature (T), air vapor content (e), and thermal heat transport (H). Through water mass balance, we reveal that leaf pressure potential is dynamically influenced by atmospheric evaporation demand and soil moisture content, challenging the notion of capillarity as the sole determinant. Building on Schymanski and Or's (2017) research, we extend it by explicitly incorporating the canopy. Even within the "big leaf" approach (Bonan et al., 2021), we introduce a dependency on leaf area index (Lc) in formulas to accurately consider the canopy's impact. Additionally, we provide a detailed treatment of radiation, accounting for the canopy's influence, following Ryu et al. (2011) and de Pury (1995) methodologies.

In the realm of canopy analysis, our contribution reveals discrepancies compared to common simplistic approaches, shedding light on unique aspects of the subject matter.