Biometeorology, ESPM 129 1Lecture 30, Stomatal Conductance, Part 3, theory November 17, 2010 Instructor: Dennis Baldocchi Professor of Biometeorology Ecosystem Science Division Department of Environmental Science, Policy and Management 345 Hilgard Hall University of California, Berkeley Berkeley, CA 94720 Topics to be Covered A. Phenomenological Stomatal Conductance Models 1. The multiplicative model of PG Jarvis 2. Transpiration Conductance Theories of Mott and Parkhurst, Monteith B. Coupled Photosynthesis-Stomatal Conductance Models 1. Norman/Wong, stomata operate to keep ci/Ca constant 2. Ball Berry Algorithm 3 Leuning C. Optimal Carbon Gain for Water Use Models 1. Cowan/Farquhar theory 2. Optimal use of water with time, Makela, Farquhar D. Coupled Soil Moisture Models 1. Tardieu et al. (ABA) 2. Williams and Tuzet et al models (link to Soil water potential) 3. Sala and Tenhunen, alteration of BallBerry Slope 8. AJ Jarvis and Davies Model 9. Add Dewar (2002, PCE) coupled Tardieu/Leuning model L32.1 Introduction A hierarchy of models exist for computing stomatal conductance. One class uses multiplicative algorithms that adjust a reference value according to changes in environmental variables. A second approach links gs to transpiration. A third method scales stomatal conductance to photosynthesis. A fourth approach optimizes the use of water for the gain of carbon. The fifth method ties stomatal conductance to the status of theBiometeorology, ESPM 129 2soil water profile and adjusts gs for soil moisture deficits. In this lecture we will overview the cited classes of stomatal conductance models. Having a quantitative means of assessing stomatal conductance is imperative for assessing leaf energy balance and photosynthesis. L31.2 Phenomenological Models L31.2.1. P.G. Jarvis Algorithm For the past decade, many climate and weather models (Dickinson 1983; Sellers and Dorman 1987) and gaseous deposition models (Baldocchi, Hicks et al. 1987; Niyogi, Alapaty et al. 2003) have used the multiplicative and empirical model of Jarvis (Jarvis 1976) to calculate stomatal conductance of leaves, gs. This stomatal conductance model has much appeal, for it considers the impact of a light, temperature, humidity and soil moisture conditions on stomatal conductance and gaseous deposition. This model assumes that gs is a multiplicative function of photosynthetically active radiation (PAR), temperature, humidity deficits, molecular diffusivity, soil moisture stress and carbon dioxide. ggI fTfDf fCspa()()()()() A rectangular hyperbola function is used to assess the light response. Functions that can be used include a function based on the rectangular hyperbola approach: gIgIIppp()max or an asymptotic exponential function (Jones 1992): gI kIpp( ) exp( )1 The beta factor is a curvature coefficient. It represents the light level when gs is one half its maximum value. Polynomial functions are used to describe the temperature response, as stomatal conductance is limited by low and high temperatures and exhibits a broad maximum. fTTTTTTTTTaaholhahoTTTThool() /FHGIKJFHGIKJ fT kT Ta() ( )max 12Biometeorology, ESPM 129 3The response to humidity by stomata is complex. It is affected by whether there are feedback or feedforward effects. Stomatal conductance can either decrease linearly or asymtoptically with D: fD kD()1 fD kD( ) exp( ) When there are feedforward effects, an increase in D causes gs to decline directly. E decreases solely in response to the decrease in gs (gEgDss()) When there are feedback effects, an increase in D can impose a decreases gs, but it also increases the leaf temperature which can promote D and E, gEDgDss(,). Soil water potential causes gs to decrease in a non-linear manner too. fn()( ( ))/1121 The algorithm of Jarvis considers no feedbacks between stomatal conductance and the surface energy balance. Stomatal conductances are not updated to reflect changes in leaf temperatures and humidities. One can also argue, from a modelling standpoint, that it is inappropriate to apply the Jarvis (Jarvis 1976) model in an iterative mode. The Jarvis model is diagnostic and does not include feedback loops among stomatal conductance, internal CO2, transpiration, humidity deficits and leaf water potential that are described by Farquhar et al. (Farquhar 1978) and Jones (Jones 1992). The multiplicative, stomatal conductance algorithm requires a considerable amount of tuning and calibration to yield reasonable mass and energy flux densities (Sellers, Shuttleworth et al. 1989; Baldocchi 1992). For example, information on maximum conductances and curvature coefficients for the light, temperature, humidity deficit and soil moisture response functions are needed.Biometeorology, ESPM 129 4 Figure 1 Graphical representation of the functional responses of the subcomponents of the Jarvis model. Table 1 Stomatal conductance parameters for the Jarvis stomatal conductance model, from (Baldocchi, Hicks et al. 1987) variable units spruce oak corn Soybean Min rs s m-1 232 145 242 65 B(par) W m-2 25 22 66 10 Tmin C -5 10 5 5 Tmax C 35 45 45 45 Topt C 9 24 to 32 22-25 25 B(vpd) KPa-1 -0.0026 0 0 0 Mpa -2.1 -2.0 -0.8 -1.1 A. Capacity, Maximal Stomatal Conductance PAR (mol m-2 s-1)0 500 1000 1500 2000 2500normalized stomatal conductance0.00.20.40.60.81.01.2Tair (C)0 10203040vapor pressure deficit (kPa)012345normalized stomatal conductance0.00.20.40.60.81.01.2MPa)-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.0Biometeorology, ESPM 129 5As the literature becomes full of data on stomatal characteristics, several teams have attempted to synthesize the wide range of results and examine if there are any patterns in behavior according to plant physiology or functional type. Korner (Korner, Scheel et al. 1979) revised his 1976 analysis and has produced the most comprehensive survey to date. The following table summarizes maximum stomatal conductances according to biome. Table 2 Survey of maximum stomatal conductances by functional type, Korner (1994) gmax mmol m-2 s-1 std dev Woody vegetation tundra, deciduous shrub 270 91 tundra, evergreen shrub 235 127 conifer forests 234 99 temperate deciduous 190 71 Mediterranean deciduous shrub 235 87 Mediterranean evergreen shrub 203 108 Eucalyptus