Theor Appl Climatol DOI 10.1007/s00704-016-1841-7
ORIGINAL PAPER
Effective crop evapotranspiration measurement using time-domain reflectometry technique in a sub-humid region R. K. Srivastava 1 & R. K. Panda 2 & Debjani Halder 3
Received: 27 May 2015 / Accepted: 31 May 2016 # Springer-Verlag Wien 2016
Abstract The primary objective of this study was to evaluate the performance of the time-domain reflectometry (TDR) technique for daily evapotranspiration estimation of peanut and maize crop in a sub-humid region. Four independent methods were used to estimate crop evapotranspiration (ETc), namely, soil water balance budgeting approach, energy balance approach—(Bowen ratio), empirical methods approach, and Pan evaporation method. The soil water balance budgeting approach utilized the soil moisture measurement by gravimetric and TDR method. The empirical evapotranspiration methods such as combination approach (FAO-56 Penman–Monteith and Penman), temperature-based approach (Hargreaves–Samani), and radiation-based approach (Priestley–Taylor, Turc, Abetw) were used to estimate the reference evapotranspiration (ET0). The daily ETc determined by the FAO-56 Penman-Monteith, Priestley-Taylor, Turc, Pan evaporation, and Bowen ratio were found to be at par with the ET values derived from the soil water balance budget; while the methods Abetw, Penman, and Hargreaves-Samani were not found to be ideal for the determination of ETc. The study illustrates the in situ applicability of the TDR method in order to make it possible for a user to choose the best way for the optimum water consumption for a given crop in a subhumid region. The study suggests that the FAO-56 Penman–
* R. K. Srivastava
[email protected]
1
Agricultural and Food Engineering Department, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
2
School of Infrastructure, Indian Institute of Technology, Bhubaneswar 751013, India
3
Department of Agronomy, Uttar Banga KrishiViswavidyalaya, Pundibari, Cooch Behar 736165, India
Monteith, Turc, and Priestley–Taylor can be used for the determination of crop ETc using TDR in comparison to soil water balance budget. Abbreviations ASW Available soil water (mm) TDR Time domain reflectometry ET Evapotranspiration (mm) Crop evapotranspiration (mm) ETc Reference evapotranspiration (mm) ETo I Net irrigation depth (mm) Kc Crop coefficient TAW Total available soil water (mm) θFC Volumetric soil moisture at field capacity (m3 m−3) Volumetric soil moisture at wilting point (m3 m−3) θWP Volumetric soil water content (m3 m−3) θv ρg Bulk soil density Soil water content by the gravimetric method θg (m3 m−3) Ww Weight of wet (g) Dry soil (g) Wd v Velocity (m/s) Ka Soil’s bulk dielectric constant c Speed of light (m/s) Eq Equation A Sum of irrigation and rain (mm) ΔW Variation of soil water (mm) λ Latent heat of vaporization (2.501 MJ kg−1) Net radiation (W m−2) Rn G Soil heat flux (W m−2) γ Psychrometric constant (kPa °C−1) ΔT Temperature (°C) Actualsaturation vapor pressure (kPa) Δea U2 Wind speed (ms−1) at 2 m height, Δ Slope of the vapor pressure curve (kPa0C−1)
Srivastava R.K. et al.
es GM
Saturation vapor pressure (kPa) Gravimetric method
1 Introduction The major authoritative component of water balance is evapotranspiration which affects the processes such as biomass accumulation and groundwater recharge of natural ecosystems. The daily evapotranspiration from an ecosystem is difficult to measure accurately, and various techniques have been used and compared at different scales to obtain a reliable estimate (Rana and Katerji 2002; Schelde et al. 2011). Water use efficiency can be improved through irrigation scheduling, which impacts the crop evapotranspiration (ETc). ETc differs from crop to crop because of a variation in climatic conditions and crop canopy, which is a product of reference crop evapotranspiration (ET0) and crop-coefficient (Kc) (Doorenbos and Pruitt 1977; Kashyap and Panda 2001; Zhao et al. 2010; Djaman and Irmak 2013). Accurate determination of reference ET0 has been done on different crops under different climatic conditions (Jensen et al. 1990; Allen et al. 1998; Kashyap and Panda 2001; Lu et al. 2005; Trajkovic and Kolakovic 2009; Azhar Aftab and Perera, 2011; Zhao et al. 2010; Tabari et al. 2013; Kisi 2014; Djaman et al., 2015; Valipour 2015). The time-domain reflectometry (TDR) technique has now been widely accepted for the measurement of in situ volumetric water content θ (m3 m−3) (Walker et al. 2004), both in laboratory and field conditions (Topp et al. 1980; Dalton and Vangenuchten 1986; Mastrorilli et al. 1998; Jones et al. 2002; Skierucha et al. 2008; Coppola et al. 2013). The use of TDR for soil water measurement was initiated by Topp et al. (1980). It has gained advantages over gravimetric method with respect to small volume measurement and quick response (Skierucha et al. 2008). The use of multiple probes in sequential order with the help of TDR multiplexing was reported by Skierucha et al. 2008, who measured the change in layer-wise soil water content, both in temporal and spatial patterns. TDR probes are useful for soil–water balance measurement at plot scale and at hourly interval starting from a few centimeters of the soil surface. Maize and peanut were chosen as the experimental crops since they widely cultivated in winter season as an alternative crop to rice in sub-humid regions and possess different patterns of soil water depletion. Out of the two crops, maize is a water-sensitive and deep-rooted crop (0.9 m or more), on the contrary, peanut is a shallow-rooted plant (Allen et al. 1998). The major objective of the study was to examine daily estimates of evapotranspiration (ET) from an agricultural field using four independent techniques such as TDR-based soil moisture measurement, energy balance technique (Bowen
ratio), empirical methods (Penman, FAO-56 Penman– Monteith, Hargreaves-Samani, Turc, Abtew, and Priestley– Taylor methods), and Pan evaporation. As an evaluation of these independent methods, ET was calculated for the maize and peanut crops. Further, based on the performance in terms of ET estimation, the best method for ETc was selected that could suggest efficiently the optimal amount of irrigation required for both the crops in a sub-humid region. These independent techniques help in the measurement of water dynamics in the crop growth. Moreover, it also estimates the temporal variation in ET during irrigation scheduling and regional water allocating in a sub-humid region (Jhajharia et al. 2004; Schelde et al. 2011; Kumar et al. 2015).
2 Materials and methods 2.1 Study area Crop experiments were conducted in 1470 m2 area at the experimental farm of the Agricultural and Food Engineering Department, Indian Institute of Technology, Kharagpur, India (22.33° N latitude and 87.33° E longitude) in the winter season of the years 2013 and 2014. The farm is situated at an altitude of 48 m above the sea level. The climate of Kharagpur is classified as sub-humid. It foresees hot and humid summer in April and May, rainy during June to September, moderately warm and dry autumn in October and November, dry winter in December and January, and moderate spring in February and March. The area receives an average rainfall of about 1462 mm. The average temperature ranges between 21 and 32 °C. The soil of this region is classified as a lateritic type with sandy loam texture, which is taxonomically grouped under the group BAlfisol.^ Agrometeorological data were recorded by an automated weather station located on the agriculture farm. 2.2 Crop field experiment For the field experiment, two crops were selected, namely, maize and peanut. Maize crop experiment was conducted in the year 2013 and the same was repeated in year 2014 on the same sowing date. Peanut crop experiment was conducted in 2013. The field experiment was conducted in 24 plots under maize and 48 plots under peanut. The set of experiments for peanut was confined to 24 plots only instead of 48 plots to maintain the aspect ratio equal for both the crops. The whole set of crop field experiment was conducted in triplicates, and observations were taken after the germination of the crop and even at different growth stages for both crops. Maize of hybrid variety Tx367, under irrigated conditions, was planted on a plot size of 5 m × 4 m each, on 5 January (medium duration) and, subsequently, harvested after 90 days (10 April).
Effective crop evapotranspiration measurement
Fertilizer was applied in irrigated maize at a rate of 80 kg ha−1of urea, 100 kg ha−1 of single super phosphate (SSP), and 120 kg ha −1 of muriate of potash (MOP). Similarly, peanut TMV-2 variety, under irrigated conditions was planted on a plot size of 5 m × 4 m each, on 14 January (medium duration) and, subsequently, harvested after 90 days (22 April). Before sowing peanut seeds of TMV-2 variety, seeds were treated with Rhizobium culture at a rate of 25 kg ha−1 for the efficient nodulation and nitrogen fixation during sowing. Fertilizer was applied in irrigated peanut at a rate of 20 kg ha−1 of urea, 60 kg ha−1 of single super phosphate (SSP), and 20 kg ha−1 of muriate of potash (MOP). The whole experiment was designed following the split-plot technique for both peanut and maize crops. The seeds were sown at a depth of 5 cm with 30 cm × 20 cm spacing for maize while, at 10 cm with 30 cm × 20 cm spacing in case of peanut. All the plots were irrigated with measured amount of water up to root zone depth in order to ensure no water stress occurs during the cropping season. The irrigation amount of crops was measured using a water meter. The crop irrigation schedule for peanut and maize crop is shown in Fig 1a, b, respectively. 2.3 Soil moisture measurement 2.3.1 Gravimetric method The gravimetric method is perhaps the most simple and accurate technique, commonly used for measuring the soil moisture content, hence, used for the irrigation management purpose (Mastrorilli et al. 1998; Rana and Katerji 2002). The estimation of soil water content using gravimetric method (θg) could be easily be done if the weight of wet (Ww) and dry soil (Wd) are known (Rana and Katerji 2002). During the field experiment, sampling of each plot was done at four depths (0–20, 20–40, 40–60, 60–90 cm) once a week. The collected samples were used to determine weight of the soil. Subsequently, the drying of soil samples was done at 105 °C for 24 h, until the moisture was driven off in the hot air oven. After removing from the oven, soil samples were cooled down to room temperature and weighed again to calculate the dry soil weight. The bulk soil density (ρg) was calculated for the undisturbed soil samples, from which the volumetric soil water content (θv) was calculated (Mastrorilli et al. 1998). 2.3.2 Time domain reflectometry The principles of the TDR method have been reported in a number of studies (e.g., Topp et al. 1980, 1982; Dalton and Van Genuchten 1986; Rajkai and Rydn, 1992; Weitz et al. 1997; Noborio 2001; Jones et al. 2002; Dobriyal et al. 2012). To sum up the TDR principle in few words, we can say that it is based upon the propagation velocity (v) of an
electromagnetic energy when it traverses in the form of a pulse through the soil via probe. The velocity is determined in a soil when short electrical pulses are transmitted through a probe (Noborio 2001). The propagation velocity (v = 2 l/t) is calculated from the travel time (t) and the length (l) of the probe. Thus, from the travel time analysis, the soil’s bulk dielectric constant (Ka) (Eq. 1) is (using Eq. 1), from which the volumetric water content (θv) is inferred (Topp et al. 1980, 1982; Dalton and Van Genuchten 1986; Noborio 2001). Water has a comparably high dielectric constant (about 80) compared with the dry soil (<5). Hence, soil’s bulk dielectric constant (Ka)(Eq. 1) is a function that confides strongly on the volume of soil water surrounding the probe and on the propagation velocity (v = 2 L/t) (Topp et al. 1980; Mastrorilli et al. 1998; Jones et al. 2002; Bittelli et al. 2008; Dobriyal et al. 2012). 2 2 C Ct ¼ ð1Þ Ka ¼ V 2L where, c is the speed of light (velocity of the electromagnetic waves) in a vacuum (3 × 108 m/s) and t is the travel time for the pulse to traverse the length of the embedded waveguide (down and back, 2 L). Soil water content measurements were made daily with a TDR TRIME (IMKO Gmbh, Germany) (IMKO, 2000) (Noborio 2001). The distribution of voltage pulses was done around a coaxial cable of length 3 m, and this cable was connected to a TDR probe (0.45 m in length). Access tubes were installed vertically up to 1 m (10 cm above the soil surface and 90 cm into the soil) in the middle of each plot, and the probe was inserted into the soil to access the tubes at different depths (20, 40, 60, 90 cm), respectively, for the measurement of soil water content. Calibration of the probe The layer wise soil moisture was measured by TDR from the emergence of the plant until harvest with TDR TRIME (IMKO GmBH, Germany) (IMKO 2000). TDR was calibrated for each probe to estimate the water content of the soil (Rajkai and Rydn, 1992; Mastrorilli et al. 1998; Jones et al. 2002), and validation was done by comparison with the gravimetric method using the soil sample near the TDR probes during maize and peanut crop experiment. The Ka values were measured according to Eq. (1) with the parameter provided by TDR. Validation of the soil moisture obtained by TDR was done by comparing it with the gravimetric method. Probe calibration was done during a 2week period. During this period, the soil was sampled at same depths as of the probes daily at four places around the probes (Mastrorilli et al. 1998). Figure 2 shows calibration of probe following procedure given by Topp et al. (1980) (Eq. 2). The volumetric water content (θv) ranged between the field capacity (22.7 %) and the wilting point (10.9 %) of the soil, and Ka values lied between 4 and 15. The relation of these two
Srivastava R.K. et al. 35
8
Rain (mm)
6
25 20
4
15 10
2
5 0
Irrigatoin (mm)
Irrigation (mm)
30
Irrigation (mm)
Rain (mm)
2
30 1.5
25 20
1
15 10
Rain (mm)
Irrigation (mm)
35
Rain (mm)
Fig 1 The irrigation amount (mm) (black vertical bar) and rain (mm) (gray vertical bar) of a peanut crop for the year 2013, b maize crop for the year 2013, and c 2014
0.5
5 1
8
15 22 29 38 45 52 57 64 71 78 83 88
0
0
0
Days after sowing
Days after sowing
(b)
(a) 35
Irrigation (mm)
Rain (mm)
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40
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30
15
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5
Rain (mm)
Irrigatoin (mm)
30
0
0
Days after sowing
(c)
parameters Ka and θv was fitted in a polynomial equation (Eq. 2) (Topp et al. 1980; Mastrorilli et al. 1998): Ka¼ 3:03 þ 9:3θv þ 146:0θv 2 −66:7θv 3
ð2Þ
2.4 Evapotranspiration estimate (ET) 2.4.1 Water balance Crop evapotranspiration (ETc) was calculated using the soil water budget equation (Allen et al. 1998; Zhao et al. 2010) (Eq. 3): ETc ¼ R þ I þ Dp ΔSM–D
ð3Þ
where ETc is the crop evapotranspiration, ΔSM is the variation of moisture between two successive days, R is the rainfall (mm), I is the irrigation (mm), Dp is the deep percolation (mm), and D is drainage (mm).
2.4.2 The Bowen ratio method The estimation of ET0 for both the crops was done by energy balance approach using (Eq. 4). This micrometeorological method (Eq. 4) needs values of Rn and G, temperatures at two heights of humid and dry air at constant flux layer (ΔT is temperature gradient and Δe is vapor pressure) (Mastrorilli et al. 1998; Rana and Katerji 2002; Zhao et al. 2010). The latent energy (LE) is calculated by energy balance equation using the Bowen ratio (β = H/LE). The Bowen ratio is calculated by β = γ ΔT Δe (Mastrorilli et al. 1998; Zhao et al. 2010). Rn −G ð4Þ λET ¼ 1 þ γ Δ T=Δ e where Rn is the net radiation (W m−2), λ (2.501 MJ kg−1) is the latent heat of vaporization, ΔT is the temperature (°C−1), G is the soil heat flux (W m−2) and γ the psychometric constant (kPa °C−1), and Δea is the vapor pressure differences (kPa). The crop evapotranspiration ETc (mm day−1) was obtained by dividing the latent heat flux (λET) with the latent heat of vaporization (λ).
2.4.3 The Penman method The combination of energy and aerodynamic transport to estimate ET0 was first reported by Penman (1948) (Kashyap and Panda 2001; Hillel 2004, Tabari et al. 2013) (Eq. 5):
Fig 2 Relationship between soil bulk dielectric constant (Ka) and volumetric soil water content (θv, m3 m−3) at Kharagpur, following procedure of Topp et al. (1980)
ET0 ¼
0:408 Δ ðRn–GÞ þ 6:43 γ ð1 þ 0:053 u2 ÞD Δþγ
where D is vapor pressure deficit (kPa).
ð5Þ
Effective crop evapotranspiration measurement
2.4.4 Penman–Monteith FAO-56 method
2.4.8 Priestley–Taylor method
The FAO-56 Penman-Monteith method was used in the present study (Allen et al. 1998; Zhao et al. 2010) (Eq. 6) to estimate daily evapotranspiration ETo (mm day−1).
The Priestley–Taylor method (Eq. 10) was used to estimate the evaporation under no or low advective condition (Priestley and Taylor 1972; Zhao et al. 2010):
ETo ¼
900 U 2 ðes −ea Þ T a þ 273 Δ þ γ*ð1 þ 0:34*U 2 Þ
0:408*Δ*ðRn −GÞ þ γ*
ð6Þ
where Rn is the net radiation (W m−2), γ is the psychometric constant (kPa°C−1), U2 is the wind speed (ms−1) at 2 m height, G is the soil heat flux density (W m−2), Ta is the mean daily air temperature (°C), Δ is the slope of the vapor pressure curve (kPa°C−1), and ea. and es are the actual and saturation vapor pressure (kPa), respectively.
The Hargreaves method is described as (Hargreaves and Samani 1985; Kashyap and Panda 2001; Valipour 2015) (Eq. 7): pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð7Þ ET0 ¼ 0:0023 Ra T avg þ 17:8 T max −T min where Ra is the water equivalent of the extraterrestrial radiation (mm day−1); Tmax, Tmin, and Tavg are the daily maximum, minimum, and mean air temperature (°C), respectively; 0.0023 is the original empirical coefficient.
2.4.6 Turc method The estimation of the evapotranspiration (ET0) could be done by Turc method which requires air temperature and solar radiation (W m−2) (Turc 1961; Kashyap and Panda 2001; Xu et al. 2008; Valipour 2015) (Eq. 8). 1 T ðRs þ 50Þ λ T avg þ 15
Δ ðRn −GÞ λ ðΔ þ γ Þ
ð8Þ
where Tavg is the daily mean air temperature (°C) and Rs is the solar radiation (W m−2).
ð10Þ
where α is an empirically dimensionless correction of 1.26. 2.4.9 Pan evaporation method Pan evaporation was used to estimate evapotranspiration (ETo ) (Eq. 11) (Rana and Katerji 2002; Jhajharia and Dhiman, 2006): ET ¼ Kp Epan
2.4.5 The Hargreaves method
ET0 ¼ ð0:013Þ
ET ¼ α
ð11Þ
where Kp is a pan coefficient and EPan is measured evaporation from a class A evaporation Pan (mm d−1). The pan coefficient depends upon the speed of the wind and relative humidity (Jensen 1974). 2.4.10 Crop coefficient Crop coefficient (Kc) is expressed as the ratio of ETc to ET0 which depends primarily on four characteristics, i.e., crop height, canopy resistance, albedo, and evaporation from the soil (Allen et al. 1998; Kashyap and Panda 2001; Zhao et al. 2010). Crop coefficient (kc) was estimated using Eqs. 12 and 13, which is illustrated and recommended by FAO-56 (Allen et al. 1998; Zhao et al. 2010): Kc ¼ KcðTabÞ 0:3 h þ ½0:04 ðu2 −2Þ−0:004ðRHmin −45Þ 3
ð12Þ
Kc ¼ max 0:3 h 1:2 þ ½0:04ðu2 −2Þ−0:004ðRH min −45Þ ; fK c þ 0:05g 3
ð13Þ
2.4.7 Abtew method
where Kc(Tab) is taken from Table 17 of FAO-56 (Allen et al. 1998), RHmin is the mean daily minimum relative humidity, and h is the plant height (Allen et al. 1998; Zhao et al. 2010).
The Abtew (Abtew 1996; Valipour 2015) method was used to estimate the evapotranspiration (ET0) using solar radiation (W m−2) and maximum temperature (Eq. 9).
2.5 Statistical analysis
ET0 ¼ 0:01786
RS T max λ
where Rs is the solar radiation (W m−2).
ð9Þ
The comparison between different independent methods was done by error analysis. For each method, the mean absolute error (MAE) and the root mean square error (RMSE) were calculated by using eqs. 14 and 15 (Kisi 2014):
80
4
60
3
1 0
40
Saturaon VPD
2
20
Rh Jan
Apr
Jul Months
0
Oct
12
160 Net Radiation (Wm-2)
100
5
10
120
8 6
80 40 0
Jan
Apr
Jul Months
(a)
2 0
Oct
(b) 35
3.5
30
3
25
2.5
20
2
15
1.5
10
Temp.
1
WS
0.5
5 0
Jan
Mar
May Jul Months
Sep
Wind Speed (mVV-1)
Air Temp. (°C)
4
Net Radiaon Soil Heat flux density
Soil Heat flux density (W m-2)
6
Relative Humidity (%)
Fig 3 a, b, and c Temporal variation of measured and estimated major weather parameters at Kharagpur for the year 2013
Vapor pressure Deficit ( kpa)
Srivastava R.K. et al.
0
Nov
(c) rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 XN RMSE ¼ ðX i −Y i Þ2 i¼1 N 1 X n X i −Y i MRE ¼ 100 i¼1 Y N i
ð14Þ ð15Þ
January respectively, with a monthly average of 3.71 kPa (Fig 3a). The monthly soil latent flux density and net radiation maximum values were exhibited in April while minimum in December with an average of 7.69 and 110.83 W m−2, respectively (Fig 3b). The average air temperature annually was 26.64 °C. The wind speed attained maximum value in May, with an average of 2.06 m s−1 for a whole year (Fig 3c).
3 Results and discussion
3.2 Daily soil water content
3.1 Meteorological data
The daily soil moisture was measured with TDR, and this measured soil moisture was introduced in a soil balance budget (Eq. 3) to obtain crop evapotranspiration on a regular scale basis. The measurement of the water content was done gravimetrically (θg) and by TDR (θTDR). For the maize crop experiment, sampling of the soil at four different depths (0.20, 0.40, 0.60, 0.90 m) and linear correlations were obtained for the gravimetric and TDR method (Eq. 16 to 19):
Fig 4 Temporal variation of the soil water content in maize crop at four different depths: 0.20, 0.40, 0.60, and 0.90 m. Soil water content was measured by TDR (lines) and gravimetric (points) method
Soil water content (mm)
The temporal variation of major weather parameters at Kharagpur, a sub-humid climatic region is given in Fig 3. The daily metrological data recorded were precipitation, wind speed, relative humidity, and maximum and minimum temperature. The soil latent heat flux and vapor pressure deficit were estimated using the approach illustrated in Allen et al. 1998. The maximum value (98.10 %) of relative humidity was observed in September while minimum value (57.59 %) in March. The average relative humidity recorded monthly was 74.86 %. The saturation vapor pressure deficit maximum and minimum values were 4.21 kPa in June and 2.28 kPa in
θg ¼ 0:918*θTDR þ 1:413 r2 ¼ 0:85; no:of points ¼ 24 at 0:20 m ð16Þ
210
GM @0.2 m
180
TDR @0.2 m
150
GM @0.40 m
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TDR @ 0.4 m GM
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Effective crop evapotranspiration measurement Soil water content (cm)
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0
0
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8
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22
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64
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78
83
88
IRR Rain
Irrigation (mm)
Fig 5 Depth wise temporal soil moisture variation measured by TDR (solid line) and gravimetric (marker) for a maize and b peanut crop. Black vertical bars represent irrigation (mm)
Soil water content (cm)
30
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0.6 GM
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Irrigation (mm) 0.20 m GM
Irrigation (mm)
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0.4 TDR
0.9 m TDR
140
8
0.4 m GM
0.9m GM
(a)
1
0.2 mTDR
0.6 TDR
Days after sowing
0
0.2 m GM
0.40 m TDR 0.40 m GM 0.40 m TDR 0.60 m GM 0.60 m TDR
0
Days after sowing
(b)
θg ¼ 0:958*θTDR þ 0:716 r2 ¼ 0:89; no:of points ¼ 24 at 0:40 m
peanut crop experiment. The variation of soil water content with time for four soil layers is shown in Fig 4 for the two wetting–drying cycles. The TDR results were found to be accurate when the volumetric water content varied between 10 and 22 % for a 2-week period. The TDR accuracy was further confirmed by high value of r2 and a slope of regression line close near to 1. From the daily comparison made by TDR and gravimetrical measurements at each 20-cm soil profile, it is quite evident that both techniques gave almost similar results for maize as well as for peanut as shown in Fig 5a, b). After each furrow irrigation, the daily soil water content in the soil was measured by TDR method which measures the soil water content in the soil continuously and also by the gravimetric method which measures the soil water content, after each 24 h, when the
ð17Þ θg ¼ 1:072* θTDR þ 1:552 r2 ¼ 0:85; no:of points ¼ 24 at 0:60 m ð18Þ θg ¼ 0:925*θTDR þ 1:433 r2 ¼ 0:85; no:of points ¼ 24 at 0:90 m ð19Þ The soil moisture measured depth wise with TDR (θTDR) was validated by comparing it with the gravimetric method (Fig 4). Similar results were obtained for the
Table 1
Crop coefficient, LAI, irrigation, and rainfall at different stages of growth of maize and peanut crop
Phenophesical stage
Initial Mid Season Development Late season Total
Maize (2013)
Peanut (2013)
Maize (2014)
LAI (m2 m−2)
Kc
Irrigation (mm)
Rain (mm)
LAI (m2 m−2)
Kc
Irrigation (mm)
Rain (mm)
LAI (m2 m−2)
Kc
Irrigation (mm)
Rain (mm)
0.12 1.79 4.57 2.78 2.315
0.29 0.93 1.17 0.73 0.78
20.00 105.00 60.00 80.00 265.00
0.00 0.10 3.40 26.60 30.1
0.2 0.45 1.97 1.46 1.02
0.22 0.85 1.12 0.88 0.7675
25 60 70 55 210
0 0.1 3.4 8.1 11.6
0.2 1 4.04 3.77 2.2525
0.29 0.95 1.16 0.83 0.80
25 45 45 50 165
7.9 64.9 65.8 37.6 176.2
Srivastava R.K. et al. 8
SWB
8
FAO 56 method
ETC (mm/day)
ETC (mm/day)
6 4 2 0
1
13
21
29
37
50
58
68
77
SWB
4 2 1
13
21
ETC (mm/day)
37
50
58
Days after sowing
(a)
(b)
SWB
7
29
Days after sowing
8 8
Penman method
6
0
87
Hargreaves temperature method
ETC (mm/day)
Fig 6 Daily crop evapotranspiration (ETc) from a irrigated maize estimated by soil water balance (SWB) infusing water storage variance as measured by the TDR and a FAO56 PM b Penman c Hargreaves d Priestly–Taylor e Turc f Abtew g Bowen ratio and h Pan evaporation for the year 2013
6 5 4 3 2
SWB
68
77
87
Turc method
6 4 2
1 0
1
13
21
29
37
50
58
68
77
0
87
1
13
21
Days after sowing
29 37 50 58 Days after sowing
(c)
PT method
ETC (mm/day)
ETC (mm/day)
SWB
6 5 4 3 2
87
SWB
68
77
87
Abetw
6 4 2
1 0
1
13
21
29
37
50
58
68
77
84
0
90
1
13
21
Days after sowing
29 37 50 58 Days after sowing
(e)
(f) 7
7
SWB
6
Bowen ratio method
5 4 3 2 1 0
SWB
6
ETc, mm/day
ETC (mm/day)
77
(d) 8
7
68
Pan Evaporation method
5 4 3 2 1
1
13
21
29
37
50
58
68
77
87
0
1
13
21
29
37
50
58
Days after sowing
Days after sowing
(g)
(h)
water has percolated into the soil. Thus, both of the methods were found to be in good agreement when the water content in the soil was to be measured. 3.3 Evapotranspiration In this study, the results suggest that the value of water content available in the soil measured by TDR can be introduced in Eq. 3 in the form of daily variations in the soil moisture (ΔSM) which gave daily ETc value. The crop coefficients were estimated using Eqs. 12 and 13 are shown in Table 1 for maize and peanut crop, respectively. The daily ETc estimated from the soil water balance (Eq. 3) was compared with ETc estimated from FAO-56 Penman–Monteith (Fig 6a, 7a, and 8a), Penman (Fig 6b, 7b, and 8b), Hargreaves Samani (Fig 6c, 7c, and 8c), Turc (Fig 6d, 7d, and 8c), Priestley–Taylor (Fig 6e, 7e, and 8e), Abtew (Fig 6f, 7f, and 8c), Bowen ratio (Fig 6g, 7g, and 7h), and Pan evaporation (Fig 6h,7h, and 8h), methods.
68
77
87
The daily ETc estimated from FAO-56 PM (Eq. 6) closely follow the SWB method (Fig 6a, 7a, and 8a). The Penman method relies on a combination of energy balance and aerodynamic transport (Hillel 2004). Based on this method, it overestimated the daily ETc in comparison to SWB method especially during the mid-season (Fig 6b, 7b, and 8b) of crop growth. The ETc estimated by temperature based Hargreaves–Samani method matched the ETc estimated by SWB method for both maize and peanut crop but during the mid-season it was over estimated (Fig 6c, 7c, and 8c). One of the possible causes for this over estimation might be an increase in temperature during March and April months. The daily ETc estimated by radiation based Turc (Fig 6d, 7d, and 8d), Priestley–Taylor (PT) (Fig 6e, 7e, and 8e), and Abtew (Fig 6f, 7f, and 8f) methods also matched the ETc estimated by the SWB method for both the crops. Figure 6g, 7g, and 8g show the underestimation of ETc by Bowen ratio in comparison to SWB method during the mid and harvesting
Effective crop evapotranspiration measurement SWB
FAO 56 method
6
7
5
6
ETC (mm/day)
ETC (mm/day)
7
4 3 2 1 0
1
13
21
29
37
50
58
68
77
Penman method
5 4 3 2 1 0
87
SWB
1
13
21
29
Days after sowing
37
(a) SWB
4 3 2 1
SWB
6
4 3 2 1
1
13
21
7
29
37
50
58
68
77
0
87
1
13
21
29
37
SWB
6
50
58
68
77
87
Days after sowing
(d) 7
PT method
SWB
6
ETC (mm/day)
ETC (mm/day)
87
Turc method
(c)
5 4 3 2 1
abetw
5 4 3 2 1
1
13
21
29
37
50
58
68
77
0
87
1
13
21
Days after sowing
29
37
6
SWB
50
58
68
77
87
Days after sowing
(e)
(f)
Bowen ratio method
7
5
ETc (mm/day)
ETC (mm/day)
77
5
Days after sowing
0
68
7
Hargreaves temperature method
5
0
58
(b)
ETC (mm/day)
ETC (mm/day)
6
50
Days after sowing
4 3 2 1
SWB
Pan Evaporation method
6 5 4 3 2 1 0
0 1
13
21
29
37
50
58
68
77
87
Days after sowing
1
13
21
29
37
50
58
68
77
87
Days after sowing
(g)
(h)
Fig 7 Daily crop evapotranspiration (ETc) from a irrigated peanut estimated by soil water balance (SWB) infusing water storage variance as measured by the TDR and a FAO-56 PM b Penman c Hargreaves d Priestly–Taylor e Turc f Abtew g Bowen ratio and h Pan evaporation for the year 2013
stage of maize and peanut crop. The Bowen ratio (β) (Eq. 4) primarily depends on temperature gradient and was higher during the end of March and April. Due to a rise in temperature gradient, the field becomes dryer and relative humidity gradient becomes lower and, hence, the received energy is used to warm the surface as a result of which steepness in the temperature gradient is observed in case of Bowen ratio method (Malek 1993; Malek and Bingham 1993; Hillel 2004). The Pan evaporation (Eq. 11) method is based on pan coefficient which depends particularly on the relative humidity and
wind speed and thereby underestimates the of ETc in comparison to SWB method (Fig 6h, 7h, and 8h). 3.4 Statistical analysis The performance of evapotranspiration methods was evaluated using statistical analysis such as root mean square error (RMSE, mm/day), mean relative error (MRE, %), R2, and slope as shown in Table 2. The methods were ranked according to R2, MRE (%), and RMSE. The FAO-56PM method
Srivastava R.K. et al. 7
SWB
ETc (mm/day)
ET C (mm/day)
Penman method
7
5 4 3 2 1 0
SWB
8
FAO 56 method
6
6 5 4 3 2 1
1
13
21
29
37
50
58
68
77
0
87
1
13
21
29
Days after sowing
37
SWB
ETc (mm/day)
ETc, mm/day
SWB
6
6 5 4 3 2
5 4 3 2
1
13
21
29
37
50
58
68
77
0
87
1
13
21
29
37
58
68
77
87
68
77
87
(d) 7.00
7
SWB
PT method
SWB
6.00
ETc (mm.day)
6
ETc, mm/day
50
Days after sowing
(c)
5 4 3 2
Abetw
5.00 4.00 3.00 2.00 1.00
1
0.00 1
13
21
29
37
50
58
68
77
84
1
13
21
29
37
50
58
Days after sowing
Days after sowing
(f)
(e) 7
7
SWB
Bowen ratio method
SWB
6
ETc (mm/day)
6
ETc (mm/day)
87
Turc method
Days after sowing
5 4 3 2
Pan Evaporation method
5 4 3 2 1
1 0
77
1
1
0
68
7
Hargreaves temperature method
7
0
58
(b)
(a) 8
50
Days after sowing
1
13
21
29
37
50
58
68
77
87
Days after sowing
(g)
0
1
13
21
29
37
50
58
68
77
87
Days after sowing
(h)
Fig 8 Daily crop evapotranspiration (ETc) from a irrigated maize estimated by soil water balance (SWB) infusing water storage variance as measured by the TDR and a FAO-56 PM b Penman c Hargreaves d Priestly–Taylor e Turc f Abtew g Bowen ratio and h Pan evaporation for the year 2014
received the highest rank. The relationship between the daily crop evapotranspiration (ETc ) estimates by each method against the soil water balance budget evapotranspiration approach (SWB-ETc) is shown in Figs 9 and 11 for maize and Fig 10 for peanut crop, respectively. The FAO-56PM method gave very good results with R2 of 94 % for both maize and peanut crops while in case of Turc and Priestly–Taylor method R2 ranged between 74 and 85 %; high values of R2 were
obtained for Pan evaporation, Bowen ratio, Abtew, Hargreaves and Penman, respectively, but it was slightly lesser than FAO-56PM, Turc and Priestly–Taylor method, respectively. The least MRE value was obtained for FAO56PM. The best RMSE values of 0.22 and 0.28 (mm/day) were obtained for FAO-56PM for both maize and peanut crop, respectively (Fig. 11). The Turc method overestimated the daily ETc by 1.39 % with an R2 of 0.85 in case of maize
Effective crop evapotranspiration measurement Table 2
Statistical performance of different methods versus SWB method for estimating ETc
Rank Methods
Maize (2013) Slope R2
Maize (2014)
Peanut (2013)
RMSE MRE* (%) Slope R2 (mm/day)
RMSE MRE* (%) Slope R2 (mm/day)
RMSE MRE* (%) (mm/day)
1
FAO-56PM
0.99
0.94 0.22
−0.34
0.98
0.93 0.29
−0.38
0.98
0.9
0.28
−0.99
2
Turc
0.99
0.85 0.41
−1.39
0.96
0.7
0.53
1.12
1.03
0.73 0.39
1.51
3
Priestley-Taylor
1
0.74 0.5
2.32
1.02
0.85 0.41
2.27
1.012 0.8
4 5
Pan evaporation Bowen ratio
0.94 0.94
0.73 0.49 0.71 0.47
−2.9 −3.91
0.91 0.91
0.76 0.63 0.85 0.54
−4.38 −5.68
6 7
Abtew 1.07 Hargreaves Samani 1.09
0.77 0.57 0.72 0.73
7.4 9.6
0.99 1.07
0.7 0.51 0.72 0.86
8
Penman
0.72 0.76
12.89
1.12
0.76 0.85
1.98
0.94 0.94
0.77 0.46 0.77 0.44
−2.89 −3.09
5.96 7.65
1.01 1.04
0.75 0.47 0.78 0.5
4.17 5.44
15.26
1.15
0.79 0.72
11.44
(+) Shows over estimated and (−) shows under estimated with respect to the measured value
by 2.72 % with an R2 of 0.70 in the same region. The Priestly– Taylor method underestimated the daily ETc by −2.32 for
crop. Similar results were reported by Kashyap and Panda (2001) for the potato crop which overestimated the daily ETc
5 4 3
RMSE = 0.22 MRE = -0.34
2 1 0
8 7
2
4
6
4 3 2
RMSE = 0.50 MRE = 2.32
1 2
8
RMSE = 0.49 MRE = -2.90
1 0
0
RMSE = 0.41 MRE = -1.39
1 2
4
6
8
6 5 4 3
RMSE = 0.76 MRE = 12.89
2 1 0
0
2
5 4 3
RMSE = 0.73 MRE = 0.96 4
6
SWB ETc (mm/day)
(g)
8
Bowen ratio ETC (mm/day)
6
2
6
8
2
4
6
8
8
y = 1.0716x R² = 0.7781
7 6 5 4 3
RMSE = 0.57 MRE = 7.40
2 1 0
0
2
4
6
8
SWB ETc ( mm/day)
(f)
(e)
y = 1.0929x R² = 0.7272
1
4
SWB ETc (mm/day)
(d)
2
8
y = 1.1003x R² = 0.7217
7
SWB ETc (mm/day)
Hargreaves ETc (mm/day)
2
(c)
2
0
3
(b)
3
0
8
4
(a)
4
7
6
5
SWB ETc (mm/day)
5
8
4
6
SWB ETc (mm/day)
y = 0.9909x R² = 0.852
0
5
0
y = 0.9474x R² = 0.7381
7
6
0
8
8
y = 1.0092x R² = 0.747
7
SWB ETc ( mm/day)
6
0
Pristely-Taylor ETc (mm/day)
6
0
Turc ETc (mm/day)
8
Pan Evaporation ETc (mm/day)
y = 1.0167x - 0.0809 R² = 0.9478
7
Penman ETc (mm/day)
FAO 56 ETc (mm/day)
8
Abetw ETc (m/day)
a
1.1
0.33
y = 0.9498x R² = 0.7181
7 6 5 4 3 2
RMSE = 0.47 MRE =-2.35
1 0
0
2
4
6
8
SWB ETc (mm/day)
(h)
Fig 9 The relationship between the daily crop evapotranspiration (ETc) estimate of each method against the soil water balance budget evapotranspiration (SWB-ETc) for maize crop during the year 2013
6 5 4 3 2
RMSE = 0.29 MRE = -0.38
1 0
0
2
4
y = 1.0204x R² = 0.8554
6
5
5
4
4
3
3
2
2
RMSE = 0.41 MRE = 2.27
0
8
0
SWB ETc (mm/day)
2
Penman ETc (mm/day)
Turc ETc (mm/day)
5 4 3 2
RMSE = 0.53 MRE = 1.12
1 0
2
4
6
7
3 2
RMSE = 0.85 MRE = 15.26
1 0
2
3 2
RMSE = 0.86 MRE = 7.65 4
6
SWB ETc (mm/day)
(g)
8
Bowen ratio ETc (mm/day)
Hargresive ETC (mm/day)
4
2
6
8
8
4
6
8
y = 0.9946x R² = 0.7065
7 6 5 4 3 2 1
RMSE = 0.51 MRE = 5.96
0 0
2
4
6
8
SWB ETc (mm/day)
(e)
5
0
4
SWB ETc (mm/day)
6
0
8
4
0
8
y = 1.0775x R² = 0.7286
1
2
(c)
5
(d) 7
0
SWB ETC (mm/day)
6
SWB ETc, mm/day
8
0 8
y = 1.121x R² = 0.7682
8
6
0
6
(b)
y = 0.9618x R² = 0.7086
7
4
RMSE = 0.63 MRE = -4.38
1
SWB ETc (mm/day)
(a) 8
6
1
6
y = 0.9155x R² = 0.7639
Pan Evaporation ETc (mm/day)
7
7
7
y = 0.9859x R² = 0.9342
Abtew ETc (mm/day)
8
PT ETc (mm/day)
FAO 56 PM ETc (mm/day)
Srivastava R.K. et al.
(f)
y = 0.8746x R² = 0.7477
7 6 5 4 3 2 1 0
RMSE = 0.72 MRE = -8.51 0
2
4
6
8
SWB ETc (mm/day)
(h)
Fig 11 The relationship between the daily crop evapotranspiration (ETc) estimate of each method against the soil water balance budget evapotranspiration (SWB-ETc) for maize crop during the year 2014
maize crop with an R2 of 0.74. Similar results were reported by Kashyap and Panda (2001) for the potato crop which underestimated the daily ETc by −6.28 % with an R2 of 0.77 in the same region while for arid region contrasting results were reported by Zhao et al. (2010) which overestimated the daily ETc by 0.39 % with an R2 of 0.81 in case of maize crop. The reason for the contrasting estimation of the daily ETc might be due to the temperature difference between the sub-humid and arid regions. The Hargreaves–Samani method underestimated the daily ETc by −5.44 % with an R2 of 0.78 in the case of maize crop (Kashyap and Panda 2001; Zhao et al. 2010). Thus, Hargreaves–Samani and Priestly– Taylor methods could serve as alternative methods when the data of only air temperature is available while Turc could be an alternative method when the radiation is taken into consideration (Zhao et al. 2010). The Penman method underestimated the daily ETc by −12.89 % with an R2 of
0.72 for the maize crop. Similar results were obtained for the potato crop grown in the same sub-humid region which underestimated the daily ETc by −11.87 % with an R2 of 0.78 (Kashyap and Panda 2001). The daily ETc maximum and minimum values for maize and peanut crops are shown in Table 3.The Abtew, Hargreaves, and Penman methods overestimated the daily ETc by 7.4, 9.6, 12.89 % in case of maize for the year 2013 and 5.96, 7.65, 15.26 % for the year 2014, while 4.17, 5.44, 11.44 % in case of peanut for the year 2013, respectively. The Pan evaporation and Bowen ratio underestimated the daily ETc by −2.9 and −3.91 % in case of maize for the year 2013 and −4.38 and −5.68 % for the year 2014, while −2.89 and −3.09 % in case of peanut for the year 2013, respectively. The total ETc (mm day−1) values model wise for maize and peanut crop are shown in Table 4.
4 3 2
RMSE = 0.28 MRE = -0.99
1 0
0
2
4
6
4 3 2 1 0
0
4
2
RMSE = 0.39 MRE = 1.51
1 2
4
5 4 3 2 1 0
6
RMSE = 0.72 MRE = 11.44 0
0
2
4
6
2
4
4 3
RMSE = 0.50 MRE = 5.44 2
4
6
Bowen ratio ETc (mm/day)
y = 1.0483x R² = 0.7829
1
3 2 1
RMSE = 0.47 MRE = 4.17 0
2
6
4
6
SWB ETc (mm/day)
(e)
6
2
4
0
6
y = 1.0153x R² = 0.754
5
SWB ETc (mm/day)
(d) Hargreaves ETc (mm/day)
RMSE = 0.46 MRE = -2.89
1
6
y = 1.1151x R² = 0.7944
SWB ETc (mm/day)
0
2
(c)
3
0
3
(b)
4
5
4
0
6
= 0.9426x R² = 0.7647
(a) 6
0
2
5
SWB ETc (mm/day)
y = 1.0337x R² = 0.7395
5
RMSE = 0.33 MRE = 1.98
6y
SWB ETc (mm/day)
Penman ETc (mm/day)
Turc ETc (mm/day)
y = 1.0126x R² = 0.8034
5
SWB ETc (mm/day)
6
0
6
Pan Evaporston ETc (mm/day)
y = 0.9882x R² = 0.9085
5
Abtew ETc (mm/day)
FAO-56 PM ETc (mm/day)
6
Pristely-Taylor ETc (mm/day)
Effective crop evapotranspiration measurement
(f)
y = 0.9475x R² = 0.7782
5 4 3 2
RMSE = 0.44 MRE = -3.09
1 0
0
2
4
6
SWB ETc (mm/day)
SWB ETc (mm/day)
(h)
(g)
Fig 10 The relationship between the daily crop evapotranspiration (ETc) estimate of each method against the soil water balance budget evapotranspiration (SWB-ETc) for peanut crop during the year 2013
Table 3 ETc maximum and minimum values (mm day−1) for maize and peanut crop experiment
Methods
SWB FAO-56PM Turc Priestley Taylor Pan Evaporation Bowen ratio Abtew Hargreaves samani Penman
Maize 2013
Peanut 2013
Maize 2014
ETc minimum (mm day−1)
ETc maximum (mm day−1)
ETc minimum (mm day−1)
ETc maximum (mm day−1)
ETc minimum (mm day−1)
ETc maximum (mm day−1)
2.00 2.04 2.35 2.48 2.40 2.19 2.68 2.02
5.90 6.02 5.76 6.17 5.77 5.58 6.52 6.82
1.72 1.50 1.58 1.78 1.16 1.86 1.57 1.23
5.09 5.26 5.24 5.68 4.82 5.08 5.62 5.31
1.44 2.11 1.76 1.43 2.05 1.34 2.20 1.37
5.96 6.06 5.93 6.30 5.80 5.90 5.65 6.28
2.77
7.19
1.68
6.59
2.58
7.29
Srivastava R.K. et al. Table 4
Total ETc (mm/day) values model wise for maize and peanut crop
Methods
Maize 2013 Peanut 2013 Maize 2014 ETc(mm day−1) ETc(mm day−1) ETc(mm day−1)
SWB
262
221
286
FAO-56PM Turc
259 268
218 223
280 292
Priestly Taylor
269
228
295
Pan Evaporation
242
203
238
Bowen ratio Abtew
216 316
202 315
214 348
Hargreaves samani 362
243
368
Penman
351
380
389
4 Conclusions Eight methods comprising of four independent methods were used for estimating ETc for maize and peanut crops in a subhumid location namely Kharagpur, in eastern India. The results showed that the temporal variation of the ETc was significant among the four different independent methods. In comparison to SWB method, the result revealed that FAO56PM gave the best estimate of daily ETc in a sub-humid region. The alternative methods that can be used to estimate the daily ETc other than FAO-56PM are Turc and Priestly– Taylor. The Penman, Hargreaves, and Abtew are not recommended for the ETc estimation, particularly in the sub-humid region. Out of all the methods used during the study to evaluate daily ETc, the FAO-56PM fitted the best. From this study, it is quite evident that TDR does possess gripping possibilities in the future to study the distribution of water with time while experimenting in different climatic conditions along with keeping a track of good resolution and accuracy. TDR can also work very well as a tool for the estimation of ETc and can even estimate ETc accurately when the experimental fields are relatively small in size.
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