Journal of Irrigation and Drainage Engineering

Laplace transformation, integral, and numerical solution methods to the Lewis and Milne surface irrigation volume balance equation are presented and discussed. Six formulations of the volume balance equation are presented. These consist of combinations of one of three infiltration equation (Kostiakov, extended Kostiakov, or SCS) and one of two advance equations (power or SCS). A simple and direct method based on the Kostiakov infiltration equation and the power advance equation is suggested for field use in determining infiltration from advance data and for calculations of irrigation efficiencies. This method and formulation accurately predicted the field and laboratory runoff data analyzed in Part II of this paper.

Laplace transformation, integral, and numerical solutions and six empirical formulations to the Lewis and Milne surface irrigation volume balance equation were evaluated using field and laboratory data. These formulations and the proposed solution methods are presented in Part I of this paper. The field data were from published experiments, and the laboratory data were obtained from a 61‐m model border with a computer‐controlled infiltrating bed which could simulate a wide range of infiltration characteristics. The results indicated that a simple and direct method of analysis based on the Kostiakov infiltration equation and the power advance equation satisfactorily predicted observed runoff volumes. Furthermore, this method accurately determined the infiltration characteristics that were simulated by the model border.

The general problem of advance and recession of irrigation water on an initially dry surface is formulated using the kinematic‐wave theory. In this part of the study, the infiltration rate is assumed constant in time and space. Analytical solutions for the advance and recession are used to derive expressions for volumes in surface storage and cumulative volumes of infiltration and runoff during all phases of one irrigation cycle. This comprehensive analytical model is then tested using field data. Its usefulness and limitations are discussed.

A variable infiltration rate model for surface irrigation is developed. The derivations and the forms of the equations used are similar to the case where the infiltration rate is constant. A mean infiltration rate is assumed to vary from $t=0$ to $t=T_{\mathrm{co}}\text{.}$ Expressions for the mean infiltration rate are derived for the advance and storage phases using Horton, Kostiakov, and the modified Kostiakov infiltration equations. The model is then tested using field data.

The characteristics of square‐edged and round‐nosed, rectangular, broad‐crested weirs are studied under free‐flow and submergedflow conditions. The discharge coefficient, $C_d\text{,}$ of a weir having height P and length L is found to be a function of the upstream head, H, causing flow and the radius, R, of the upstream top corner. For a given head, under free‐flow conditions, a semiempirical relationship between $C_d\text{,}$ H/P, and R/P is derived using the momentum relationships. For the square‐edged weir, the effect of nonhydrostatic distribution of pressure is taken into account in the formulation of the momentum equation. In addition, for the round‐nosed weir, new relations are developed to supplement the existing results for square‐edged weirs. Experimental data are presented to validate the proposed dependence of $C_d$ on H/P with R/P as the group parameter. Under drowned‐flow conditions, the submergence limit for a broad‐crested weir varies with the ratios $H/P$ and $R/P\text{.}$ The flow‐reduction factor for a given submergence is dependent on the degree of rounding of the upstream top corner.

This paper presents a method for describing and evaluating some of the major factors that cause nonuniformity in surface irrigation systems. Methods including the following are presented for statistically combining these effects: variations in opportunity times (e.g., caused by nonparallel advance and recession curves), variations in soil infiltration properties, variations in land grading, and variations in advance rates. A simulation model is used to test the derived equations for a typical example.

A mathematical model, based on volume balance and Muskingum type storage‐discharge relation, is presented for design and evaluation of furrow irrigation systems. Three field data sets from Colorado farms are used to test the model. The Muskingum model is simple and found to effectively simulate the hydraulics of every phase of furrow irrigation. The relative error of simulated results is less than 7% for predicted advance, less than 4.7% for outflow during storage phase, less than 5% for recession, and less than 7% for opportunity time. More testing is, however, necessary to define limitations and strengths of the model, and to enable regionalization of the model parameters.

Two simple models are developed to predict the advance rate of flow in furrows. The first model is developed using a modified version of Muskingum flood‐routing techniques. The second model is developed by assuming that the flow is approximately steady within each furrow reach. Both models use power functions to describe the surface and subsurface profiles. The models are compared to observed furrow data on three different farms. For furrows that quickly reach steady‐state infiltration and have relatively high infiltration losses, both models predict the advance times reasonably well. For furrows that gradually reach steady‐state infiltration and have relatively low infiltration losses, the Muskingum model predicts observed values with good accuracy, whereas the steady flow‐rate model greatly overpredicted the advance rate.

A set of design functions that relate system performance to design variables in graded border irrigation was developed and verified. A dimensional analysis approach is used to combine the independent variables into a reduced number of independent dimensionless parameters. A computer simulation model is used to obtain the variation of the dependent performance parameters with the independent dimensionless parameters. Dimensional analysis techniques are used to obtain functional relationships between each of the dependent parameters and the independent dimensionless parameters. Field data and the Soil Conservation Service's design charts were used to verify the developed quality parameter functions.

Several methods for measuring the rate of infiltration in a volcanic ash soil are compared on the basis of field measurements. Methods that use stagnant water give lower values of soil infiltration rate than those that use flowing water. The performances of the Kostiakov and the modified Kostiakov infiltration equations are analyzed for seven methods. These equations closely match field data collected with each technique used. Functional relationships among the infiltration rate equations are also obtained for each method of infiltration.

The difference in sugarcane evapotranspiration (ET), sugarcane yield, and soil moisture content between drip irrigation and subirrigation, are compared using four lysimeters, each 5.5‐m diameter by 1.2‐m deep. Plant cane with two ratoons are grown. The results show that the soil moisture content in the profile with the subirrigation system is much greater than with the drip irrigation system. Before canopy closure of the plant cane, ET from drip irrigation is significantly lower than from subirrigation; whereas, after canopy closure for the two ratoons, the ET from drip irrigation is significantly higher than from subirrigation. Cane yield from drip irrigation is significantly higher than from subirrigation. About 95 kg and 109 kg of water are required to produce 1 kg of cane yield for drip irrigation and subirrigation, respectively.

A new concept in surface irrigation efficiency, termed deficit/excess efficiency, is presented; it has potential for use as an objective function for optimization purposes in the design and operation of on‐farm irrigation systems. This concept, which yields a unimodal function of the volume of water applied, combines selected characteristics of application efficiency, storage efficiency, and Christiansen's uniformity coefficient. Under normal conditions, small applications of water produce high application efficiency, but a low uniformity coefficient and storage efficiency; conversely, large applications produce a high uniformity coefficient and storage efficiency, but low application efficiency. Thus, none of these latter terms are unimodal functions of the volume of water applied. The proposed deficit/excess efficiency can be modified according to management criteria to assign a benefit or penalty to the amount of runoff, deep percolation, and under irrigation in the irrigated field. Algebraic relationships between deficit/excess efficiency and other efficiency terms are presented. A field example comparing this efficiency term with others is provided.

An adjusted F factor to compute pressure head loss in pipes having multiple, equally spaced outlets is derived for any given distance from the first outlet to the beginning of the pipe. The proposed factor is dependent on the number of outlets and is expressed as a function of the Christiansen's F factor. It may be useful to irrigation engineers to estimate friction loss in sprinkle and trickle irrigation laterals and manifolds, as well as gated pipes.

Some weather simulation procedures require mean values of potential evapotranspiration (ETP) and the standard deviations in ETP. For purposes of irrigation planning and design it may be desirable to know the probable deviations from mean values of ETP. Various crop production or crop yield models have been developed that require input of daily measurements of climate. A weather simulation procedure utilizing a monthly climatic data base can be substituted for the daily climatic data to produce very comparable results. The weather simulation procedure recommended requires the standard deviation of ETP. A series of monthly mean values of maximum and minimum temperatures provides the required data for estimating mean ETP and the standard deviation. If only long‐term mean maximum and minimum temperatures and the mean temperatures for a series of years are available, the standard deviation of mean temperature provides a means for making an estimate of the standard deviation in ETP. The relationship is influenced by latitude and elevation. Relationships are presented for use in estimating the standard deviation of ETP.

A friction correction factor (F_cp) for use in the estimation of friction loss in a center-pivot irrigation system lateral is derived. The results obtained using the F_cp are compared with the results obtained using other methods of estimating friction loss. A significant difference in the estimated friction loss was observed between this coefficient and the one derived by Christiansen for linear-move sprinkler systems.

The submerged flow discharge characteristics of throatless flumes are derived on the basis of a semi‐empirical analysis. A pressure correction factor is determined experimentally to account for the non‐hydrostatic pressure distribution at the throat section of the flume which acts as a control. This factor is incorporated in the governing equation which is developed on the basis of momentum principles. Both the present and the previously published experimental data are used to validate the expressions developed for the discharge passing through the flume. The data are presented as design charts which can be used to determine the discharge passing through the flume for free flow and submerged flow conditions. Under free flow conditions, considerable head losses occur in the expanding section of the flume. Consequently, if conservation of head is an important criteria, the use of the throatless flume under submerged flow conditions is recommended.

Small watershed storm runoff in the southwestern United States is dominated by intense, short-duration convective rains of limited areal extent. Most commonly, flood peak estimates are based on rainfall predictions found in the National Oceanic and Atmospheric Administration (NOAA) Atlas 2, a precipitation-frequency atlas for the Western United States. Records of short-duration rainfall (5 to 30 min. duration) from a dense network of recording rain gauges in southeastern Arizona indicate that flood peaks based on NOAA Atlas 2 for less frequent events (50-yr. and 100-yr. frequencies) for small watersheds are underestimated.