Hindawi Publishing Corporation Applied and Environmental Science Volume 2013, Article ID 957956, 10 pages http://dx.doi.org/10.1155/2013/957956

Research Article Sediment Transport Model for a Surface System

Damodhara R. Mailapalli,1 Narendra S. Raghuwanshi,2 and Rajendra Singh2

1 BiologicalSystemsEngineering,UniversityofWisconsin,Madison,WI53706,USA 2 Agricultural and Food Engineering Department, Indian Institute of Technology, Kharagpur 721302, India

Correspondence should be addressed to Damodhara R. Mailapalli; [email protected]

Received 16 March 2013; Revised 25 June 2013; Accepted 11 July 2013

Academic Editor: Keith Smettem

Copyright © 2013 Damodhara R. Mailapalli et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Controlling irrigation-induced is one of the important issues of and surface water impairment. Irrigation models are useful in managing the irrigation and the associated ill effects on agricultural environment. In this paper, a physically based surface irrigation model was developed to predict sediment transport in irrigated furrows by integrating an irrigation hydraulic model with a quasi-steady state sediment transport model to predict sediment load in furrow irrigation. The irrigation hydraulic model simulates flow in a furrow irrigation system using the analytically solved zero-inertial overland flow equations and 1D-Green-Ampt, 2D-Fok, and Kostiakov-Lewis equations. Performance of the sediment transport model wasevaluatedforbareandcroppedfurrowfields.Theresultsindicated that the sediment transport model can predict the initial sediment rate adequately, but the simulated sediment rate was less accurate for the later part of the irrigation event. Sensitivity analysis of the parameters of the sediment module showed that the soil erodibility coefficient was the most influential parameter for determining sediment load in furrow irrigation. The developed modeling tool can be used as a water management tool for mitigating sediment loss from the surface irrigated fields.

1. Introduction for 4% slope and 26.4 kg per furrow for 1.6% slope in an −1 irrigation event. Mailapalli et al. [6]estimatedas0.4Mgha Surface irrigation is a widely used farming system for crop −1 of soil loss for bare and 0.2 Mg ha for cropped furrow production as it requires less skilled labour and involves fields in an irrigation event. Sediment flow from agricultural less operational cost. Surface irrigation systems contributed to about 90% of the world’s crop land irrigation promoting fields can cause downstream water quality degradation and furrow irrigation as the main application method [1]. How- eutrophication by carrying soil and plant nutrients and other ever, poor design and management, nonuniformity of water pollutants. application, and over-irrigation featured in surface irrigation Amount of soil loss from a furrow depends on furrow are responsible for inefficient irrigation, leading to wastage stream size, velocity, and soil susceptibility to erosion (erodi- of water, water logging, salinization, and pollution of surface bility). In furrow irrigation, water delivered through siphon and ground . Irrigated agriculture is under tubesorgatedpipespicksupsoilparticlesandcarriesthem serious risk due to substantial soil losses from highly erodible down the furrow. The furrow stream continues to pick up [2–4]. The sediment transport in an irrigation season sedimentsuntilitsenergyequalstothatneededtocarrysoil varies with the number of previous , flow rate, soil particles. Furrow stream size and velocity decrease with the type, field slope, and field length [5, 6]. Berg and Carter waterfront advance along the furrow due to water loss as [2] reported annual losses of sediments ranging from 1 to infiltration. At some point along the furrow, the capacity of −1 141 Mg ha in Southern Idaho. Koluvek et al. [7]measured the flow to transport the accumulated sediment decreases −1 0.2 to 50 Mg ha of soil loss per season in Washington and and the net deposition occurs [6, 9]. Most of the sediments −1 1to22Mgha per irrigation in Wyoming. Brown et al. [8] eroded at the head end of the field settle out before reaching observed a maximum sediment loss of 79.5 kg per furrow the tail end. Trout [4] studied on-field distribution of erosion 2 Applied and Environmental Soil Science and sedimentation in irrigated furrows and found that the 2.1. Overland Flow Module. The governing equations for erosion rates on the upper quarter of the furrows were 6 simulating flow in the furrows are as follows: to 20 times greater than the average rates from the field. Fernandez-G´ omez´ et al. [10] studied the furrow erosion on (i) conservation of mass equation loamy textured alluvial and clay loam cracking soil and found 𝜕𝐴 𝜕𝑢 𝜕𝐴 + 𝐴+ 𝑢=−𝑞 (1) thatthenetratesofsoillossintheupperpartofthefurrow 𝜕𝑡 𝜕𝑥 𝜕𝑥 were up to six times higher than the average net rate for the whole furrow. However, as the infiltration rate decreases (ii) conservation of momentum equation with time, the flow rate increases and influences the sediment transport at the tail end. Everts and Carter [11]reportedthat 𝜕ℎ 𝑢2 𝑞 𝑢 =𝑆 − + , (2) from 40 to 90% of soil leaving a field is eroded from the last 𝜕𝑥 0 𝐾2𝑅4/3 𝑔 𝐴 9 to 15 m of each furrow. 2 Mathematical models can predict sediment load under where 𝐴(𝑥, 𝑡) is the wetted cross-sectional area (m ), 𝑢(𝑥, 𝑡) −1 different field conditions and save time and money on field is the flow velocity (m s ), 𝑡 is the time (s), 𝑥 is the distance 2 −1 experimental trials. The irrigation-induced erosion can be along the furrow (m), 𝑞(𝑥, 𝑡) is the infiltration rate (m s ), modeled using empirical or statistical [12–14], conceptual ℎ(𝑥, 𝑡) is the water depth (m), 𝑆0 is the bottom slope (—), 𝐾 [15–17], and physically based [18–21] models. These models is the Manning-Strickler coefficient (—), 𝑅 is the hydraulic differ in terms of complexity, processes considered, and the −2 radius (m), and 𝑔 is the gravitational constant (m s ). data required for model calibration and model use [14]. Of these, the physically based models are based on the solution of conservation of mass and momentum equations 2.2. Infiltration Module. Infiltration rate is calculated by for flow and the conservation of mass equation for sediment 𝑑𝐼 (𝑡) 𝑞 (𝑥,) 𝑡 = , (3) transport. The physically based models are also termed as 𝑑𝑡 process-based models [13]astheystillrelyonempirical 3 equations to describe erosion processes. Wu and Meyer where 𝐼(𝑡) is the cumulative infiltration (m /m), which is [18]developedaconceptualandphysicallybasedmodel, determined by (i) 1D-Green Ampt model, (ii) 2D-Fok model, ROWERO for simulating transport of nonuniform sediment and (iii) Kostiakov-Lewis model. The option for choosing an along flatland furrows and the modeling tool may not be infiltration equation in the irrigation model can be useful in applicable for graded furrows. Strelkoff et al. [19]developed selecting a better modeling approach for simulating overland SRFR for simulating flow, soil erosion, and deposition at flow and infiltration. variouspointsalongthefurrowusingLaursen[22], Yang [23], and Yalin [24] sediment transport equations. However, (i) 1D-Green Ampt Model. The one-dimensional vertical infil- theSRFRusesnumericaltechniquetosolvetheflowequa- tration depth is estimated by Green and Ampt [31]equation: tions. Trout [4], Bjorneberg et al. [20], and Bjorneberg and Trout [21] used WEPP (Water Erosion Prediction Project) 𝐼 (𝑡) =𝑧(𝑡) Δ𝜃 model for predicting flow and sediment transport in furrow 𝑧+(ℎ−𝑆 ) (4) irrigation. Review of the supporting documentation and the 𝑧 (𝑡) =(ℎ−𝑆 )[ ( av )] − 𝐾 𝑡, av ln (ℎ − 𝑆 ) 𝑠 literature revealed a number of unnecessary and possibly av flawed assumptions within the hydraulic components of the WEPP model [25]thatneedtobefocusedonforaccurate where 𝑧(𝑡) is the vertical depth of the wetting front (m) Δ𝜃 = 3 −3 prediction of irrigation-induced erosion. (𝜃𝑠 −𝜃𝑖) isthechangeinmoisturecontent(m m ), 𝜃𝑠 is the 3 −3 saturated moisture content (m m ), 𝜃𝑖 is the initial moisture The hydraulic component of furrow irrigation can be 3 −3 accurately modeled using the irrigation model presented by content (m m ), 𝐾𝑠 is the satiated hydraulic conductivity −1 𝑆 Mailapalli et al. [26]. They used analytical solution of zero- (m s ), and av is the effective suction head at the wetting inertia equations for simulating overland flow and multiple front (m). infiltration models such as 2D-Fok27 [ ], 1D-Green Ampt [28] and Kostiakov-Lewis [29] for estimating infiltration. In this (ii) 2D-Fok Infiltration Model. The general equation for 2D- paper, we attempted to integrate a quasi-steady state sediment infiltration27 [ ]isgivenby transportmodeldescribedbyTroutandNeibling[30]to 1 𝐼 (𝑡) =(2ℎ𝑥 +𝑏𝑧+ 𝜋𝑥 𝑧) Δ𝜃, the hydraulic component of Mailapalli et al. [26] irrigation 2𝐷 ℎ 2 ℎ (5) model and evaluated performance of model integration for estimating irrigation-induced erosion. where 2𝐾 0.5 𝑥 =[ 𝑠 (ℎ − 𝑆 )𝑡] , (6) 2. Theoretical Considerations ℎ Δ𝜃 av

Theoretical background of the hydraulic component of the where 𝑥ℎ is the horizontal wetting front (m), 𝑏 is the base −1 irrigation model [26] and sediment transport model [30]and width (m), and 𝐾𝑠 is the hydraulic conductivity (m s )ofthe their integration is briefly described below. wetted part of the soil profile. Applied and Environmental Soil Science 3

(iii) Kostiakov-Lewis (KL) Model [29]. The infiltration equa- 2.3.4. Estimation of Model Parameters. Equation (10)repre- tion used to determine 𝐼(𝑡) is sents steady-state sediment transport equation for predicting the erosion and deposition processes in the irrigation fur- 𝐵𝑘 𝐼 (𝑡) =𝐴𝑘𝑡 +𝑓0𝑡, (7) rows. It involves several parameters to be estimated before using the equation for modelling sediment transport. The 3 −1 −𝐵𝑘 where, 𝐴𝑘 (m m s )and𝐵𝑘 (—) are the fitted parameters; following sections describe the estimation of tractive force or 2 −1 𝜏 𝜏 and 𝑓0 is the basic infiltration rate (m s ). hydraulic shear ( ), critical shear ( 𝑐), soil erodibility coeffi- cient (𝐾𝑟)andtransportcapacity(𝑇𝑐), which are essential for estimation of sediment load (𝑞𝑠). 2.3. Sediment Transport Model (a) Tractive Force (𝜏). The tractive force or hydraulic shear 2.3.1. Governing Equations. The irrigation-induced soil ero- acting on the perimeter of the furrow, which is responsible sion or deposition over a distance 𝑥 in furrows is modeled for soil detachment, was calculated by the following tractive using continuity equation [30, 32]: force equation [34]. 𝜏=𝛾𝑅𝑆, 𝜕𝑞 𝜕 (𝑐ℎ) 0 (13) 𝑠 +𝜌 =𝐷 +𝐷, 𝑠 𝑟 𝑙 (8) −3 𝜕𝑥 𝜕𝑡 where 𝛾 is the unit weight of water (N m ). 𝑞 −1 −1 𝜌 where 𝑠 is the sediment load (kg m s ), 𝑠 is the mass (b) Critical Shear Force (𝜏𝑐). The critical hydraulic shear −3 𝑐 density of sediment particles (kg m ), is the concentration 𝜏𝑐 3 −3 force ( ) is determined by using the following pedotransfer of the sediment in the flow (m m ), ℎ is the flow depth (m), −2 −1 functions [35]. 𝐷𝑟 is the rill erosion rate (kg m s ), 𝑥 is the distance along For the soils containing 30% or more sand, the slope (m), 𝑡 is the time (s), and 𝐷𝑙 isthedeliveryrateof −2 −1 𝜏 = 2.67 + 0.065 − 0.058 , erosion from interrill area (kg m s ). 𝑐 PC PVFS (14) For quasi-steady state (𝜌𝑠(𝜕(𝑐ℎ)/𝜕𝑡)), =0 condition in where PC is the percentage clay and PVFS is the percentage furrows and sediment from interrill area is negligible (𝐷𝑙 =0) of very fine sand. and (8)canbewrittenas For the soils containing less than 30% sand,

𝑑𝑞𝑠 =𝐷, (9) 𝜏𝑐 =3.5. (15) 𝑑𝑥 𝑟 (c) Soil Erodibility (𝐾𝑟). The soil erodibility𝐾 ( 𝑟) is determined 𝐷 =𝛼(𝑇 −𝑞) 𝐷 =𝛼𝑇 Assume 𝑟 𝑑 𝑐 𝑠 and 𝑐 𝑑 𝑐,andsubstitutein by using the following pedo-transfer function [35]: (9) to yield an equation for sediment load: For the soils containing 30% or more sand, −(𝐷 /𝑇 )𝑥 𝑞 =𝑇 (1−𝑒 𝑐 𝑐 ) , (−1.84OM) 𝑠 𝑐 (10) 𝐾𝑟 = 0.00197 + 0.00030PVFS + 0.03863𝑒 , (16) where 𝛼𝑑 is the first-order reaction coefficient for deposition where OM is the organic matter (%). −1 −1 −1 (m ), 𝑇𝑐 is the sediment transport capacity (kg m s ), and For the soils containing less than 30% sand, −2 −1 𝐷𝑐 is the detachment capacity (kg m s ). (−0.2PC) 𝐾𝑟 = 0.0069 + 0.134𝑒 . (17)

2.3.2. Soil Erosion (𝐸𝑓). Most erosion models recognize that (d) Transport Capacity (𝑇𝑐). Sediment transport capacity net erosion decreases as sediment load increases. The net was calculated by Yalin’s equation [24]. Foster and Meyer erosion, 𝐸𝑓, is proportional to the difference between the [15] concluded that Yalin’s equation is the most appropriate sediment transport capacity (𝑇𝑐) and sediment load (𝑞𝑠), for shallow flows associated with upland erosion. The Yalin resulting in [33]. equation is defined as Consider 1/2 1/2 1 𝐸 𝑇𝑐 = 0.635 (SG) 𝑑𝜌𝑤 𝜏𝑠 𝛿[1− ln (1 + 𝛽)] (18) 𝑓 𝑞𝑠 𝛽 =1− . (11) 𝐷𝑐 𝑇𝑐 −0.4 0.5 𝛽 = 2.45(SG) (𝑌 ) 𝛿 (19a) 2.3.3. Soil Deposition (𝐷𝑓). Since soil is a porous media, the cr flow rate decreases with the distance down the furrow, and 𝑌 𝐷 𝑇 𝑇 𝛿= −1 thus, 𝑐 and 𝑐 also decrease. As flow rate decreases, 𝑐 𝑌 (19b) eventually becomes less than the sediment load, resulting in cr 𝐷 deposition. The deposition of the soil ( 𝑓)alongthefurrow 𝜏𝑠/𝜌𝑤 𝑌= , (19c) is modelled by the following equation [33]: (SG −1) 𝑔𝑑 𝑑𝑇 𝑐 where, SG is the particle-specific gravity, 𝜌𝑤 is the density 𝐷𝑓 =− (𝑇𝑐 ≤𝑞𝑥). (12) −3 𝑑𝑥 of water (kg m ), 𝑑 is the particle diameter (m), 𝑌 is the 4 Applied and Environmental Soil Science

Start

Input parameters Q0, S0, n, Kt, Kr, h𝛾, t, x

x=x+dx

Total shear stress 𝜏=𝛾RS

Transport capacity 1.5 Tc =Kt𝜏

A B Detachment capacity Dc =Kr(𝜏 −c 𝜏 ) Sediment load at a distance x Soil deposition (Df) or erosion (Ef) Sediment load

(−D𝑐x/T𝑐) qs =Tc⌈1−e ⌉ x≤L Yes

Deposition No Yes Erosion dT q ≤T E =D[1−(q /T )] D =− c s c f c s c No f dx Sediment load (qs) at the tail end

A B Stop

(a) (b)

Figure 1: Flowchart showing the working of sediment transport module. dimensionless shear stress, 𝑌 is the dimensionless critical 2.4. Model Integration. In the erosion model, the transport cr −2 shear from Shield’s Diagram, 𝜏𝑠 is the shear stress (N m ), capacity (𝑇𝑐) and the detachment capacity (𝐷𝑐)arethetwo and 𝛽 and 𝛿 are the dimensionless parameters. Critical important parameters to be determined at a distance 𝑥 𝑌 shear stress ( cr) was determined by the following regression from the head end of the furrow. The sediment transport equation from Shield’s Diagram: capacity (𝑇𝑐) was determined using the YE and MYE ((18)to (22)). Figure 1 shows the algorithm used to model sediment 𝑌 = 0.002235𝑥 5 − 0.06034𝑥 4 + 0.20307𝑥 3 Log10 cr 𝑐 𝑐 𝑐 transport in irrigated furrows using MYE. The algorithm used (20) forYEwasthesameasMYE(Figure1). During the simulation + 0.054252𝑥 2 − 0.636397𝑥 , 𝑐 𝑐 run, the irrigation model estimates discharge and determines the sediment transport capacity (𝑇𝑐) and detachment capacity where (𝐷𝑐). Then, the model estimates sediment load𝑞 ( 𝑠), erosion 𝑑√(SG −1) 𝑔𝑑 (𝐸𝑓), and deposition (𝐷𝑓)atadistance𝑥 from the head end 𝑥 = (𝑆 ) ,𝑆= , (21) 𝑐 log10 ∗ ∗ 4V and time 𝑡. The sediment load estimation is terminated when the discharge in the furrow is zero. where 𝑆∗ is the sediment fluid parameter, (m s) and V is the 2 −1 kinematic viscosity of water, (m s ). When 𝜏 is much greater than the critical shear stress (𝜏𝑐) 3. Model Evaluation for transport of detached particles, the Yalin equation (YE) reduced to a simplified equation (MYE) as follows [36]: Performance of the sediment transport module was evaluated for bare and cropped furrow fields. Furrow experiments 3/2 𝑇𝑐 =𝐾𝑡𝜏 , (22) were conducted on a 4 m × 60mplotintheFieldWater Management Laboratory, Agricultural and Food Engineering −1/2 1/2 2 where 𝐾𝑡 is the transport coefficient (kg m s ). Department, 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 −6 −6 𝐾𝑠 (m/s) 1.0 × 10 1.1 × 10 𝑆 av (m) 0.13 0.13 3 −1 −𝐵𝑘 −4 −4 Infiltration 𝐴𝑘 (m m s ) 5.0 × 10 5.35 × 10

𝐵𝑘 (—) 0.4 0.42 2 −1 𝑓0 (m s ) 0.0 0.0 −2 𝜏𝑐 (N m ) 0.0 0.0 −1 −6 −5 𝐾𝑟 (s m ) 5.0 × 10 1.0 × 10 −1/2 1/2 2 𝐾𝑡 (kg m s ) 0.01 0.02 Erosion SG 2.65 2.65 −5 −5 𝑑 (m) 1.8 × 10 2.8 × 10 − −6 −6 V (s m 1) 8.9 × 10 8.9 × 10

Table 2: Model performance for simulating sediment loss for bare field.

2D-Fok and Chiang 1D-Green Ampt KL-infiltration function Date of Transport Observed (kg) Simulated RMSE Simulated RMSE Simulated RMSE irrigation capacity equation − 𝐼 − 𝐼 − 𝐼 (kg) ×10 5 (kg) 𝑎 (kg) ×10 5 (kg) 𝑎 (kg) ×10 5 (kg) 𝑎 YE 0.32 0.40 1.2 0.67 0.42 1.4 0.62 0.45 1.5 0.59 6th Feb-04 MYE 0.32 0.39 1.2 0.65 0.42 1.5 0.60 0.45 1.8 0.55 YE 0.47 0.60 3.1 0.13 0.61 2.9 0.13 0.65 3.2 0.15 17th Feb-04 MYE 0.47 0.61 3.2 0.11 0.63 3.3 0.12 0.65 3.6 0.16 YE 0.91 0.81 1.4 0.65 0.76 1.5 0.61 0.81 1.6 0.57 21st Feb-04 MYE 0.91 0.72 1.4 0.65 0.72 1.6 0.59 0.76 1.9 0.55 YE 1.28 0.93 1.3 0.66 0.92 1.5 0.61 0.92 1.6 0.58 29th Feb-04 MYE 1.28 0.94 1.3 0.65 0.93 1.6 0.54 0.91 1.9 0.55 YE is the Yalin transport equation. MYE is the modified Yalin transport equation. sandy loam and contained 69% sand (61.7% PVFS), 17% silt, 9thApril,16thMayand23rdMay,2005using0.7,0.6,0.5, −1 14% clay and 0.43% organic matter. The bulk density and 0.4, and 0.3 L s , respectively. The furrows were not tilled 3 porosity of the soil were 1.54 g/cm and 40%, respectively. between irrigations during 2004 and 2005. Three free draining furrows of parabolic shape, 40 m long, Some of the input parameters required for overland flow, 0.30 m wide, and 0.15 m deep were fabricated in the exper- infiltration and sediment transport modules were estimated imental plot. The furrows have centre-to-centre distance of from the field data37 [ ] and these were considered as base 0.8 m and a slope of 0.5%. The center furrow was considered line input parameters for model testing. The Green and 𝐾 𝑆 as study furrow and the two side furrows served as buffer Ampt hydraulic parameters such as 𝑠 and av were deter- to the center furrow. Three digital flow meters (wheel type) mined using field data and pedo-transfer functions [38]. The were installed at the inlet of three furrows to set the desired Kostiakov-Lewis parameters 𝐴𝑘, 𝐵𝑘,and𝑓0 were estimated inflow rate to each furrow. Plastic buckets (3-litre capacity) by using ring infiltrometer data37 [ ]. The management and wereusedtocollectrun-offattheendofastudyfurrowatan geometric parameters for these field conditions were used interval of 10 min. from [38]. The critical shear (𝜏𝑐)andthesoilerodibility The run-off samples were oven-dried and the sediment coefficient (𝐾𝑟) were determined using (14), (15), (16), and 3 −1 left in each sample was weighed. The run-off rate (m /s) and (17). The estimated values of 𝐾𝑟 and 𝜏𝑐 were 0.04 s m and 3 the corresponding sediment weight (kg/m )wereusedto 0.001,respectively.ThevaluesofSGandV were taken as 2.65 −6 −1 estimate sediment rate (kg/s). The details on experiments and and 8.9 × 10 sm , respectively. The mean diameter (𝑑) −5 data collection procedure are presented by Mailapalli et al. ofthesedimentparticleforbarefieldwas1.8× 10 mand [6]. The three furrows were irrigated at the same time on 6th, × −5 𝑠𝑡 cropped field was 2.8 10 m[37]. The cropped field has 17th, 21 , and 29th February 2004 using constant inflow rates coarser particles than the bare field as the irrigations were −1 of 0.2, 0.3, 0.4, and 0.5 L s ,respectivelyonbarefurrowfield. performed first on the bare field and it may lost most of the In 2005, sunflower (Helianthus annuus L.) crop was grown on fine particles as run-off. three furrow beds having a plant-to-plant spacing of 45 cm. The simulations were first performed using the field 𝐾 𝐾 𝑆 𝐴 𝐵 The three furrows were irrigated on 3rd March, 30th March, observed values of input parameters ( , 𝑠, av, 𝑘, 𝑘, 6 Applied and Environmental Soil Science −5 −5 12 12

×10 10

×10 10 8 8 6 6 4 4 2 2 Sediment load (kg/s) Sediment Sediment load (kg/s) Sediment 0 0 0 30 60 90 120 150 0 30 60 90 120 150 Time (min) Time (min) Observed 1D-GA Observed 1D-GA 2D-Fok KL 2D-Fok KL (a) (b)

Figure 2: Comparison of observed and simulated sediment load (using YE) for (a) 6th February 2004 and (b) 17th February 2004 irrigation event.

−6 −1 𝜏𝑐 and 𝐾𝑟) for estimating sediment load for both bare and found to be 5.0 × 10 sm and 0.01 for bare and 1.0 × −5 −1 cropped field conditions using the three infiltration models. 10 sm and 0.02 for cropped field conditions, respectively. Of these simulations, the best and the worst model per- Table 1 presents the input data used for infiltration and formances were selected for both bare and cropped furrow erosion parameters for bare and cropped field conditions. conditions, and model performance was studied graphi- cally.Itwasassumedthatinfiltrationisthekeycomponent 4.1. Sediment Transport in Bare Furrow Field. The model of irrigation management and was given first priority for performance was inconsistent in predicting the sediment selecting the best and worst simulations, followed by run-off load using all three infiltration equations. Furthermore, the rate, sediment yield, waterfront advance and recession times. YEperformedslightlybetterthantheMYEinmostofthe ± Sensitivity analysis was carried out to study the effect of 5 cases. The 2D-Fok infiltration function resulted in low RMSE ± 𝐾 𝐾 and 10% changes in the values of 𝑟 and 𝑡 on the sediment and high 𝐼𝑎 values as compared to those obtained using load, estimated by the YE and MYE. 1D-Green Ampt and KL infiltration models (Table 2). Thus, The performance of the irrigation model for predicting the irrigation model performed well in simulating sediment sediment load was evaluated by estimating root mean square load using the 2D-Fok infiltration function followed by 1D- 𝐼 error (RMSE) and index of agreement ( 𝑎). Green Ampt and KL-infiltration functions. The performance Consider indices (Table 2) suggested that the model performance for 𝑁 2 sediment load in bare furrow field was the best and the worst √ ∑𝑖=1 [𝑀(𝑖) − 𝐸(𝑖)] RMSE = for irrigation events of 6th Feb 2004 and 17th Feb 2004, 𝑁 respectively. Therefore, these events were selected for further (23) analysis. Figures 2 and 3 show comparison between observed ∑𝑁 (𝑀 (𝑖) −𝐸(𝑖))2 𝐼 = 1.0 − 𝑖=1 , and simulated outputs for the best (6th February 2004) and 𝑎 󵄨 󵄨 󵄨 󵄨 2 ∑𝑁 (󵄨𝐸 (𝑖) − 𝑀󵄨 + 󵄨𝑀 (𝑖) − 𝑀󵄨) the worst (17th February 2004) irrigation events using YE and 𝑖=1 󵄨 󵄨 󵄨 󵄨 MYE, respectively. where 𝑀(𝑖) is the measured value, 𝐸(𝑖) is the estimated value, The irrigation model with YE and MYE predicted initial 𝑁 isthenumberofdatapoints,and𝑀 isthemeanofthe increase in sediment load well. However, both YE and MYE observed values. were not able to predict the decreasing trend of sediment rate with elapsed time. The possible reason could be that the sediment load estimation takes the run-off rate into account 4. Results and Discussion which increases with elapsed time. Figures 2 and 3 also show The visual observation of the trends between observed and that the model performed equally well using 2D-Fok, 1D- simulated sediment loads (not shown here) by 2D-Fok, 1D- Green Ampt, and KL infiltration models. However, sediment Green Ampt, and KL infiltration equations depicted that the load predictions using the YE were slightly better than the sediment load predictions were not good with the baseline MYE. values of 𝜏𝑐 and 𝐾𝑟.Hence,𝜏𝑐 wasassumedaszero,and𝐾𝑟 and 𝐾𝑡 were considered as calibration parameters for simulating 4.2. Sediment Transport in Cropped Furrow Field. 2D-Fok sediment load. During the calibration process, the base values infiltration function resulted in lower RMSE values and of 𝐾𝑟 and 𝐾𝑡 were tuned by increasing or decreasing their higher 𝐼𝑎 values compared to those obtained using 1D-Green base values. For each run, model predicted sediment load was Ampt and KL infiltration functions (Table 3). Further, RMSE compared with its observed counterpart using the estimated and 𝐼𝑎 values also suggested that the irrigation model with YE performance indices. Finally, the values of 𝐾𝑟 and 𝐾𝑡 were performed slightly better than that with MYE. Based on the Applied and Environmental Soil Science 7

12 −5 −5 12 10 10 ×10 ×10 8 8 6 6 4 4 2 2 Sediment load (kg/s) Sediment Sediment load (kg/s) Sediment 0 0 0 30 60 90 120 150 0 30 60 90 120 150 Time (min) Time (min) Observed 1D-GA Observed 1D-GA 2D-Fok KL 2D-Fok KL (a) (b)

Figure 3: Comparison of observed and simulated sediment load (using MYE) for (a) 6th February 2004 and (b) 17th February 2004 irrigation events.

Table 3: Model performance for simulating sediment loss for cropped field.

2D-Fok and Chiang 1D-Green Ampt KL-infiltration function Date of Transport capacity equation Observed (kg) Simulated RMSE Simulated RMSE Simulated RMSE irrigation − 𝐼 − 𝐼 − 𝐼 (kg) ×10 5 (kg) 𝑎 (kg) ×10 5 (kg) 𝑎 (kg) ×10 5 (kg) 𝑎 YE 1.12 1.15 8 0.55 1.18 8 0.54 1.19 9 0.45 3rd Mar-05 MYE 1.12 1.17 9 0.55 1.18 9 0.53 1.19 9 0.44 YE 1.07 0.97 9 0.53 0.96 9 0.51 0.95 13 0.42 30th Mar-05 MYE 1.07 0.88 9 0.54 0.90 9 0.51 0.93 13 0.42 YE 1.02 0.93 4 0.83 0.99 4 0.78 1.00 6 0.72 9th Apr-05 MYE 1.02 0.95 4 0.83 1.00 4 0.73 1.04 7.5 0.69 YE 0.63 0.78 3 0.85 0.79 3 0.81 0.84 6 0.75 16th May-05 MYE 0.63 0.77 4 0.84 0.77 4.2 0.83 0.82 7 0.72 YE 0.29 0.42 4 0.83 0.47 4 0.80 0.54 7 0.72 23rd May-05 MYE 0.29 0.46 5 0.82 0.47 6 0.80 0.54 8 0.70

performance indices, it is clear that the model performance infiltration functions. The variation in 𝐾𝑡 did not have much in predicting sediment load was the best and the worst in effect on the sediment load whereas the percentage change simulating irrigation events of 16th May and 30th March in 𝐾𝑟 caused the sediment load change at the same rate (by 2005, respectively. For these two irrigation events, the model which 𝐾𝑟 is changed). Hence, for 2D-infiltration model, 𝐾𝑟 predicted sediment load was compared with their observed is the most sensitive parameter for estimating sediment load counterparts and the results are shown in Figures 4 and 5 for forbothYEandMYE.For1D-infiltrationequation,theeffect YE and MYE, respectively. of change in 𝐾𝑡 and 𝐾𝑟 on the sediment yield is the same as Both YE and MYE predicted initial increase in sediment thecasewith2D-infiltrationmodel.Thechangein𝐾𝑡 had loadwell.However,asincaseofbarefurrowcondition,both very little effect on the sediment load that resulted with KL YE and MYE were not able to predict the decreasing trend infiltration model. The increase in 𝐾𝑟 increased the sediment of sediment rate with elapsed time. The model performed load at the same rate for both YE and MYE. equally well using 2D-Fok, 1D-Green Ampt and KL infiltra- tion equations (Figures 4 and 5). Furthermore, the irrigation 5. Conclusions model with YE predicted the sediment load slightly better than the one with the MYE (Table 3). Irrigation-induced erosion accounts most part of the dif- fuse agricultural pollution causing downstream impairment 4.3. Sensitivity Analysis of Model Parameters. Sensitivity of and eutrophication. In this study, a steady state sediment the model parameters in predicting sediment load was transport model was integrated with a physically based studied for 16th May 2005 event. The effect of ±5and furrow irrigation model, which consists of three infiltration ±10% changes in 𝐾𝑟 and 𝐾𝑡 (Table 4)onthesimulated equations (2D-Fok, 1D-Green Ampt, and Kostiakov-Lewis). sediment load was estimated by YE and MYE, considering all The integrated irrigation model was evaluated for estimating 8 Applied and Environmental Soil Science

Table 4: Sensitivity analysis of erosion module parameters.

Percentage change in sediment load Input parameter Percentage change 2D-Fok and Chiang 1D-Green Ampt KL infiltration function MYEYEMYEYEMYEYE −10% 0 NA 0.13 NA −0.24 NA −1/2 1/2 2 −5% 0 NA 0.13 NA 0 NA 𝐾𝑡 (kg m s ) 5% 0.13 NA 0.39 NA 0.12 NA 10% 0.13 NA 0.39 NA 0.24 NA −10% −9.96 −9.99 −9.61 −10 −9.74 −10.7 −1 −5% −4.85 −4.99 −4.68 −4.94 −4.87 −4.99 𝐾𝑟 (s m ) 5% 5.11 4.99 5.19 5.06 4.99 4.99 10% 10.09 10.58 10 10.13 9.87 9.99 −4 3.5 −4 3.5 3

×10 3 ×10 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 Sediment load (kg/s) Sediment 020406080 load (kg/s) Sediment 0 20406080 Time (min) Time (min) Observed 1D-GA Observed 1D-GA 2D-Fok KL 2D-Fok KL (a) (b)

Figure 4: Comparison of observed and simulated sediment load (using YE) for (a) 16th May 2005 and (b) 30th March 2005 irrigation events. −4 −4 3.5 3.5 3

3 ×10 ×10 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 Sediment load (kg/s) Sediment Sediment load (kg/s) Sediment 0 204060800 20406080 Time (min) Time (min)

Observed 1D-GA Observed 1D-GA 2D-Fok KL 2D-Fok KL (a) (b)

Figure 5: Comparison of observed and simulated sediment load (using MYE) for (a) 16th May 2005 and (b) 30th March 2005 irrigation event. sediment load using two sediment transport capacity equa- sediment transport in free drained furrows. However, the tions(YalinandthemodifiedYalinequations)forbareand irrigation model could not adequately simulate the sediment cropped field conditions. The sediment load prediction using load in the last phase of irrigation. Although this has a theYalinandthemodifiedYalinequationswasfoundtobe minor impact on the overall sediment load, it will be the identical; however, the modified Yalin equation may be a subject of future model refinement. The irrigation model better choice as it requires less number of input parameters. uses an analytical solution for zero-inertial flow equations The sensitivity analysis revealed that the soil erodibility and this compared favourably to the full numerical hydraulic coefficient is the most influential parameter in predicting models [39]. This paper describes the procedure for coupling Applied and Environmental Soil Science 9

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