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This paper presents a simple and quick method for estimating furrow infiltration using a single advance point based on the volume balance equation. The furrow infiltration and water front advance along the furrow are assumed to follow the modified Kostiakov infiltration and power advance equations, respectively. The volume balance equation, including these equations, is simplified to a function containing two parameters, i.e., the exponents of power advance and Kostiakov infiltration equation (with a prior-known basic infiltration rate). These parameters are estimated by minimizing the function to zero using a quasi-Newton search algorithm, provided with Excel Solver. The estimated exponents are used to determine the Kostiakov infiltration parameters. The proposed one-point method is tested with seven independent furrow irrigation evaluation data sets and the estimated cumulative infiltration is compared with the observed counterparts. Performance of the proposed method was evaluated using the root-mean-square error and index of agreement ([I.sub.a]). The results show that the proposed one-point method estimated cumulative infiltration is closer to the observed; the method performed as good as Valiantzas' method. Shepard's method did not perform well for the tested data sets. The algorithm and the results of the proposed method reveal that the proposed method can be used as a tool for quick estimation of furrow infiltration using a single advance point. DOI: 10.1061/(ASCE)0733-9437(2008)134:6(788) CE Database subject headings: Furrow irrigation; Infiltration; Simulation models.

This study investigates the utility of artificial neural networks (ANNs) for estimation of daily grass reference crop evapotranspiration (ETo) and compares the performance of ANNs with the conventional method (Penman-Monteith) used to estimate ETo. Several issues associated with the use of ANNs are examined, including different learning methods, number of processing elements in the hidden layer(s), and the number of hidden layers. Three learning methods, namely, the standard back-propagation with learning rates of 0.2 and 0.8, and backpropagation with momentum were considered. The best ANN architecture for estimation of daily ETo was obtained for two different data sets (Sets 1 and 2) for Davis, Calif. Using data of Set 1, the networks were trained with daily climatic data (solar radiation, maximum and minimum temperature, maximum and minimum relative humidity, and wind speed) as input and the Penman-Monteith (PM) estimated ETo as output. The best ANN architecture was selected on the basis of weighted standard error of estimate (WSEE) and minimal ANN architecture. The ANN architecture of 6-7-1, (six, seven, and one neuron(s) in the input, hidden, and output layers, respectively) gave the minimum WSEE (less than 0.3 mm/day) for all learning methods. This value was lower than the WSEE (0.74 mm/day) between the PM method and lysimeter measured ETo as reported by Jensen et al. in 1990. Similarly, ANNs were trained, validated, and tested using the lysimeter measured ETo and corresponding climatic data (Set 2). Again, all learning methods gave less WSEE (less than 0.60 mm/day) as compared to the PM method (0.97 mm/day). Based on these results, it can be concluded that the ANN can predict ETo better than the conventional method (PM) for Davis. CE Database keywords: Neural networks; Evapotranspiration; Wave propagation.

Evapotranspiration (ET) is a major component of the hydrologic cycle and its accurate estimation is essential for hydrological studies. In the past, various estimation methods have been developed for different climatological data, and the accuracy of these methods varies with climatic conditions. Therefore, a user-friendly decision support system (DSS) was developed for estimation of the reference value, ETo. For given data availability and climatic conditions, the developed model estimates ETo with the best available method out of the nine methods. The ETo estimation methods are based on combination theory, radiation, temperature, and pan evaporation; the model selects the best ETo estimation method based on ASCE rankings. In order to evaluate the DSS, various tests were conducted with different data availability conditions for five climatological stations (Davis, Bellary, Kharagpur, Jagdalpur, and Bombay). The decisions made by the model exactly matched the ASCE rankings. For the three climatic stations Davis, Jagdalpur, and Kharagpur, ETo values were estimated by all applicable methods using the user defined options menu and were compared with the Penman-Monteith ETo estimates, which were taken as the standard. Based on the weighted average standard error of the estimate, the Hargreaves and FAO-24 Blaney-Criddle methods ranked first, respectively, for the Davis and Jagdalpur stations. The 1982 Kimberly-Penman method ranked first for Kharagpur. The DSS model is a user-friendly tool for estimating ETo under different data availability and climatic conditions. CE Database keywords: Evapotranspiration; Decision support systems; Hydrologic models.

A zero-inertia furrow irrigation model with specified space solution was used to investigate the effects of variability in furrow inflow rate and spatial variability in infiltration, geometry, and roughness on end-of-furrow advance, average infiltrated depth, and Christiansen's and distribution uniformities. Extensive field-gathered infiltration, geometry, and roughness data were used as input to the zero-inertia model. Simulations were performed on a single furrow as well as fieldwide. Variable furrow inflow was incorporated into the fieldwide analysis. Model simulations were evaluated to determine the importance to irrigation performance of variability in each input variable. Variability of furrow physical characteristics, in decreasing order of their relative impact on furrow irrigation performance, were furrow inflow rate, infiltration, geometry, and roughness for the conditions studied.

Irrigation districts are made up of multiple units that are hydrologically connected. If the irrigation units are arranged in parallel, an improvement of the on-field irrigation consumptive use coefficient (ICUC) has more impact on the district ICUC than if the irrigation units are arranged in series. But water quality degrades with the number of reuses. Knowing the topological relations of the irrigation units, the water use in an irrigation district may be analyzed at high and low spatial resolution. A site-specific analysis was conducted on a complex irrigation district (Tulelake Irrigation District) located in a valuable ecosystem in Northern California. Simulated applied water and drainage were greater for areas having high water-consuming crops. The estimated concentration of salts was higher in the center and southern areas. Concentration was higher for soils high in organic matter and for areas where water was reused several times. For comparison purposes, even a complex irrigation district may be reduced to an equivalent number of command areas arranged perfectly in series.

Furrow irrigation performance is affected by spatial variability of infiltration; thus, its characterization is essential for accurate performance evaluation. A time-series modeling approach was used to characterize the spatial and temporal correlation structure of field-measured infiltration data. The time-series analysis indicated minimal spatial correlation of infiltration characteristics along the furrow for the space intervals used (5 m). The time-series analysis led to a strategy by which relationships between infiltration characteristics at short- and long-intake opportunity times for a limited number of infiltration tests could be used to 'extend' infiltration information gathered by doing shorter duration tests at other furrow locations.

Several different finite-element grid configurations were evaluated for use in the numerical approximation of steady and transient flow to a single drain. By comparing the numerically simulated drain flow rates and head distributions with analytic values, a nested configuration was found to be appropriate for an effective drain radius of 0.01 m, and a square configuration was suitable for an effective drain radius of 0.05 m. Using an analytic solution, a method was developed to determine the distance of influence of a drain as a function of its effective radius and the geometry of its flow domain. The distance of influence was found to be independent of material type. An appropriate between-drain grid spacing was selected for the numerical simulation of multiple drains by increasing the grid mesh spacing outside the distance of influence. The position of the water table and drain flow rate with time were used to evaluate the between-drain grid spacing for transient variably saturated flow. Grid Peclet and Courant numbers, together with the shape of the solute advance front, were used to evaluate the suitability of the selected single drain configuration and between-drain grid spacing for solute transport. The resulting finite-element grid configuration for single and multiple drains ensures a stable efficient numerical solution, and it has applicability to numerical modeling of multiple subsurface drains.

The effects of partial infiltration and furrow geometry information on furrow irrigation design and economic return to water were quantified on a single furrow (reference furrow) and field-wide (10-furrow set) basis using a kinematic-wave furrow irrigation model in conjunction with an economic optimization model. A furrow sampled at 10 locations was assumed to represent the actual field condition. Subsamples were randomly drawn from the 10 samples and return to water was maximized. These suboptimal designs were applied to the actual furrows and monetary loss due to lack of information was simulated. The monetary loss was less for furrow irrigation designs having high inflow rates ($0.38/furrow, $17/ha) than for the low inflow rates ($2.27/furrow, $100/ha). Average loss decreased from $31/ha ($0.71/furrow) to $0/ha in the case of the reference furrow, and from $1.0/furrow ($44/ha) to $0.3/furrow ($13/ha) in the case of the 10-furrow set for the samples sizes of 1 and 10, respectively.

Assessment of the surface storage is of great importance in hydrological surface irrigation. For the Horton infiltration law used in the ALIVE model (Advanced LInear VElocity), an accurate measurement of surface storage is the key to successfully predicting infiltration. For the Kostiakov function, the conclusion is paradoxical due to the fact that this law systematically underpredicts infiltration for times greater than the time used for fitting. Measuring surface storage accurately is cumbersome, and, consequently, most of the models use empirical formulas, which are reasonable, if not always precise. The constant mean cross-section assumption that is implied in hydrological models is discussed from a practical point of view. A representation of nonuniform storage distribution is presented through the ALIVE approach, and the feasibility of an inverse solution is discussed. Finally, field records and numerical tests indicate that if the variation of the cross-section remains low (less than half or double the mean) and is randomly distributed the constant mean cross-section assumption is acceptable. With large variations in the flow cross section, the error is lumped with variation in infiltration characteristics. Low variations that are not randomly distributed can affect the infiltration evaluation process. Models using the Kostiakov function are much more sensitive to this phenomenon than the ALIVE model, which uses the Horton law. The reason is likely that the ALIVE model is based on the analysis of the advance rate as a function of distance x[prime](x) rather than advance time at given location [t.sub.a](x).

A seasonal furrow irrigation model was constructed from soil moisture, kinematic-wave hydraulic, and economic optimization models to study the effects of heterogeneity in water balance, soil water holding properties and rooting depth, and infiltration functions on furrow irrigation design (flow rate and cutoff time), bean yield, and net return to water. Irrigation designs achieving nearly 100% irrigation adequacies were unchanged by heterogeneity in water balance, soil water properties, and rooting depth, but both bean yield and net return to water decreased with increasing heterogeneity. Irrigation designs were sensitive to infiltration characteristics and to irrigation interval. At a given irrigation interval, bean yield was insensitive to infiltration characteristics but consistently decreased with increasing irrigation interval. Net return to water was less for spatially variable infiltration functions as compared to homogeneous infiltration conditions. Using mean evapotranspiration (ET) of a grass reference crop (ETo) resulted in slightly higher bean yield and net return to water as compared to observed ETo (1992 season values of grass reference crop ET). Spatial and temporal variability in infiltration gave the same optimal irrigation interval (10 d) under both ETo conditions for the chosen irrigation criteria (80% irrigation adequacy at cutoff time). Both ETo conditions led to essentially the same design inflow rates. Errors in inflow volume were less than 12 and 3.5%, respectively, for individual irrigations and on a seasonal basis. Irrigation scheduling and surface irrigation design can be forecast at the beginning of the growing season for the conditions studied using historical mean ETo if spatial and temporal variability of infiltration are considered.

A seasonal furrow irrigation model consisting of submodels to predict irrigation schedule (water balance), irrigation design (surface irrigation hydraulics), and crop yield (yield function) under spatially and temporally variable conditions was developed and verified with the field data. The model was used to predict irrigation performance for each irrigation event during the season, soil moisture before each irrigation, seasonal evapotranspiration (ET), and bean yield along the furrow at 10-m intervals. In addition, measured inputs along the furrow, including heterogeneous infiltration, soil moisture, and yield were used in conjunction with the model to estimate mean (17.3%) and variation in available water-holding capacity (AWC) (15.4%-19.8%). Variation in crop yield represents an integrated effect of variability in infiltration, soil water characteristics, root depth, soil fertility, microclimate, fertilizer and pesticide applications, plants, and disease. Using the calibrated model, nearly 88% of the variance in ET estimated with the yield function was explained by simulated variation in infiltration characteristics, soil water-holding capacity, and root depth. By assuming homogeneous infiltration characteristics, soil water properties, and root depth, the average absolute error in seasonal ET increased by only 0.6 cm but the variance explained decreased to 30%. Although in absolute terms the impact of heterogeneity seems negligible, Raghuwanshi (1994) showed that heterogeneity strongly affected the optimal flow rate and irrigation time as well as net returns to water.

One of the basic assumptions of the hydrological volume balance models in surface irrigation implies that furrow inflow instantaneously increases to a constant rate: the step-flow condition. Unfortunately this assumption is not always met in the field. Inflow variation is mainly due to the operations required to switch from one set to another, even with an automated furrow irrigation system such as gated pipe. In that regard, siphons are less sensitive to the operations and may be generally considered as a step-flow application system. Furthermore, the presence of a flume at the upstream end of the furrow can also perturb flow. The resulting gradual increase in flow reduces the stream advance rate at the beginning of the run. However, we demonstrate that later in the advance phase the velocity converges to the standard step-flow solution. Generally, advance-phase evaluation models incorrectly attribute the front slowdown to a very high infiltration rate. Two models were compared. The first, the Elliott and Walker model limited to the advance phase, identifies a Kostiakov-Lewis infiltration function with the constant term of infiltration set equal to zero. The second, the advance linear velocity (ALIVE) model, identifies a Horton function from the analysis of the advance rate. This study, based on analytical developments and on 72 furrow irrigation events, shows that the Elliott and Walker model is influenced by a non - step-inflow variation and underpredicts the infiltration amount. In contrast, the ALIVE model proposed by the writers is not as sensitive to the initial behavior of the flow, because it uses two-term rate functions for advance and infiltration.

A flow-balance equation of surface irrigation is used to solve, section by section, the advance problem on heterogeneous soils. The advance-linear-velocity (ALIVE) solution as a function of time is a sum of exponential terms. Within a section, the properties are uniform, and two linear relationships between the advance rate x prime(t) and the distance x(t) result. The inverse problem is solved step by step, identifying and Horton infiltration law of the studied section from the record of the velocity and the knowledge of the infiltration in the previous sections. Theoretical examples and field experiments are compared. When applying a standard evaluation approach, assuming a uniform infiltration function to an heterogeneous soil misleading results can occur. Perturbations in the advance rate can lead to an incorrect infiltration function when using either the standard ALIVE or Kostiakov-based hydrologic models. However, a nonstandard ALIVE procedure is feasible since the distinction between the sections having different infiltration properties can be detected. To apply the velocity analysis, a high density of advance points is required.

The reliability of furrow-infiltration parameters computed from advance measurements was analyzed. Lumped parameters were obtained using the least-squares approach. The objective function was formulated using advance time and velocity observations as a function of distance. Predicted values were calculated with a finite difference hydrodynamic model with wetted perimeter-dependent infiltration. The Extended Kostiakov equation was used to describe infiltration-rate variation with time. Reliability was examined by comparing recorded total intake and runoff with values predicted with the single average parameters. Results showed that reliability of coefficients depends on the relationship between infiltration variability, furrow length, and inflow rate. In particular, relatively short irrigation times hampered the identification of the steady infiltration rate. Spatial trends in infiltration rates affected the reliability of parameters as well. The magnitude and nature of the resulting prediction errors was found to be dependent on the direction of the trend relative to the flow direction. In general, velocities appeared to provide better estimates of average infiltration characteristics than advance times but weighted least squares may be required to compute the parameters from field data.

This paper analyzes the convergence of a numerical model for the quantification of lumped furrow infiltration parameters. The model minimizes the squared difference of observed and model-predicted advance times as a function of distance. An alternative objective function was formulated in terms of velocity of the advancing wave. Predicted values were obtained with a hydrodynamic irrigation model with wetted-perimeter-dependent infiltration. Solutions were computed with the Marquardt method. The three parameters of the empirical extended Kostiakov equation were estimated when nonuniformity of infiltration was the only source of variability in the advance curve. Faster convergence and larger radius of convergence resulted from fitting velocities rather than advance times. Measurement errors and system perturbations impeded the simultaneous identification of three parameters, while computation of two coefficients from highly variable velocities required the application of weighted least squares. Similar parameters were obtained from few or many observations, but convergence improved with smaller data sets.

The computation of wetted-perimeter-dependent intake in a furrow irrigation simulation model using an empirical infiltration formula was examined. Different formulations were applied under increasing and decreasing depth of flow (and wetted-perimeter) conditions. Four computational methods were compared for the former condition and only one was tested for the latter. The merit of the procedures was evaluated in relation to the performance of a finite difference unsteady surface flow model. The hydraulic model was developed using fixed spatial increments and variable time steps and solved with a shooting technique. Differences in advance trajectory resulted from application of each formulation, and numerical accuracy was also different with each computational method. Convergence of the shooting solution was obtained with all infiltration formulas during the advance phase, but there were noticeable differences in convergence rate. Only one of the formulas provided consistent results during storage and recession calculations. Numerical instability resulted as well from the application of the procedures with limited convergence.

Infiltration was measured with a newly developed flow-through infiltrometer at 20-27 sites in a 21 ha (52-acre) cotton field in the northern region of the San Joaquin Valley of California. The results were comparable with infiltration measured with a neutron probe. The infiltrometer allowed water to flow through the infiltrometer when a rate test was not being conducted. Furthermore, the water level and quality inside the infiltrometer was the same as the water flowing past in the remainder of the furrow. Variability contributed by soil infiltration characteristics and intake opportunity time was quantified for preirrigation as well as for three postplant irrigations. The mean and variability of infiltration were greater for the preplant than the postplant irrigations, and soil variability contributed more to total infiltration variability than did the variability in intake opportunity time. Because the infiltration pattern was temporally correlated between postplant irrigations, representative sites rather than a complete field interrogation could be used to estimate mean and variability of infiltration.

A hydrodynamic furrow irrigation model was developed by a modification of the shooting method solution that incorporates storage, depletion and recession phases of irrigation. The solution can also simulate simultaneous advance and recession. Computer and simulation studies were performed to test the accuracy and efficiency of the method. The model uses stochastic infiltration which allows it to compute irrigation flow. There may be convergence problems with the solution causing a loss of precision.

Previously, surface irrigation hydraulic models used the principle of mass conservation to simulate the advance of water along the field and to solve the inverse problem of finding the infiltration function from measurements of advance. A flow rate rather than a volume balance theory, in combination with an advance function that is more physically realistic than the usual power function, is introduced. in which the Horton equation is used to describe infiltration, [Mathematical Expression Omitted]. In this equation, [Q.sub.in] is the inflow rate per furrow or per unit width of border; A is the average cross-sectional area of the stream; x'(t) is advance rate at irrigation time t; I is infiltration rate from Horton's equation; u is advance time to position x; and t - u is intake-opportunity time at x. An exponential advance rate function emerges from the solution of the flow rate equation. Furthermore. the inverse problem is solved in the same manner, a given exponential advance rate function leads to the determination of a Horton law infiltration function. The resulting advance rate, if expressed as a function of distance [x' = f(x)], shows two distinctive linear decreasing parts from which infiltration parameters as well as surface storage emerge., Direct infiltration measurement methods and volume balance equations used to describe infiltration functions from field advance trajectories in surface irrigation result in a high significant error rate for long times. The advance linear velocity (ALIVE) theory using the exponential Horton equation for infiltration proves more accurate for both short and long times. Moreover, ALIVE can estimate storage and steady-state infiltration rates without outflow measurements. With known infiltration function, flow rate and surface storage, ALIVE can accurately predict surface water advance.

Evapotranspiration is an essential component of the hydrologic cycle, and its accurate estimation is necessary for many hydrologic studies. Via the pan coefficient (Kp), pan evaporation data are widely used to estimate grass reference crop evapotranspiration (ETo). An equation for predicting Kp that includes both categorical (wind run and relative humidity) and quantitative (fetch length) data was developed using the indicator regression approach. The developed equation predicted Kp values better than the existing equations.

The principles of irrigation and drainage in cracking soils differ markedly from non-cracking soils, and are not thoroughly understood. This paper presents a conceptual model to simulate water and salt flows in cracking soils of the Imperial Valley, CA, in the presence of ground water that contributes partially to ET demand of crops. A salt reactivity function is introduced in the model to account for mineral precipitation (salt deposition) and mineral dissolution (salt pick up). The conceptual water flow model assumes that surface irrigation water moves into the cracks, infiltrates horizontally to wet the soil profile and a fraction bypasses below the root zone into the shallow ground water and is retained for later crop extraction via upflow. Then, water drains vertically through the soil profile step by step, and root water extractions are calculated. When ET exceeds available water upflow of ground water is calculated. Provision for reclamation leaching before the next crop is also made. The associated conceptual salt transport model involves complete mixing of invading and resident soil water. Salt concentration from ET is subjected to a salt reactivity function to obtain salt deposition of calcite and gypsum to obtain salt concentration after precipitation. This reactivity function is also used in the inverse when two or more waters mix to transform salt after precipitation to salt concentration after ET. The flow of salts follows the water transport algorithum. The model has been applied to a point in the Imperial Valley and observed data from Bali et al. () was used for calibration. Simulated point data from four successive years of alfalfa, reclamation leaching, wheat and lettuce are evaluated in this paper. [ABSTRACT FROM AUTHOR]