## 1. Introduction and Background

[2] Physically and combination-based calculations of actual evapotranspiration (*E*_{Ta}) [i.e., Penman-Monteith [*Monteith*, 1965]] require quantification of the canopy resistance (*r*_{c}). Water vapor from vegetative surfaces has to overcome diffusive resistances as it transpires from the stomatal cavities and through the boundary layer to the atmosphere. The term stomatal resistance (*r*_{s}) is used to describe the diffusive resistance to water vapor flux from the epidermal stomatal cavities to the leaf surface. Soil moisture also encounters capillary resistance as it evaporates and diffuses from the soil surface to the microclimate. *Monteith* [1965] conceptualized these resistances and combined them into a *r*_{c} term which was originally integrated into the Penman-Monteith (PM) “big leaf” model as an extension of a combination-based model by *Penman* [1948]. *Monteith* [1965] noted that *r*_{c} is not purely physiological because it includes the external resistance across the boundary layer, which are variable with wind speed and other environmental factors. While conceptually innovative, the gap of knowledge between the single leaf and plant canopy created difficulty in the development of reliable methods to combine the dynamic diffusive processes in the stomata and the boundary layer into a simple model [*Lhomme*, 1991].

[3] Quantifying *r*_{c} has been the subject of many studies. Applying the Ohm's law analogy, *Monteith* [1965] illustrated *r*_{c} as being proportional to the vapor pressure difference (potential difference) between the leaf surface and the microclimate surrounding the canopy and inversely proportional to the water vapor flux [current, *e*_{s}(*T*)] and leaf temperature (*T*_{L}). In the PM method, the surface temperature and humidity are eliminated by combining the bulk aerodynamic and heat balance relationships [*Webb*, 1984]. Although the analogy is physically sound, it is practically difficult to quantify *T*_{L} and *e*_{s}(*T*) at a specific level within the canopy continuously. The spatial and temporal variation in *e*_{s}(*T*) and *T*_{L} in the canopy further compound the complexity of using the analogy. The complexity to comprehend and quantify *r*_{c} has compelled researchers [*Tanner*, 1963; *Brutsaert*, 1982] to even question its physical significance. *Philip* [1966] suggested, “canopy resistance is an artifact of a somewhat unrealistic analysis, and its physiological significance is questionable.” Despite the lack of a practical and physically sound methodology to estimate *r*_{c} for a variety of vegetation, climatic, soil water status, and management conditions, the PM method has been widely regarded by the scientific community as one of the most robust and accurate approaches to quantify evaporative losses from plant communities.

[4] Considering the simpler Monteith's one-layer and 1-D “big leaf” approach, *Szeicz and Long* [1969] introduced a widely applied procedure to estimate *r*_{c} as a quotient of mean *r*_{s} and effective green leaf area index (LAI). They assumed that when soil evaporation is negligible *r*_{c} represents effective *r*_{s} of all leaves acting as resistances in parallel. *Jarvis* [1981] proposed a novel approach for estimating *r*_{c} as the sum of the *r*_{s} values of all individual leaves in an imaginary column through the canopy standing on a unit area of ground. This proposal was further investigated by *Leverenz et al.* [1982], *Whitehead et al.* [1984], and *Beadle et al.* [1985] toward developing a multilayer approach. A multilayer approach, independent of wind speed, to estimate *r*_{c} was presented by *Lhomme* [1991], and the resulting observed *r*_{c} value was considered as a good physiological parameter when soil evaporation is negligible. Another multilayer model of *r*_{c} represents and captures the radiant energy at several levels in the canopy and the heat exchanges between leaves and air at these levels in terms of the layer average *r*_{s} to water vapor flow and leaf boundary layer resistance to water vapor and sensible heat flow [*Shuttleworth*, 2006]. *Juang et al.* [2008] present the results of extensive analyses and interpretation of first-, second-, and third-order closure models to investigate the radiative and turbulence transfer scheme for within and above canopy scalar transfer. Using a fixed *r*_{s} value for well-watered plants has also been suggested [*Monteith*, 1965; *Szeicz and Long*, 1969]. However, computing *r*_{c} by simply averaging different layers of *r*_{s} can be problematic since *e*_{s}(*T*) and vapor pressure deficit (VPD) are dynamic within the canopy, and changes in VPD and *e*_{s}(*T*) would influence *r*_{c}. Another foremost methodology to estimate *r*_{c} and evaporative losses from plant communities is the sap flux method. This method provides a unique intermediate between leaf and whole canopy level measurements, and it has been shown recently that the sap flux and porometer measurements of stomatal and canopy conductance match well [*Meinzer and Grantz*, 1990; *Meinzer et al.*, 1995; *Saliendra et al.*, 1995; *Sperry*, 2000; *Ewers et al.*, 2007]. Furthermore, research on the VPD and soil moisture response of *r*_{c} has been shown to match plant hydraulic theory well [*Whitehead*, 1998; *Oren et al.*, 1999; *Ewers et al.*, 2005; *Franks*, 2004], which is recently being integrated into models of transpiration and by implication of *E*_{Ta} [*Mackay et al.*, 2003; *Pataki and Oren*, 2003; *Ewers et al.*, 2008]. The plant hydraulic theory and its functions, especially the relationship between soil water, xylem properties, and leaf conductance (*g*), are presented and discussed in detail by *Meinzer and Grantz* [1990], *Sperry et al.* [1993], *Sperry and Pockman* [1993], *Saliendra et al.* [1995], *Sperry et al.* [1998], *Sperry* [2000], and *Franks* [2004]. The sap flux method has an advantage over the porometric measurements of *g* in that it does not disturb the leaf boundary layer. However, the practical application of the sap flux method is somewhat more widespread for woody vegetation rather than agronomic plants.

[5] Following the milestone multiplicative empirical *r*_{s} model from the study of the response of *r*_{s} to environmental variables by *Jarvis* [1976], a different approach to estimating *r*_{c} is the scaling-up of measured or estimated *r*_{s} to *r*_{c}. The fortunate capability of porometers to measure *r*_{s} has made the “scaling-up” approach a motivating and worthy subject to research. *Baldocchi et al.* [1991], *Rochette et al.* [1991], *Ehleringer and Field* [1993], and most recently *Irmak et al.* [2008] presented unique approaches of scaling-up *r*_{s} to *r*_{c}. The majority of these approaches, however, overlook the impact of atmospheric CO_{2} levels on stomatal control of water loss from plant communities in the scaling-up process. Following up on a steady-state coupled water and carbon model developed by *Katul et al.* [2003], recently, *Katul et al.* [2009a] developed a stomatal optimization theory describing the effects of atmospheric CO_{2} levels on leaf photosynthesis and transpiration rates that can be implemented in large-scale climate models. They showed that the cost of unit of water loss increases with atmospheric CO_{2}. Comparisons of their formulation results against gas exchange data collected in a pine forest showed that the formulation correctly predicted the condition under which CO_{2}-enriched atmosphere will cause increasing assimilation and decreasing *g*.

[6] In the scaling-up approach, each researcher scaled up *r*_{s} to *r*_{c} as a function of different microclimatological and/or physiological variables with successful applications. Nevertheless, difficulties and availability of *r*_{c} data for a variety of vegetation surfaces at different development stages and for a range of soil water and climatic conditions impose impediments to the practical application of the PM model to estimate evaporative losses from certain vegetation surfaces. Even if the *r*_{s} values of a given vegetation surface can be predicted with a reasonable accuracy, the challenge is still overcoming the added difficulties in the process of scaling up leaf level *r*_{s} to *r*_{c} to represent an integrated resistance from plant communities to quantify field-scale evaporative losses using the PM model [*Irmak et al.*, 2008]. Jarvis model estimates *r*_{s}, but *r*_{c} rather than *r*_{s} is needed as an input for the PM model. Any contributions to estimate *r*_{c} from more easily obtainable climatic variables, while maintaining the scientific merit and validity and robustness of the approach, can significantly augment the utilization of the Jarvis and PM models in practice by the water resource community. As an alternative to the physically based model scaling-up approach, an empirical approach is to estimate *r*_{c} from microclimatic observations. Our specific objectives with this research were to (1) develop a set of generalized-linear empirical models to estimate *r*_{c} as a function of microclimatic variables for a nonstressed maize canopy, (2) investigate the relationships between primary microclimatic factors and *r*_{c}, and (3) present the practical implementation of the new models via experimental validation using scaled-up *r*_{c} data of porometer-measured leaf stomatal resistance data that were measured through an extensive field campaign in 2006. For further validation of the developed *r*_{c} models, we estimated actual evapotranspiration (*E*_{Ta}) for maize canopy on an hourly basis using modeled *r*_{c} from all models and compared the *E*_{Ta} estimates with the Bowen ratio energy balance system (BREBS)-measured *E*_{Ta} for an independent data set in 2005.