Article Type:
Research Article

Temporal Upscaling of Rice Evapotranspiration Based on Canopy Resistance in a Water-Saving Irrigated Rice Field

Xiaoyin Liu College of Agricultural Science and Engineering, and State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, Jiangsu, China

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Junzeng Xu College of Agricultural Science and Engineering, and State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, Jiangsu, China

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Shihong Yang College of Agricultural Science and Engineering, and State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, Jiangsu, China

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Yuping Lv College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou, Jiangsu, China

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Yang Zhuang Changzhou City Urban Flood Control Project Management Office, Changzhou, Jiangsu, China

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Online Publication:
16 Jul 2020
Print Publication:
01 Jul 2020
DOI:
https://doi.org/10.1175/JHM-D-19-0260.1
Page(s):
1639–1654
Free access

Abstract

An important element of the hydrologic cycle, the hydrometeorological parameter of evapotranspiration (ET), is critical in the development of effective water resources planning and irrigation scheduling. The ET varies in response to changes in resistance at the canopy surface rc and soil moisture content θ, especially under water-saving irrigation (WSI) practices. Drawing on data collected by eddy covariance in WSI rice paddies in eastern China in 2015 and 2016, variations in ET were studied by calculating and analyzing hourly canopy resistance rch and daily canopy resistance rcd. Discrepancies were noted between true daily ET ⁡(ETtrd) with respect to the estimated daily ET ⁡(ETrcd) at different periods [0700–1600 local time (UTC + 8)]. To estimate ETrcd in the WSI rice fields, the mean rch value between 0900 and 1000 LT, and between 1000 and 1100 LT performed considerably better than rch for a single time. Seasonal estimated ET ⁡(ETrcs) can be accurately calculated by interpolating rcd at different time intervals, thereby achieving a greater correlation and consistency at 2-day intervals. Then a generalized two-segment line of rcd variation was used to calculate ETrcs, achieving good results and showing that in the absence of observational data, ETrcs could be easily calculated through a simplified pattern of variability. In conclusion, an ET temporal upscaling method for a WSI paddy, based on variation in rch and rcd values, was optimized and is recommended for local application. Future work will focus on temporal upscaling of ET by extrapolating remote sensing instantaneous estimates to daily values.

Corresponding author: Shihong Yang, ysh7731@hhu.edu.cn

Abstract

An important element of the hydrologic cycle, the hydrometeorological parameter of evapotranspiration (ET), is critical in the development of effective water resources planning and irrigation scheduling. The ET varies in response to changes in resistance at the canopy surface rc and soil moisture content θ, especially under water-saving irrigation (WSI) practices. Drawing on data collected by eddy covariance in WSI rice paddies in eastern China in 2015 and 2016, variations in ET were studied by calculating and analyzing hourly canopy resistance rch and daily canopy resistance rcd. Discrepancies were noted between true daily ET ⁡(ETtrd) with respect to the estimated daily ET ⁡(ETrcd) at different periods [0700–1600 local time (UTC + 8)]. To estimate ETrcd in the WSI rice fields, the mean rch value between 0900 and 1000 LT, and between 1000 and 1100 LT performed considerably better than rch for a single time. Seasonal estimated ET ⁡(ETrcs) can be accurately calculated by interpolating rcd at different time intervals, thereby achieving a greater correlation and consistency at 2-day intervals. Then a generalized two-segment line of rcd variation was used to calculate ETrcs, achieving good results and showing that in the absence of observational data, ETrcs could be easily calculated through a simplified pattern of variability. In conclusion, an ET temporal upscaling method for a WSI paddy, based on variation in rch and rcd values, was optimized and is recommended for local application. Future work will focus on temporal upscaling of ET by extrapolating remote sensing instantaneous estimates to daily values.

Corresponding author: Shihong Yang, ysh7731@hhu.edu.cn
Keywords: Evapotranspiration; Hydrometeorology; Soil moisture; Surface fluxes; Crop growth; Vegetation-atmosphere interactions

1. Introduction

Showing great temporal variability, evapotranspiration (ET), a key process in the hydrological cycle, serves as an important link between underlying surface and near-surface turbulence dynamics (Kalma and Calder 1994; Kalma et al. 2008; Wang and Dickinson 2012; Jiang et al. 2016). Key to studying a wide range of ecosystems (Valentijn et al. 2006; Cleugh et al. 2007; Katerji and Rana 2006), ET must be accurately determined at different temporal scales to properly assess an ecosystem’s energy balance (Liu et al. 2017) or to improve an agroecosystem’s water management protocols (Kang et al. 2003; Mu et al. 2011). Variations in meteorological conditions and crop physiology traits result in a significant temporal variation in ET and energy balance (Farah et al. 2004; Gentine et al. 2007). Finding that ET in wheat (Triticum æstivum L.) fields varied significantly across temporal scales, Gentine et al. (2007) noted that canopy coverage and soil moisture content θ were key factors in estimating daily ET (ETd) from hourly ET (ETh) data. Guo et al. (2014) suggested that net radiation strongly affected both diurnal variation in ETh and seasonal variation in ETd, whereas vapor pressure deficit solely and strongly affected ETh. In practice, agricultural water management and hydrometeorological studies generally require ET at daily or longer time scales (Farah et al. 2004; Colaizzi et al. 2006; Tang et al. 2015). However, for large regions and long-term monitoring, ET measurements are labor-intensive and require a large investment in equipment, making the acquisition of accurate daily regional- or global-scale ET estimates a challenge. Remote sensing, which can cope with the spatial variability of surface characteristics, is an ideal tool for acquiring instantaneous spatial ET data at the regional scale, especially in regions with nonhomogeneous vegetation cover and a complex terrain (Verstraeten et al. 2005; Allen et al. 2007; Chowdary et al. 2009). However, as remote sensing only provides primary instantaneous estimates of ET, methods to extrapolate ETd from instantaneous remote sensing observations are needed.

Several methods, including the evaporative fraction method, crop coefficient method, canopy resistance method, Katerji–Perrier, advection-aridity method, and daily sine function, can be used to estimate ETd, based on the assumption that the diurnal course of ET is similar to that of solar irradiance (Shuttleworth 1989; Malek et al. 1992; Zhang and Lemeur 1995; Colaizzi et al. 2006; Allen et al. 2007; Hoedjes et al. 2008; Han et al. 2011; Chen et al. 2013). Shuttleworth (1989) was the first to note that the evaporation fraction, defined as the ratio between latent heat flux and available energy (Rn–G, where Rn is the net radiation and G is the ground heat flux), was constant over a certain period of the day in clear weather, and that the evaporation fraction at noon was close to the daily average. An ET conversion method from ETh to ETd was established with the evaporation fraction as an intermediate variable (Zhang and Lemeur 1995; Hoedjes et al. 2008). Allen et al. (2007) extrapolated ETh to ETd using the crop coefficient as an intermediate variable. With canopy resistance as the intermediate variable, ETd was estimated based on ETh by Liu et al. (2012) in Australia. However, these methods have different applicabilities and strengths given their different theoretical foundations and supportive research.

The canopy resistance rc method, involving the determination of crop-specific rc according to theories of energy balance and aerodynamics applied at different temporal scales, allows a rational upscaling of ET for various crops. In quantitative analysis, the rc value reflects the variation in canopy conditions and represents critical controls on heat and vapor flux transfer through the soil–plant–atmosphere continuum (SPAC) system within the canopy (Finnigan et al. 2003). The ET exhibits its specific variations in response to changes in rc at the canopy surface (Ershadi et al. 2015; Xu et al. 2017). Accordingly, studying variations in rc can provide insights into changes in crop ET. The variability in underlying surface and climate conditions has largely precluded the development of an apparatus or method for the direct measurement of rc at crop surfaces. However, rc can be inversed from results of latent and sensible heat fluxes, radiation balance, and some other relevant variables using the Penman–Monteith (PM) equation (Oue 2005; Katerji et al. 2011). Most studies which have employed rc in achieving a temporal upscaling of ET have been reported for upland crops (Rana et al. 1997; Lecina et al. 2003; Yan et al. 2015), and have played an important role in exploring temporal variability in ET. Liu et al. (2012) was the first to try to upscale daytime ETh [1200–1300 local time (LT; UTC + 8)] to ETd, with rc as an intermediate variable, doing so for corn (Zea mays L.) and canola (Brassica napus L.). Yet, the specific time for ETh measurement which works the best for daily ET estimation is different across sites due to differences in the underlying surface or microclimatic conditions.

Rice (Oryza sativa L.) is the main cereal crop cultivated in China, particularly in the middle and lower reaches of the Yangtze River, which is the largest rice belt in China (Ding et al. 2017). The area planted to rice in this region, and rice extends over roughly 20 × 106 ha, accounting for about 50% of the nation’s rice cropping area (Ministry of Water Resources of China 2016). Impact assessments under different future climate scenarios show solar radiation to be gradually decreasing as is the availability of water resources for rice in south China (Tao et al. 2013; Yang et al. 2014). Seriously challenges of food security and global water scarcity are motivating regulators to adopt water-saving irrigation (WSI) practices for rice cultivation (Belder et al. 2004; Kato et al. 2011). Extensive use of WSI is the inevitable choice of agricultural development in China, and it is also an important in fulfilling rules of “water-saving priority” for water resources management in China. Meanwhile, the widespread implementation of WSI results in changes in energy interception, θ, and crop growth, as well as heat and vapor flux transfer within the rice canopy (Gao et al. 2003; Castellvi et al. 2006; Linquist et al. 2015). Yet information regarding the energy balance and aerodynamics, as well as changes in rc in WSI rice fields, remains unclear. Accordingly, whether a method performs well or not in estimating rice ET should be assessed, as is the selection of the most representative time for rch.

Therefore, the objectives of this study were 1) to explore the diurnal variation (during daytime) of rc for WSI rice; 2) to estimate daily ET ⁡(ETrcd) from rch as an intermediate variable; 3) to select an appropriate time interval for estimating seasonal ET (ETs) based on daily canopy resistance rcd; 4) to propose a generalized seasonal process of rc for the estimation of ETrcs in rice paddies subjected to WSI practice in east China. The results will facilitate the application of the proposed rc upscaling procedure in agriculture and hydrometeorology for estimating ETd at regional scale over WSI rice field from remote sensing data.

2. Materials and methods

a. Site description and field management

Field measurements were conducted during rice seasons in 2015 and 2016 at the Kunshan Irrigation and Drainage Experiment Station (latitude 31°15′15″N, longitude 120°57′43″E), situated in China’s Tai Lake region. This area is subject to a subtropical monsoon climate bringing 1097.1 mm yr−1 in precipitation and generating potential evaporation (measured by an E601 evaporation pan) of 1365.9 mm yr−1. The mean daily temperature Ta and relative humidity (RH) were 24.6°C and 81.5% during rice season, respectively. The volumetric saturated soil moisture θs, field capacity θf, and wilting point θw were 0.502, 0.392, and 0.179 m3 m−3, respectively. Rice seedlings, at interrow and intrarow spacings of 0.23 and 0.16 m, respectively, were transplanted to the field on 27 June 2015 and 1 July 2016. The rice was irrigated when the soil moisture approached a threshold, according to local WSI practices. These varied according to the crop’s phenological stage (Xu et al. 2012). Detailed records of irrigation events are presented in Table 1. Fertilizers and pesticides were applied to the WSI rice field according to the local farming practice.

Table 1.

Irrigation records in WSI rice field in 2015 and 2016.

Table 1.

An open-path eddy covariance (EC) system was installed at the site to measure the water and heat fluxes over flat rice fields with a fetch of about 200 m in all directions. Rice is the unique crop at the station, and is short and of consistent height. The EC system, which was aligned perpendicular to the prevailing southeast wind direction, was made up of a CSAT3A sonic anemometer (Campbell Scientific Inc., United States) and an EC150 open-path infrared gas analyzer (Campbell Scientific Inc., United States) operating at a frequency of 10 Hz, both installed 2.5 m above the soil surface. To ensure the quality and integrity of meteorological data, an EC system and an automatic meteorological station (WS-STD1, DELTA-T, United Kingdom) were employed to measure net radiation Rn, air temperature Ta, wind speed u, atmospheric pressure Pa, precipitation P, soil heat flux Gs, volumetric θ, and soil temperature Ts (measured at depths of 0.10, 0.20, and 0.30 m).

To trigger irrigation, the θ of the 0–0.20-m soil layer was measured daily (when soil was not flooded) at 0800 LT, using time domain reflectometry (TDR; Trase system, Soil Moisture Equipment, United States) and buried waveguides. The soil saturation level θr (as the ratio of θ and θs), water depth Δd, and wetting–drying cycles, as influenced by irrigation and precipitation events in WSI fields in 2015 and 2016, are depicted in Fig. 1. Canopy height h and leaf area index (LAI) were measured for 20 specific plants at 5-day intervals. Daily h and LAI were determined by linear interpolation (Fig. 2).

Fig. 1.
Fig. 1.

Variation of soil moisture conditions and corresponding precipitation P and irrigation I under water-saving irrigation during the rice cropping seasons of (a) 2015 and (b) 2016 (θr and Δd represent soil saturation level and water depth, respectively).

Citation: Journal of Hydrometeorology 21, 7; 10.1175/JHM-D-19-0260.1

Fig. 2.
Fig. 2.

Variation of (a) canopy height h and (b) leaf area index (LAI) under water-saving irrigation in rice, for the 2015 and 2016 seasons.

Citation: Journal of Hydrometeorology 21, 7; 10.1175/JHM-D-19-0260.1

Rice ET at canopy and field scales were measured independently by weighing microlysimeters (ETML) and EC system (ETEC). Three weighing microlysimeters were installed in the WSI rice field, and used to measure hourly ETML ⁡(ETMLh) based on the hourly mass change. The configuration and location of the lysimeters and the method of ETML measurement were described in greater detail in Liu et al. (2018a). In our previous work, slight differences were found in both amplitude and phase between ETML and ETEC because of a spatial scale effect (Liu et al. 2018a). A relationship was developed between measured ETML and ETEC values, such that field scale ET could be calculated from ET measured at the canopy scale, and termed ETtr in the present study. In conclusion, measured ETEC values served to compute canopy resistance by the PM equation, and the ETtr calculated from measured ETML values were used as the true ET, compared with the estimated value, to evaluate the performance of the ET upscaling method.

b. Data analysis and quality control of the EC system

For the data quality control of the EC measurement, raw data (10 Hz) were processed by EdiRe, and necessary corrections (e.g., coordinate rotation via 2D rotation, sonic virtual temperature conversion for sensible heat flux, density fluctuation correction for latent heat flux, spectral loss correction, and spike detection) were implemented following procedures outlined in the literature (Anthoni et al. 2004; Mauder et al. 2006; Ueyama et al. 2012; Masseroni et al. 2013). Flux data were averaged in 30-min blocks. The prevailing wind in the rice growing season is a southeast trade. The source area was estimated based on procedures and parameters selected based on the results of Kljun et al. (2004), along with atmospheric conditions and wind directions (Aubinet et al. 2012). Fluxes were discarded when the calculated footprint was beyond the edge of the study area of WSI paddy field (Masseroni et al. 2012). When the observations exceeded the mean value by more than threefold the standard deviation, it was labeled a spike (Falge et al. 2001a). Likewise, values measured during or within one hour before or after precipitation events were excluded (Anderson and Wang 2014). Flux data were filtered when the friction velocity u* was lower than a threshold of 0.1 m s−1 (Anthoni et al. 2004). Finally, the missing flux date, accounting for approximately 22% over the whole rice season from 2015 to 2016, were determined by linear interpolation (for lacunae ≤ 3 h) or, for long data gaps, by a mean diurnal average method within a 10-day window (Falge et al. 2001b).

To improve the energy balance for EC measurement in the rice field, surface soil heat flux G0 was calculated based on Gs—measured by heat flux plates buried at a depth of 0.08 m—by integrating the soil heat storage Q in soil above the soil heat flux plate, calculated on the basis of soil temperature and moisture data (Meyers and Hollinger 2004; Liu et al. 2017). The daily energy balance ratio (EBR), calculated by using the corrected fluxes, averaged 0.93 and 0.85 in the 2015 and 2016 rice seasons, respectively. Any energy gap is entirely related to the underestimation of sensible and latent heat fluxes (Wilson et al. 2002; Foken 2008; Foken et al. 2011). The energy balance was closed through the evaporative fraction (EF) method (Gebler et al. 2015). The estimated EF values during the 2015 and 2016 rice cultivation seasons are shown in Fig. 3. Then, after the energy balance closure correction, the latent flux (LE) assessed over 30-min intervals and then used to calculate rice ET (Chávez et al. 2009; Gebler et al. 2015).

Fig. 3.
Fig. 3.

Variation of evaporative fraction (EF) under water-saving irrigation in the 2015 and 2016 rice seasons.

Citation: Journal of Hydrometeorology 21, 7; 10.1175/JHM-D-19-0260.1

c. Method for temporal upscaling

1) Hourly-to-daily upscaling

To estimate the ETrcd based on field measurement at a specific hour, with rch as an intermediate variable, Eq. (1) was used to calculate the daytime hourly rch for 0700–0800, 0800–0900, 0900–1000, 1000–1100, 1100–1200, 1200–1300, 1300–1400, 1400–1500, and 1500–1600 LT (UTC + 8) based on hourly ETEC and meteorological variables. Then, the hourly ETECh measurement at each specific hour was extended to a daily scale through the canopy resistance method, using daily meteorological data [Eq. (2)] (Malek et al. 1992; Liu et al. 2011):

rch=rah[Δh⁡(Rnh−G0h)+ρhCp⁡(esh−eah)rch−λhETECh⁡(Δh+γh)]γhλhETECh,
λdETrcd=Δd⁡(Rnd−G0d)+ρdCp⁡(esd−ead)radΔd+γd⁡(1+rchrcd),

where d and h as superscripted letters indicate the parameter’s daily- and hourly-averaged values, respectively; ea is the actual vapor pressure (kPa); es is the saturation and vapor pressure (kPa), where es − ea is the vapor pressure deficit (VPD); ra is the aerodynamic resistance of water vapor transfer from the surface to ambient air (s m−1); rc is the canopy resistance of water vapor transfer from the surface to ambient air (s m−1); Cp is the specific heat capacity of air, Cp = 1.013 × 10−3 MJ kg−1 °C−1; ETEC is the evapotranspiration measured by systems (mm); ETML is the evapotranspiration measured by microlysimeters (mm); ETrcd is the daily evapotranspiration (mm) estimated by upscaling; G0 is surface soil heat flux (MJ m−2 s−1), where G0 = Gs + Q, with Gs being the soil heat flux measured at 0.80 m beneath the soil surface and Q being the change in soil heat storage in the 0–0.80-m surface soil layer; P is the atmospheric pressure (kPa); Rn is net radiation (MJ m−2 s−1); Ta is the average temperature (°C); γ is the psychometric constant (kPa °C−1), γ = 0.001 63 P/λ; λ is the latent flux of heat (MJ kg−1), λ = 2.501 − (2.361 × 10−3)Ta; ρ is the density of dry air (kg m−3); and Δ is the slope of the saturation-to-vapor pressure curve (kPa °C−1).

Assuming that samples passing quality control were generally near neutral atmospheric stability, the aerodynamic resistance ra is calculated at either an hourly rah or daily rad time scale, based on hourly or daily average wind speeds [Eq. (3)] (Alves et al. 1998):

ra=lnzm−dz0m lnzh−dz0hk2u

where d is zero-plane displacement height (m), with d = 0.63h; h is the rice canopy height (m); k is von Kármán’s constant (0.41); u is wind speed at 2.5 m above the soil surface (m s−1); zh is the height of relative humidity measurements (m); zm is the height of wind measurements (2.5 m in the EC system); z0h is the roughness length governing transfer of heat and vapor (m), z0h = 0.1z0m; and z0m is roughness length governing momentum transfer (m), z0m = 0.123h.

2) The daily-to-seasonal upscaling

In both 2015 and 2016, Eq. (4) was used to calculate the rcd at sparse specific days based on ETrcd measured by EC ⁡(ETECd) after energy balance correction, along with meteorological variables of rice growth period. For days without ETECd measurements, rcd was calculated by linear interpolation between two adjacent known values of rcd, prior to ETrcd being calculated according to rcd and daily meteorological data. Assuming ETECd to be measured at intervals of 2, 5, 10, 15, and 20 days, rcd values on these days were calculated first, and then for days without ETECd measurement rcd values were interpolated. In the end, ETrcd values over the full rice growing season were estimated and averaged as seasonal average daily ET ⁡(ETECs) by Eq. (5) (Malek et al. 1992; Liu et al. 2011):

rcd=rad[Δd⁡(Rnd−G0d)+ρdCp⁡(esd−ead)]rad−λdETECd⁡(Δd+γd)γdλdETECd,
ETrcs=1λdm∑k=1k=m[Δkd⁡(Rnkd−G0kd)+ρkdCpk⁡(eskd−eakd)rakdΔkd+γkd⁡(1+rckdrakd)],

where k represents the day of the season; m is the total number of days in the season; s and h superscripted letters indicate the parameter’s seasonal- and daily averaged values, respectively; and ETrcs is the calculated seasonal average daily value during the rice growing season (mm day−1).

d. Statistical analysis

The ETtr calculated from the measured ETML values were used as the true ET, to compare with estimated upscaling value. Linear regression slope, coefficient of determination (R2), root-mean-square error (RMSE), and index of agreement (IOA) were used to assess the performance of the temporal upscaling method, and reveal the agreement between the estimated and true ET:

R2=[∑i=1i=n⁡(Oi−O¯)⁡(Pi−P¯)∑i=1i=n⁡(Oi−O¯)2∑i=1i=n⁡(Pi−P¯)2¯]2,
RMSE=∑i=1i=n⁡(Pi−Oi)2N,
IOA=1−∑i=1i=n⁡(Pi−Oi)2∑i=1i=n⁡(|Pi−O¯|+|Oi−O¯|)2¯ ,

where n is the number of samples; Pi and Oi are the ith estimated and true values, respectively, where i = 1, 2, 3, …, n; and P¯ and O¯ are the mean estimated and true values, respectively.

3. Results and discussion

a. Daily ET ⁡(ETrcd) estimated based on hourly canopy resistance rc

1) Variation in hourly canopy resistance ⁡(rch) during daytime

Diurnal variation of mean rch in rice season is shown in Fig. 4. In the morning (0700–0800 LT), rch was negative, and then increased gradually to be positive during 0800–0900 LT. Then, rch was almost constant from 0900 to 1200 LT, before a slight decrease between 1200 and 1300 LT. This is owing to increased stomatal conductance at noon when the light is strongest (Alves et al. 1998; Allen et al. 2006). After this, rch tended to increase rapidly, more than 150 s m−1 at 1500–1600 LT both in 2015 and 2016. Theoretically, canopy resistance should be high in the morning and evening, due to the lower light intensity and leaf stomatal conductance. However, the rch in the morning was extremely low (even less than zero prior to 0800 LT), and the average rch was 35 s m−1 with little variation during morning hours (0900–1200 LT). A result of rc < 0 in current study (circled in red in Fig. 4) is the result of inversion by the PM equation, which is an artificial effect of the algorithm. Specifically, vapor condensation occurred in early morning within the rice field when the air humidity was high, especially before sunrise (generally RH higher than 95%) (Malek et al. 1999; Kabela et al. 2009; Hanisch et al. 2015; Liu et al. 2018b). Meanwhile, the soil hygroscopic water (during the nonflooding period in WSI rice paddy) was easy to produce in which the air humidity was high, and it accumulated prior to sunrise (Verhoef et al. 2006; Zhang et al. 2015). That favored the process of evapotranspiration over a short period after sunrise. As a result, the measured actual ET increased, and the rch, inversed from actual hourly ET by the PM equation is extremely low. Similar results were reported by Malek et al. (1992), Allen et al. (2006), and Perez et al. (2006), who found that rch was negative or had no defined value in the early morning. Thus, canopy resistance inversed by the PM equation should be treated seriously and cannot be derived simply when dew formation occurs or when leaves are covered with dew.

Fig. 4.
Fig. 4.

Diurnal variation in average hourly canopy resistance rch during daytime in the 2015 and 2016 rice seasons. Note: 1) The abscissa in the figure at the label 8:00 represents the eigenvalue of the period 0700–0800 LT, and so on. 2) The result of <0 during the period of 0700–0800 LT is an artificial effect of the algorithm, making no physical nor physiological sense. 3) Error bars represent the standard error of the mean.

Citation: Journal of Hydrometeorology 21, 7; 10.1175/JHM-D-19-0260.1

It should also be noted that rch tended to increase, with high values in the afternoon. This phenomenon is partially ascribed to the hourly time course of the environmental variables in the afternoon. The values of rch, which were influenced by climatic factors, increased drastically after 1300 LT, showing an opposite variation to Rn − G0 and a similar variation to Ta or VPD (Fig. 5). In fact, canopy resistance is subject to the variation in Rn − G0 (or Rn) in two ways: (i) crop stomatal conductance decreases with a decrease in radiation intensity; and (ii) as the source of energy for evaporation and transportation in the field energy balance, a decrease in Rn − G0 tends to result in low rch in the afternoon. Clearly, canopy resistance also depends highly on VPD (Fig. 5). When the VPD increases, i.e., Ta increases while the air humidity decreases, the air water potential is lower than the leaf water potential, resulting in the increase of water loss by transpiration and the decline in leaf water potential. With the decrease of the leaf–air water potential difference, the transpiration rate is limited and the canopy temperature increases, which causes a relatively high rch in later afternoons. The increase tendency in rice rch in the afternoon agrees well with results on grass, either in semiarid or Mediterranean climates, that showed that hourly canopy resistance increased in the afternoon in an irregular parabolic pattern (Todorovic 1999; Lecina et al. 2003; Allen et al. 2006; Perez et al. 2006). Results on upland crops (soybean or winter wheat) whose canopy resistance increased in the afternoon with the largest increment occurring during sunset (Bailey and Davies 1981; Hu et al. 2005).

Fig. 5.
Fig. 5.

The diurnal variation of average hourly (a) available energy (Rn − G0), (b) vapor pressure deficit (VPD), and (c) air temperature Ta during daytime in the 2015 and 2016 rice seasons.

Citation: Journal of Hydrometeorology 21, 7; 10.1175/JHM-D-19-0260.1

2) Estimating ETrcd from rch at a specific time

Daily simulated rice ET (i.e., ETrcd), was calculated from daily meteorological data and rch at different daytime hours [Eq. (2)]. Performance of ETrcd calculations against the true ETtrd in the 2015 and 2016 rice season is shown in Fig. 6. For ETECd estimated from rch at specific times from 0700 to 1600 LT, the regression slope between ETrcd and ETtrd decreased gradually, with the maximum values of 1.201 and 1.189 at 0700–0800 LT in 2015 and 2016, and minimum values of 0.805 and 0.851 at 1500–1600 LT, respectively. Correspondingly, ETrcd calculated based on rch at different hours reduced gradually from values greater than the true ETtrd to values inferior to it, i.e., from 4.801 to 3.118 mm day−1 in 2015 ⁡(ETtrd=3.835 mm day−1), and from 4.671 to 3.299 mm day−1 in 2016 ⁡(ETtrd=3.816 mm day−1). The error of the estimated ETrcd was large when it was calculated with rch at sunset or sunrise (Fig. 6). The ETrcd, estimated with rch from 0900 to 1000 LT or 1000 to 1100 LT, matched well with ETtrd. The correlations between ETrcd and ETtrd were the best in those periods, with high R2 (>0.90) and IOA (>0.97), and low RMSE (<0.51 mm h−1).

Fig. 6.
Fig. 6.

Average diurnal variation in model performance based on statistical indexes (slope, RMSE, R2, and IOA) for ET estimation during daytime in the 2015 and 2016 rice seasons.

Citation: Journal of Hydrometeorology 21, 7; 10.1175/JHM-D-19-0260.1

The reason these two hours provide the best estimation may be related to the neutral stability assumption for the atmospheric boundary layer. In several current studies on ra model implementation, neutral atmospheric stability conditions have been assumed rather than actual stability conditions (Brunet et al. 1994; Anadranistakis et al. 2000; Patton et al. 2016). Results showed that an acceptable accuracy in ET estimation was achieved when it was estimated at weekly or longer intervals or scale (Anadranistakis et al. 1999). This suggests that the assumption of neutral stability was easily satisfied. However, when ET was estimated on a short time scale (intraday variation), the actual atmospheric stability conditions should be taken into account (Dupont and Patton 2012; Liu et al. 2015), although some studies have shown that it is feasible to neglect the correction of atmospheric stability in calculating crop ET (Van Zyl and De Jager 1987; Zhou et al. 1994).

The frequency of atmospheric stability (neutral stability, stable and unstable situations) are generally associated with diurnal variation. Stable conditions mainly occur at night, while unstable conditions may dominate around noon. From night to daytime, the atmospheric stability varies from stable to unstable, and the occurrence of neutral stability conditions are observed to be dominant in the morning (0900–1100 LT) and afternoon (1400–1600 LT). During other periods, the boundary layer is often either unstable or stable, which violates the neutral stability assumption, and consequently the equation of ra is invalid. In addition, considering the tendency in rch variation is smallest from 0900 to 1100 LT, it is preferred for temporally upscaling rice ET from hourly to daily.

3) Improving the performance in ETrcd estimation

According to the results in Fig. 6 and Table 2, the ETrcd estimated based on rch during 0900–1000 LT or 1000–1100 LT matched ETtrd well, compared with other specific hours. Furthermore, the average value of rch during 0900–1000 LT and 1000–1100 LT performed much better in ETrcd estimation than the rch from a single hour (either 0900–1000 LT or 1000–1100 LT) in a WSI rice field (shown in Fig. 6 and Table 2). For the 2015 dataset, the estimated ETrcd was 3.789 mm day−1; the RMSE was 0.422 mm day−1, and the R2 and IOA were 0.934 and 0.983, respectively, based on rch averaged across the period of 0900–1100 LT. For the 2016 dataset, the calculated value was also in acceptable agreement with the true value: R2 = 0.945, RMSE = 0.431 mm day−1, and IOA = 0.988. Therefore, one can improve the predictive performance of rice ETrcd estimation in WSI fields by averaging the rch across the periods of 0900–1000 LT and 1000–1100 LT.

Table 2.

Performance of the ET estimation by the canopy resistance method for a WSI rice field.

Table 2.

b. Seasonal ET ⁡(ETrcs) estimated based on daily canopy resistance ⁡(rcd)

1) Seasonal variation of rice rcd

Seasonal variation of daily rice rcd inversed by ETECd in 2015 and 2016 is shown in Fig. 7. During the first 100 days after transplantation, the value of rcd fluctuated in a narrow range around the average value over this period (41.8 and 39.3 s m−1 in 2015 and 2016, respectively), which was much lower than the value of 70 s m−1 of a reference crop surface (Allen et al. 1989; Todorovic 1999). In the maturity period at the end of the rice season (100+ days after transplanting), rcd increased linearly with time up to a value above 200 s m−1 when soil moisture declined, and the rice canopy showed gradual senescence.

Fig. 7.
Fig. 7.

Daily rice canopy resistance rcd calculated inversely based on EC measured ETECd in (a) 2015 and (b) 2016, corresponding to variation in soil moisture conditions θ.

Citation: Journal of Hydrometeorology 21, 7; 10.1175/JHM-D-19-0260.1

Notably, the variation of rcd in a WSI rice field was different from that of grass under optimal water conditions, as well as that of upland crops. For grass, rcd varied in a parabolic pattern, with rcd at the beginning and end of the year being much higher than rcd in June to July (minimum of 45 s m−1) (Todorovic 1999). For upland crops, lower θ and lower canopy coverage in early growth stages resulted in low evaporation and crop transpiration; consequently, the value of rcd was relatively large (Irmak et al. 2013; Bastidas-Obando et al. 2017). However, in the WSI rice field, evaporation from the interplant (soil or water) surface was high in the early stage (regreening and early tillering stages) when the temperature and radiation were higher. The rcd, inversed by PM (characterized as a single-source “big leaf” model by which the sources of heat and water vapor from rice field were considered to occur at a single level within the canopy), was generally smaller than that of upland crops. In middle phenological stages, when rice growth was vigorous and crop ET was high, rcd was minimal. Since the θ is much greater in a WSI rice field than in upland fields, the rice rcd was smaller than that of upland crops and grass (Lecina et al. 2003; Jiang et al. 2016; Bastidas-Obando et al. 2017). In the rice crop’s mature period, the leaves’ ability to transpire weakens; meanwhile, Rn decreases and θ is relatively low, resulting in a low ET. Accordingly, the calculated rcd increased. The increasing tendency in the rice crop’s rcd at the mature stage was in close agreement with rcd values for upland crops (Lecina et al. 2003; Bastidas-Obando et al. 2017).

In 2015 and 2016, on days when the field was flooded or the soil at saturation, the average rcd values were 32.2 and 33.1 s m−1, respectively. These values were inferior to the seasonal average value for rcd (52.3 and 50.4 s m−1 in 2015 and 2016, respectively) and much lower than the average rcd for days without flooding water (62.3 and 58.3 s m−1 in 2015 and 2016, respectively). On days without flooding water in the WSI rice field, rcd increased with a decrease in θ from θs to θf or an even lower moisture level (Fig. 7). Similar results, where rcd was generally low on days with sufficient soil moisture were noted in different ecosystems: e.g., agricultural crops, pastures, forest, and bare soil (McNaughton and Jarvis 1991; Zhang and Lemeur 1995).

2) Estimating ETrcs by interpolating rcd at different intervals

Based on the ETECd measured by EC at intervals of 2, 5, 10, 15, and 20 days, seasonal rice evapotranspiration ETrcs was estimated at these different time intervals. The calculated values were underestimated to a certain extent (approximately 0.3 mm day−1) compared with ETtrs (Table 3). The regression slopes between the estimated and true values ranged between 0.892 and 0.922. Generally, the correlations were acceptable both in 2015 and 2016, with the R2 greater than 0.90 and 0.93, RMSE less than 0.47 and 0.49 mm day−1, and IOA up to 0.97 and 0.98, respectively.

Table 3.

Statistics for the performance of the upscaling method over the full growth period of the rice crop.

Table 3.

Theoretically, the longer the interval, the more likely it is to misrepresent the rcd of the whole season. The correlation and consistency between the estimated and true values were higher at 2-day intervals. The accuracy of estimation was slightly reduced for intervals of 5, 10, 15, and 20 days, but the difference in performance among different intervals was not clear and the simulation results were also good, because the seasonal variability pattern of rcd was simple and consistent. Specifically, the ETrcs estimated with a 20-day interval was almost the same as the result with 5-day interval, and was closer to ETtrs than ETrcs estimated with 10- or 15-day intervals with 2015 dataset.

Moreover, a fixed rcd value, the seasonal average rcd of 52.3 and 50.4 s m−1 in 2015 and 2016. respectively, was used to estimate the ETrcs, and the variation of rcd was generalized as a two-segment line (red dotted line in Fig. 7) and was compared with the results from the canopy resistance method shown in Table 3. The ETrcs, computed from the fixed rcd value with regression slopes of 0.886 and 0.891 in 2015 and 2016, respectively, was smaller than values estimated by the varied rcd and the true values, although the correlation was also very good. The ETrcs computed based on the generalized rcd were more accurate and consistent, compared with some interpolation results. The ETrcs values of 3.570 and 3.547 mm day−1 in 2015 and 2016, respectively, showed RMSE values of 0.438 and 0.468 mm day−1, R2 of 0.910 and 0.934, and IOA of 0.974 and 0.980. In general, ETrcs in WSI rice field can be accurately estimated by the upscaling method, which is recommended over linear interpolation for longer intervals, since its accuracy is not significantly reduced and the data inputs can be effectively reduced. Additionally, the ETrcs simulation based on the generalized rcd was also an effective and easy method when there was a lack of measured data.

3) The generalized rcd line for ET estimation

The overall variability pattern of rcd was simplified as a two-segment line during the WSI rice season (Fig. 7). The two-segment line can be described as 1) constant for the first 100 days after transplanting and 2) a linear increase during the maturity stages after 100 days from transplanting. According to the local calibrated results for 2015 and 2016, the two-segment line can be expressed in Eq. (9), where d represents the number of days after transplanting. This was used to calculate the ETrcs in the WSI paddy and was compared with the ETtrs values in the same years, as shown in Fig. 8. For the 2015 dataset, the four accuracy indicators, slope, R2, RMSE, and IOA had values of 0.915, 0.910, 0.441 mm h−1, and 0.974, while in 2016 these values were 0.912, 0.933, 0.470 mm h−1, and 0.980, respectively. The overall result was even better than the estimation through the rc upscaling method by linear interpolation over longer intervals (10-, 15-, or 20-day intervals), which indicated that the ET of WSI paddy can be calculated accurately through the simplified variability pattern of rcd in the absence of observed data:

rcd={40.6, d≤100,5d−459.45, 100<d≤120.
Fig. 8.
Fig. 8.

Regression analysis of the simulated daily ET ⁡(ETtrd) calculated based on the generalized rcd line and true ET ⁡(ETtrd) in the rice seasons of (a) 2015 and (b) 2016.

Citation: Journal of Hydrometeorology 21, 7; 10.1175/JHM-D-19-0260.1

The linear equation [Eq. (9)] for estimating rice rcd of is much simpler than the empirical model used for other types of vegetation (Kelliher et al. 1995; Alves and Pereira 2000; Liu et al. 2012; Yan et al. 2015). It is simple and performs well in calculating rice ET in the east China, but the constant rc in the first 100 days of rice growth is very hard to assess since the vegetation’s canopy resistance varies with prevailing climatic conditions (Ortega-Farias et al. 2010; Zhao et al. 2015). Furthermore, if this simple equation, which is believed to be a local result, performs acceptably or not in other locations remains unknown. To plan rational irrigation, more work needs to be carried out at other sites to find generic methods of rcd estimation with fewer measurements.

4. Conclusions

With canopy resistance rc as an intermediate variable, rice ET was upscaled temporally either from hourly to daily or from daily to seasonal, based on diurnal variation of hourly rc ⁡(rch) and seasonal variation of daily rc ⁡(rcd) The daily ET ⁡(ETrcd) estimated with rch during the hours of 0900–1000 LT or 1000–1100 LT showed close agreement with the true value ⁡(ETtrd). Moreover, in an WSI rice field, the average rch value over the periods of 0900–1000 LT and 1000–1100 LT combined performed much better in ETrcd estimation than the rch from a single hour. For daily-to-seasonal upscaling, the ETrcs calculated by interpolating rcd at different time intervals underestimated rice ET to a certain extent compared with ⁡(ETtrs), with a 2-day interval offering the best performance. A generalized two-segment line can be used for depicting the seasonal variation of rcd and estimating ETrcs. In conclusion, canopy resistance (rc) is a test competent in estimating rice ET by upscaling hourly ET to daily ET or upscaling daily ET to seasonal ET. Hourly rc measured during the hours of 0900–1000 LT and 1000–1100 LT is suitable for estimating daily ET based on instantaneous estimates of ET by remote sensing. In case of sparse data availability, seasonal ET of rice can be estimated by linear interpolation the rcd, or by calculating rcd with a simple two-segment linear equation. Future validation will be conducted to estimate rice ET with more field measurements in a greater variety of stations, or with remote sensing data.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (51809075), the Natural Science Foundation of Jiangsu Province (BK20180506), the Fundamental Research Funds for the Central Universities (B200202097) and the Postdoctoral Science Foundation of China (2019M651680). The authors declare no conflict of interest.

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