Elementary mathematics sheds light on the transpiration budget under
water stress
Abstract
This paper aims to establish a method to accurately describe
transpiration by employing appropriate physical equations. Although some
simplifications are made, including use of a simplified treatment of
turbulence and neglecting of the thermal capacity of transpiring leaves,
it is argued that the chosen scheme has general validity in identifying
the primary mechanisms governing transpiration. To achieve this
objective, a traditional treatment involving five equations, including
the mass budget, is used. Initially, a simplified approach that does not
consider the water budget is introduced to outline the general procedure
to explicitly address canopies. Subsequently, the water budget is
incorporated to appropriately account for water stress in transpiration.
In this context, a novel linearization of the extended
Clausius-Clapeyron equation, incorporating the Kelvin effect, is
employed. It is demonstrated that the well-known Penman formula emerges
as one of the solutions within a system of equations, providing
estimates for temperature (T), vapor content in air (e), and the thermal
transport of heat (H). The method, initially conceived for homogeneous
canopies, is expanded to encompass sun-shade canopy layers. By employing
the water mass balance, the trade-off between atmospheric evaporation
demand and the water delivery capacity of the soil and stem is
elucidated. Notably, it is revealed that the pressure potential within
leaves is not solely determined by capillarity, but rather represents
the dynamic outcome of the intricate interactions within the
soil-plant-atmosphere continuum. These findings highlight differences
from more simplistic approaches commonly employed, particularly
concerning canopies. Overall, this study presents a methodological
framework to accurately describe transpiration, incorporating key
equations and addressing the complex dynamics involved in the
soil-plant-atmosphere continuum, and suggests various directions of
research in the field.