Water Resources Research

On the dynamics of canopy resistance: Generalized linear estimation and relationships with primary micrometeorological variables



[1] The 1-D and single layer combination-based energy balance Penman-Monteith (PM) model has limitations in practical application due to the lack of canopy resistance (rc) data for different vegetation surfaces. rc could be estimated by inversion of the PM model if the actual evapotranspiration (ETa) rate is known, but this approach has its own set of issues. Instead, an empirical method of estimating rc is suggested in this study. We investigated the relationships between primary micrometeorological parameters and rc and developed seven models to estimate rc for a nonstressed maize canopy on an hourly time step using a generalized-linear modeling approach. The most complex rc model uses net radiation (Rn), air temperature (Ta), vapor pressure deficit (VPD), relative humidity (RH), wind speed at 3 m (u3), aerodynamic resistance (ra), leaf area index (LAI), and solar zenith angle (Θ). The simplest model requires Rn, Ta, and RH. We present the practical implementation of all models via experimental validation using scaled up rc data obtained from the dynamic diffusion porometer-measured leaf stomatal resistance through an extensive field campaign in 2006. For further validation, we estimated ETa by solving the PM model using the modeled rc from all seven models and compared the PM ETa estimates with the Bowen ratio energy balance system (BREBS)-measured ETa for an independent data set in 2005. The relationships between hourly rc versus Ta, RH, VPD, Rn, incoming shortwave radiation (Rs), u3, wind direction, LAI, Θ, and ra were presented and discussed. We demonstrated the negative impact of exclusion of LAI when modeling rc, whereas exclusion of ra and Θ did not impact the performance of the rc models. Compared to the calibration results, the validation root mean square difference between observed and modeled rc increased by 5 s m−1 for all rc models developed, ranging from 9.9 s m−1 for the most complex model to 22.8 s m−1 for the simplest model, as compared with the observed rc. The validation r2 values were close to 0.70 for all models, and the modeling efficiency ranged from 0.61 for the most complex model to −1.09 for the simplest model. There was a strong agreement between the BREBS-measured and the PM-estimated ETa using modeled rc. These findings can aid in the selection of a suitable model based on the availability and quality of the input data to predict rc for one-step application of the PM model to estimate ETa for a nonstressed maize canopy.

1. Introduction and Background

[2] Physically and combination-based calculations of actual evapotranspiration (ETa) [i.e., Penman-Monteith [Monteith, 1965]] require quantification of the canopy resistance (rc). 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 (rs) 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 rc 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 rc 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 rc has been the subject of many studies. Applying the Ohm's law analogy, Monteith [1965] illustrated rc 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, es(T)] and leaf temperature (TL). 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 TL and es(T) at a specific level within the canopy continuously. The spatial and temporal variation in es(T) and TL in the canopy further compound the complexity of using the analogy. The complexity to comprehend and quantify rc 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 rc 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 rc as a quotient of mean rs and effective green leaf area index (LAI). They assumed that when soil evaporation is negligible rc represents effective rs of all leaves acting as resistances in parallel. Jarvis [1981] proposed a novel approach for estimating rc as the sum of the rs 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 rc was presented by Lhomme [1991], and the resulting observed rc value was considered as a good physiological parameter when soil evaporation is negligible. Another multilayer model of rc 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 rs 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 rs value for well-watered plants has also been suggested [Monteith, 1965; Szeicz and Long, 1969]. However, computing rc by simply averaging different layers of rs can be problematic since es(T) and vapor pressure deficit (VPD) are dynamic within the canopy, and changes in VPD and es(T) would influence rc. Another foremost methodology to estimate rc 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 rc 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 ETa [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 rs model from the study of the response of rs to environmental variables by Jarvis [1976], a different approach to estimating rc is the scaling-up of measured or estimated rs to rc. The fortunate capability of porometers to measure rs 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 rs to rc. The majority of these approaches, however, overlook the impact of atmospheric CO2 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 CO2 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 CO2. Comparisons of their formulation results against gas exchange data collected in a pine forest showed that the formulation correctly predicted the condition under which CO2-enriched atmosphere will cause increasing assimilation and decreasing g.

[6] In the scaling-up approach, each researcher scaled up rs to rc as a function of different microclimatological and/or physiological variables with successful applications. Nevertheless, difficulties and availability of rc 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 rs 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 rs to rc 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 rs, but rc rather than rs is needed as an input for the PM model. Any contributions to estimate rc 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 rc from microclimatic observations. Our specific objectives with this research were to (1) develop a set of generalized-linear empirical models to estimate rc as a function of microclimatic variables for a nonstressed maize canopy, (2) investigate the relationships between primary microclimatic factors and rc, and (3) present the practical implementation of the new models via experimental validation using scaled-up rc data of porometer-measured leaf stomatal resistance data that were measured through an extensive field campaign in 2006. For further validation of the developed rc models, we estimated actual evapotranspiration (ETa) for maize canopy on an hourly basis using modeled rc from all models and compared the ETa estimates with the Bowen ratio energy balance system (BREBS)-measured ETa for an independent data set in 2005.

2. Materials and Methods

2.1. General Field Experimental Procedures

[7] Detailed descriptions of experimental procedures were presented by Irmak and Mutiibwa [2009], and only a brief description will be provided here. Extensive field data collection campaigns on rs, leaf area index (LAI), plant height (h), and microclimatic variables, including incoming shortwave radiation (Rs), net radiation (Rn), leaf level photosynthetic photon flux density (PPFD), VPD, wind speed at 3 m (u3), air temperature (Ta) at 2 m, relative humidity (RH) at 2 m, and other variables, were carried out in the summer of 2005 and 2006 at the South Central Agricultural Laboratory near Clay Center, Neb (latitude 40°34′N, longitude 98°08′W, and is 552 m mean sea level). Data were collected from a 13.5 ha maize (Zea mays L.) field irrigated with a subsurface drip irrigation system. Field maize hybrid Pioneer 33B51 with a comparative relative maturity of 113 to 114 days was planted at 0.76 m row spacing with a seeding rate of approximately 73,000 seeds ha−1 and planting depth of 0.05 m. Maize was planted on 22 April, emerged on 12 May, and reached full canopy closure on 4 July 2005. It reached silking stage on 12 July, matured on 7 September, and was harvested on 17 October in 2005. In 2006, maize was planted on 12 May with a planting density of 74,130 seeds ha−1. Plants emerged on 20 May, reached complete canopy closure on 8 July, reached the silking stage on 15 July, started to mature on 13 September, and were harvested on 5 October 2006. The experimental field was irrigated two or three times a week to meet full plant water requirements. In 2005, total rainfall from 22 April to 30 September was 307 mm, and a total of 225 mm irrigation water was applied with the first irrigation starting on 30 June [69 days after planting (DAP)]. In 2006, total rainfall during the growing season (12 May to 30 September) was 362 mm, and a total of 172 mm of irrigation water was applied with the first irrigation starting on 16 June (35 DAP). The plant-available soil water in the effective plant rooting depth in the top 0.90 m soil layer was kept between near field capacity and the maximum allowable depletion to avoid plant water stress. Plants were fertilized based on soil samples taken prior to planting to determine the fertilizer needs with regular pest and disease control being undertaken when appropriate.

2.2. Evapotranspiration and Other Surface Energy Flux Measurements

[8] The surface energy balance components, including ETa and microclimatic variables were measured using a deluxe version of a Bowen ratio energy balance system (BREBS, Radiation and Energy Balance Systems, REBS, Inc., Bellevue, Wash) that was installed in the middle of the experimental field with a fetch distance of 520 m in the north-south direction and 280 m in the east-west direction. Net radiation was measured using a REBS Q*7.1 net radiometer that was installed approximately 4.5 m above the soil surface. Incoming and outgoing shortwave radiation envelopes were measured simultaneously using a REBS model THRDS7.1 (Radiation and Energy Balance Systems, REBS, Inc., Bellevue, Wash) double-sided total hemispherical radiometer that was sensitive to wavelengths from 0.25 to 60 μm. The chromel-constant and thermocouple for the Ta and RH probes (model THP04015 for Ta and THP04016 for RH; REBS, Inc., Bellevue, Wash), with a resolution of 0.0055°C for Ta and 0.033% for RH, were used to measure Ta and RH gradients. The BREBS used an automatic exchange mechanism that physically exchanged the Ta and RH sensors at two heights above the canopy. Ta and RH sensors were exchanged during the last 2 min of each 15 min interval. The left exchanger tube that houses the Ta and RH probes was in the lower position during the first and third 15 min periods of each hour, and the right tube was in the lower position during the second and fourth 15 min periods of each hour. Rainfall was recorded using a model TR-525 rainfall sensor (Texas Electronics, Inc., Dallas, Tex). Soil heat flux density (G) was measured using three REBS HFT-3.1 heat flux plates and three soil thermocouples. Each plate was placed at a depth of 0.06 m below the soil surface. The REBS STP-1 soil thermocouple probes were installed in close proximity to each plate at a depth of 0.06 m below the soil surface. Measured G values were adjusted to soil temperatures and soil water content as measured using three REBS SMP1R soil moisture probes. One soil moisture probe was installed in close proximity to each soil heat flux plate. Wind speed and direction at 3 m were monitored using a model 034B cup anemometer (Met One Instruments, Grant Pass, Ore). All variables were sampled every 60 s, averaged, and recorded every hour for energy balance calculations using a model CR10X datalogger and AM416 Relay Multiplexer (Campbell Scientific, Inc., Logan, Utah). The BREBS was closely supervised and general maintenance was provided at least once a week. Maintenance included cleaning the thermocouples and housing units (exchanger tubes), servicing radiometers by cleaning domes, checking/replacing the desiccant tubes, and making sure that the radiometers were properly leveled. The radiometer domes were replaced every 3–4 months. The lower exchanger tube was always kept at least about 1.0 m above the canopy throughout the growing season. The distance between the lower and upper exchanger tubes was kept at 0.90 m throughout the season [Irmak et al., 2008; Irmak and Mutiibwa, 2008; Irmak and Irmak, 2008].

2.3. Stomatal Resistance and Plant Physiological Measurements

[9] A model AP4 dynamic diffusion porometer (Delta-T Devices, Ltd., Cambridge, UK) that was equipped with an unfiltered GaAsP photodiode light sensor with a spectral response similar to photosynthetically active radiation response was used to measure rs on randomly selected green, healthy, and fully expanded leaves. Detailed description of number of rs measurements, dates, and measurement protocols were presented by Irmak et al. [2008] and Irmak and Mutiibwa [2009]. Precautions were taken to maintain each leaf's natural orientation during the rs measurements. Each reading corresponded to one complete diffusion cycle in which the sensor and leaf reached equilibrium with the RH. Readings were taken by orienting the position of the instrument user behind the plant and sunlight shadow (i.e., the plant leaves that were being measured were always between the instrument user and the sunlight) so that the shading of the sensors and the leaf was prevented. The readings were taken from the near-central portion of young and mature leaves. LAI was measured using a model LAI-2000 plant canopy analyzer (LI-COR Biosciences, Lincoln, Neb). Once a week, the field measurements were taken starting when LAI was about 1.2. On average, a total of 60 LAI measurements were taken on each measurement day and averaged for the day. Plant height was also measured from the soil surface to the tip of the tallest leaf from approximately 50 randomly selected plants.

2.4. Modeling Canopy Resistance

[10] Here we strategically evaluated the estimation of rc from several directly measured environmental variables such as Rn, RH, Ta, u3, and LAI. Readily available field-measurable variables (Rn, Ta, and RH) were given priority in modeling rc by including them in all models developed. In addition, computed variables such as aerodynamic resistance (ra), VPD, and solar zenith angle (Θ) were incorporated into the analysis to determine their role in the variation in rc. Solar zenith angle was included with the hypothesis that it can help to capture temporal variability in rc arising from the diurnal solar movement across the sky, such that as the sun moves across the horizon, there is a continuous redistribution of direct and diffuse sunlight in the canopy, subsequently affecting rc. The ra was evaluated with an expression that is derived from turbulent transfer and assuming a logarithmic wind profile [Thom, 1975; Monteith and Unsworth, 1990]. Following Brutsaert and Stricker [1979], we computed ra (s m−1) as

equation image

where zm is the height of wind measurements (3 m), zh is the height of humidity measurements (2 m), d is the zero plane displacement height (m), zoh is the roughness length governing transfer of heat and water vapor (m), zom is the roughness length governing momentum transfer (m), k is von Karman's constant (0.41), and uz is the wind speed at height z (3 m; m s−1). We used measured plant height (h, m) to compute d, zom, and zoh following the study of Monteith et al. [1965], Plate [1971], and Brutsaert [1982]

equation image
equation image
equation image

Since wind speed may induce temporary stomatal closure [Salisbury and Ross, 1992; Kramer, 1983], in addition to transfer of vapor and heat in the canopy, ra may have an indirect effect on rc. Thus, we incorporated u3 into the models. Net radiation was included in all models because stomata generally do not respond to changes in the other environmental variables unless there is sufficient light for photosynthesis to occur [Norman, 1979; Campbell, 1982; Massman and Kaufmann, 1991; Irmak et al., 2008].

[11] The observed rc data used in this study as the reference rc values to develop the models were scaled up from measured rs values that were previously presented by Irmak et al. [2008] and Irmak and Mutiibwa [2009]. The modeling in this study is for empirically predicting rc and not for scaling up rs to rc. Irmak et al. [2008] presented a methodology for scaling up rs to rc utilizing rs versus a leaf level PPFD response curve that was measured through an extensive field campaign for a nonstressed maize canopy in 2006. Irmak and Mutiibwa [2008] measured rs for subsurface drip-irrigated nonstressed maize plants and integrated a number of microclimatic and in-canopy radiation transfer parameters to scale up rs to rc. With the espousal of microclimatic and plant factors such as LAI for sunlit and shaded leaves, Θ, h, and direct and diffuse solar radiation, they scaled up rs on an hourly basis as a main function of measured PPFD.

[12] The proposed rc models of this study were developed using STATISTICA™ software (version 7.1, StatSoft, Inc., Tulsa, Okla) utilizing the generalized-linear/nonlinear model tool. The module is a comprehensive implementation of the general linear model. With this approach, both linear and nonlinear effects for any number and type of predictor variables (Rn, RH, u3, Ta, VPD, LAI, ra, and Θ) on a discrete or continuous dependent variable (rc) can be analyzed [McCullagh and Nelder, 1989]. The generalized model is a generalization of the linear regression model, such that effects of climatic variables on rc can be tested for categorical predictor variables, as well as for effects for continuous predictor variables. A categorical predictor variable is a variable, measured on a nominal scale, whose categories identify class or group membership, which is used to predict responses on one or more dependent variables. The general form of the generalized-linear equation we used was built upon Jarvis-type parameterization and relates a dependent variable (rc) to a set of quantitative independent variables (Rn, RH, u3, Ta, VPD, LAI, ra, and Θ)

equation image

where e is the error variability that cannot be accounted for by the predictors; note that the expected value of e is assumed to be zero, while the relationship in the generalized-linear model is assumed to be

equation image

where e is the error, and z (…) is a function. Formally, the inverse function of z(…), say f(…), is called the link function. The models were developed systematically and had a decreasing number of predictor variables from a maximum of eight predictors to a minimum of three. The form of the equations can be expressed as

equation image
equation image
equation image
equation image
equation image
equation image
equation image

where rc_iis the canopy resistance estimated from model i (s m−1), Rn is net radiation (W m−2), Ta is air temperature (°C), RH is relative humidity (%), u3 is wind speed measured at 3 m (s m−1), ra is aerodynamic resistance (m s−1), LAI is green leaf area index, Θ is the solar zenith angle (degrees), a is the intercept, and b, c, d, e, f, g, h, and k are the coefficients of Rn, Ta, VPD, RH, u3, ra, LAI, and Θ, respectively, with all micrometeorological variables having hourly units.

2.5. Calibration and Validation of Proposed Canopy Resistance Models

[13] The scaled up hourly rc data set used for calibration ranged from 19 June 2006 to 15 July 2006, and the data set for validation covered the period from 16 July 2006 to 31 August 2006. The coefficients of the models were optimized for the best fit of predicted values to observed values, i.e., maximizing the coefficient of determination (r2) and minimizing the root mean square difference (RMSD) between measured and model-estimated rc. In the calibration and validation, the rc values that were observed from measured and scaled-up rs values that were presented by Irmak et al. [2008] were used as the actual (reference) rc values. These data sets were used to estimate (optimize) parameters for all seven rc models. New parameters were estimated by searching over the parameter space to minimize the RMSD between observed (scaled-up) and model-estimated rc. The optimized parameters replaced the original parameters and new rc values were calculated for each model. The assumption we made in the model development was that there was no interaction effect of independent variables on rc; thus, the variables act independently. All models were developed for an hourly time step using hourly input variables.

[14] Hourly rc values computed from the seven models were compared to hourly rc values (scaled up from measured rs by Irmak et al., 2008) for the 2006 growing season for validation. We further extended the validation of these models using the 2005 growing season. However, there was no measured rs or scaled-up rc data available in 2005. For further validation of our models in 2005, we estimated rc values from the seven models from measured input variables to solve the PM model for hourly actual evapotranspiration (ETa) and compared the estimated ETa values with the BREBS-measured ETa. The form of the PM equation we used is

equation image

where λETa is the latent heat flux density (W m−2), G is the soil heat flux density (W m−2), Δ is the slope of the saturation vapor pressure and air temperature curve (Pa °C−1), ρ is the air density (kg m−3), cp is the specific heat of air (J kg−1 °C−1), γ is the psychometric constant (Pa °C−1), es and ea, respectively, are the saturation and actual vapor pressure of air (Pa) where esea represents VPD, and Rn is the net radiation (W m−2).

2.6. Statistical Analyses

[15] The ability of the proposed rc models to predict the resistances was analyzed using three statistics. The r2 was used as a measure of goodness of fit (i.e., the measure of total variance accounted for by the model). The RMSD was used as a measure of the total difference between the predicted and observed rc values. We used modeling efficiency (EF) to asses the fraction of the variance of the observed values which is explained by the model, so EF provides good measure of model performance. In the EF, the higher values indicate better agreement and the best model is the one with a value of EF closest to unity. Physically, EF is the ratio of the mean square error to the variance in the observed data and subtracted from unity. The EF is an improvement in model evaluation in that it is sensitive to differences in the observed and model-simulated means and variances. However, because of the squared differences, EF can be overly sensitive to extreme values. The EF is expressed as

equation image

where Oi and Pi are the observed and predicted rc values, respectively, and equation image is the mean of observed data. All statistical analyses were performed using STATISTICA™ (ver. 7.1, StatSoft, Inc., Tulsa, Okla).

3. Result and Discussion

3.1. Climatic Conditions

[16] A summary of the measured meteorological data for the 2005 and 2006 growing seasons and long-term (32 year) average values are presented in Table 1. During 2006, the year used for model calibration, rainfall from April through July (245 mm) was less than the long-term average (374 mm). August was wetter than average (119 mm versus 83 mm), and daily average incoming shortwave solar radiation (Rs) was less (224 W m−2) as compared with the previous 4 months of the growing season. Maximum Ta was 1.5 to 3.5°C higher than the long-term average from May to July. Similarly, Rs was 18 to 31 W m−2 greater than the long-term average in the same time period. Relative humidity was also less in 2006 than in an average year. Average wind speed was very similar to long-term average values. From March to August 2006, the Ta_min was, on average, 1.3°C higher than the long-term average. Overall, 2006 was warmer and drier than an average year. Year 2005, which was used for model validation, was drier than a normal year with 72% normal total rainfall. On a seasonal average Ta_max in 2005 was 0.6°C higher than the average with Ta_max in September averaging 2.2°C higher than the average. The warmest month was July with an average Ta_max of 30.4°C. The seasonal average Ta_min was 1.4°C higher, and Rs was 14 W m−2 higher than the average. Wind speed and relative humidity values were similar to the long-term average values.

Table 1. Meteorological Parameters Measured for the Period of March–October at Clay Center, Neba
PeriodMeteorological VariableMarchAprilMayJuneJulyAugustSeptemberOctober
  • a

    Wind speed at 3 m (u3), maximum and minimum air temperature (Ta_max and Ta_min), average relative humidity (RHavg), average incoming shortwave radiation (Rs), average net radiation (Rn), and total rainfall.

2005u3 (m s−1)
Ta_max (°C)11.617.323.328.430.427.827.519.4
Ta_min (°C)−
RHavg (%)66.868.563.671.270.778.368.267.2
Rs (W m−2)150.4206.5259.0279.3283.0223.1207.8145.6
Rn (W m−2)71.0108.5138.7172.1174.4132.8111.259.2
Rainfall (mm)52.464.441.777.169.660.442.632.2
2006u3 (m s−1)
Ta_max (°C)9.120.524.329.630.327.822.916.1
Ta_min (°C)−
RHavg (%)72.764.661.065.273.479.871.370.3
Rs (W m−2)157.6214.0256.3288.4278.4224.8181.8120.4
Rn (W m−2)72.0111.4141.8169.5174.0142.1108.553.8
Rainfall (mm)4.346.560.154.283.8118.975.921.8
Long-term average (1975–2007)u3 (m s−1)
Ta_max (°C)10.517.022.528.130.329.225.318.3
Ta_min (°C)−
RHavg (%)69.866.371.370.273.274.568.867.2
Rs (W m−2)156.6196.0225.0259.8259.8228.5184.4131.1
Rainfall (mm)40.059.0112.0110.

3.2. Seasonal Patterns of Hourly Canopy and Aerodynamic Resistances

[17] Hourly rc decreased from early season during partial canopy toward midseason in early July, remained relatively stable until mid-August, and increased again, slightly, until late August (Figure 1a). Similar to other studies [Monteith, 1995; Alves et al., 1998; Perez et al., 2006], we observed a typical theoretically expected parabolic variation in the diurnal trend of rc in Figure 1a, characterized by a high resistance in the morning, gradually decreasing to a minimum in between 13:00 and 16:00 pm and gradually increasing in the afternoon until sunset. The profile of the graph is explained by the soil-plant-atmosphere continuum such that as long as the soil profile can supply the water to meet the evaporative atmospheric demand, rc will decrease with increasing radiation. However, when the evaporative demand exceeds the rate of soil water absorption at the root zone, typically in the afternoon, rc may increase to reduce transpiration.

Figure 1.

(a) Seasonal pattern of hourly canopy resistance (rc) and aerodynamic resistance (ra) in relation to leaf area index (LAI), and (b) and seasonal daily pattern of maximum, average, and minimum canopy resistance for a nonstressed maize canopy.

[18] From 19 June until first week of July, rc was at its greatest values ranging from a daily minimum of 50–60 s m−1 to around 200 s m−1. The rc and LAI showed an inverse relationship, where rc decreased as LAI increased. rc remained relatively stable when LAI reached 3.5–4.0. The maximum rc occurred on 24 June at 09:00 am as 216 s m−1. During that hour, the following conditions were observed: LAI = 1.6, u3 = 3.3 m s−1, Ta = 17.9°C, RH = 93.9%, Rs = 109.3 W m−1, and Rn = 57.4 W m−2, with a moderate atmospheric demand (VPD = 0.80 kPa). This high rc value (216 s m−1) can also be a result of dew formation on the leaves. On average, rc fluctuated within a magnitude of about 50 s m−1 diurnally. Diurnal fluctuations were greatest (>70–75 s m−1) early in the season and least (≈30 s m−1) in the midseason. The maximum diurnal fluctuation range of rc was observed on 24 June as 140 s m−1. ra followed a similar trend as rc throughout the season with lower magnitudes (Figure 1a). ra was also high during the early season when plant was short, gradually decreased toward midseason, and slightly increased again after mid-August. ra ranged from approximately 3 s m−1 in midseason to around 60 s m−1 in early season. The maximum ra was obtained on 25 June as 67.7 s m−1 when h = 1.8 m, LAI = 1.57, and within a daily average rc = 98.3 s m−1. ra remained relatively constant during the mid season due to constant h (ranging between 2 and 2.2 m), fluctuating in a narrow range between 10 to 20 s m−1. The seasonal average ra was 15.9 s m−1.

3.3. Relationship Between rc and Micrometeorological Variables

[19] The relationships between rc versus Ta, RH, VPD, Rn, Rs, u3, wind direction, LAI, Θ, and ra on an hourly basis are presented in Figures 2a2j, respectively. We used linear regression, exponential, or power functions as the best-fit functions, depending on the distribution of the data. The relationships between rc versus u3, wind direction, and Θ were weak. There was a strong relationship between rc and Ta, and the Ta range during the season was between 15.7°C to 39°C (Figure 2a). We found larger values and a larger range of values of rc for Ta values <29°C. rc responded to Ta in a much narrower range for temperatures >29°C. Although there was a general trend of increasing rc with increasing RH, this relationship is not strong (r2 = 0.12, Figure 2b). The response of rc to VPD was stronger than to RH with r2 = 0.23. Aphalo and Jarvis [1991] investigated the response of stomata to leaf surface humidity and temperature and showed that the relationship between g and RH was different when measured at the same temperature rather than at different temperatures. They observed a reversible response to RH under constant temperature and that there was also a response to temperature under constant RH. An inversely proportional response was consistently obtained when g was expressed in relation to VPD. Mott and Parkhurst [1991] and Oren et al. [1999] showed that the response of stomata is not to VPD (or RH) directly, but it is the transpiration rate which responds directly to VPD. However, this may not be the only mechanism that causes changes in rs. Other factors such as change in leaf water potential as a result of transpiration responding to VPD is most likely responsible for changes in rs due to this signal (respond to change in water potential) transferring to the guards cells. A number of leaf-level semi-empirical models used different forms of functions of either RH or VPD when modeling stomatal response. For example, the models proposed by Ball et al. [1987] (Ball-Berry model) and Collatz et al. [1991] suggest that g is somewhat linear in RH. Others semiempirical in VPD (based on Leuning et al. [1995]) and a new class of models based on optimization theories suggest a VPD0.5 dependence of g (i.e., a power-law versus exponential). Another study showed a log(VPD) dependence of g [Oren et al., 1999]. Oren et al. [1999] also showed that stomatal sensitivity is proportional to the magnitude of g at low VPD (equation image1 kPa) and concluded that plant species with high g at low VPD show a greater sensitivity to VPD. The linear model presented by Katul et al. [2009b] is consistent with aforementioned studies in terms of the dependency of g to VPD. The main rationale of using RH rather than VPD in our models will be discussed in section 3.4.

Figure 2.

Relationship between canopy resistance (rc) and primary microclimatic variables: (a) air temperature (Ta), (b) relative humidity (RH), (c) vapor pressure deficit (VPD), (d) net radiation (Rn), (e) incoming shortwave radiation (Rs), and (f) wind speed at 3 m (u3) (n = 755 for each case). Relationship between canopy resistance (rc) and main microclimatic variables: (g) wind direction, (h) leaf area index (LAI), (i) solar zenith angle (Θ), and (j) aerodynamic resistance (ra) (n = 755 for each case).

Figure 2.


[20] As expected, the response of rc to Rn was much stronger than for Rs (Figures 2d and 2e) (r2 = 0.34 for Rn versus r2 = 0.10 for Rs), since Rn, rather than Rs, represents the amount of energy intercepted at the canopy level that cause a response in stomata. Higher rc values were observed at lower Rn values due to the larger magnitude of stomatal closure at lower Rn even when other environmental factors change. The maximum rc (216 s m−1) occurred at Rn = 0.33 MJ m−2 h−1, and the minimum usually occurred when Rn was greater than 2 MJ m−2 h−1. There were many hours when rc did not respond to changes in Rn due to the control of rc by other microclimatological variables. Even though there is enough Rn, high u3, low VPD, small LAI, and low Ta will have an impact in controlling the opening or closure of stomata. Stomatal response to both Rn and Rs was discussed in detail by Irmak and Mutiibwa [2009]. We observed several different groupings of rc with Rn in Figure 2d that does not occur as much with Rs in Figure 2e. The reason for this fluctuation or groupings is not clear to the authors. While the relationship between rc and u3 is not very clear, there was a tendency of increasing rc with increasing u3. The highest rc values were obtained in the u3 range of 2 to 4 m s−1 (Figure 2f). As observed by Monteith et al. [1965], there is slight evidence in Figure 2f that the rc responds to u3 at higher wind speeds, but the changes in rc are too small.

[21] Figure 2h presents the relationship between daily LAI and hourly rc. The relationship between the rc and LAI is the strongest among all variables (r2 = 0.41). rc decreased gradually as LAI increased from 1.20 to 5.30. The magnitude of diurnal fluctuation in rc was greater in the early season than in the middle and late season. The larger variations in rc at lower LAI and partial canopy cover early in the season were caused by the dry soil surface and higher soil evaporation. The inverse relationship between LAI and rc did not hold after approximately LAI = 4.0, although diurnal fluctuation in rc was still present. Both variables remained relatively stable for the rest of the season. While the impact of soil surface evaporation on rc is not fully understood, rc usually increases as soil water is depleted. Ham and Heilman [1991] showed that the within-canopy aerodynamic and soil resistance to water vapor transport from the soil surface were greater than those for the canopy even at low wind speeds. Although Tanner [1963] suggested that rc contains an aerodynamic component depending on wind speed, our findings support the suggestion of Monteith et al. [1965] that resistance is governed primarily by LAI (Figure 2h), light (Figure 2d), temperature (Figure 2a), and VPD (Figure 2c) and is independent of the intensity of turbulent mixing above or within the canopy. This may suggest a high canopy coupling (omega factor, Ω) [McNaughton and Jarvis, 1983; Jarvis and McNaughton, 1986] between canopy and microclimate above the canopy surface. While quantification of Ω was beyond the scope of this study, it is a powerful parameter that describes how strongly the VPD at the canopy surface is linked the boundary layer above the canopy and examines the contribution of radiation and VPD to the transpiration rate [Jarvis and McNaughton, 1986].

[22] The relationship between rc and ra is presented in Figure 2j. The deviation between both resistances is smaller in the low resistance range, while rc is always larger than ra. On a seasonal average, rc was 3.5 times larger than ra. It is expected that ra would be smaller than rc because the evaporative loss is mainly controlled by rc. Thus, higher resistance exists at the canopy level for vapor transport. Also, ra is often the dominant mechanism for the absorption of momentum by vegetation so that the resistance to the exchange of momentum between the canopy and surrounding air is smaller than the corresponding resistances to the exchange of heat and vapor, which depend on molecular diffusion alone [Monteith and Unsworth, 1990]. Monteith and Unsworth [1990] analyzed the ratio rc/ra for several mature forest sites and found that the ratio rc/ra is about 50. The ratio can be used as an indicator of the evaporative ratio from wet versus dry canopies. They stated that larger ratios of rc/ra (e.g., 50) would show that evaporation from forest canopies wet with rain would proceed much faster than from dry canopies exposed to the same microclimatic conditions. Consequently, forests in regions where rain is frequent tend to use more water by evaporation from foliage and transpiration than shorter plants growing nearby. They reported that this contrasts with the situation for many agricultural plants, such as maize, for which minimum values of rc are typically 100 s m−1 but rc/ra is often close to unity. In our case, the minimum rc ranged from 40 to 100 s m−1 (Figure 1b). We found that the hourly rc/ra ratios for our experimental conditions ranged from 1.2 to 14 (Figure 3) with a seasonal average ratio of 5.1, which is much lower than the forest canopy as reported by Monteith and Unsworth [1990]. Although we did not observe a distinct pattern in the ratio throughout the season, it was lower early in the season, ranging from 1.0 to 8.0; greater in the midseason, fluctuating between 2 and 14, and remained relatively stable around 6.0 from mid-August to the end of the season, although fluctuations were still present. In general, we found that the rc/ra ratio tended to decrease sharply after rain events.

Figure 3.

Hourly ratios of canopy resistance (rc) to aerodynamic resistance (ra) (rc/ra) in relation to precipitation for a nonstressed maize canopy.

3.4. Canopy Resistance Model Calibration and Validation Results

[23] The calibration coefficients b, c, d, e, f, g, h, and k and the intercepts (a) for the 2006 growing season for the seven models (equations 713) are presented in Table 2. Model calibration performance results are presented in Figures 4a4g. Models rc_1, rc_2, rc_3, and rc_4 had very similar r2 (∼0.95) and RMSD (∼5.0 s m−1). Model rc_1 had the highest number of modeling variables (Rn, Ta, VPD, RH, u3, ra, LAI, and Θ). Models rc_6 and rc_7 had very similar performance and had the poorest r2 of 0.44 and highest RMSD of 17.4 s m−1. These two models had the least number of modeling variables, rc_6 with 4 variables (Rn, Ta, RH, and u3) and rc_7 with 3 variables (Rn, Ta, and RH). The model rc_5 had a good r2 of 0.93 and low RMSD of 6.3 s m−1. The observed seasonal mean rc was 75 s m−1, and the means from all seven models were very similar to the observed value. Estimates from the first five models were very good with very little scatter in the data around the 1:1 line. Models rc_6 and rc_7 overestimated in the range of 0 to around 90 s m−1 and underestimated at greater values. The data scatter increased for both models in the higher rc range. The coefficients for Ta and RH for models rc_6 and rc_7 are different than other models, whereas the coefficients for other variables were similar for most models. The variation in coefficients for Ta and RH for models rc_6 and rc_7 may be due to exclusion of LAI from these two models such that the influence of Ta and RH on rc was different than other models in the absence of LAI in estimating rc.

Figure 4.

Calibration (19 June to 15 July 15) performance results for the seven canopy resistance (rc) models (n = 405 for each case).

Table 2. Calibration Coefficientsa for the Seven Models Developed to Predict Canopy Resistance as a Function of Net Radiation, Air Temperature, Vapor Pressure Deficit, Relative Humidity, Wind Speed at 3 m, Aerodynamic Resistance, Leaf Area Index, and Solar Zenith Angle
CoefficientVariableModels and Coefficients
  • a

    a, b, c, d, e, f, g, h, and k; measured mean rc was 75 s m−1.

 Mean rc74.974.874.974.974.975.075.0

[24] The seasonal distribution of the hourly residuals that were calculated from the regression between the model estimates of rc (rc_1 through rc_7) versus observed rc for the calibration data set are presented in Figure 5. Models rc_1 though rc_5 had lower residuals than the models rc_6 and rc_7. The residuals for the models rc_1 through rc_5 showed similar trends and tend to fluctuate between similar ranges of −20 to 20 s m−1. The residuals were higher early in the growing season and fluctuated in a narrower range towards the end of the season. Models rc_6 and rc_7 had larger residual fluctuations ranging from −35 to 65 s m−1.The residuals for these two models were high early in the season, gradually decreased toward the midseason, and remained negative from early July to the end of July. Model rc_1 had the lowest and models rc_6 and rc_7 had the largest residuals. Overall, the sum of squares of the residuals were 8470, 9331, 8649, 8768, 12,754, 45,345, and 45,472 for the models rc_1 through rc_7, respectively. The mean squares of the residuals were 24.8, 27.7, 25.7, 26, 37.8, 134.6, and 135 for the same models, respectively. Except LAI, we did not observe any clear trend of the residuals with respect to any of the micrometeorological drivers measured.

Figure 5.

Distribution of residuals of regression between modeled canopy resistance (rc_1 through rc_7) and observed rc for the growing season (19 June to 15 July 2006) for the calibration data set (n = 339).

3.5. Validation of rc Models for Estimating Observed rc in 2006

[25] We validated the models in two ways. First, the models were used to estimate rc from 21 July to 30 August in 2006 growing season and the validation results are presented in Figure 6. Compared to the calibration results, the validation RMSD values increased by about 5 s m−1 for all models, and the r2 decreased to a range of 0.69 to 0.73. The r2 of 0.71 and 0.70 was a significant improvement in performance for models rc_6 and rc_7, which had a calibration r2 of 0.44. Models rc_1, rc_2, rc_3, rc_4, and rc_5 had means ranging from 50.3 to 51.5 s m−1, which was close to the observed mean (55.9 s m−1). The means of rc_6, and rc_7 were 76.1 and 75.9 s m−1. With the EF ranging from 0.57 to 0.65, models rc_1, rc_2, rc_3, rc_4, and rc_5 demonstrated a high efficiency since values of EF close to 1 signify a good modeling performance. Although the RMSD and r2 results of models rc_6, and rc_7 were acceptable, the EF values were −1.096 and −1.087, respectively. A negative EF indicates that the squared difference between the model predictions and the observed values is larger than the variability in the observed data. Thus, the observed mean is a better predictor than the model. The poor EF of models rc_6 and rc_7 was further depicted by the slopes, which showed an overestimation of 33% by both models (Figure 6). Model rc_6 is different from rc_7 because of the inclusion of u3; however, from the statistical results in Table 2, the two models presented similar performance. It appears that the performance of models rc_6 and rc_7 was compromised by using fewer variables that influence rc.

Figure 6.

Validation (16 July to 31 August 2006) performance results for the seven canopy resistance (rc) models (n = 405 for each case).

[26] Overall, model rc_5 performance had the best agreement with the data. The model had the smallest RMSD of 9.3 s m−1, highest r2 of 0.73, the highest EF of 0.65 with only 6% underestimation. Model rc_5 has 5 variables (Rn, Ta, RH, u3, and LAI) with the latter being the only variable not measured by a typical weather station. This is an encouraging performance of the model using readily available weather station data. LAI has been used in both single and multiple layered models as a weighting or scaling factor of rs to estimate rc [Szeicz and Long, 1969; Sinclair et al., 1976; Whitehead and Jarvis, 1981; Bailey and Davies, 1981; Seller et al., 1986]. Similar to the results presented by Beadle et al. [1985], we observed that the rc is considerably influenced by seasonal changes in LAI, and we demonstrated the negative impact of exclusion of LAI, the only plant physiological variable, on rc in the performance of models rc_6, and rc_7, where performance statistics were poor compared to the other models that included LAI.

[27] The performance of model rc_1, which used eight variables, was not different from models rc_2, rc_3, rc_4, and rc_5, which used 5 to 7 variables. To select the better variable between VPD and RH for modeling rc, models rc_2 and rc_3 were developed with the same number of variables but with one, model rc_2, using VPD and the model rc_3, using RH. Clearly, the results in Figure 6b versus 6c suggest that RH was a better predictor than VPD with a smaller RMSD and greater r2 and EF. In model rc_3, using RH instead of VPD resulted in 4%, 6%, and 8% improvement in r2, RMSD, and EF, respectively. However, the residuals for model rc_2 and rc_3 were similar in magnitude and distribution and the improvement in predicted rc using rc_3 was not statistically significant (P > 0.05) than predictions of rc_2. Nevertheless, since the objective of the study was to model rc from weather station-measured climate variables, this was an important finding, and as such, RH rather than VPD was used as a variable for the rest of the models (rc_3, rc_4, rc_5, rc_6, and rc_7).

[28] Baldocchi et al. [1991], Finnigan and Raupach [1987], Alves et al. [1998], and Alves and Pereira [2000] have pointed out that rc contains additional nonphysiological information pertaining to the ra in the canopy. Therefore, model rc_3 was set up to be different from model rc_4 by the inclusion of ra. However, similar to the results obtained by Finnigan and Raupach [1987], the results (r2 and EF) in Figures 6c and 6d showed that ra added a minimal improvement in estimating rc. Conversely, elimination of Θ as an independent variable from the model rc_5 resulted in an improvement in RMSD, r2, and EF. This suggests that ra and Θ are of minimal importance in the modeling of rc. The results demonstrate that models like rc_5, with the variables Rn, RH, Ta, u3, and LAI rather than including all variables, such as in model rc_1, can provide good performance. This might be due to the fact that inclusion of many independent variables in rc modeling can also increase the variability, error, and uncertainty associated with obtaining those variables, thus, negatively impacting the model performance. On the other hand, enough independent variables must be accounted for when modeling rc and our results indicated that the model rc_5 seems to represent this balance (number of variables versus performance).

[29] Figures 6a6g show a cluster of points of small rc values which gradually spread out and decrease in number with increasing variability as the resistances increase. This shows that for a well-watered field, rc is dominated by small resistance values, with a few high resistance values generally observed in the morning, late afternoon, and during advection and extreme conditions. In comparison to the 1:1 line, the graphs show that models rc_1, rc_2, rc_3, rc_4, and rc_5 underestimated resistance, whereas rc_6 and rc_7 overestimated observed rc. Models, rc_1, rc_2, rc_3, rc_4, and rc_5 underestimated observed rc by 8%, 10%, 8%, 8%, and 6%, respectively. Both rc_6 and rc_7 overestimated by 33%. In Figures 6a6g, we observed an increase in variability with increasing rc for all models. Increased variability could be associated with the rigidity of the models to adjust and depict the limiting variables during extreme conditions. For instance, in the morning hours, Rn is the limiting factor of rc. In the afternoon, studies [Adams et al., 1991] have shown that VPD, which is regulated by RH, is typically the limiting factor.

3.6. Validation of rc Models for Estimating ETa in 2005

[30] Further validation of rc model performance was done on an independent data set by estimating rc from each model on an hourly basis and then using the PM model as a one-step procedure to estimate ETa from modeled rc. We then compared the PM-estimated ETa to the BREBS-measured ETa on an hourly basis. The seasonal distribution of hourly BREBS-measured ETa data from 1 May to 31 August that were used is presented in Figure 7. Hourly ETa ranged from near zero to 1.16 mm h−1. There was a strong agreement between the BREBS-measured and the PM-estimated ETa (Figure 8a8g for models rc_1 through rc_7, respectively). The results show that the performance of all models is similar with r2 ranging from 0.88 to 0.90. The RMSD ranged from 0.09 mm h−1for models rc_6 and rc_7 to 0.13 to 0.15 mm h−1 for other models. The ETa estimated with rc from models rc_6 and rc_7 marginally underestimated BREBS-measured ETa by only 1%, performing better than the models rc_1, rc_2, rc_3, rc_4, and rc_5, which overestimated BREBS-measured ETa by 17%, 18%, 16%, 16%, 16%, and 16%, respectively. The ETa predicted with rc models rc_6 and rc_7 had a mean of 0.52 which was closely similar to the mean of measured ETa (0.53 mm h−1). The means of ETa predicted with canopy resistance estimated from models rc_1, rc_2, rc_3, rc_4, and rc_5 were 0.61, 0.62, 0.61, 0.61, and 0.61 mm h−1, respectively. The ETa predicted using rc_6 and rc_7 had a standard deviation of 0.24 mm h−1 which was less than the standard deviation of the other five models (0.27 mm h−1).

Figure 7.

Seasonal (1 May to 31 August 2005) distribution of Bowen ratio energy balance system (BREBS)-measured hourly actual evapotranspiration (ETa) for well-watered maize canopy (n = 2952).

Figure 8.

Comparison of Penman-Monteith (PM)-estimated hourly actual evapotranspiration (ETa), using estimated canopy resistance (rc) from the seven models developed in this study, and the Bowen ratio energy balance system (BREBS)-measured hourly ETa for a well-watered maize canopy.

[31] Unlike the results of rc validation in 2006, the 2005 results clearly demonstrate that estimating ETa using rc estimated from models rc_6 and rc_7 performed better than using the rest of the models. However, models rc_6 and rc_7 overestimated observed rc (Figures 6f and 6g, respectively). Thus, one would have expected these models to estimate lower ETa as compared with the BREBS-measured ETa, but the ETa estimates of both models were within 1% of the BREBS ETa. This may be due to the combination of three reasons. First, it is likely that the PM model overestimated ETa, but since the rc_6 and rc_7 models were producing lower ETa due to overestimation of rc, this offset the overestimation by the PM model as compared with the BREBS measurements. Steduto et al. [2003] and Rana et al. [1994] showed that the PM equation overestimates in cases with low ET values. Perez et al. [2006], Zhang et al. [2008], and Irmak and Mutiibwa [2009] showed that the PM equation can overestimate ETa during full canopy cover, especially during periods of high evaporative atmospheric demand. This is because during complete canopy cover and especially during periods with high evaporative atmospheric demand conditions when there is available soil water supply, the variable rc approach in the PM model assigns a small resistance value which is assumed to be homogeneous for the whole canopy when in reality some leaves in the canopy are shaded and/or aged and may not contribute to the transpiration rate at the same level as the sunlit and young leaves [Irmak and Mutiibwa, 2009]. Younger and sunlit leaves would have lower rc values than the older and shaded leaves, thus, transpiring at different levels and contributing differently to the total evaporative losses estimated by the PM model. It would be expected that the ETa rate estimated from the PM model to be less than those measured values. Thus, the ETa measured by the BREBS may better represent the total evaporative losses from the whole canopy accounting for ETa from various levels of shading and leaves with different ages.

[32] The second possible explanation is, especially in relation to the performance of the PM model in high atmospheric demand conditions, that the rc may have been underestimated by models rc_6 and rc_7 in our case rather than the PM model itself overestimating during high evaporative demand conditions. The underestimation of rc in our case might be due to not accounting for the VPD by Irmak et al. [2008] during the scaling-up rs to rc process, which is especially important during high evaporative demand settings. Furthermore, some variables may have been misestimated due to experimental and instrumental errors. Relative humidity, for example, is never perfectly estimated [Ewers and Oren, 2000] and the Rn measurements may not have been perfect. In addition, the BREBS-measured ETa contains some measurement error as well. The third possible explanation is the potential insensitivity of ETa to rc. It has been suggested that ETa is estimated more accurately than estimated rc because ETa depends only in part on rc [Stewart, 1988; Stewart and Gay, 1989; Gash et al., 1989]. The sensitivity analyses by Finnigan and Raupach [1987], Stewart [1988], and Gash et al. [1989] indicate that the ETa is fairly insensitive to rc for agronomical plants. If the ETa is insensitive to rc, then the better performance of models rc_6 and rc_7 in estimating ETa could be an artifact of a random performance based on the 2005 ETa and climate data set. We further tested this by evaluating the sensitivity of ETa to rc for our data set in the next section.

3.7. Sensitivity of PM Model to rc

[33] Figure 9 presents the change in ETa (mm h−1) as estimated from the PM model per 10 s m−1 increase in observed rc. The cumulative percent change in PM-estimated ETa versus changes in rc for a morning and noon hour of the same day are also included in the same figure. While we kept all the variables constant during the analyses, we conducted the sensitivity analyses for a randomly selected day (19 June), and analyzed the sensitivity of ETa to rc for a morning hour (09:00 am) and a noon hour (1:00 pm) for the same day to asses whether the ETa shows different response in two different microclimatic conditions for a canopy in the same environment. The observed rc was increased from zero to 300 s m−1 with 10 s m−1 increments, and the ETa rate and the percent change in ETa from the PM model were calculated for both hours. The initial (base) ETa and rc values along with the other microclimatic variables measured at 09:00 am and 1:00 pm are presented in Table 3. The response of ETa to changes in rc was similar for morning and noon hours with decreasing trend in ETa as rc increased. With the initial rc (185 s m−1 for 09:00 am and 100 s m−1 for 1:00 PM) and other measured microclimatic variables, the PM-estimated ETa at 09:00 and 1:00 pm, respectively, were 0.09 mm h−1 and 0.46 mm h−1. A unit (10 s m−1) increase in rc had slightly higher decrease in ETa for 1:00 pm, and the exponent of the ETa versus rc lines for 1:00 pm was slightly higher (−0.0041) than the one for 09:00 am (−0.0043) (Figure 9). The a values in the exponential functions (equations are not shown on Figure 9) (0.738 and 0.2203) are analogous to an intercept because these are the values of the functions when X = 0 since exp(0) = 1. Since the exponents are similar, a value is more influential on the rate of change (the derivatives of the exponential functions) in ETa. The magnitude of the average rate of change in ETa at 1:00 pm was greater [−0.001744 mm h−1 decrease in ETa (negative sign indicates decrease) per 1 s m−1 increase in rc] than for 09:00 am (−0.00053 mm h−1 decrease in ETa per 1 s m−1 increase in rc). ETa did not respond to changes in rc after about 210 s m−1 in the morning and after 270 s m−1 at 1:00 pm. Even though the rate of change was greater for the 1:00 pm curve, a unit increase in rc had slightly higher percentage decrease in ETa in the morning. This is due to the solar radiation being significantly higher at noon than in the morning (888 versus 283 W m−2). Since the solar radiation is the primary regulator of rc, when there is sufficient light to keep stomata fully open, a unit increase in rc would be expected to have lower impact on ETa under the same amount of radiation when the radiation is kept constant. This is because the role of other environmental variables in controlling stomata would be greater when there is no sufficient light in the morning.

Figure 9.

Response of Penman-Monteith (PM) model-estimated actual evapotranspiration (ETa) to changes in canopy resistance (rc) for a morning and noon hour of the same day (19 June 2006) for a nonstressed maize canopy and cumulative percent change in Penman-Monteith (PM) model-estimated actual evapotranspiration (ETa) versus changes in canopy resistance (rc) for a morning and noon hour of the same day (19 June 2006) for a nonstressed maize canopy.

Table 3. Measured Environmental Variables at 09:00 am and 1:00 pm Where the Sensitivity of Penman-Monteith-Estimated Actual Evapotranspiration to Canopy Resistance was Determineda
Measured VariableUnit09:00 am1:00 pm
  • a

    The variables included air temperature (Ta), incoming shortwave radiation (Rs), net radiation (Rn), soil heat flux (G), vapor pressure deficit (VPD), relative humidity (RH), aerodynamic resistance (ra, calculated from equation 1), wind speed at 3 m (u3), wind direction, and base values for rc and ETa.

RsW m−2283.2888.4
RnW m−2200.0638.9
GW m−219.463.8
ras m−129.827.3
u3m s−12.54.1
u3 directionDegreesEast-southeastEast
Base rcs m−1185100
Base ETamm h−10.090.46

[34] The cumulative percent change in ETa, reached −286% for morning and −262% at 1:00 pm (Figure 9) with the negative sign indicating decrease in ETa. In total, the ETa decreased from 0.27 to 0.07 mm at 09:00 am and from 0.87 to 0.24 mm h−1 at 1:00 pm when rc increased from 0 to 300 s m−1. Until 100 s m−1, the response of ETa to change in rc was never zero and was very similar for both the morning and noon hour (Figure 9). After 100 s m−1 for the morning and 200 s m−1 for the noon hour, the PM model sometimes showed no response (zero decrease in ETa) to increase in rc every 10 or 20 s m−1; thus, ETa response fluctuated in a wider range for the morning hour. Zero decrease in ETa was observed only three times for 1:00 pm at higher rc values (240, 280, and 300 s m−1). While we conducted the sensitivity analyses for only 1 day with morning and noon hours, the sensitivity of the PM ETa may show variation with time of the season due to changes in canopy and due to aerodynamic and energy terms of the model showing different sensitivities to dynamic micrometeorological conditions. However, while the magnitude of the sensitivity of the model may show variations, the trend and the relative sensitivity of the PM ETa to rc should be similar throughout the season.

[35] To evaluate the relationship between observed rc and ETa throughout the season in 2006, we graphed observed scaled-up hourly rc values against BREBS-measured hourly ETa in Figure 10 and found a strong relationship between the two variables. The rc and ETa data points in Figure 10 include those measured diurnally, usually from 09:00 am to 5:00 or 6:00 pm, from 19 June through 31 August 2006. The relationship was explained with an exponential decay function (Y = aebx; a = 2.414 and b = 0.0274). On an hourly time step, rc alone was able to explain 54% of the variability (r2 = 0.54) in ETa, further indicating a strong dependence of ETa on rc. The terms a and b had standard deviation of 0.1435 and 0.0011, respectively, with both terms being statistically significant (P < 0.0001). Figure 10 shows that most of the higher ETa rates were observed at the lower rc range (40 to 100 s m−1). The ETa rate decreased gradually as rc increased. The highest BREBS-measured ETa rate (1.28 mm h−1) occurred when observed rc was 44.3 s m−1. The higher rc and lower ETa values in Figure 11 were observed in early morning hours and cloudy days with low solar radiation. These results and the sensitivity analyses demonstrate that the PM-estimated ETa is very sensitive to changes in rc, but this response is dynamic and is impacted by other factors, but more so by the amount of light (radiation). Thus, it appears that the good performance of model rc_6 and rc_7 in Figure 8 is most likely due to the overestimation of the PM model, likely due to underestimation of rc by models rc_6 and rc_7, as compared with the BREBS-measured ETa and not due to the insensitivity of the ETa to rc.

Figure 10.

Relationship between observed scaled-up canopy resistance (rc) and Bowen ratio energy balance system (BREBS)-measured actual evapotranspiration (ETa) for a nonstressed maize canopy. The rc values were obtained from measured and scaled-up leaf stomatal resistance values as reported by Irmak et al. [2008] and Irmak and Mutiibwa [2009].

Figure 11.

Sensitivity of the Penman-Monteith (PM) model to canopy resistance (rc) (λETa/rc, equation 16).

[36] Figures 9 and 10 investigate the sensitivity of the PM ETa to rc implicitly. To explicitly determine the sensitivity of the PM model-estimated ETa to rc, we solved the following equation (all variables have been previously defined in equation 14):

equation image

The ratio of ∂λETa/∂rc essentially represents the sensitivity coefficients of the PM with respect to rc. We plotted the hourly ratios (09:00 am to 6:00 pm) as a function of time in Figure 11. Daily average ratios also included in the figure. The hourly ratios ranged from near zero to 0.016 with a seasonal average of 0.006. The ratio was lowest early in the morning, was at maximum during midday, and started to decrease toward late afternoon. This diurnal trend is due to response of rc to increase magnitude of the radiation, temperature, and other micrometeorological variables with time. The ratios were lower early in the season and largest in midseason during complete canopy cover and maximum LAI from mid-July to early August and decreased again toward the end of the season. The lower values in the late season is most likely due to insensitivity of the PM model to rc as a result of physiological maturity and leaf senescence as the influence of the rc on ETa is minimal in these conditions.

4. Conclusions

[37] We investigate the relationships between primary micrometeorological parameters and canopy resistance (rc) and present seven models using a generalized-linear model approach to estimate rc for a nonstressed maize canopy. The most complex rc model uses net radiation (Rn), air temperature (Ta), vapor pressure deficit (VPD), relative humidity (RH), wind speed at 3 m (u3), aerodynamic resistance (ra), leaf area index (LAI), and solar zenith angle (Θ) as inputs. The simplest model requires Rn, Ta, and RH. The relationship between rc versus u3, wind direction, and Θ was weak. There was a strong relationship between rc and Ta. Although there was a general trend of increasing rc with increasing RH, this relationship was not strong. While the relationship between rc and u3 is not very clear, there was a tendency of increasing rc with increasing u3. The highest rc values were obtained in the u3 range of 2 to 4 m s−1. The relationship between the rc and LAI is inverse and is the strongest among all variables. Upon validation, the rc model that used Rn, Ta, RH, u3, and LAI had the best agreement with the observed rc data. Exclusion of LAI resulted in reduced performance and exclusion of ra and Θ from models did not impact the performance of the rc models. The BREBS-measured and the PM-estimated ETa, using modeled rc, were in close agreement. Given that most of the micrometeorological variables needed for the rc models could be measured with a typical weather station, and the physiological variables, such as LAI, could be estimated with a reasonable accuracy, the performance obtained from all rc models is an encouraging step toward empirical modeling of rc for one-step application of the PM model for estimating ETa for nonstressed maize canopy. The purpose of the study was not to rank the models but rather to present empirical models predicting rc with different numbers of environmental variables and evaluate their performances to better understand the impact of different environmental variables on rc. Our findings could aid in the selection of a suitable model based on the availability and quality of the input data to predict rc for one-step application of the PM model to estimate ETa.