Aerodynamic Resistance and Penman–Monteith Evapotranspiration over a Seasonally Two-Layered Canopy in Semiarid Central Australia

James Cleverly Plant Functional Biology and Climate Change Cluster, School of the Environment, and Australian Supersite Network and OzFlux, Terrestrial Ecosystem Research Network, University of Technology, Sydney, Broadway, New South Wales, Australia

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Chao Chen Plant Functional Biology and Climate Change Cluster, School of the Environment, University of Technology, Sydney, Broadway, New South Wales, Australia

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Nicolas Boulain Plant Functional Biology and Climate Change Cluster, School of the Environment, University of Technology, Sydney, Broadway, New South Wales, Australia

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Randol Villalobos-Vega Plant Functional Biology and Climate Change Cluster, School of the Environment, University of Technology, Sydney, Broadway, New South Wales, Australia

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Ralph Faux Plant Functional Biology and Climate Change Cluster, School of the Environment, University of Technology, Sydney, Broadway, New South Wales, Australia

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Nicole Grant Plant Functional Biology and Climate Change Cluster, School of the Environment, University of Technology, Sydney, Broadway, New South Wales, Australia

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Qiang Yu Plant Functional Biology and Climate Change Cluster, School of the Environment, University of Technology, Sydney, Broadway, New South Wales, Australia

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Derek Eamus Plant Functional Biology and Climate Change Cluster, School of the Environment, and Australian Supersite Network and OzFlux, Terrestrial Ecosystem Research Network, and National Centre for Groundwater Research and Training, University of Technology, Sydney, Broadway, New South Wales, Australia

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Abstract

Accurate prediction of evapotranspiration E depends upon representative characterization of meteorological conditions in the boundary layer. Drag and bulk transfer coefficient schemes for estimating aerodynamic resistance to vapor transfer were compared over a semiarid natural woodland ecosystem in central Australia. Aerodynamic resistance was overestimated from the drag coefficient, resulting in limited E at intermediate values of vapor pressure deficit. Large vertical humidity gradients were present during the summer, causing divergence between momentum and vapor transport within and above the canopy surface. Because of intermittency in growth of the summer-active, rain-dependent understory and physiological responses of the canopy, leaf resistance varied from less than 50 s m−1 to greater than 106 s m−1, in which the particularly large values were obtained from inversion of drag coefficient resistance. Soil moisture limitations further contributed to divergence between actual and reference E. Unsurprisingly, inclusion of site-specific meteorological (e.g., vertical humidity gradients) and hydrological (e.g., soil moisture content) information improved the accuracy of predicting E when applying Penman–Monteith analysis. These results apply regardless of canopy layering (i.e., even when the understory was not present) wherever atmospheric humidity gradients develop and are thus not restricted to two-layer canopies in semiarid regions.

Corresponding author address: James Cleverly, Plant Functional Biology and Climate Change Cluster, School of the Environment, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia. E-mail: james.cleverly@uts.edu.au

Abstract

Accurate prediction of evapotranspiration E depends upon representative characterization of meteorological conditions in the boundary layer. Drag and bulk transfer coefficient schemes for estimating aerodynamic resistance to vapor transfer were compared over a semiarid natural woodland ecosystem in central Australia. Aerodynamic resistance was overestimated from the drag coefficient, resulting in limited E at intermediate values of vapor pressure deficit. Large vertical humidity gradients were present during the summer, causing divergence between momentum and vapor transport within and above the canopy surface. Because of intermittency in growth of the summer-active, rain-dependent understory and physiological responses of the canopy, leaf resistance varied from less than 50 s m−1 to greater than 106 s m−1, in which the particularly large values were obtained from inversion of drag coefficient resistance. Soil moisture limitations further contributed to divergence between actual and reference E. Unsurprisingly, inclusion of site-specific meteorological (e.g., vertical humidity gradients) and hydrological (e.g., soil moisture content) information improved the accuracy of predicting E when applying Penman–Monteith analysis. These results apply regardless of canopy layering (i.e., even when the understory was not present) wherever atmospheric humidity gradients develop and are thus not restricted to two-layer canopies in semiarid regions.

Corresponding author address: James Cleverly, Plant Functional Biology and Climate Change Cluster, School of the Environment, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia. E-mail: james.cleverly@uts.edu.au

1. Introduction

One-fifth of the global land area is arid or semiarid, where water scarcity can limit productivity in agricultural and native vegetation. Except where groundwater is present, evapotranspiration E in arid regions is second only to precipitation P as the largest component of the hydrometeorological cycle (Sheffield et al. 2010); thus, accurate knowledge of E is required for managing water resources (Er-Raki et al. 2010; Tabari et al. 2012). Australia is the driest permanently inhabited continent on Earth, with over 70% of the land surface characterized as (semi) arid (Eamus and Froend 2006), where the seasonality of moisture limitations exerts strong control over vegetation characteristics and E (Hutley et al. 2005; O'Grady et al. 2009).

To provide a reference of E (E0), the Food and Agricultural Organization adopted standard parameterization of the Penman–Monteith (PM) model for a reference grass crop (FAO56; Allen et al. 1998). This mechanistic model incorporates plant physiological constraints (Monteith 1965) into Penman's original model that combines available energy QA with atmospheric constraints (Penman 1948). FAO56 remains the most feasible and widely adopted method for predicting E across the globe (Steduto et al. 2003). The importance of FAO56 as a tool in water resources management is unequalled because of its simplicity and intercomparability among various crop and ecosystem types (Lemeur and Zhang 1990).

With the growth of worldwide eddy covariance (EC) networks, FAO56's aerodynamic resistance and surface conductance GS terms can be evaluated by inverting the equation with measured values of actual E (Reichstein et al. 2002; Wohlfahrt et al. 2009). Numerous computational methods are used to estimate aerodynamic resistance to momentum flux ram as a function of the drag coefficient CD, either directly (i.e., from the friction coefficient u* in moderately unstable conditions; Isaac et al. 2004) or inferentially from the logarithmic profile of wind speed U above a surface (Allen et al. 1998; Brutsaert 1982). Likewise, aerodynamic resistance to vapor transfer r is determined either directly from surface-to-air gradients of specific humidity (i.e., the bulk transfer coefficient CE; Brutsaert 1982; Stull 1988) or inferentially from CD, in which case r and ram are equivalent. While direct assessment of r is preferred because of the unambiguous relationship between CE and r, measurements of vertical profiles in humidity are historically rare and r must be inferred from CD (Brutsaert 1982; Cleugh et al. 2004).

Errors in Penman–Monteith (PM) predictions have been observed at low to moderate values of D (Whitley et al. 2009). Thus, we hypothesized that these errors are the result of differences between r (from CE) and ram (from CD). This study compares r to ram by inverting the PM equation at an OzFlux EC site in semiarid, central Australia (Cleverly 2011). To clarify variable designations, the generic subscript x will represent m for momentum or υ for vapor (e.g., GSx represents GSm when derived from ram). Likewise, subscripts a and S refer to aerodynamic and surface, respectively.

2. Measurements and methods

a. Aerodynamic resistance to momentum and vapor transfer

Application of ram to vapor transport follows an inverse function of U and CD, which can be estimated from canopy structural characteristics (Allen et al. 1998; Stull 1988):
e1
where k is von Kármán's constant (0.41), zm (m) is the measurement height, zd (m) is the displacement height (⅔ of the canopy height zc), and z0m and z0υ (m) are the roughness lengths for momentum and vapor, respectively. The logarithmic profile that underpins ram is not applicable below the height zd; thus, ram was computed for a single layer representing the canopy surface.
Alternatively, aerodynamic resistance to vapor transport r was determined as a function of U and CE, which is determined as a function of U, kinematic vapor flux (), and the specific humidity (q; kg kg−1) gradient between the surface and air (qaq0) (Brutsaert 1982; Stull 1988):
e2
Equation (2) is directly analogous to Ohm's law. Using profile measurements of q, r was solved during each half hour across two atmospheric layers during one of three scenarios (Fig. 1): 1) when r across the base layer was zero or undefined (base short circuit), 2) when r across the top layer was zero or undefined (top short circuit), or 3) when r across both layers was defined (parallel circuit). Layer boundaries were set to zm, the effective canopy surface height (zsurface = zd + z0), and the soil surface (zsoil; Fig. 1). Measurement heights for the finite difference qaq0 were set, for example, to zm and zsurface in the top layer.
Fig. 1.
Fig. 1.

Conditional three-circuit, two-layer aerodynamic resistance model. See text for variable descriptions.

Citation: Journal of Hydrometeorology 14, 5; 10.1175/JHM-D-13-080.1

b. Meteorology and eddy covariance

E and were measured using the eddy covariance method as fully described for this site in Eamus et al. (2013). Flux measurements were made at a height of 11.7 m (zm) for vapor and momentum (CSAT3, Campbell Scientific Inc., Logan, Utah; LI7500, Li-Cor Biosciences, Lincoln, Nebraska) and 12.6 m for radiation (CNR1, Kipp & Zonen, Delft, Netherlands). Surface soil moisture was measured across the top 10-cm depth (CS616, Campbell Scientific) and in profiles to 1-m depth (CS605, Campbell Scientific; Cleverly et al. 2013). Soil porosity was 0.36 ± 0.005 m3 m−3 above the variable-depth hardpan (Cleverly et al. 2013). Additionally, temperature and humidity measurements were made at heights of 11.7 m (zm), 6.5 m (zc), 4.25 m (zd), and 2 m (HMP45C, Vaisala, Helsinki, Finland). Given the separation required to resolve differences between HMP45C measurements, q0 and qa were obtained within each layer by linearly extrapolating paired measurements of q with height. That is, q0 was extrapolated from the slope [(zmzc)/(qmqc)] in the top layer and from the slope [(zd − 2)/(qdq2)] in the base layer. All measurements were collected during the calendar year 2012 over a two-layer (canopy and soil plus intermittent understory) surface.

c. Penman–Monteith: Surface and canopy conductance

The PM equation was inverted to compare GSm to G. In both cases, GSx includes conductance from soil, understory, and canopy surfaces (Brutsaert 1982). Inversion of the PM equation was computed as
e3
where QA is the difference between net radiation flux and ground heat flux, ρa is the density of moist air, cP is the heat capacity of moist air, D is the vapor pressure deficit, Δ is the slope of the saturation vapor pressure curve against temperature, and γ is the psychrometric coefficient. For comparison to physiological measures of conductance (G), units were converted as G (mmol m−2 s−1) = ρa (g m−3) G (m s−1)/0.018 (g mmol−1).
Additionally, FAO56 was applied using rax to estimate E0x (Allen et al. 1998; Jensen et al. 1990):
e4
Canopy conductance (GC) was estimated in place of GS as a function of leaf resistance (rL) and leaf area index (LAI): GC−1 = rL/(0.5 LAI), in which rL (100 s m−1) is the leaf resistance of a well-illuminated grass crop (Allen et al. 1998; Jensen et al. 1990). E0m is equal to FAO56 for this site's canopy characteristics (i.e., zm, zd, z0). LAI was interpolated to daily values by applying a spline function to the Moderate Resolution Imaging Spectroradiometer (MODIS) LAI product (Cleverly et al. 2013). Mulga ecosystem rL was determined by inverting the LAI relationship: rLx = GSx−1 (0.5 LAI). Additional limitations of soil moisture (below air dry) and small D on evaporation (Choudhury and Monteith 1988) and large D on stomatal function (Ball et al. 1987; Leuning 1995) were included in the calculation of E0 by using the Water, Atmosphere, Vegetation, Energy and Solutes (WAVES) model, which is a soil–vegetation–atmosphere transfer scheme that employs PM and maintains balance in model complexity among carbon, energy, and water processes (McCallum et al. 2010; Zhang and Dawes 1998).

3. Results

Surface soil moisture content had a strong influence over atmospheric moisture gradients across each layer (Figs. 2a–c). Short circuits (i.e., qaq0 > 0) were restricted to periods when soil moisture content was low: <0.2 m3 m−3 for the top layer (Fig. 2a), <0.05 m3 m−3 in the base layer (Fig. 2b), and <0.12 m3 m−3 across the full layer (Fig. 2c). Atmospheric humidity gradients were larger and more consistently negative (i.e., qa < q0) in the base layer than across the top and full layers (Fig. 2). The largest gradients in the top and base layers were observed in late spring (5 November) and early summer (22 December), respectively (Fig. 2d), which represent the start of the growing season in the canopy and understory, respectively (Cleverly et al. 2013; Eamus et al. 2013; Ma et al. 2013).

Fig. 2.
Fig. 2.

Specific humidity q profiles through the canopy and atmosphere, scaled by atmospheric layer thickness Δz. Subscripts represent measurement height. (a)–(c) The difference between q measured at two heights (subscripts: m, measurement; c, canopy; 2, 2 m). (d) Atmospheric q profile (± standard error) during the period of maximal gradients in the top layer (2100–2300 LST 22 Dec 2012; squares and broken line) and in the base layer (0130–0400 LST 5 Nov 2012; circles and solid line).

Citation: Journal of Hydrometeorology 14, 5; 10.1175/JHM-D-13-080.1

Figure 3 shows the comparison of GSm and G. Most values were smaller than 15 mmol m−2 s−1 (Figs. 3a,c). The slope between GSm and G was smaller than 1:1, indicating that values of GSm tended to be smaller than G (Figs. 3a–c). Notable exceptions in which GSm > G occurred at intermediate values of G (Figs. 3a,c). Likewise, when integrated over a day, GSm exceeded G at low values, which was more pronounced in the top layer alone than when the complete model (Fig. 1) was used for computing G (Fig. 3b). When scaled to the same units as GSx, aerodynamic conductance to momentum Gam was much smaller than G and only marginally larger than GSm (Fig. 3d).

Fig. 3.
Fig. 3.

Comparison of CD-based (GSm and Gam) and CE-based (G and G) conductances. Comparison of surface conductances G vs GSm at (a),(c) 30-min and (b) daily time scales. Dashed line shows 1:1 line. In (b), complete (squares and solid line) and top layer (circles and broken line) are shown. In (c), top layer (filled squares and solid line), full layer (open squares and broken line), and base layer (circles and dash–dotted line) are shown. (d) Aerodynamic conductance to vapor transfer G vs momentum transfer Gam.

Citation: Journal of Hydrometeorology 14, 5; 10.1175/JHM-D-13-080.1

Maximal values of G and GSm declined exponentially in response to increasing D (Fig. 4a). At small (<0.5 kPa) and large (>4 kPa) values of D, G, and GSm were similar (Fig. 4a). However, at intermediate values of D, maximal values of GSm were smaller than maximal values of G (Fig. 4a). In the top layer, G was large and restricted to low and intermediate values of D (<4 kPa; Fig. 4b). In contrast, in the base layer, which is solvable only during the top-layer short circuit, G was generally smaller than 5 mmol m−2 s−1 and was restricted to intermediate and large values of D (>0.5 kPa; Fig. 4b).

Fig. 4.
Fig. 4.

G or GSm as a function of vapor pressure deficit D. (a) Complete model G (squares) and GSm (circles). (b) Top (squares) and base (circles) layers. The inset is the same as in (b) but with top layer superimposed over base layer.

Citation: Journal of Hydrometeorology 14, 5; 10.1175/JHM-D-13-080.1

Figure 5 illustrates daily totals of P, E, G, and GSm along with average air temperature (Ta) and D. Winter (June–August) was particularly dry; thus, E and resultant conductances were negligible (Fig. 5). The D in the winter was often small (minimal daily average 0.6 kPa) because of low temperature. Rainfall events resulted in further reductions in D (minimal daily average 0.3 kPa) during any season and at any temperature (Fig. 5b). During periods when E was large, G was larger in the top layer than in the full layer (Fig. 5c). The G from the base layer was small but prominent in the early autumn (March; Fig. 5c). The complete model showed a stronger conductance response following rainfall than the top layer alone (Fig. 5d); GSm followed the same general pattern as G, but with smaller values (Fig. 5d).

Fig. 5.
Fig. 5.

Daily patterns of (a) P and air temperature at a height of 2 m (Ta), (b) E and D, (c) G, and (d) G and GSm.

Citation: Journal of Hydrometeorology 14, 5; 10.1175/JHM-D-13-080.1

In general, r and rLm were in close agreement except during late summer (Fig. 6a). Consequently, E0υ and E0m followed similar patterns (Fig. 6b). A phase shift was observed between EC-based actual E (Ea) and all formulations of E0 such that peaks in Ea preceded peaks in E0 by approximately 2–8 days (Fig. 6b). Divergence between E0υ and E0m occurred during the dry period of the late summer when Ta and D were large (cf. Figs. 5 and 6). Application of WAVES E0 resulted in an improved fit to Ea (Fig. 6b), especially during the early autumn (Fig. 6b). During summer (e.g., mid-January to mid-February), discrepancy remained between Ea and WAVES but was of smaller magnitude than the difference between Ea and E0x (Fig. 6b).

Fig. 6.
Fig. 6.

Daily patterns of leaf resistance rL and E. (a) The rL determined from surface resistance inverted with r (r, solid line) or ram (rLm, dashed line). Grass reference rL shown as a horizontal broken line at 100 s m−1. (b) Actual E from EC measurements (broken line) and E0 parameterized with r (E0υ, dashed line), ram (E0m, solid line), or from the output of the WAVES model (dash–dotted line).

Citation: Journal of Hydrometeorology 14, 5; 10.1175/JHM-D-13-080.1

4. Discussion

The estimation of ram as a function of the CD leads to overprediction of GSm at small values of E and to underprediction of GSm at large values of E (Figs. 3b and 5b,d,e). Steduto et al. (2003) similarly observed overprediction of E0 by FAO56 at low values of E0 and underprediction at high values. These patterns of over- and underprediction were observed during the summer when atmospheric gradients in specific humidity q were large (cf. Figs. 2 and 6b), which was the time of year when ram was expected to underpredict r. Surface conductance computed from r (G) was much smaller than aerodynamic conductance of vapor G (Fig. 3) and consequently reduced the influence of errors in estimation of G on the determination of G and E0 (Fig. 3).

To accurately fit E0 to prevailing conditions, a large amount of meteorological data is required (Dehbozorgi and Sepaskhah 2012; Tian and Martinez 2012). Failure to account for the influence of atmospheric gradients in q by CD resulted in underestimation of GSm at small to moderate values of vapor pressure deficit (0.5 kPa < D < 3.5 kPa; Fig. 4a). This underestimation occurred because ram was too large relative to r, thus reducing the strength of the aerodynamic term ρacP [Eqs. (3) and (4)]. Because E is sensitive to small variations in GSm regardless of the CD formulation that is used (Shahrokhnia and Sepaskhah 2012), measurement of atmospheric humidity profiles improved PM estimates of E0 by more closely matching the true site-specific aerodynamic resistance (cf. Figs. 2, 5, and 6).

Leaf-level stomatal resistance rL was variable and much larger than for the grass reference (i.e., 100 s m−1, Fig. 6a). A constant rL accounts for neither nonphysiological (Steduto et al. 2003) nor physiological contributions to canopy conductance GC in vegetation that demonstrates large physiological responses to precipitation. The Mulga plants under investigation here are a good example of vegetation that experiences only partial stomatal closure at low water potential (<−5 MPa) and large D (O'Grady et al. 2009). Natural ecosystems are characterized by complex soil and atmospheric moisture gradients that change with soil moisture, growth responses in understory vegetation, and stress responses in the upper canopy (Cleverly et al. 2013).

Mismatch between Ea and E0 occurred because of 1) the delay between precipitation and vegetation greening, 2) unaccounted soil moisture limitations on rL, and 3) seasonal divergence between r and ram. The lag of E0 behind Ea following precipitation was the result of 1) the dependence of E0 on LAI and 2) heterogeneously rapid drying of the soil surface, which leads to underestimation of E0 by WAVES (cf. Fig. 6 and Cleverly et al. 2013). Thus, E0 failed to capture the initial pulse of evaporation, which can be particularly important in semiarid areas with intermittent rainfall (Cleverly et al. 2013; Eamus et al. 2013). Application of WAVES improved the fit between E0 and Ea, especially during seasons when E0υ and E0m were equivalent (Fig. 6). Altogether, accurate prediction of E0 was dependent upon 1) characterization of r that was responsive to atmospheric humidity profiles and 2) identification of leaf physiological and soil moisture (Choi et al. 2012) limitations on E that are not modeled by PM.

Acknowledgments

This work was supported by grants from the Australian Government's Terrestrial Ecosystems Research Network (TERN; www.tern.org.au) and the National Centre for Groundwater Research and Training (NCGRT).

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  • Zhang, L., and Dawes W. , Eds., 1998: WAVES: An integrated energy and water balance model. CSIRO Land and Water Tech. Rep. 31/98, 218 pp. [Available online at http://www.clw.csiro.au/products/waves/.]

  • Fig. 1.

    Conditional three-circuit, two-layer aerodynamic resistance model. See text for variable descriptions.

  • Fig. 2.

    Specific humidity q profiles through the canopy and atmosphere, scaled by atmospheric layer thickness Δz. Subscripts represent measurement height. (a)–(c) The difference between q measured at two heights (subscripts: m, measurement; c, canopy; 2, 2 m). (d) Atmospheric q profile (± standard error) during the period of maximal gradients in the top layer (2100–2300 LST 22 Dec 2012; squares and broken line) and in the base layer (0130–0400 LST 5 Nov 2012; circles and solid line).

  • Fig. 3.

    Comparison of CD-based (GSm and Gam) and CE-based (G and G) conductances. Comparison of surface conductances G vs GSm at (a),(c) 30-min and (b) daily time scales. Dashed line shows 1:1 line. In (b), complete (squares and solid line) and top layer (circles and broken line) are shown. In (c), top layer (filled squares and solid line), full layer (open squares and broken line), and base layer (circles and dash–dotted line) are shown. (d) Aerodynamic conductance to vapor transfer G vs momentum transfer Gam.

  • Fig. 4.

    G or GSm as a function of vapor pressure deficit D. (a) Complete model G (squares) and GSm (circles). (b) Top (squares) and base (circles) layers. The inset is the same as in (b) but with top layer superimposed over base layer.

  • Fig. 5.

    Daily patterns of (a) P and air temperature at a height of 2 m (Ta), (b) E and D, (c) G, and (d) G and GSm.

  • Fig. 6.

    Daily patterns of leaf resistance rL and E. (a) The rL determined from surface resistance inverted with r (r, solid line) or ram (rLm, dashed line). Grass reference rL shown as a horizontal broken line at 100 s m−1. (b) Actual E from EC measurements (broken line) and E0 parameterized with r (E0υ, dashed line), ram (E0m, solid line), or from the output of the WAVES model (dash–dotted line).

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