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 raυ 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 raυ and ram are equivalent. While direct assessment of raυ is preferred because of the unambiguous relationship between CE and raυ, measurements of vertical profiles in humidity are historically rare and raυ 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 raυ (from CE) and ram (from CD). This study compares raυ 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

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
c. Penman–Monteith: Surface and canopy conductance
3. Results
Surface soil moisture content had a strong influence over atmospheric moisture gradients across each layer (Figs. 2a–c). Short circuits (i.e., qa − q0 > 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).
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 GSυ. Most values were smaller than 15 mmol m−2 s−1 (Figs. 3a,c). The slope between GSm and GSυ was smaller than 1:1, indicating that values of GSm tended to be smaller than GSυ (Figs. 3a–c). Notable exceptions in which GSm > GSυ occurred at intermediate values of GSυ (Figs. 3a,c). Likewise, when integrated over a day, GSm exceeded GSυ at low values, which was more pronounced in the top layer alone than when the complete model (Fig. 1) was used for computing GSυ (Fig. 3b). When scaled to the same units as GSx, aerodynamic conductance to momentum Gam was much smaller than Gaυ and only marginally larger than GSm (Fig. 3d).
Comparison of CD-based (GSm and Gam) and CE-based (GSυ and Gaυ) conductances. Comparison of surface conductances GSυ 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 Gaυ vs momentum transfer Gam.
Citation: Journal of Hydrometeorology 14, 5; 10.1175/JHM-D-13-080.1
Maximal values of GSυ and GSm declined exponentially in response to increasing D (Fig. 4a). At small (<0.5 kPa) and large (>4 kPa) values of D, GSυ, and GSm were similar (Fig. 4a). However, at intermediate values of D, maximal values of GSm were smaller than maximal values of GSυ (Fig. 4a). In the top layer, GSυ 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, GSυ 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).
GSυ or GSm as a function of vapor pressure deficit D. (a) Complete model GSυ (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, GSυ, 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, GSυ was larger in the top layer than in the full layer (Fig. 5c). The GSυ 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 GSυ, but with smaller values (Fig. 5d).
Daily patterns of (a) P and air temperature at a height of 2 m (Ta), (b) E and D, (c) GSυ, and (d) GSυ and GSm.
Citation: Journal of Hydrometeorology 14, 5; 10.1175/JHM-D-13-080.1
In general, rLυ 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).
Daily patterns of leaf resistance rL and E. (a) The rL determined from surface resistance inverted with raυ (rLυ, 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 raυ (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 raυ. Surface conductance computed from raυ (GSυ) was much smaller than aerodynamic conductance of vapor Gaυ (Fig. 3) and consequently reduced the influence of errors in estimation of Gaυ on the determination of GSυ 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 raυ, thus reducing the strength of the aerodynamic term ρacP
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 raυ 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 raυ 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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