Errors of kinematic-wave and diffusion-wave approximations for time-independent flows in infiltrating channels

Time-independent (or steady-state) cases of channel flow were treated and errors of the kinematic-wave and diffusion-wave approximations derived for finite flow at the upstream end. The diffusion-wave approximation was found to be in excellent agreement with the dynamic wave representation, with error magnitudes of 0.2% for values of KF ₀ ² 7.5, where K is the kinematic-wave number and f ₀ is the Froude number. Even for small values of KF ₀ ² (e.g., KF ₀ ² =0.75), the errors were typically in the range of 1.3 to 3.7%. The approximate analytical diffusion-wave solution performed poorly with error magnitudes greater than 30% even for large values of KF ₀ ² . The kinematic-wave approximation was also found to be in good agreement with the dynamic-wave representation with errors of about 1.2% for KF ₀ ² =7.5 and varying from 15 to 44% for KF ₀ ² =0.75.     

A mathematical model for border irrigation II. Vertical and horizontal recession phases

Summary This paper, second in a series of three, develops a mathematical model, using the volume balance approach, to simulate vertical and horizontal recession of border irrigation. An equation is proposed for computing Manning's roughness factor N in both laminar and transitional flow regimes in recession phases. The model has four parameters which can be determined experimentally. Experimental data from ten vegetated as well as nonvegetated borders were used to verify the model. Average difference (AD) between calculated and observed vertical recession times was less than 4.4 min, and between calculated and observed horizontal recession times less than 4.6 min for the ten experimental data sets. Average relative error (ARE) in computed horizontal recession was less than 13% for these data sets. The model was found to be especially accurate for Reynold's number between 1,800 and 2,500.     

Modeling soil water dynamics in a drip-irrigated intercropping field under plastic mulch

Intercropping, drip irrigation, and the use of plastic mulch are important management practices, which can, when utilized simultaneously, increase crop production and save irrigation water. Investigating soil water dynamics in the root zone of the intercropping field under such conditions is essential in order to understand the combined effects of these practices and to promote their wider use. However, not much work has been done to investigate soil water dynamics in the root zone of drip-irrigated, strip intercropping fields under plastic mulch. Three field experiments with different irrigation treatments (high T1, moderate T2, and low T3) were conducted to evaluate soil water contents (SWC) at different locations, for different irrigation treatments, and with respect to dripper lines and plants (corn and tomatoes). Experimental data were then used to calibrate the HYDRUS (2D/3D) model. Comparison between experimental data and model simulations showed that HYDRUS (2D/3D) described different irrigation events and SWC in the root zone well, with average relative errors of 10.8, 9.5, and 11.6 % for irrigation treatments T1, T2, and T3, respectively, and with corresponding root mean square errors of 0.043, 0.035, and 0.040 cm³ cm^?3, respectively. The results showed that the SWC in the shallow root zone (0–40 cm) was lower under non-mulched locations than under mulched locations, irrespective of the irrigation treatment, while no significant differences in the SWC were observed in the deeper root zone (40–100 cm). The SWC in the shallow root zone was significantly higher for the high irrigation treatment (T1) than for the low irrigation treatment, while, again, no differences were observed in the deeper root zone. Simulations of two-dimensional SWC distributions revealed that the low irrigation treatment (T3) produced serious severe water stress (with SWCs near the wilting point) in the 30–40 cm part of the root zone, and that using separate drip emitter lines for each crop is well suited for producing the optimal soil water distribution pattern in the root zone of the intercropping field. The results of this study can be very useful in designing an optimal irrigation plan for intercropped fields.     

Surface drainage requirement of crops: Application of a piecewise linear model for evaluating submergence tolerance

Crop tolerance to land submergence is an important criterion for designing a surface drainage system for agricultural lands. This paper collates the available data from various places in India related to the studies on the submergence tolerance of crops. The paper hypothesizes that a piecewise linear model could be used to describe crop response to land submergence. According to this hypothesis, there would be no yield decline for a few initial days of submergence. If submergence continues beyond this period then there would be linear decline in yield. The unknown parameters in the model are: optimum yield, threshold time and the slope which represents the per cent yield reduction per day of additional submergence beyond the threshold.Data in respect of wheat, pigeon peas, cowpeas, pearlmillet, maize and groundnuts indicate that the model describes the data well, although in many cases the threshold is 0.0. The yield reduction varies from 5.3 to 23.2% for each day of submergence beyond the threshold. It appears that to allow for more than 1–2 days of submergence will result in more than 10% reducation in yield of dryfoot crops. For the maize crop, the seedling stage is the most sensitive stage followed by the silking stage. The grain formation stage is the least sensitive, although even at this stage the threshold is 0.0 and yield reduction is 9.3% for each day of submergence beyond the threshold. The data for 9 test crops from Texas and Venezuela were well described by the model. It is concluded that the piecewise linear model is a useful tool for describing submergence tolerance of crops and for working out surface drainage requirements for a given level of yield reduction. Frequency analysis of the daily rainfall data from some selected locations indicates that there is every likelihood of submergence at most of the stations. It is suggested that there is an urgent need for developing wet farming techniques analogous to dry farming techniques.     

An improved Lewis-Milne equation for the advance phase of border irrigation

Summary The Lewis-Milne (LM) equation has been widely applied for design of border irrigation systems. This equation is based on the concept of mass conservation while the momentum balance is replaced by the assumption of a constant surface water depth. Although this constant water depth depends on the inflow rate, slope and roughness of the infiltrating surface, no explicit relation has been derived for its estimation. Assuming negligible border slope, the present study theoretically treats the constant depth in the LM equation by utilizing the simple dam-break wave solution along with boundary layer theory. The wave front is analyzed separately from the rest of the advancing water by considering both friction and infiltration effects on the momentum balance. The resulting equations in their general form are too complicated for closed-form solutions. Solutions are therefore given for specialized cases and the mean depth of flow is presented as a function of the initial water depth at the inlet, the surface roughness and the rate of infiltration. The solution is calibrated and tested using experimental data.Abbreviations a (t) advance length - c mean depth in LM equation - c _f friction factor - c _h Chezy's friction coefficient - g acceleration due to gravity - h(x, t) water depth - h ₀ water depth at the upstream end - i() rate of infiltration - f(x, t) discharge - q₀ constant inflow discharge - S _f energy loss gradient or frictional slope - S₀ bed slope - t time - u(x, t) mean velocity along the water depth - x distance - Y() cumulative infiltration - (t) distance separating two flow regions - infiltration opportunity time     

Sensitivity analysis of optimal operation of irrigation supply systems with water quality considerations

A model for optimal operation of water supply/irrigation systems of various water quality sources, with treatment plants, multiple water quality conservative factors, and dilution junctions is presented. The objective function includes water cost at the sources, water conveyance costs which account for the hydraulics of the network indirectly, water treatment cost, and yield reduction costs of irrigated crops due to irrigation with poor quality water. The model can be used for systems with supply by canals as well as pipes, which serve both drinking water demands of urban/rural consumers and field irrigation requirements. The general nonlinear optimization problem has been simplified by decomposing it to a problem with linear constraints and nonlinear objective function. This problem is solved using the projected gradient method. The method is demonstrated for a regional water supply system in southern Israel that contains 39 pipes, 37 nodes, 11 sources, 10 agricultural consumers, and 4 domestic consumers. The optimal operation solution is described by discharge and salinity values for all pipes of the network. Sensitivity of the optimal solution to changes in the parameters is examined. The solution was found to be sensitive to the upper limit on drinking water quality, with total cost being reduced by 5% as the upper limit increases from 260 to 600 mg Cl l^–1. The effect of income from unit crop yield is more pronounced. An increase of income by a factor of 20 results in an increase of the total cost by a factor of 3, thus encouraging more use of fresh water as long as the marginal cost of water supply is smaller than the marginal decrease in yield loss. The effect of conveyance cost becomes more pronounced as its cost increases. An increase by a factor of 100 results in an increase of the total cost by about 14%. The network studied has a long pipe that connects two distinct parts of the network and permits the supply of fresh water from one part to the other. Increasing the maximum permitted discharge in this pipe from 0 to 200 m³ h^–1 reduces the total cost by 11%. Increasing the maximum discharge at one of the sources from 90 to 300 m³ h^–1 reduces the total cost by about 8%.     

Hydraulic-hydrological simulations of canal-command for irrigation water management

A modelling system that combines the hydraulic simulations of the canal and hydrological simulations of the irrigated command is introduced. It uses MIKE 11 and MIKE SHE, two well-established modelling systems, for the hydraulic and hydrological simulations respectively. In addition, it also has an irrigation scheduling module and a crop growth module. The modelling system is applied to the Mahanadi Reservoir Irrigation Scheme, a large irrigation project in Central India. The results show that presently a significant amount of water is wasted in the command during the monsoon season. It is demonstrated that the minimization of this wastage could lead to a substantial crop production in the subsequent dry season. Furthermore, the simulations illustrate the versatility of the modelling system for planning and analysing the various aspects of an irrigation project.     

Past, present and future criteria to breed crops for water-limited environments in West Africa

Asia's Green Revolution of the 1960s and 1970s has largely bypassed West Africa, and “modern” (high-yielding, input responsive) germplasm for staple crops has found comparatively little adoption, except for systems that are have good access to markets and sufficient water resources. It is unlikely, however, that breeding objectives conserving traditional crop characteristics as found in extensive systems would have been more successful. The authors identify systems caught in the agricultural transition from subsistence to intensified, market-oriented production as the most important target for crop improvement, and provide examples of new breeding objectives for cowpea, sorghum and upland rice. In each of these cases, breeders, with the help of physiologists, have developed innovative plant-type concepts that combine improved yield potential and input responsiveness with specific traditional crop characteristics that remain essential during the agricultural transition. In the case of cowpea, dual-purpose varieties were developed that produce a good grain yield due to an erect plant habit, then produce new leaves enabling a second harvest of green foliage. For upland rice systems that are limited by labour (mainly needed to control weeds that abound due to shortened fallow periods), a weed competitive plant type was developed from Oryza sativa × Oryza glaberrima crosses. Lastly, sorghum breeders who had previously deselected photoperiod sensitivity are now re-inserting sensitivity into plants having “modern” architecture, in order to allow for flexible sowing dates while maintaining an agro-ecologically optimal time of flowering near the end of the wet season. The ecophysiological basis of these plant types, their place in current and future cropping systems, as well as the problem of under-funding for their realisation, are discussed.     

“WaterMan”: an on-farm water management game with heuristic capabilities

A modern computer-based simulation tool (WaterMan) in the form of a game for on-farm water management was developed for application in training events for farmers, students, and irrigators. The WaterMan game utilizes an interactive framework, thereby allowing the user to develop scenarios and test alternatives in a convenient, risk-free environment. It includes a comprehensive soil water and salt balance calculation algorithm. It also employs heuristic capabilities for modeling all of the important aspects of on-farm water management, and to provide quantitative performance evaluations and practical water management advice to the trainees. Random events (both favorable and unfavorable) and different strategic decisions are included in the game for more realism and to provide an appropriate level of challenge according to player performance. Thus, the ability to anticipate the player skill level, and to reply with random events appropriate to the anticipated level, is provided by the heuristic capabilities used in the software. These heuristic features were developed based on a combination of two artificial intelligence approaches: (1) a pattern recognition approach and (2) reinforcement learning based on a Markov decision processes approach, specifically the Q-learning method. These two approaches were combined in a new way to account for the difference in the effect of actions taken by the player and action taken by the system in the game world. The reward function for the Q-learning method was modified to reflect the suggested classification of the WaterMan game as what is referred to as a partially competitive and partially cooperative game.