Biosystems Engineering (2002) 82 (4), 479–484doi:10.1006/bioe.2002.0088, available online at http://www.idealibrary.com onSW}Soil and Water

1

Determination of Infiltration Rate for Every-other Furrow Irrigation

A. R. Sepaskhah; H. Afshar-Chamanabad

Irrigation Department, College of Agriculture, Shiraz University, Shiraz 71365, I.R. Iran; e-mail of corresponding author:sepas@hafez.shirazu.ac.ir

(Received 21 May 2001; accepted in revised form 19 April 2002; published online 11 July 2002)

Surface irrigation, including every-other and ordinary furrow irrigation is used more than pressurizedirrigation due to the low cost and energy requirements. However, more precise selection of design parametersfor efficient design of surface irrigation is required for higher irrigation efficiency and the accurate predictionof the infiltration rate is of prime importance. Furthermore, the infiltration parameters may be different inordinary and every-other furrow irrigation in different inflow rates. Therefore, this research was conducted todetermine the parameters of Lewis–Kostiakov infiltration equation in ordinary and every-other furrowirrigation with different inflow rates based on the data obtained in the advancing stage (method I) and in bothadvancing and storage stages (method II). The results indicated that the Lewis–Kostiakov equation should bemodified for furrow irrigation with different inflow rates Q by multiplication of Qg except for the firstirrigation in which Q multiplication is not needed. However, the value of exponent g is lower when all datafrom the advancing and storage stages (method II) are used for calculation of the infiltration parameters. It isalso concluded that the infiltration parameters for every-other furrow irrigation are higher than those forordinary furrow irrigation. Furthermore, the data from the advancing and storage stages (method II) are moreappropriate for the calculation of infiltration parameters than the data from the advancing stage (method I),due to the fact that in method II, data were calculated from complete furrow irrigation including advancingand storage stages. # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved

1. Introduction

Surface irrigation is used more than pressurizedirrigation due to low cost and energy requirements.Innovative surface irrigation techniques are usedfor higher irrigation efficiency, among which every-other furrow irrigation decreases deep percolation,thereby increasing water use efficiency (Sepaskhah &Kamgar-Haghighi, 1997; Hodges et al., 1989b; Stoneet al., 1982). However, precise design for surfaceirrigation is required for higher irrigation efficiencyand accurate prediction of the infiltration rate is ofprime importance (Zerhun et al., 1996; Hodges et al.,1989a). Many researchers used the Lewis–Kostiakovequation for infiltration in furrow irrigation andproposed methods for determination of its parameters(Elliott & Walker, 1982; Elliott et al., 1983; Hopmans,1989; Scaloppi et al., 1995).One of the earliest infiltration equations was an

empirical model developed by Kostiakov (1932). The

537-5110/02/$35.00 47

equation has the following form:

Z ¼ kta ð1Þ

where Z is the cumulative infiltration in m, t is the intakeopportunity time in min, and k and a are empiricalparameters obtained from infiltration tests on a givensoil. The infiltration rate is obtained by derivative ofEqn (1):

I ¼ akta�1 ð2Þ

where I is the infiltration rate in mmin�1. The majordisadvantage of this equation is that it predicts aninfiltration rate approaching zero with increasing time,which is known to be incorrect. A constant term can beadded to Eqn (2) to correct this problem so that Eqn (1)becomes

Z ¼ kta þ fot ð3Þ

where fo is some value representing the final infiltrationrate as t becomes large (Walker, 1989).

9 # 2002 Silsoe Research Institute. Published by

Elsevier Science Ltd. All rights reserved

A. R. SEPASKHAH; H. AFSHAR-CHAMANABAD480

A flow cross-sectional area, m2

Ao water cross-sectional area at thebeginning of the furrow

a infiltration equation constanta1, a2, b1,b2, c, M

constants for determination ofgeometric characteristics

fo basic infiltration rate, m�3m�1min�1

I infiltration rate, mmin�1

k infiltration equation constantL furrow length, mp advancing equation constantp1, p2 parameters of furrow geometric

characteristicsn Manning roughness coefficientQin inflow rate, m3 s�1

Qout outflow rate, m3 s�1

r advancing equation constantSo slope of furrow bottom, mm�1

T top width of water flow, mt elapsed time, minVx right-hand side of Eqn (18)Wp wetted perimeter of flow, mx distance from the beginning of the

furrow, mY water depth, mZ infiltrated water, m3m�1

g an arbitrary exponentsy surface storage water profile shape

factorsz infiltrated water profile shape factor

Notation

Trout (1992) concluded an inverse relationshipbetween infiltration and flow velocity in furrow irriga-tion. However, Izadi and Wallender (1985) foundpositive correlations between infiltration rate and wettedperimeter. As both flow velocity and wetted perimeterincrease with flow rate, their opposing effects oninfiltration can result in little apparent effect when flowrates change (Trout, 1992). Then, the infiltration mayhave the following form:

Z ¼ ðkta þ fotÞQin ð4Þ

where Qin is the inflow rate in furrow in m3 s�1.

In every-other furrow irrigation, half of the furrowsremain dry during irrigation, therefore, horizontal flowin dry furrows is an important component of infiltra-tion. So, the infiltration equation parameters might bedifferent from those in ordinary furrow irrigation. Thesedifferences in the parameters of the infiltration equationmay result in variation in the advance curve for every-other furrow irrigation (Hodges et al., 1989).Furthermore, the inflow rate may influence the

infiltration equation parameters due to increasing flowcross-sectional area or wetting perimeter. Most of theinvestigators used furrow hydraulic data for advancingwater to calculate the infiltration parameters. However,Scaloppi et al. (1995) used the data obtained in theadvancing and storage stages of furrow irrigation forcalculation of infiltration parameters and believed thattheir method results in more accurate parameters ofinfiltration.The objective of this research was to determine the

parameters of Lewis–Kostiakov infiltration equation inordinary and every-other furrow irrigation with differentinflow rates based on data obtained in advancing stageand in both advancing and storage stages.

2. Materials and methods

This experiment was conducted at Badjgah Agricul-tural Experiment Station, Shiraz University, located16 km north of Shiraz. The field soil was a clay loam andits physico-chemical properties are shown in Table 1.Nine furrows with a spacing of 60 cm and a length of100m, and nine furrows with a spacing of 120 cm (every-other furrow irrigation) and a length of 100m wereestablished in this field (Fig. 1). The longitudinal slopeof furrows were 0�4%. The inflow rates were 0�4, 0�8 and1�1 l s�1 for ordinary and every-other furrow irrigation.The constant inflow rates were taken from controlvalves connected to a polyethylene pipe provided aconstant head by a reservoir with a height of 3�4m.Overflow of water from this reservoir guaranteed theconstant head. For each inflow treatment, two furrowswere considered as guards at both sides of the treatmentfurrows.A ruler was driven vertically every 10m into

the bottom of the experimental furrows (stations)and at each station, a horizontal ruler was set. As theinflow water entered the furrows and reached eachstation, the time of reach, water depth, surface waterwidth, flow cross-section and wetted perimeter at allstations before that station were determined by themethod proposed by Walker and Skogerboe (1987).These measurements were taken during the advancingand the storage phases. At the storage phase, outflow atthe end of each furrow was determined by calibratedWashington State College (WSC) flumes (James, 1988).Then the relationships between these geometric para-meters and water depth were determined. The long-itudinal slope of the furrow bottom was also determinedafter each irrigation.

Table 1Some physico-chemical properties of the soil used in the experiment

Depth, cm Sand, % Silt, % Clay, % pH Organic matter, % Bulk density g cm�3 Saturated water content, %

0–30 35 35 30 8�0 2�0 1�43 40�7540–54 23 38 39 8�2 } 1�43 40�7554–112 21 39 40 8�0 0�7 } }

Fig. 1. The experimental field layout

INFILTRATION RATE DETERMINATION 481

2.1. Computation of infiltration parameters

For a given inflow rate, cross-section, slope andwetted perimeter Lewis–Kostiakov equation is pre-sented in Eqn (3). The basic infiltration rate fo inm3m�1min�1 is obtained from the following equation:

fo ¼ ðQin � QoutÞ=L ð5Þ

where Qin and Qout are the inflow and outflow rates inm3 s�1 after a long time (more than 4 h at basicinfiltration rate) and L the furrow length in m.Walker (1989) used the empirical equation describing

the advance curve in furrow irrigation to determine theinfiltration parameters (k; a) as follows:

x ¼ ptr ð6Þ

where x is the distance from beginning of the furrow inm, and p and r are constants.Applying the water balance equation in furrow and

Eqn (4) for infiltration, the following is obtained

(Walker & Skogerboe, 1987):

Qint ¼ syAox þ szktax þ ð fotxÞ=ð1þ rÞ ð7Þ

where sz is the infiltrated water profile shape factor andcan be estimated by the following equation (Walker,1989):

sz ¼ ða þ rð1� aÞ þ 1Þ=ðð1þ rÞð1þ aÞÞ ð8Þ

where a in this equation is the same as the exponent inEqn (1). The surface storage water profile shape factorsy is taken as equal to 0�75 (Walker, 1989). The watercross-sectional area Ao at the beginning of the furrowcan be calculated by the following equation:

Ao ¼ ðQinn=ðp1S1=2o Þ1=p2 Þ ð9Þ

where n is the Manning roughness coefficient and variesbetween 0�02 and 0�15 for different stages of wheatgrowth in the experimental field (Walker, 1989; Sepas-khah & Bondar, 2002). Furrow irrigation is a commonpractice in wheat cultivation, in which the broadcastedseed is irrigated with furrows. The slope of furrowbottom is denoted by So in mm

�1, and p1 and p2 are the

A. R. SEPASKHAH; H. AFSHAR-CHAMANABAD482

furrow geometric characteristic parameters. These para-meters can be estimated as follows:

p1 ¼ að1�667�p2Þ1 =b0�6671 ð10Þ

p2 ¼ 1�667� 0�667b2=a2 ð11Þ

where a1, a2, b1 and b2 are the coefficients of empiricalequation as follows which are determined by regressionanalysis:

Wp ¼ b1Yb2 ð12Þ

A ¼ a1Ya2 ð13Þ

where A is the flow cross-sectional area in m2, Wp is thewetted perimeter of flow in m, and Y is the water depthin m. The wetted parameter Wp may be determined byusing the top width of flow T in m and the water depthY . Furthermore, the top width of flow T can beestimated as follows:

T ¼ cY M ð14Þ

where c and M are constants. However, as stated byStrelkoff and Clemmens (2000), top width and flow areacan be power functions of depth, but the wettedperimeter cannot be. Insisting that, it can lead to errorsin excess of 25%. This analysis, however, indicated thatfor the present investigation the power function forwetted perimeter and depth was obtained as

Wp ¼ 5�34Y 0�95 ð15Þ

with a value for the coefficient of determinationR2 ¼ 0�897.To determine k and a from Eqn (7) two procedures

were used, namely: method I using data only from theadvancing stage; and method II using data from boththe advancing and storage stages.

2.2. Advance stage only

In this procedure, method I, all data for the stationsinstead of two-point method of Walker and Skogerboe(1987) were used in Eqn (7). The two-point method maybe suitable when the furrow cross-section and slope areuniform throughout its length. When this condition isnot met with, the more general procedure, using all datapoints, could be more appropriate. Therefore, Eqn (7) iswritten as follows:

Vx ¼ szkta ð16Þ

where

Vx ¼ Qint=x � syAo � fot=ð1þ rÞ ð17Þ

The infiltrated volume of water per unit length by thefirst term of the Lewis–Kostiakov equation is calculatedfrom right-hand side of Eqn (17), Vx. Then, by

regression analysis between lnVx and ln t, the valuesof a and Vx1 (value of Vx at 1min elapsed time) areobtained. So, the value of k is calculated as follows:

k ¼ Vx1=sz ð18Þ

2.3. Advancing and storage stages

This procedure, method II, is similar to method Iexcept the data were obtained from advancing andstorage stages and then used in the water balanceequation [Eqn (7)]. In this procedure, the surface storagewas determined by measuring the water depth and cross-sectional area of flow from the furrow hydraulicgeometry at all stations. Furthermore, the outflow atthe end of the furrow end at the storage stage was alsomeasured by a calibrated Washington State College(WSC) flume and was used in the water balanceequation.

3. Results and discussion

The measured soil water content before each irriga-tion (1–7) at depths of 0–105 cm were similar (data notshown). The mean slope of the furrow bottom beforeeach irrigation was about 0�4%.The exponent in Eqn (6) was different for the various

inflow rates as follows:

r ¼ 0�729þ 0�0795Qin ð19Þ

with a value for R2 ¼ 0�17.Due to this very small value of R2, the average value

of r for all treatments and irrigations (1–7) as 0�79 wasused in the calculations. The mean basic infiltrationrates are shown in Table 2. It is clear that at higherinflow rates the basic infiltration rate is higher due togreater wetted perimeter.The relationship between infiltration and inflow rate

may not be linear. Using the data obtained for advanceof water front, hydraulic geometry of furrow in acomputer program written by Afshar–Chamanabad(1997), the parameters of Lewis–Kostiakov equationfor the first and subsequent irrigations and ordinary andevery-other furrow irrigations with different inflow rateswere calculated by a non-linear curve-fitting procedureas follows:

Z ¼ ðkta þ fotÞQgin ð20Þ

where g is an arbitrary exponent.The results for different parameters of Eqn (20) are

shown in Table 3. The results indicated that theinfiltration equation [Eqn (20)] for the first ordinaryirrigation at two different methods of calculation is not

INFILTRATION RATE DETERMINATION 483

dependent on the inflow rates and were almost similar.However, for every-other furrow irrigation even at thefirst irrigation, the infiltration equation was dependenton the inflow rates. This is due to the higher infiltrationcapacity of every-other furrow irrigation than that ofordinary furrow irrigation, therefore, the water depthand the wetted perimeter remain low in the every-otherfurrow irrigation. However, the value of the exponent gfor the inflow rate was lower in method II (0�17 versus

0�67).Uniform inflow rate in furrow irrigation may result in

an excessive runoff and low irrigation applicationefficiency. However, cutback furrow irrigation withdifferent inflow rates at first and second stages (advan-cing and storage stages, respectively) of irrigation mayreduce the runoff and enhance the irrigation applicationefficiency. Furthermore, the inflow rates may be differentdue to difference in the length of furrow under a givensoil and design conditions. Therefore, Eqn (20) may beused to determine the infiltration with various inflowrates.In general, the exponent for the inflow rate g for

method II of calculation was lower than that for methodI. The dry-to-wet boundary length in furrow irrigation

Table 2

Basic infiltration rates at different irrigation treatments andinflow rates

Irrigationtreatment

Inflow rate,ls�1

Basic infiltration

rate, m3 m�1 s�1

Ordinary 1�1 0�00021furrow 0�8 0�00018

0�4 0�00014

Every-other 1�1 0�00021furrow 0�8 0�00018

0�4 0�00014

Tabl

Parameters of Lewis–Kostiakov infiltration equation

Method of calculation Irrigationtreatment

Irrigationumbe

I (Advancing stage only) Ordinary FirstNext

Every-other FirstNext

II (Advancing and storage stages) Ordinary FirstNext

Every-other FirstNext

during the advancing stage may adversely affect thelateral water movement in soil. This boundary length isdominated during the infiltration process in method I.Therefore, the effect of inflow rate in infiltration ishigher which is depicted by greater exponent for inflowrate. The cumulative infiltrated water as a function oftime for ordinary and every-other furrow irrigations atan inflow rate of 1�1 l s�1 with methods I and II areshown in Figs 2 and 3. The infiltrated water in every-other furrow irrigation with method II of calculation isgreater than that for ordinary furrow irrigation (Fig. 2).However, the reverse is obtained for method I ofcalculation (Fig. 3). The reasons for this may be due toerrors in the estimation of the surface storage volumeand selection of values for n, and the use of data for theadvancing stage only. In method II of calculation, these

e 3

for different irrigation treatments and inflow rates

nr

Infiltration parameters Coefficient ofdetermination

k a g (R2)

0�0014 0�55 0�0 0�860�0012 0�64 0�63 0�890�0014 0�55 0�67 0�960�0020 0�39 0�17 0�94

0�0012 0�56 0�0 0�980�0017 0�41 0�23 0�960�0017 0�54 0�17 0�910�0025 0�36 0�29 0�95

Fig. 2. Cumulative infiltration for 1�1 l s�1 inflow rate calculatedwhen using data of advancing stage (method I) in ordinaryfurrow (dashed line) and every-other furrow irrigation (solid

line)

Fig. 3. Cumulative infiltration for 1�1 l s�1 inflow rate calculatedwhen using data from advancing and storage stages (method II)in ordinary furrow (dashed line) and every-other furrow

irrigation (solid line)

A. R. SEPASKHAH; H. AFSHAR-CHAMANABAD484

errors do not exist in the calculation and the surfacestorage volumes are calculated directly from themeasured cross- sectional area. Furthermore, the datafor advancing and storage stages were used in thecalculations which consider a longer period of time forinfiltration which is more realistic. Therefore, it may beconcluded that the second method of calculation is moreaccurate than the first method.

4. Conclusion

The Lewis–Kostiakov infiltration equation was mod-ified for furrow irrigation with different inflow rates Q,raised by an exponent g except for the first irrigation inwhich the Q multiplication is not needed. However, thevalue of exponent g is lower when all data for theadvancing and storage stages (method II) are used forcalculation of the infiltration parameters. It is alsoconcluded that the cumulative infiltration for every-other furrow irrigation is higher than that for ordinaryfurrow irrigation. Furthermore, the data of advancingand storage stages (method II) are more appropriate forthe calculation of infiltration parameters than those ofadvancing stage (method I).

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