Evaporative fraction and its application in estimating daily evapotranspiration of water-saving irrigated rice field

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Research papers

Evaporative fraction and its application in estimating daily evapotranspiration of water-saving irrigated rice field ⁎

Xiaoyin Liua,b,c, Junzeng Xua,b,c, , Xinyi Zhoua, Weiguang Wangb, Shihong Yanga,b,c a

College of Agricultural Engineering, Hohai University, 210098 Nanjing, Jiangsu Province, People’s Republic of China State Key Laboratory of Hydrology-water Resources and Hydraulic Engineering, Hohai University, 210098 Nanjing, Jiangsu Province, People’s Republic of China c Cooperative Innovation Center for Water Safety & Hydro Science, Hohai University, 210098 Nanjing, Jiangsu Province, People’s Republic of China b

A R T I C LE I N FO

A B S T R A C T

This manuscript was handled by Marco Borga, Editor-in-Chief, with the assistance of Sally Thompson, Associate Editor

Evaporative fraction (EF), which is known to exhibit variation in response to changes in crop species, soil and meteorologic conditions, plays an important role in interpreting the components of energy budget and estimating evapotranspiration (ET), while such information is scarce for humid rice fields. The present study discussed the variation of energy balance components and then examined the pattern of hourly, daytime and daily EF after monitoring energy components by eddy covariance for water-saving irrigated (WSI) rice paddies of 2015 and 2016. Then the daily ET was estimated by an improved EF up-scaling method in the subtropical monsoon climate region of East China. Diurnally, hourly EF is deemed as an approximately concave-up shape in different growth stages of rice season. The seasonal average EF varies gently, with a minimum around 10:00–11:00 AM. Seasonally, the mean daytime EF for the whole growth stage is 0.86, 7% lower than the daily value. Daily EF exhibits mostly higher than 0.8 except later yellow ripening period, approaching 1.0 in the milk stage. EF over WSI rice exhibits obviously greater than the reports that from upland crops. In addition, differences are noted in the results with respect to the daily ET estimation by EF up-scaling method. The estimated daily ET (ETEF,d) from hourly EF during 10:00–11:00 h is highly correlated to the measured ET (ETtrue) by the weighed micro-lysimeters though the ETEF,d value is underestimated. Such a considerable gap serves in forming a relationship between ETEF,d and ETtrue,d, that is, by simply multiplying the representativeness ET value based on the EF up-scaling method by a correction procedure calibrated for this region. In conclusion, an improved EF up-scaling method is proposed for extrapolating remote sensing based ET estimates to daily values.

Keywords: Rice Evaporative fraction Evapotranspiration Available energy Up-scaling method

1. Introduction More than 65% Chinese population take rice as the staple food, however, the impact of climate change is intensifying the contradiction between water supply and water consumption in rice field (Zhang et al., 2005; Tao et al., 2013; Yang et al., 2014; Ling et al., 2019). The middle and lower reaches of the Yangtze River is the largest rice belt in China (Peng et al., 1995; Ding et al., 2017; Wang et al., 2017), with about 20 million hm2 planting area of rice, accounting for about 50% of the national rice cropping area (National Bureau of Statistics of China, 2016). Meanwhile, the impact assessment with different climate scenarios showed that the solar radiation is gradually decreasing and the availability of available water resources for rice in south China is decreasing (Tao et al., 2013; Yang et al., 2014). That means climate change will seriously challenge the rice production and food security

(Lv et al., 2018; Ling et al., 2019). In addition, although the total water consumption in China has been increasing slowly since 1949, the proportion of agricultural water consumption in total water consumption has been decreasing year by year. In 1949, 1980 and 2000, the proportion of agricultural water consumption in total water consumption was 97.1%, 84.3% and 68.8%, respectively, and decreased to 61.3% by 2011 (Wang et al., 2010). The contradiction between water supply and water consumption, the impact of climate change and the challenge of food security 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 only choice of agricultural development in China, and it is also an important manifestation of the idea of water control (“water saving priority”) in China. The rice WSI practices applied more than 16.7 million ha in some provinces in China (Jiangsu,

⁎ Corresponding author at: State Key Laboratory of Hydrology-water Resources and Hydraulic Engineering, Hohai University, 1 Xikang Road, Nanjing 210098, People’s Republic of China. E-mail address: [email protected] (J. Xu).

https://doi.org/10.1016/j.jhydrol.2019.124317 Received 17 July 2019; Received in revised form 23 October 2019; Accepted 3 November 2019 Available online 11 November 2019 0022-1694/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Xiaoyin Liu, et al., Journal of Hydrology, https://doi.org/10.1016/j.jhydrol.2019.124317

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variable daytime EF in the upscaling of instantaneous ET data. In practice, the EF over the course of a daytime is essentially time-dependent and can be highly depends on soil moisture availability, canopy cover fraction, stages of development, relative humidity, as well as the biological characteristics of vegetation in an area (Dirmeyer et al., 1999; Wever et al., 2002; Gentine et al., 2007; Chávez et al., 2009; Hoedjes et al., 2008), whereas the surface energy budget affects the microclimate of the vegetation canopy (Hossen et al., 2012). Thus, there is moreover no consensus on the general trend of daytime EF fluctuations, which can vary for a given location (Van Niel et al., 2011). Gentine et al. (2007) investigated that the self-preservation of daytime EF should be revised, and a concave-up shape of EF was obtained with more representative. Hoedjes et al. (2008) underlined that the daytime EF remained fairly constant under dry conditions while followed a concave-up shape under wet conditions. Allen et al. (2007) presented that the hourly EF observed for the clipped grass showed continuing decline, while showed pronounced rise for sugar beets in the afternoon. Selecting the most representative hourly EF properly is essential in estimating daily ET by upscaling the instant result by remote sensing, since EF varied greatly in the daytime. Yet, the time with the most representative varied among sites and underlying surface. Most studies suggested that EF around noon or the daily average performed acceptable (Sugita and Brutsaert, 1991; Brutsaert and Sugita, 1992; Kustas et al., 1994; Shuttleworth et al., 1989; Chávez et al., 2009). Yet, some studies shown that non-noon moments are more representative (Stewart et al., 1996; Li et al., 2008). But a considerable gap between the estimated (either based on noon time or non-noon hourly EF) and measured daily ET always exists. For EF around noon, it was found underestimate daytime ET by 5–10% compared with the measurements by Bowen ratio (Sugita and Brutsaert,1991), or with an underestimation 0.3 mm day−1 for corn ET by eddy covariance energy balance systems (Chávez et al., 2009). It also underestimated daily ET by 8% compared to the daytime average EF (Kustas et al., 1994). When it comes to nonnoon EF, Li et al. (2008) demonstrated the daytime ET estimated by EF during 14:00–15:00 h was highly correlated to the measured ET, but a considerable underestimation still existed. Previous studies on EF upscaling method involved several vegetation land surfaces, yet information regarding the components of energy budget and the diurnal pattern of EF in WSI rice fields, as well as its application for rice ET estimation, remains unclear. Moreover, if the method developed in other land surfaces performed well or not in WSI rice field should be investigated, as well as the most representative time in hourly EF selection. This study therefore aims to (1) analyze diurnal pattern of hourly EF, and seasonal variation of daily or daytime average EF over WSI rice based on measurement by eddy covariance energy balance systems; (2) investigate the representativeness of time-of-day EF in estimating daily ET, which enable accurate prediction of regional ET for WSI rice in the Yangtze Basin. The results will facilitate the application of the proposed EF upscaling procedure in agriculture and hydrology for estimating daily ET at regional scale over WSI rice field from remote sensing data.

Zhejiang, Anhui, Jiangxi, Heilongjiang, Jilin, etc.), more than 50-percent of the China's rice fields (Peng and Xu, 2012). Meanwhile, the widespread implementation of WSI has led to drying-wetting cycles which results in the changes in the energy interception and partition, soil moisture 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). Water management based on crop water requirements is the fundamental requirement and central mission in regional agriculture, which can be detected by the accurate calculation of crop evapotranspiration (ET) (Li et al., 2008; De Oliveira et al., 2009; Bezerra et al., 2015). ET is a key process in the hydrological cycle and a key linkage between underlying surface and near-surface turbulence dynamics, which shows great temporal and spatial variability because of complex interactions between soil, vegetation and climate (Allen et al., 2007; Kalma et al., 2008; Wang and Dickinson, 2012; Hao, 2016; Jiang et al., 2016). Extensive use of WSI will change ET, thus it is very important if we knew and accurately estimate ET. The crop ET has been estimated from several methodologies such as water balance (Malek and Bingham, 1993; Choudhury et al., 2013), lysimeter (Tyagi et al., 2000; Anapalli et al., 2016), and micrometeorological methods like eddy covariance (Hossen et al., 2012; Yang et al., 2016) and Bowen ratio energy balance (Zhang et al., 2010; Escarabajal-Henarejos et al., 2015). However, these methods, required heavy workloads or many expensive investments for large regions and long-term observation, assume homogeneous vegetation cover and structure (Li et al., 2012), which makes accurate daily ET estimation at the regional and global scales a challenge. Remote sensing, without these problems, can cope with the spatial variability of surface characteristics, which is ideal for deriving spatially continuous fields of instantaneous ET data using energy balance components at the regional scale (Verstraeten et al., 2005; Allen et al., 2007; Chowdary et al., 2009). Then the data are often used in the prediction of daily ET, irrigation scheduling, water resources planning, water regulation, and are essential components of general hydrologic and soil moisture models. In practice, any attempt to improve the efficiency of agricultural water management and examine the water and energy balance transmission should be based on reliable estimates of daily ET (Delogu et al., 2012; Liu et al., 2017). That is to say, instantaneous ET are relatively unimportant unless they can be used to predict daily ET. Thus, methods for daily ET extrapolation from instantaneous observations using remote sensing are needed, which may be an effective approach to resolve the problems that Remote sensing only provides essentially instantaneous estimates of ET, and the upscaling relationship should be investigated and demonstrated by studies that used primarily local (in situ) observations. Upscaling hourly ET to daily ET based on remote sensing data is the most popular method to estimate regional daily ET. Several methods, including evaporative fraction (EF) method, crop coefficient method, canopy resistance method, Katerji-Perrier, advectio-aridity method, and daily sine function, can be used for the estimation of daily ET, based on the assumption that the diurnal course of ET is similar to that of solar irradiance (Shuttleworth et al., 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., 2013Chen et al., 2013). The evaporative fraction (EF, defined as the ratio between latent heat flux and available energy at the land surface), is an important parameter, reflecting the distribution of surface available energy and interpreting the components of energy budget. It can be derived based the micrometeorological data in conjunction with remotely sensed measurements to determine ET. The EF method is one of the most popular schemes for temporal upscaling. The effectiveness of the EF method has been investigated by numerous studies that used local available energy observations and assumed that EF was relatively constant during the daytime (Jackson et al., 1983; Shuttleworth et al., 1989; Brutsaert and Sugita, 1992; Kustas et al., 1993; Sobrino et al., 2007; Ryu et al., 2012; Tang et al., 2017). Additional studies have done to incorporate a

2. Materials and methods 2.1. Site description The study site is a paddy field at the Kunshan Irrigation and Drainage Experiment Station (N 31°15′15″, E 120°57′43″), which is located in the Tai-Lake region of China. This 200 m × 150 m field has been used exclusively for paddy cultivation for about 10 years. The soil is hydragric anthrosol, with a bulk density of 1.30 g cm−3. The site is in a subtropical monsoon climate, with a hot and rainy summer. Annual mean precipitation is 1097.1 mm, and annual evaporation (measured by E601 evaporation pan) is 1365.9 mm. The routine cropping pattern is rice–wheat. Mean air temperature and relative humidity (RH) are 24.6 °C and 81.5% during rice season, respectively. The volumetric 2

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saturated soil moisture (θs), field capacity (θf), and wilting point (θw) are 0.502, 0.392 and 0.179 m3, respectively. Rice, planted at inter- and intrarow spacings of 0.23 and 0.16 m respectively, is cultivated from early summer (June 27th, 2015 and July 1st, 2016) to middle autumn (October 25th, 2015 and November 3rd, 2016). The paddy soil was non-flooded during most of the growth season, which was irrigated when the soil moisture approaches the low thresholds, according to the local water-saving irrigation (WSI) practice-controlled irrigation, either inside the lysimeters or in open rice fields surrounded. The low thresholds for controlled irrigation is slightly different among various growth stages as reported by Xu et al. (2012). The detailed records of irrigation events are listed in Table 1, and the corresponding wettingdrying cycles in WSI field in 2015 and 2016 rice season was shown in Fig. 1. Relative soil moisture content (θr, as the ratio of θ to θs), and ponding water depth (Δd) were used to describe the field water condition. Fertilizers and pesticides were applied to the WSI rice field according to the local farmer’s practice.

Table 1 Irrigation records in WSI rice field in 2015 and 2016.

Paddy preparing Re-greening Tillering

Jointing-booting Heading-flowering Milky stage Whole rice season

2015

2016

Date (MonthDay)

Irrigation amount (mm)

Date (MonthDay)

Irrigation amount (mm)

6–23 – 7–5 7–25 – – – 8–9 9–3 9–7 9–16 –

118.0 – 30.4 70.2 – – – 48.1 38.6 46.3 43.2 394.9

6–28 7–6 7–8 7–18 7–22 7–28 8–9 – – 9–5 – –

115 35 39.5 52.5 52 41.9 45.5 – – 37 – 418.4

60

0

50

P

ǻG (mm)

20

-1

I

40

ǻG

30

P aQG I (mm G )

Growth stages

40

șr

60

20 10

80

100

100

șr (%)

90 80

(a)

70 60 0

10

20

30

40

50

60

70

80

90

100

110

120

Day (G)

60

20

-1

ǻG (mm)

50 P

40

40

I

30

ǻG

20

șr

P aQG I (mm G )

0

60

10

80

1000

100

șr (%)

90 80

(b)

70 60 0

10

20

30

40

50

60

70

Day (G)

80

90

100

110

120

Fig. 1. Variation of soil moisture condition and corresponding precipitation (P) and irrigation (I) under water-saving irrigation in rice season of (a) 2015 and (b) 2016. (θr and Δd represent relative soil moisture content and water depth respectively). 3

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for sensible heat flux, density fluctuation correction for latent heat flux, spectral loss correction, and spike detection) were implemented following the procedure outlined in literatures (Anthoni et al., 2004; Mauder et al., 2006; Ueyama et al., 2012; Masseroni et al., 2013). Flux data were averaged every 30 min blocks. The source area was estimated through the same approach as taken by Kljun et al. (2004) and Aubinet et al. (2012), which originated within a distance of 100–120 m upwind of the EC stations (Masseroni et al., 2012). The flux data were filtered when the friction velocity (u*) was lower than the threshold of 0.1 m s−1 (Anthoni et al., 2004). Finally, the missing data, accounting for approximately 22% of the entire rice season from 2015 to 2016, were determined by linear interpolation for gap within 3 h or by a mean diurnal average method within a 10-day window for long data gaps (Falge et al., 2001).

2.2. Field measurement Field measurements were conducted during rice seasons in 2015 and 2016. Rice is the unique crop in the station, short and consistent. It provides a sufficient upwind fetch of uniform land cover for measuring energy fluxes using an open-path eddy covariance (EC) systems. The EC system, which was aligned perpendicular to the prevailing wind direction (southeast direction), was composed of a CSAT3A sonic anemometer (Campbell Scientific Inc., USA) and an EC150 open-path infrared gas analyzer (Campbell Scientific Inc., USA) operating at a frequency of 10 Hz, both at 2.5 m above the soil surface. Three weighed micro-lysimeters were installed in the WSI rice field, aligned with the EC system in the northwest direction, and used to measure hourly ET (ETML) based on the mass change at canopy scale. Two of the three micro-lysimeters were used to calculate ETML, and one was used for load cell calibration. Each of the micro-lysimeters used for mass balance calculation was composed of an inner cylinder, an outer cylinder, weighing system, data recording system, and draining apparatus. The inner cylinders were planted with rice. Each lysimeter received four rice plants, and the cultivation practices including fertilizer and pesticides application were applied to the micro-lysimeters as the same with surrounding fields. The inner cylinder was replaced by an object with a fixed weight of 143 kg in the micro-lysimeter used for load cell calibration. The configuration, location and measurement of the lysimeters were described in Liu et al. (2018) in more detail. An automatic micro-meteorological measurement system (WSSTD1, DELTA-T, UK) together with EC system were used to measure net radiation (Rn), air temperature (Ta), wind speed (u), atmospheric pressure (Pa), precipitation (P), vapor pressure deficit (VPD), soil heat flux at the depth of 0.08 m beneath the soil surface (Gs), volumetric soil moisture content (θ), and soil temperature (Ts) were measured at 0.10 m, 0.20 m, and 0.30 m continuously, to ensure the quality and integrity of meteorological data. The seasonal variation of VPD was provided in Fig. 2, which was a climatic indicator affected the water and heat exchange simultaneously. To trigger the irrigation, soil moistures in 0–20 cm soil θ were measured daily (when soil was non-flooding) at 8:00 A.M. using a time domain reflectometry (TDR; Trase system, Soil Moisture Equipment, USA) and waveguides buried at this depth. Canopy height (hc) and leaf area index (LAI) were measured manually every five days, and for the days between measurements were determined by linear interpolation (Fig. 3).

2.4. Surface energy balance The energy balance of a terrestrial surface is expressed as (Hossen et al., 2012) (1)

Rn − G0 − S = LE + Hs

where Rn, G0, S, LE, and Hs, represent the net radiation, surface soil heat flux, storage energy in the biomass, latent heat flux, and sensible heat flux, respectively (units: W m−2). Calorimetric method, the most popular approach that combines the soil heat flux plate approach and calorimetry, was followed to calculate G0 term in current research. G0 was calculated as the sum of soil heat flux at a depth of 8 cm (Gs), change in energy storage (Q) in the 8 cm soil layer above, and change in energy storage in the flooding water (Gw) (Heusinkveld et al., 2004), which can be expressed as: (2)

G0 = Q + Gs + Gw

Assuming that the soil was mostly non-flooded in water-saving irrigation paddy field, Gw is neglected. The Q can be determined based on the change in soil temperature (Meyers and Hollinger, 2004; Heitman et al., 2010): (3)

Q = (ΔT∙Cs ∙d )/Δt

where ΔT is the change in soil temperature (°C), Cs is the heat capacity of the moist soil (J g−1 K−1), d is the soil thickness (cm), and Δt is the time step, Δt = 30 min. The air heat capacity is small compared with those of soil and water, and the volume fraction of soil organic matter is negligible. Thus, Cs for moist mineral soils was simplified as (Masseroni et al., 2014; Kustas and Daughtry, 1990)

2.3. Data processing and quality control of EC measurements

Cs = ρb Cd + θv ρw Cw

(4) −3

where ρb is the bulk density (1.35 g cm ), ρw is the density of water (1.0 g cm−3), Cw is the heat capacity of water (4.190 J kg−1 K−1), θv is the volumetric soil water content. Cd is the heat capacity of a dry

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 3

2015

2.5

2016

VPD (kpa)

2

1.5 1 0.5 0 27-Jun

17-Jul

6-Aug

26-Aug

15-Sep

5-Oct

Date Fig. 2. Average daily vapor pressure deficit (VPD) for rice season of 2015 and 2016. 4

25-Oct

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Fig. 3. Variation of (a) canopy height (hc) and (b) leaf area index (LAI) under water-saving irrigation in rice season of 2015 and 2016. (Rice seedlings were transplanted on June 27, 2015 and July 1, 2016).

mineral soil, which is 840 J kg−1 K−1 (Hanks and Ashcroft, 1980). In addition, S deduced from a concentration profile method inside the canopy (Papale et al., 2006; Leuning et al., 2012) was low and ignorable (mostly fell in the range of −10 to 10 W m−2, and accounted for less than 2% of the available energy during the rice cultivation season).. To evaluate surface energy balance closure, daily energy balance ratio (EBR), calculated by using the corrected fluxes, were average as 0.93 and 0.85 in 2015 and 2016 rice seasons, respectively, higher than that reported by studies at FLUXNET sites (Baldocchi et al., 2001; Wilson et al., 2002). The energy balance deficit problem was entirely related to the underestimation of sensible and latent heat fluxes as indicated in literatures (Wilson et al., 2002; Foken, 2008; Foken et al., 2011). And the energy gap could be closed through the evaporative fraction method (Gebler et al., 2014).

2.6. Measured and estimated ET Rice ET were measured independently by the weighed micro-lysimeters (ETML) and EC system (ETEC) for canopy and field scales in current study. In our previous work, slight difference was found in magnitude and phase between ETML and ETEC because of the spatial scale effect (Liu et al., 2018). The relationship between measured ETML and ETEC values was proposed, thus, the field scale ET could be calculated by the measured ET at canopy scale according to the relationship, termed as ETtrue in current research. EF in different periods of daytime (7:00–8:00, 8:00–9:00, 9:00–10:00, 10:00–11:00, 11:00–12:00, 12:00–13:00, 13:00–14:00, 14:00–15:00, and 15:00–16:00 GMT+8) were calculated using Eq. (5) based on available energy measurement during the corresponding periods. Then, the daily ET (ETEF,d) was estimated based on daily available energy and hourly EF by Eq. (6) (Sugita and Brutsaert, 1991).

ETEF , d = 86400 × EF / λd × (Rn − G0)d

2.5. Evaporation fraction and enforcing energy balance closure

where ETEF,d is the “hourly-to-daily” up-scaling ET estimation through the evaporation fraction method (mm day−1); λ is the latent flux of heat (MJ kg−1), λ = 2. 501 (2. 361 × 10−3) Ta; Ta is the average daily temperature (°C); the subscripts d indicates the average daily (24 h) value. Taken daily EF as standard value, the EF in different time intervals (7:00–8:00, 8:00–9:00 … 15:00–16:00 h) were used instead of daily EF to calculate daily ETEF,d using Eq. (6). It should be noted that, ETEF,d or ETtrue,d is “daily” rather than “daytime” ET, because (Rn–G0)d is calculated for 24-hours. If the daytime ET needs to be calculated, Rn–G0 should be the value during daylight period in Eq. (6). With ETtrue calculated by the measured ETML as standard value, daily ET value estimated from different hour-of-day EF (ETEF) were evaluated by calculating the linear regression slope, coefficient of determination (R2), root mean square error (RMSE), and

Evaporation fraction (EF) is defined as the ratio of latent heat flux to available energy (Rn–G0) (Shuttleworth et al., 1989; Nutini et al., 2014):

EF = LE /(Rn − G0)

(6)

(5)

Using Eq. (5), EF can be calculated at either an hourly scale, or at a daily scale. On this basis, the energy gap can be closed by distributing the energy balance deficit (EBD, calculated as Rn–G0–LE–Hs) to the sensible and latent heat fluxes according to the EF closure method, which consists of three steps as introduced by Kessomkiat et al. (2013) and Gebler et al. (2014).

5

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index of agreement (IOA). The R2, RMSE and IOA were calculated as the following equations: n

R2 =

n

condition during yellow ripening stage without irrigation. Notably, Rn–G0 decreased suddenly and abruptly during the transition periods from daytime to nighttime, resulting in big gap between LE and Rn–G0, with Rn–G0 < 0 and LE > 0. This phenomenon can be ascribed to the difference in variation phase of Rn and G0. During the same periods during daytime to nighttime transition, Rn decreased rapidly from positive to negative. However, the transmission of energy from the air to the soil heat flux plate through a thickness of soil was not an instantaneous process, some time being necessary for the heat flux plate to response to the energy change (Poblete-Echeverría et al., 2014). Thus, the decrease in G0 lagged behind Rn, led to the uncertainly negative energy (Rn–G0) in this period.

n

− 2 − − − ⎤ ⎧⎡ ∑ (Oi − O ⎞⎟ (Pi − P ) ⎥/[ ∑ (Oi − O) ∑ (Pi − P )]} ⎨ ⎢ i=1 i=1 ⎠ ⎦ i=1 ⎩⎣

(7)

n

RMSE =

∑ (Pi − Qi)2 /N

(8)

i=1 n

n

−

−

IOA = 1 − [∑ (Pi − Oi )2 / ∑ (|Pi − O | + |Oi − O |)2] i=1

i=1

(9)

where, Pi and Oi are the estimated and measured values, respectively; P¯ and O¯ are the mean estimated and measured values, respectively; and N is the number of samples.

3.2. Mean diurnal variation of EF in the different rice growth stages Because Rn–G0 is close to zero in the nighttime and is uncertain value during the transition periods from daytime to nighttime, the hourly EF is easy to fluctuate abruptly, thus only estimated EF during the daytime from 7:00 to 16:00 h is included. Diurnal variation of EF and their error bars of the rice in the different growth stages of 2015 and 2016 (re-greening, early tillering, middle tillering, later tillering, jointing and booting, heading to flowering, milk and yellow ripening stage) are shown in Fig. 5. EF exhibits an approximately concave-up shape, with a minimum at noon (10:00–11:00, 11:00–12:00, or 12:00 –13:00 in different growth stages of rice season), but it fluctuates occasionally which are probably caused by cloud, rainy events and other non-fair weather conditions. Hence, when weather conditions are variable, the hypothesis of constant EF during the daytime may not be satisfied, and the procedure may result in considerable error (Lhomme and Elguero, 1999; Gentine et al., 2007; Chávez et al., 2009). Near sunrise and sunset, hourly EF increase sharply in most growth stages. Available energy that appears in the denominator of EF is small near these times (Gentine et al., 2007). The error bars of EF varied

3. Results and discussion 3.1. Mean diurnal variation of energy budget components in different rice phenological stages The stage-average energy balance components (Rn–G0, LE and Hs) varied in a unimodal shape in each of rice phenological stages (Fig. 4). Usually, the value of LE was largely affected by Rn–G0, and the curve of its diurnal variation was basically the same as Rn–G0. Compared with Hs, the diurnal variation amplitude of LE was much greater. The LE flux was the main consumer of the external drive energy; hence, the estimation of ET (water in millimeter equivalent to LE) is the most important process in determining the exchanges of energy and mass in a paddy field. In addition, the proportion of LE to available energy was relatively low in the yellow ripening stage, less than 80 per-cents. Reasons might be related to the decreased transpiration rate of rice in the non-vigorous growth stage, as well as to the lower soil moisture

Fig. 4. Diurnal variations (over a 24-h period) of energy budget components (Rn–G0, LE and Hs) at different phenological stages for rice season of (a) 2015 and (b) 2016. (RE, IT, MT, LT, JB, HF, MI and YR represents the regreening, early tillering, middle tillering, later tillering, jointing and booting, heading to flowering, milk and yellow ripening stage, respectively; numbers in parentheses represent the number of days in each phenological stage).

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Fig. 5. The diurnal variation of average hourly evaporation fraction (EF) and its error bar during daytime in the different phenological stages of 2015 and 2016. ((a)–(h) and (i)–(p) are RE, IT, MT, LT, JB, HF, MI and YR of 2015 and 2016, respectively; RE, IT, MT, LT, JB, HF, MI and YR represents the re-greening, early tillering, middle tillering, later tillering, jointing and booting, heading to flowering, milk and yellow ripening stage, respectively; the “Average” (red line in bold) is hourly EF averaged over the whole rice growth season).

0.9). During the milk period, the daily EF reaches another peak; then daily EF in the yellow ripening stage significantly reduces to about 0.8 and the mean EF for the whole growth season is 0.92. In 2016, the daily EF in the re-greening stage varies less remarkably, and then increases gradually; it reaches 1.0 in several days of milk stage, and then drops sharply along with the decrease of soil moisture (also falls below 0.8). The mean daily EF for the whole growth season is 0.92. The difference in seasonal variation of daily EF between 2015 and 2016, is ascribed to the rice phenological traits influenced by meteorological condition (Liu et al., 2018). Additionally, the EF values in current study are obviously greater than the reports that from upland crops, e.g., wheat, vines, cotton, and so on (Gentine et al., 2007; Li et al., 2008; Bezerra et al., 2015; Bagley et al., 2017), which is ascribed to the moist soil water environment and the subtropical monsoon climate. The soil moisture content of paddy field is wetter than dryland, even if it is under the water-saving irrigation practice. Meanwhile, the larger vapor pressure deficit and solar radiation in subtropical monsoon climate make latent heat flux an absolute major energy consumption item. They are also greater than the result of Kar and Kumar (2016), who reported that the daily EF was 79–82% in different cultivars (cv. Lalat and Gayatri) and two rainfed rice seasons of 2008 and 2009. For the Boro rice

dramatically especially during the growth period with lower Rn–G0 energy flux (see Figs. 4 and 5). There is no significant difference in EF among different growth stages except in yellow ripening. During yellow ripening, the lowest EF occurs, with average EF about 0.79, due to lower available energy, canopy coverage and soil moisture on that stage. Fig. 5 also shows the mean diurnal cycle of hourly EF averaged over the whole rice growth days (red line in bold). The hourly EF exhibits a typical concave-up shape, with a gentle variation during 10:00–14:00 period and a minimum around 10:00–11:00 AM. Therefore, the hourly EF during 10:00–14:00 period may lead to less error in daily evapotranspiration estimation.

3.3. Seasonal variation in daily or daytime EF Seasonal variation of daily or daytime EF and the events of precipitation and irrigation in the whole WSI rice growing season in 2015 and 2016 are shown in Fig. 6. In 2015, the daily EF in the re-greening stage approximately stabilizes at 0.88. The daily EF increases gradually, reaching their respective maximum 1.0 in the late tillering stage, and then decreases along with time to milk maturity (mostly higher than 7

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the great difference in climate and soil moisture condition in the daytime, the result in EF calculation is more suddenly and abruptly at daytime scale than daily scale.

(transplanted on 29 January) and the Aman rice (transplanted on 20 August) periods, EF were 0.71 and 0.74 on seasonal average respectively, reported by Hossen et al. (2012). The daytime (defined as the time between 7:00–16:00 of a day) EF values, are also shown in Fig. 6. The daytime EF fluctuates obviously with the daily EF during the rice growth stage, suddenly and abruptly increasing after every irrigation or heavy rain..For example, rainfall on 22 October (113 days after transplantation in 2016) increased EF from 0.72 to 0.92, and irrigation on 5 July (ninth day after transplantation in 2015) increased EF from 0.77 to 0.86. The results agree with Kustas et al. (1993) and Li et al. (2008), although the climatic conditions and crop species are different. In this study, the WSI rice field is located in the subtropical monsoon climate region, with the specific wettingdrying cycle of soil condition, thus the energy partition will tend to increase ET (water in millimeter equivalent to LE in energy balance) after the rapid increase of soil water content, as resulted from irrigation and precipitation. In addition, the mean daytime EF for the whole growth stage of 2015 and 2016 are almost the same, about 0.86, lower than the daily values since the assumption of EF variation is not satisfied during nighttime. Actually, this difference term, regardless of nocturnal energy distribution and the contribution of night ET, can be as large as 7%. Many papers discussed the contribution of nighttime ET, like Tolk et al. (2006), who reported the nighttime ET was 3% over a cotton season for a dryland, 7.2% for an irrigated alfalfa crop, and as much as 12% in the semi-arid high plains. Sugita and Brutsaert (1991) and Chávez et al. (2009) emphasized that a 24-h period should be considered in daily ET estimation by extrapolating instantaneous values since nighttime ET may not be negligible. Notable, a comparison of the variation of daily vs. daytime EF values shows the latter value varies greatly and abruptly in both years, possible as results of the temporal scale difference in daily and daytime EF calculation. The energy transfer, including LE, is a continuous process. The energy, stored in the soil, canopy air, and biomass in the daytime, is partly released at night. Therefore, the sum of LE and Hs is larger than the available energy during nighttime. As the result of the energy balance of nighttime and daytime errors, as well as

3.4. Time-of-day representativeness of EF in estimating daily ET Daily estimated rice ET, termed as ETEF,d, was predicted by Eq. (6) with daily available energy data and hourly EF at different daytime hours. Performance of ETEF,d calculation against the measured ETtrue,d in 2015 and 2016 rice seasons are shown in Fig. 7. For ETEF,d estimated based on hourly EF at the specific local time from 07:00 to 16:00, the regression slope between ETEF,d and ETture,d is always less than 1.0 both in 2015 and 2016, reaching the minimum at noon and then increase. Correspondingly, ETEF,d calculated based on EF at different hours underestimate the true value (ETtrue,d = 3.835 and 3.816 mm day−1 in 2015 and 2016, respectively). The error of the estimated ETEF,d is great when it is calculated with hourly EF at sunset or sunrise period (Fig. 7). The correlations between ETEF,d and ETtrue,d are much better during 10:00–11:00, with higher R2 of 0.983 and 0.987, higher IOA of 0.993 and 0.996, and lower RMSE of 0.291 and 0.221 mm day−1 in 2015 and 2016, respectively, although underestimation is non-ignorable. A meaningful question is if there is a time of day when EF is most representative or has the best performance in ET estimation. This is an important issue in ET estimation by remote sensing with EF method based on instantaneous observations. However, it seems difficult to give a universal best hour of measurements valid for different sites, because the choice of hour will depend on the crop species, soil and canopy surface, and meteorological conditions of the study site. In general, the estimation of EF around noon would be representative of the daily average, and is preferred to be used for ET up-scaling from hourly to daily (Shuttleworth et al., 1989; Crago, 1996; Colaizzi et al., 2006; Chávez et al., 2009). In our case, the regression slope between ETEF,d and ETture,d was never greater than 1.0. The value of the EF taken around midday is smaller than the daytime average. This may lead to underestimation of daytime ET. In addition, during the night, the EF shows large variations and is highly unstable. This means using the EF 8

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Fig. 7. The average diurnal variation of model performance statistical indexes for ET estimation during daytime in 2015 and 2016 rice season: (a) slope, (b) RMSE, (c) R2 and (d) IOA.

daily ETture,d in current research. For practical purposes, correction procedure proposed should be simple. Considering vapor pressure deficit (VPD) is the key factor affecting ET especially at night (Li et al., 2008; Ding et al., 2010), it is used to set up the correction procedure by Eureqa software v.0.83. Data in 2015 and 2016 rice season were used for calibration and validation of the proposed ET correction procedure, and correlation was as follows:

up-scaling method results in an underestimation of daily ET over WSI rice field, with any one-time-of-day EF value, and a modification is worth exploring. Results for performance of ETEF based on 10:00–11:00 periods, compared with the ETture, and the corresponding available energy (Rn–G0) during the rice growth stage are reported in Fig. 8. In both rice seasons, seasonal simulated ETEF and the measured ETtrue varied in a consistent pattern, but different from other regions as a result of difference in magnitude and process of Rn–G0. Several researches indicated that rice ET generally got the maximum in the heading to flowering stage with the maximum LAI (Tyagi et al., 2000; Timm et al., 2014). For example, rice ET reached maximum of 7 mm day−1 when LAI was at its peak (flowering stage), and decreased with decrease of LAI in maturation stage, reported by Timm et al. (2014). The similar phenomenon was reported in Japan (Tyagi et al., 2000) and in California (Hatala et al., 2012). While in current study, both ETture and ETEF reached the maximum in the late (2015) and middle (2016) tillering stage, and then decreased along with the crop growth in late season. The difference in seasonal variation of rice ET among different years and other regions are ascribed to the rice phenological traits (Liu et al., 2018). For early rice which transplanted in spring or early summer, the vigorous growth stage coincides with the period in July or August with highest solar radiation. For later rice which mostly transplanted in later summer, the vigorous growth stage occurs in September, when the temperature and radiation are lower than in July or August. As a result, ET, largely affected by Rn, is generally larger in late July or early August (middle and late tillering stages) for later rice. Furthermore, the results depicted in Fig. 8 also confirm that ETEF and ETture frequently has a considerable gap, an underestimation of 15.6% and 13.4% on average for 2015 and 2016 seasonal ETtrue, respectively. Such a stable and considerable gap bring forward a demand in forming a rational relationship between the ETEF,d calculated by the best time-of-day representativeness (10:00–11:00) of EF and effective

ETsim, d = a∙ETEF , d + b∙VPDd

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where ETsim,d is the simulated daily ET with the correction procedure; ETEF,d is the estimated daily ET by up-scaling using EF during10:00–11:00 period; VPDd is the daily mean vapor pressure deficit (kPa); and a and b are the locally calibrated constant. This attempt is illustrated in Fig. 9 in which ETsim,d is modified with a = 1 and b = 0.5, respectively, based on the calibration dataset. The result for validation is satisfactory, with a high correlation coefficient of 1.027, lower RMSE of 0.205 mm day−1, much better than that without correction. R2 and IOA are 0.987 and 0.996 for validation dataset, both very close to 1.0 and the same as results without correction. In summary, the result confirms that the proposed procedure can be useful for practical purposes. Specially, even if the time of satellite overpass is not consistent with the best time-of-day representativeness of EF in estimating daily ET, the relationship between them can be established according to the diurnal variation of hourly EF in advance. 4. Conclusions This study is aimed at analyzing and providing insights into the diurnal and seasonal behavior of EF and its time-of-day representativeness in estimating daily ET. Variation of energy budget components was used to explain the exchanges of energy and the patterns observed in EF in the WSI paddy 9

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(10:00–11:00) representativeness of EF and ETtrue,d is quite high (R2 of 0.983 and 0.987, IOA of 0.993 and 0.996), the underestimation can be as large as 15.6% and 13.4% on average for 2015 and 2016, respectively. Then, a correction procedure is proposed by simply incorporating variable of VPD to form a liner regression equation with ET value following the EF up-scaling method as independent variable. It resulted in satisfactory result for daily ET estimation by an improved EF up-scaling method. It will provide a scientific basis and a useful tool for accurately estimating daily ET at regional scale over WSI rice field from remote sensing data in this region. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements Fig. 9. Comparison between estimated daily ET using EF up-scaling method with and without correction (ETsim and ETEF) and the measured value (ETtrue).

This work was supported by the National Natural Science Foundation of China (No. 51809075), the Fundamental Research Funds for the Central Universities (2018B00414), the Natural Science Foundation of Jiangsu Province (BK20180506) and the China Postdoctoral Science Foundation (2019M651680).

field. Diurnal variation of EF exhibits an approximately concave-up shape in different growth stages of rice season, and the mean diurnal cycle exhibits a typical concave-up shape, with a gentle variation during 10:00–14:00 period and a minimum around 10:00–11:00 AM. Seasonally, the range of daily EF is mostly higher than 0.8 except in later yellow ripening period, with an average of 0.92 which is obviously greater than the reports that from upland crops. The result in EF calculation varied more suddenly and abruptly at daytime scale than daily scale. The mean daytime EF for the whole growth stage is 0.86, 7% lower than the daily values. A comparison of estimated ETEF,d based on hourly EF with the measured ETtrue,d reveals that, the regression slope is mostly lower than 1.0. The correlation between ETEF,d estimated with the best time-of-day

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