Stomatal Conductance Modeling to Estimate the Evapotranspiration of Natural and Agricultural Ecosystems

This chapter presents some of the available modelling techniques to predict stomatal conductance at leaf and canopy level, the key driver of the transpiration component in the evapotranspiration process of vegetated surfaces. The process-based models reported, are able to predict fast variations of stomatal conductance and the related transpiration and evapotranspiration rates, e.g. at hourly scale. This high–time resolution is essential for applications which couple the transpiration process with carbon assimilation or air pollutants uptake by plants.


Introduction
This chapter presents some of the available modelling techniques to predict stomatal conductance at leaf and canopy level, the key driver of the transpiration component in the evapotranspiration process of vegetated surfaces.The process-based models reported, are able to predict fast variations of stomatal conductance and the related transpiration and evapotranspiration rates, e.g. at hourly scale.This high-time resolution is essential for applications which couple the transpiration process with carbon assimilation or air pollutants uptake by plants.

Stomata as key drivers of plant's transpiration
Evapotranspiration from vegetated areas, as suggested by the name, has two different components: evaporation and transpiration.Evaporation refers to the exchange of water from the liquid to the gaseous phase over living and non-living surfaces of an ecosystem, while transpiration indicates the process of water vaporisation from leaf tissues, i.e. the mesophyll cells of leaves.Both processes are driven by the available energy and the drying potential of the surrounding air, but transpiration depends also on the capacity of plants to replenish the leaf tissues with water coming from the roots through their hydraulic conduction system, the xylem.This capacity depends directly on soil water availability (i.e.soil water potential), which contributes to the onset of the water potential gradient within the soil-plant-atmosphere continuum.Moreover, since the cuticle -a waxy coating covering the leaf surface-is nearly impermeable to water, the main part of leaf transpiration (about 95%) results from the diffusion of water vapour through the stomata.Stomata are little pores in the leaf lamina which provide lowresistance pathways to the diffusional movement of gases (CO 2 , H 2 O, air pollutants) from outside to inside the leaf and vice versa.Following complex signal pathways, environmental, osmotic and hormonal, stomata regulate their opening area and thus the water vapour loss from leaves.When the evaporative demand is bigger than the water replenishing capability from the xylem, stomata closes partially or even totally.High evaporative demands can be due to elevated air temperature, high leaf-to-air vapour pressure deficit (VPD), and intense winds.Stomatal closure can also be caused by high concentration of carbon dioxide in the mesophyll space.Stomata, thus, directly control plant transpiration preventing plants from excessive drying, and acting as key drivers of water vapour movements from vegetated surfaces to the atmosphere.This chapter illustrates the modelling techniques to predict the stomatal behaviour of vegetation at high-resolution time scale, and the related water fluxes.

Modelling stomatal behaviour: The Jarvis-Stewart model and the Ball-Berry model
Stomata play an essential role in the regulation of both water losses by transpiration and CO 2 uptake for photosynthesis and plant growth.Stomatal aperture is controlled by the turgor pressure difference between the guard cells surrounding the pore and the bulk leaf epidermis.In order to optimize CO 2 uptake and water losses in rapidly changing environmental conditions, plants have evolved the ability to control stomatal aperture in the order of seconds.Stomatal aperture responds to multiple environmental factors such as, solar radiation, temperature, drought, VPD, wind speed, and sub-stomatal CO 2 concentrations.The availability of modern physiological instrumentation (diffusion porometers, gasexchange analyzers) has allowed to measure leaf stomatal conductance (g s ) in field conditions and to study how environmental variables influence this parameter.However, measurements of g s by porometers and gas-exchange analyzers can be made only when foliage is dry, and long-term enclosure in measuring chamber may lead to changes in the physiological state of the leaves.Consequently measurements in the field are usually made intensively over selected periods of a few hours in selected days.Furthermore, stomatal conductance values depend also upon the physiological condition of the plant, which relates to the weather of the previous days as well as to the previous season for perennial species.Therefore it is important to have continuous g s measurements over the whole vegetative season in order to improve the interpretation of other physiological data such as photosynthesis rate and carbon assimilation.An alternative to very frequent measurements of g s in the field is to predict them from models that describe its dependency on environmental factors.These models can be parameterized using the available field measurements conducted on occasional periods.Furthermore, modeling appears the most effective tool for integration, simulation and prediction purposes concerning the effects of climatic global change on vegetation.Stomatal conductance is among the processes that have been most extensively modeled during the last decades.In their excellent review, Damour et al. (2010) describe 35 stomatal conductance models classified as: 1. models based on climatic control only 2. models mainly based on the gs-photosynthesis relationship 3. models mainly based on an Abscisic Acid (ABA) control 4. models mainly based on the turgor regulation of guard cell.
The next paragraphs provides information on two early developed g s models which are currently among the most widely used: the multiplicative model of Jarvis (1976) based on climatic control and later modified by Stewart (1988), and the Ball Berry model (1988), based on g s -photosynthesis relationship.

The Jarvis-Stewart model
The stomatal conductance model developed by Jarvis (1976) can be defined as an empirical multiplicative model based on the observed responses of g s to environmental factors.The assumption of this model is that the influence of each environmental factor on g s is independent of the others and can be determined by boundary line analysis (Webb 1972).The Jarvis model, in its first form, integrates the responses of g s to light intensity, leaf temperature, vapour pressure deficit, ambient CO 2 concentration and leaf water potential, according to the following equation: where Q is the quantum flux density (E m -2 s -1 ), T l is the leaf temperature (°C), VPD l is the leaf-to-air vapour pressure deficit calculated at leaf temperature (kPa), C a is the ambient CO 2 concentration (ppm) and  is leaf water potential (MPa).Stewart (1988) further implemented this model adopting the assumption that the functions of environmental variables have values between zero and unit and exert their influence reducing the maximum stomatal conductance of the plant (g smax ), a species-specific value depending on leaf stomatal density, that can be defined as the largest value of conductance observed in fully developed leaves -but not senescent -of well-watered plants under optimal climatic conditions (Körner et al., 1979).This value can be derived from field measurements conducted under the above mentioned optimal conditions.Furthermore, in Stewart formulation, quantum flux density is replaced by global solar radiation, leaf temperature by air temperature, leaf-to-air vapour pressure deficit by air vapour pressure deficit and leaf water potential by soil moisture deficit measured in the first meter of soil (i.e.soil water content, SWC).Stewart also omitted f(C a ) because the effect of CO 2 ambient concentrations was considered negligible: this simplification allows for an easier data collection to run the model, but it must be kept in mind that C a change considerably among seasons and thus the simplification may lead to a considerable error, especially when the model is used for annual g s behavior of evergreen species.
The model is defined by the following equation: It is important to notice that f(Q) can also be replaced by the more specific f(PAR), based on the photosynthetically active radiation.Each function has a characteristic shape described by the following equations: where where f(SWC) = 1 when SWC=SWC max Since g s depends on four major variables, field measurements do not usually show a clear relationship with any of the considered variables.Often, g s is reduced below the value expected for a value of a single independent variable, as the result of the influences of the other variables.As a consequence, the coefficients of each function must be derived with boundary-line analysis, plotting all field measurements of relative g s (g srel = g s /g smax ) against each environmental variable considered separately.Provided that enough measurements have been adequately performed to cover variable space, the upper limit of the scatter diagram indicates the response of g s to the particular independent variable, when the other variables are not limiting.An example of boundary-line analysis is reported in figure taken from Gerosa et al. (2009): The main criticism formulated against this kind of approach is that the interactive effects between environmental factors are not properly taken into account, since interactions are only partially explained by the multiplicative nature of the model which simply multiplies concomitant effects, avoiding any synergistic interaction.
where AWHC is the available water holding capability of the sandy soil between the wilting point ( WP = 0.114 m 3 m -3 for our sandy loam soil) and the field capacity ( FC =0.195 m 3 m -3 ).The running equations were: Eq. 32 represents the water loss of plant ecosystem through the transpiration of the two layers (F H20, t-1 ) in the previous time step.Since water fluxes are expressed as rates (mm s -1 ), for an hourly time step, as in our cases, their values must be multiplied by 3600 in order to get the water consumed in one hour.AW t is the available water in the soil after water inputs and consumptions.The effects of runoff and groundwater level rising have been neglected due to the flatness of the ecosystem and the groundwater level which were deeper than the root exploration depth.SWC represents the soil water content expressed as percentage of field capacity, as requested by the f(SWC) function of the stomatal sub-models.

The atmospheric sub-model and the resistive network
The resistance R a was calculated by using Eq.19 and Eq.21, with z m =33 m the measurement height, h= 26.3 m the canopy height, u* the friction velocity, u the horizontal wind speed, L the Monin-Obhukhov length, d=2/3•h the zero-plane displacement height and z 0 =1/10•h the roughness length.
The laminar sub-layer resistances of the layers 1 and 2 (R b1 and R b2 ) were both calculated using the Eq.23 given u*.
The stomatal resistances of the layers 1 and 2 (R stom1 and R stom2 ) were calculated using the stomatal sub-model having estimated the leaf temperatures the air temperature T and the heat fluxes H: where R b,heat was calculated using the Eq.23 with Sc=0.67 and Pr=0.71.
Then the vapour pressure deficit VPD = e s (T l )e(T) was derived from the T l for the calculation of e s (T l ) and from the air temperature T and the relative humidity RH for the actual e: e(T)=UR • e s (T).
The vapour pressure of the saturated air can be calculated from the well-known Teten-Murray empirical equation: which gives e s in kPa when T is expressed as °K.
The stomatal resistance of the crown R stom1 was obtained as the reciprocal of the stomatal conductance obtained by the Jarvis-Stewart sub-model fed with PAR, T leaf , VPD and SWC t , the latter being the soil water content calculated with the Eq.32 .
Stomatal Conductance Modeling to Estimate the Evapotranspiration of Natural and Agricultural Ecosystems 417 The understory R stom2 was obtained in a similar way but considering a understory g max (=1.87 cm s -1 ) and the PAR fraction reaching the below canopy vegetation instead of the original PAR: where k is the light extinction factor within the canopy, set to 0.54, and LAI 1 is the leaf area index of the crown, assumed to be equal to 2 at maximum leaf expansion.
The in-canopy resistance R inc was calculated following Erisman et al. (1994): where h is the canopy height and LAI 1 the leaf area index of the crown.
The stomata of the big leaves of the two layers of Figure 4 (G 1 and G 2 ) were assumed as water generators driven by the difference of water concentration between the leaves (χ sat ), assumed water saturated al leaf temperature T l , and the air (χ air ): where being 2.165 the ratio between the molar weight of water molecules M w (18 g mol -1 ) and the gas constant R (8.314 J mol -1 K -1 ) if e and e s are expressed in Pa (multiplied by 1000 if expressed in kPa).
Then the total water flux of the ecosystem F H2O could be calculated by composing all the resistances and the generators within the modelled resistive network, following the electrical composition rules for resistances and generators in series and in parallel, and applying the scaling strategy according to the LAI: F H2O = G eq / (R eq + R a ) / 1000 (kg m -2 s -1 = mm s -1 ) (43) where LAI 2 is the leaf area index of the understory vegetation (=0.5)

Comparison with EC measurements
Concurrent measurements of E were performed over the same ecosystem by means of eddy covariance technique with instrumentation set-up according to Gerosa et al. (2005).
The comparison between the direct E measurements and the modelled ones allowed the evaluation of model performance.