# Extending the Schymanski-Or formula to a multi-layer canopy model

## Keywords

Evapotranspiration Penman-Monteith Multi-layer Canopy Radiotion

## Start Date

25-6-2018 2:00 PM

## End Date

25-6-2018 3:20 PM

## Abstract

During the last year a new formula for the transpiration was proposed (Schymanski and Or, 2017). That study was carried on a single leaf and highlights omissions in the classical transpiration formula (Penman-Monteith) that implies an error of more than 50% on the transpiration estimate. The main advantages of this new formulation are given by the correct representation of hypostamatous leaves and the two sided exchange of sensible heat in a planar leaf. In this study it is presented a method for the application of the Schymanski-Or formula at the canopy-scale.

One of the main issue is represented by the correct representation of the spatial heterogeneity that affects the solar radiation. In fact, if we can assume air temperature, the relative humidity and the wind velocity approximately constant inside the canopy, this is not true for radiation, especially for the short wave component, because radiation is affected by the geometry of the canopy, by the inclination of each leaf and the reflected and diffuse radiation inside the canopy.

To reduce this complexity, it is possible to model the canopy as a multi-layer absorbing medium modeled using a modification of the Lambert-Beer law. In this case the extinction coefficient of the canopy is also made functionally dependent on the leaf area index in order to keep in consideration the seasonal dynamics of canopies.

The total canopies transpiration, therefore, is made dependent on the differentiated radiation absorbed by its different parts and the different temperatures they have.

Extending the Schymanski-Or formula to a multi-layer canopy model

During the last year a new formula for the transpiration was proposed (Schymanski and Or, 2017). That study was carried on a single leaf and highlights omissions in the classical transpiration formula (Penman-Monteith) that implies an error of more than 50% on the transpiration estimate. The main advantages of this new formulation are given by the correct representation of hypostamatous leaves and the two sided exchange of sensible heat in a planar leaf. In this study it is presented a method for the application of the Schymanski-Or formula at the canopy-scale.

One of the main issue is represented by the correct representation of the spatial heterogeneity that affects the solar radiation. In fact, if we can assume air temperature, the relative humidity and the wind velocity approximately constant inside the canopy, this is not true for radiation, especially for the short wave component, because radiation is affected by the geometry of the canopy, by the inclination of each leaf and the reflected and diffuse radiation inside the canopy.

To reduce this complexity, it is possible to model the canopy as a multi-layer absorbing medium modeled using a modification of the Lambert-Beer law. In this case the extinction coefficient of the canopy is also made functionally dependent on the leaf area index in order to keep in consideration the seasonal dynamics of canopies.

The total canopies transpiration, therefore, is made dependent on the differentiated radiation absorbed by its different parts and the different temperatures they have.

## Stream and Session

Stream D: Modeling Environmental Fate of Contaminants, Human Well-being and Public Healt

D1: Environmental Fluid Mechanics – Theoretical, Modelling, and Experimental Approaches