Eduardo Bautista, Ph.D. Research Hydraulic Engineer USDA-ARS U.S. Arid Land Agricultural Research Center Cardon Lane, Maricopa, AZ 95138

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1 Eduardo Bautista, Ph.D. Research Hydraulic Engineer USDA-ARS U.S. Arid Land Agricultural Research Center Cardon Lane, Maricopa, AZ

2 Well-designed and managed surface irrigation systems can attain high levels of distribution uniformity and application efficiency, with low energy (and labor) inputs

3 Great minds think alike! And their first name is Eduardo

4 Background and problem statement Furrow infiltration model Implications for operations analysis and design Application to field data Conclusions

5 [CATEGORY NAME], [VALUE] ma, [PERCENTAGE] [CATEGORY NAME], [VALUE] ma, [PERCENTAGE] [CATEGORY NAME], [VALUE] ma, [PERCENTAGE] Gravity Sprinkler Drip &Subirrigation

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8 A z W, W FS z NRCS NRCS A z = infiltrated volume/length[l 2 ] z = Infiltration depth given by soil infiltration family IF [L] W NRCS = empirical wetted perimeter [L] FS = furrow spacing [L] In which.. a z kt c k, a, c = empirical constants with appropriate units, specific to the IF [L] W NRCS = f(slope, discharge, hydraulic resistance, and a constant to account for lateral infiltration)

9 W Az ICF Z W a In which.. ref a Z Kref t Bref t b A z = infiltrated volume/length[l 2 ] ICF = irrigation condition factor [-] W ref = reference wetted perimeter [L] W a = wetted perimeter at normal flow for actual flow rate, slope, and roughness [L] FS = furrow spacing [L] K, a, B = empirical constants with appropriate units, specific to the IF [L 2 ]

10 Empirical infiltration equation in combination with wetted perimeter option NRCS wetted perimeter No effect (furrow spacing) Upstream wetted perimeter (WP0)

11 No effect (Furrow spacing)

12 Users of furrow irrigation models and analytical tools need to provide design and operational recommendations They need to provide those recommendations with limited knowledge of how changes in wetted perimeter along a furrow during one event, or from one irrigation to the next as a result of changes in average inflow rate, affect infiltration conditions

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14 Infiltration area (cm^2) 1.6E E E E E E E E E+00 VG_Loam_B20SS2 R² = Wetted perimeter (cm) Simulation with Richards equation -HYDRUS 2D/3D Uniform soil Water retention curve - van Genuchten Soil parameters from HYDRUS database Uniform initial water content (30% AW) Trapezoidal furrow Constant water pressure

15 Infiltration rates vary linearly with wetted perimeter (Fangmeier and Ramsey, 1978) In a clay loam soil, wetted perimeter explains only 33% of the variability of infiltration (Izadi and Wallender, 1985)

16 Infiltration varies in proportion to wetted perimeter, but only with tests with stagnant water; flowing water induces erosion and seal formation and negates the effect of increasing wetted perimeter (Trout, 1992) Infiltration varies as (WP/WPr)^b, with b varying during the irrigation season (Oyonarte et al, 2002)

17 The actual wetted perimeter effect lies somewhere in between no effect and the effect predicted from physical principles

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19 A z = cumulative infiltration [L 2 ] W* = adjusted wetted perimeter [L] W = wetted d perimeter [L]; z z = 1-D infiltration [L] S o = soil sorptivity [L/T 0.5 ]; θ 0 = water content at the pressure source[-] θ n = initial water content [-] γ = empirical parameter [-] 2 0 A St z z W* W( ) s 0

20 E=(Az/W-z) (cm) Varies linearly with time, when the flow depth is constant VG_Loam_B20SS2 E A z W * z R² = Time (h)

21 S K h h 0 2 s s 0 avg f (Haverkamp et al., 1988) h f 0 h Kh ( ) K s dh (Bouwer, 1964) h avg W h0 z( y) ds W ds z z h avg

22 Van Genuchten Brooks-Corey

23 E Az z W * E Az( t) z( t) W a

24 A ( t ) A ( t ) Z 2( t ) E( t ) z i z i 1 i i In which Z 2( t ) z( t ) W ( h( t )) i i a i Et ( ) i 2 S0( havg ( ti ))( ti ti 1) Wa( h( ti)) W ( t ) s 0 r i VG Soil model Ks = 0.04 cm/min θ r = θ s = θ 0 = 0.12 n = 1.47 [-] α = [1/cm] γ=1.0

25 Approximate solution has been added to developmental version of WinSRFR (5.x) 1D-infiltration contribution (z) calculated with the Green-Ampt formula Computationally efficient

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27 Identify optimal operational strategies (inflow rate vs. cutoff time) for a furrow irrigation system assuming Infiltration varies with wetted perimeter, as computed with the Warrick-Green-Ampt (WGA) formulation Infiltration is independent of wetted perimeter (Modified Kostiakov formula, in combination with the furrow spacing wetted perimeter option MK-FS) Average infiltration varies linearly depending on the upstream wetted perimeter (MK-WP0)

28 Length = 300 m Cross section = trapezoid (B=10 cm,ss=2) Infiltration requirement = 9 cm Soil = sandy clay loam (Rosetta) VG Soil model Ks = 2.3 cm/h θr = 0.1 θs = 0.39 n = 1.48 [-] α = [1/cm] hf = 3.6 cm θ0 = 0.134

29 Case 1 Slope = DSBC = free draining Case 2 Slope = DSBC = Blocked

30 Define infiltration parameters for WGA, MK-FS-, and MK-WP0 scenarios Conduct simulations with each infiltration formulation varying unit flow rate and cutoff time Develop performance contours to identify solutions that meet the requirement

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32 AZ (M²) Initial simulation conducted with WGA infiltration option Inflow rate and cutoff time selected to satisfy Dreq Selected infiltration results computed at x = E-01 m 1.00E E E E E E TIME (H)

33 Fitted infiltration curve to Modified Kostiakov equation a Az Kt Bt Parameters for the MK-FS formulation are the K k FS, b While parameters for the MK-WP 0 formulation are K k WP B FS B, b WP 0 0

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36 MK-FS MK-WP0

37 MK-WP0 WGA

38 ADVANCE TIME (MIN) CUTOFF TIME (MIN) Advance time 1000 Cutoff time UNIT INFLOW RATE L/S WGA MK_FS MK_WP UNIT INFLOW RATE L/S WGA MK_FS MK_WP0

39 DULQ APPLICATION EFFICIENCY (%) DUlq AE (%) UNIT INFLOW RATE L/S WGA MK_FS MK_WP UNIT INFLOW RATE L/S WGA MK_FS MK_WP0

40 Slope =

41 ADVANCE TIME (MIN) CUTOFF TIME (MIN) Advance time UNIT INFLOW RATE L/S WGA MK-FS MK-WP0 Cutoff time UNIT INFLOW RATE L/S WGA MK_FS MK_WP0

42 DULQ AND AE (%) UNIT INFLOW RATE L/S WGA MK_FS MK_WP0

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44 Elliott et al. (1980). Furrow irrigation field evaluation data. Colorado St. Univ. Data sets Printz: Irrigation 3, Set 2, Furrows 3 and 5 Benson Irrigation 2, Set 2, Furrows 1,3,5 Matchett Irrigation 2, Set 3, Furrows 1,3,5 Available data Advance, recession times Inflow-outflow hydrographs Furrow geometry, bottom elevations, depth hydrographs Approximate field location, texture

45 Using the field evaluation data, computed an infiltration function (Modified-Kostiakov-Furrow Spacing) From the approximate farm location, identified the likely soil from the NRCS Web Soil Survey database Used WSS data and pedotransfer function (Rawls and Brakensiek, 1985) to determine the WGA parameters for the selected soil Used the estimated WGA parameters to simulate the irrigation events using the field evaluation data

46 FLOW RATE (L/S) INFILTRATION DEPTH (MM) INFILTRATION DEPTH (MM) TIME (H) INFILTRATION FUNCTION (U/S) ADVANCE AND RECESSION TIME TIME (H) DISTANCE (M) MK-FS WGA MK_FS MK_FS WGA WGA OBS OBS RUNOFF INFILTRATION TIME (H) DISTANCE (M) MK WGA OBS-qin OBS-RO MK-FS WGA

47 INFILTRATION DEPTH (MM) TIME (H) MK MK MK WGA WGA WGA

48 INFILTRATION DEPTH (MM) INFILTRATION DEPTH (MM) PRINTZ BENSON TIME (H) TIME (H) MK MK MK MK MK WGA WGA WGA WGA WGA

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50 The WGA formulation is a promising alternative for modeling furrow infiltration coupled with the unsteady flow equations of surface irrigation

51 The current empirical approach used in WinSRFR for furrow design and operational analysis, which assumes no wetted perimeter effect on infiltration, has the potential for severely overestimating DUlq, but mostly with sloping, free-draining furrows The alternative empirical approach for modeling furrow infiltration, based on WP0/WPr, also has the potential for overestimating Dulq, and does not lead to better operational decisions, at least for the example presented here

52 The analysis shows that with both sloping/freedraining and near-level/blocked furrows, there is a range of flow rates beyond which the assumed wetted perimeter effect has little effect on advance time. The selected operational recommendation needs to use a flow rate in that range.

53 With sloping, free-draining furrows, analysis with wetted perimeter dependent infiltration (WGA) will lead to more conservative estimates of DUlq and operational decisions For the near-level, blocked furrow example presented, all methods yield similar estimates of DUlq and operational recommendations

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55 RO/DP UNIT INFLOW RATE L/S WGA MK_FS MK_WP0