Optimization of furrow irrigation performance of sugarcane fields based on inflow and geometric parameters using WinSRFR in Southwest of Iran

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Optimization of furrow irrigation performance of sugarcane fields based on inflow and geometric parameters using WinSRFR in Southwest of Iran Reza Mazareia, Amir Soltani Mohammadia,*, Abd Ali Naseria, Hamed Ebrahimianb, Zahra Izadpanaha a b

Irrigation and Drainage Department, Faculty of Water Sciences Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran Department of Irrigation and Reclamation Eng., College of Agriculture and Natural Resources, University of Tehran, Karaj, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Furrow irrigation WinSRFR 4.1.3 Sugarcane Efficiency

Accurate design, suitable management and optimization of irrigation design parameters play an important role in increasing the performance of furrow irrigation. The main objective of this study was to optimize the performance of furrow irrigation using WinSRFR in the fields of Salman Farsi Agro Industry sugarcane, located in the southwest of Iran. For this purpose, field experiments were conducted under nine blocked-ended furrows with the length of 250 m, the top width of 1.83 m and slope of 0.04 % and in three inflow treatments (1.0, 1.5 and 2.0 L/s) with three repetitions. The WinSRFR software was employed to optimize the combination of irrigation parameters such as inflow rate, cut-off time and field geometry. Objective function (OF) including application efficiency, distribution uniformity and deep percolation was also employed to optimize the performance. The results showed that using 1.0 L/s inflow rate could increase OF by 35.99 % which was the best performance compared to 1.5 and 2.0 l/s. Changing furrow length from 250 m to 200 m showed that OF value increased by 39.8.% ; however, changing it to 300 m, OF decreased by 7.7 %. In addition, changing slope from 0.04 to 0.03 % decreased OF by 0.9.%, while changing it to 0.05 % OF was improved by 1 %. On the other hand, changing the inflow and cut-off time, field length and combinations of them led to the increased OF by 25, 8.39 and 31 %, respectively. Finally, to obtain the maximum performance in sugarcane fields, inflow rate of 3 L/s and cut-off time of 379.5 min were suggested.

1. Introduction Surface irrigation is the oldest and common irrigation method due to the low cost and energy requirements compared to sprinkler and drip irrigation. Thus, many studies have been carried out to increase the efficiency of surface irrigation systems (Walker and Skogerboe, 1987). Surface irrigation covers about 80 % of the total irrigated lands in Iran. Moreover, suitable design and logical management of the surface irrigation can led to increased water use efficiency and cultivated area (Ebrahimian and Liaghat, 2011; Lalehzari and Boroomand Nasab, 2017). Because of suitable aeration in the root zone, furrow irrigation is the best method in surface irrigation (Wu et al., 2017). However, furrow irrigation has some problems such as low efficiency, poor distribution uniformity and high deep percolation (Elliott et al., 1993; Moravejalahkami et al., 2009). The inappropriate management, design, and implementation are the important reasons for poor performance of surface irrigation systems (Ebrahimian and Liaghat, 2011). It is possible to design and evaluate furrow irrigation systems using

⁎

different simulation models. In past years, many researchers used some models to improve the performance of surface irrigation (Gillies et al., 2010; Koech et al., 2014; Morris et al., 2015). It is necessary to use simulation models such as SURDEV (Jurriens et al., 2001), SIRMOD (Walker, 2003), WinSRFR (Bautista et al., 2012), SIDES (Adamala et al., 2014), SURCOS (Burguete et al., 2014) and SISCO (Gillies and Smith, 2015) to reduce costs and design time (Mahdizadeh Khasraghi et al., 2015). Bautista et al. (2009) used WinSRFR software to evaluate field events, characterize infiltration and optimize the combination of irrigation parameters. In addition, Gonzlez et al. (2011, 2016) evaluated performance of surface irrigation and applied a new method to improve field topography. The results of this study showed that optimum slope depends on the infiltration, length and inflow rate. Finally, this method could be used to calculate the optimal slope. It is difficult to manage surface irrigation because of large number of effective parameters. Therefore, it is necessary to use the most effective parameters for improvement of irrigation performance. According to Raine et al. (1997); Smith et al. (2005); Bautista et al. (2009); Morris et al. (2015)

Corresponding author. E-mail address: [email protected] (A.S. Mohammadi).

https://doi.org/10.1016/j.agwat.2019.105899 Received 16 June 2019; Received in revised form 2 November 2019; Accepted 4 November 2019 0378-3774/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Reza Mazarei, et al., Agricultural Water Management, https://doi.org/10.1016/j.agwat.2019.105899

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fields located in southwest of Iran (latitudes 31°00ʹ30ʺ-32°30ʹ00ʺN and longitudes 48°15ʹ00ʺ-48°40ʹ40ʺE), as shown in Fig. 1. The average rainfall of the study area is 266 mm and the annual evaporation is 2788 mm. Total area of the Salman Farsi Agro Industry is over 14,000 ha; however, its cultivated area is 12,000 ha. All fields were divided into rectangular fields of 25 ha (250 m * 1000) area, all of which have subsurface drainage in the depth of 1.8 m. In this district, all fields are irrigated using furrow irrigation and low-pressure hydroflume. Irrigation usually starts in May and continues until early November. During the sugarcane growth period in this area, the applied irrigation water is 3000 mm with peak crop water use of 10−13 mm/d (Veysi et al., 2017).

studies, inflow rate and cut-off time are the most effective parameters. Morris et al. (2015) suggested that inflow rate of the range of 2–7 L/s and cut-off time from 50 to 300 min were suitable for the best performance. According to Walker and Skogerboe (1987); Clemmens et al. (1999) and Chen et al. (2012), geometric parameters such as slope, length and cross section are effective parameters as well. According to Chen et al. (2012), suitable field geometry could increase irrigation application efficiency up to 26.7.%. Anwar et al. (2016) reported that application efficiency and distribution uniformity are the common indicators for evaluation of surface irrigation; while, Gonzlez et al. (2011) used distribution uniformity as performance indicator. Chen et al. (2012) used application efficiency, average depth applied and distribution uniformity. Reddy et al. (2013) used application efficiency and water requirements. Morris et al. (2015) used application efficiency, requirement efficiency and deep-percolation. Finally, Kifle et al. (2017) used different indicators such as application efficiency, distribution uniformity, and deep-percolation and runoff volume, as indicators. Sugarcane fields (Seven plantation sites) are the major agricultural activities in the southwest of Iran (cover an area about 100,000 ha) which have become largest sources of water consumption. On the other hand, inappropriate design and unsuitable optimizations of irrigation parameters lead to decrease efficiency and non-uniform distribution of water in the furrow. So, to optimize irrigation parameters and suggest accurate approach, the aim of current study were defined as follows:

2.2. Field measurements Field experiments were carried out on R5-22 fields of sugarcane with the age of Raton 2 and there were three different irrigation events from 14 September to 31 October 2016. To evaluate irrigation system, all experiments were conducted on the furrows of 250 m in length, 1.83 m in space and 0.04 % in slope. In this study, nine block-ended furrows were irrigated under three repetitions and values of 1.0, 1.5 and 2.0 L/s for inflow rate. First, inflow rate was measured by W.S.C flume type 2. The furrows were divided into 10 stations that advance and recession time were recorded at each of the stations (Fig. 2). The SIPAR_ID model was used to estimate the roughness coefficient (Rodriguez and Martos, 2008). Results of the field measurements are summarized in Table 1.

a The first objective of this study is to evaluate WinSRFR ability for simulating furrow irrigation. b The second objective is to achieve the best combination of inflow rate and cut-off time. c The third purpose in the current study is to suggest the best combination of irrigation technical parameters. Finally, the last goal is to analyse different inflow rates, cut-off time, field layout and combination of them for improving furrow irrigation performance.

2.3. WinSRFR software WinSRFR is a new software for evaluating and simulating the surface irrigation. WinSRFR integrates the earlier software such as SRFR (Strelkoff et al., 1998), BORDER (Strelkoff et al., 1996) and BASIN (Clemmens et al., 1995). WinSRFR needs different data to analyse irrigation performance. Data required for software include inflow, geometric properties and depth of water application. In the current study, the Event Analysis World was used to estimate and calibrate the infiltration parameters. Furthermore, the operation analysis and Physical Design World were used to evaluate the irrigation and geometric parameters. WinSRFR software consists of Zero-Inertia and KinematicWave model. In the current study, we used the zero-inertia model to

2. Materials and methods 2.1. Study area Data used in the current study were collected from Salman Farsi Agro-Industry Sugarcane fields, on a clay-loam soil texture. Sugarcane

Fig. 1. Location of Salman Farsi Agro Industry unit in Southwest Iran. 2

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Fig. 2. Field layout and experimental setting.

and Kostiakov–Lewis parameters can be found using following Eq. [4] to [7].

simulate and evaluate furrow irrigation performance (Bautista et al., 2015).

Q0 t = σy A0 x +

3. Infiltration parameters

Ids

(4)

α + r (1 − α ) + 1 (1 + α )(1 + r )

σy = The modified Kostiakov-Lewis equation is one of the most useful infiltration equations in surface irrigation (Hanson et al., 1993). In this study, the Kostiakov-Lewis equation was used to calculate the infiltration. WinSRFR software used two point methods (Elliot and Walker, 1982) to estimate infiltration coefficients. In the present study, cumulative infiltration was estimated using the Kostiakov–Lewis equation as follows [1]:

Z = kt α + f0 t

α=

k=

(1)

Qin − Qout L

log( VL V0.5L ) log( tL t0.5L )

(6)

VL σZ tLα

(7)

Where σy is surface profile shape factor (0.77); σZ is subsurface profile shape factor; A0 is wetted area at the upstream (m2) and I stands for infiltration rate as f (x, t) (m/s). In which

V0.5L =

(2)

And

Where L is the length of furrow (m); Qin and Qout are inflow and runoff rate (m3/min), respectively. The advance curve is simple power function, found using the following Eq. [3] (Elliot and Walker, 1982; Walker and Skogerboe, 1987):

VL =

pt r

(5)

Kostiakov-Lewies parameters such as a and k were determined as follows:

Where Z is cumulative infiltration in units of volume per length of furrow (m3m-1); t represents elapse time of infiltration (min); f0 is the basic infiltration rate (m3m-1min-1); and finally, k and α are empirical coefficients (a = dimensionless, k = m3/minα.m-1). The basic infiltration rate is determined using the following Eq. [2] (Walker and Skogerboe, 1987):

x=

x

For determining σz , following Eq. [5]:

3.1. Determination of Kostiakov-Lewis parameters

f0 =

∫0

f t0.5L Q0 t0.5L − σy A0 − 0 0.5L 1+r

(8)

f tL Q0 tL − σy A0 − 0 L 1+r

(9)

3.2. Calibration of infiltration parameters

(3)

Due to the sensitivity of furrow irrigation performance to infiltration parameters, it is necessary to calibrate them. In this paper, Kostiakov-Lewis coefficients were calibrated using Event Analysis World and Merriam and Keller (1978) method in the WinSRFR

Where x is water front advance (m); t is time from the start of inflow (min) and r and p are fitting parameters. Cumulative infiltration (Z) obtained by Eq. [1] can be accomplished with the Lewis-Milne Integral Table 1 Data summary for the experimental furrows in all irrigation event. Furr.NO Irri. NO. 1

2

3

Q(L/s)

1 1

2 1.5

3 2

4 1

5 1.5

6 2

7 1

8 1.5

9 2

n Vin (m3) Tco (min) n Vin (m3) Tco (min) n Vin (m3) Tco (min)

0.216 50.75 913 0.175 60.65 1100 0.221 122.5 2300

0.1251 63.99 772 0.0274 70.39 820 0.0388 76.77 994

0.0174 85.68 696 0.0369 84.16 780 0.026 121.7 1095

0.1153 57.35 1053 0.163 74.51 1390 0.1236 135.81 1040

0.025 71.15 873 0.09 121.9 1310 0.094 94.15 1150

0.065 94.91 827 0.1084 149.97 1230 0.0533 119.88 1174

– – – 0.1155 94.95 1751 0.0777 94.67 1720

– – – 0.1284 71.66 856 0.063 87.14 1060

– – – 0.0528 82.36 749 0.023 112.94 1100

n: Manning roughness coefficient; Vin: Inflow volume (m3); Tco: Cut-off time (min). 3

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Table 2 The coefficients of Kostiakov-Lewis equation for three irrigation events and different furrows. Furr.

Irrigation 1 a

k ( mm hr a )

f0 ( mm hr )

Irrigation 2 a

k ( mm hr a )

f0 ( mm hr )

Irrigation 3 a

k ( mm hr a )

f0 ( mm hr )

1 2 3 4 5 6 7 8 9

0.32 0.34 0.15 0.26 0.15 0.30 – – –

42.46 52.20 119.90 56.29 84.17 70.05 – – –

0.97 1.30 0.83 0.73 2.10 4.00 – – –

0.21 0.17 0.25 0.15 0.20 0.20 0.15 0.25 0.20

50.62 90.08 89.87 89.49 133.39 143.00 124.90 70.41 93.52

2.45 0.85 0.80 1.50 1.20 3.69 0.60 1.50 1.40

0.15 0.10 0.20 0.15 0.20 0.11 0.20 0.11 0.11

141.59 86.96 148.37 175.17 98.12 154.58 111.06 114.62 145.19

1.50 3.50 0.80 1.00 2.34 3.20 0.50 2.30 3.20

*In the first irrigation event due to non-uniform slope in three furrow (number of 7, 8 and 9), these furrow were not investigated.

software. In this study, infiltration coefficients were calibrated manually. At first, measured values of α and f0 were used as infiltration coefficients. Then, to estimate k, different combinations of α and f0 were tested over an approximate range until the measured and simulated advance-recession curve could found the best convergence. Calibrated coefficients for three irrigation events were summarized in Table 2.

3.5. Statistical analysis

3.3. Irrigation performance parameters

NRMSE = (

The advance-recession curve was simulated by the WinSRFR software. In this study, three statistical criteria were used to analyze software's accuracy. These statistical criteria were: (1) Normalized Root Mean Square Error (NRMSE), (2) distribution to 45° line (λ) and (3) Wilmot agreement (d) as follows [14] to [16]:

In this study, three parameters were used to estimate performance of irrigation. For this purpose, soil moisture samples were taken using Auger core sampler before and after (48 h) irrigation at the three (first, mid and end) points along the furrow and in the three depths (0–30, 30–60 and 60−90 cm). Finally, three performance parameters were used in this study including Application Efficiency (AE), Distribution Uniformity (DU) and Deep-percolation (DP):

AE =

Zi × 100 Zd

(10)

DU =

ZLQ × 100 Z¯

(11)

Z DP = P × 100 Z¯

N

∑1 (Oi − Pi )2 N

) × 100

(14) (15)

Pi = λ × Oi N

∑1 (Oi − Pi )2 ⎡ ⎤ d=1−⎢ N ¯ | + |Pi − O¯ |)2 ⎥ (| O O − ∑ i 1 ⎣ ⎦

(16)

where Oi and Pi are the observed and predicted values of the advancerecession times, respectively; N is the number of measurements; and finally (O¯ ) ¯is the average measurement. If λ < 1 it's means Oi is more than Pi and if λ > 1 means Pi is more than Oi. Also the high accuracy in simulation in when d = 1. In addition, the Relative Error (RE) criterion was used to compare the field and simulated performance parameters:

RE = (12)

Vs − Vs × 100 Vs

(18)

where Vs and Vo are the simulated and observed values, respectively.

where Zi, Zd, ZLQ, Z ¯ and ZP are the depth of water added to the root zone (mm); depth of water applied to the furrow (mm); mean water depth infiltrated in the lower quarter (mm); the mean of depths infiltrated over the furrow length (mm) and depth of deep percolated water (mm) determined from root zone water balance; respectively.

4. Results and discussion 4.1. Advance and recession times The accuracy of the WinSRFR software in simulating advance and recession times was evaluated by comparing it with the measured data. Table 3 reports the results of advance and recession trajectory based on three statistical criteria (NRMSE, d and λ). According to Table 3, NRMSE, d and λ values varied from 6.91 to 22.36 %, 0.84 to 0.98 and 0.97 to 0.99, respectively, which the average values of NRMSE, d and λ in the first irrigation event are 14.1.%, 0.98 and 0.94, respectively. The results in the first irrigation event were significantly accurate compared to second and third irrigation events that these could be due to the different geometric properties, roughness coefficients, advance curve, as well as the high distribution uniformity in the furrows. Finally, the total average values of NRMSE, d, and λ (15.9.%, 0.98, and 0.96) showed the good accuracy in simulated advance times using WinSRFR software (except at the end of the field because of unsuitable slope). Recession trajectory depends on how the k value is influenced by the water infiltration rate and irrigation time (Xu et al., 2019). Due to low-slope (about 0.04 %) and subsurface drainage system, recession times in all stations were recorded with short intervals. The results of recession trajectory in Table 3 showed that NRMSE, d and λ values varied from 6.07–9.05 %, 0.5 to 0.76 and 0.97–1.01 for first irrigation

3.4. Objective function The inflow rate, cut-off time and field characteristics are the most important parameters affecting performance of furrow irrigation (Bautista et al., 2009). The performance contours were generated using the WinSRFR software to optimize performance. In this paper, inflow rate and cut-off time and geometric parameters were evaluated using operation analysis and Physical Design Worlds via WinSRFR, respectively. Finally, the objective function (OF) was employed to optimize the performance of furrow irrigation system.

OF = (α × AE ) + (β × DU ) − (γ × DP )

1 O¯

(13)

Which, α=β=γ = 0.33 To optimize the performance, three alternatives were evaluated. At the first alternative, physical parameters (field geometry) were assumed constant and inflow rate and cut-off time were changed. In the second alternative, inflow rate and cut-off time were constant and physical parameters were changed. Finally, inflow rate, cut-off time and physical parameters were altered. 4

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Table 3 Comparison of the measured and simulated advance and recession times using statistical indicators. NRMSE (%)

λ (-)

d (-)

Irri. NO.

Furr. NO.

Advance

Recession

Advance

Recession

Advance

Recession

1

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

6.90 8.95 18.23 6.50 21.93 22.36 .. * .. .. 10.83 14.81 20.63 7.61 20.31 16.92 17.22 11.23 20.70 11.97 14.79 20.99 12.79 14.80 24.04 12.28 14.44 30.99

6.07 9.05 8.68 7.43 6.16 7.25 .. .. .. 10.91 7.17 8.63 6.47 7.20 4.24 3.87 5.63 3.57 2.83 7.62 4.07 1.57 4.65 3.89 3.32 9.27 5.97

0.99 0.99 0.98 0.99 0.97 0.97 .. .. .. 0.99 0.99 0.98 0.99 0.98 0.98 0.98 0.99 0.98 0.99 0.98 0.98 0.99 0.99 0.97 0.99 0.99 0.96

0.76 0.5 0.72 0.66 0.71 0.51 .. .. .. 0.23 0.84 0.64 0.59 0.63 0.87 0.85 0.93 0.95 0.84 0.44 0.86 0.79 0.78 0.9 0.74 0.75 0.65

0.97 0.98 0.94 0.98 0.95 0.84 .. .. .. 1.00 0.99 0.91 1.00 0.99 0.95 1.02 1.04 0.90 0.97 0.93 0.93 1.00 0.97 0.96 0.96 0.99 0.98

0.99 1.00 1.00 0.99 1.01 0.97 .. .. .. 1.01 1.01 0.99 0.98 1.02 1.01 1.03 1.02 0.99 0.99 1.00 0.99 1.00 1.00 1.02 0.98 1.02 1.04

2

3

* In first irrigation event due to non-uniform slope in three furrow (number of 7, 8 and 9), these furrow were not investigated.

volume in different irrigation events. The average values of cut-off time and inflow volume in first event were 855.7 min and 70.6 m3, in the second event were 1109.5 min and 90.1 m3, which these values were lower than those obtained from third event (1292.5 min and 107.3 m3). This results indicated that the acceptable irrigation performance parameters were achieved in reasonable cut-off time and inflow volume. Xu et al. (2019) also reported that variation in inflow volumes, affecting irrigation performance, was mainly caused by variation in infiltration and manning roughness coefficient. Finally, average values of AE, DU and DP were 60.9, 76.4 and 39.1 %, respectively. Different studies reported similar results such as Izadi et al. (1991), Dalton et al. (2001); Smith et al. (2005), Reddy et al. (2015) and Kifle et al. (2017); Salahou et al. (2018), Xu et al. (2019 and Nie et al. (2019). The irrigation performance parameters under different dinflow rate were compared in Table 5. These studies showed that AE was ranged from 50 to 70 %. As seen in Table 5, the highest and lowest values of OF were obtained for inflow rate of 1 L/s (35.9 %) and 2 L/s (25.4 %), respectively. Low-slope (about 0.04 %), heavy soil texture (clay-loam) and longer opportunity time led to the highest OF for 1 L/s compared to other inflows. Because of limits in topography, the highest performance indicators (AE, DU and DP) were occurred in 3 L/s and cut-off times of 324.7, 383.5 and 429.5 min for the first, second and third irrigation events, respectively (Fig. 3). Fig. 3 shows that under the first irrigation, the maximum values of AE, DU and DP are 67.9, 87.3 and 12.3 %, respectively. In the

event, 3.57–10.91%, 0.23 to 0.95 and 0.98–1.03 for second irrigation event, 1.57–30.99%, 0.44 to 0.90 and 0.98–1.04 for third irrigation event. The average values of NRMSE, d and λ were 6.1.%, 0.71, and 0.98 in simulating recession times, respectively, showing a high accuracy of the software. These results are agreement with Abbasi et al. (2003); Chen et al. (2012); Anwar et al. (2016); Sayari et al. (2017) and Xu et al. (2019) who reported that WinSRFR accuracy is reasonable for simulation of advance and recession curves. 4.2. Performance analysis Table 4 summarizes the results of AE, DU and DP for three irrigation events for an application depth of 100 mm. The highest AE (74 %) and OF (40.3 %) was determined at the first event. Given the suitable slope and no compact soil, more volume of water was applied to root zone, which would decrease DP (26 %). The minimum value of AE (48.5 %) and OF (12.2 %) was obtained for the third irrigation event. This could be because of longer cut-off time and unsuitable topography (because of traffic of agricultural machinery) of the second and third event. The AE and DU values in second irrigation event (74 and 77.05 %) and first event (60.22 and 74.02 %) were higher than those obtained from third event (48.56 and 39.78 %), which the lower values of DU in third event is due to high inflow volume and insufficient water stored in root zone. The values of DP in first and second events were lower than third irrigation event. This finding could be because of cut-off time and inflow

Table 5 Values of objective function for various inflow rates (%).

Table 4 The average values of the performance indicators of furrow irrigation system in three irrigation events (%).

Q (L/ s)

Irri. N . O.

AE

DU

DP

OF

Irri. N. O.

1

1.5

2

1 2 3 Avg. (%)

75.50 60.22 48.56 61.43

74.02 77.05 39.78 74.85

26.33 39.78 51.44 39.19

40.65 32.17 12.18 32.04

1 2 3 Avg. (%)

52.44 35.90 19.34 35.89

40.52 33.59 30.45 34.85

29.00 27.03 20.08 25.37

5

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Fig. 3. Performance parameters relative to flow management variables (a: first irrigation, b: second irrigation and c: third irrigation).

second event, the maximum values of AE, DU and DP were 75.7, 75 and 28.5 %, respectively. Finally, in the third event, 4.1, 2.7 and 31.6.% were obtained for maximum values of AE, DU and DP, respectively.

4.3. Simulating the performance parameters with WinSRFR

Fig. 4. Comparison of measured and simulated performance indicators (a: first irrigation, b: second irrigation, c: third irrigation).

A comparison between experimental data and simulated results based on the statistical criteria such as RE and R2 is summarized in Fig. 4. For all irrigation events, the simulated irrigation indicators differed from field measured values. The results of Fig. 4 shows the RE and R2 of DU were 16.02 % and 0.47 for first event, 13.5.% and 0.11 for second event and 20.44 % and 0.5 for third event, whereas for AE, the values of RE between simulated and measured data in three irrigation

events are 6.26, 5.19 and 13.35 %, respectively. Also for AE, the values of R2 were 0.87, 0.97 and 0.86, respectively. This is because of many reasons and the most important reason may be that the inflow volume and cut-off time in all irrigation events were greater than required values. These reason led to the applied water depths were more than required water depth (Zreq = 100 mm) and this results are agreements 6

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sensitive. Increasing inflow rate from 1 L/s to 1.5, 2, 2.5 and 3 L/s increased AE by 7.8, 11.9, 14.6 and 16.5.%, DU by 8.1, 11.9, 14.6 and 16.6.%, OF by 7.8, 11.9, 14.6 and 16.5.%, and decreased DP by 7.9, 12.1, 14.9 and 16.8.%, respectively. According to this results changing inflow rate from 1.0 L/s to 1.5, 2.0, 2.5 and 3.0 L/s increased AE and DU more than 20 % and decreased DP up to 30 %. Changing inflow to the range of 1.5−3 L/s could improve OF about 25 %. The optimal performance indicators were obtained when the inflow rate increased to 3 L/s (values of 74.92, 75.09 and 24.92 % for AE, DU and DP. respectively). Salahou et al. (2019) also reported that by increasing and decreasing inflow rate, the irrigation performance indicators increased and decreased, respectively. The results are similar to other studies such as Morris et al. (2015); Anwar et al. (2016); Akbar et al. (2016) and Nie et al. (2019), showing that reasonable combination of Qin and cut-off time increased AE to 75–90% and this results indicated that an optimal inflow variables can be used for design of furrow irrigation in sugarcane fields; which can increase irrigation performance.

Table 6 Results of irrigation performance indicators under different values of slope, length and inflow rate (%). S (%)

L(m)

Q(L/s)

AE (%)

DU (%)

DP (%)

OF (%)

0.03

200

1 1.5 2 2.5 3 1 1.5 2 2.5 3 1 1.5 2 2.5 3 1 1.5 2 2.5 3 1 1.5 2 2.5 3 1 1.5 2 2.5 3 1 1.5 2 2.5 3 1 1.5 2 2.5 3 1 1.5 2 2.5 3

61.96 68.38 72.13 74.54 75.96 57.83 65.17 69.38 72.21 74.08 53.79 62.17 67.00 69.96 72.21 62.71 69.25 73.04 75.29 76.50 58.38 66.17 70.33 72.92 74.92 54.21 62.96 67.96 70.58 72.83 63.33 69.88 73.46 75.83 77.58 58.83 66.92 70.46 73.13 75.08 54.79 63.71 68.04 70.50 72.83

62.15 68.55 72.30 74.76 76.49 57.89 65.25 69.52 72.31 74.29 53.86 62.13 66.94 70.03 72.22 62.80 69.47 73.18 75.68 77.44 58.47 66.59 70.36 73.11 75.05 54.79 62.94 67.92 70.52 72.68 63.41 70.00 73.25 76.05 77.88 59.00 66.87 70.44 73.23 75.20 54.81 63.67 68.05 70.39 72.72

37.96 31.50 27.58 25.17 23.38 42.04 34.96 30.50 27.75 25.67 46.29 37.92 33.00 30.08 27.83 37.29 30.54 26.88 24.21 22.58 41.71 33.83 29.58 26.79 24.92 45.83 37.08 32.04 29.50 27.21 36.75 30.04 26.46 23.92 22.08 41.21 33.21 29.54 26.79 24.88 45.33 36.46 32.04 29.67 27.67

28.43 34.79 38.56 40.96 42.59 24.31 31.50 35.77 38.53 40.49 20.25 28.50 33.31 36.27 38.48 29.11 35.70 39.38 41.83 43.35 24.80 32.64 36.67 39.35 41.27 20.85 29.31 34.27 36.83 39.04 29.70 36.24 39.68 42.23 44.02 25.29 33.19 36.75 39.46 41.38 21.21 30.00 34.34 36.70 38.90

250

300

0.04

200

250

300

0.05

200

250

300

4.5. Changing geometric parameters For studying effect of geometric parameters on furrow irrigation performance, values of 1 L/s, 250 m and 0.04 % were considered for Qin, length and slope, respectively, as field condition. In this study, different furrow lengths such as 200, 250, and 300 m were employed to improve the performance indicators. According to Table 7, changing slope from 0.04 to 0.03 % decreased AE, DU and OF by 0.93, 1 and 0.9. %, respectively, and increased DP by 0.8.%. When slope was 0.05 %, the values of AE, DU and OF increased to 0.79, 0.91, 0.99 %, respectively; however, DP decreased by 1.2.%. These results indicated that the three performance indicators increased as the slope increased, which this is because of decreasing of volume stored in the furrow. The results of current study are agreements with Salahou et al. (2019). The results indicated that slope had low effect on the performance of furrow irrigation. As seen in Table 7, when field length decreased from 250 m to 200 m, AE and DU, respectively, increased by 7.42 and 7.41 % and DP reduced by 10.59 %. These results led to improving OF by 9.39 %. On the other hand, when furrow length was 300 m, AE and DU decreased by 7.14 and 6.29 %, respectively, and DP increased by 9.89 %. Because of this change, the average value of objective function was improved about 7.7.%. Xu et al. (2019) also reported that AE values reduce by increasing field length. Also they showed the total amount of water that percolated deeply increased with increasing border length. Other researchers such as Bai et al. (2010) and Chen et al. (2012) reported similar results. These studies suggested that geometric parameters (i.e. field length, width and slope) affect the irrigation performance.

with Nie et al. (2019). It is clear that AE (values of 8.3.% and 0.90 for RE and R2, respectively) was more accurate than DU (values of 16.65 % and 0.24 for RE and R2, respectively) and DP (values of 15.6.% and 0.93 for RE and R2, respectively). The results showed that the software had a high accuracy in simulating DP. In the second event, reasonable cut-off time and suitable topography led to high AE and DU and low DP. Results of Fig. 4 illustrates that the high DP (from 5 to 55 %) led to low performance. This is because of many reasons such as unsuitable topography, geometric properties and longer cut-off time. The results showed that the simulated DU was more than measured. This is because of unsuitable slope in length of furrows, which model can’t consider this properties and insufficient water stored in root zone.

4.6. Optimal combinations of design parameters In this study, parameters affecting the performance analysis were classified in two cases. The first case is Qin and cut-off time and other case is furrow length and slope. To evaluate the performance, 1 L/s, 250 m and 0.04 %, respectively, for inflow rate, length and slope were considered as standard condition. In this study, the Physical Design World of the WinSRFR software was used to optimize length and slope.

4.4. Optimal inflow variables

Table 7 Effect of slope and length changes on the performance indicators based on relative error (%).

Bautista et al. (2009) evaluated surface irrigation using WinSRFR and suggested that inflow rate and cut-off time can led to maximum performance of furrow irrigation system and they are the most effective parameters compared to other parameters. In the current section, we employed different inflow rate (Qin) and cut-off time to improve the performance. All results are summarized in Table 6. As indicated in Table 6 for larger changing in inflow rate, the AE, DU and DP were less

S (%) L (m)

7

0.03 0.05 200 300

AE

DU

DP

OF

−0.93 0.79 7.42 −7.14

−1.00 0.91 7.41 −6.29

0.80 −1.20 −10.59 9.89

−0.90 0.95 8.39 −7.70

Agricultural Water Management xxx (xxxx) xxxx

R. Mazarei, et al.

Fig. 3 shows that the maximum values of AE and DU and minimum value of DP were obtained for inflow rate of 3 L/s, length of 200 m for and slope of 0.05 %. When design parameters were changed, the AE and DU was increased more than 25 % and DP was decreased by 39 %. Consequently, OF was improved more than 30 % because of changing design parameters. Therefore, reasonable combinations of design parameters led to 6 % increase of OF compared to the OF value under only changing inflow variables.

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5. Conclusion In this study, we used the WinSRFR software to evaluate the performance of furrow irrigation. The Kostiakov–Lewis equation was employed to estimate the infiltration characteristics. Then, these parameters were calibrated using Merriam-Claire volume balance method. The software ability to simulate advance and recession curves using three statistical criteria (NRMSE, λ and d) was analysed. The results showed that WinSRFR software had a high accuracy in simulation of advance and recession curves. The results also showed that inflow rate of 1 L/s with 35.99 % for OF had the best performance. In addition, based on the findings of this study, the WinSRFR software estimates AE more accurately than DU and DP. Finally, changing inflow rate and cut-off time led to maximum OF and consequently, it can be used to improve the irrigation performance. The results also showed that high performance was achieved in the inflow rate of 3 L/s and cutoff time of 379.5 min. Declaration of interests 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. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Acknowledgments The authors would like to thank Shahid Chamran University of Ahvaz and Salman Farsi Sugarcane Agro-Industry for the financial and other supports. We also thank two anonymous reviewers of this journal for their helpful comments and suggestions. References Abbasi, F., Shooshtari, M.M., Feyen, J., 2003. Evaluation of various surface irrigation numerical simulation models. J. Irrig. Drain. Eng. 129 (3), 208–213. Adamala, S., Raghuwanshi, N.S., Mishra, A., 2014. Development of surface irrigation systems design and evaluation software (SIDES). J. Comput. Electron. Agric. Akbar, G., Ahmad, M.M., Ghafoor, A., Khan, M., Islam, Z., 2016. Irrigation efficiencies potential under surface irrigation farms in Pakistan. J. Eng. Appl. Sci. 35 (2), 15–23. Anwar, A.A., Ahmad, W., Bhatti, M.T., Haq, Z.U., 2016. The potential of precision surface irrigation in the Indus basin irrigation system. J. Irrig. Sci. 34 (5), 379–396. Bai, M.J., Xu, D., Li, Y.N., Pereira, L.S., 2010. Stochastic modelling of basins micro topography: analysis of spatial variability and model testing. J. Irrig. Sci. 28 (2), 157–172. Bautista, E., Clemmens, A.J., Strelkoff, T.S., 2009. Modern analysis of surface irrigation systems with WinSRFR. J. Agric Water Manag. 96 (7), 1146–1154. Bautista, E., Schlegel, J.L., Strelkoff, T.S., 2012. WinSRFR 4.1 User Manual. Arid Land Agricultural Research Cent. Bautista, E., Schlegel, J., Clemmens, A., 2015. The SRFR 5 modelling system for surface irrigation. J. Irrig. Drain. Eng. 42 (1), 04015038.1–040150380.11. Burguete, J., Lacasta, A., García-Navarro, P., 2014. SURCOS: a software tool to simulate irrigation and fertigation in isolated furrows and furrow networks. J. Comput. Elect. Agr. 103, 91–103. Chen, B., Ouyang, Z., Zhang, S.H., 2012. Evaluation of hydraulic process and performance of border irrigation with different regular bottom configurations. J. Resources Ecol. 3 (2), 151–160. Clemmens, A.J., Dedrick, A.R., Strand, R.J., 1995. BASIN 2.0. A Computer Program for

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