Figures
Abstract
The dual-source Shuttleworth-Wallace model has been widely used to estimate and partition crop evapotranspiration (λET). Canopy stomatal conductance (Gsc), an essential parameter of the model, is often calculated by scaling up leaf stomatal conductance, considering the canopy as one single leaf in a so-called “big-leaf” model. However, Gsc can be overestimated or underestimated depending on leaf area index level in the big-leaf model, due to a non-linear stomatal response to light. A dual-leaf model, scaling up Gsc from leaf to canopy, was developed in this study. The non-linear stomata-light relationship was incorporated by dividing the canopy into sunlit and shaded fractions and calculating each fraction separately according to absorbed irradiances. The model includes: (1) the absorbed irradiance, determined by separately integrating the sunlit and shaded leaves with consideration of both beam and diffuse radiation; (2) leaf area for the sunlit and shaded fractions; and (3) a leaf conductance model that accounts for the response of stomata to PAR, vapor pressure deficit and available soil water. In contrast to the significant errors of Gsc in the big-leaf model, the predicted Gsc using the dual-leaf model had a high degree of data-model agreement; the slope of the linear regression between daytime predictions and measurements was 1.01 (R2 = 0.98), with RMSE of 0.6120 mm s−1 for four clear-sky days in different growth stages. The estimates of half-hourly λET using the dual-source dual-leaf model (DSDL) agreed well with measurements and the error was within 5% during two growing seasons of maize with differing hydrometeorological and management strategies. Moreover, the estimates of soil evaporation using the DSDL model closely matched actual measurements. Our results indicate that the DSDL model can produce more accurate estimation of Gsc and λET, compared to the big-leaf model, and thus is an effective alternative approach for estimating and partitioning λET.
Citation: Ding R, Kang S, Du T, Hao X, Zhang Y (2014) Scaling Up Stomatal Conductance from Leaf to Canopy Using a Dual-Leaf Model for Estimating Crop Evapotranspiration. PLoS ONE 9(4): e95584. https://doi.org/10.1371/journal.pone.0095584
Editor: Ben Bond-Lamberty, DOE Pacific Northwest National Laboratory, United States of America
Received: November 10, 2013; Accepted: March 28, 2014; Published: April 21, 2014
Copyright: © 2014 Ding et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This research was partially supported by the National Natural Science Foundation of China (51321001 and 51309223), the National High-Tech Research and Development Program (2011AA100502 and 2013AA102904) and the Ph.D. Programs Foundation of Ministry of Education of China (20130008120007). The research is also supported by the Program of Introducing Talents of Discipline to Universities (B14002). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Introduction
Accurate estimation of evapotranspiration (λET) is important in understanding terrestrial hydrological cycles because λET is the largest component in the terrestrial water balance after precipitation [1]. In agricultural production, improved estimation of crop λET is also needed to develop precise irrigation scheduling and enhance water use efficiency, as soil water depletion is mostly determined by the rate of λET [2], [3], [4]. However, direct measurement of λET is often difficult, costly and not available in many regions [5], [6]. Therefore, mathematical models are needed to estimate λET using readily measurable meteorological and environmental variables.
Vegetation transpiration (Tr) and soil evaporation (Es), which are controlled by different biotic and physical processes, are the two major components of λET. Transpiration is strongly linked to crop productivity since it occurs concurrently with photosynthetic gas exchange [7]. Quantifying Tr is also critical to accurately predict the response of crop functioning and physiology to changing climate [8]. Because the two separate processes occur simultaneously, there is no simple way to distinguish between them [9], [10].
Several models have been developed to calculate λET and separately estimate soil evaporation and transpiration [11], [12], [13]. Shuttleworth and Wallace [14] described a dual-source model with a resistance-energy combination, which could separately predict Tr and Es, and is also sufficiently simple [8]. This model has been widely used and can also be used to gain an understanding of the interaction of biophysical and hydrological processes in the crop canopy [14], [15]. Determination of different resistances or conductances (the reciprocal of resistance) is necessary for its practical application. Specifically, canopy stomatal conductance (Gsc) is often calculated by scaling up leaf stomatal conductance of the leaves acting in parallel while treating the canopy as one big-leaf, hereafter the big-leaf approach [8], [16].
The weakness of using the big-leaf approach is that the use of mean absorbed radiation can significantly overestimate Gsc, especially in dense canopies, because the light response of stomata is non-linear [17], [18]. Moreover, the overestimation of Gsc by the big-leaf approach often occurred when using total leaf area index (LAI) to scale up stomatal conductance. To mitigate the overestimation of Gsc, researchers have used the effective or sunlit LAI (LAIe) instead of total LAI [16], [18]. But, the relationship between LAIe and LAI is empirical and varies with the vegetation type and solar radiation angle. Therefore, models of Gsc should consider the non-linear response of stomata to irradiance as well as heterogeneous radiation profiles in the canopy. Beam and diffuse radiation penetrating the canopy must be considered separately due to differential attenuation in canopies, as should visible and near-infrared wavebands due to differential absorption by leaves [12], [19]. A multilayers model could account for the mechanism of radiation penetration [20], [21], but it is useless in practical applications [22]. Some studies indicate that radiation penetration within the canopy could be simplified by splitting the canopy into two fractions of leaves: sunlit and shaded [18], [23], [24]. Leuning et al. [25] used a multilayer model to show that photosynthesis from a canopy is closely approximated when calculated as the separate sums of sunlit and shaded fractions, weighted by their respective leaf area within the canopy. However, few studies have calculated Gsc using the approach of sunlit and shaded leaves (hereafter, the dual-leaf approach) in the dual-source S-W model for estimating λET.
Soil surface resistance (rss) is another key parameter for partitioning λET in the dual-source model because above-canopy λET is contaminated by flux from the soil substrate as variations in leaf area affect soil exposure, soil evaporation and absorbed radiation [14], [26]. To reduce soil evaporation in the field, the ground is often mulched with plastic film, and this technique is widely used in northwest China [10], [27]. But the effect of ground mulching on soil evaporation has not been taken into account when parameterizing rss in the dual-source model. In this study, a dual-leaf model of Gsc was developed by scaling up leaf stomatal conductance using the corresponding absorbed irradiance for the sunlit and shaded leaves separately, which overcomes the limitations of the big-leaf model. The dual-leaf model developed here was then incorporated into the dual-source model to estimate and partition λET. We evaluated the dual-source dual-leaf model (DSDL) by comparing the model estimations of λET with measurements taken in an irrigated maize field mulched with plastic film.
Model Development for Evapotranspiration and Canopy Stomatal Conductance
1 Dual-source Evapotranspiration Model
The λET in the dual-source model was partitioned into two components, canopy transpiration (λTc) and soil evaporation (λEs) with a resistance network [14].(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)where PMc and PMs are the terms similar to those in Penman–Monteith model for canopy transpiration and soil evaporation, respectively, and ωc and ωs are the weighting factors for the crop canopy and soil components, respectively. λ is the heat of water vaporization, ρ is air density, Cp is the specific heat of dry air at constant pressure, Δ is the slope of the saturation vapor pressure curve, γ is the psychrometric constant, VPD is vapor pressure deficit, and A and As are the total available energy and available energy for soil, respectively. rsc is canopy stomatal resistance, rss is soil surface resistance, rac is canopy boundary layer resistance, ras is soil boundary layer resistance between soil and vegetative canopy, and raa is aerodynamic resistance between canopy source and reference height, respectively. The calculation procedures of the other resistances except rsc and rss are given in Appendix S1.
(9)
(10)
(11)where Rn and Rns are net radiation above the canopy and at the soil surface, respectively, and G is the soil heat flux. The canopy extinction coefficient of net radiation, κR, is dependent on leaf orientation and solar zenith angle (ζ) [17].
(12)where GL is 0.5 for a spherical leaf angle distribution. ζ, the angle subtended by the sun at the center of the earth, is perpendicular to the surface of the earth and calculated as in Appendix S1.
The two components, λTc and λEs were now calculated along with the VPD at the canopy source height (Do).(13)
(14)
(15)
The measured rsc was obtained by inverting Eq. (14), with λTc calculated by the known or measured λET and λEs.(16)
(17)
2 Irradiance within Crop Canopy
Incident PAR light above the canopy (Qo) was divided into diffuse (Qod) and beam irradiance (Qob) through the fraction of diffuse radiation (fd).(18)
(19)
The fd was calculated from a simple model of atmospheric attenuation of radiation [17], [28].(20)where τa is the atmospheric transmittance, fa is the forward scattering coefficient of PAR in atmosphere, and ma is the optical air mass, which can be calculated as follows.
(21)where P is local atmospheric pressure and P0 is atmospheric pressure at sea level.
At a depth ξ in the canopy, three types of irradiance can be calculated: the total beam, Qℓ,bt (unintercepted beam plus down scattered beam), direct beam, Qℓ,b (unintercepted beam) and the diffuse flux, Qℓ,d [17], [29].(22)
(23)
(24)
(25)
(26)
(27)where α is absorptivity of leaves for irradiation, ρcb and ρcd are canopy reflectance for beam and diffuse irradiance respectively with a randomly spherical leaf-angle distribution, ρh is canopy reflectance for beam irradiance with a horizontal leaf-angle distribution, and κd is an extinction coefficient for diffuse radiation.
The absorbed irradiance in a canopy height (Qℓ) consists of the total beam radiation (Qℓ,bt) and the diffuse radiation (Qℓ,d).(28)
The total irradiance absorbed by the entire canopy (Qc) per unit ground area was determined by integrating Qℓ over the total LAI.(29)
The irradiance absorbed by the sunlit fraction in a specific canopy height (Qℓ,sl) can be given as the sum of direct-beam (Qℓ,b), diffuse (Qℓ,d) and scattered-beam components (Qℓ,s).(30)
(31)
The irradiance absorbed by the sunlit fraction in the entire canopy (Qsl) was obtained by integrating Qℓ,sl over the total LAI.(32)
(32a)
(32b)
(32c)
The total irradiance absorbed (Qc) is the sum of the two parts, irradiance absorbed by the separate sunlit (Qsl) and shade fractions (Qsh) of the canopy. Thus, Qsh was calculated as the difference between Qc and Qsl.(33)
3 Leaf and Canopy Stomatal Conductance
The stomatal conductance is represented by gs for a single leaf and Gsc for the entire canopy.
3.1. Leaf stomatal conductance.
The leaf gs can be calculated using the Jarvis-Stewart type multiple formulae [30], [31], [32].(34)where gsmax is the maximum value of the leaf stomatal conductance and Fxi is the stress function of the specific environmental variables (xi), 0≤Fxi≤1. The original model used short-wave radiation as the light variable. Here we have used the photosynthetically active radiation absorbed by canopy leaves (Qa) because stomatal aperture is determined by the received visible wavelength radiation, rather than short-wave radiation [17], [18], [33]. In addition, we incorporated the environmental stress impact on gs by VPD and available soil water as follows.
(35)
(36)
(37)
(38)where the kQ, kD and kw are the stress coefficients of Qa, VPD and extractable soil water in the root zone (θE), and θ, θF and θW are the measured soil moisture, field capacity and wilting point in the root zone, respectively.
3.2. Big-leaf model of canopy stomatal conductance.
The canopy stomatal conductance in the big-leaf model (Gsc1) is estimated by scaling up gs weighing by the effective LAI (LAIe) as if the canopy is a single big-leaf [16], [18], [32].(39)where gs1 is the mean leaf stomatal conductance for the entire big-leaf and can be calculated by Eq. (34) based on the mean absorbed irradiance of the entire canopy using Eq. (29); LAIe is empirically equal to the actual LAI for LAI≤2, LAI/2 for LAI≥4, and 2.0 for others [16].
3.3. Dual-leaf model of canopy stomatal conductance.
In the dual-leaf model, Gsc (Gsc2) is calculated by summing the contributions of sunlit and shaded fractions, Gsl and Gsh, respectively, which are scaled up using the associated gs weighted by their respective fractions of LAI [18], [24].(40)where gsl and gsh are the mean leaf stomatal conductance for sunlit and shaded leaves, respectively, and can be calculated by Eq. (34) based on the separate absorbed irradiance using Eqs. (32) and (33). LAIsl and LAIsh are LAI for sunlit and shaded leaves in the entire canopy, respectively.
Assuming that all leaves in a canopy are randomly distributed, the fraction of sunlit leaves (fℓ,sl) in a specific canopy depth declines exponentially with cumulative leaf area (ξ) [29], [34].(41)
(42)where κb is an extinction coefficient for beam radiation, Ld is leaf area density, z is height above ground, and hc is canopy height. LAIsl is therefore calculated by integrating fℓ,sl for the entire canopy.
4 Soil Surface Resistance
In this study, rss was directly calculated with a function dependent on surface soil water content [35], accounting for the effect of plastic mulching on reduction of soil evaporation by introducing a term for fraction of plastic mulch, fm [i.e. rss is divided by the area of exposed substrate per unit ground area (1−fm)].(45)where θg is the average soil water content between 0–0.1 m, θs is the saturated water content of surface soil, and b1, b2, and b3 are the empirical coefficients.
Materials and Methods
1 Experimental Arrangement
The experiments were conducted in an irrigated maize field in 2009 and 2010 at Shiyanghe Experimental Station for Water-saving in Agriculture and Ecology of the China Agricultural University in Gansu Province in northwest China (N 37°52′, E 102°50′, Altitude 1581 m). Grain maize was sown on April 21 and May 2, and harvested on September 28 and September 26 in 2009 and 2010, respectively. The ground was partly mulched with plastic films with a width of 100 cm, and there was bare soil of 65 and 45 cm in width between two film rows in 2009 and 2010, respectively. Maize seed was sown in holes of 5.0 cm diameter under the plastic films, with a row spacing of 50 and 45 cm and a plant spacing of 24 and 23 cm for 2 years. Maize was not sown in the bare soil. This planting scheme had an actual density of 76,300 and 82,500 plants ha−1 for 2009 and 2010, respectively. Actual fractions of ground-mulching were ∼0.5 and 0.6, respectively, which were defined as one minus the ratio of the summed surface areas of bare soil and holes to ground area. For the 0–1.0 m soil depth, the soil type was silt loam, with a bulk density of 1.38 g cm−3, a field capacity of 0.30 m3 m−3, and a wilting point of 0.12 m3 m−3. Over the entire growing season, maize was border-irrigated four times, with a total irrigation water amount of 420 mm for both years. The amount of each irrigation event was measured by a water meter. Each irrigation amount was 105 mm on June 15, July 6, July 29 and August 20, 2009, and 105, 120, 90, and 105 mm on June 22, July 27, August 5 and August 29, 2010, respectively.
2 Measurements of Evapotranspiration and Soil Evaporation
λET was measured using an eddy covariance (EC) system installed in the center of the maize field. The EC consists of a fast response 3D sonic anemometer (CSAT3, Campbell Scientific Inc., UT, USA), a Krypton hygrometer (KH20, Campbell Scientific Inc.) and a temperature and humidity sensor (HMP45C, Vaisala Inc., Helsinki, Finland). All sensors were connected to a data logger (CR5000, Campbell Scientific, Inc.). The sonic anemometer and Krypton hygrometer were installed at a height of 1.0 m over the crop canopy. Net radiation (Rn) was measured by a net radiometer (NR-LITE, Kipp & Zonen, Delft, Netherlands), installed at a height of 3.5 m. Two soil heat fluxes (HFP01, Hukseflux, Delft, Netherlands) were installed at a soil depth of 8.0 cm under the plastic film and bare soil. Soil temperature above each soil heat flux plate was measured using thermocouples at depths of 0.0 cm, 2.0 cm and 6.0 cm. Soil water content from 0–10.0 cm was measured using a soil moisture reflectometer (EnviroSMART, Sentek Sensor Technologies, SA, Australia). Ground heat flux (G) was estimated by correcting heat fluxes at 8.0 cm for heat storage above the transducers. The heat storage was determined from changes in soil temperature and moisture above the transducers. Based on the covariance of the 10 Hz air temperature and specific humidity with vertical wind velocity, the latent heat flux in 30 min durations was computed using the eddy covariance methodology with the CarboEurope recommendations [36]. Daytime λET was adjusted by the Bowen-ratio forced closure method, and nighttime λET was adjusted using the filtering interpolation method as proposed by Ding et al. [37].
Soil evaporation (Es) was measured by the micro-lysimeter. Eight micro-lysimeter cylinders, made from PVC tubes with a diameter of 10 cm and height of 20 cm, were installed in bare soil between two plastic film rows. The cylinders were weighed at 20∶00 every day by an electric scale with a precision of 0.1 g. The micro-lysimeters were reinstalled within one day after each irrigation and heavy rain. Es at the field scale can be calculated by weighting the fraction of ground-mulching (fm) from the following equation.(46)where
is the mean weight change of micro-lysimeter every day, Ae is the cross sectional area of the micro-lysimeters (78.5 cm2 here), ρw is water density (1.0 g cm−3) and 10 is a conversion factor for changing units from cm to mm.
3 Other Measurements
Solar radiation, precipitation, air temperature, relative humidity and wind speed were measured with a standard automatic weather station (Hobo, Onset Computer Corp., USA) at a height of 2.0 m above the ground. Volumetric soil water content in the root zone (θrz) was measured with PVC access tubes using the portable device Diviner 2000 (Sentek Sensor Technologies). Measurements were made at intervals of 0.1 m with a maximal soil depth of 1.0 m at intervals of 3–5 days. Additional samplings were conducted before and after irrigation events, as well as after rainfall events. The measurements were calibrated by oven drying of soil samples. Interpolation was applied between consecutive irrigations to determine θr for each day. In addition, two sets of ECH2O probes (Decagon Devices Inc., Pullman, WA, USA) were added to monitor soil moisture at 30 min intervals in 2010.
Ten maize plants were randomly selected to measure leaf length and width, and height at intervals of ∼10 days during the growing season. Leaf area was calculated by summing the rectangular area of each leaf (leaf length×maximum width) multiplied by a factor of 0.74, a conversion factor obtained by analyzing the ratio of the rectangular area to the real area measured by an AM300 (ADC BioScientific Ltd., UK). LAI is defined as maize green leaf area per unit ground area. The daily LAI was obtained by linear interpolation.
Leaf-scale physiological measurements were performed to derive the stomatal conductance model parameters. A LI-6400 portable photosynthesis system (Li-Cor Inc., Lincoln, NE, USA) was used to measure leaf stomatal conductance on the first fully expanded leaf, which is the fourth leaf counted from the top of the shoot. The diurnal measurements of leaf gas exchange were performed once every 2 h from 8∶00 to 18∶00 on six sunny days in 10 randomly selected maize plants. Care was taken to keep leaves in their natural positions during measurement. The response of leaf stomatal conductance to varying PAR was measured at 30°C and at a CO2 concentration of 400 mol mol−1 on 29 August, 2009. Measurements were taken at PAR levels of 2000, 1600, 1300, 1000, 800, 600, 400, 200, 100, 50, 20, and 0 µmol m−2 s−1. The stomatal light-response curve was fit by a rectangular hyperbola to obtain the parameter values of kQ using the Jarvis-Stewart model.
4 Model Performance
Half-hourly Gsc and λET were calculated using the big-leaf and dual-leaf models Eqs. (39) and (40) with the dual-source equation based on the half-hourly measured meteorological data. The LAI and soil water were set as constants at the half-hourly time scale. Daily λET was calculated using Eqs. (39) and (40) with the dual-source equation based on the measured average daily meteorological data. We evaluated the two models by comparing with measurements taken over an irrigated maize field.
The parameters in the Jarvis-Stewart model were obtained using measurements of the stomatal light-response curve and the diurnal leaf gas exchange calculated by non-linear least-squares analysis (SPSS 13.0, SPSS Inc., Chicago, IL, USA). There were ∼15 days with no crop cover before the emergence of maize, providing the opportunity to parameterize the empirical coefficients in the soil surface resistance model using the flux observations.
The coefficient of determination (R2), root mean square error (RMSE) and the Willmott’s index of agreement (d) were used to evaluate model performance [38].
Results
1 Model Parameter Estimation and Sensitivity
From the stomatal light-response curve, we obtained best-fitting estimates of kQ by non-linear least-squares analysis using the Jarvis-Stewart model (Table 1). The stress coefficients of VPD and θE, kD and kw, were optimized using the diurnal measurements of leaf gas exchange (Table 1). Soil surface resistance (rss) was calculated by inverting the flux-resistance equation for the case of no crops [12]. Based on the relationship between rss and relative soil water content (θg/θs) of the top soil, the best-fitting parameters of b1, b2 and b3 were obtained (Table 1).
The big-leaf model estimates did not closely match the response of Gsc to incident PAR above the canopy (Qo) predicted by the dual-leaf model (Fig. 1). At lower LAI (2.0), the big-leaf model overestimated Gsc by up to 47.4% at an intermediate irradiance (300 W m−2). At higher LAI (5.0), the big-leaf model overestimated Gsc when Qo<200 W m−2 and underestimated Gsc when Qo>200 W m−2. The sensitivity of the dual-leaf model was further analyzed by investigating the variations of the sunlit and shaded leaf area index (LAIsl and LAIsh) against the different LAI (Fig. 2). LAIsl approached a maximum of 1.6 when LAI≥3.0, while LAIsh almost linearly increased as LAI increased. As a result, the ratios of LAIsl and LAIsh to LAI (Λsl and Λsh) nonlinearly decreased and increased, respectively, as LAI increased.
Gsc1 and Gsc2 are calculated by the big-leaf and dual-leaf canopy stomatal resistance models, respectively.
The ratios of LAIsl and LAIsh to LAI (Λsl and Λsh) are also shown.
The diurnal variations of modeled irradiance absorbed by the entire canopy (Qc) and its separation into sunlit and shaded fractions (Qsl and Qsh) are shown in Fig. 3a at higher LAI = 5.0, using the measured diurnal courses of meteorological and environmental variables from June 23, 2009. Qc, Qsl and Qsh exhibited the typical diurnal patterns, while Qsh had a lower magnitude than Qsl throughout the day. The average Qsl accounted for 84.2% of the Qc. The partitioning of leaves into sunlit and shaded fractions continually changes throughout the day (Fig. 3b). LAIsl was a convex parabola, while LAIsh was a concave parabola. The magnitude of LAIsh was greater than LAIsl even during midday when the solar zenith angle is lowest at the higher LAI, which is consistent with the result in Fig. 2. The diurnal distributions of Gsc calculated by the big-leaf model (Gsc1) and dual-leaf model (Gsc2) and its separation between sunlit and shaded fractions (Gsl and Gsh) are presented in Fig. 3c. Gsc1 was significantly lower than Gsc2 through most of the day at the higher LAI. Gsh showed a pattern similar to Gsl, while the magnitude of Gsh was lower than Gsl. The maximum difference between them occurred at the midday around 11∶00.
Qo is the total irradiance above the canopy, Qc is the irradiance absorbed by the entire canopy, and is separated into the irradiance absorbed by the sunlit leaves of the canopy (Qsl) and irradiance absorbed by the shaded leaves of the canopy (Qsh). LAIsl and LAIsh are the sunlit and shaded fractions of LAI, respectively. Gsc1 and Gsc2 are the canopy stomatal conductance calculated by the big-leaf and dual-leaf models, respectively; Gsc2 is separated into the sunlit and shaded canopy stomatal resistance, Gsl and Gsh, respectively.
2 Comparisons of Canopy Stomatal Conductance by Big-leaf and Dual-leaf Models
Diurnal patterns of Gsc calculated by the big-leaf and dual-leaf models (Gsc1 and Gsc2, respectively) and the measured Gsc (Gscm) calculated by using Eq. (17) are shown in Fig. 4 for four typical clear-sky days in different growth stages of maize in 2009. The diurnal courses of the Gsc1 and Gsc2 were similar to the Gscm, but there were differences in magnitude. Gsc1 was significantly lower than Gscm, while Gsc2 closely matched Gscm at higher LAI (Fig. 4c). Gsc1 was higher than Gscm at the lower LAI where there was still good agreement between Gsc2 and Gscm values (Fig. 4b and d). Although the slope of the linear regression between Gsc1 and Gscm was 0.97, Gsc1 was overestimated at the lower Gscm and underestimated at the higher Gscm (Fig. 5a), as shown by the lower R2 of 0.81, greater RMSE of 1.7047 mm s−1 and lower d of 0.9563, indicating that the big-leaf model yielded large errors for estimating Gsc. In contrast, the slope of the linear regression between Gsc2 and Gscm was 1.01, with an R2 of 0.98, RMSE of 0.6120 mm s−1 and d of 0.9951, indicating that there was good data-model agreement between predictions and measurements (Fig. 5b).
Leaf area index (LAI) was 0.16, 2.62, 5.38 and 2.99, on (a) May 22, (b) June 23, (c) July 27, and (d) September 17, respectively.
3 Comparisons of Crop Evapotranspiration by Big-leaf and Dual-leaf Models
Diurnal variations of half-hourly λET calculated by the dual-source big-leaf (λET1) and dual-leaf models (λET2), and measured λET (λETm), respectively are presented for four typical clear-sky days in different growth stages of maize in 2009 (Fig. 6). The diurnal patterns of estimated λET were similar to the measurements. λET1 was overestimated at lower LAI, and underestimated at higher LAI. The linear regression presented that λET1 was overestimated by 8.7% (R2 = 0.97) and 19.7% (R2 = 0.96) for LAI = 2.62 and 2.99, respectively (Fig. 6b and d). λET1 was underestimated by 13.9% (R2 = 0.97) for LAI = 5.38 (Fig. 6c). In contrast, λET2 had a good agreement with measurements for differing LAI, with a linear slope of 1.01 and an R2 of 0.97.
Leaf area index (LAI) was 0.16, 2.62, 5.38 and 2.99, on (a) May 22, (b) June 23, (c) July 27, and (d) September 17, respectively.
The irrigation scheduling and mulching fractions in 2009 and 2010 were different (See section 3.1), which yielded different LAI and soil water regimes for the two years (See Figure 1 and Table 1 in Ding et al.[39]). The maximum and averaged values of LAI respectively were 5.4 and 3.1 for 2009, and 4.7 and 2.7 for 2010. The extractable soil water in the root zone (θE) was significantly different between the two years. Before the first and second irrigation events in 2010, there were 9 and 12 days of θE below 50% total available water in the root zone (TAW), which was regarded as a threshold of crop water stress [13]. Conversely, most θE was higher than 50% of TAW in 2009. All of these differences led to differing λET and its components, which provided a good dataset to test the big-leaf and dual-leaf models over two different hydrometeorological and management strategies.
The scatterplots of half-hourly λET exhibited that λET1 was overestimated for lower values and underestimated for higher values, respectively (Fig. 7a and 7c). Total λET1 was underestimated, with a slope of linear regression of 0.94 (R2 = 0.83) and 0.93 (R2 = 0.82), respectively, for 2009 and 2010. RMSE was 72.22 and 70.97 W m−2, and d was 0.9521 and 0.9472 for 2009 and 2010, respectively (Table 2). In contrast, there was good data-model agreement between measurements and estimated half-hourly λET2 in 2009 and 2010 (Fig. 7b and 7d). The slopes of linear regressions between the estimates and measurements were 1.02 and 1.03, with R2 of 0.90 and 0.88, RMSE of 58.06 and 62.31 W m−2 and d of 0.9706 and 0.9626 for 2009 and 2010, respectively (Table 2). Daily estimated λET2 enhanced data-model agreement, with R2 of 0.91 for the 2 years despite the linear slopes were the same as those of half-hourly values (data not shown). The statistical test showed that the slopes were not significantly different with one (P = 0.114 and 0.092), and the intercepts were not significantly different with zero (P = 0.215 and 0.174) for the 2 years.
Seasonal variations of daily estimated and measured Es using Eq. (15) combined with Eqs. (39) and (40) are presented in Fig. 8 for 2009 and 2010. Both the dual-source big-leaf and dual-leaf models could capture the variability of Es even when irrigation or precipitation occurred and when the canopy partially covered the ground during the initial growth stages. However, daily values of Es1 were underestimated at the early and late stages and overestimated at the middle stage (Fig. 8a and b). In general, total Es1 was underestimated by 5% and 7% for 2009 and 2010, respectively (Fig. 8c and d). In contrast, there was satisfactory data-model agreement between predicted and measured Es using the DSDL model for the two years. The slopes of linear regressions between estimates and measurements were 1.02 (R2 = 0.68) and 1.01 (R2 = 0.73), with RMSE of 0.1220 and 0.1565 mm d−1 and d of 0.9129 and 0.9218 for 2009 and 2010, respectively (Table 2).
Seasonal variations of the estimated and measured Es against days after sowing (DAS) are presented in (a) and (b). The linear regressions between them are presented in (c) and (d).
Discussion
In this paper, we have extended the big-leaf model by developing a dual-leaf model. The dual-leaf model presented here is an improvement over the previous big-leaf model, as more realistic non-uniform vertical profiles of radiation and stomatal conductance are now incorporated into the model. The penetration of beam radiation, its variation and the dynamics of sunlit and shaded LAI throughout the day all affect the ability of the big-leaf model to simulate diurnal changes in Gsc [18], [29]. In the dual-leaf model, these canopy features can be explicitly incorporated by dividing the canopy into sunlit and shaded fractions and modeling each fraction of Gsc by scaling up the respective stomatal conductance separately. It is more complex than the big-leaf model, but the dynamic partitioning of LAI and irradiance between sunlit and shaded leaves has further reduced the errors associated with simplifying the leaves to only a big-leaf using either the total or empirically effective LAI.
The ability of the dual-leaf model was examined by comparing the estimated values and actual measurements. In contrast to significant errors by the big-leaf model, the dual-leaf model accurately reproduced the variation of Gsc (Fig. 4 and 5). One reason the dual-leaf model works so well is that it accommodates the nonlinear response of stomata to light [25], [40]. Stomata-light responses of leaves can vary with depth in the canopy and this variation can be incorporated by partitioning the canopy into several layers and estimating the sunlit and shaded leaf fractions in each layer [20], [34]. However, usually this is not necessary and a single, representative light response curve can be used for the entire canopy [17], [40]. In the dual-leaf model, the entire Gsc may be calculated by summing contributions of sunlit and shaded leaves. These two contributions are added separately because sunlit leaves will be light-saturated while shaded leaves will be in the linear portion of the light-stomata relationship [18], [33]; thus Gsc is not proportional to average light levels [18]. Because of the nonlinear relationship between stomatal conductance and PAR, the predicted Gsc will be overestimated when the average absorbed PAR is used to scale up the leaf stomatal conductance for the entire canopy as in the big-leaf model [17], [40]. On the other hand, the Gsc is underestimated when the effective LAI is used to scale up the leaf stomatal conductance at higher LAI ((Fig. 4c). Since the nonlinear relationship was considered and the sunlit-shaded method was introduced in the dual-leaf model, estimates using the dual-leaf model closely match the measured Gsc (Fig. 4 and 5).
The performance of the DSDL for estimating λET was investigated. The DSDL is robust for estimating λET over a range of canopy leaf areas and environmental variables (Fig. 6, Fig. 7 and Table 2). The good data-model agreement indicated the strengths of the DSDL model as a model framework and the reference for validating other approaches of calculating the Gsc using the dual-leaf model. Our framework of modeling λET also provided a soil evaporation estimation model Eq.(15) with a modified soil surface resistance term, which is useful for enhancing crop production by reducing the Es fraction of λET [10], [15].
The DSDL model is physically process-based, yet sufficiently simple to be effectively parameterized. The dual-leaf model requires only four additional equations, Eqs (32), (33), (43) and (44), beyond those required in the model of leaf stomatal conductance, to calculate the LAI and absorbed irradiance of the sunlit and shaded leaves. This simplicity makes it attractive for incorporation into in crop models, land surface schemes, and regional or global water cycle studies [29], [40]. This model can also be used to assess effects of climate change on crop ecophysiology.
Conclusions
In this paper, a dual-leaf model for scaling-up stomatal conductance from the leaf to the canopy level was developed through the dynamic partitioning of the leaf area index and irradiance between sunlit and shaded leaves. In the model, canopy stomatal conductance was calculated by dividing the canopy into sunlit and shaded fractions and each fraction was modeled separately based on the absorbed irradiances. The dual-leaf model provided estimates of Gsc which were nearly the same as measurements, and were significantly more accurate than those of the big-leaf model. Our results showed excellent agreements between λET measurements gathered by the eddy covariance technique over an irrigated maize field during 2009 and 2010 under two different hydrometeorological and management conditions, and estimates of λET using the DSDL. The framework of the model can also satisfactorily estimate soil evaporation. Our proposed model provides an alternative approach to calculate λET, which is simple and attractive for incorporation into other comprehensive crop models.
Supporting Information
Appendix S1.
Resistances calculations and solar geometry.
https://doi.org/10.1371/journal.pone.0095584.s001
(DOCX)
Acknowledgments
We thank the two anonymous reviewers for their constructive comments that have helped to improve the manuscript.
Author Contributions
Conceived and designed the experiments: RD SK TD. Performed the experiments: RD YZ. Analyzed the data: RD YZ. Contributed reagents/materials/analysis tools: SK TD. Wrote the paper: RD SK TD XH YZ.
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