Infiltration parameters from surface irrigation advance and run-off data
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- Gillies, M.H. & Smith, R.J. Irrig Sci (2005) 24: 25. doi:10.1007/s00271-005-0004-x
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A computer model was developed to employ runoff data in the calculation of the infiltration parameters of the modified Kostiakov equation. The model (IPARM) uses a simple volume balance approach to estimate the parameters from commonly collected field data. Several data sets have been used to verify the procedure. Infiltration parameters were calculated using both advance and runoff data combined and advance data alone. Simulations of each example using SIRMOD were compared to the measured data to identify the possible benefits of the procedure. The inclusion of runoff did not compromise the ability to reproduce the advance curve however the simulations are more capable of reproducing the measured runoff rates and volumes and therefore offer better estimations of the total volume applied to the soil (in one case a reduction in error of the total infiltration from 22% to 1%). This procedure will be of most benefit where the infiltration parameters are expected to represent soil hydraulic characteristics for times greater than the completion of the advance phase. Further analysis has shown that the infiltration parameters are more sensitive to runoff than the advance highlighting the requirement for accurate field measurement and a weighting factor between the advance and runoff errors.
Surface irrigation is the oldest yet still the most common form of irrigation throughout the world although it traditionally suffers from many problems such as low efficiency and low uniformity. It is possible to improve the performance of most surface irrigation systems through the implementation of optimal management practices such as selection of correct inflow rates and cut-off times. Identification of the correct management requires the study of the complex interaction between irrigation water and the agricultural soil. Therefore it is fair to infer that a significant obstacle in the path of improving irrigation performance is the difficulty of estimating the infiltration function (Elliott et al. 1983).
A common assumption is that data collected during the advance stage provides sufficient information to determine the hydraulic behaviour of a soil. Two such methods in common use are the two-point method (Elliott and Walker 1982) and the INFILT optimisation (McClymont and Smith 1996). Both approaches are based on the simple yet robust combination of the modified Kostiakov equation and the volume balance model.
The flaw of such infiltration from advance schemes is that the soil behaviour may change during the irrigation. Large variability is often noted between the infiltration functions in the same field, which is more noticeable where the water reaches the end of the field early compared to the total inflow time (Scaloppi et al. 1995). Simulations using the estimated infiltration characteristic often provide a good fit to the advance data but commonly result in a poor reproduction of the run-off and recession curves thereby indicating the inadequacy of the infiltration function. It is more beneficial to gain precise knowledge of the total infiltrated volume than just providing an accurate reproduction of the advance data.
Variations in the inflow rate often occur in the early stages of an irrigation event. The volume balance equations usually employ a “step inflow” assumption; that is, the inflow is assumed to reach its final steady rate immediately. Techniques based on advance data alone can be adversely affected by any initial variation of inflow rates (Renault and Wallender 1996). In most cases any initial inflow variation has little impact on the run-off from the tail end of the field.
Previous studies have indicated the benefits of including the run-off phase in the optimisation. Scaloppi et al. (1995) deduced that it provides a better fit to measured data compared to parameters based on advance or run-off data alone. Also infiltration parameters based entirely on the advance phase are more sensitive to errors in the estimation of surface storage volumes (Renault and Wallender 1997).
The multilevel calibration technique (Walker 2005) is one recent example of such a procedure. It uses the advance time, runoff hydrograph and recession time to calculate the infiltration parameters and the value of Manning n. The multilevel approach provides a closer fit to the runoff curve than the two point method; however, it lacks the same capacity to predict the advance trajectory. The requirement for recession data may be a problem, often water does not drain freely from the field following the conclusion of the irrigation.
The aim of this paper is to present a simplified optimisation scheme that calculates infiltration parameters based on both the advance and storage phases of furrow irrigation. The proposed technique gives improved estimates of the final infiltration rate over those techniques based on the advance only, without the requirement for the irrigation to last long enough to reach a steady run-off rate. Such a technique should provide an infiltration function that is applicable for longer times, that is, for a larger portion of the irrigation time.
The constants p and r are selected so that the function best matches the advance data (performed by least squares).
As well as the measured advance (distances and times), the model requires measurements of the run-off volumes at various times during the storage phase. In field trials it is usual to measure the run-off hydrograph (run-off rate). The run-off volume at any particular time is calculated by the trapezoidal rule, assuming that the run-off hydrograph is linear between each run-off measurement.
The weighting factor, w is included to enable the user to easily change the relative sensitivity of the objective function to the errors of the advance distance or runoff volume.
This objective function can also be expressed in terms of errors in both advance and runoff time. This results in parameter values very similar to those from Eq. 17 but requires further iterative computations as some of the terms in the model such as the subsurface shape factors (Eqs. 7, 8) are time dependant.
The optimisation scheme is based on the technique introduced by McClymont and Smith (1996); each of the three parameters (a,k and fo) is incremented individually until the error reduces no further. Following this the parameters are incremented in the same direction as before but as a group until the error again cannot be reduced further. These two steps are repeated until the objective function is not improved by either the individual or group search. Now the step size is reduced and the whole process repeats.
During the design process it was noticed that occasionally the program jumped to the next smallest step size too quickly or remained incrementing at a particular step size for a long period of time. To overcome these problems the optimisation increases the group step size each time the program loops back to the individual parameter search.
The initial step sizes for the parameter optimisation are selected based on maximum stability combined with minimum execution time. The initial step sizes can be changed but experimentation has found the 0.01, 0.0001 and 0.00001 for the step sizes of a, k and f0 respectively work with most data sets.
Comprehensive tests were carried out to determine the sensitivity of the model to various inputs. These showed that the model is not significantly sensitive to furrow geometry but is influenced by other inputs such as the Manning constant.
Convergence can be compromised by the selection of improper starting estimates. This is overcome by the inclusion of an algorithm to perform an initial rough parameter search. Also, limits have been included to ensure that the parameters do not reach unrealistic values (for example all three parameters are kept positive). Other similar techniques such as the INFILT model have difficulty in identifying a unique set of infiltration parameters. The proposed model should help to overcome this problem due to the increased constraints on the infiltration curve.
The model has been coded in C++ to create an executable program (IPARM); once it is loaded the user is required to enter input data.
The model requires a number of input measurements. Firstly the advance data in the form of distances and corresponding times, the technique requires a minimum of two advance points. Secondly the run-off data is made up of run-off rates (in l/s) measured at various times during the storage phase (the model is not valid during the depletion and recession phases). Other inputs include field slope, Manning n or upstream flow depth, inflow rate and the field length.
Comparing the selected data sets
Furrow length (m)
Advance time (min)
Inflow time (min)
Cut off time (min)
The Benson and Printz trials were carried out in Colorado on clay loam and sandy loam soils, respectively (Walker 2005). The Benson case study is an example where the advance phase of the irrigation is relatively short compared to the storage phase.
The two Downs case studies represent field measurements from neighbouring furrows in the same irrigation on cracking clay soil at Macalister, Darling Downs, Australia (Dalton et al. 2001). The two data sets are titled Downs1 (Irrigation 2 furrow 3) and Downs2 (Irrigation 2 furrow 2).
The final two data sets, Brazil and Merkley, were sourced from Scaloppi et al. (1995). Both of these, in particular the Merkley trial are typical examples of where the advance data does not cover an adequate time to enable the accurate calculation of the infiltration function from the advance data alone.
Infiltration parameters were calculated for each irrigation using the maximum available number of both run-off and advance points for each data set. The optimisation was performed with equal weighting on both the advance and storage phases (see Eq. 17). To identify the improvement offered by of the proposed technique, the infiltration parameters were also calculated from advance data alone, with results similar to those produced by INFILT (McClymont and Smith 1996). Values for the upstream flow area were calculated from estimates of Manning n and the furrow geometry.
The surface irrigation simulation model SIRMOD (Walker 1999) was then used to simulate the irrigation events using the different sets of infiltration parameters. In each case the values for a,k and fo were entered into the model and the value of the Manning n was adjusted to cause the model to predict the end of the advance phase correctly. All simulations were performed by SIRMOD II using the full hydrodynamic model option. SIRMOD produces advance curves and run-off hydrographs that can be compared with the measured data. Other outputs include the total infiltration and total outflow.
Results and discussion
Estimated infiltration parameters
For a number of the trials the value of a is reduced to zero when using the advance data only (Table 2). In some cases this may be a limitation of that approach, but in some instances, such as Downs 1 and 2, it may simply be reflecting the cracking nature of the soil. In those cases IPARM also returns very low values for a.
Summary of results from SIRMOD simulations
At end of recorded time
Total, at end of irrigation (Italic cells are estimated)
In summary the inclusion of the run-off data in the identification of the modified Kostiakov parameters gives a greatly improved estimate of the parameters and hence improved cumulative infiltration curve. It retains the ability of the simulations to predict the advance function and it improves the accuracy of run-off and infiltration predictions during later stages of the irrigation.
Number of run-off and advance points
Advance data for Merkley
Run-off data for Merkley
Weighting between run-off and advance data
The weighing factor allows the user to change the relative importance of the advance and run-off data in the optimization of the infiltration function. It functions as a multiplier on the sum of errors in the predicted run-off volumes in Eq. 17. A value of 1 (100%) causes the relative error of the advance (Eq. 15) and the run-off (Eq. 16) to be of equal significance. The model will ignore the run-off if the weight is 0 and will ignore the advance data if the weight is given an extremely large value.
Recommendations for the technique
The proposed parameter estimation procedure performed satisfactorily for the case studies presented here, however the volume balance model is based on a number of simplifications that may limit its application in certain conditions. The inflow rate throughout the entire irrigation should be constant with time as relatively small fluctuations may significantly impact on both the advance trajectory and runoff hydrograph. The model is only designed to apply during the storage phase therefore it is only valid to use runoff data collected during the inflow time. Further the location of the runoff measurement should be such that the measurement does not impose a backwater on the flow in the furrow.
The results of this study suggest that infiltration can be calculated more accurately from the combination of advance data and run-off rates measured during the storage phase of an irrigation. Current techniques that depend completely on the advance phase result in infiltration parameters that cannot accurately predict run-off volumes. The use of run-off data enables the extrapolation of the infiltration curve to greater times, which is of particular importance where the advance reaches the end of the furrow early in the irrigation time.