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Department of Land Resource Science, Univ. of Guelph, Guelph, ON, Canada N1G 2W1
* Corresponding author (jwarland{at}uoguelph.ca)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHE PENMAN-MONTEITH EQUATIONNUMERICAL SIMULATIONSRESULTS AND DISCUSSIONSUMMARYCONCLUSIONSREFERENCES |
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Abbreviations: B&B, Ball and Berry model • D&M, Denmead and Millar model • ICM, ideal canopy model • P-M, Penman–Monteith equation
Department of Land Resource Science, Univ. of Guelph, Guelph, ON, Canada N1G 2W1
* Corresponding author (jwarland{at}uoguelph.ca)
Received for publication November 25, 2006.
A multi-layer model, combining Lagrangian dispersion at the canopy level with Ohm's Law analogy at the leaf level, was used in numerical simulations to assess the leaf-to-canopy scale translation of surface resistances. The model produced unique profiles of fluxes and scalar concentrations that satisfied both the dispersion and leaf models. Environmental factors and canopy architecture were varied, and stomatal conductance was simulated using either a simple relationship with net radiation or the Ball and Berry model to account for feedback mechanisms. Results showed that, when the assumptions of the Penman–Monteith equation were met, scaled-up leaf conductance closely matched the bulk canopy conductance. However, as the scenarios modeled departed from the ideal conditions of Penman–Monteith, the agreement decreased. In particular, correct estimation of the aerodynamic resistance, through correct parameterization of the roughness length for sensible heat, was identified as a key issue.
Abbreviations: B&B, Ball and Berry model • D&M, Denmead and Millar model • ICM, ideal canopy model • P-M, Penman–Monteith equation
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHE PENMAN-MONTEITH EQUATIONNUMERICAL SIMULATIONSRESULTS AND DISCUSSIONSUMMARYCONCLUSIONSREFERENCES |
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In the original formulation of the combination equation (Monteith, 1965), it was assumed that the bulk canopy resistance (rc) was primarily dependent on stomatal resistance. Later on, however, Monteith (1981) recognized that "it is not evident a priori whether rc can be regarded as a physiological resistance depending mainly on stomatal components or whether it contains a significant aerodynamic element"; at the same time, he cited a number of theoretical and experimental studies whose results supported the physiological significance of the bulk canopy resistance. The appeal of a strong physiological component in the bulk canopy resistance is that it justifies the leaf-to-canopy scale translation of resistances or, more precisely, of conductances. The scaled-up stomatal resistance is thus defined by Rtot = 
–1, where h is canopy height, gst is stomatal conductance, and 
is the leaf area density. If rc is purely physiological, then rc = Rtot.
The validity of scaling-up from stomatal to canopy resistance has not always been supported by empirical studies. Rochette et al. (1991) measured leaf conductance within a maize canopy and concluded that none of the scaling-up methods they tried were appropriate to estimate the bulk canopy resistance calculated as a residual term in the Penman–Monteith equation (rres). This paper distinguishes between empirical estimates of canopy resistance (rres) calculated assuming the other terms in Penman–Monteith contain no systematic errors and the "true" canopy resistance (rc), which may or may not be purely physiological. In a careful examination of the problem, Raupach (1995) analytically compared different model canopies and concluded that, for typical dry canopies, rres was close to the inverse of the parallel sum of leaf conductances and is, therefore, approximately a physiological parameter of the system. On the other hand, Alves et al. (1998) stated that "the bulk surface [canopy] resistance of dense crops cannot be obtained by simple averaging of stomatal conductances because the driving force [profile of saturation deficit] is not kept constant within the canopy."
Different approaches have been used to address the problem of scaling-up from leaf to canopy: direct measurements of leaf stomatal resistance at different levels in the canopy (Rochette et al., 1991), analysis of the behavior of (observed) rres (Alves et al., 1998), analytical integration of a multi-layer canopy model to a single-layer model (Shuttleworth, 1976; Raupach, 1995), and simulation of evapotranspiration with a multi-layer canopy where the modeled leaf stomatal resistances were compared to the residual term rres (Raupach and Finnigan, 1988; Paw U and Meyers, 1989). An underlying assumption in these approaches has been that the Penman–Monteith equation can adequately describe the scenarios under consideration, which may not always be the case. When the Penman–Monteith equation is used to describe situations that depart markedly from the ideal situation for which it was derived (e.g., full canopy cover, aerodynamic resistance for heat and vapor equal, etc.), the physiological significance of the empirical canopy resistance, rres, is expected to be compromised.
It is practically impossible to measure with certainty all the relevant terms under field conditions to empirically analyze the scaling-up problem. Use of a numerical ideal canopy model (ICM), which can simulate both leaf behavior and canopy turbulent dispersion, could provide insight into the circumstances when rres 
Rtot, if the ICM also correctly simulates rres = Rtot when the assumptions of Penman–Monteith are strictly met. In the work reported here, an ICM was developed to study the role of in-canopy turbulent dispersion on the scaling-up issue. The model simulates leaf-level function in the canopy layers where stomatal resistance is simulated by either the simple Denmead and Millar (1976) formulation or the more sophisticated Ball and Berry model (Ball et al., 1987). Dispersion in the ICM was simulated using the Lagrangian dispersion analysis of Warland and Thurtell (2000), which describes the relationship between the source strength of scalar in each canopy layer and the resultant concentration profile. This study asks two questions: (i) does P-M describe the behavior of an ideal multi-layer canopy wherein leaf functioning is determined by a physiological model and transport is governed by Lagrangian dispersion? (ii) If so, under what circumstances does P-M fail to reproduce the ICM? Though it is possible that this model may fail for different reasons than empirical measurements, the results will nonetheless provide insight into the problem and a guide for future field work.
This study develops an ICM to investigate the relationship between rres and Rtot as conditions deviate from the ideal assumptions of Penman–Montieth. The study is heuristic in nature; the ICM is not intended to quantitatively reproduce the ‘true’ behavior of the system, however, in so far as its output is logical and qualitatively consistent with observed canopy behavior, it can provide insight into how violations of the underlying assumptions lead to discrepancies between rres and Rtot.
In the following sections, we first review the Penman–Monteith equation and the various resistances used in the analysis. Second, we present the ICM used in the study and discuss the model outputs. The final sections discuss the use of the ICM in a variety of ways to diagnose the scaling-up problem.
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THE PENMAN–MONTEITH EQUATION |
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TOPABSTRACTINTRODUCTIONTHE PENMAN-MONTEITH EQUATIONNUMERICAL SIMULATIONSRESULTS AND DISCUSSIONSUMMARYCONCLUSIONSREFERENCES |
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Etot) states:
 | [1] |
is the slope of the saturation vapor pressure against temperature, 
is the psychrometric coefficient, 
a is air density, cp is the specific heat of air at constant pressure, Atot is the total energy available to the system (net radiation less soil heat flux), ra is the aerodynamic resistance between the source height and the reference height, and D is the vapor pressure deficit at reference height. Note that, because P-M is a "big-leaf" model and does not differentiate between canopy and soil components, the evapotranspiration and available energy are explicitly stated as totals for the surface (i.e., including both canopy and soil). Several issues with the application of P-M can be identified. First, the essential assumption in P-M is that sources of sensible and latent heat have the same temperature (Monteith, 1981). Therefore, any situation where the source-sink temperatures for sensible and latent heat are different should not be expected to be properly described by this equation. Thom (1975) is more precise when he states that rc can be an accurate measure of the bulk stomatal resistance of a particular plant community only insofar as the aerodynamic values of vapor pressure and canopy temperature provide good estimates of the actual mean conditions on the surfaces of the transpiring elements. Strict application of this assumption requires that the vertical profile of the Bowen ratio is constant, since otherwise the mean source heights for water vapor and sensible heat will be different, and therefore at different temperatures.
Another significant issue is that the bulk aerodynamic resistance, ra, must be correctly estimated. As an example of the difficulties inherent in this task, Paw U and Meyers (1989) showed, through numerical experiments, that the displacement heights for water vapor flux and heat flux were affected by changes in stomatal resistances. This result suggests that ra may not be a strictly aerodynamic parameter, but depend in part on stomatal functioning.
Finally, as the canopy cover decreases, the meaning of rc becomes increasingly unclear since the soil begins to have a greater role within the system. On the one hand, the big-leaf approach of P-M does not distinguish between soil and canopy; on the other hand, when studying the relationship between canopy and leaf resistances, it does not seem justifiable to include the soil contribution to the canopy energy budget. The analysis below examines a full canopy (leaf area index = 4) to minimize this issue; further, only the energy available to the canopy and the canopy transpiration are included in the calculation of rres from the P-M equation.
Resistance Calculations for the Scaling-Up Analysis
An Expression for the Residual Resistance
The following rearrangement of the Penman–Monteith equation was used to calculate the bulk canopy resistance as a residual:
 | [2] |
Ec) is considered to avoid the confounding influence of the soil.
When the first term on the right-hand-side of Eq. [2] is close to zero, the magnitude of rres becomes independent of the value of the bulk aerodynamic resistance. This condition occurs when:
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Scaled-Up Stomatal Resistance
The total (scaled-up) canopy resistance from the ICM is given by the inverse of the parallel sum of leaf conductances:
 | [4] |
i is the leaf area for layer i, and n is the number of layers into which the canopy has been divided.
Estimation of the Bulk Aerodynamic Resistance
The following relationships are assumed in the estimation of the bulk aerodynamic resistance:
 | [5] |
 | [6] |
The bulk aerodynamic resistance is defined by:
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Because ra, and therefore rres, can be computed using either parameterization of z0H, this paper will distinguish rresM for z0H = z0M and as rresH for z0H = 0.2z0M. When the distinction is not relevant to the discussion, the subscript will not be used.
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NUMERICAL SIMULATIONS |
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TOPABSTRACTINTRODUCTIONTHE PENMAN-MONTEITH EQUATIONNUMERICAL SIMULATIONSRESULTS AND DISCUSSIONSUMMARYCONCLUSIONSREFERENCES |
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The Ideal Canopy Model
The model iteratively solves for flux and concentration profiles of water vapor and temperature (sensible heat), which simultaneously satisfy Ohm's Law analogy at the leaf-level and turbulent dispersion through the canopy. A Lagrangian dispersion model relates concentration and source profiles; these in turn must satisfy the leaf-level model. The iteration procedure finds values of foliar and air temperature and humidity, which satisfy both leaf and canopy models. The gradients of temperature and humidity between the leaf and the air must produce fluxes from Ohm's Law analogy, which, when used in the dispersion equation, produce identical air temperature and humidity profiles. The dispersion matrix couples the model layers and guarantees a unique solution because, for a given set of turbulence conditions, there is one unique concentration profile for a given source profile (Warland and Thurtell, 2000).
The Lagrangian Dispersion Matrix
The dispersion matrix, described in detail in Warland and Thurtell (2000), relates source and concentration profiles of any scalar within and above the canopy. It allows the calculation of the profile of concentration gradients of some scalar (e.g., temperature) that corresponds to a given spatial distribution of the respective source-sink (e.g., sensible heat flux profile) since the concentration gradient in each layer is defined by the sum of the gradients created by each source layer. Mathematically:
 | [8] |
i is the resultant profile of concentration gradients for the scalar under consideration. Translating the profile of concentration gradients into a profile of scalar concentrations only requires that the scalar concentration at one point in the system be known (e.g., temperature at reference height).
The dispersion matrix, Mij, is derived from Lagrangian dispersion theory (Taylor, 1921; Raupach, 1987). According to this theory, from the initial time when the particles are "marked" the particle cloud initially disperses in a linear fashion and at large travel times the cloud becomes diffusive; these are the near-field and far-field regimes, respectively. The average time over which a particle's motion remains correlated with its previous movements is the Lagrangian time scale (
L). The profiles of the turbulence statistics L and 
w (standard deviation of the vertical wind speed), within and immediately above the canopy are the only inputs needed to define Mij. In the present study, empirical equations, following van den Hurk and McNaughton (1995), were used to simulate these profiles as
 | [9] |
 | [10] |
The Canopy Model
For the model runs discussed here, the canopy and the air above it were each divided into 20 layers, with vertical leaf distribution being described by a beta function, following van den Hurk and McNaughton (1995). A simple exponential decay function was used to simulate both net radiation and irradiance within the canopy and no distinction was made between shaded and sunlit leaves. Separating sunlit and shaded leaves improves the simulation of plant C uptake; however, the purpose of the ICM was not to quantitatively simulate canopy photosynthesis. The use of the Ball-Berry model (discussed below) provided feedback between the environment and stomatal functioning, testing a possible role of dispersion in inducing feedback. The leaf boundary layer resistance was proportional to the square root of the ratio between leaf width (0.02 m) and wind speed in the layer (Jones, 1983). The height dependence of wind speed within the foliage was described by an exponential function (de Cionco, 1972) and a constant attenuation coefficient was assumed; effects of canopy architecture or leaf area index on this decay function (Meyers et al., 1998) were not included. The partitioning of the net radiation at the soil surface was imposed, with soil latent and sensible heat fluxes as boundary conditions to the canopy lowest layer, and soil heat flux G as a constant fraction (0.40) of the net radiation at the soil surface (Choudhury et al., 1987). These choices were made to enable clear focus on the issue of an aerodynamic component to rc. These choices are roughly equivalent to having the model simulate a very generic canopy rather than a particular crop or ecosystem.
The leaf stomatal conductance was modeled in two ways. The first approach used the relationship by Denmead and Millar (1976) for wheat:
 | [11] |
The other approach used the Ball and Berry model (Ball et al. (1987), as described in Collatz et al., 1991), referred to hereafter as B&B. This model allowed us to explore more deeply if feedback between leaf and canopy scales had some impact on the relationship between rres and the leaf stomatal resistance. The B&B model uses the following empirical relationship to express the stomatal conductance:
 | [12] |
The use of the B&B model necessitated the addition of a leaf assimilation model for the simulation of An. In this context, not only does An contribute to determine the value of the stomatal conductance via Eq. [12] but also depends on it, since one of the factors that contributes to determine the net assimilation rate (An) is the CO2 mole fraction at the site of fixation (ci), which, in turn, depends on the magnitude of the stomatal conductance (using Ohm's analogy). This interrelationship between An and gsw is of importance for the iteration procedure explained below.
The leaf assimilation model used to simulate An was based on the model proposed by Collatz et al. (1991) for C3 leaves. This model describes leaf CO2 assimilation as the minimum of three limiting rates: (i) rate limited by the efficiency of the photosynthetic enzyme system (Rubisco), (ii) rate limited by electron transport, and (iii) rate limited by the capacity of the leaf to export or utilize the products of photosynthesis. This type of approach is based on the biochemical model of leaf photosynthesis presented by Farquhar et al. (1980). Models of leaf CO2 assimilation similar to the one proposed by Collatz et al. (1991) have been used in a number of studies (Harley and Tenhunen, 1991; Sellers et al., 1996; de Pury and Farquhar, 1997; Grossman-Clarke et al., 2001), showing some diversity in the algorithms that describe the rate-limited processes, the number and type of processes assumed to limit photosynthesis, parameterization, and temperature effects included in the model. For the leaf assimilation model used in this study, not all algorithms came from Collatz et al. (1991); the electron-transport limited rate of photosynthesis followed de Pury and Farquhar (1997), as did the description of temperature effects on the CO2 compensation point and on the potential rate of electron transport.
Some of the shortcomings of Eq. [12] include breakdown at very low light, humidity, and CO2 levels (Anderson et al., 2000). In the present study, preliminary simulations using the B&B model and the original Collatz et al. (1991) model produced implausible results that seemed to be related to the presence of large (simulated) temperatures within the canopy. Since some of the simulation scenarios included high temperature above the canopy, the above-mentioned modifications to the original Collatz et al. model were aimed at allowing plausible stomatal functioning at higher temperatures. In any event, the accurate simulation of leaf photosynthesis was not strictly relevant to the purpose of this study so long as the modeled stomatal functioning was comparable to a generic crop.
When the numerical simulation included the B&B model, soil respiration became a boundary condition to the canopy's lowest layer. A constant rate of soil respiration of 0.03 mg CO2 m–2 s–1 (da Costa et al., 1986) was assumed and temperature effects on this rate were not considered.
Iterative Procedure
When running the model, the final profiles of latent (E) and sensible (H) heat fluxes within the canopy had to match two conditions: first, within each layer, fluxes between leaves and the air should be describable by the Ohm's Law analogy; second, the concentration profiles of temperature and water vapor within the canopy air should be defined by the flux profiles (i.e., source/sink strengths) through the dispersion matrix. To accomplish this agreement, an initial partition of net radiation into E and H profiles was imposed which, in turn, originated profiles of scalars within the canopy air (via the dispersion matrix). Since leaf stomatal and boundary-layer resistances were given, the Ohm's Law analogy was used in each layer to make two foliage temperature estimates, one from H, designated TfH, and another from E, designated TfE. If these temperatures did not coincide, the first condition was not matched and a "next foliar temperature" (and its saturation vapor value) was estimated, for each layer, based on the difference between TfH and TfE, so that new profiles of E and H could be calculated for the next iteration, again with Ohm's law. In the next iteration, the dispersion matrix was used again and new profiles of TfH and TfE were determined. With each iteration, the difference between TfH and TfE became smaller until they coincided, meaning that the two conditions mentioned above had been met. In practice, iteration proceeded until the maximum difference between TfH and TfE was <10–12°C.
The expressions used to calculate TfH and the saturation vapor pressure at TfE, designated eTfE*, in each canopy layer, were
 | [13] |
 | [14] |
E' are sensible and latent heat flux for the canopy layer respectively, rbz is the leaf boundary layer resistance, T(z) is the air temperature at the layer level, ea is the vapor pressure of the air at the layer level, (z) is the leaf area index for the layer, and gst is leaf conductance. The value TfE was found by inverting Tetens’ equation.
When the B&B model was used, the calculation of net CO2 uptake (An) was performed immediately after calculating latent and sensible heat fluxes. The "leaf temperature" required by the An subroutine was then taken as the middle value between TfH and TfE. An initial guess for stomatal conductance was needed to simulate the profile of TfE in the first iteration. In the first iteration, an initial profile of An was imposed by assuming an initial guess value for the CO2 concentration at the site of fixation (ci). This initial profile determined the concentration profile of CO2 within the canopy air (ca) via the dispersion matrix. The values of CO2 concentration and relative humidity at the leaf surface (cs and hs) needed in the B&B model were obtained, via Ohm's analogy, using outputs from both the An and E subroutines. Stomatal conductance were estimated through the B&B model as well as the resultant ci through Ohm's analogy. These values of stomatal conductance and ci were the ones used in the next iteration for the calculation of new TfE and An profiles. Hypothetically, the final profile of An should be the one capable of providing the profiles of stomatal conductance (via the B&B model) and ca (via the dispersion matrix), which will determine a profile of ci (via Ohm's analogy) defining the same final profile of An (via the leaf assimilation model). The model used in the present study was able to obtain this final profile of An with one reservation explained below.
The use of the B&B model was not appropriate when An 
0 (Collatz et al., 1991). Moreover, simulated An was negative for some layers in the canopy when the estimated rate of gross CO2 uptake (Ag) was not larger than the estimated rate of "day respiration" (Rd) since An = Ag – Rd, completely precluding the use of the B&B model in these layers since negative values of stomatal conductance could then be obtained. This scenario of unrealistic estimates of stomatal conductance was overcome, in the present study, by imposing a lower limit to the stomatal conductance. In these particular cases, stomatal conductances were not determined by the value of An via the B&B model but by an imposed lower limit. An upper limit to stomatal conductance was also imposed to avoid numerical instability. The lower and upper limits used were 0.5 and 50 mm s–1, respectively. Steady-state conditions are assumed in all simulations presented below.
Scenarios for Analysis
To examine the scaling-up problem, runs of the multi-layer model were performed for a set of scenarios representing a range of environmental conditions. These scenarios were defined by systematically varying the follow variables:
Es): soil evaporation was either 0% (dry soil) or 80% (wet soil) of the energy available at the soil surface (Rns – G). The soil heat flux (G) was assumed to be 40% of the net radiation reaching the soil (Rns) for all scenarios. 
xp–1(1 – x)q–1, where ß(p,q) = 
01tp–1(1 – t)q–1dt), were used in this study:All runs presented here used u* = 0.4 m s–1. Preliminary runs, not shown here, indicated that the imposed u* had negligible impact on the results. Net radiation (Rn) and solar irradiance (I0) at the top of the canopy: all runs presented here used Rn = 700 W m–2 and I0 = 2000 µmol m–2 s–1.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHE PENMAN-MONTEITH EQUATIONNUMERICAL SIMULATIONSRESULTS AND DISCUSSIONSUMMARYCONCLUSIONSREFERENCES |
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For all scenarios, the model behaved well during the iteration procedure, converging uniformly toward a solution with less than 40 iterations. In this simulation study, no attempt was made to compare obtained profiles with experimental observations; however, every run of the model resulted in physically plausible final profiles of fluxes and scalar concentrations. Figure 1 shows the final profiles of sensible and latent heat within the canopy, air temperature and foliar temperature, and vapor pressure obtained for one particular scenario. Note that the lowest point in the flux profiles includes the soil surface flux.
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The Effect of Canopy Architecture
The agreement between the residual resistance and the total canopy resistance depended on the choice of z0M or z0H and the leaf area distribution. Though it was suggested above that this is due to the need to correctly estimate ra, another possible explanation is that the canopy architecture, defined by the leaf area density profile, has a direct effect on the relationship between rres and Rtot, which is independent of any indirect effect it may have on the estimation of the bulk aerodynamic resistance. To test this explanation, the model was run in scenarios where the air temperature was fixed at either 35°C or 15°C and the relative humidity was guessed, in each run, until the canopy transpiration provided by the multi-layer model was very close to equilibrium evaporation, making the value of rres independent of the bulk aerodynamic resistance; this was done for two cases: Es = 0 and Es = 0.8[Rns – G]. Results from these runs are summarized in Table 2
, which shows that when Es= 80% of Rns – G, rres = Rtot irrespective of the leaf area density profile, whereas when Es = 0, rres/Rtot varied between 0.86 and 0.96 depending on T and the leaf area density profile. Canopy architecture had little effect on rres/Rtot, except for a small discrepancy when the soil was dry and the leaf area densest in the lower canopy.
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Congruent Source Profiles
Central to the derivation of P-M is the assumption that the sources of sensible and latent heat have the same temperature (Monteith, 1981). To strictly meet this assumption requires that the profiles of sensible and latent heat fluxes be congruent, that is, constant Bowen ratio throughout the canopy layers. When this condition is not met, the meaning of a representative canopy temperature becomes dubious since it may be different for sensible and latent heat fluxes. In addition the canopy height of the hypothetical "big-leaf" surface would also not be coincident for sensible and latent heat fluxes.
In this section, we examine the relationship between rres and Rtot for an ideal canopy with congruent source profiles. To do so, profiles of canopy fluxes were imposed to maintain a constant Bowen ratio; the same Bowen ratio was also imposed at the soil surface. From these imposed source profiles, the dispersion matrix provided profiles of air temperature and humidity. From these, profiles of foliage temperature and saturation vapor pressure were calculated, allowing for the profile of gst to be computed as an output by rearranging Eq. [14]. Using the profile of gst, and the assumption that rc = Rtot, values of ra were computed as a residual from P-M.
This procedure was done once for one scenario for each architecture, giving three ra values, shown in Table 4 . Also shown in Table 4 are the model output Rtot and rres/Rtot for several scenarios using these ra values. Under these conditions, excellent agreement between rres and Rtot was obtained. Further, when these ra values were used in the model runs shown in Table 1 (noncongruent source profiles), rres/Rtot varied between 0.96 and 1.04 for p;q = 4;2 and 0.88 to 1.11 for p;q = 2;4. This shows that, in the ICM, ra is only a function of canopy architecture, as it should be, and that correct determination of this parameter essentially eliminates any difficulty in scaling-up from gst to Rtot with only minor disagreement due to the violation of the congruent source profile assumption. This result further emphasizes the importance of correctly estimating z0H (and therefore ra) in applying P-M, and shows that both parameterizations used in this study are limited in applicability to certain specific conditions.
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SUMMARY |
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TOPABSTRACTINTRODUCTIONTHE PENMAN-MONTEITH EQUATIONNUMERICAL SIMULATIONSRESULTS AND DISCUSSIONSUMMARYCONCLUSIONSREFERENCES |
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Some caution is advisable, then, when large discrepancies between rres and Rtot are reported. It could be the case that the models involved in the estimation of these resistances (the Penman–Monteith equation for rres and some other model for the estimation of Rtot) are not able to adequately describe the scenarios under consideration, due to, for example, noncongruent source profiles. A practical inconsistency between rres and Rtot should not automatically imply that rc is not a strict physiological parameter. In some cases, it could also mean that either Rtot or the profile of leaf conductances is not being modeled or measured accurately. Moreover, it could be that the Penman–Monteith equation is being used for a scenario for which it is not appropriate, such as when the canopy is partly wet.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONTHE PENMAN-MONTEITH EQUATIONNUMERICAL SIMULATIONSRESULTS AND DISCUSSIONSUMMARYCONCLUSIONSREFERENCES |
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In the present study simulated values of rres and Rtot were generally close irrespective of the inclusion of feedback mechanisms when estimating leaf conductances. Moreover, hypothetical canopies with congruent source profiles always had rres = Rtot. The results suggest that there could be another explanation to the large discrepancies between rres and Rtot sometimes reported in the literature. To pursue this issue, a distinction has to be made between rres and rc. The bulk canopy resistance used in the P-M equation is the canopy resistance. The problem with this resistance is that it cannot be measured directly and independently; it can only be estimated by rearranging the P-M equation. It is then more properly termed the residual resistance.
The Penman–Monteith equation, as formulated in Eq. [1], implies that (i) fluxes between source-sink height and reference height have constant values, meaning that no flux convergence/divergence exists between these points; (ii) the energy available to the system equals the sum of sensible and latent heat fluxes; (iii) the aerodynamic resistance between these points is properly described by a bulk value ra; (iv) the same bulk aerodynamic resistance is valid for both sensible and latent heat, in other words raH = raV; (v) the aerodynamic temperature is a good estimate of the actual mean conditions on the surfaces of the transpiring elements; and (vi) the scenario under analysis corresponds to one of the intended cases for its use. Violation of any of these requirements in a specific situation would mean that the use of the Penman–Monteith equation is not appropriate or that not all the variables within the equation are being estimated or measured correctly. Only when all of these requirements are satisfied may one have confidence that rres is a good estimate of rc.
Failure to satisfy some of the requirements mentioned above, on the other hand, could cause a discrepancy between rres and Rtot that should not be interpreted as a weak physiological significance of the bulk canopy resistance since, in this case, the problem could rely on the discrepancy between rres and rc. The rres that is "measured" in practice is just a residual term so that its value is merely the one that forces some formulation of the Penman–Monteith equation to work in a specific situation. In this context, a large discrepancy between rres and Rtot could also be evidence of a situation departing markedly from the P-M model just described.
The results of this study support rc being a physiological parameter that integrates all stomatal resistances within the canopy, and ra being strictly aerodynamic. The correct estimation of ra, even if raH = raV holds for the situation under analysis, is particularly important since it contributes to the determination of the value of the aerodynamic temperature, surrogate for the actual mean temperature of the transpiring elements. The determination of z0H and the method used to correct for nonneutral atmospheric conditions are important factors in the estimation of ra; none of these procedures are without problems.
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TOPABSTRACTINTRODUCTIONTHE PENMAN-MONTEITH EQUATIONNUMERICAL SIMULATIONSRESULTS AND DISCUSSIONSUMMARYCONCLUSIONSREFERENCES |
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