Journal of Irrigation and Drainage Engineering

The effect of changing the trajectory angle of a medium‐sized irrigation sprinkler operating in windy conditions has been studied using a computersimulation model. The model, which has been verified both in still air and under windy conditions, shows that the trajectory angle that maximizes distance of throw is a function of the wind velocity and varies from 29° in still air to less than 5° in winds greater than 8 m/s. The advantage gained from trajectory angles greater than 25° in still air is quickly overcome by the disadvantages in range reduction and drift in relatively light winds. When choosing the appropriate trajectory angle, consideration should be given to the drop‐size distribution and the wind velocity, because wind drift and range both depend upon drop size and trajectory angle.

A model is developed for simulating the vertical movement of water through a crop's root system. The root‐water flow model is then coupled to a variably‐ saturated flow model via a root extraction term that is a function of the water pressure gradient across the root‐soil interface as well as soil and root parameters. The resulting root‐soil water flow model is a coupled pair of partial differential equations that describe the macroscopic movement of water through a root‐soil system. Rainfall, irrigation, and evaporation are treated as sources of potential soilsurface flux, and transpiration is treated as a source of potential root‐surface flux. Solution of the model is accomplished by using a Galerkin finite element method. The model is verified by comparing simulated and field measured soil‐water content levels. The comparisons show a very good agreement between simulated and measured soil‐water contents. The root extraction distribution, cumulative flow from an underlying water table, and sensitivity of model results to changes in root parameters are also analyzed.

A kinematic‐wave furrow model with spatial variability of infiltration is developed to solve directly for advance times. In addition, infiltration varies with wetted perimeter. During advance, the system of nonlinear equations is solved implicitly for flow area and time step using the double‐sweep technique. During runoff and recession, flow area is found explicitly cell‐by‐cell at each specified time step. Including spatially varying infiltration as well as wetted perimeter effects improves furrow irrigation simulation when compared with the results of previous kinematic‐wave models.

Project‐scale optimal on‐farm designs considering total water availability and also the variability in the on‐farm parameters are obtained using a two‐stage programming approach in a mode of maximizing the net benefits from the project area. This provides the basis for comparing the consequences of projectscale design and operation under modes of volumetric equity and iso‐efficiency. A methodology to subdivide the project area into different distinct portions is developed. A sample application indicates that there could be a wide variation in flow requirements in all the three modes. Variations in net on‐farm benefits under modes of project‐scale optimality and volumetric equity are also large. The sample study indicates that the iso‐efficiency design results in near‐optimal project‐scale returns with uniform unit benefits in the different areas.

A hydrologic balance model has been developed that employs neutron probe readings for soil moisture content coupled with measured amounts of precipitation and irrigation. The major objective of the model is to estimate evapotranspiration over time periods corresponding to the frequency of neutron probe readings. Earlier versions of the model were successfully applied to determine differentials of evapotranspiration over limited horizontal distances in crop water production function field experiments. The current version of the model was specifically developed for application in a regional evapotranspiration experiment requiring model flexibility to respond to a wide range of hydrologic conditions. Example output from the model applied to the regional evapotranspiration experiment is indicated. A scheme for testing parameterization of various components of the hydrologic cycle using the model is presented.

Methods of calculating irrigation project profits are described systematically. The combined effects of irrigation and agricultural technical measures (before and after irrigation) increase production. Therefore, the increased output value should be allocated between the “irrigation” and the “agricultural” sectors. Irrigation project planners are given several allocating methods based on calculating irrigation benefits at home and abroad.

Three stochastic weather models are developed for use with nonpoint‐source pollution simulation models that require sequences of daily precipitation and mean daily temperature. Two simple models have parameters that can be estimated from available secondary data. Both generate temperature and precipitation independently. A third model represents a more sophisticated approach and requires primary data for parameter estimation. A model validation analysis was attempted using three U.S. weather stations. The first two models did not reproduce the higher‐order moments or the tail of the wet‐dry precipitation distribution. All models used normal temperature distributions which did not reproduce the higher‐order moments of the observed temperature distributions. Using historical and generated weather data as input to the Cornell Nutrient Simulation model, annual runoff and percolation, and dissolved nitrogen and phosphorus losses were compared. The third model gave output that was not statistically different from that obtained with the historical weather data; the first two models occasionally gave statistically different values. Using the mean annual losses given by historical weather data as a basis, model errors were less than 20%.

The analytical solution proposed by Rao and Sarma for predicting growth of groundwater mounds resulting from infiltration into bounded aquifers is examined for validity when the aquifer is assumed infinite in size. Rao and Sarma concluded that an aquifer can be assumed infinite when the ratio of corresponding linear dimensions of the aquifer and infiltration surface (A/L) is made arbitrarily large; they used $A/L=50\text{,}$ 60, and 70. Under such conditions mound height at the center should approach a constant value. Contrary to Rao and Sarma's conclusions, the writers find that maximum mound height appears to depend on the relative size of the aquifer in a specific fashion, exhibiting a maximum value when $A/L=200\text{.}$ Above this value predicted mound height gradually drops to zero. In addition, agreement among their solution, the infinite aquifer solutions published by Hantush, and a solution for circular infiltration areas derived by the writers is limited to the case where $A/L=200\text{.}$ In spite of this inconsistency, the equation proposed by Rao and Sarma may be programmed for solution without knowledge of advanced mathematical concepts. For the physical parameters used, their solution is judged to be a relatively quick and easy way to predict maximum mound height, so long as A/L is assigned a value of 200.

Information about future as well as current legal regulation of weather modification is an important element in planning and operating weather modification projects. Government agencies have made and will continue to make legal changes to reflect new societal conditions. Legal regulation of weather modification is being altered in terms of regulatory de‐emphasis, cost sharing, and liability law changes. With regulatory de‐emphasis, weather modification regulation by requiring professional licenses of project operators and permits for modification projects and mandating record keeping and reporting to government agencies has been the norm. The extent of such regulation, however, is diminishing. With cost sharing, weather modification project sponsors who use government funds are being required by law and executive policy to bear a larger share of operational and regulatory costs. Finally, with liability law changes, operators and their sponsors now have less exposure to legal liability than before because legislative tort law reform is changing substantive and procedural liability law and the law of damages. This should affect future liability insurance availability, coverage, and cost.

Dupuit's formula is generalized to define the phreatic (free) surface for a porour media that consisted of vertical layers of different thickness and hydraulic properties. The approach results in transforming the heterogeneous porous media to a homogeneous one.