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  • View in gallery

    Location of the study site including measurement of eddy covariance and experiment for plastic-mulched cotton in Aler City of Xinjiang in China.

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    Comparison of daily ET in cotton field estimated by the modified Priestley–Taylor model with that measured by eddy covariance in (a) 2013 and (b) 2014.

  • View in gallery

    (a) Daily ET estimated by the modified Priestley–Taylor model in cotton plots under three mulch fractions and (b) comparison of periodical cumulative ET under three different mulch fractions estimated by the modified Priestley–Taylor model with that calculated via water balance 2014.

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    Comparison of the modified Priestley–Taylor coefficient in cotton plots under three mulch fractions in 2014.

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    Effect of LAI changes (by ±50%; see legend in upper-right corner) on the modified bulk Priestley–Taylor coefficient under 60% mulch fraction during the whole cotton growing season in 2014.

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    Effect of mulch fraction changes (by ±50%; see legend in upper-right corner) on the modified bulk Priestley–Taylor coefficient under 60% mulch fraction during the whole cotton growing season in 2014.

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    Sensitivity coefficient for the modified bulk Priestley–Taylor coefficient with respect to the input parameters of (a) LAI and (b) air temperature (maximum temperature Tmax and minimum temperature Tmin) under the 60% mulch fraction cotton plot during the whole growing season in 2014.

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    Comparison of daily ET in the cotton field estimated by the original Priestley–Taylor coefficient of 1.26 with that observed by eddy covariance in (a) 2013 and (b) 2014.

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Modification and Validation of Priestley–Taylor Model for Estimating Cotton Evapotranspiration under Plastic Mulch Condition

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  • 1 Key Laboratory of Agricultural Water Resources, Hebei Laboratory of Agricultural Water-Saving, Center for Agricultural Resources Research, Institute of Genetics and Developmental Biology, Chinese Academy of Sciences, Shijiazhuang, and University of Chinese Academy of Sciences, Beijing, China
  • 2 Key Laboratory of Agricultural Water Resources, Hebei Laboratory of Agricultural Water-Saving, Center for Agricultural Resources Research, Institute of Genetics and Developmental Biology, Chinese Academy of Sciences, Shijiazhuang, China
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Abstract

Compared with more comprehensive physical algorithms such as the Penman–Monteith model, the Priestley–Taylor model is widely used in estimating evapotranspiration for its robust ability to capture evapotranspiration and simplicity of use. The key point in successfully using the Priestley–Taylor model is to find a proper Priestley–Taylor coefficient, which is variable under different environmental conditions. Based on evapotranspiration partition and plant physiological limitation, this study developed a new model for estimating the Priestley–Taylor coefficient incorporating the effects of three easily obtainable parameters such as leaf area index (LAI), air temperature, and mulch fraction. Meanwhile, the effects of plastic film on the estimation of net radiation and soil heat flux were fully considered. The reliability of the modified Priestley–Taylor model was testified using observed cotton evapotranspiration from eddy covariance in two growing seasons, with high coefficients of determination of 0.86 and 0.81 in 2013 and 2014, respectively. Then, the modified model was further validated by estimating cotton evapotranspiration under three fractions of mulch cover: 0%, 60%, and 100%. The estimated values agreed well with the measured values via water balance analysis. It can be found that seasonal variation of the modified Priestley–Taylor coefficient showed a more reasonable pattern compared with the original coefficient of 1.26. Sensitivity analysis showed that the modified Priestley–Taylor coefficient was more sensitive to LAI than to air temperature. Overall, the modified model has much higher accuracy and could be used for evapotranspiration estimation under plastic mulch condition.

Corresponding author address: Prof. Yonghui Yang, Key Laboratory of Agricultural Water Resources, Hebei Laboratory of Agricultural Water-Saving, Center for Agricultural Resources Research, Institute of Genetics and Developmental Biology, Chinese Academy of Sciences, 286 Huaizhong Road, Shijiazhuang 050021, China. E-mail: yonghui.yang@sjziam.ac.cn

Abstract

Compared with more comprehensive physical algorithms such as the Penman–Monteith model, the Priestley–Taylor model is widely used in estimating evapotranspiration for its robust ability to capture evapotranspiration and simplicity of use. The key point in successfully using the Priestley–Taylor model is to find a proper Priestley–Taylor coefficient, which is variable under different environmental conditions. Based on evapotranspiration partition and plant physiological limitation, this study developed a new model for estimating the Priestley–Taylor coefficient incorporating the effects of three easily obtainable parameters such as leaf area index (LAI), air temperature, and mulch fraction. Meanwhile, the effects of plastic film on the estimation of net radiation and soil heat flux were fully considered. The reliability of the modified Priestley–Taylor model was testified using observed cotton evapotranspiration from eddy covariance in two growing seasons, with high coefficients of determination of 0.86 and 0.81 in 2013 and 2014, respectively. Then, the modified model was further validated by estimating cotton evapotranspiration under three fractions of mulch cover: 0%, 60%, and 100%. The estimated values agreed well with the measured values via water balance analysis. It can be found that seasonal variation of the modified Priestley–Taylor coefficient showed a more reasonable pattern compared with the original coefficient of 1.26. Sensitivity analysis showed that the modified Priestley–Taylor coefficient was more sensitive to LAI than to air temperature. Overall, the modified model has much higher accuracy and could be used for evapotranspiration estimation under plastic mulch condition.

Corresponding author address: Prof. Yonghui Yang, Key Laboratory of Agricultural Water Resources, Hebei Laboratory of Agricultural Water-Saving, Center for Agricultural Resources Research, Institute of Genetics and Developmental Biology, Chinese Academy of Sciences, 286 Huaizhong Road, Shijiazhuang 050021, China. E-mail: yonghui.yang@sjziam.ac.cn

1. Introduction

Accurate estimation of evapotranspiration (ET) is critical for deepening our understanding of land–atmosphere interactions, the water cycle, and water resources management (Lawrence et al. 2007; Schlesinger and Jasechko 2014; Wang et al. 2014). Different models have been developed toward this effort as direct measurement of evapotranspiration is not only difficult (Xu and Chen 2005; Turner 1989), but also not readily available in several regions around the world. It is now over 200 years since Dalton’s classic work that significantly enhanced the estimation of evapotranspiration via equations (Oliver and Oliver 2003). However, evapotranspiration is a complicated process that is driven by weather, crop, and management conditions (such as plastic mulch and straw mulch). Plastic mulch is widely used in cultivated lands in most arid and semiarid regions across the globe. It not only suppresses weed and increases yield and water-use efficiency (Ham et al. 1993; Ramakrishna et al. 2006; Liu et al. 2009), but also significantly changes substrate characteristics and field micrometeorological conditions that in turn influences surface energy partitioning and evapotranspiration. This effect would be variable under different mulch fractions because of the complex changes in microenvironment and energy transfer (Liakatas et al. 1986; Tarara 2000). These land-cover changes and model bias have a big influence on the accuracy of estimated evapotranspiration across a range of scales (Allen et al. 1998; Yang et al. 2012; Sterling et al. 2012). Thus, adjusting existing general models to adapt to specific natural conditions or agricultural settings is important for more reliable estimation of evapotranspiration.

The Priestley–Taylor model is expressed as the product of Priestley–Taylor coefficient and the equilibrium term (Priestley and Taylor 1972) based on the assumption that the equilibrium term (Slatyer and McIlroy 1961) is significantly larger than the aerodynamic term, where Δ is the slope of the saturation vapor pressure curve, γ is the psychrometric constant, and Rn and G are the net radiation and surface soil heat flux, respectively. As a simplification of the Penman–Monteith model, the Priestley–Taylor approach can be accurate where aerodynamic and surface resistance is not available (Tanner and Jury 1976; Davies and Allen 1973). The key issue in successfully using the Priestley–Taylor model lies with finding the right Priestley–Taylor coefficient, which is 1.26 for saturated conditions and open water bodies (Priestley and Taylor 1972; Parlange and Katul 1992). This coefficient has worked well for perennial ryegrass (Pereira 2004) and vegetated areas (Lhomme 1997; Ding et al. 2013).

Compared with lysimeter data, however, the 1.26 Priestley–Taylor coefficient significantly underestimates evapotranspiration for arid conditions (Berengena and Gavilàn 2005; Benli et al. 2010) while slightly overestimating it for humid conditions (Yoder et al. 2005). Compared with volume balance analysis, however, the 1.26 Priestley–Taylor coefficient underestimates free water evaporation for dry hydrological conditions while overestimating it for wet hydrological conditions (Arasteh and Tajrishy 2008). On the other hand, the Priestley–Taylor coefficient can be quite variable (Kustas et al. 1996; Castellvi et al. 2001; Diaz-Espejo et al. 2005) and inconsistent over the whole growing season for maize and wheat (Lei and Yang 2010; Zhang et al. 2004). Therefore, establishing a unique equation for estimating Priestley–Taylor coefficient has remained a significant research issue. Also, little attempt has been made to adjust net radiation and surface soil heat flux in the Priestley–Taylor model under plastic mulch conditions, which is virtually critical in the absence of observation data.

Cotton is a major cash crop in the arid northwestern China. As average annual precipitation is only around 49.5 mm in the Tarim River basin, nearly all croplands are irrigated. Currently, agriculture accounts for over 97% of the total water consumption in the region (Zhang et al. 2012). To improve water-use efficiency, over the past several years, most of the cotton fields have been switched from flood irrigation to drip irrigation with plastic mulch (Zhong et al. 2009). Such cultivation technique has now become the dominant agronomic practice in most arid and semiarid regions in China and also around the world (Kasirajan and Ngouajio 2012).

The objective of this study was to adjust the general Priestley–Taylor model to adapt to plastic mulch conditions. First, the estimation processes of surface albedo and surface soil heat flux were modified in full consideration of the effects of plastic mulch conditions. Next, an analytic solution to the Priestley–Taylor coefficient was developed based on plant physiological limitations and evapotranspiration partitioning. Finally, the modified Priestley–Taylor model was validated using eddy covariance and was then applied to predict experimental conditions.

2. Model descriptions

a. Parameter calibration for plastic mulch condition

1) Surface reflectance

When solar radiation reaches a plastic film surface, a fraction is reflected into the atmosphere, but most of the solar radiation directly penetrates the plastic film. The solar radiation penetrating the plastic film is reflected again into the atmosphere by the soil surface underneath the film. In addition, multiple reflections between the plastic film and the below soil surface are also included in the process. According to these physical processes, surface reflectance can be described as follows (Fan et al. 2015):
e1
namely,
e2
where and are reflectance and transmittance of plastic film, respectively, and is soil surface reflectance.
According to Maclaurin series,
e3
therefore, surface reflectance can be written as
e4
Then, based on the parameterization scheme proposed by Yang et al. (2012) and further taking into consideration the effect of mulch fraction, solar zenith angle, leaf area index, and soil moisture, surface reflectance under plastic mulch condition is calculated as follows:
e5
where is mulch fraction; LAI is leaf area index; is soil water content at 10-cm soil depth; is solar zenith angle; and a, b, and c are fitted constants based on our experimental observations, taken as −0.422, 1.422, and −0.035, respectively, in this study.

2) Net radiation

After adjustment of surface albedo, net shortwave radiation is calculated as
e6
where is solar radiation (MJ m−2 day−1).
Net longwave radiation is calculated using an average of the maximum and the minimum air temperature to the fourth power based on the Stefan–Boltzmann equation:
e7
where is the Stefan–Boltzmann constant, and are maximum and minimum absolute temperatures during the 24-h period (K), is actual vapor pressure (kPa), and is calculated clear-sky radiation (MJ m−2 day−1). Details for calculating of relevant variables of , , and are provided by Allen et al. (1998). The terms and express the corrections for air humidity and for cloudiness, respectively (Allen et al. 1998).
Finally, net radiation under plastic mulch condition is calculated as the difference of net incoming shortwave radiation and net outgoing longwave radiation:
e8

3) Surface soil heat flux

Generally, surface soil heat flux is strongly correlated with radiation reaching the soil surface, which is exponential attenuation with net radiation. Therefore, surface soil heat flux under plastic mulch condition could be estimated using adjusted net radiation and leaf area index in an exponential attenuation equation as
e9
where , , and are fitted constants based on our experimental observations, taken as 0.047, 3.3, and 1.5, respectively, in this study. Therefore, the fraction of surface soil heat flux relative to net radiation under plastic mulch condition is calculated as
e10

b. Actual bulk Priestley–Taylor coefficient under plastic mulch condition

Actual field evapotranspiration is calculated as the sum of canopy transpiration , soil evaporation , and wet canopy evaporation . The basic principle is from Priestley–Taylor equation and plant physiological constraints. Canopy transpiration is calculated as
e11
where the term expresses the transpiration under energy-limited condition, where means modified Priestley–Taylor coefficients for canopy under energy-limited condition and means net radiation intercepted by crop canopy under plastic mulch condition, and the term expresses the actual water and temperature constraints. Similarly, soil evaporation under plastic mulch condition is calculated as the sum of saturated soil evaporation and unsaturated soil evaporation:
e12
where the term represents the saturated fraction of soil evaporation, and the term represents the unsaturated fraction of soil evaporation, where means modified Priestley–Taylor coefficients for soil under energy-limited condition and means net radiation obtained by soil surface under plastic mulch condition. Wet canopy evaporation is calculated as
e13
where is the wet surface fraction and is an index of soil water deficit, which is calculated as follows (Yao et al. 2014):
e14
e15
where DT is diurnal air temperature range and is the plant temperature constraint, which is calculated as (June et al. 2004):
e16
where is air temperature (°C); is optimum plant growth temperature (°C), set as 26°C in this study; is plant moisture constraint; and is green canopy fraction, calculated as follows (Fisher et al. 2008):
e17
e18
where is fraction of photosynthetically available radiation (PAR) absorbed by green vegetation cover and is fraction of PAR intercepted by total vegetation cover, calculated as (Ershadi et al. 2014):
e19
where soil adjusted vegetation index (SAVI) is calculated as
e20
and is vegetation cover fraction, which can be calculated using the fraction of net radiation transmission reaching the soil surface :
e21
where is calculated based on the Beer–Lambert law as
e22
where is canopy extinction coefficient of radiation, which is taken as 0.58 for cotton crop (Tayir et al. 2006; Liu et al. 2013). Then and are modified Priestley–Taylor coefficients for soil and canopy, respectively, under energy-limited condition, which are estimated as (Tanner and Jury 1976)
e23
e24
where is Priestley–Taylor coefficient under energy-limited condition with a full canopy cover, taken as 1.26; is taken as 0.55 (Morgan et al. 2003); and and are net radiation obtained by soil surface and intercepted by crop canopy, respectively (W m−2), which are estimated as follows:
e25
e26
Actual evapotranspiration under plastic mulch condition can also be estimated as
e27
where is the bulk Priestley–Taylor coefficient. Therefore,
e28
Namely,
e29
Finally, an analytical formula for is obtained as
e30

c. Plot scale water balance

Cotton evapotranspiration for three different mulch fraction plots is calculated as the residual of the soil water balance (Rana and Katerji 2000; Hunsaker et al. 2011):
e31
where and are the soil water storages within the 0–150-cm soil layer measured on the first and second measurement dates, respectively (mm); and are irrigation and precipitation, respectively (mm); is field runoff (mm); and is drainage measured between the first and second dates (mm). Because there was no water runoff from the plots, was set at zero in this study.

d. Evaluation of model performance

The performance of the models was evaluated using the root-mean-square error (RMSE), the index of agreement d (Willmott 1982), and the ratio r between modeled and observed values of evapotranspiration. The equations used for the evaluation measures are
e32
e33
and
e34
The model performance is optimum for low RMSE values and for d and r values nearing unity.

e. Uncertainty analysis

The effect of uncertainty in input variables on the modified bulk Priestley–Taylor coefficient is estimated using the method of Moffat (1988):
e35
where represents the modified bulk Priestley–Taylor coefficient, represents the input variables for calculating the modified bulk Priestley–Taylor coefficient, and is the sensitivity coefficient.

3. Materials and methods

a. Study site

The study site is the Soil and Water Conservation Monitoring Station in Aksu Oasis near Aler City (see Fig. 1). The station is situated in Tarim River basin at 40°37′N, 81°11′E and at 1013 m MSL. The station lies in a typical temperate desert climate zone, with average annual sunshine of 2892 h, >10°C cumulative daily temperature of 4081°C per annum, average annual precipitation of 50 mm, and average annual open-water evaporation of 1987 mm. Soil texture in the region is largely sandy loam, with an average bulk density of 1.58 g cm−3 in the 0–1.6-m soil profile.

Fig. 1.
Fig. 1.

Location of the study site including measurement of eddy covariance and experiment for plastic-mulched cotton in Aler City of Xinjiang in China.

Citation: Journal of Hydrometeorology 17, 4; 10.1175/JHM-D-15-0151.1

b. Experiment design

1) Field experiment and eddy covariance system

Cotton (Gossypium hirsutum L., Xinluzhong-37) was planted at mean row spacing of 35 cm and mean plant spacing of 10 cm. The cotton was planted at two alternating row widths of 10 cm (narrow row) and 60 cm (wide row). Drip tape was placed at the center of the wide row in an east–west direction. Each wide row (including the drip tape) was covered with transparent polyethylene plastic film and tightly pegged into the soil at the edges. The width of pure bare soil between two successive plastic films was 50 cm. The area under plastic mulch accounted for about 69% of the total cotton field. To ensure that the study was consistent with actual local conditions in the region, the cotton field was irrigated, fertilized, and managed in accordance with the local practices.

An eddy covariance system (see Fig. 1), oriented toward the direction of the prevailing winds (northeast), was installed in the center of a large cotton field (520 m × 225 m) to measure latent heat. The area surrounding the study site was also flat and homogeneous cotton fields, which ensured a large measurement fetch. The eddy covariance system consisted of a three-dimensional (3D) sonic anemometer (model CSAT3, Campbell Scientific Inc., Logan, Utah, United States) and an open-path infrared gas analyzer (model LI-7500, LI-COR Inc., Lincoln, Nebraska, United States). The sensors were installed at 3.0 m above the ground surface, above the highest cotton canopy by about 2.23 m. Three-dimensional wind velocity and vapor concentration were sampled at a frequency of 10 Hz. Monitoring results were averaged at 30-min intervals and postprocessed in Eddypro 5.1.1 (LI-COR Inc.) software for quality control. The detailed corrections include 1) the double rotation method for tilt correction used to correct any misalignment of the sonic anemometer to the local wind streamlines; 2) turbulent fluctuations detrended by the block average method; 3) time lag compensation done by the covariance maximization method; 4) density fluctuation compensation by the method of Webb et al. (1980); 5) flux quality check (Mauder and Foken 2006) and footprint estimation (Kljun et al. 2004); 6) high- and low-pass-filtering effect corrections by the method of Moncrieff et al. (2004) and Moncrieff et al. (1997), respectively; 7) statistical tests of raw data screening by the method of Vickers and Mahrt (1997); and 8) error-driven flux random uncertainty estimation by the method of Finkelstein and Sims (2001). The data from several main periods [day of year (DOY) 107–115 and DOY 238–247 in 2013 and DOY 115–123, DOY 129–136, and DOY 201–232 in 2014] were missing because of a power failure of the instruments.

2) Plot experiment and water balance observation

The experimental plots were 3.33 m in length, 2 m in width, and 2 m in vertical depth from the land surface. The plots were geometrically set up at the center of a large homogeneous flat cotton field. Three drip irrigation treatments (nonplastic mulch, 60% plastic mulch, and 100% plastic mulch) were set up on the DOY 118 in 2014. In each treatment, cotton (Gossypium hirsutum L., Xinluzhong-37) was planted at row spacing of 0.3 m, plant spacing of 0.11 m, and density of 26 plants per square meter. There were a total of six rows per plot, where the rows were divided into narrow and wide rows according to row spacing. The two nearest rows with widths of 0.3 and 0.4 m were defined as the narrow and wide row, respectively. In each treatment, a drip line with 11 emitters was placed in the center of each narrow row in the east–west direction. Each narrow row with drip line under the 60% and 100% mulch fraction treatments was covered with transparent polyethylene plastic film.

The cotton plots were irrigated at about 7-day intervals during the growing season, and the irrigation scheme was adjusted in relation to soil moisture and precipitation in the months of June–September. The soil moisture was regularly measured using neutron probe (503DR hydroprobe, CPN International Inc., United States) both before and after an irrigation or precipitation event. The neutron probe was calibrated in advance by the oven-dried method. Using polypropylene random (PPR) access tubes placed in the plots, the soil moisture measurement was taken at 5, 10, 20, 30, 50, 70, 90, 110, 130, and 150 cm soil depth. Three measurements were taken at each depth. Given the patchy surface characteristics of the plots, two PPR access tubes were installed in every plot. One of the access tubes was placed at the center of the middle narrow row and the other at the center of the wide row. The two tubes were generally buried at the approximate geometrical center of each plot. Volumetric soil moisture content of the soil sample around the neutron probe tube at each depth was calculated from measured water content (by weight) and bulk density of the sample. Concurrently, the counts from the neutron probe were also recorded. Then the equations used for calibration analysis were based on the counts and relative volumetric soil moisture content at the same soil depth. Deep percolation reaching the closed bottom of each plot was collected and measured in a calibrated bucket.

c. Other measurements

Air temperature, relative humidity, wind speed, and precipitation were measured at the 2.0-m height above the ground surface using standard automatic instruments in a nearby meteorology station. LAI was directly measured by taking a statistically significant sample of foliage from cotton canopy at seedling stage and indirectly measured every 10 days by hand-held LAI-2000 Plant Canopy Analyzer (LI-COR Inc.) at other growth stages.

4. Results

a. Examination of the model performance with eddy covariance

Validation of the estimated cotton evapotranspiration by the modified Priestley–Taylor model was conducted using daily eddy covariance observations in the years of 2013 and 2014 (Fig. 2). The fitted line for the scatterplot was near the 1:1 line, with a coefficient of determination r2 of 0.86 for 2013 (Fig. 2a) and 0.81 for 2014 (Fig. 2b). The RMSE, d, and r presented in Table 1 suggested that the modified Priestley–Taylor model performed well for the cotton growing season in 2013 and 2014 at daily scale. It was found that the model had a slight overestimation and underestimation for 2013 and 2014, respectively, as suggested by the values of d. The difference in the model performance between 2013 and 2014 was attributed to the variations in LAI and air temperature. It is noted that there is an underestimation for days with evapotranspiration less than 2 mm−1 day in both 2013 and 2014.

Fig. 2.
Fig. 2.

Comparison of daily ET in cotton field estimated by the modified Priestley–Taylor model with that measured by eddy covariance in (a) 2013 and (b) 2014.

Citation: Journal of Hydrometeorology 17, 4; 10.1175/JHM-D-15-0151.1

Table 1.

Statistical results for daily ET in cotton fields estimated by the modified Priestley–Taylor model in comparison with that measured by eddy covariance in 2013 and 2014.

Table 1.

b. Examination of the model performance under different mulch fractions

The modified Priestley–Taylor model was used to estimate cotton evapotranspiration for three different mulch fraction conditions in the year of 2014 (see Fig. 3a). It shows that daily cotton evapotranspiration was the highest under the nonplastic mulch condition during the whole growth stage. Then the 60% plastic mulch fraction had lower cotton evapotranspiration before DOY 170, after which day it was similar to that of nonplastic mulch treatment. The 100% plastic mulch fraction had the lowest cotton evapotranspiration during the whole growth stage. Figure 3b plots cumulative daily cotton evapotranspiration estimated by the modified Priestley–Taylor model and water balance method. The fitted line for the scatterplot was near the upper side of the 1:1 line for both nonplastic mulch and 60% plastic mulch fraction plots. Conversely, the fitted line for the scatterplot was near the lower side of the 1:1 line for the 100% plastic mulch fraction plot. The RMSE, d, and r presented in Table 2 revealed that the estimated cumulative cotton evapotranspiration by the modified Priestley–Taylor model under the three different mulch fractions has a good performance with that calculated by water balance in 2014.

Fig. 3.
Fig. 3.

(a) Daily ET estimated by the modified Priestley–Taylor model in cotton plots under three mulch fractions and (b) comparison of periodical cumulative ET under three different mulch fractions estimated by the modified Priestley–Taylor model with that calculated via water balance 2014.

Citation: Journal of Hydrometeorology 17, 4; 10.1175/JHM-D-15-0151.1

Table 2.

Statistical results for cumulative ET under the different fractions of mulched cotton plots estimated by the modified Priestley–Taylor model in comparison with that calculated by water balance in 2014.

Table 2.

c. Comparison of the modified bulk Priestley–Taylor coefficient under different mulch fraction plots

The modified bulk Priestley–Taylor coefficient was largely different from the 1.26 (see Fig. 4) widely used coefficient for the Priestley–Taylor model. The ranges of the modified bulk Priestley–Taylor coefficient were 0.54–1.71, 0.24–1.88, and 0–1.70 for the nonplastic mulch, 60% for plastic mulch, and 100% for plastic mulch conditions, respectively. The modified bulk Priestley–Taylor coefficient was highest under the nonplastic mulch condition, followed by the 60% and then the 100% plastic mulch conditions before DOY 180. During this period, LAI for the three treatments was relatively small and thus with small canopy transpiration. The magnitude of the bulk Priestley–Taylor coefficient was mainly driven by direct effect of plastic film on soil evaporation. After DOY 180, the modified bulk Priestley–Taylor coefficient, however, was highest under the 60% plastic mulch condition, because the canopy transpiration dominated in total evapotranspiration because of large canopy and LAI. Therefore, it can be deduced that when LAI is low, the bulk Priestley–Taylor coefficient is controlled by mulch fraction. And when LAI is high, it is affected by LAI. After DOY 220, resulting from higher LAI, the modified bulk Priestley–Taylor coefficient for the nonplastic mulch condition was higher than that for the 100% plastic mulch condition. This also was attributed to large canopy and high LAI under the nonplastic mulch condition.

Fig. 4.
Fig. 4.

Comparison of the modified Priestley–Taylor coefficient in cotton plots under three mulch fractions in 2014.

Citation: Journal of Hydrometeorology 17, 4; 10.1175/JHM-D-15-0151.1

d. Effect of LAI and mulch fraction on the modified Priestley–Taylor coefficient

Figure 5 depicts the variations of bulk Priestley–Taylor coefficient under different percentage changes of LAI over the whole growing season. Compared with that under the 60% mulch condition (the common agronomy practice in the study area), the modified bulk Priestley–Taylor coefficient varied from −27% to 20% when LAI fluctuates from −50% to 50%. Figure 6 plots the variations of bulk Priestley–Taylor coefficient along with fluctuations in mulch fraction. Compared with the 60% mulch condition, the modified bulk Priestley–Taylor coefficient varied from 75% to −75% for mulch fraction fluctuating from −50% to 50%. Different from LAI, the effect of mulch fraction on bulk Priestley–Taylor coefficient was mainly evident before DOY 160. This was critical for producers to gauge the proper duration of plastic mulch that ensures optimum water saving. The mean variation in the modified bulk Priestley–Taylor coefficient was nearly 3% for LAI at 10% change in gradient. However, the mean variation in the modified bulk Priestley–Taylor coefficient increased to 11% for mulch fraction change of the same gradient. This suggested that the response of the modified bulk Priestley–Taylor coefficient to variations in mulch fraction was larger than that in LAI.

Fig. 5.
Fig. 5.

Effect of LAI changes (by ±50%; see legend in upper-right corner) on the modified bulk Priestley–Taylor coefficient under 60% mulch fraction during the whole cotton growing season in 2014.

Citation: Journal of Hydrometeorology 17, 4; 10.1175/JHM-D-15-0151.1

Fig. 6.
Fig. 6.

Effect of mulch fraction changes (by ±50%; see legend in upper-right corner) on the modified bulk Priestley–Taylor coefficient under 60% mulch fraction during the whole cotton growing season in 2014.

Citation: Journal of Hydrometeorology 17, 4; 10.1175/JHM-D-15-0151.1

e. Sensitivity and uncertainty analysis of the modified Priestley–Taylor coefficient

The sensitivity coefficients for the bulk Priestley–Taylor coefficient with respect to LAI are positive numbers with a range from 0.06 to 0.37 (see Fig. 7a), indicating the bulk Priestley–Taylor coefficient increases with the increase of LAI. The sensitivity coefficients were larger at the initial (before DOY 160) and late (after DOY 260) stages than at the middle stage. This suggested that the bulk Priestley–Taylor coefficient is relatively insensitive to LAI for large canopy and high LAI conditions. Compared with LAI, the sensitivity coefficients for the bulk Priestley–Taylor coefficient with respect to air temperature were much weaker, ranging from −0.02 to 0.04 and −0.04 to 0.02 for maximum and minimum air temperature, respectively (see Fig. 7b). The sensitivity coefficients for maximum air temperature were negative before DOY 170, and then positive. It is suggested that the bulk Priestley–Taylor coefficient decreases with increasing maximum air temperature at the initial stage, while it increases with increasing maximum air temperature at other stages. By contrast, the changes of sensitivity coefficient for bulk Priestley–Taylor coefficient with respect to minimum air temperature were the reverse. Based on the 95% confidence level, the resulting overall uncertainty in LAI, maximum air temperature, and minimum air temperature was 3.39%, 0.29%, and 0.29%, respectively.

Fig. 7.
Fig. 7.

Sensitivity coefficient for the modified bulk Priestley–Taylor coefficient with respect to the input parameters of (a) LAI and (b) air temperature (maximum temperature Tmax and minimum temperature Tmin) under the 60% mulch fraction cotton plot during the whole growing season in 2014.

Citation: Journal of Hydrometeorology 17, 4; 10.1175/JHM-D-15-0151.1

5. Discussion and conclusions

a. Improvements in model development

Because of its simplicity and robustness, the Priestley–Taylor algorithm is widely used to estimate evapotranspiration for a wide range of vegetation and climatic conditions. Several forms of modification have been proposed for the Priestley–Taylor coefficient based on previous studies. Using an atmospheric boundary model coupled with the Penman–Monteith equation, De Bruin (1983) noted that the Priestley–Taylor coefficient primarily depended on surface resistance. Stannard (1993) separated the contributions of canopy and soil to bulk Priestley–Taylor coefficient and developed another formula driven by LAI and precipitation. These and several other studies paid little attention to plant limitations and plastic mulch conditions. Ding et al. (2013) developed an equation for Priestley–Taylor coefficient mainly based on soil water stress for evaporation under plastic mulch conditions. Although it has been proven to have good performance for maize, the equation required a range of not easily available observation parameters including soil water moisture, field capacity, wilting point, residual water content, and saturated water content. Instead, this study developed a new formula for the Priestley–Taylor coefficient based mainly on energy and plant physiological limitations (expressed in terms of air temperature and LAI) on evaporation under plastic mulch conditions. As a result, the new formula requires only an easily available input meteorological parameter (air temperature), LAI, and fraction of plastic mulch. Therefore, the modified model would have higher operability and potential for application in estimating evapotranspiration, including by remote sensing technology. Moreover, we offered the parameterization scheme for net radiation and soil heat flux, fully considering the modification of plastic film on light and heat transfer. This has not yet been reported and therefore could be valuable for regions where data are largely unavailable, especially in arid areas. Plant physiological limitations in this study were expressed as air temperature and LAI (Fisher et al. 2008). Taking into consideration the performance of the model, it has some errors at initial stages of cotton growth (as shown in section 4a). Thus, there is the need for further studies on other easily available parameters that influence physiological limitations on evapotranspiration.

b. Improvements in model performance

Statistical analyses have shown that the modified model performs well in comparison with eddy covariance at field scale and water balance at plot scale. To further show the performance of the modified model, we made additional analyses by comparing the performance of the modified Priestley–Taylor coefficient with the original coefficient of 1.26. By comparing Fig. 8 with Fig. 2, it can be found that the modified Priestley–Taylor coefficient produced much more accurate evapotranspiration than the original coefficient of 1.26. The modified method has much higher coefficients of determination (0.86 vs 0.49 in 2013 and 0.81 vs 0.45 in 2014) and lower RMSEs (0.81 vs 0.99 in 2013 and 0.80 vs 0.93 in 2014). From Fig. 4, it can also be found that the seasonal variation of the modified Priestley–Taylor coefficient shows a more reasonable growing pattern compared with the original coefficient of 1.26. This indicates that the modified model substantially improves the accuracy of evapotranspiration estimation under plastic mulch conditions. Overall, the modified Priestley–Taylor model proves to be a simple yet a fairly robust, reliable, and acceptable model for estimation of evapotranspiration under plastic mulch conditions.

Fig. 8.
Fig. 8.

Comparison of daily ET in the cotton field estimated by the original Priestley–Taylor coefficient of 1.26 with that observed by eddy covariance in (a) 2013 and (b) 2014.

Citation: Journal of Hydrometeorology 17, 4; 10.1175/JHM-D-15-0151.1

c. Modified bulk Priestley–Taylor coefficient

The variation in the Priestley–Taylor coefficient was large during the whole cotton growing stage, which is consistent with other reports for maize (Ding et al. 2013) and wheat (Lei and Yang 2010). The difference was that the range of variation in the Priestley–Taylor coefficient in this study was larger than that reported in other studies. This was somehow attributed to high atmospheric evaporation in the study area. Consistent with other experimental results (Allen et al. 1998; Ding et al. 2013), our study suggested that when LAI was low, the modified Priestley–Taylor coefficient was low under high mulch fraction. It can also be deduced that plastic mulch can both increase or decrease the Priestley–Taylor coefficient at the middle or late growing stage because of its effects on LAI and canopy development from the results of 60% and 100% plastic mulch fraction plots in this study.

Many factors would affect the Priestley–Taylor coefficient. Former studies had obtained several threshold values influencing the Priestley–Taylor coefficient, such as 3.0 m2 m−2 for LAI and 15–20 mm s−1 for canopy conductance (Ding et al. 2013; Lei and Yang 2010). In their studies, canopy conductance was indirectly obtained by inverting the Penman–Monteith equation. The friction velocity, a parameter for calculating canopy conductance, was measured by the eddy covariance system, which is unavailable for data-scare regions. Thus, there was the need to directly take into account plant physiological limitations in expressing stomata performance. Agam et al. (2010) specifically investigated the effects of LAI and vapor pressure deficit on plant canopy and bulk Priestley–Taylor coefficient. The study showed that the canopy-driven Priestley–Taylor coefficient of 1.3 did not significantly degrade model performance, except under very high vapor pressure deficit conditions. However, it would produce large errors if a constant Priestley–Taylor coefficient of 1.3 was used, as shown by the variations in the estimated values for the different mulch fractions in this study. It was noted that LAI affected bulk Priestley–Taylor coefficient during almost the whole growing season. However, the effect of mulch fraction on bulk Priestley–Taylor coefficient was mainly at the seedling stage. This study suggested that the modified bulk Priestley–Taylor coefficient was more sensitive to the variations in LAI than air temperature. This provided insight not only into the interpretation of water-saving measures under plastic mulch condition, but also the analyses of the effects of changes in temperature or agronomic factors (such as LAI) on evapotranspiration due to climate change or breeding in relation to hydrometeorology.

Acknowledgments

We greatly appreciate Shumin Han, Yanmin Yang, and Zhanyao Lü for their help with the field experiments. We would like to thank Xinyao Zhou, Shaojie Bi, and Shuanliang Guo for their help with programming. We sincerely appreciate the helpful comments and suggestions from Dr. Steven Margulis and the two anonymous reviewers. We are also thankful to Ping Wang, Mingfa Li, and Xiaogang Li for helping us cope with daily challenges during the hot observation season. This study was funded by the International Collaborative Project (2012DFG90290) of China’s Ministry of Science and Technology, Natural Science Foundation of Hebei Province of China (D2015503016), and JSPS project (25302001) of Japan Science Promotion Society (JSPS).

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