Hindawi Publishing CorporationApplied and Environmental Soil ScienceVolume 2013 Article ID 957956 10 pageshttpdxdoiorg1011552013957956
Research ArticleSediment Transport Model for a Surface Irrigation System
Damodhara R Mailapalli1 Narendra S Raghuwanshi2 and Rajendra Singh2
1 Biological Systems Engineering University of Wisconsin Madison WI 53706 USA2Agricultural and Food Engineering Department Indian Institute of Technology Kharagpur 721302 India
Correspondence should be addressed to Damodhara R Mailapalli damiitkgpgmailcom
Received 16 March 2013 Revised 25 June 2013 Accepted 11 July 2013
Academic Editor Keith Smettem
Copyright copy 2013 Damodhara R Mailapalli et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
Controlling irrigation-induced soil erosion is one of the important issues of irrigation management and surface water impairmentIrrigation models are useful in managing the irrigation and the associated ill effects on agricultural environment In this papera physically based surface irrigation model was developed to predict sediment transport in irrigated furrows by integrating anirrigation hydraulic model with a quasi-steady state sediment transport model to predict sediment load in furrow irrigation Theirrigation hydraulic model simulates flow in a furrow irrigation system using the analytically solved zero-inertial overland flowequations and 1D-Green-Ampt 2D-Fok and Kostiakov-Lewis infiltration equations Performance of the sediment transport modelwas evaluated for bare and cropped furrow fields The results indicated that the sediment transport model can predict the initialsediment rate adequately but the simulated sediment rate was less accurate for the later part of the irrigation event Sensitivityanalysis of the parameters of the sediment module showed that the soil erodibility coefficient was the most influential parameterfor determining sediment load in furrow irrigation The developed modeling tool can be used as a water management tool formitigating sediment loss from the surface irrigated fields
1 Introduction
Surface irrigation is a widely used farming system for cropproduction as it requires less skilled labour and involvesless operational cost Surface irrigation systems contributedto about 90 of the worldrsquos crop land irrigation promotingfurrow irrigation as the main application method [1] How-ever poor design and management nonuniformity of waterapplication and over-irrigation featured in surface irrigationare responsible for inefficient irrigation leading to wastageof water water logging salinization and pollution of surfaceand ground water resources Irrigated agriculture is underserious risk due to substantial soil losses from highly erodiblesoils [2ndash4] The sediment transport in an irrigation seasonvaries with the number of previous irrigations flow rate soiltype field slope and field length [5 6] Berg and Carter[2] reported annual losses of sediments ranging from 1 to141Mg haminus1 in Southern Idaho Koluvek et al [7] measured02 to 50Mg haminus1 of soil loss per season in Washington and1 to 22Mg haminus1 per irrigation in Wyoming Brown et al [8]observed a maximum sediment loss of 795 kg per furrow
for 4 slope and 264 kg per furrow for 16 slope in anirrigation event Mailapalli et al [6] estimated as 04Mg haminus1
of soil loss for bare and 02Mg haminus1 for cropped furrowfields in an irrigation event Sediment flow from agriculturalfields can cause downstream water quality degradation andeutrophication by carrying soil and plant nutrients and otherpollutants
Amount of soil loss from a furrow depends on furrowstream size velocity and soil susceptibility to erosion (erodi-bility) In furrow irrigation water delivered through siphontubes or gated pipes picks up soil particles and carries themdown the furrow The furrow stream continues to pick upsediments until its energy equals to that needed to carry soilparticles Furrow stream size and velocity decrease with thewaterfront advance along the furrow due to water loss asinfiltration At some point along the furrow the capacity ofthe flow to transport the accumulated sediment decreasesand the net deposition occurs [6 9] Most of the sedimentseroded at the head end of the field settle out before reachingthe tail end Trout [4] studied on-field distribution of erosion
2 Applied and Environmental Soil Science
and sedimentation in irrigated furrows and found that theerosion rates on the upper quarter of the furrows were 6to 20 times greater than the average rates from the fieldFernandez-Gomez et al [10] studied the furrow erosion onloamy textured alluvial and clay loam cracking soil and foundthat the net rates of soil loss in the upper part of the furrowwere up to six times higher than the average net rate forthe whole furrow However as the infiltration rate decreaseswith time the flow rate increases and influences the sedimenttransport at the tail end Everts and Carter [11] reported thatfrom 40 to 90 of soil leaving a field is eroded from the last9 to 15m of each furrow
Mathematical models can predict sediment load underdifferent field conditions and save time and money on fieldexperimental trials The irrigation-induced erosion can bemodeled using empirical or statistical [12ndash14] conceptual[15ndash17] and physically based [18ndash21] models These modelsdiffer in terms of complexity processes considered and thedata required for model calibration and model use [14]Of these the physically based models are based on thesolution of conservation of mass and momentum equationsfor flow and the conservation of mass equation for sedimenttransport The physically based models are also termed asprocess-based models [13] as they still rely on empiricalequations to describe erosion processes Wu and Meyer[18] developed a conceptual and physically based modelROWERO for simulating transport of nonuniform sedimentalong flatland furrows and the modeling tool may not beapplicable for graded furrows Strelkoff et al [19] developedSRFR for simulating flow soil erosion and deposition atvarious points along the furrow using Laursen [22] Yang[23] and Yalin [24] sediment transport equations Howeverthe SRFR uses numerical technique to solve the flow equa-tions Trout [4] Bjorneberg et al [20] and Bjorneberg andTrout [21] used WEPP (Water Erosion Prediction Project)model for predicting flow and sediment transport in furrowirrigation Review of the supporting documentation and theliterature revealed a number of unnecessary and possiblyflawed assumptions within the hydraulic components of theWEPP model [25] that need to be focused on for accurateprediction of irrigation-induced erosion
The hydraulic component of furrow irrigation can beaccurately modeled using the irrigation model presented byMailapalli et al [26] They used analytical solution of zero-inertia equations for simulating overland flow and multipleinfiltrationmodels such as 2D-Fok [27] 1D-Green Ampt [28]and Kostiakov-Lewis [29] for estimating infiltration In thispaper we attempted to integrate a quasi-steady state sedimenttransport model described by Trout and Neibling [30] tothe hydraulic component of Mailapalli et al [26] irrigationmodel and evaluated performance of model integration forestimating irrigation-induced erosion
2 Theoretical Considerations
Theoretical background of the hydraulic component of theirrigationmodel [26] and sediment transport model [30] andtheir integration is briefly described below
21 Overland Flow Module The governing equations forsimulating flow in the furrows are as follows
(i) conservation of mass equation
120597119860
120597119905+120597119906
120597119909119860 +
120597119860
120597119909119906 = minus119902 (1)
(ii) conservation of momentum equation
120597ℎ
120597119909= 1198780
minus1199062
119870211987743+119902
119892
119906
119860 (2)
where 119860(119909 119905) is the wetted cross-sectional area (m2) 119906(119909 119905)is the flow velocity (m sminus1) 119905 is the time (s) 119909 is the distancealong the furrow (m) 119902(119909 119905) is the infiltration rate (m2 sminus1)ℎ(119909 119905) is the water depth (m) 119878
0
is the bottom slope (mdash) 119870is the Manning-Strickler coefficient (mdash) 119877 is the hydraulicradius (m) and 119892 is the gravitational constant (m sminus2)
22 Infiltration Module Infiltration rate is calculated by
119902 (119909 119905) =119889119868 (119905)
119889119905 (3)
where 119868(119905) is the cumulative infiltration (m3m) which isdetermined by (i) 1D-Green Amptmodel (ii) 2D-Fokmodeland (iii) Kostiakov-Lewis model The option for choosing aninfiltration equation in the irrigation model can be useful inselecting a better modeling approach for simulating overlandflow and infiltration
(i) 1D-Green Ampt Model The one-dimensional vertical infil-tration depth is estimated by Green and Ampt [31] equation
119868 (119905) = 119911 (119905) Δ120579
119911 (119905) = (ℎ minus 119878av) [ln(119911 + (ℎ minus 119878av)
(ℎ minus 119878av))] minus 119870
119904
119905
(4)
where 119911(119905) is the vertical depth of the wetting front (m) Δ120579 =(120579119904
minus 120579119894
) is the change in moisture content (m3mminus3) 120579119904
is thesaturatedmoisture content (m3mminus3) 120579
119894
is the initial moisturecontent (m3mminus3) 119870
119904
is the satiated hydraulic conductivity(m sminus1) and 119878av is the effective suction head at the wettingfront (m)
(ii) 2D-Fok Infiltration Model The general equation for 2D-infiltration [27] is given by
1198682119863
(119905) = (2ℎ119909ℎ
+ 119887119911 +1
2120587119909ℎ
119911)Δ120579 (5)
where
119909ℎ
= [2119870119904
Δ120579(ℎ minus 119878av) 119905]
05
(6)
where 119909ℎ
is the horizontal wetting front (m) 119887 is the basewidth (m) and119870
119904
is the hydraulic conductivity (m sminus1) of thewetted part of the soil profile
Applied and Environmental Soil Science 3
(iii) Kostiakov-Lewis (KL) Model [29] The infiltration equa-tion used to determine 119868(119905) is
119868 (119905) = 119860119896
119905119861119896 + 119891
0
119905 (7)
where119860119896
(m3mminus1 sminus119861119896) and119861119896
(mdash) are the fitted parametersand 119891
0
is the basic infiltration rate (m2 sminus1)
23 Sediment Transport Model
231 Governing Equations The irrigation-induced soil ero-sion or deposition over a distance 119909 in furrows is modeledusing continuity equation [30 32]
120597119902119904
120597119909+ 120588119904
120597 (119888ℎ)
120597119905= 119863119903
+ 119863119897
(8)
where 119902119904
is the sediment load (kgmminus1 sminus1) 120588119904
is the massdensity of sediment particles (kgmminus3) 119888 is the concentrationof the sediment in the flow (m3mminus3) ℎ is the flow depth (m)119863119903
is the rill erosion rate (kgmminus2 sminus1) 119909 is the distance alongthe slope (m) 119905 is the time (s) and 119863
119897
is the delivery rate oferosion from interrill area (kgmminus2 sminus1)
For quasi-steady state (120588119904
(120597(119888ℎ)120597119905) = 0) condition infurrows and sediment from interrill area is negligible (119863
119897
= 0)and (8) can be written as
119889119902119904
119889119909= 119863119903
(9)
Assume 119863119903
= 120572119889
(119879119888
minus 119902119904
) and 119863119888
= 120572119889
119879119888
and substitute in(9) to yield an equation for sediment load
119902119904
= 119879119888
(1 minus 119890minus(119863119888119879119888)119909) (10)
where 120572119889
is the first-order reaction coefficient for deposition(mminus1) 119879
119888
is the sediment transport capacity (kgmminus1 sminus1) and119863119888
is the detachment capacity (kgmminus2 sminus1)
232 Soil Erosion (119864119891
) Most erosion models recognize thatnet erosion decreases as sediment load increases The neterosion 119864
119891
is proportional to the difference between thesediment transport capacity (119879
119888
) and sediment load (119902119904
)resulting in [33]
Consider
119864119891
119863119888
= 1 minus119902119904
119879119888
(11)
233 Soil Deposition (119863119891
) Since soil is a porous media theflow rate decreases with the distance down the furrow andthus 119863
119888
and 119879119888
also decrease As flow rate decreases 119879119888
eventually becomes less than the sediment load resulting indeposition The deposition of the soil (119863
119891
) along the furrowis modelled by the following equation [33]
119863119891
= minus119889119879119888
119889119909(119879119888
le 119902119909
) (12)
234 Estimation of Model Parameters Equation (10) repre-sents steady-state sediment transport equation for predictingthe erosion and deposition processes in the irrigation fur-rows It involves several parameters to be estimated beforeusing the equation for modelling sediment transport Thefollowing sections describe the estimation of tractive force orhydraulic shear (120591) critical shear (120591
119888
) soil erodibility coeffi-cient (119870
119903
) and transport capacity (119879119888
) which are essential forestimation of sediment load (119902
119904
)(a) Tractive Force (120591) The tractive force or hydraulic shearacting on the perimeter of the furrow which is responsiblefor soil detachment was calculated by the following tractiveforce equation [34]
120591 = 1205741198771198780
(13)
where 120574 is the unit weight of water (Nmminus3)
(b) Critical Shear Force (120591119888
) The critical hydraulic shearforce (120591
119888
) is determined by using the following pedotransferfunctions [35]
For the soils containing 30 or more sand
120591119888
= 267 + 0065PC minus 0058PVFS (14)
where PC is the percentage clay and PVFS is the percentageof very fine sand
For the soils containing less than 30 sand
120591119888
= 35 (15)
(c) Soil Erodibility (119870119903
)The soil erodibility (119870119903
) is determinedby using the following pedo-transfer function [35]
For the soils containing 30 or more sand
119870119903
= 000197 + 000030PVFS + 003863119890(minus184OM)
(16)
where OM is the organic matter ()For the soils containing less than 30 sand
119870119903
= 00069 + 0134119890(minus02PC)
(17)
(d) Transport Capacity (119879119888
) Sediment transport capacitywas calculated by Yalinrsquos equation [24] Foster and Meyer[15] concluded that Yalinrsquos equation is the most appropriatefor shallow flows associated with upland erosion The Yalinequation is defined as
119879119888
= 0635 (SG) 119889120588119908
12
120591119904
12
120575 [1 minus1
120573ln (1 + 120573)] (18)
120573 = 245(SG)minus04(119884cr)05
120575 (19a)
120575 =119884
119884crminus 1 (19b)
119884 =120591119904
120588119908
(SG minus 1) 119892119889 (19c)
where SG is the particle-specific gravity 120588119908
is the densityof water (kgmminus3) 119889 is the particle diameter (m) 119884 is the
4 Applied and Environmental Soil Science
minusqs = Tclceil1 minus e( D119888xT119888)rceil
Ef = Dc[1 minus (qsTc)]
Start
Input parameters
Transport capacity
Detachment capacity
Total shear stress
No Yes
Sediment load
Erosion Deposition
B
Q0 S0 n Kt Kr h120574 t x
x = x + dx
120591 = 120574RS
Tc = Kt12059115
Dc = Kr(120591 minus 120591c)
Df = minusdTc
dx
qs le Tc
A
(a)
No
Yes
the tail end
Sediment load at a distance x
Stop
BA
x le L
Sediment load (qs) at
Soil deposition (Df) or erosion (Ef)
(b)
Figure 1 Flowchart showing the working of sediment transport module
dimensionless shear stress 119884cr is the dimensionless criticalshear from Shieldrsquos Diagram 120591
119904
is the shear stress (Nmminus2)and 120573 and 120575 are the dimensionless parameters Criticalshear stress (119884cr) was determined by the following regressionequation from Shieldrsquos Diagram
Log10
119884cr = 0002235119909119888
5
minus 006034119909119888
4
+ 020307119909119888
3
+ 0054252119909119888
2
minus 0636397119909119888
(20)
where
119909119888
= log10
(119878lowast
) 119878lowast
=119889radic(SG minus 1) 119892119889
4V (21)
where 119878lowast
is the sediment fluid parameter (m s) and V is thekinematic viscosity of water (m2 sminus1)
When 120591 is much greater than the critical shear stress (120591119888
)for transport of detached particles the Yalin equation (YE)reduced to a simplified equation (MYE) as follows [36]
119879119888
= 119870119905
12059132
(22)
where119870119905
is the transport coefficient (kgminus12m12 s2)
24 Model Integration In the erosion model the transportcapacity (119879
119888
) and the detachment capacity (119863119888
) are the twoimportant parameters to be determined at a distance 119909
from the head end of the furrow The sediment transportcapacity (119879
119888
) was determined using the YE and MYE ((18) to(22)) Figure 1 shows the algorithm used to model sedimenttransport in irrigated furrows usingMYEThealgorithmusedfor YEwas the same asMYE (Figure 1) During the simulationrun the irrigationmodel estimates discharge and determinesthe sediment transport capacity (119879
119888
) and detachment capacity(119863119888
) Then the model estimates sediment load (119902119904
) erosion(119864119891
) and deposition (119863119891
) at a distance 119909 from the head endand time 119905 The sediment load estimation is terminated whenthe discharge in the furrow is zero
3 Model Evaluation
Performance of the sediment transportmodule was evaluatedfor bare and cropped furrow fields Furrow experimentswere conducted on a 4m times 60m plot in the Field WaterManagement Laboratory Agricultural and Food EngineeringDepartment IIT Kharagpur India The soil in the plot was
Applied and Environmental Soil Science 5
Table 1 Input data for infiltration and erosion components
Component Parameter Bare field Cropped field
Infiltration
119870119904
(ms) 10 times 10minus6
11 times 10minus6
119878av (m) 013 013119860119896
(m3 mminus1 sminus119861119896 ) 50 times 10minus4
535 times 10minus4
119861119896
(mdash) 04 0421198910
(m2 sminus1) 00 00
Erosion
120591119888
(Nmminus2) 00 00119870119903
(smminus1) 50 times 10minus6
10 times 10minus5
119870119905
(kgminus12 m12 s2) 001 002SG 265 265
119889 (m) 18 times 10minus5
28 times 10minus5
V (smminus1) 89 times 10minus6
89 times 10minus6
Table 2 Model performance for simulating sediment loss for bare field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
YE is the Yalin transport equationMYE is the modified Yalin transport equation
sandy loam and contained 69 sand (617 PVFS) 17 silt14 clay and 043 organic matter The bulk density andporosity of the soil were 154 gcm3 and 40 respectivelyThree free draining furrows of parabolic shape 40m long030m wide and 015m deep were fabricated in the exper-imental plot The furrows have centre-to-centre distance of08m and a slope of 05 The center furrow was consideredas study furrow and the two side furrows served as bufferto the center furrow Three digital flow meters (wheel type)were installed at the inlet of three furrows to set the desiredinflow rate to each furrow Plastic buckets (3-litre capacity)were used to collect run-off at the end of a study furrow at aninterval of 10min
The run-off samples were oven-dried and the sedimentleft in each sample was weighed The run-off rate (m3s) andthe corresponding sediment weight (kgm3) were used toestimate sediment rate (kgs)The details on experiments anddata collection procedure are presented by Mailapalli et al[6]The three furrows were irrigated at the same time on 6th17th 21119904119905 and 29th February 2004 using constant inflow ratesof 02 03 04 and 05 L sminus1 respectively on bare furrow fieldIn 2005 sunflower (Helianthus annuus L) crop was grown onthree furrow beds having a plant-to-plant spacing of 45 cmThe three furrows were irrigated on 3rd March 30th March
9th April 16th May and 23rd May 2005 using 07 06 0504 and 03 L sminus1 respectively The furrows were not tilledbetween irrigations during 2004 and 2005
Some of the input parameters required for overland flowinfiltration and sediment transport modules were estimatedfrom the field data [37] and these were considered as baseline input parameters for model testing The Green andAmpt hydraulic parameters such as 119870
119904
and 119878av were deter-mined using field data and pedo-transfer functions [38] TheKostiakov-Lewis parameters 119860
119896
119861119896
and 1198910
were estimatedby using ring infiltrometer data [37] The management andgeometric parameters for these field conditions were usedfrom [38] The critical shear (120591
119888
) and the soil erodibilitycoefficient (119870
119903
) were determined using (14) (15) (16) and(17) The estimated values of 119870
119903
and 120591119888
were 004 smminus1 and0001 respectively The values of SG and V were taken as 265and 89 times 10minus6 smminus1 respectively The mean diameter (119889)of the sediment particle for bare field was 18 times 10minus5m andcropped field was 28 times 10minus5m [37] The cropped field hascoarser particles than the bare field as the irrigations wereperformed first on the bare field and it may lost most of thefine particles as run-off
The simulations were first performed using the fieldobserved values of input parameters (119870 119870
119904
119878av 119860119896 119861119896
6 Applied and Environmental Soil Science
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
0
2
4
6
8
10
12
Observed2D-Fok
1D-GAKL
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 2 Comparison of observed and simulated sediment load (using YE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevent
120591119888
and 119870119903
) for estimating sediment load for both bare andcropped field conditions using the three infiltration modelsOf these simulations the best and the worst model per-formances were selected for both bare and cropped furrowconditions and model performance was studied graphi-cally It was assumed that infiltration is the key componentof irrigation management and was given first priority forselecting the best and worst simulations followed by run-offrate sediment yield waterfront advance and recession timesSensitivity analysis was carried out to study the effect of plusmn5and plusmn10 changes in the values of119870
119903
and119870119905
on the sedimentload estimated by the YE and MYE
The performance of the irrigation model for predictingsediment load was evaluated by estimating root mean squareerror (RMSE) and index of agreement (119868
119886
)Consider
RMSE = radicsum119873
119894=1
[119872(119894) minus 119864(119894)]2
119873
119868119886
= 10 minussum119873
119894=1
(119872 (119894) minus 119864 (119894))2
sum119873
119894=1
(10038161003816100381610038161003816119864 (119894) minus 119872
10038161003816100381610038161003816+10038161003816100381610038161003816119872 (119894) minus 119872
10038161003816100381610038161003816)2
(23)
where119872(119894) is the measured value 119864(119894) is the estimated value119873 is the number of data points and 119872 is the mean of theobserved values
4 Results and Discussion
The visual observation of the trends between observed andsimulated sediment loads (not shown here) by 2D-Fok 1D-Green Ampt and KL infiltration equations depicted that thesediment load predictions were not good with the baselinevalues of 120591
119888
and119870119903
Hence 120591119888
was assumed as zero and119870119903
and119870119905
were considered as calibration parameters for simulatingsediment loadDuring the calibration process the base valuesof 119870119903
and 119870119905
were tuned by increasing or decreasing theirbase values For each runmodel predicted sediment loadwascompared with its observed counterpart using the estimatedperformance indices Finally the values of 119870
119903
and 119870119905
were
found to be 50 times 10minus6 smminus1 and 001 for bare and 10 times
10minus5 smminus1 and 002 for cropped field conditions respectivelyTable 1 presents the input data used for infiltration anderosion parameters for bare and cropped field conditions
41 Sediment Transport in Bare Furrow Field The modelperformance was inconsistent in predicting the sedimentload using all three infiltration equations Furthermore theYE performed slightly better than the MYE in most of thecasesThe 2D-Fok infiltration function resulted in low RMSEand high 119868
119886
values as compared to those obtained using1D-Green Ampt and KL infiltration models (Table 2) Thusthe irrigation model performed well in simulating sedimentload using the 2D-Fok infiltration function followed by 1D-Green Ampt and KL-infiltration functions The performanceindices (Table 2) suggested that the model performance forsediment load in bare furrow field was the best and the worstfor irrigation events of 6th Feb 2004 and 17th Feb 2004respectively Therefore these events were selected for furtheranalysis Figures 2 and 3 show comparison between observedand simulated outputs for the best (6th February 2004) andtheworst (17th February 2004) irrigation events using YE andMYE respectively
The irrigation model with YE and MYE predicted initialincrease in sediment load well However both YE and MYEwere not able to predict the decreasing trend of sedimentrate with elapsed time The possible reason could be that thesediment load estimation takes the run-off rate into accountwhich increases with elapsed time Figures 2 and 3 also showthat the model performed equally well using 2D-Fok 1D-Green Ampt and KL infiltration models However sedimentload predictions using the YE were slightly better than theMYE
42 Sediment Transport in Cropped Furrow Field 2D-Fokinfiltration function resulted in lower RMSE values andhigher 119868
119886
values compared to those obtained using 1D-GreenAmpt and KL infiltration functions (Table 3) Further RMSEand 119868119886
values also suggested that the irrigationmodel with YEperformed slightly better than that with MYE Based on the
Applied and Environmental Soil Science 7
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
Observed2D-Fok
1D-GAKL
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 3 Comparison of observed and simulated sediment load (usingMYE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevents
Table 3 Model performance for simulating sediment loss for cropped field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
(kg)RMSE
times10minus5 (kg) 119868119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
3rd Mar-05 YE 112 115 8 055 118 8 054 119 9 045
MYE 112 117 9 055 118 9 053 119 9 044
30th Mar-05 YE 107 097 9 053 096 9 051 095 13 042
MYE 107 088 9 054 090 9 051 093 13 042
9th Apr-05 YE 102 093 4 083 099 4 078 100 6 072
MYE 102 095 4 083 100 4 073 104 75 069
16th May-05 YE 063 078 3 085 079 3 081 084 6 075
MYE 063 077 4 084 077 42 083 082 7 072
23rd May-05 YE 029 042 4 083 047 4 080 054 7 072
MYE 029 046 5 082 047 6 080 054 8 070
performance indices it is clear that the model performancein predicting sediment load was the best and the worst insimulating irrigation events of 16th May and 30th March2005 respectively For these two irrigation events the modelpredicted sediment load was compared with their observedcounterparts and the results are shown in Figures 4 and 5 forYE and MYE respectively
Both YE and MYE predicted initial increase in sedimentload well However as in case of bare furrow condition bothYE and MYE were not able to predict the decreasing trendof sediment rate with elapsed time The model performedequally well using 2D-Fok 1D-Green Ampt and KL infiltra-tion equations (Figures 4 and 5) Furthermore the irrigationmodel with YE predicted the sediment load slightly betterthan the one with the MYE (Table 3)
43 Sensitivity Analysis of Model Parameters Sensitivity ofthe model parameters in predicting sediment load wasstudied for 16th May 2005 event The effect of plusmn5 andplusmn10 changes in 119870
119903
and 119870119905
(Table 4) on the simulatedsediment load was estimated by YE andMYE considering all
infiltration functions The variation in 119870119905
did not have mucheffect on the sediment load whereas the percentage changein 119870119903
caused the sediment load change at the same rate (bywhich 119870
119903
is changed) Hence for 2D-infiltration model 119870119903
is the most sensitive parameter for estimating sediment loadfor both YE andMYE For 1D-infiltration equation the effectof change in 119870
119905
and 119870119903
on the sediment yield is the same asthe case with 2D-infiltration model The change in 119870
119905
hadvery little effect on the sediment load that resulted with KLinfiltration model The increase in119870
119903
increased the sedimentload at the same rate for both YE and MYE
5 Conclusions
Irrigation-induced erosion accounts most part of the dif-fuse agricultural pollution causing downstream impairmentand eutrophication In this study a steady state sedimenttransport model was integrated with a physically basedfurrow irrigation model which consists of three infiltrationequations (2D-Fok 1D-Green Ampt and Kostiakov-Lewis)The integrated irrigation model was evaluated for estimating
8 Applied and Environmental Soil Science
Table 4 Sensitivity analysis of erosion module parameters
Input parameter Percentage changePercentage change in sediment load
2D-Fok and Chiang 1D-Green Ampt KL infiltration functionMYE YE MYE YE MYE YE
119870119905
(kgminus12 m12 s2)
minus10 0 NA 013 NA minus024 NAminus5 0 NA 013 NA 0 NA5 013 NA 039 NA 012 NA10 013 NA 039 NA 024 NA
Figure 4 Comparison of observed and simulated sediment load (using YE) for (a) 16thMay 2005 and (b) 30thMarch 2005 irrigation events
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(a)
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(b)
Figure 5 Comparison of observed and simulated sediment load (using MYE) for (a) 16th May 2005 and (b) 30th March 2005 irrigationevent
sediment load using two sediment transport capacity equa-tions (Yalin and the modified Yalin equations) for bare andcropped field conditionsThe sediment load prediction usingthe Yalin and the modified Yalin equations was found to beidentical however the modified Yalin equation may be abetter choice as it requires less number of input parametersThe sensitivity analysis revealed that the soil erodibilitycoefficient is the most influential parameter in predicting
sediment transport in free drained furrows However theirrigation model could not adequately simulate the sedimentload in the last phase of irrigation Although this has aminor impact on the overall sediment load it will be thesubject of future model refinement The irrigation modeluses an analytical solution for zero-inertial flow equationsand this compared favourably to the full numerical hydraulicmodels [39] This paper describes the procedure for coupling
Applied and Environmental Soil Science 9
the sediment module to the zero-inertial irrigation modeland design for simulating infiltration though layered soils[37] This is one of the advantages of the integrated modelfor investigating the impact of soil layering on sedimenttransport The other advantage is the use of the model aseducational tool for studying the effect of various infiltrationand sediment capacity equations on the sediment rate Theintegrated model can also be used as a management toolto determine optimum water delivery to irrigated furrowsor borders for attaining better irrigation performance withminimum soil loss The modeling approach can also beintegrated with nutrient transport models where sedimentbound nutrient losses contribute substantially to total non-point nutrient losses from agricultural fields
Acknowledgments
Theauthors are grateful toVolkswagenFoundations StiftungGermany for providing financial support which made therealization of this work possible The technical support forthe model development by Prof G H Schmitz and Prof FLennartz is gratefully acknowledged
References
[1] Food and Agriculture Organization AQUASTAT httpwwwfaoorgnrwateraquastatwater useindexstm 2013
[2] R D Berg and D L Carter ldquoFurrow erosion and sedimentlosses on irrigated croplandrdquo Journal of Soil amp Water Conser-vation vol 35 no 6 pp 267ndash270 1980
[3] W D Kemper T J Trout M J Brown and R C RosenauldquoFurrow erosion and water and soil managementrdquo Transactionsof the American Society of Agricultural Engineers vol 28 no 5pp 1564ndash1572 1985
[4] T J Trout ldquoFurrow irrigation erosion and sedimentationon-field distributionrdquo Transactions of the American Society ofAgricultural Engineers vol 39 no 5 pp 1717ndash1723 1996
[5] L Mateos and J V Giraldez ldquoSuspended load and bed load inirrigation furrowsrdquo Catena vol 64 no 2-3 pp 232ndash246 2005
[6] D R Mailapalli N S Raghuwanshi and R Singh ldquoSedimenttransport in furrow irrigationrdquo Irrigation Science vol 27 no 6pp 449ndash456 2009
[7] P K Koluvek K K Tanji and T J Trout ldquoOverview ofsoil erosion from irrigationrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 929ndash946 1993
[8] M J Brown D L Carter G A Lehrsch and R E SojkaldquoSeasonal trends in furrow irrigation erosion in southernIdahordquo Soil Technology vol 8 no 2 pp 119ndash126 1995
[9] T J Trout ldquoSediment transport in irrigation furrowsrdquo in Pro-ceedings of the 10th International Soil ConservationOrganizationMeeting Held May 24ndash29 1999 at Purdue University and theUSDA-ARS National Soil Erosion Research Laboratory D EStott R H Mohtar and G C Steinhardt Eds pp 710ndash7162001
[10] R Fernandez-Gomez L Mateos and J V Giraldez ldquoFurrowirrigation erosion and managementrdquo Irrigation Science vol 23no 3 pp 123ndash131 2004
[11] C J Everts and D L Carter Furrow Erosion and Topsoil LossesCurrent information series no 586 College of AgricultureUniversity of Idaho Moscow Russia 1981
[12] K J Fornstrom and J Borelli ldquoDesign and management pro-cedure for minimising erosion from furrow irrigated croplandrdquoPaper 84-2595 American Society of Association Executives StJoseph Mich USA 1994
[13] R P C Morgan ldquoThe European soil erosion model an updateon its structure and research baserdquo inConserving Soil ResourcesEuropean Perspectives R J Rickson Ed pp 286ndash299 CABIntOxton Scotland UK 1995
[14] W S Merritt R A Letcher and A J Jakeman ldquoA reviewof erosion and sediment transport modelsrdquo EnvironmentalModelling and Software vol 18 no 8-9 pp 761ndash799 2003
[15] G R Foster and L D Meyer ldquoMathematical simulation ofupland erosion by fundamental erosion mechanicsrdquo Presentand Prospective Technology for Predicting Sediment Yield andSourcesUSDAARSPublicationARS-S40USDAAgriculturalResearch Service Nat Tech Information Service SpringfieldVa USA 1972
[16] M B Abbott J C Bathurst J A Cunge P E OrsquoConnell andJ Rasmussen ldquoAn introduction to the European hydrologicalsystemmdashsysteme hydrologique Europeen ldquoSHErdquo 1 historyand philosophy of a physically-based distributed modellingsystemrdquo Journal of Hydrology vol 87 no 1-2 pp 45ndash59 1986
[17] A J Jakeman and G M Hornberger ldquoHow much complexityis warranted in a rainfall-runoff modelrdquo Water ResourcesResearch vol 29 no 8 pp 2637ndash2649 1993
[18] C CWu and L DMeyer ldquoSimulating transport of nonuniformsediment along flatland furrowsrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 32 no 5 pp 1651ndash16611989
[19] T S Strelkoff A J Clemmens and B V Schmidt SRFR Version321-a Model for Simulating Surface Irrigation in Borders Basinsand Furrows USWCL USDAARS Phoenix Ariz USA 1998
[20] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[21] D L Bjorneberg and T J Trout ldquoEvaluating WEPP predictedon-field furrow erosionrdquo in Proceedings of the 10th InternationalSoil Conservation Organization (ISCO rsquo99) West Lafayette IndUSA May 1999
[22] E M Laursen ldquoThe total sediment load of streamsrdquo Journal ofHydraulics Divison vol 84 pp 1530-1ndash1530-36 1958
[23] C T Yang ldquoIncipient motion and sediment transportrdquo Journalof Hydraulics Divison vol 99 no 10 pp 1679ndash1704 1973
[24] M S Yalin ldquoAn expression for bed-load transportationrdquo Journalof Hydraulics Divison vol 89 no 3 pp 221ndash250 1963
[25] T S Strelkoff and D L Bjorneberg ldquoHydraulic modeling ofirrigation-induced furrow erosionrdquo in Proceedings of the 10thInternational Soil Conservation Organization Conference D EStott R H Mohtar and G C Steinhardt Eds Sustaining theGlobal Farm pp 699ndash705 West Lafayette Ind USA May 1999
[26] D R Mailapalli R Singh and N S Raghuwanshi ldquoPhysicallybased model for simulating flow in furrow irrigation I modeldevelopmentrdquo Journal of Irrigation and Drainage Engineeringvol 135 no 6 pp 739ndash746 2009
[27] Y S Fok and S H Chiang ldquo2-D infiltration equations for fur-row irrigationrdquo Journal of Irrigation and Drainage Engineeringvol 110 no 2 pp 208ndash217 1984
[28] M D Rao N S Raghuwanshi and R Singh ldquoDevelopmentof a physically based 1D-infiltration model for irrigated soilsrdquoAgricultural Water Management vol 85 no 1-2 pp 165ndash1742006
10 Applied and Environmental Soil Science
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
and sedimentation in irrigated furrows and found that theerosion rates on the upper quarter of the furrows were 6to 20 times greater than the average rates from the fieldFernandez-Gomez et al [10] studied the furrow erosion onloamy textured alluvial and clay loam cracking soil and foundthat the net rates of soil loss in the upper part of the furrowwere up to six times higher than the average net rate forthe whole furrow However as the infiltration rate decreaseswith time the flow rate increases and influences the sedimenttransport at the tail end Everts and Carter [11] reported thatfrom 40 to 90 of soil leaving a field is eroded from the last9 to 15m of each furrow
Mathematical models can predict sediment load underdifferent field conditions and save time and money on fieldexperimental trials The irrigation-induced erosion can bemodeled using empirical or statistical [12ndash14] conceptual[15ndash17] and physically based [18ndash21] models These modelsdiffer in terms of complexity processes considered and thedata required for model calibration and model use [14]Of these the physically based models are based on thesolution of conservation of mass and momentum equationsfor flow and the conservation of mass equation for sedimenttransport The physically based models are also termed asprocess-based models [13] as they still rely on empiricalequations to describe erosion processes Wu and Meyer[18] developed a conceptual and physically based modelROWERO for simulating transport of nonuniform sedimentalong flatland furrows and the modeling tool may not beapplicable for graded furrows Strelkoff et al [19] developedSRFR for simulating flow soil erosion and deposition atvarious points along the furrow using Laursen [22] Yang[23] and Yalin [24] sediment transport equations Howeverthe SRFR uses numerical technique to solve the flow equa-tions Trout [4] Bjorneberg et al [20] and Bjorneberg andTrout [21] used WEPP (Water Erosion Prediction Project)model for predicting flow and sediment transport in furrowirrigation Review of the supporting documentation and theliterature revealed a number of unnecessary and possiblyflawed assumptions within the hydraulic components of theWEPP model [25] that need to be focused on for accurateprediction of irrigation-induced erosion
The hydraulic component of furrow irrigation can beaccurately modeled using the irrigation model presented byMailapalli et al [26] They used analytical solution of zero-inertia equations for simulating overland flow and multipleinfiltrationmodels such as 2D-Fok [27] 1D-Green Ampt [28]and Kostiakov-Lewis [29] for estimating infiltration In thispaper we attempted to integrate a quasi-steady state sedimenttransport model described by Trout and Neibling [30] tothe hydraulic component of Mailapalli et al [26] irrigationmodel and evaluated performance of model integration forestimating irrigation-induced erosion
2 Theoretical Considerations
Theoretical background of the hydraulic component of theirrigationmodel [26] and sediment transport model [30] andtheir integration is briefly described below
21 Overland Flow Module The governing equations forsimulating flow in the furrows are as follows
(i) conservation of mass equation
120597119860
120597119905+120597119906
120597119909119860 +
120597119860
120597119909119906 = minus119902 (1)
(ii) conservation of momentum equation
120597ℎ
120597119909= 1198780
minus1199062
119870211987743+119902
119892
119906
119860 (2)
where 119860(119909 119905) is the wetted cross-sectional area (m2) 119906(119909 119905)is the flow velocity (m sminus1) 119905 is the time (s) 119909 is the distancealong the furrow (m) 119902(119909 119905) is the infiltration rate (m2 sminus1)ℎ(119909 119905) is the water depth (m) 119878
0
is the bottom slope (mdash) 119870is the Manning-Strickler coefficient (mdash) 119877 is the hydraulicradius (m) and 119892 is the gravitational constant (m sminus2)
22 Infiltration Module Infiltration rate is calculated by
119902 (119909 119905) =119889119868 (119905)
119889119905 (3)
where 119868(119905) is the cumulative infiltration (m3m) which isdetermined by (i) 1D-Green Amptmodel (ii) 2D-Fokmodeland (iii) Kostiakov-Lewis model The option for choosing aninfiltration equation in the irrigation model can be useful inselecting a better modeling approach for simulating overlandflow and infiltration
(i) 1D-Green Ampt Model The one-dimensional vertical infil-tration depth is estimated by Green and Ampt [31] equation
119868 (119905) = 119911 (119905) Δ120579
119911 (119905) = (ℎ minus 119878av) [ln(119911 + (ℎ minus 119878av)
(ℎ minus 119878av))] minus 119870
119904
119905
(4)
where 119911(119905) is the vertical depth of the wetting front (m) Δ120579 =(120579119904
minus 120579119894
) is the change in moisture content (m3mminus3) 120579119904
is thesaturatedmoisture content (m3mminus3) 120579
119894
is the initial moisturecontent (m3mminus3) 119870
119904
is the satiated hydraulic conductivity(m sminus1) and 119878av is the effective suction head at the wettingfront (m)
(ii) 2D-Fok Infiltration Model The general equation for 2D-infiltration [27] is given by
1198682119863
(119905) = (2ℎ119909ℎ
+ 119887119911 +1
2120587119909ℎ
119911)Δ120579 (5)
where
119909ℎ
= [2119870119904
Δ120579(ℎ minus 119878av) 119905]
05
(6)
where 119909ℎ
is the horizontal wetting front (m) 119887 is the basewidth (m) and119870
119904
is the hydraulic conductivity (m sminus1) of thewetted part of the soil profile
Applied and Environmental Soil Science 3
(iii) Kostiakov-Lewis (KL) Model [29] The infiltration equa-tion used to determine 119868(119905) is
119868 (119905) = 119860119896
119905119861119896 + 119891
0
119905 (7)
where119860119896
(m3mminus1 sminus119861119896) and119861119896
(mdash) are the fitted parametersand 119891
0
is the basic infiltration rate (m2 sminus1)
23 Sediment Transport Model
231 Governing Equations The irrigation-induced soil ero-sion or deposition over a distance 119909 in furrows is modeledusing continuity equation [30 32]
120597119902119904
120597119909+ 120588119904
120597 (119888ℎ)
120597119905= 119863119903
+ 119863119897
(8)
where 119902119904
is the sediment load (kgmminus1 sminus1) 120588119904
is the massdensity of sediment particles (kgmminus3) 119888 is the concentrationof the sediment in the flow (m3mminus3) ℎ is the flow depth (m)119863119903
is the rill erosion rate (kgmminus2 sminus1) 119909 is the distance alongthe slope (m) 119905 is the time (s) and 119863
119897
is the delivery rate oferosion from interrill area (kgmminus2 sminus1)
For quasi-steady state (120588119904
(120597(119888ℎ)120597119905) = 0) condition infurrows and sediment from interrill area is negligible (119863
119897
= 0)and (8) can be written as
119889119902119904
119889119909= 119863119903
(9)
Assume 119863119903
= 120572119889
(119879119888
minus 119902119904
) and 119863119888
= 120572119889
119879119888
and substitute in(9) to yield an equation for sediment load
119902119904
= 119879119888
(1 minus 119890minus(119863119888119879119888)119909) (10)
where 120572119889
is the first-order reaction coefficient for deposition(mminus1) 119879
119888
is the sediment transport capacity (kgmminus1 sminus1) and119863119888
is the detachment capacity (kgmminus2 sminus1)
232 Soil Erosion (119864119891
) Most erosion models recognize thatnet erosion decreases as sediment load increases The neterosion 119864
119891
is proportional to the difference between thesediment transport capacity (119879
119888
) and sediment load (119902119904
)resulting in [33]
Consider
119864119891
119863119888
= 1 minus119902119904
119879119888
(11)
233 Soil Deposition (119863119891
) Since soil is a porous media theflow rate decreases with the distance down the furrow andthus 119863
119888
and 119879119888
also decrease As flow rate decreases 119879119888
eventually becomes less than the sediment load resulting indeposition The deposition of the soil (119863
119891
) along the furrowis modelled by the following equation [33]
119863119891
= minus119889119879119888
119889119909(119879119888
le 119902119909
) (12)
234 Estimation of Model Parameters Equation (10) repre-sents steady-state sediment transport equation for predictingthe erosion and deposition processes in the irrigation fur-rows It involves several parameters to be estimated beforeusing the equation for modelling sediment transport Thefollowing sections describe the estimation of tractive force orhydraulic shear (120591) critical shear (120591
119888
) soil erodibility coeffi-cient (119870
119903
) and transport capacity (119879119888
) which are essential forestimation of sediment load (119902
119904
)(a) Tractive Force (120591) The tractive force or hydraulic shearacting on the perimeter of the furrow which is responsiblefor soil detachment was calculated by the following tractiveforce equation [34]
120591 = 1205741198771198780
(13)
where 120574 is the unit weight of water (Nmminus3)
(b) Critical Shear Force (120591119888
) The critical hydraulic shearforce (120591
119888
) is determined by using the following pedotransferfunctions [35]
For the soils containing 30 or more sand
120591119888
= 267 + 0065PC minus 0058PVFS (14)
where PC is the percentage clay and PVFS is the percentageof very fine sand
For the soils containing less than 30 sand
120591119888
= 35 (15)
(c) Soil Erodibility (119870119903
)The soil erodibility (119870119903
) is determinedby using the following pedo-transfer function [35]
For the soils containing 30 or more sand
119870119903
= 000197 + 000030PVFS + 003863119890(minus184OM)
(16)
where OM is the organic matter ()For the soils containing less than 30 sand
119870119903
= 00069 + 0134119890(minus02PC)
(17)
(d) Transport Capacity (119879119888
) Sediment transport capacitywas calculated by Yalinrsquos equation [24] Foster and Meyer[15] concluded that Yalinrsquos equation is the most appropriatefor shallow flows associated with upland erosion The Yalinequation is defined as
119879119888
= 0635 (SG) 119889120588119908
12
120591119904
12
120575 [1 minus1
120573ln (1 + 120573)] (18)
120573 = 245(SG)minus04(119884cr)05
120575 (19a)
120575 =119884
119884crminus 1 (19b)
119884 =120591119904
120588119908
(SG minus 1) 119892119889 (19c)
where SG is the particle-specific gravity 120588119908
is the densityof water (kgmminus3) 119889 is the particle diameter (m) 119884 is the
4 Applied and Environmental Soil Science
minusqs = Tclceil1 minus e( D119888xT119888)rceil
Ef = Dc[1 minus (qsTc)]
Start
Input parameters
Transport capacity
Detachment capacity
Total shear stress
No Yes
Sediment load
Erosion Deposition
B
Q0 S0 n Kt Kr h120574 t x
x = x + dx
120591 = 120574RS
Tc = Kt12059115
Dc = Kr(120591 minus 120591c)
Df = minusdTc
dx
qs le Tc
A
(a)
No
Yes
the tail end
Sediment load at a distance x
Stop
BA
x le L
Sediment load (qs) at
Soil deposition (Df) or erosion (Ef)
(b)
Figure 1 Flowchart showing the working of sediment transport module
dimensionless shear stress 119884cr is the dimensionless criticalshear from Shieldrsquos Diagram 120591
119904
is the shear stress (Nmminus2)and 120573 and 120575 are the dimensionless parameters Criticalshear stress (119884cr) was determined by the following regressionequation from Shieldrsquos Diagram
Log10
119884cr = 0002235119909119888
5
minus 006034119909119888
4
+ 020307119909119888
3
+ 0054252119909119888
2
minus 0636397119909119888
(20)
where
119909119888
= log10
(119878lowast
) 119878lowast
=119889radic(SG minus 1) 119892119889
4V (21)
where 119878lowast
is the sediment fluid parameter (m s) and V is thekinematic viscosity of water (m2 sminus1)
When 120591 is much greater than the critical shear stress (120591119888
)for transport of detached particles the Yalin equation (YE)reduced to a simplified equation (MYE) as follows [36]
119879119888
= 119870119905
12059132
(22)
where119870119905
is the transport coefficient (kgminus12m12 s2)
24 Model Integration In the erosion model the transportcapacity (119879
119888
) and the detachment capacity (119863119888
) are the twoimportant parameters to be determined at a distance 119909
from the head end of the furrow The sediment transportcapacity (119879
119888
) was determined using the YE and MYE ((18) to(22)) Figure 1 shows the algorithm used to model sedimenttransport in irrigated furrows usingMYEThealgorithmusedfor YEwas the same asMYE (Figure 1) During the simulationrun the irrigationmodel estimates discharge and determinesthe sediment transport capacity (119879
119888
) and detachment capacity(119863119888
) Then the model estimates sediment load (119902119904
) erosion(119864119891
) and deposition (119863119891
) at a distance 119909 from the head endand time 119905 The sediment load estimation is terminated whenthe discharge in the furrow is zero
3 Model Evaluation
Performance of the sediment transportmodule was evaluatedfor bare and cropped furrow fields Furrow experimentswere conducted on a 4m times 60m plot in the Field WaterManagement Laboratory Agricultural and Food EngineeringDepartment IIT Kharagpur India The soil in the plot was
Applied and Environmental Soil Science 5
Table 1 Input data for infiltration and erosion components
Component Parameter Bare field Cropped field
Infiltration
119870119904
(ms) 10 times 10minus6
11 times 10minus6
119878av (m) 013 013119860119896
(m3 mminus1 sminus119861119896 ) 50 times 10minus4
535 times 10minus4
119861119896
(mdash) 04 0421198910
(m2 sminus1) 00 00
Erosion
120591119888
(Nmminus2) 00 00119870119903
(smminus1) 50 times 10minus6
10 times 10minus5
119870119905
(kgminus12 m12 s2) 001 002SG 265 265
119889 (m) 18 times 10minus5
28 times 10minus5
V (smminus1) 89 times 10minus6
89 times 10minus6
Table 2 Model performance for simulating sediment loss for bare field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
YE is the Yalin transport equationMYE is the modified Yalin transport equation
sandy loam and contained 69 sand (617 PVFS) 17 silt14 clay and 043 organic matter The bulk density andporosity of the soil were 154 gcm3 and 40 respectivelyThree free draining furrows of parabolic shape 40m long030m wide and 015m deep were fabricated in the exper-imental plot The furrows have centre-to-centre distance of08m and a slope of 05 The center furrow was consideredas study furrow and the two side furrows served as bufferto the center furrow Three digital flow meters (wheel type)were installed at the inlet of three furrows to set the desiredinflow rate to each furrow Plastic buckets (3-litre capacity)were used to collect run-off at the end of a study furrow at aninterval of 10min
The run-off samples were oven-dried and the sedimentleft in each sample was weighed The run-off rate (m3s) andthe corresponding sediment weight (kgm3) were used toestimate sediment rate (kgs)The details on experiments anddata collection procedure are presented by Mailapalli et al[6]The three furrows were irrigated at the same time on 6th17th 21119904119905 and 29th February 2004 using constant inflow ratesof 02 03 04 and 05 L sminus1 respectively on bare furrow fieldIn 2005 sunflower (Helianthus annuus L) crop was grown onthree furrow beds having a plant-to-plant spacing of 45 cmThe three furrows were irrigated on 3rd March 30th March
9th April 16th May and 23rd May 2005 using 07 06 0504 and 03 L sminus1 respectively The furrows were not tilledbetween irrigations during 2004 and 2005
Some of the input parameters required for overland flowinfiltration and sediment transport modules were estimatedfrom the field data [37] and these were considered as baseline input parameters for model testing The Green andAmpt hydraulic parameters such as 119870
119904
and 119878av were deter-mined using field data and pedo-transfer functions [38] TheKostiakov-Lewis parameters 119860
119896
119861119896
and 1198910
were estimatedby using ring infiltrometer data [37] The management andgeometric parameters for these field conditions were usedfrom [38] The critical shear (120591
119888
) and the soil erodibilitycoefficient (119870
119903
) were determined using (14) (15) (16) and(17) The estimated values of 119870
119903
and 120591119888
were 004 smminus1 and0001 respectively The values of SG and V were taken as 265and 89 times 10minus6 smminus1 respectively The mean diameter (119889)of the sediment particle for bare field was 18 times 10minus5m andcropped field was 28 times 10minus5m [37] The cropped field hascoarser particles than the bare field as the irrigations wereperformed first on the bare field and it may lost most of thefine particles as run-off
The simulations were first performed using the fieldobserved values of input parameters (119870 119870
119904
119878av 119860119896 119861119896
6 Applied and Environmental Soil Science
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
0
2
4
6
8
10
12
Observed2D-Fok
1D-GAKL
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 2 Comparison of observed and simulated sediment load (using YE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevent
120591119888
and 119870119903
) for estimating sediment load for both bare andcropped field conditions using the three infiltration modelsOf these simulations the best and the worst model per-formances were selected for both bare and cropped furrowconditions and model performance was studied graphi-cally It was assumed that infiltration is the key componentof irrigation management and was given first priority forselecting the best and worst simulations followed by run-offrate sediment yield waterfront advance and recession timesSensitivity analysis was carried out to study the effect of plusmn5and plusmn10 changes in the values of119870
119903
and119870119905
on the sedimentload estimated by the YE and MYE
The performance of the irrigation model for predictingsediment load was evaluated by estimating root mean squareerror (RMSE) and index of agreement (119868
119886
)Consider
RMSE = radicsum119873
119894=1
[119872(119894) minus 119864(119894)]2
119873
119868119886
= 10 minussum119873
119894=1
(119872 (119894) minus 119864 (119894))2
sum119873
119894=1
(10038161003816100381610038161003816119864 (119894) minus 119872
10038161003816100381610038161003816+10038161003816100381610038161003816119872 (119894) minus 119872
10038161003816100381610038161003816)2
(23)
where119872(119894) is the measured value 119864(119894) is the estimated value119873 is the number of data points and 119872 is the mean of theobserved values
4 Results and Discussion
The visual observation of the trends between observed andsimulated sediment loads (not shown here) by 2D-Fok 1D-Green Ampt and KL infiltration equations depicted that thesediment load predictions were not good with the baselinevalues of 120591
119888
and119870119903
Hence 120591119888
was assumed as zero and119870119903
and119870119905
were considered as calibration parameters for simulatingsediment loadDuring the calibration process the base valuesof 119870119903
and 119870119905
were tuned by increasing or decreasing theirbase values For each runmodel predicted sediment loadwascompared with its observed counterpart using the estimatedperformance indices Finally the values of 119870
119903
and 119870119905
were
found to be 50 times 10minus6 smminus1 and 001 for bare and 10 times
10minus5 smminus1 and 002 for cropped field conditions respectivelyTable 1 presents the input data used for infiltration anderosion parameters for bare and cropped field conditions
41 Sediment Transport in Bare Furrow Field The modelperformance was inconsistent in predicting the sedimentload using all three infiltration equations Furthermore theYE performed slightly better than the MYE in most of thecasesThe 2D-Fok infiltration function resulted in low RMSEand high 119868
119886
values as compared to those obtained using1D-Green Ampt and KL infiltration models (Table 2) Thusthe irrigation model performed well in simulating sedimentload using the 2D-Fok infiltration function followed by 1D-Green Ampt and KL-infiltration functions The performanceindices (Table 2) suggested that the model performance forsediment load in bare furrow field was the best and the worstfor irrigation events of 6th Feb 2004 and 17th Feb 2004respectively Therefore these events were selected for furtheranalysis Figures 2 and 3 show comparison between observedand simulated outputs for the best (6th February 2004) andtheworst (17th February 2004) irrigation events using YE andMYE respectively
The irrigation model with YE and MYE predicted initialincrease in sediment load well However both YE and MYEwere not able to predict the decreasing trend of sedimentrate with elapsed time The possible reason could be that thesediment load estimation takes the run-off rate into accountwhich increases with elapsed time Figures 2 and 3 also showthat the model performed equally well using 2D-Fok 1D-Green Ampt and KL infiltration models However sedimentload predictions using the YE were slightly better than theMYE
42 Sediment Transport in Cropped Furrow Field 2D-Fokinfiltration function resulted in lower RMSE values andhigher 119868
119886
values compared to those obtained using 1D-GreenAmpt and KL infiltration functions (Table 3) Further RMSEand 119868119886
values also suggested that the irrigationmodel with YEperformed slightly better than that with MYE Based on the
Applied and Environmental Soil Science 7
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
Observed2D-Fok
1D-GAKL
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 3 Comparison of observed and simulated sediment load (usingMYE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevents
Table 3 Model performance for simulating sediment loss for cropped field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
(kg)RMSE
times10minus5 (kg) 119868119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
3rd Mar-05 YE 112 115 8 055 118 8 054 119 9 045
MYE 112 117 9 055 118 9 053 119 9 044
30th Mar-05 YE 107 097 9 053 096 9 051 095 13 042
MYE 107 088 9 054 090 9 051 093 13 042
9th Apr-05 YE 102 093 4 083 099 4 078 100 6 072
MYE 102 095 4 083 100 4 073 104 75 069
16th May-05 YE 063 078 3 085 079 3 081 084 6 075
MYE 063 077 4 084 077 42 083 082 7 072
23rd May-05 YE 029 042 4 083 047 4 080 054 7 072
MYE 029 046 5 082 047 6 080 054 8 070
performance indices it is clear that the model performancein predicting sediment load was the best and the worst insimulating irrigation events of 16th May and 30th March2005 respectively For these two irrigation events the modelpredicted sediment load was compared with their observedcounterparts and the results are shown in Figures 4 and 5 forYE and MYE respectively
Both YE and MYE predicted initial increase in sedimentload well However as in case of bare furrow condition bothYE and MYE were not able to predict the decreasing trendof sediment rate with elapsed time The model performedequally well using 2D-Fok 1D-Green Ampt and KL infiltra-tion equations (Figures 4 and 5) Furthermore the irrigationmodel with YE predicted the sediment load slightly betterthan the one with the MYE (Table 3)
43 Sensitivity Analysis of Model Parameters Sensitivity ofthe model parameters in predicting sediment load wasstudied for 16th May 2005 event The effect of plusmn5 andplusmn10 changes in 119870
119903
and 119870119905
(Table 4) on the simulatedsediment load was estimated by YE andMYE considering all
infiltration functions The variation in 119870119905
did not have mucheffect on the sediment load whereas the percentage changein 119870119903
caused the sediment load change at the same rate (bywhich 119870
119903
is changed) Hence for 2D-infiltration model 119870119903
is the most sensitive parameter for estimating sediment loadfor both YE andMYE For 1D-infiltration equation the effectof change in 119870
119905
and 119870119903
on the sediment yield is the same asthe case with 2D-infiltration model The change in 119870
119905
hadvery little effect on the sediment load that resulted with KLinfiltration model The increase in119870
119903
increased the sedimentload at the same rate for both YE and MYE
5 Conclusions
Irrigation-induced erosion accounts most part of the dif-fuse agricultural pollution causing downstream impairmentand eutrophication In this study a steady state sedimenttransport model was integrated with a physically basedfurrow irrigation model which consists of three infiltrationequations (2D-Fok 1D-Green Ampt and Kostiakov-Lewis)The integrated irrigation model was evaluated for estimating
8 Applied and Environmental Soil Science
Table 4 Sensitivity analysis of erosion module parameters
Input parameter Percentage changePercentage change in sediment load
2D-Fok and Chiang 1D-Green Ampt KL infiltration functionMYE YE MYE YE MYE YE
119870119905
(kgminus12 m12 s2)
minus10 0 NA 013 NA minus024 NAminus5 0 NA 013 NA 0 NA5 013 NA 039 NA 012 NA10 013 NA 039 NA 024 NA
Figure 4 Comparison of observed and simulated sediment load (using YE) for (a) 16thMay 2005 and (b) 30thMarch 2005 irrigation events
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(a)
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(b)
Figure 5 Comparison of observed and simulated sediment load (using MYE) for (a) 16th May 2005 and (b) 30th March 2005 irrigationevent
sediment load using two sediment transport capacity equa-tions (Yalin and the modified Yalin equations) for bare andcropped field conditionsThe sediment load prediction usingthe Yalin and the modified Yalin equations was found to beidentical however the modified Yalin equation may be abetter choice as it requires less number of input parametersThe sensitivity analysis revealed that the soil erodibilitycoefficient is the most influential parameter in predicting
sediment transport in free drained furrows However theirrigation model could not adequately simulate the sedimentload in the last phase of irrigation Although this has aminor impact on the overall sediment load it will be thesubject of future model refinement The irrigation modeluses an analytical solution for zero-inertial flow equationsand this compared favourably to the full numerical hydraulicmodels [39] This paper describes the procedure for coupling
Applied and Environmental Soil Science 9
the sediment module to the zero-inertial irrigation modeland design for simulating infiltration though layered soils[37] This is one of the advantages of the integrated modelfor investigating the impact of soil layering on sedimenttransport The other advantage is the use of the model aseducational tool for studying the effect of various infiltrationand sediment capacity equations on the sediment rate Theintegrated model can also be used as a management toolto determine optimum water delivery to irrigated furrowsor borders for attaining better irrigation performance withminimum soil loss The modeling approach can also beintegrated with nutrient transport models where sedimentbound nutrient losses contribute substantially to total non-point nutrient losses from agricultural fields
Acknowledgments
Theauthors are grateful toVolkswagenFoundations StiftungGermany for providing financial support which made therealization of this work possible The technical support forthe model development by Prof G H Schmitz and Prof FLennartz is gratefully acknowledged
References
[1] Food and Agriculture Organization AQUASTAT httpwwwfaoorgnrwateraquastatwater useindexstm 2013
[2] R D Berg and D L Carter ldquoFurrow erosion and sedimentlosses on irrigated croplandrdquo Journal of Soil amp Water Conser-vation vol 35 no 6 pp 267ndash270 1980
[3] W D Kemper T J Trout M J Brown and R C RosenauldquoFurrow erosion and water and soil managementrdquo Transactionsof the American Society of Agricultural Engineers vol 28 no 5pp 1564ndash1572 1985
[4] T J Trout ldquoFurrow irrigation erosion and sedimentationon-field distributionrdquo Transactions of the American Society ofAgricultural Engineers vol 39 no 5 pp 1717ndash1723 1996
[5] L Mateos and J V Giraldez ldquoSuspended load and bed load inirrigation furrowsrdquo Catena vol 64 no 2-3 pp 232ndash246 2005
[6] D R Mailapalli N S Raghuwanshi and R Singh ldquoSedimenttransport in furrow irrigationrdquo Irrigation Science vol 27 no 6pp 449ndash456 2009
[7] P K Koluvek K K Tanji and T J Trout ldquoOverview ofsoil erosion from irrigationrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 929ndash946 1993
[8] M J Brown D L Carter G A Lehrsch and R E SojkaldquoSeasonal trends in furrow irrigation erosion in southernIdahordquo Soil Technology vol 8 no 2 pp 119ndash126 1995
[9] T J Trout ldquoSediment transport in irrigation furrowsrdquo in Pro-ceedings of the 10th International Soil ConservationOrganizationMeeting Held May 24ndash29 1999 at Purdue University and theUSDA-ARS National Soil Erosion Research Laboratory D EStott R H Mohtar and G C Steinhardt Eds pp 710ndash7162001
[10] R Fernandez-Gomez L Mateos and J V Giraldez ldquoFurrowirrigation erosion and managementrdquo Irrigation Science vol 23no 3 pp 123ndash131 2004
[11] C J Everts and D L Carter Furrow Erosion and Topsoil LossesCurrent information series no 586 College of AgricultureUniversity of Idaho Moscow Russia 1981
[12] K J Fornstrom and J Borelli ldquoDesign and management pro-cedure for minimising erosion from furrow irrigated croplandrdquoPaper 84-2595 American Society of Association Executives StJoseph Mich USA 1994
[13] R P C Morgan ldquoThe European soil erosion model an updateon its structure and research baserdquo inConserving Soil ResourcesEuropean Perspectives R J Rickson Ed pp 286ndash299 CABIntOxton Scotland UK 1995
[14] W S Merritt R A Letcher and A J Jakeman ldquoA reviewof erosion and sediment transport modelsrdquo EnvironmentalModelling and Software vol 18 no 8-9 pp 761ndash799 2003
[15] G R Foster and L D Meyer ldquoMathematical simulation ofupland erosion by fundamental erosion mechanicsrdquo Presentand Prospective Technology for Predicting Sediment Yield andSourcesUSDAARSPublicationARS-S40USDAAgriculturalResearch Service Nat Tech Information Service SpringfieldVa USA 1972
[16] M B Abbott J C Bathurst J A Cunge P E OrsquoConnell andJ Rasmussen ldquoAn introduction to the European hydrologicalsystemmdashsysteme hydrologique Europeen ldquoSHErdquo 1 historyand philosophy of a physically-based distributed modellingsystemrdquo Journal of Hydrology vol 87 no 1-2 pp 45ndash59 1986
[17] A J Jakeman and G M Hornberger ldquoHow much complexityis warranted in a rainfall-runoff modelrdquo Water ResourcesResearch vol 29 no 8 pp 2637ndash2649 1993
[18] C CWu and L DMeyer ldquoSimulating transport of nonuniformsediment along flatland furrowsrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 32 no 5 pp 1651ndash16611989
[19] T S Strelkoff A J Clemmens and B V Schmidt SRFR Version321-a Model for Simulating Surface Irrigation in Borders Basinsand Furrows USWCL USDAARS Phoenix Ariz USA 1998
[20] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[21] D L Bjorneberg and T J Trout ldquoEvaluating WEPP predictedon-field furrow erosionrdquo in Proceedings of the 10th InternationalSoil Conservation Organization (ISCO rsquo99) West Lafayette IndUSA May 1999
[22] E M Laursen ldquoThe total sediment load of streamsrdquo Journal ofHydraulics Divison vol 84 pp 1530-1ndash1530-36 1958
[23] C T Yang ldquoIncipient motion and sediment transportrdquo Journalof Hydraulics Divison vol 99 no 10 pp 1679ndash1704 1973
[24] M S Yalin ldquoAn expression for bed-load transportationrdquo Journalof Hydraulics Divison vol 89 no 3 pp 221ndash250 1963
[25] T S Strelkoff and D L Bjorneberg ldquoHydraulic modeling ofirrigation-induced furrow erosionrdquo in Proceedings of the 10thInternational Soil Conservation Organization Conference D EStott R H Mohtar and G C Steinhardt Eds Sustaining theGlobal Farm pp 699ndash705 West Lafayette Ind USA May 1999
[26] D R Mailapalli R Singh and N S Raghuwanshi ldquoPhysicallybased model for simulating flow in furrow irrigation I modeldevelopmentrdquo Journal of Irrigation and Drainage Engineeringvol 135 no 6 pp 739ndash746 2009
[27] Y S Fok and S H Chiang ldquo2-D infiltration equations for fur-row irrigationrdquo Journal of Irrigation and Drainage Engineeringvol 110 no 2 pp 208ndash217 1984
[28] M D Rao N S Raghuwanshi and R Singh ldquoDevelopmentof a physically based 1D-infiltration model for irrigated soilsrdquoAgricultural Water Management vol 85 no 1-2 pp 165ndash1742006
10 Applied and Environmental Soil Science
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
(iii) Kostiakov-Lewis (KL) Model [29] The infiltration equa-tion used to determine 119868(119905) is
119868 (119905) = 119860119896
119905119861119896 + 119891
0
119905 (7)
where119860119896
(m3mminus1 sminus119861119896) and119861119896
(mdash) are the fitted parametersand 119891
0
is the basic infiltration rate (m2 sminus1)
23 Sediment Transport Model
231 Governing Equations The irrigation-induced soil ero-sion or deposition over a distance 119909 in furrows is modeledusing continuity equation [30 32]
120597119902119904
120597119909+ 120588119904
120597 (119888ℎ)
120597119905= 119863119903
+ 119863119897
(8)
where 119902119904
is the sediment load (kgmminus1 sminus1) 120588119904
is the massdensity of sediment particles (kgmminus3) 119888 is the concentrationof the sediment in the flow (m3mminus3) ℎ is the flow depth (m)119863119903
is the rill erosion rate (kgmminus2 sminus1) 119909 is the distance alongthe slope (m) 119905 is the time (s) and 119863
119897
is the delivery rate oferosion from interrill area (kgmminus2 sminus1)
For quasi-steady state (120588119904
(120597(119888ℎ)120597119905) = 0) condition infurrows and sediment from interrill area is negligible (119863
119897
= 0)and (8) can be written as
119889119902119904
119889119909= 119863119903
(9)
Assume 119863119903
= 120572119889
(119879119888
minus 119902119904
) and 119863119888
= 120572119889
119879119888
and substitute in(9) to yield an equation for sediment load
119902119904
= 119879119888
(1 minus 119890minus(119863119888119879119888)119909) (10)
where 120572119889
is the first-order reaction coefficient for deposition(mminus1) 119879
119888
is the sediment transport capacity (kgmminus1 sminus1) and119863119888
is the detachment capacity (kgmminus2 sminus1)
232 Soil Erosion (119864119891
) Most erosion models recognize thatnet erosion decreases as sediment load increases The neterosion 119864
119891
is proportional to the difference between thesediment transport capacity (119879
119888
) and sediment load (119902119904
)resulting in [33]
Consider
119864119891
119863119888
= 1 minus119902119904
119879119888
(11)
233 Soil Deposition (119863119891
) Since soil is a porous media theflow rate decreases with the distance down the furrow andthus 119863
119888
and 119879119888
also decrease As flow rate decreases 119879119888
eventually becomes less than the sediment load resulting indeposition The deposition of the soil (119863
119891
) along the furrowis modelled by the following equation [33]
119863119891
= minus119889119879119888
119889119909(119879119888
le 119902119909
) (12)
234 Estimation of Model Parameters Equation (10) repre-sents steady-state sediment transport equation for predictingthe erosion and deposition processes in the irrigation fur-rows It involves several parameters to be estimated beforeusing the equation for modelling sediment transport Thefollowing sections describe the estimation of tractive force orhydraulic shear (120591) critical shear (120591
119888
) soil erodibility coeffi-cient (119870
119903
) and transport capacity (119879119888
) which are essential forestimation of sediment load (119902
119904
)(a) Tractive Force (120591) The tractive force or hydraulic shearacting on the perimeter of the furrow which is responsiblefor soil detachment was calculated by the following tractiveforce equation [34]
120591 = 1205741198771198780
(13)
where 120574 is the unit weight of water (Nmminus3)
(b) Critical Shear Force (120591119888
) The critical hydraulic shearforce (120591
119888
) is determined by using the following pedotransferfunctions [35]
For the soils containing 30 or more sand
120591119888
= 267 + 0065PC minus 0058PVFS (14)
where PC is the percentage clay and PVFS is the percentageof very fine sand
For the soils containing less than 30 sand
120591119888
= 35 (15)
(c) Soil Erodibility (119870119903
)The soil erodibility (119870119903
) is determinedby using the following pedo-transfer function [35]
For the soils containing 30 or more sand
119870119903
= 000197 + 000030PVFS + 003863119890(minus184OM)
(16)
where OM is the organic matter ()For the soils containing less than 30 sand
119870119903
= 00069 + 0134119890(minus02PC)
(17)
(d) Transport Capacity (119879119888
) Sediment transport capacitywas calculated by Yalinrsquos equation [24] Foster and Meyer[15] concluded that Yalinrsquos equation is the most appropriatefor shallow flows associated with upland erosion The Yalinequation is defined as
119879119888
= 0635 (SG) 119889120588119908
12
120591119904
12
120575 [1 minus1
120573ln (1 + 120573)] (18)
120573 = 245(SG)minus04(119884cr)05
120575 (19a)
120575 =119884
119884crminus 1 (19b)
119884 =120591119904
120588119908
(SG minus 1) 119892119889 (19c)
where SG is the particle-specific gravity 120588119908
is the densityof water (kgmminus3) 119889 is the particle diameter (m) 119884 is the
4 Applied and Environmental Soil Science
minusqs = Tclceil1 minus e( D119888xT119888)rceil
Ef = Dc[1 minus (qsTc)]
Start
Input parameters
Transport capacity
Detachment capacity
Total shear stress
No Yes
Sediment load
Erosion Deposition
B
Q0 S0 n Kt Kr h120574 t x
x = x + dx
120591 = 120574RS
Tc = Kt12059115
Dc = Kr(120591 minus 120591c)
Df = minusdTc
dx
qs le Tc
A
(a)
No
Yes
the tail end
Sediment load at a distance x
Stop
BA
x le L
Sediment load (qs) at
Soil deposition (Df) or erosion (Ef)
(b)
Figure 1 Flowchart showing the working of sediment transport module
dimensionless shear stress 119884cr is the dimensionless criticalshear from Shieldrsquos Diagram 120591
119904
is the shear stress (Nmminus2)and 120573 and 120575 are the dimensionless parameters Criticalshear stress (119884cr) was determined by the following regressionequation from Shieldrsquos Diagram
Log10
119884cr = 0002235119909119888
5
minus 006034119909119888
4
+ 020307119909119888
3
+ 0054252119909119888
2
minus 0636397119909119888
(20)
where
119909119888
= log10
(119878lowast
) 119878lowast
=119889radic(SG minus 1) 119892119889
4V (21)
where 119878lowast
is the sediment fluid parameter (m s) and V is thekinematic viscosity of water (m2 sminus1)
When 120591 is much greater than the critical shear stress (120591119888
)for transport of detached particles the Yalin equation (YE)reduced to a simplified equation (MYE) as follows [36]
119879119888
= 119870119905
12059132
(22)
where119870119905
is the transport coefficient (kgminus12m12 s2)
24 Model Integration In the erosion model the transportcapacity (119879
119888
) and the detachment capacity (119863119888
) are the twoimportant parameters to be determined at a distance 119909
from the head end of the furrow The sediment transportcapacity (119879
119888
) was determined using the YE and MYE ((18) to(22)) Figure 1 shows the algorithm used to model sedimenttransport in irrigated furrows usingMYEThealgorithmusedfor YEwas the same asMYE (Figure 1) During the simulationrun the irrigationmodel estimates discharge and determinesthe sediment transport capacity (119879
119888
) and detachment capacity(119863119888
) Then the model estimates sediment load (119902119904
) erosion(119864119891
) and deposition (119863119891
) at a distance 119909 from the head endand time 119905 The sediment load estimation is terminated whenthe discharge in the furrow is zero
3 Model Evaluation
Performance of the sediment transportmodule was evaluatedfor bare and cropped furrow fields Furrow experimentswere conducted on a 4m times 60m plot in the Field WaterManagement Laboratory Agricultural and Food EngineeringDepartment IIT Kharagpur India The soil in the plot was
Applied and Environmental Soil Science 5
Table 1 Input data for infiltration and erosion components
Component Parameter Bare field Cropped field
Infiltration
119870119904
(ms) 10 times 10minus6
11 times 10minus6
119878av (m) 013 013119860119896
(m3 mminus1 sminus119861119896 ) 50 times 10minus4
535 times 10minus4
119861119896
(mdash) 04 0421198910
(m2 sminus1) 00 00
Erosion
120591119888
(Nmminus2) 00 00119870119903
(smminus1) 50 times 10minus6
10 times 10minus5
119870119905
(kgminus12 m12 s2) 001 002SG 265 265
119889 (m) 18 times 10minus5
28 times 10minus5
V (smminus1) 89 times 10minus6
89 times 10minus6
Table 2 Model performance for simulating sediment loss for bare field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
YE is the Yalin transport equationMYE is the modified Yalin transport equation
sandy loam and contained 69 sand (617 PVFS) 17 silt14 clay and 043 organic matter The bulk density andporosity of the soil were 154 gcm3 and 40 respectivelyThree free draining furrows of parabolic shape 40m long030m wide and 015m deep were fabricated in the exper-imental plot The furrows have centre-to-centre distance of08m and a slope of 05 The center furrow was consideredas study furrow and the two side furrows served as bufferto the center furrow Three digital flow meters (wheel type)were installed at the inlet of three furrows to set the desiredinflow rate to each furrow Plastic buckets (3-litre capacity)were used to collect run-off at the end of a study furrow at aninterval of 10min
The run-off samples were oven-dried and the sedimentleft in each sample was weighed The run-off rate (m3s) andthe corresponding sediment weight (kgm3) were used toestimate sediment rate (kgs)The details on experiments anddata collection procedure are presented by Mailapalli et al[6]The three furrows were irrigated at the same time on 6th17th 21119904119905 and 29th February 2004 using constant inflow ratesof 02 03 04 and 05 L sminus1 respectively on bare furrow fieldIn 2005 sunflower (Helianthus annuus L) crop was grown onthree furrow beds having a plant-to-plant spacing of 45 cmThe three furrows were irrigated on 3rd March 30th March
9th April 16th May and 23rd May 2005 using 07 06 0504 and 03 L sminus1 respectively The furrows were not tilledbetween irrigations during 2004 and 2005
Some of the input parameters required for overland flowinfiltration and sediment transport modules were estimatedfrom the field data [37] and these were considered as baseline input parameters for model testing The Green andAmpt hydraulic parameters such as 119870
119904
and 119878av were deter-mined using field data and pedo-transfer functions [38] TheKostiakov-Lewis parameters 119860
119896
119861119896
and 1198910
were estimatedby using ring infiltrometer data [37] The management andgeometric parameters for these field conditions were usedfrom [38] The critical shear (120591
119888
) and the soil erodibilitycoefficient (119870
119903
) were determined using (14) (15) (16) and(17) The estimated values of 119870
119903
and 120591119888
were 004 smminus1 and0001 respectively The values of SG and V were taken as 265and 89 times 10minus6 smminus1 respectively The mean diameter (119889)of the sediment particle for bare field was 18 times 10minus5m andcropped field was 28 times 10minus5m [37] The cropped field hascoarser particles than the bare field as the irrigations wereperformed first on the bare field and it may lost most of thefine particles as run-off
The simulations were first performed using the fieldobserved values of input parameters (119870 119870
119904
119878av 119860119896 119861119896
6 Applied and Environmental Soil Science
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
0
2
4
6
8
10
12
Observed2D-Fok
1D-GAKL
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 2 Comparison of observed and simulated sediment load (using YE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevent
120591119888
and 119870119903
) for estimating sediment load for both bare andcropped field conditions using the three infiltration modelsOf these simulations the best and the worst model per-formances were selected for both bare and cropped furrowconditions and model performance was studied graphi-cally It was assumed that infiltration is the key componentof irrigation management and was given first priority forselecting the best and worst simulations followed by run-offrate sediment yield waterfront advance and recession timesSensitivity analysis was carried out to study the effect of plusmn5and plusmn10 changes in the values of119870
119903
and119870119905
on the sedimentload estimated by the YE and MYE
The performance of the irrigation model for predictingsediment load was evaluated by estimating root mean squareerror (RMSE) and index of agreement (119868
119886
)Consider
RMSE = radicsum119873
119894=1
[119872(119894) minus 119864(119894)]2
119873
119868119886
= 10 minussum119873
119894=1
(119872 (119894) minus 119864 (119894))2
sum119873
119894=1
(10038161003816100381610038161003816119864 (119894) minus 119872
10038161003816100381610038161003816+10038161003816100381610038161003816119872 (119894) minus 119872
10038161003816100381610038161003816)2
(23)
where119872(119894) is the measured value 119864(119894) is the estimated value119873 is the number of data points and 119872 is the mean of theobserved values
4 Results and Discussion
The visual observation of the trends between observed andsimulated sediment loads (not shown here) by 2D-Fok 1D-Green Ampt and KL infiltration equations depicted that thesediment load predictions were not good with the baselinevalues of 120591
119888
and119870119903
Hence 120591119888
was assumed as zero and119870119903
and119870119905
were considered as calibration parameters for simulatingsediment loadDuring the calibration process the base valuesof 119870119903
and 119870119905
were tuned by increasing or decreasing theirbase values For each runmodel predicted sediment loadwascompared with its observed counterpart using the estimatedperformance indices Finally the values of 119870
119903
and 119870119905
were
found to be 50 times 10minus6 smminus1 and 001 for bare and 10 times
10minus5 smminus1 and 002 for cropped field conditions respectivelyTable 1 presents the input data used for infiltration anderosion parameters for bare and cropped field conditions
41 Sediment Transport in Bare Furrow Field The modelperformance was inconsistent in predicting the sedimentload using all three infiltration equations Furthermore theYE performed slightly better than the MYE in most of thecasesThe 2D-Fok infiltration function resulted in low RMSEand high 119868
119886
values as compared to those obtained using1D-Green Ampt and KL infiltration models (Table 2) Thusthe irrigation model performed well in simulating sedimentload using the 2D-Fok infiltration function followed by 1D-Green Ampt and KL-infiltration functions The performanceindices (Table 2) suggested that the model performance forsediment load in bare furrow field was the best and the worstfor irrigation events of 6th Feb 2004 and 17th Feb 2004respectively Therefore these events were selected for furtheranalysis Figures 2 and 3 show comparison between observedand simulated outputs for the best (6th February 2004) andtheworst (17th February 2004) irrigation events using YE andMYE respectively
The irrigation model with YE and MYE predicted initialincrease in sediment load well However both YE and MYEwere not able to predict the decreasing trend of sedimentrate with elapsed time The possible reason could be that thesediment load estimation takes the run-off rate into accountwhich increases with elapsed time Figures 2 and 3 also showthat the model performed equally well using 2D-Fok 1D-Green Ampt and KL infiltration models However sedimentload predictions using the YE were slightly better than theMYE
42 Sediment Transport in Cropped Furrow Field 2D-Fokinfiltration function resulted in lower RMSE values andhigher 119868
119886
values compared to those obtained using 1D-GreenAmpt and KL infiltration functions (Table 3) Further RMSEand 119868119886
values also suggested that the irrigationmodel with YEperformed slightly better than that with MYE Based on the
Applied and Environmental Soil Science 7
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
Observed2D-Fok
1D-GAKL
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 3 Comparison of observed and simulated sediment load (usingMYE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevents
Table 3 Model performance for simulating sediment loss for cropped field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
(kg)RMSE
times10minus5 (kg) 119868119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
3rd Mar-05 YE 112 115 8 055 118 8 054 119 9 045
MYE 112 117 9 055 118 9 053 119 9 044
30th Mar-05 YE 107 097 9 053 096 9 051 095 13 042
MYE 107 088 9 054 090 9 051 093 13 042
9th Apr-05 YE 102 093 4 083 099 4 078 100 6 072
MYE 102 095 4 083 100 4 073 104 75 069
16th May-05 YE 063 078 3 085 079 3 081 084 6 075
MYE 063 077 4 084 077 42 083 082 7 072
23rd May-05 YE 029 042 4 083 047 4 080 054 7 072
MYE 029 046 5 082 047 6 080 054 8 070
performance indices it is clear that the model performancein predicting sediment load was the best and the worst insimulating irrigation events of 16th May and 30th March2005 respectively For these two irrigation events the modelpredicted sediment load was compared with their observedcounterparts and the results are shown in Figures 4 and 5 forYE and MYE respectively
Both YE and MYE predicted initial increase in sedimentload well However as in case of bare furrow condition bothYE and MYE were not able to predict the decreasing trendof sediment rate with elapsed time The model performedequally well using 2D-Fok 1D-Green Ampt and KL infiltra-tion equations (Figures 4 and 5) Furthermore the irrigationmodel with YE predicted the sediment load slightly betterthan the one with the MYE (Table 3)
43 Sensitivity Analysis of Model Parameters Sensitivity ofthe model parameters in predicting sediment load wasstudied for 16th May 2005 event The effect of plusmn5 andplusmn10 changes in 119870
119903
and 119870119905
(Table 4) on the simulatedsediment load was estimated by YE andMYE considering all
infiltration functions The variation in 119870119905
did not have mucheffect on the sediment load whereas the percentage changein 119870119903
caused the sediment load change at the same rate (bywhich 119870
119903
is changed) Hence for 2D-infiltration model 119870119903
is the most sensitive parameter for estimating sediment loadfor both YE andMYE For 1D-infiltration equation the effectof change in 119870
119905
and 119870119903
on the sediment yield is the same asthe case with 2D-infiltration model The change in 119870
119905
hadvery little effect on the sediment load that resulted with KLinfiltration model The increase in119870
119903
increased the sedimentload at the same rate for both YE and MYE
5 Conclusions
Irrigation-induced erosion accounts most part of the dif-fuse agricultural pollution causing downstream impairmentand eutrophication In this study a steady state sedimenttransport model was integrated with a physically basedfurrow irrigation model which consists of three infiltrationequations (2D-Fok 1D-Green Ampt and Kostiakov-Lewis)The integrated irrigation model was evaluated for estimating
8 Applied and Environmental Soil Science
Table 4 Sensitivity analysis of erosion module parameters
Input parameter Percentage changePercentage change in sediment load
2D-Fok and Chiang 1D-Green Ampt KL infiltration functionMYE YE MYE YE MYE YE
119870119905
(kgminus12 m12 s2)
minus10 0 NA 013 NA minus024 NAminus5 0 NA 013 NA 0 NA5 013 NA 039 NA 012 NA10 013 NA 039 NA 024 NA
Figure 4 Comparison of observed and simulated sediment load (using YE) for (a) 16thMay 2005 and (b) 30thMarch 2005 irrigation events
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(a)
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(b)
Figure 5 Comparison of observed and simulated sediment load (using MYE) for (a) 16th May 2005 and (b) 30th March 2005 irrigationevent
sediment load using two sediment transport capacity equa-tions (Yalin and the modified Yalin equations) for bare andcropped field conditionsThe sediment load prediction usingthe Yalin and the modified Yalin equations was found to beidentical however the modified Yalin equation may be abetter choice as it requires less number of input parametersThe sensitivity analysis revealed that the soil erodibilitycoefficient is the most influential parameter in predicting
sediment transport in free drained furrows However theirrigation model could not adequately simulate the sedimentload in the last phase of irrigation Although this has aminor impact on the overall sediment load it will be thesubject of future model refinement The irrigation modeluses an analytical solution for zero-inertial flow equationsand this compared favourably to the full numerical hydraulicmodels [39] This paper describes the procedure for coupling
Applied and Environmental Soil Science 9
the sediment module to the zero-inertial irrigation modeland design for simulating infiltration though layered soils[37] This is one of the advantages of the integrated modelfor investigating the impact of soil layering on sedimenttransport The other advantage is the use of the model aseducational tool for studying the effect of various infiltrationand sediment capacity equations on the sediment rate Theintegrated model can also be used as a management toolto determine optimum water delivery to irrigated furrowsor borders for attaining better irrigation performance withminimum soil loss The modeling approach can also beintegrated with nutrient transport models where sedimentbound nutrient losses contribute substantially to total non-point nutrient losses from agricultural fields
Acknowledgments
Theauthors are grateful toVolkswagenFoundations StiftungGermany for providing financial support which made therealization of this work possible The technical support forthe model development by Prof G H Schmitz and Prof FLennartz is gratefully acknowledged
References
[1] Food and Agriculture Organization AQUASTAT httpwwwfaoorgnrwateraquastatwater useindexstm 2013
[2] R D Berg and D L Carter ldquoFurrow erosion and sedimentlosses on irrigated croplandrdquo Journal of Soil amp Water Conser-vation vol 35 no 6 pp 267ndash270 1980
[3] W D Kemper T J Trout M J Brown and R C RosenauldquoFurrow erosion and water and soil managementrdquo Transactionsof the American Society of Agricultural Engineers vol 28 no 5pp 1564ndash1572 1985
[4] T J Trout ldquoFurrow irrigation erosion and sedimentationon-field distributionrdquo Transactions of the American Society ofAgricultural Engineers vol 39 no 5 pp 1717ndash1723 1996
[5] L Mateos and J V Giraldez ldquoSuspended load and bed load inirrigation furrowsrdquo Catena vol 64 no 2-3 pp 232ndash246 2005
[6] D R Mailapalli N S Raghuwanshi and R Singh ldquoSedimenttransport in furrow irrigationrdquo Irrigation Science vol 27 no 6pp 449ndash456 2009
[7] P K Koluvek K K Tanji and T J Trout ldquoOverview ofsoil erosion from irrigationrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 929ndash946 1993
[8] M J Brown D L Carter G A Lehrsch and R E SojkaldquoSeasonal trends in furrow irrigation erosion in southernIdahordquo Soil Technology vol 8 no 2 pp 119ndash126 1995
[9] T J Trout ldquoSediment transport in irrigation furrowsrdquo in Pro-ceedings of the 10th International Soil ConservationOrganizationMeeting Held May 24ndash29 1999 at Purdue University and theUSDA-ARS National Soil Erosion Research Laboratory D EStott R H Mohtar and G C Steinhardt Eds pp 710ndash7162001
[10] R Fernandez-Gomez L Mateos and J V Giraldez ldquoFurrowirrigation erosion and managementrdquo Irrigation Science vol 23no 3 pp 123ndash131 2004
[11] C J Everts and D L Carter Furrow Erosion and Topsoil LossesCurrent information series no 586 College of AgricultureUniversity of Idaho Moscow Russia 1981
[12] K J Fornstrom and J Borelli ldquoDesign and management pro-cedure for minimising erosion from furrow irrigated croplandrdquoPaper 84-2595 American Society of Association Executives StJoseph Mich USA 1994
[13] R P C Morgan ldquoThe European soil erosion model an updateon its structure and research baserdquo inConserving Soil ResourcesEuropean Perspectives R J Rickson Ed pp 286ndash299 CABIntOxton Scotland UK 1995
[14] W S Merritt R A Letcher and A J Jakeman ldquoA reviewof erosion and sediment transport modelsrdquo EnvironmentalModelling and Software vol 18 no 8-9 pp 761ndash799 2003
[15] G R Foster and L D Meyer ldquoMathematical simulation ofupland erosion by fundamental erosion mechanicsrdquo Presentand Prospective Technology for Predicting Sediment Yield andSourcesUSDAARSPublicationARS-S40USDAAgriculturalResearch Service Nat Tech Information Service SpringfieldVa USA 1972
[16] M B Abbott J C Bathurst J A Cunge P E OrsquoConnell andJ Rasmussen ldquoAn introduction to the European hydrologicalsystemmdashsysteme hydrologique Europeen ldquoSHErdquo 1 historyand philosophy of a physically-based distributed modellingsystemrdquo Journal of Hydrology vol 87 no 1-2 pp 45ndash59 1986
[17] A J Jakeman and G M Hornberger ldquoHow much complexityis warranted in a rainfall-runoff modelrdquo Water ResourcesResearch vol 29 no 8 pp 2637ndash2649 1993
[18] C CWu and L DMeyer ldquoSimulating transport of nonuniformsediment along flatland furrowsrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 32 no 5 pp 1651ndash16611989
[19] T S Strelkoff A J Clemmens and B V Schmidt SRFR Version321-a Model for Simulating Surface Irrigation in Borders Basinsand Furrows USWCL USDAARS Phoenix Ariz USA 1998
[20] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[21] D L Bjorneberg and T J Trout ldquoEvaluating WEPP predictedon-field furrow erosionrdquo in Proceedings of the 10th InternationalSoil Conservation Organization (ISCO rsquo99) West Lafayette IndUSA May 1999
[22] E M Laursen ldquoThe total sediment load of streamsrdquo Journal ofHydraulics Divison vol 84 pp 1530-1ndash1530-36 1958
[23] C T Yang ldquoIncipient motion and sediment transportrdquo Journalof Hydraulics Divison vol 99 no 10 pp 1679ndash1704 1973
[24] M S Yalin ldquoAn expression for bed-load transportationrdquo Journalof Hydraulics Divison vol 89 no 3 pp 221ndash250 1963
[25] T S Strelkoff and D L Bjorneberg ldquoHydraulic modeling ofirrigation-induced furrow erosionrdquo in Proceedings of the 10thInternational Soil Conservation Organization Conference D EStott R H Mohtar and G C Steinhardt Eds Sustaining theGlobal Farm pp 699ndash705 West Lafayette Ind USA May 1999
[26] D R Mailapalli R Singh and N S Raghuwanshi ldquoPhysicallybased model for simulating flow in furrow irrigation I modeldevelopmentrdquo Journal of Irrigation and Drainage Engineeringvol 135 no 6 pp 739ndash746 2009
[27] Y S Fok and S H Chiang ldquo2-D infiltration equations for fur-row irrigationrdquo Journal of Irrigation and Drainage Engineeringvol 110 no 2 pp 208ndash217 1984
[28] M D Rao N S Raghuwanshi and R Singh ldquoDevelopmentof a physically based 1D-infiltration model for irrigated soilsrdquoAgricultural Water Management vol 85 no 1-2 pp 165ndash1742006
10 Applied and Environmental Soil Science
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
Figure 1 Flowchart showing the working of sediment transport module
dimensionless shear stress 119884cr is the dimensionless criticalshear from Shieldrsquos Diagram 120591
119904
is the shear stress (Nmminus2)and 120573 and 120575 are the dimensionless parameters Criticalshear stress (119884cr) was determined by the following regressionequation from Shieldrsquos Diagram
Log10
119884cr = 0002235119909119888
5
minus 006034119909119888
4
+ 020307119909119888
3
+ 0054252119909119888
2
minus 0636397119909119888
(20)
where
119909119888
= log10
(119878lowast
) 119878lowast
=119889radic(SG minus 1) 119892119889
4V (21)
where 119878lowast
is the sediment fluid parameter (m s) and V is thekinematic viscosity of water (m2 sminus1)
When 120591 is much greater than the critical shear stress (120591119888
)for transport of detached particles the Yalin equation (YE)reduced to a simplified equation (MYE) as follows [36]
119879119888
= 119870119905
12059132
(22)
where119870119905
is the transport coefficient (kgminus12m12 s2)
24 Model Integration In the erosion model the transportcapacity (119879
119888
) and the detachment capacity (119863119888
) are the twoimportant parameters to be determined at a distance 119909
from the head end of the furrow The sediment transportcapacity (119879
119888
) was determined using the YE and MYE ((18) to(22)) Figure 1 shows the algorithm used to model sedimenttransport in irrigated furrows usingMYEThealgorithmusedfor YEwas the same asMYE (Figure 1) During the simulationrun the irrigationmodel estimates discharge and determinesthe sediment transport capacity (119879
119888
) and detachment capacity(119863119888
) Then the model estimates sediment load (119902119904
) erosion(119864119891
) and deposition (119863119891
) at a distance 119909 from the head endand time 119905 The sediment load estimation is terminated whenthe discharge in the furrow is zero
3 Model Evaluation
Performance of the sediment transportmodule was evaluatedfor bare and cropped furrow fields Furrow experimentswere conducted on a 4m times 60m plot in the Field WaterManagement Laboratory Agricultural and Food EngineeringDepartment IIT Kharagpur India The soil in the plot was
Applied and Environmental Soil Science 5
Table 1 Input data for infiltration and erosion components
Component Parameter Bare field Cropped field
Infiltration
119870119904
(ms) 10 times 10minus6
11 times 10minus6
119878av (m) 013 013119860119896
(m3 mminus1 sminus119861119896 ) 50 times 10minus4
535 times 10minus4
119861119896
(mdash) 04 0421198910
(m2 sminus1) 00 00
Erosion
120591119888
(Nmminus2) 00 00119870119903
(smminus1) 50 times 10minus6
10 times 10minus5
119870119905
(kgminus12 m12 s2) 001 002SG 265 265
119889 (m) 18 times 10minus5
28 times 10minus5
V (smminus1) 89 times 10minus6
89 times 10minus6
Table 2 Model performance for simulating sediment loss for bare field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
YE is the Yalin transport equationMYE is the modified Yalin transport equation
sandy loam and contained 69 sand (617 PVFS) 17 silt14 clay and 043 organic matter The bulk density andporosity of the soil were 154 gcm3 and 40 respectivelyThree free draining furrows of parabolic shape 40m long030m wide and 015m deep were fabricated in the exper-imental plot The furrows have centre-to-centre distance of08m and a slope of 05 The center furrow was consideredas study furrow and the two side furrows served as bufferto the center furrow Three digital flow meters (wheel type)were installed at the inlet of three furrows to set the desiredinflow rate to each furrow Plastic buckets (3-litre capacity)were used to collect run-off at the end of a study furrow at aninterval of 10min
The run-off samples were oven-dried and the sedimentleft in each sample was weighed The run-off rate (m3s) andthe corresponding sediment weight (kgm3) were used toestimate sediment rate (kgs)The details on experiments anddata collection procedure are presented by Mailapalli et al[6]The three furrows were irrigated at the same time on 6th17th 21119904119905 and 29th February 2004 using constant inflow ratesof 02 03 04 and 05 L sminus1 respectively on bare furrow fieldIn 2005 sunflower (Helianthus annuus L) crop was grown onthree furrow beds having a plant-to-plant spacing of 45 cmThe three furrows were irrigated on 3rd March 30th March
9th April 16th May and 23rd May 2005 using 07 06 0504 and 03 L sminus1 respectively The furrows were not tilledbetween irrigations during 2004 and 2005
Some of the input parameters required for overland flowinfiltration and sediment transport modules were estimatedfrom the field data [37] and these were considered as baseline input parameters for model testing The Green andAmpt hydraulic parameters such as 119870
119904
and 119878av were deter-mined using field data and pedo-transfer functions [38] TheKostiakov-Lewis parameters 119860
119896
119861119896
and 1198910
were estimatedby using ring infiltrometer data [37] The management andgeometric parameters for these field conditions were usedfrom [38] The critical shear (120591
119888
) and the soil erodibilitycoefficient (119870
119903
) were determined using (14) (15) (16) and(17) The estimated values of 119870
119903
and 120591119888
were 004 smminus1 and0001 respectively The values of SG and V were taken as 265and 89 times 10minus6 smminus1 respectively The mean diameter (119889)of the sediment particle for bare field was 18 times 10minus5m andcropped field was 28 times 10minus5m [37] The cropped field hascoarser particles than the bare field as the irrigations wereperformed first on the bare field and it may lost most of thefine particles as run-off
The simulations were first performed using the fieldobserved values of input parameters (119870 119870
119904
119878av 119860119896 119861119896
6 Applied and Environmental Soil Science
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
0
2
4
6
8
10
12
Observed2D-Fok
1D-GAKL
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 2 Comparison of observed and simulated sediment load (using YE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevent
120591119888
and 119870119903
) for estimating sediment load for both bare andcropped field conditions using the three infiltration modelsOf these simulations the best and the worst model per-formances were selected for both bare and cropped furrowconditions and model performance was studied graphi-cally It was assumed that infiltration is the key componentof irrigation management and was given first priority forselecting the best and worst simulations followed by run-offrate sediment yield waterfront advance and recession timesSensitivity analysis was carried out to study the effect of plusmn5and plusmn10 changes in the values of119870
119903
and119870119905
on the sedimentload estimated by the YE and MYE
The performance of the irrigation model for predictingsediment load was evaluated by estimating root mean squareerror (RMSE) and index of agreement (119868
119886
)Consider
RMSE = radicsum119873
119894=1
[119872(119894) minus 119864(119894)]2
119873
119868119886
= 10 minussum119873
119894=1
(119872 (119894) minus 119864 (119894))2
sum119873
119894=1
(10038161003816100381610038161003816119864 (119894) minus 119872
10038161003816100381610038161003816+10038161003816100381610038161003816119872 (119894) minus 119872
10038161003816100381610038161003816)2
(23)
where119872(119894) is the measured value 119864(119894) is the estimated value119873 is the number of data points and 119872 is the mean of theobserved values
4 Results and Discussion
The visual observation of the trends between observed andsimulated sediment loads (not shown here) by 2D-Fok 1D-Green Ampt and KL infiltration equations depicted that thesediment load predictions were not good with the baselinevalues of 120591
119888
and119870119903
Hence 120591119888
was assumed as zero and119870119903
and119870119905
were considered as calibration parameters for simulatingsediment loadDuring the calibration process the base valuesof 119870119903
and 119870119905
were tuned by increasing or decreasing theirbase values For each runmodel predicted sediment loadwascompared with its observed counterpart using the estimatedperformance indices Finally the values of 119870
119903
and 119870119905
were
found to be 50 times 10minus6 smminus1 and 001 for bare and 10 times
10minus5 smminus1 and 002 for cropped field conditions respectivelyTable 1 presents the input data used for infiltration anderosion parameters for bare and cropped field conditions
41 Sediment Transport in Bare Furrow Field The modelperformance was inconsistent in predicting the sedimentload using all three infiltration equations Furthermore theYE performed slightly better than the MYE in most of thecasesThe 2D-Fok infiltration function resulted in low RMSEand high 119868
119886
values as compared to those obtained using1D-Green Ampt and KL infiltration models (Table 2) Thusthe irrigation model performed well in simulating sedimentload using the 2D-Fok infiltration function followed by 1D-Green Ampt and KL-infiltration functions The performanceindices (Table 2) suggested that the model performance forsediment load in bare furrow field was the best and the worstfor irrigation events of 6th Feb 2004 and 17th Feb 2004respectively Therefore these events were selected for furtheranalysis Figures 2 and 3 show comparison between observedand simulated outputs for the best (6th February 2004) andtheworst (17th February 2004) irrigation events using YE andMYE respectively
The irrigation model with YE and MYE predicted initialincrease in sediment load well However both YE and MYEwere not able to predict the decreasing trend of sedimentrate with elapsed time The possible reason could be that thesediment load estimation takes the run-off rate into accountwhich increases with elapsed time Figures 2 and 3 also showthat the model performed equally well using 2D-Fok 1D-Green Ampt and KL infiltration models However sedimentload predictions using the YE were slightly better than theMYE
42 Sediment Transport in Cropped Furrow Field 2D-Fokinfiltration function resulted in lower RMSE values andhigher 119868
119886
values compared to those obtained using 1D-GreenAmpt and KL infiltration functions (Table 3) Further RMSEand 119868119886
values also suggested that the irrigationmodel with YEperformed slightly better than that with MYE Based on the
Applied and Environmental Soil Science 7
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
Observed2D-Fok
1D-GAKL
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 3 Comparison of observed and simulated sediment load (usingMYE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevents
Table 3 Model performance for simulating sediment loss for cropped field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
(kg)RMSE
times10minus5 (kg) 119868119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
3rd Mar-05 YE 112 115 8 055 118 8 054 119 9 045
MYE 112 117 9 055 118 9 053 119 9 044
30th Mar-05 YE 107 097 9 053 096 9 051 095 13 042
MYE 107 088 9 054 090 9 051 093 13 042
9th Apr-05 YE 102 093 4 083 099 4 078 100 6 072
MYE 102 095 4 083 100 4 073 104 75 069
16th May-05 YE 063 078 3 085 079 3 081 084 6 075
MYE 063 077 4 084 077 42 083 082 7 072
23rd May-05 YE 029 042 4 083 047 4 080 054 7 072
MYE 029 046 5 082 047 6 080 054 8 070
performance indices it is clear that the model performancein predicting sediment load was the best and the worst insimulating irrigation events of 16th May and 30th March2005 respectively For these two irrigation events the modelpredicted sediment load was compared with their observedcounterparts and the results are shown in Figures 4 and 5 forYE and MYE respectively
Both YE and MYE predicted initial increase in sedimentload well However as in case of bare furrow condition bothYE and MYE were not able to predict the decreasing trendof sediment rate with elapsed time The model performedequally well using 2D-Fok 1D-Green Ampt and KL infiltra-tion equations (Figures 4 and 5) Furthermore the irrigationmodel with YE predicted the sediment load slightly betterthan the one with the MYE (Table 3)
43 Sensitivity Analysis of Model Parameters Sensitivity ofthe model parameters in predicting sediment load wasstudied for 16th May 2005 event The effect of plusmn5 andplusmn10 changes in 119870
119903
and 119870119905
(Table 4) on the simulatedsediment load was estimated by YE andMYE considering all
infiltration functions The variation in 119870119905
did not have mucheffect on the sediment load whereas the percentage changein 119870119903
caused the sediment load change at the same rate (bywhich 119870
119903
is changed) Hence for 2D-infiltration model 119870119903
is the most sensitive parameter for estimating sediment loadfor both YE andMYE For 1D-infiltration equation the effectof change in 119870
119905
and 119870119903
on the sediment yield is the same asthe case with 2D-infiltration model The change in 119870
119905
hadvery little effect on the sediment load that resulted with KLinfiltration model The increase in119870
119903
increased the sedimentload at the same rate for both YE and MYE
5 Conclusions
Irrigation-induced erosion accounts most part of the dif-fuse agricultural pollution causing downstream impairmentand eutrophication In this study a steady state sedimenttransport model was integrated with a physically basedfurrow irrigation model which consists of three infiltrationequations (2D-Fok 1D-Green Ampt and Kostiakov-Lewis)The integrated irrigation model was evaluated for estimating
8 Applied and Environmental Soil Science
Table 4 Sensitivity analysis of erosion module parameters
Input parameter Percentage changePercentage change in sediment load
2D-Fok and Chiang 1D-Green Ampt KL infiltration functionMYE YE MYE YE MYE YE
119870119905
(kgminus12 m12 s2)
minus10 0 NA 013 NA minus024 NAminus5 0 NA 013 NA 0 NA5 013 NA 039 NA 012 NA10 013 NA 039 NA 024 NA
Figure 4 Comparison of observed and simulated sediment load (using YE) for (a) 16thMay 2005 and (b) 30thMarch 2005 irrigation events
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(a)
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(b)
Figure 5 Comparison of observed and simulated sediment load (using MYE) for (a) 16th May 2005 and (b) 30th March 2005 irrigationevent
sediment load using two sediment transport capacity equa-tions (Yalin and the modified Yalin equations) for bare andcropped field conditionsThe sediment load prediction usingthe Yalin and the modified Yalin equations was found to beidentical however the modified Yalin equation may be abetter choice as it requires less number of input parametersThe sensitivity analysis revealed that the soil erodibilitycoefficient is the most influential parameter in predicting
sediment transport in free drained furrows However theirrigation model could not adequately simulate the sedimentload in the last phase of irrigation Although this has aminor impact on the overall sediment load it will be thesubject of future model refinement The irrigation modeluses an analytical solution for zero-inertial flow equationsand this compared favourably to the full numerical hydraulicmodels [39] This paper describes the procedure for coupling
Applied and Environmental Soil Science 9
the sediment module to the zero-inertial irrigation modeland design for simulating infiltration though layered soils[37] This is one of the advantages of the integrated modelfor investigating the impact of soil layering on sedimenttransport The other advantage is the use of the model aseducational tool for studying the effect of various infiltrationand sediment capacity equations on the sediment rate Theintegrated model can also be used as a management toolto determine optimum water delivery to irrigated furrowsor borders for attaining better irrigation performance withminimum soil loss The modeling approach can also beintegrated with nutrient transport models where sedimentbound nutrient losses contribute substantially to total non-point nutrient losses from agricultural fields
Acknowledgments
Theauthors are grateful toVolkswagenFoundations StiftungGermany for providing financial support which made therealization of this work possible The technical support forthe model development by Prof G H Schmitz and Prof FLennartz is gratefully acknowledged
References
[1] Food and Agriculture Organization AQUASTAT httpwwwfaoorgnrwateraquastatwater useindexstm 2013
[2] R D Berg and D L Carter ldquoFurrow erosion and sedimentlosses on irrigated croplandrdquo Journal of Soil amp Water Conser-vation vol 35 no 6 pp 267ndash270 1980
[3] W D Kemper T J Trout M J Brown and R C RosenauldquoFurrow erosion and water and soil managementrdquo Transactionsof the American Society of Agricultural Engineers vol 28 no 5pp 1564ndash1572 1985
[4] T J Trout ldquoFurrow irrigation erosion and sedimentationon-field distributionrdquo Transactions of the American Society ofAgricultural Engineers vol 39 no 5 pp 1717ndash1723 1996
[5] L Mateos and J V Giraldez ldquoSuspended load and bed load inirrigation furrowsrdquo Catena vol 64 no 2-3 pp 232ndash246 2005
[6] D R Mailapalli N S Raghuwanshi and R Singh ldquoSedimenttransport in furrow irrigationrdquo Irrigation Science vol 27 no 6pp 449ndash456 2009
[7] P K Koluvek K K Tanji and T J Trout ldquoOverview ofsoil erosion from irrigationrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 929ndash946 1993
[8] M J Brown D L Carter G A Lehrsch and R E SojkaldquoSeasonal trends in furrow irrigation erosion in southernIdahordquo Soil Technology vol 8 no 2 pp 119ndash126 1995
[9] T J Trout ldquoSediment transport in irrigation furrowsrdquo in Pro-ceedings of the 10th International Soil ConservationOrganizationMeeting Held May 24ndash29 1999 at Purdue University and theUSDA-ARS National Soil Erosion Research Laboratory D EStott R H Mohtar and G C Steinhardt Eds pp 710ndash7162001
[10] R Fernandez-Gomez L Mateos and J V Giraldez ldquoFurrowirrigation erosion and managementrdquo Irrigation Science vol 23no 3 pp 123ndash131 2004
[11] C J Everts and D L Carter Furrow Erosion and Topsoil LossesCurrent information series no 586 College of AgricultureUniversity of Idaho Moscow Russia 1981
[12] K J Fornstrom and J Borelli ldquoDesign and management pro-cedure for minimising erosion from furrow irrigated croplandrdquoPaper 84-2595 American Society of Association Executives StJoseph Mich USA 1994
[13] R P C Morgan ldquoThe European soil erosion model an updateon its structure and research baserdquo inConserving Soil ResourcesEuropean Perspectives R J Rickson Ed pp 286ndash299 CABIntOxton Scotland UK 1995
[14] W S Merritt R A Letcher and A J Jakeman ldquoA reviewof erosion and sediment transport modelsrdquo EnvironmentalModelling and Software vol 18 no 8-9 pp 761ndash799 2003
[15] G R Foster and L D Meyer ldquoMathematical simulation ofupland erosion by fundamental erosion mechanicsrdquo Presentand Prospective Technology for Predicting Sediment Yield andSourcesUSDAARSPublicationARS-S40USDAAgriculturalResearch Service Nat Tech Information Service SpringfieldVa USA 1972
[16] M B Abbott J C Bathurst J A Cunge P E OrsquoConnell andJ Rasmussen ldquoAn introduction to the European hydrologicalsystemmdashsysteme hydrologique Europeen ldquoSHErdquo 1 historyand philosophy of a physically-based distributed modellingsystemrdquo Journal of Hydrology vol 87 no 1-2 pp 45ndash59 1986
[17] A J Jakeman and G M Hornberger ldquoHow much complexityis warranted in a rainfall-runoff modelrdquo Water ResourcesResearch vol 29 no 8 pp 2637ndash2649 1993
[18] C CWu and L DMeyer ldquoSimulating transport of nonuniformsediment along flatland furrowsrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 32 no 5 pp 1651ndash16611989
[19] T S Strelkoff A J Clemmens and B V Schmidt SRFR Version321-a Model for Simulating Surface Irrigation in Borders Basinsand Furrows USWCL USDAARS Phoenix Ariz USA 1998
[20] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[21] D L Bjorneberg and T J Trout ldquoEvaluating WEPP predictedon-field furrow erosionrdquo in Proceedings of the 10th InternationalSoil Conservation Organization (ISCO rsquo99) West Lafayette IndUSA May 1999
[22] E M Laursen ldquoThe total sediment load of streamsrdquo Journal ofHydraulics Divison vol 84 pp 1530-1ndash1530-36 1958
[23] C T Yang ldquoIncipient motion and sediment transportrdquo Journalof Hydraulics Divison vol 99 no 10 pp 1679ndash1704 1973
[24] M S Yalin ldquoAn expression for bed-load transportationrdquo Journalof Hydraulics Divison vol 89 no 3 pp 221ndash250 1963
[25] T S Strelkoff and D L Bjorneberg ldquoHydraulic modeling ofirrigation-induced furrow erosionrdquo in Proceedings of the 10thInternational Soil Conservation Organization Conference D EStott R H Mohtar and G C Steinhardt Eds Sustaining theGlobal Farm pp 699ndash705 West Lafayette Ind USA May 1999
[26] D R Mailapalli R Singh and N S Raghuwanshi ldquoPhysicallybased model for simulating flow in furrow irrigation I modeldevelopmentrdquo Journal of Irrigation and Drainage Engineeringvol 135 no 6 pp 739ndash746 2009
[27] Y S Fok and S H Chiang ldquo2-D infiltration equations for fur-row irrigationrdquo Journal of Irrigation and Drainage Engineeringvol 110 no 2 pp 208ndash217 1984
[28] M D Rao N S Raghuwanshi and R Singh ldquoDevelopmentof a physically based 1D-infiltration model for irrigated soilsrdquoAgricultural Water Management vol 85 no 1-2 pp 165ndash1742006
10 Applied and Environmental Soil Science
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
YE is the Yalin transport equationMYE is the modified Yalin transport equation
sandy loam and contained 69 sand (617 PVFS) 17 silt14 clay and 043 organic matter The bulk density andporosity of the soil were 154 gcm3 and 40 respectivelyThree free draining furrows of parabolic shape 40m long030m wide and 015m deep were fabricated in the exper-imental plot The furrows have centre-to-centre distance of08m and a slope of 05 The center furrow was consideredas study furrow and the two side furrows served as bufferto the center furrow Three digital flow meters (wheel type)were installed at the inlet of three furrows to set the desiredinflow rate to each furrow Plastic buckets (3-litre capacity)were used to collect run-off at the end of a study furrow at aninterval of 10min
The run-off samples were oven-dried and the sedimentleft in each sample was weighed The run-off rate (m3s) andthe corresponding sediment weight (kgm3) were used toestimate sediment rate (kgs)The details on experiments anddata collection procedure are presented by Mailapalli et al[6]The three furrows were irrigated at the same time on 6th17th 21119904119905 and 29th February 2004 using constant inflow ratesof 02 03 04 and 05 L sminus1 respectively on bare furrow fieldIn 2005 sunflower (Helianthus annuus L) crop was grown onthree furrow beds having a plant-to-plant spacing of 45 cmThe three furrows were irrigated on 3rd March 30th March
9th April 16th May and 23rd May 2005 using 07 06 0504 and 03 L sminus1 respectively The furrows were not tilledbetween irrigations during 2004 and 2005
Some of the input parameters required for overland flowinfiltration and sediment transport modules were estimatedfrom the field data [37] and these were considered as baseline input parameters for model testing The Green andAmpt hydraulic parameters such as 119870
119904
and 119878av were deter-mined using field data and pedo-transfer functions [38] TheKostiakov-Lewis parameters 119860
119896
119861119896
and 1198910
were estimatedby using ring infiltrometer data [37] The management andgeometric parameters for these field conditions were usedfrom [38] The critical shear (120591
119888
) and the soil erodibilitycoefficient (119870
119903
) were determined using (14) (15) (16) and(17) The estimated values of 119870
119903
and 120591119888
were 004 smminus1 and0001 respectively The values of SG and V were taken as 265and 89 times 10minus6 smminus1 respectively The mean diameter (119889)of the sediment particle for bare field was 18 times 10minus5m andcropped field was 28 times 10minus5m [37] The cropped field hascoarser particles than the bare field as the irrigations wereperformed first on the bare field and it may lost most of thefine particles as run-off
The simulations were first performed using the fieldobserved values of input parameters (119870 119870
119904
119878av 119860119896 119861119896
6 Applied and Environmental Soil Science
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
0
2
4
6
8
10
12
Observed2D-Fok
1D-GAKL
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 2 Comparison of observed and simulated sediment load (using YE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevent
120591119888
and 119870119903
) for estimating sediment load for both bare andcropped field conditions using the three infiltration modelsOf these simulations the best and the worst model per-formances were selected for both bare and cropped furrowconditions and model performance was studied graphi-cally It was assumed that infiltration is the key componentof irrigation management and was given first priority forselecting the best and worst simulations followed by run-offrate sediment yield waterfront advance and recession timesSensitivity analysis was carried out to study the effect of plusmn5and plusmn10 changes in the values of119870
119903
and119870119905
on the sedimentload estimated by the YE and MYE
The performance of the irrigation model for predictingsediment load was evaluated by estimating root mean squareerror (RMSE) and index of agreement (119868
119886
)Consider
RMSE = radicsum119873
119894=1
[119872(119894) minus 119864(119894)]2
119873
119868119886
= 10 minussum119873
119894=1
(119872 (119894) minus 119864 (119894))2
sum119873
119894=1
(10038161003816100381610038161003816119864 (119894) minus 119872
10038161003816100381610038161003816+10038161003816100381610038161003816119872 (119894) minus 119872
10038161003816100381610038161003816)2
(23)
where119872(119894) is the measured value 119864(119894) is the estimated value119873 is the number of data points and 119872 is the mean of theobserved values
4 Results and Discussion
The visual observation of the trends between observed andsimulated sediment loads (not shown here) by 2D-Fok 1D-Green Ampt and KL infiltration equations depicted that thesediment load predictions were not good with the baselinevalues of 120591
119888
and119870119903
Hence 120591119888
was assumed as zero and119870119903
and119870119905
were considered as calibration parameters for simulatingsediment loadDuring the calibration process the base valuesof 119870119903
and 119870119905
were tuned by increasing or decreasing theirbase values For each runmodel predicted sediment loadwascompared with its observed counterpart using the estimatedperformance indices Finally the values of 119870
119903
and 119870119905
were
found to be 50 times 10minus6 smminus1 and 001 for bare and 10 times
10minus5 smminus1 and 002 for cropped field conditions respectivelyTable 1 presents the input data used for infiltration anderosion parameters for bare and cropped field conditions
41 Sediment Transport in Bare Furrow Field The modelperformance was inconsistent in predicting the sedimentload using all three infiltration equations Furthermore theYE performed slightly better than the MYE in most of thecasesThe 2D-Fok infiltration function resulted in low RMSEand high 119868
119886
values as compared to those obtained using1D-Green Ampt and KL infiltration models (Table 2) Thusthe irrigation model performed well in simulating sedimentload using the 2D-Fok infiltration function followed by 1D-Green Ampt and KL-infiltration functions The performanceindices (Table 2) suggested that the model performance forsediment load in bare furrow field was the best and the worstfor irrigation events of 6th Feb 2004 and 17th Feb 2004respectively Therefore these events were selected for furtheranalysis Figures 2 and 3 show comparison between observedand simulated outputs for the best (6th February 2004) andtheworst (17th February 2004) irrigation events using YE andMYE respectively
The irrigation model with YE and MYE predicted initialincrease in sediment load well However both YE and MYEwere not able to predict the decreasing trend of sedimentrate with elapsed time The possible reason could be that thesediment load estimation takes the run-off rate into accountwhich increases with elapsed time Figures 2 and 3 also showthat the model performed equally well using 2D-Fok 1D-Green Ampt and KL infiltration models However sedimentload predictions using the YE were slightly better than theMYE
42 Sediment Transport in Cropped Furrow Field 2D-Fokinfiltration function resulted in lower RMSE values andhigher 119868
119886
values compared to those obtained using 1D-GreenAmpt and KL infiltration functions (Table 3) Further RMSEand 119868119886
values also suggested that the irrigationmodel with YEperformed slightly better than that with MYE Based on the
Applied and Environmental Soil Science 7
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
Observed2D-Fok
1D-GAKL
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 3 Comparison of observed and simulated sediment load (usingMYE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevents
Table 3 Model performance for simulating sediment loss for cropped field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
(kg)RMSE
times10minus5 (kg) 119868119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
3rd Mar-05 YE 112 115 8 055 118 8 054 119 9 045
MYE 112 117 9 055 118 9 053 119 9 044
30th Mar-05 YE 107 097 9 053 096 9 051 095 13 042
MYE 107 088 9 054 090 9 051 093 13 042
9th Apr-05 YE 102 093 4 083 099 4 078 100 6 072
MYE 102 095 4 083 100 4 073 104 75 069
16th May-05 YE 063 078 3 085 079 3 081 084 6 075
MYE 063 077 4 084 077 42 083 082 7 072
23rd May-05 YE 029 042 4 083 047 4 080 054 7 072
MYE 029 046 5 082 047 6 080 054 8 070
performance indices it is clear that the model performancein predicting sediment load was the best and the worst insimulating irrigation events of 16th May and 30th March2005 respectively For these two irrigation events the modelpredicted sediment load was compared with their observedcounterparts and the results are shown in Figures 4 and 5 forYE and MYE respectively
Both YE and MYE predicted initial increase in sedimentload well However as in case of bare furrow condition bothYE and MYE were not able to predict the decreasing trendof sediment rate with elapsed time The model performedequally well using 2D-Fok 1D-Green Ampt and KL infiltra-tion equations (Figures 4 and 5) Furthermore the irrigationmodel with YE predicted the sediment load slightly betterthan the one with the MYE (Table 3)
43 Sensitivity Analysis of Model Parameters Sensitivity ofthe model parameters in predicting sediment load wasstudied for 16th May 2005 event The effect of plusmn5 andplusmn10 changes in 119870
119903
and 119870119905
(Table 4) on the simulatedsediment load was estimated by YE andMYE considering all
infiltration functions The variation in 119870119905
did not have mucheffect on the sediment load whereas the percentage changein 119870119903
caused the sediment load change at the same rate (bywhich 119870
119903
is changed) Hence for 2D-infiltration model 119870119903
is the most sensitive parameter for estimating sediment loadfor both YE andMYE For 1D-infiltration equation the effectof change in 119870
119905
and 119870119903
on the sediment yield is the same asthe case with 2D-infiltration model The change in 119870
119905
hadvery little effect on the sediment load that resulted with KLinfiltration model The increase in119870
119903
increased the sedimentload at the same rate for both YE and MYE
5 Conclusions
Irrigation-induced erosion accounts most part of the dif-fuse agricultural pollution causing downstream impairmentand eutrophication In this study a steady state sedimenttransport model was integrated with a physically basedfurrow irrigation model which consists of three infiltrationequations (2D-Fok 1D-Green Ampt and Kostiakov-Lewis)The integrated irrigation model was evaluated for estimating
8 Applied and Environmental Soil Science
Table 4 Sensitivity analysis of erosion module parameters
Input parameter Percentage changePercentage change in sediment load
2D-Fok and Chiang 1D-Green Ampt KL infiltration functionMYE YE MYE YE MYE YE
119870119905
(kgminus12 m12 s2)
minus10 0 NA 013 NA minus024 NAminus5 0 NA 013 NA 0 NA5 013 NA 039 NA 012 NA10 013 NA 039 NA 024 NA
Figure 4 Comparison of observed and simulated sediment load (using YE) for (a) 16thMay 2005 and (b) 30thMarch 2005 irrigation events
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(a)
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(b)
Figure 5 Comparison of observed and simulated sediment load (using MYE) for (a) 16th May 2005 and (b) 30th March 2005 irrigationevent
sediment load using two sediment transport capacity equa-tions (Yalin and the modified Yalin equations) for bare andcropped field conditionsThe sediment load prediction usingthe Yalin and the modified Yalin equations was found to beidentical however the modified Yalin equation may be abetter choice as it requires less number of input parametersThe sensitivity analysis revealed that the soil erodibilitycoefficient is the most influential parameter in predicting
sediment transport in free drained furrows However theirrigation model could not adequately simulate the sedimentload in the last phase of irrigation Although this has aminor impact on the overall sediment load it will be thesubject of future model refinement The irrigation modeluses an analytical solution for zero-inertial flow equationsand this compared favourably to the full numerical hydraulicmodels [39] This paper describes the procedure for coupling
Applied and Environmental Soil Science 9
the sediment module to the zero-inertial irrigation modeland design for simulating infiltration though layered soils[37] This is one of the advantages of the integrated modelfor investigating the impact of soil layering on sedimenttransport The other advantage is the use of the model aseducational tool for studying the effect of various infiltrationand sediment capacity equations on the sediment rate Theintegrated model can also be used as a management toolto determine optimum water delivery to irrigated furrowsor borders for attaining better irrigation performance withminimum soil loss The modeling approach can also beintegrated with nutrient transport models where sedimentbound nutrient losses contribute substantially to total non-point nutrient losses from agricultural fields
Acknowledgments
Theauthors are grateful toVolkswagenFoundations StiftungGermany for providing financial support which made therealization of this work possible The technical support forthe model development by Prof G H Schmitz and Prof FLennartz is gratefully acknowledged
References
[1] Food and Agriculture Organization AQUASTAT httpwwwfaoorgnrwateraquastatwater useindexstm 2013
[2] R D Berg and D L Carter ldquoFurrow erosion and sedimentlosses on irrigated croplandrdquo Journal of Soil amp Water Conser-vation vol 35 no 6 pp 267ndash270 1980
[3] W D Kemper T J Trout M J Brown and R C RosenauldquoFurrow erosion and water and soil managementrdquo Transactionsof the American Society of Agricultural Engineers vol 28 no 5pp 1564ndash1572 1985
[4] T J Trout ldquoFurrow irrigation erosion and sedimentationon-field distributionrdquo Transactions of the American Society ofAgricultural Engineers vol 39 no 5 pp 1717ndash1723 1996
[5] L Mateos and J V Giraldez ldquoSuspended load and bed load inirrigation furrowsrdquo Catena vol 64 no 2-3 pp 232ndash246 2005
[6] D R Mailapalli N S Raghuwanshi and R Singh ldquoSedimenttransport in furrow irrigationrdquo Irrigation Science vol 27 no 6pp 449ndash456 2009
[7] P K Koluvek K K Tanji and T J Trout ldquoOverview ofsoil erosion from irrigationrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 929ndash946 1993
[8] M J Brown D L Carter G A Lehrsch and R E SojkaldquoSeasonal trends in furrow irrigation erosion in southernIdahordquo Soil Technology vol 8 no 2 pp 119ndash126 1995
[9] T J Trout ldquoSediment transport in irrigation furrowsrdquo in Pro-ceedings of the 10th International Soil ConservationOrganizationMeeting Held May 24ndash29 1999 at Purdue University and theUSDA-ARS National Soil Erosion Research Laboratory D EStott R H Mohtar and G C Steinhardt Eds pp 710ndash7162001
[10] R Fernandez-Gomez L Mateos and J V Giraldez ldquoFurrowirrigation erosion and managementrdquo Irrigation Science vol 23no 3 pp 123ndash131 2004
[11] C J Everts and D L Carter Furrow Erosion and Topsoil LossesCurrent information series no 586 College of AgricultureUniversity of Idaho Moscow Russia 1981
[12] K J Fornstrom and J Borelli ldquoDesign and management pro-cedure for minimising erosion from furrow irrigated croplandrdquoPaper 84-2595 American Society of Association Executives StJoseph Mich USA 1994
[13] R P C Morgan ldquoThe European soil erosion model an updateon its structure and research baserdquo inConserving Soil ResourcesEuropean Perspectives R J Rickson Ed pp 286ndash299 CABIntOxton Scotland UK 1995
[14] W S Merritt R A Letcher and A J Jakeman ldquoA reviewof erosion and sediment transport modelsrdquo EnvironmentalModelling and Software vol 18 no 8-9 pp 761ndash799 2003
[15] G R Foster and L D Meyer ldquoMathematical simulation ofupland erosion by fundamental erosion mechanicsrdquo Presentand Prospective Technology for Predicting Sediment Yield andSourcesUSDAARSPublicationARS-S40USDAAgriculturalResearch Service Nat Tech Information Service SpringfieldVa USA 1972
[16] M B Abbott J C Bathurst J A Cunge P E OrsquoConnell andJ Rasmussen ldquoAn introduction to the European hydrologicalsystemmdashsysteme hydrologique Europeen ldquoSHErdquo 1 historyand philosophy of a physically-based distributed modellingsystemrdquo Journal of Hydrology vol 87 no 1-2 pp 45ndash59 1986
[17] A J Jakeman and G M Hornberger ldquoHow much complexityis warranted in a rainfall-runoff modelrdquo Water ResourcesResearch vol 29 no 8 pp 2637ndash2649 1993
[18] C CWu and L DMeyer ldquoSimulating transport of nonuniformsediment along flatland furrowsrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 32 no 5 pp 1651ndash16611989
[19] T S Strelkoff A J Clemmens and B V Schmidt SRFR Version321-a Model for Simulating Surface Irrigation in Borders Basinsand Furrows USWCL USDAARS Phoenix Ariz USA 1998
[20] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[21] D L Bjorneberg and T J Trout ldquoEvaluating WEPP predictedon-field furrow erosionrdquo in Proceedings of the 10th InternationalSoil Conservation Organization (ISCO rsquo99) West Lafayette IndUSA May 1999
[22] E M Laursen ldquoThe total sediment load of streamsrdquo Journal ofHydraulics Divison vol 84 pp 1530-1ndash1530-36 1958
[23] C T Yang ldquoIncipient motion and sediment transportrdquo Journalof Hydraulics Divison vol 99 no 10 pp 1679ndash1704 1973
[24] M S Yalin ldquoAn expression for bed-load transportationrdquo Journalof Hydraulics Divison vol 89 no 3 pp 221ndash250 1963
[25] T S Strelkoff and D L Bjorneberg ldquoHydraulic modeling ofirrigation-induced furrow erosionrdquo in Proceedings of the 10thInternational Soil Conservation Organization Conference D EStott R H Mohtar and G C Steinhardt Eds Sustaining theGlobal Farm pp 699ndash705 West Lafayette Ind USA May 1999
[26] D R Mailapalli R Singh and N S Raghuwanshi ldquoPhysicallybased model for simulating flow in furrow irrigation I modeldevelopmentrdquo Journal of Irrigation and Drainage Engineeringvol 135 no 6 pp 739ndash746 2009
[27] Y S Fok and S H Chiang ldquo2-D infiltration equations for fur-row irrigationrdquo Journal of Irrigation and Drainage Engineeringvol 110 no 2 pp 208ndash217 1984
[28] M D Rao N S Raghuwanshi and R Singh ldquoDevelopmentof a physically based 1D-infiltration model for irrigated soilsrdquoAgricultural Water Management vol 85 no 1-2 pp 165ndash1742006
10 Applied and Environmental Soil Science
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
Figure 2 Comparison of observed and simulated sediment load (using YE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevent
120591119888
and 119870119903
) for estimating sediment load for both bare andcropped field conditions using the three infiltration modelsOf these simulations the best and the worst model per-formances were selected for both bare and cropped furrowconditions and model performance was studied graphi-cally It was assumed that infiltration is the key componentof irrigation management and was given first priority forselecting the best and worst simulations followed by run-offrate sediment yield waterfront advance and recession timesSensitivity analysis was carried out to study the effect of plusmn5and plusmn10 changes in the values of119870
119903
and119870119905
on the sedimentload estimated by the YE and MYE
The performance of the irrigation model for predictingsediment load was evaluated by estimating root mean squareerror (RMSE) and index of agreement (119868
119886
)Consider
RMSE = radicsum119873
119894=1
[119872(119894) minus 119864(119894)]2
119873
119868119886
= 10 minussum119873
119894=1
(119872 (119894) minus 119864 (119894))2
sum119873
119894=1
(10038161003816100381610038161003816119864 (119894) minus 119872
10038161003816100381610038161003816+10038161003816100381610038161003816119872 (119894) minus 119872
10038161003816100381610038161003816)2
(23)
where119872(119894) is the measured value 119864(119894) is the estimated value119873 is the number of data points and 119872 is the mean of theobserved values
4 Results and Discussion
The visual observation of the trends between observed andsimulated sediment loads (not shown here) by 2D-Fok 1D-Green Ampt and KL infiltration equations depicted that thesediment load predictions were not good with the baselinevalues of 120591
119888
and119870119903
Hence 120591119888
was assumed as zero and119870119903
and119870119905
were considered as calibration parameters for simulatingsediment loadDuring the calibration process the base valuesof 119870119903
and 119870119905
were tuned by increasing or decreasing theirbase values For each runmodel predicted sediment loadwascompared with its observed counterpart using the estimatedperformance indices Finally the values of 119870
119903
and 119870119905
were
found to be 50 times 10minus6 smminus1 and 001 for bare and 10 times
10minus5 smminus1 and 002 for cropped field conditions respectivelyTable 1 presents the input data used for infiltration anderosion parameters for bare and cropped field conditions
41 Sediment Transport in Bare Furrow Field The modelperformance was inconsistent in predicting the sedimentload using all three infiltration equations Furthermore theYE performed slightly better than the MYE in most of thecasesThe 2D-Fok infiltration function resulted in low RMSEand high 119868
119886
values as compared to those obtained using1D-Green Ampt and KL infiltration models (Table 2) Thusthe irrigation model performed well in simulating sedimentload using the 2D-Fok infiltration function followed by 1D-Green Ampt and KL-infiltration functions The performanceindices (Table 2) suggested that the model performance forsediment load in bare furrow field was the best and the worstfor irrigation events of 6th Feb 2004 and 17th Feb 2004respectively Therefore these events were selected for furtheranalysis Figures 2 and 3 show comparison between observedand simulated outputs for the best (6th February 2004) andtheworst (17th February 2004) irrigation events using YE andMYE respectively
The irrigation model with YE and MYE predicted initialincrease in sediment load well However both YE and MYEwere not able to predict the decreasing trend of sedimentrate with elapsed time The possible reason could be that thesediment load estimation takes the run-off rate into accountwhich increases with elapsed time Figures 2 and 3 also showthat the model performed equally well using 2D-Fok 1D-Green Ampt and KL infiltration models However sedimentload predictions using the YE were slightly better than theMYE
42 Sediment Transport in Cropped Furrow Field 2D-Fokinfiltration function resulted in lower RMSE values andhigher 119868
119886
values compared to those obtained using 1D-GreenAmpt and KL infiltration functions (Table 3) Further RMSEand 119868119886
values also suggested that the irrigationmodel with YEperformed slightly better than that with MYE Based on the
Applied and Environmental Soil Science 7
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Observed2D-Fok
1D-GAKL
Sedi
men
t loa
d (k
gs)
times10
minus5
(a)
Observed2D-Fok
1D-GAKL
0
2
4
6
8
10
12
0 30 60 90 120 150Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus5
(b)
Figure 3 Comparison of observed and simulated sediment load (usingMYE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevents
Table 3 Model performance for simulating sediment loss for cropped field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
(kg)RMSE
times10minus5 (kg) 119868119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
3rd Mar-05 YE 112 115 8 055 118 8 054 119 9 045
MYE 112 117 9 055 118 9 053 119 9 044
30th Mar-05 YE 107 097 9 053 096 9 051 095 13 042
MYE 107 088 9 054 090 9 051 093 13 042
9th Apr-05 YE 102 093 4 083 099 4 078 100 6 072
MYE 102 095 4 083 100 4 073 104 75 069
16th May-05 YE 063 078 3 085 079 3 081 084 6 075
MYE 063 077 4 084 077 42 083 082 7 072
23rd May-05 YE 029 042 4 083 047 4 080 054 7 072
MYE 029 046 5 082 047 6 080 054 8 070
performance indices it is clear that the model performancein predicting sediment load was the best and the worst insimulating irrigation events of 16th May and 30th March2005 respectively For these two irrigation events the modelpredicted sediment load was compared with their observedcounterparts and the results are shown in Figures 4 and 5 forYE and MYE respectively
Both YE and MYE predicted initial increase in sedimentload well However as in case of bare furrow condition bothYE and MYE were not able to predict the decreasing trendof sediment rate with elapsed time The model performedequally well using 2D-Fok 1D-Green Ampt and KL infiltra-tion equations (Figures 4 and 5) Furthermore the irrigationmodel with YE predicted the sediment load slightly betterthan the one with the MYE (Table 3)
43 Sensitivity Analysis of Model Parameters Sensitivity ofthe model parameters in predicting sediment load wasstudied for 16th May 2005 event The effect of plusmn5 andplusmn10 changes in 119870
119903
and 119870119905
(Table 4) on the simulatedsediment load was estimated by YE andMYE considering all
infiltration functions The variation in 119870119905
did not have mucheffect on the sediment load whereas the percentage changein 119870119903
caused the sediment load change at the same rate (bywhich 119870
119903
is changed) Hence for 2D-infiltration model 119870119903
is the most sensitive parameter for estimating sediment loadfor both YE andMYE For 1D-infiltration equation the effectof change in 119870
119905
and 119870119903
on the sediment yield is the same asthe case with 2D-infiltration model The change in 119870
119905
hadvery little effect on the sediment load that resulted with KLinfiltration model The increase in119870
119903
increased the sedimentload at the same rate for both YE and MYE
5 Conclusions
Irrigation-induced erosion accounts most part of the dif-fuse agricultural pollution causing downstream impairmentand eutrophication In this study a steady state sedimenttransport model was integrated with a physically basedfurrow irrigation model which consists of three infiltrationequations (2D-Fok 1D-Green Ampt and Kostiakov-Lewis)The integrated irrigation model was evaluated for estimating
8 Applied and Environmental Soil Science
Table 4 Sensitivity analysis of erosion module parameters
Input parameter Percentage changePercentage change in sediment load
2D-Fok and Chiang 1D-Green Ampt KL infiltration functionMYE YE MYE YE MYE YE
119870119905
(kgminus12 m12 s2)
minus10 0 NA 013 NA minus024 NAminus5 0 NA 013 NA 0 NA5 013 NA 039 NA 012 NA10 013 NA 039 NA 024 NA
Figure 4 Comparison of observed and simulated sediment load (using YE) for (a) 16thMay 2005 and (b) 30thMarch 2005 irrigation events
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(a)
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(b)
Figure 5 Comparison of observed and simulated sediment load (using MYE) for (a) 16th May 2005 and (b) 30th March 2005 irrigationevent
sediment load using two sediment transport capacity equa-tions (Yalin and the modified Yalin equations) for bare andcropped field conditionsThe sediment load prediction usingthe Yalin and the modified Yalin equations was found to beidentical however the modified Yalin equation may be abetter choice as it requires less number of input parametersThe sensitivity analysis revealed that the soil erodibilitycoefficient is the most influential parameter in predicting
sediment transport in free drained furrows However theirrigation model could not adequately simulate the sedimentload in the last phase of irrigation Although this has aminor impact on the overall sediment load it will be thesubject of future model refinement The irrigation modeluses an analytical solution for zero-inertial flow equationsand this compared favourably to the full numerical hydraulicmodels [39] This paper describes the procedure for coupling
Applied and Environmental Soil Science 9
the sediment module to the zero-inertial irrigation modeland design for simulating infiltration though layered soils[37] This is one of the advantages of the integrated modelfor investigating the impact of soil layering on sedimenttransport The other advantage is the use of the model aseducational tool for studying the effect of various infiltrationand sediment capacity equations on the sediment rate Theintegrated model can also be used as a management toolto determine optimum water delivery to irrigated furrowsor borders for attaining better irrigation performance withminimum soil loss The modeling approach can also beintegrated with nutrient transport models where sedimentbound nutrient losses contribute substantially to total non-point nutrient losses from agricultural fields
Acknowledgments
Theauthors are grateful toVolkswagenFoundations StiftungGermany for providing financial support which made therealization of this work possible The technical support forthe model development by Prof G H Schmitz and Prof FLennartz is gratefully acknowledged
References
[1] Food and Agriculture Organization AQUASTAT httpwwwfaoorgnrwateraquastatwater useindexstm 2013
[2] R D Berg and D L Carter ldquoFurrow erosion and sedimentlosses on irrigated croplandrdquo Journal of Soil amp Water Conser-vation vol 35 no 6 pp 267ndash270 1980
[3] W D Kemper T J Trout M J Brown and R C RosenauldquoFurrow erosion and water and soil managementrdquo Transactionsof the American Society of Agricultural Engineers vol 28 no 5pp 1564ndash1572 1985
[4] T J Trout ldquoFurrow irrigation erosion and sedimentationon-field distributionrdquo Transactions of the American Society ofAgricultural Engineers vol 39 no 5 pp 1717ndash1723 1996
[5] L Mateos and J V Giraldez ldquoSuspended load and bed load inirrigation furrowsrdquo Catena vol 64 no 2-3 pp 232ndash246 2005
[6] D R Mailapalli N S Raghuwanshi and R Singh ldquoSedimenttransport in furrow irrigationrdquo Irrigation Science vol 27 no 6pp 449ndash456 2009
[7] P K Koluvek K K Tanji and T J Trout ldquoOverview ofsoil erosion from irrigationrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 929ndash946 1993
[8] M J Brown D L Carter G A Lehrsch and R E SojkaldquoSeasonal trends in furrow irrigation erosion in southernIdahordquo Soil Technology vol 8 no 2 pp 119ndash126 1995
[9] T J Trout ldquoSediment transport in irrigation furrowsrdquo in Pro-ceedings of the 10th International Soil ConservationOrganizationMeeting Held May 24ndash29 1999 at Purdue University and theUSDA-ARS National Soil Erosion Research Laboratory D EStott R H Mohtar and G C Steinhardt Eds pp 710ndash7162001
[10] R Fernandez-Gomez L Mateos and J V Giraldez ldquoFurrowirrigation erosion and managementrdquo Irrigation Science vol 23no 3 pp 123ndash131 2004
[11] C J Everts and D L Carter Furrow Erosion and Topsoil LossesCurrent information series no 586 College of AgricultureUniversity of Idaho Moscow Russia 1981
[12] K J Fornstrom and J Borelli ldquoDesign and management pro-cedure for minimising erosion from furrow irrigated croplandrdquoPaper 84-2595 American Society of Association Executives StJoseph Mich USA 1994
[13] R P C Morgan ldquoThe European soil erosion model an updateon its structure and research baserdquo inConserving Soil ResourcesEuropean Perspectives R J Rickson Ed pp 286ndash299 CABIntOxton Scotland UK 1995
[14] W S Merritt R A Letcher and A J Jakeman ldquoA reviewof erosion and sediment transport modelsrdquo EnvironmentalModelling and Software vol 18 no 8-9 pp 761ndash799 2003
[15] G R Foster and L D Meyer ldquoMathematical simulation ofupland erosion by fundamental erosion mechanicsrdquo Presentand Prospective Technology for Predicting Sediment Yield andSourcesUSDAARSPublicationARS-S40USDAAgriculturalResearch Service Nat Tech Information Service SpringfieldVa USA 1972
[16] M B Abbott J C Bathurst J A Cunge P E OrsquoConnell andJ Rasmussen ldquoAn introduction to the European hydrologicalsystemmdashsysteme hydrologique Europeen ldquoSHErdquo 1 historyand philosophy of a physically-based distributed modellingsystemrdquo Journal of Hydrology vol 87 no 1-2 pp 45ndash59 1986
[17] A J Jakeman and G M Hornberger ldquoHow much complexityis warranted in a rainfall-runoff modelrdquo Water ResourcesResearch vol 29 no 8 pp 2637ndash2649 1993
[18] C CWu and L DMeyer ldquoSimulating transport of nonuniformsediment along flatland furrowsrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 32 no 5 pp 1651ndash16611989
[19] T S Strelkoff A J Clemmens and B V Schmidt SRFR Version321-a Model for Simulating Surface Irrigation in Borders Basinsand Furrows USWCL USDAARS Phoenix Ariz USA 1998
[20] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[21] D L Bjorneberg and T J Trout ldquoEvaluating WEPP predictedon-field furrow erosionrdquo in Proceedings of the 10th InternationalSoil Conservation Organization (ISCO rsquo99) West Lafayette IndUSA May 1999
[22] E M Laursen ldquoThe total sediment load of streamsrdquo Journal ofHydraulics Divison vol 84 pp 1530-1ndash1530-36 1958
[23] C T Yang ldquoIncipient motion and sediment transportrdquo Journalof Hydraulics Divison vol 99 no 10 pp 1679ndash1704 1973
[24] M S Yalin ldquoAn expression for bed-load transportationrdquo Journalof Hydraulics Divison vol 89 no 3 pp 221ndash250 1963
[25] T S Strelkoff and D L Bjorneberg ldquoHydraulic modeling ofirrigation-induced furrow erosionrdquo in Proceedings of the 10thInternational Soil Conservation Organization Conference D EStott R H Mohtar and G C Steinhardt Eds Sustaining theGlobal Farm pp 699ndash705 West Lafayette Ind USA May 1999
[26] D R Mailapalli R Singh and N S Raghuwanshi ldquoPhysicallybased model for simulating flow in furrow irrigation I modeldevelopmentrdquo Journal of Irrigation and Drainage Engineeringvol 135 no 6 pp 739ndash746 2009
[27] Y S Fok and S H Chiang ldquo2-D infiltration equations for fur-row irrigationrdquo Journal of Irrigation and Drainage Engineeringvol 110 no 2 pp 208ndash217 1984
[28] M D Rao N S Raghuwanshi and R Singh ldquoDevelopmentof a physically based 1D-infiltration model for irrigated soilsrdquoAgricultural Water Management vol 85 no 1-2 pp 165ndash1742006
10 Applied and Environmental Soil Science
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
Figure 3 Comparison of observed and simulated sediment load (usingMYE) for (a) 6th February 2004 and (b) 17th February 2004 irrigationevents
Table 3 Model performance for simulating sediment loss for cropped field
Date ofirrigation
Transportcapacity equation Observed (kg)
2D-Fok and Chiang 1D-Green Ampt KL-infiltration functionSimulated
(kg)RMSE
times10minus5 (kg) 119868119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
Simulated(kg)
RMSEtimes10minus5 (kg) 119868
119886
3rd Mar-05 YE 112 115 8 055 118 8 054 119 9 045
MYE 112 117 9 055 118 9 053 119 9 044
30th Mar-05 YE 107 097 9 053 096 9 051 095 13 042
MYE 107 088 9 054 090 9 051 093 13 042
9th Apr-05 YE 102 093 4 083 099 4 078 100 6 072
MYE 102 095 4 083 100 4 073 104 75 069
16th May-05 YE 063 078 3 085 079 3 081 084 6 075
MYE 063 077 4 084 077 42 083 082 7 072
23rd May-05 YE 029 042 4 083 047 4 080 054 7 072
MYE 029 046 5 082 047 6 080 054 8 070
performance indices it is clear that the model performancein predicting sediment load was the best and the worst insimulating irrigation events of 16th May and 30th March2005 respectively For these two irrigation events the modelpredicted sediment load was compared with their observedcounterparts and the results are shown in Figures 4 and 5 forYE and MYE respectively
Both YE and MYE predicted initial increase in sedimentload well However as in case of bare furrow condition bothYE and MYE were not able to predict the decreasing trendof sediment rate with elapsed time The model performedequally well using 2D-Fok 1D-Green Ampt and KL infiltra-tion equations (Figures 4 and 5) Furthermore the irrigationmodel with YE predicted the sediment load slightly betterthan the one with the MYE (Table 3)
43 Sensitivity Analysis of Model Parameters Sensitivity ofthe model parameters in predicting sediment load wasstudied for 16th May 2005 event The effect of plusmn5 andplusmn10 changes in 119870
119903
and 119870119905
(Table 4) on the simulatedsediment load was estimated by YE andMYE considering all
infiltration functions The variation in 119870119905
did not have mucheffect on the sediment load whereas the percentage changein 119870119903
caused the sediment load change at the same rate (bywhich 119870
119903
is changed) Hence for 2D-infiltration model 119870119903
is the most sensitive parameter for estimating sediment loadfor both YE andMYE For 1D-infiltration equation the effectof change in 119870
119905
and 119870119903
on the sediment yield is the same asthe case with 2D-infiltration model The change in 119870
119905
hadvery little effect on the sediment load that resulted with KLinfiltration model The increase in119870
119903
increased the sedimentload at the same rate for both YE and MYE
5 Conclusions
Irrigation-induced erosion accounts most part of the dif-fuse agricultural pollution causing downstream impairmentand eutrophication In this study a steady state sedimenttransport model was integrated with a physically basedfurrow irrigation model which consists of three infiltrationequations (2D-Fok 1D-Green Ampt and Kostiakov-Lewis)The integrated irrigation model was evaluated for estimating
8 Applied and Environmental Soil Science
Table 4 Sensitivity analysis of erosion module parameters
Input parameter Percentage changePercentage change in sediment load
2D-Fok and Chiang 1D-Green Ampt KL infiltration functionMYE YE MYE YE MYE YE
119870119905
(kgminus12 m12 s2)
minus10 0 NA 013 NA minus024 NAminus5 0 NA 013 NA 0 NA5 013 NA 039 NA 012 NA10 013 NA 039 NA 024 NA
Figure 4 Comparison of observed and simulated sediment load (using YE) for (a) 16thMay 2005 and (b) 30thMarch 2005 irrigation events
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(a)
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(b)
Figure 5 Comparison of observed and simulated sediment load (using MYE) for (a) 16th May 2005 and (b) 30th March 2005 irrigationevent
sediment load using two sediment transport capacity equa-tions (Yalin and the modified Yalin equations) for bare andcropped field conditionsThe sediment load prediction usingthe Yalin and the modified Yalin equations was found to beidentical however the modified Yalin equation may be abetter choice as it requires less number of input parametersThe sensitivity analysis revealed that the soil erodibilitycoefficient is the most influential parameter in predicting
sediment transport in free drained furrows However theirrigation model could not adequately simulate the sedimentload in the last phase of irrigation Although this has aminor impact on the overall sediment load it will be thesubject of future model refinement The irrigation modeluses an analytical solution for zero-inertial flow equationsand this compared favourably to the full numerical hydraulicmodels [39] This paper describes the procedure for coupling
Applied and Environmental Soil Science 9
the sediment module to the zero-inertial irrigation modeland design for simulating infiltration though layered soils[37] This is one of the advantages of the integrated modelfor investigating the impact of soil layering on sedimenttransport The other advantage is the use of the model aseducational tool for studying the effect of various infiltrationand sediment capacity equations on the sediment rate Theintegrated model can also be used as a management toolto determine optimum water delivery to irrigated furrowsor borders for attaining better irrigation performance withminimum soil loss The modeling approach can also beintegrated with nutrient transport models where sedimentbound nutrient losses contribute substantially to total non-point nutrient losses from agricultural fields
Acknowledgments
Theauthors are grateful toVolkswagenFoundations StiftungGermany for providing financial support which made therealization of this work possible The technical support forthe model development by Prof G H Schmitz and Prof FLennartz is gratefully acknowledged
References
[1] Food and Agriculture Organization AQUASTAT httpwwwfaoorgnrwateraquastatwater useindexstm 2013
[2] R D Berg and D L Carter ldquoFurrow erosion and sedimentlosses on irrigated croplandrdquo Journal of Soil amp Water Conser-vation vol 35 no 6 pp 267ndash270 1980
[3] W D Kemper T J Trout M J Brown and R C RosenauldquoFurrow erosion and water and soil managementrdquo Transactionsof the American Society of Agricultural Engineers vol 28 no 5pp 1564ndash1572 1985
[4] T J Trout ldquoFurrow irrigation erosion and sedimentationon-field distributionrdquo Transactions of the American Society ofAgricultural Engineers vol 39 no 5 pp 1717ndash1723 1996
[5] L Mateos and J V Giraldez ldquoSuspended load and bed load inirrigation furrowsrdquo Catena vol 64 no 2-3 pp 232ndash246 2005
[6] D R Mailapalli N S Raghuwanshi and R Singh ldquoSedimenttransport in furrow irrigationrdquo Irrigation Science vol 27 no 6pp 449ndash456 2009
[7] P K Koluvek K K Tanji and T J Trout ldquoOverview ofsoil erosion from irrigationrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 929ndash946 1993
[8] M J Brown D L Carter G A Lehrsch and R E SojkaldquoSeasonal trends in furrow irrigation erosion in southernIdahordquo Soil Technology vol 8 no 2 pp 119ndash126 1995
[9] T J Trout ldquoSediment transport in irrigation furrowsrdquo in Pro-ceedings of the 10th International Soil ConservationOrganizationMeeting Held May 24ndash29 1999 at Purdue University and theUSDA-ARS National Soil Erosion Research Laboratory D EStott R H Mohtar and G C Steinhardt Eds pp 710ndash7162001
[10] R Fernandez-Gomez L Mateos and J V Giraldez ldquoFurrowirrigation erosion and managementrdquo Irrigation Science vol 23no 3 pp 123ndash131 2004
[11] C J Everts and D L Carter Furrow Erosion and Topsoil LossesCurrent information series no 586 College of AgricultureUniversity of Idaho Moscow Russia 1981
[12] K J Fornstrom and J Borelli ldquoDesign and management pro-cedure for minimising erosion from furrow irrigated croplandrdquoPaper 84-2595 American Society of Association Executives StJoseph Mich USA 1994
[13] R P C Morgan ldquoThe European soil erosion model an updateon its structure and research baserdquo inConserving Soil ResourcesEuropean Perspectives R J Rickson Ed pp 286ndash299 CABIntOxton Scotland UK 1995
[14] W S Merritt R A Letcher and A J Jakeman ldquoA reviewof erosion and sediment transport modelsrdquo EnvironmentalModelling and Software vol 18 no 8-9 pp 761ndash799 2003
[15] G R Foster and L D Meyer ldquoMathematical simulation ofupland erosion by fundamental erosion mechanicsrdquo Presentand Prospective Technology for Predicting Sediment Yield andSourcesUSDAARSPublicationARS-S40USDAAgriculturalResearch Service Nat Tech Information Service SpringfieldVa USA 1972
[16] M B Abbott J C Bathurst J A Cunge P E OrsquoConnell andJ Rasmussen ldquoAn introduction to the European hydrologicalsystemmdashsysteme hydrologique Europeen ldquoSHErdquo 1 historyand philosophy of a physically-based distributed modellingsystemrdquo Journal of Hydrology vol 87 no 1-2 pp 45ndash59 1986
[17] A J Jakeman and G M Hornberger ldquoHow much complexityis warranted in a rainfall-runoff modelrdquo Water ResourcesResearch vol 29 no 8 pp 2637ndash2649 1993
[18] C CWu and L DMeyer ldquoSimulating transport of nonuniformsediment along flatland furrowsrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 32 no 5 pp 1651ndash16611989
[19] T S Strelkoff A J Clemmens and B V Schmidt SRFR Version321-a Model for Simulating Surface Irrigation in Borders Basinsand Furrows USWCL USDAARS Phoenix Ariz USA 1998
[20] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[21] D L Bjorneberg and T J Trout ldquoEvaluating WEPP predictedon-field furrow erosionrdquo in Proceedings of the 10th InternationalSoil Conservation Organization (ISCO rsquo99) West Lafayette IndUSA May 1999
[22] E M Laursen ldquoThe total sediment load of streamsrdquo Journal ofHydraulics Divison vol 84 pp 1530-1ndash1530-36 1958
[23] C T Yang ldquoIncipient motion and sediment transportrdquo Journalof Hydraulics Divison vol 99 no 10 pp 1679ndash1704 1973
[24] M S Yalin ldquoAn expression for bed-load transportationrdquo Journalof Hydraulics Divison vol 89 no 3 pp 221ndash250 1963
[25] T S Strelkoff and D L Bjorneberg ldquoHydraulic modeling ofirrigation-induced furrow erosionrdquo in Proceedings of the 10thInternational Soil Conservation Organization Conference D EStott R H Mohtar and G C Steinhardt Eds Sustaining theGlobal Farm pp 699ndash705 West Lafayette Ind USA May 1999
[26] D R Mailapalli R Singh and N S Raghuwanshi ldquoPhysicallybased model for simulating flow in furrow irrigation I modeldevelopmentrdquo Journal of Irrigation and Drainage Engineeringvol 135 no 6 pp 739ndash746 2009
[27] Y S Fok and S H Chiang ldquo2-D infiltration equations for fur-row irrigationrdquo Journal of Irrigation and Drainage Engineeringvol 110 no 2 pp 208ndash217 1984
[28] M D Rao N S Raghuwanshi and R Singh ldquoDevelopmentof a physically based 1D-infiltration model for irrigated soilsrdquoAgricultural Water Management vol 85 no 1-2 pp 165ndash1742006
10 Applied and Environmental Soil Science
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
Figure 4 Comparison of observed and simulated sediment load (using YE) for (a) 16thMay 2005 and (b) 30thMarch 2005 irrigation events
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(a)
005
115
225
335
Observed2D-Fok
1D-GAKL
0 20 40 60 80Time (min)
Sedi
men
t loa
d (k
gs)
times10
minus4
(b)
Figure 5 Comparison of observed and simulated sediment load (using MYE) for (a) 16th May 2005 and (b) 30th March 2005 irrigationevent
sediment load using two sediment transport capacity equa-tions (Yalin and the modified Yalin equations) for bare andcropped field conditionsThe sediment load prediction usingthe Yalin and the modified Yalin equations was found to beidentical however the modified Yalin equation may be abetter choice as it requires less number of input parametersThe sensitivity analysis revealed that the soil erodibilitycoefficient is the most influential parameter in predicting
sediment transport in free drained furrows However theirrigation model could not adequately simulate the sedimentload in the last phase of irrigation Although this has aminor impact on the overall sediment load it will be thesubject of future model refinement The irrigation modeluses an analytical solution for zero-inertial flow equationsand this compared favourably to the full numerical hydraulicmodels [39] This paper describes the procedure for coupling
Applied and Environmental Soil Science 9
the sediment module to the zero-inertial irrigation modeland design for simulating infiltration though layered soils[37] This is one of the advantages of the integrated modelfor investigating the impact of soil layering on sedimenttransport The other advantage is the use of the model aseducational tool for studying the effect of various infiltrationand sediment capacity equations on the sediment rate Theintegrated model can also be used as a management toolto determine optimum water delivery to irrigated furrowsor borders for attaining better irrigation performance withminimum soil loss The modeling approach can also beintegrated with nutrient transport models where sedimentbound nutrient losses contribute substantially to total non-point nutrient losses from agricultural fields
Acknowledgments
Theauthors are grateful toVolkswagenFoundations StiftungGermany for providing financial support which made therealization of this work possible The technical support forthe model development by Prof G H Schmitz and Prof FLennartz is gratefully acknowledged
References
[1] Food and Agriculture Organization AQUASTAT httpwwwfaoorgnrwateraquastatwater useindexstm 2013
[2] R D Berg and D L Carter ldquoFurrow erosion and sedimentlosses on irrigated croplandrdquo Journal of Soil amp Water Conser-vation vol 35 no 6 pp 267ndash270 1980
[3] W D Kemper T J Trout M J Brown and R C RosenauldquoFurrow erosion and water and soil managementrdquo Transactionsof the American Society of Agricultural Engineers vol 28 no 5pp 1564ndash1572 1985
[4] T J Trout ldquoFurrow irrigation erosion and sedimentationon-field distributionrdquo Transactions of the American Society ofAgricultural Engineers vol 39 no 5 pp 1717ndash1723 1996
[5] L Mateos and J V Giraldez ldquoSuspended load and bed load inirrigation furrowsrdquo Catena vol 64 no 2-3 pp 232ndash246 2005
[6] D R Mailapalli N S Raghuwanshi and R Singh ldquoSedimenttransport in furrow irrigationrdquo Irrigation Science vol 27 no 6pp 449ndash456 2009
[7] P K Koluvek K K Tanji and T J Trout ldquoOverview ofsoil erosion from irrigationrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 929ndash946 1993
[8] M J Brown D L Carter G A Lehrsch and R E SojkaldquoSeasonal trends in furrow irrigation erosion in southernIdahordquo Soil Technology vol 8 no 2 pp 119ndash126 1995
[9] T J Trout ldquoSediment transport in irrigation furrowsrdquo in Pro-ceedings of the 10th International Soil ConservationOrganizationMeeting Held May 24ndash29 1999 at Purdue University and theUSDA-ARS National Soil Erosion Research Laboratory D EStott R H Mohtar and G C Steinhardt Eds pp 710ndash7162001
[10] R Fernandez-Gomez L Mateos and J V Giraldez ldquoFurrowirrigation erosion and managementrdquo Irrigation Science vol 23no 3 pp 123ndash131 2004
[11] C J Everts and D L Carter Furrow Erosion and Topsoil LossesCurrent information series no 586 College of AgricultureUniversity of Idaho Moscow Russia 1981
[12] K J Fornstrom and J Borelli ldquoDesign and management pro-cedure for minimising erosion from furrow irrigated croplandrdquoPaper 84-2595 American Society of Association Executives StJoseph Mich USA 1994
[13] R P C Morgan ldquoThe European soil erosion model an updateon its structure and research baserdquo inConserving Soil ResourcesEuropean Perspectives R J Rickson Ed pp 286ndash299 CABIntOxton Scotland UK 1995
[14] W S Merritt R A Letcher and A J Jakeman ldquoA reviewof erosion and sediment transport modelsrdquo EnvironmentalModelling and Software vol 18 no 8-9 pp 761ndash799 2003
[15] G R Foster and L D Meyer ldquoMathematical simulation ofupland erosion by fundamental erosion mechanicsrdquo Presentand Prospective Technology for Predicting Sediment Yield andSourcesUSDAARSPublicationARS-S40USDAAgriculturalResearch Service Nat Tech Information Service SpringfieldVa USA 1972
[16] M B Abbott J C Bathurst J A Cunge P E OrsquoConnell andJ Rasmussen ldquoAn introduction to the European hydrologicalsystemmdashsysteme hydrologique Europeen ldquoSHErdquo 1 historyand philosophy of a physically-based distributed modellingsystemrdquo Journal of Hydrology vol 87 no 1-2 pp 45ndash59 1986
[17] A J Jakeman and G M Hornberger ldquoHow much complexityis warranted in a rainfall-runoff modelrdquo Water ResourcesResearch vol 29 no 8 pp 2637ndash2649 1993
[18] C CWu and L DMeyer ldquoSimulating transport of nonuniformsediment along flatland furrowsrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 32 no 5 pp 1651ndash16611989
[19] T S Strelkoff A J Clemmens and B V Schmidt SRFR Version321-a Model for Simulating Surface Irrigation in Borders Basinsand Furrows USWCL USDAARS Phoenix Ariz USA 1998
[20] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[21] D L Bjorneberg and T J Trout ldquoEvaluating WEPP predictedon-field furrow erosionrdquo in Proceedings of the 10th InternationalSoil Conservation Organization (ISCO rsquo99) West Lafayette IndUSA May 1999
[22] E M Laursen ldquoThe total sediment load of streamsrdquo Journal ofHydraulics Divison vol 84 pp 1530-1ndash1530-36 1958
[23] C T Yang ldquoIncipient motion and sediment transportrdquo Journalof Hydraulics Divison vol 99 no 10 pp 1679ndash1704 1973
[24] M S Yalin ldquoAn expression for bed-load transportationrdquo Journalof Hydraulics Divison vol 89 no 3 pp 221ndash250 1963
[25] T S Strelkoff and D L Bjorneberg ldquoHydraulic modeling ofirrigation-induced furrow erosionrdquo in Proceedings of the 10thInternational Soil Conservation Organization Conference D EStott R H Mohtar and G C Steinhardt Eds Sustaining theGlobal Farm pp 699ndash705 West Lafayette Ind USA May 1999
[26] D R Mailapalli R Singh and N S Raghuwanshi ldquoPhysicallybased model for simulating flow in furrow irrigation I modeldevelopmentrdquo Journal of Irrigation and Drainage Engineeringvol 135 no 6 pp 739ndash746 2009
[27] Y S Fok and S H Chiang ldquo2-D infiltration equations for fur-row irrigationrdquo Journal of Irrigation and Drainage Engineeringvol 110 no 2 pp 208ndash217 1984
[28] M D Rao N S Raghuwanshi and R Singh ldquoDevelopmentof a physically based 1D-infiltration model for irrigated soilsrdquoAgricultural Water Management vol 85 no 1-2 pp 165ndash1742006
10 Applied and Environmental Soil Science
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
the sediment module to the zero-inertial irrigation modeland design for simulating infiltration though layered soils[37] This is one of the advantages of the integrated modelfor investigating the impact of soil layering on sedimenttransport The other advantage is the use of the model aseducational tool for studying the effect of various infiltrationand sediment capacity equations on the sediment rate Theintegrated model can also be used as a management toolto determine optimum water delivery to irrigated furrowsor borders for attaining better irrigation performance withminimum soil loss The modeling approach can also beintegrated with nutrient transport models where sedimentbound nutrient losses contribute substantially to total non-point nutrient losses from agricultural fields
Acknowledgments
Theauthors are grateful toVolkswagenFoundations StiftungGermany for providing financial support which made therealization of this work possible The technical support forthe model development by Prof G H Schmitz and Prof FLennartz is gratefully acknowledged
References
[1] Food and Agriculture Organization AQUASTAT httpwwwfaoorgnrwateraquastatwater useindexstm 2013
[2] R D Berg and D L Carter ldquoFurrow erosion and sedimentlosses on irrigated croplandrdquo Journal of Soil amp Water Conser-vation vol 35 no 6 pp 267ndash270 1980
[3] W D Kemper T J Trout M J Brown and R C RosenauldquoFurrow erosion and water and soil managementrdquo Transactionsof the American Society of Agricultural Engineers vol 28 no 5pp 1564ndash1572 1985
[4] T J Trout ldquoFurrow irrigation erosion and sedimentationon-field distributionrdquo Transactions of the American Society ofAgricultural Engineers vol 39 no 5 pp 1717ndash1723 1996
[5] L Mateos and J V Giraldez ldquoSuspended load and bed load inirrigation furrowsrdquo Catena vol 64 no 2-3 pp 232ndash246 2005
[6] D R Mailapalli N S Raghuwanshi and R Singh ldquoSedimenttransport in furrow irrigationrdquo Irrigation Science vol 27 no 6pp 449ndash456 2009
[7] P K Koluvek K K Tanji and T J Trout ldquoOverview ofsoil erosion from irrigationrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 929ndash946 1993
[8] M J Brown D L Carter G A Lehrsch and R E SojkaldquoSeasonal trends in furrow irrigation erosion in southernIdahordquo Soil Technology vol 8 no 2 pp 119ndash126 1995
[9] T J Trout ldquoSediment transport in irrigation furrowsrdquo in Pro-ceedings of the 10th International Soil ConservationOrganizationMeeting Held May 24ndash29 1999 at Purdue University and theUSDA-ARS National Soil Erosion Research Laboratory D EStott R H Mohtar and G C Steinhardt Eds pp 710ndash7162001
[10] R Fernandez-Gomez L Mateos and J V Giraldez ldquoFurrowirrigation erosion and managementrdquo Irrigation Science vol 23no 3 pp 123ndash131 2004
[11] C J Everts and D L Carter Furrow Erosion and Topsoil LossesCurrent information series no 586 College of AgricultureUniversity of Idaho Moscow Russia 1981
[12] K J Fornstrom and J Borelli ldquoDesign and management pro-cedure for minimising erosion from furrow irrigated croplandrdquoPaper 84-2595 American Society of Association Executives StJoseph Mich USA 1994
[13] R P C Morgan ldquoThe European soil erosion model an updateon its structure and research baserdquo inConserving Soil ResourcesEuropean Perspectives R J Rickson Ed pp 286ndash299 CABIntOxton Scotland UK 1995
[14] W S Merritt R A Letcher and A J Jakeman ldquoA reviewof erosion and sediment transport modelsrdquo EnvironmentalModelling and Software vol 18 no 8-9 pp 761ndash799 2003
[15] G R Foster and L D Meyer ldquoMathematical simulation ofupland erosion by fundamental erosion mechanicsrdquo Presentand Prospective Technology for Predicting Sediment Yield andSourcesUSDAARSPublicationARS-S40USDAAgriculturalResearch Service Nat Tech Information Service SpringfieldVa USA 1972
[16] M B Abbott J C Bathurst J A Cunge P E OrsquoConnell andJ Rasmussen ldquoAn introduction to the European hydrologicalsystemmdashsysteme hydrologique Europeen ldquoSHErdquo 1 historyand philosophy of a physically-based distributed modellingsystemrdquo Journal of Hydrology vol 87 no 1-2 pp 45ndash59 1986
[17] A J Jakeman and G M Hornberger ldquoHow much complexityis warranted in a rainfall-runoff modelrdquo Water ResourcesResearch vol 29 no 8 pp 2637ndash2649 1993
[18] C CWu and L DMeyer ldquoSimulating transport of nonuniformsediment along flatland furrowsrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 32 no 5 pp 1651ndash16611989
[19] T S Strelkoff A J Clemmens and B V Schmidt SRFR Version321-a Model for Simulating Surface Irrigation in Borders Basinsand Furrows USWCL USDAARS Phoenix Ariz USA 1998
[20] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[21] D L Bjorneberg and T J Trout ldquoEvaluating WEPP predictedon-field furrow erosionrdquo in Proceedings of the 10th InternationalSoil Conservation Organization (ISCO rsquo99) West Lafayette IndUSA May 1999
[22] E M Laursen ldquoThe total sediment load of streamsrdquo Journal ofHydraulics Divison vol 84 pp 1530-1ndash1530-36 1958
[23] C T Yang ldquoIncipient motion and sediment transportrdquo Journalof Hydraulics Divison vol 99 no 10 pp 1679ndash1704 1973
[24] M S Yalin ldquoAn expression for bed-load transportationrdquo Journalof Hydraulics Divison vol 89 no 3 pp 221ndash250 1963
[25] T S Strelkoff and D L Bjorneberg ldquoHydraulic modeling ofirrigation-induced furrow erosionrdquo in Proceedings of the 10thInternational Soil Conservation Organization Conference D EStott R H Mohtar and G C Steinhardt Eds Sustaining theGlobal Farm pp 699ndash705 West Lafayette Ind USA May 1999
[26] D R Mailapalli R Singh and N S Raghuwanshi ldquoPhysicallybased model for simulating flow in furrow irrigation I modeldevelopmentrdquo Journal of Irrigation and Drainage Engineeringvol 135 no 6 pp 739ndash746 2009
[27] Y S Fok and S H Chiang ldquo2-D infiltration equations for fur-row irrigationrdquo Journal of Irrigation and Drainage Engineeringvol 110 no 2 pp 208ndash217 1984
[28] M D Rao N S Raghuwanshi and R Singh ldquoDevelopmentof a physically based 1D-infiltration model for irrigated soilsrdquoAgricultural Water Management vol 85 no 1-2 pp 165ndash1742006
10 Applied and Environmental Soil Science
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
[29] W R Walker and G V Skogerboe Surface Irrigation Theoryand Practice Prentice Hall Englewood Cliffs NJ USA 1987
[30] T J Trout and W H Neibling ldquoErosion and sedimentationprocesses on irrigated fieldsrdquo Journal of Irrigation amp DrainageEngineering vol 119 no 6 pp 947ndash963 1993
[31] W H Green and G Ampt ldquoStudies on soil physics I the flowof air and water through soilsrdquo Journal of Agricultural Sciencesvol 4 no 1 pp 1ndash24 1911
[32] J P Bennett ldquoConcepts of mathematical modelling of sedimentyieldrdquoWater Resources Research vol 10 no 3 pp 485ndash492 1974
[33] D L Bjorneberg T J Trout R E Sojka and J K Aase ldquoEval-uating WEPP-predicted infiltration runoff and soil erosionfor furrow irrigationrdquo Transactions of the American Society ofAgricultural Engineers vol 42 no 6 pp 1733ndash1741 1999
[34] W H Graf Hydraulics of Sediment Transport McGraw-HillBook New York NY USA 1971
[35] D C Flanagan and S J Livingston Eds ldquoUSDA-water erosionprediction project WEPP user summaryrdquo NSERL Rep 11National Soil Erosion Research Laboratoy West Lafayatte IndUSA 1995
[36] S C Finkner M A Nearing G R Foster and J E GilleyldquoSimplified equation formodeling sediment transport capacityrdquoTransactions of the American Society of Agricultural Engineersvol 32 no 5 pp 1545ndash1550 1989
[37] D R Mailapalli Development and testing of physically basedmodel for simulating flow and sediment transport in furrowirrigation [PhD thesis] Agricultural and Food EngineeringDepartment Indian Institute of Technology Kharagpur India2006
[38] D R Mailapalli N S Raghuwanshi and R Singh ldquoPhysicallybased model for simulating flow in furrow irrigation II modelevaluationrdquo Journal of Irrigation and Drainage Engineering vol135 no 6 pp 747ndash754 2009
[39] G H Schmitz and G J Seus ldquoMathematical zero-inertiamodeling of surface irrigation Advance in bordersrdquo Journal ofIrrigation and Drainage Engineering vol 116 no 5 pp 603ndash6151990
