Furrow Irrigation Design with Simulation

Furrow Irrigation Design with Simulation A.J. Clemmens, M. ASCE, E. Camacho, T. S. Strelkoff, M. ASCE 1

Abstract In this paper, we present a furrow irrigation design method, wherein an unsteadyflow simulation of a single event is used to “tune” a simplified model. This tuning adjusts model parameters to match: 1) advance time to the end of the field, 2) application time, and 3) infiltration and runoff volumes. The simplified model is then applied over a range of conditions to develop performance contours that can assist the user in the design process. This model is being programmed into a user-friendly computer program. Introduction Clemmens et al. (1998) have proposed a simplified method for furrow irrigation design, in which, simple procedures are used to compute advance and recession. While designs can be developed directly with this procedure, the results may or may not match field behavior without extensive empirical calibration. Numerical models of the unsteadyflow equations can determine the advance with less dependence on empirical calibration, but these models are time consuming to run and are not sufficiently robust for simulation during design. Strelkoff and Clemmens (1994) summarize the progress on the use of these models for design — typically the development of a database of nondimensional results. Such dat abases are difficult to develop and can represent o nly a limited range of conditions. We propose a hybrid approach, wherein simulation of a single irrigation event with a hydrodynamic model is used to “tune” a simplified design model. The tuning parameters are assumed constant over a range of conditions. This allows contour maps of performance over the specified range of design conditions (shown later in Figure 2) to be generat ed relatively quickly. In this way, the number of simulation runs is minimal, reducing the overall computation time and the occurrence of computational difficulties.

1

Research Hydraulic Engineer, U.S. Water Conservation Laboratory, USDA-ARS, 4331 E. Broadway, Phoenix, AZ 85040, Professor, Technical School of Agricultural Engineers, University of Cordoba, Cordoba, Spain, and Professor, Agricultural and Biosystems Engineering, University of Arizona, Tucson, AZ.

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General Approach to Surface Irrigation Design A key objective in design and management is satisfaction of the water requirement dreq of the crop. A management decision establishes whether this target is to be met by the minimum in the post-irrigat ion distribution of infiltrated water, or by the average of the low-quarter of infiltrated depths. The argument below is presented in terms of the minimum; extension to the low quarter is straightforward. In furrows with runoff, the minimum depth typically occurs at the downstream end (for a general discussion, see Clemmens et al, 1998). In terms of Figure 1, the desired time of recession tR(L) from the lower end equals the advance time tA(L) plus Jreq, the time required to infiltrate dreq, an infiltration characteristic more important than the coefficients in the infiltration formula themselves. A secure operation, assuring satisfaction of water requirements everywhere in the furrow, would be to cut off the inflow at tco = tR(L). This however would over-irrigate even the downstream end, as water continued to run off, subjecting it to an oppo rtunitytime excess of [tlag + tR(L) - tR(0)], the lag time constituting the interval between cutoff and the start of recession, tR(0), at the upstream end. Only if the volume of water in the furrow at cutoff is negligible, could the bracketed term, above, be neglected. In the general case, the time of cutoff should be (1) Solution of equation (1) for cutoff time requires first of all calculation of advance time tA(L), and then estimates of the recession trajectory and lag time. Following Clemmens et al. 1998, simple models for estimating advance and recession times are presented in the next two sections.

Figure 1. Advance and recession curves for design satisfying the target at the downstream end.

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Assumed-Surface-Volume Method for Computing Advance Conservation of mass or volume at any time t during advance equates the inflow volume Vin(t), to the sum of the volume in surface storage Vy(t), and the infiltrated volume Vz(t). The surface vo lume can be represented by (2) where x(t) is the advance distance, A0(t) is the cross-sectional flow area at the upstream end, and Fy(t) is the surface-storage shape factor (ratio of average cross-sectional flow area over the length of the stream to A0). In a first approximation Fy can be assumed constant, typically, between 0.70 and 0.80 for furrows. If advance and infiltration are described by simple po wer functions of time, t=fx h and d=kτa, respectively, where d is infiltrated depth and f, h, k, and a are empirical constants, a constant subsurface shape factor Fz follows, approximately, (3) (For further details, see ASAE, 1994); Fz is the ratio bet ween the average infiltrated volume per unit length and that at the head of the field. The subsurface volume is then (4) where d(t) is the infiltrated depth at the head end of the field, and W is a width. Equations 3 and 4 assume that furrow infiltration is not influenced by variations in wetted perimeter, either in time or with distance down the furrow. However, the value of the Kostiakov infiltration constant k is inversely related to the chosen width, W (i.e., the constant will be smaller if based on furrow spacing rather than on some measured wetted perimeter). Given a value of W, local infiltration then depends only on the duration between the advance time tA(x) and the recession time tR(x). Given all the physical parameters of an irrigation -- furrow inflow rate (Qin), A0, σy, W, and the infiltration- equation constants -- then the advance-curve power-law constants, f and h, can be found. If a value for h is assumed, solving these equations for two given advance distances, say L and L/2, gives two advance time-distance pairs that can be used to reestimate h. The iterative procedure is converg ent because the advance is not strongly dependent on h. Further details, including application to infiltration equations other than the Kostiakov formula, can be found in Clemmens et al. (1998). The ability to accurately predict advance times with this method depends primarily on the estimates for A0 and σy. For slopes greater than about 1/10 % accuracy is reasonably good -- after just a short time, A0 is the flow area at normal depth, which can be readily calculated for the given inflow, slope, furrow cross section and estimated Manning n. Furthermore, the surface volume is then, typically, only a small fraction of the total inflow volume, so errors in Fy and A0 have an insignificant effect on advance predictions. For milder slopes, the surface volume can be a large portion of the inflow volume, even at the time of cutoff. Further, A0 increases continuously during the inflow period and may never reach normal depth.

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Simplified Method for Computing Recession Clemmens et al. (1998) approximate the time between cutoff and the time of downstream recession from the volume in surface storage. They argue that if cutoff occurs at the time when Jreq is satisfied at the downstream end, then there is a volume of water in the furrow Vy(tco) at that time that is unneeded. Thus, the cutoff time should be reduced from tR(L) by the time required for that volume to leave the furrow, either as infiltration or runo ff. Toward the end of an irrigation event, the time to add that volume upstream and the time for it to leave the furrow downstream are roughly the same (e.g., if you add 1 hr to tco, runoff duration will also increase by about 1 hr). We know the time required to apply that volume and can adjust the cutoff time accordingly; (5) where Φ1 is a tuning factor. This procedure uses Vy(tL) rather than Vy(tco) to estimate tco, because in sloping furrows, the surface volume doesn’t change very much after advance is complete and this volume is known from the above advance calculations. The recession curve is represented by a straight line, from the recession time at the upstream end to the required recession time at the downstream end, tR(L)=tA(L)+Jreq. To compute this recession curve, an estimate for the recession lag time is needed. Strelkoff (1977) estimated recession lag time in border strips with a simple equation; (6) in which Φ2, a third tuning factor, is added here and discussed in the next section. Once the power-law advance and straight-line recession curves have been determined, the distribution and volume of infiltration follow; runoff volume is the difference between inflow and infiltrated volumes. Performance parameters are then computed from these volumes. Further details can be found in Clemmens et al., 1998. Tuning the Simplified Model with Hydrodynamic Simulation For a given set of irrigat ion conditions, i.e., target depth; inflow rate; furrow geometry, roughness, and infiltration parameters – and some estimate of the tuning factors, σy, Φ1, and Φ 2 -- we can calculate the appropriate cutoff time and resulting irrigation performance. If we use this same physical data plus the computed cutoff time as input to an unsteady-flow simulation model (e.g., SRFR, Strelkoff 1990), we will get hydrodynamic predict ions of advance and recession, distribution of infiltrated water, and runoff. We view the hydrodynamic simulation as providing better predict ions than the simplified model, since it contains more physics and fewer assumptions and empiricism. For comput ing advance, the main differences between the two procedures are: the simplified procedure uses a normal-depth estimate of A0 and an assumed, constant σy to

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determine surface volume, while the hydrodynamic simulation is based on conservation of mass and momentum, without assuming upstream depth or profile shapes. The adjustment procedure matches t he advance time at the end of the field to the hydrodynamic simulation by adjusting σy. This is intended to account both for discrepancies in the actual shape fact or and any error in A0. The adjustment does not assure that advance times at other distances match, but such errors likely have a small impact on the distribution. In computing recession, the simplified model makes assumptions that may not provide the appropriate cutoff time to yield, in the hydrodynamic simulation, the target infiltrated depth at the downstream end. Once we have established σy to yield the correct advance time with the simplified model, we adjust the tuning factor Φ1 to provide the correct relationship between cutoff time and downstream infiltrated depth. At least for that cutoff time, the two procedures then give the same predicted downstream infiltrated depth. In addition to the downstream infiltrated depth, the entire recession curve may be quite different from that assumed with the simplified approach. If the target infiltration depth at the downstream end is accurately predicted, we really need only a rough idea of the rest of the infiltration profile. More important than the details of the distribution is the total infiltrated volume. A match to the infiltrated volume can be obtained by adjusting the parameter M2 in equation 6, which determines the time recession begins at the upstream end. It is assumed that all remaining errors in the advance and recession curves can be corrected by starting the straight-line recession at an appropriate time. The calculation also provides a rough confirmation that the minimum infiltrated depth is at the downstream end. This confirmation is rough since no attempt is made to match the actual recession time, and thus infiltrated depth, at the upstream end. Application to Design The design approach requires input data, and produces results, similar to the border-design program, BORDER (Strelkoff et al 1996), in which the user specifies, a given set of physical conditions, and a range of interest for the design variables -- for example, a range of furrow flow rates and field lengths. A contour map of performance over this range is then computed utilizing a grid of solution points. The approach is; 1. simulate flow for one strategically placed grid point, 2. adjust Fy, M1, and M2 in the simplified procedure to match simulation results at this one point, and 3. apply the simplified procedure over a range of design conditions with Fy, M1, and M2 from step 2. An example performance contour map is shown in Figure 2. The simulation was performed for the maximum length (800 m) and at an intermediate flow rate (2.5 l/s). The tuning parameters obtained were Fy = 0.71, M1 = 0.92, and M2 = 0.55. Simulations were performed at other points within the grid. Results for Potential Application

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Figure 2. Potential Application Efficiency based on minimum depth equal to required depth (k = 30.1 mm/hra, a = 0.51, n = 0.05, W = 1 m, S0 = 0.002, dreq = 80 mm).

Efficiency matched the simplified procedure to within 1% everywhere except the lower right corner, which differed by 2%. Preliminary analysis suggests that the adjusted simplified procedure provides reasonable results over a moderate range of conditions. How far these results can be extrapolated has yet to be defined.

References ASAE. 1994. Evaluation of irrigation furrows. ASAE EP419.1, ASAE Standards 1994, ASAE, St. Joseph, MI, p 741-746. Clemmens, A.J., Walker, W.R., Fangmeier, D.D., and Hardy, L.A. 1998. Design of Surface Systems, Chapter 14 in R.E. Elliot and M.E. Jensen ed., Design and Operation of Farm Irrigation Systems, ASAE Mono graph, Draft copy. Strelkoff, T. 1977. Algebraic computation of flow in border irrigation. J. Irrig. Drain. Div., Am. Soc. Civ. Eng. 103(1R3). 357-377. Strelkoff, T. 1990. SRFR: A Computer Program for Simulating Flo w in Surface Irrigation Furrows-Basins-Borders, WCL Report #17, U.S. Water Conservation Laborato ry, USDA/ARS, Phoenix, AZ. Strelkoff, T., and A.J. Clemmens. 1994. Dimensional analysis in surface irrigation. Irrig. Sci. 15(2/3):57-82. Strelkoff , T.S., Clemmens, A.J., Schmidt, B.V. and Slosky, E.J. 1996. Border: A Design and Management Aid for Sloping Border Irrigation Systems. Version 1.0. WCL Report #21, U.S. Water Conservation Lab., USDA/ARS, Phx., AZ. 44 p. Published by ASCE, Reston, VI