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4. Evaluation of field data

4.1 Objectives of evaluation
4.2 Performance measures
4.3 Intermediate analysis of field data
4.4 System evaluation
4.5 General alternatives for improvement
4.6 An example furrow irrigation evaluation

4.1 Objectives of evaluation

The principal objective of evaluating surface irrigation systems is to identify management practices and system configurations that can be feasibly and effectively implemented to improve the irrigation efficiency. An evaluation may show that higher efficiencies are possible by reducing the duration of the inflow to an interval required to apply the depth that would refill the root zone soil moisture deficit. The evaluation may also show opportunities for improving performance through changes in the field size and topography. Evaluations are useful in a number of analyses and operations, particularly those that are essential to improve management and control. Evaluation data can be collected periodically from the system to refine management practices and identify the changes in the field that occur over the irrigation season or from year to year. The surface irrigation system is a complex and dynamic hydrologic system and, thus, the evaluation processes are important to optimize the use of water resources in this system. A summary of the data arising from a field evaluation is enumerated below.

There are several publications describing the equipment and procedures for evaluating surface irrigation systems, but not all give a very correct methodology for interpreting the data once collected. The data analysis depends somewhat on the data collected and the information to be derived. This section will deal with two aspects of an evaluation. The first is the definition of the typical field infiltration relationship using the evaluation data describing the surface flow. The mathematical basis of the infiltration analysis will be the extended form of the Kostiakov-Lewis formula (Eq. 15). The second is the evaluation of the efficiency of the irrigation event studied. Although many performance measures have been suggested, only four will be noted herein: (1) application efficiency; (2) storage efficiency; (3) deep percolation ratio; and (4) runoff ratio. These will be defined here before detailing the analyses of infiltration and performance.

4.1.1 Field data

The field measurements outlined in the previous section provide the following elements in a field evaluation:

i. the inflow hydrograph (per furrow or per border or basin);
ii. the advance and recession of the water over the field surface;
iii. the runoff hydrograph (if the field is not dyked);
iv. the soil moisture depletion prior to the irrigation;
v. the volume of water on the soil surface at various times;
vi. infiltration and water holding capacities of the soil; and
vii. the geometry of the cross-sectional flow area.

Not all these data will be needed as part of the field evaluation. In some cases, such as infiltration, one set of data can be derived from others to reduce the time and expense of the field measurements.

4.2 Performance measures

4.2.1 Application uniformity
4.2.2 Application efficiency
4.2.3 Water requirement efficiency
4.2.4 Deep percolation ratio
4.2.5 Tailwater ratio
4.2.6 Integration measures of performance

Among the factors used to judge the performance of an irrigation system or its management, the most common are efficiency and uniformity. These parameters have been subdivided and defined in a multitude of ways as well as named in various manners. There is not a single parameter which is sufficient for defining irrigation performance. Conceptually, the adequacy of an irrigation depends on how much water is stored within the crop root zone, losses percolating below the root zone, losses occurring as surface runoff or tailwater the uniformity of the applied water, and the remaining deficit or under-irrigation within the soil profile following an irrigation. Ultimately, the measure of performance is whether or not the system promoted production and profitability on the farm. In order to index these factors in the surface irrigated environment the following assumptions can be made, the consequences of which are that performance is based on how the surface flow will be managed:

i. the crop root system extracts moisture from the soil uniformly with respect to depth and location;

ii. the infiltration function for the soil is a unique relationship between infiltrated depth and the time water is in contact with the soil (intake opportunity time); and

iii. the objective of irrigating is to refill all of the root zone.

4.2.1 Application uniformity

When a field with a uniform slope, soil and crop density receives steady flow at its upper end, a water front will advance at a monotonically decreasing rate until it reaches the end of the field. If it is not dyked, runoff will occur for a time before recession starts following shutoff of inflow. Figure 40 shows the distribution of applied water along the field length stemming from the assumptions listed above. The differences in intake opportunity time produce applied depths that are non-uniformly distributed with a characteristic shape skewed toward the inlet end of the field.

Application uniformity concerns the distribution of water over the actual field. A number of technical sources suggest the Christiansen coefficient as a measure of uniformity. Others argue in favour of an index more in line with the skewed distribution shown below. For example, Merriam and Keller (1978) propose that distribution uniformity be defined as the average infiltrated depth in the low quarter of the field, divided by the average infiltrated depth over the whole field. This term can be represented by the symbol, DU. The same authors also suggest an 'absolute distribution uniformity', DUa which is the minimum depth divided by the average depth. Thus, the evaluator can choose one that fits his or her perceptions but it should be clear as to which one is being used.

Figure 40. Distribution of applied water along a surface irrigated field showing also the depth required to refill the root zone (after Walker and Skogerboe, 1987)

4.2.2 Application efficiency

The definition of application efficiency, Ea, has been fairly well standardized as:


Losses from the field occur as deep percolation (depths greater than Zreq) and as field tailwater or runoff. To compute Ea it is necessary to identify at least one of these losses as well as the amount of water stored in the root zone. This implies that the difference between the total amount of root zone storage capacity available at the time of irrigation and the actual water stored due to irrigation be separated, i.e. the amount of under-irrigation in the soil profile must be determined as well as the losses.

4.2.3 Water requirement efficiency

The water requirement efficiency, Er, which is also commonly referred to as the storage efficiency is defined as:


The requirement efficiency is an indicator of how well the irrigation meets its objective of refilling the root zone. The value of Er is important when either the irrigations tend to leave major portions of the field under-irrigated or where under-irrigation is purposely practiced to use precipitation as it occurs. This parameter is the most directly related to the crop yield since it will reflect the degree of soil moisture stress. Usually, under-irrigation in high probability rainfall areas is a good practice to conserve water but the degree of under-irrigation is a difficult question to answer at the farm level.

4.2.4 Deep percolation ratio

The loss of water through drainage beyond the root zone is reflected in the deep percolation ratio, DPR, defined as:


High deep percolation losses aggravate waterlogging and salinity problems, and leach valuable crop nutrients from the root zone. Depending on the chemical nature of the groundwater basin, deep percolation can cause a major water quality problem of a regional nature. These losses can return to receiving streams heavily laden with salts and other toxic elements and thereby degrade the quality of water to be used by others.

4.2.5 Tailwater ratio

Losses from the irrigation system via runoff from the end of the field are indicated in the tailwater ratio, TWR:


Runoff losses pose additional threats to irrigation systems and regional water resources. Erosion of the top soil on a field is generally the major problem associated with runoff. The sediments can then obstruct conveyance and control structures downstream, including dams and regulation structures.

4.2.6 Integration measures of performance

With the five measures of performance defined above, a broad range of assessments is possible and specific remedies identified. Application efficiency is the most important in terms of design and management since it reflects the overall beneficial use of irrigation water. In later sections, a design and management strategy will be proposed in which the value of application efficiency is maximized subject to the value of requirement efficiency being maintained at 95-100 percent. This approach thereby eliminates Er from an active role in surface irrigation design or management and simultaneously maximizes application uniformity. If the analysis tends to maximize Ea, distribution uniformity is not qualitatively important and may be used primarily for illustrative purposes. Of course, some may prefer performance discussed in terms of uniformity or be primarily involved in systems where underirrigation is an objective or a problem. For these cases, uniformity is still available. The assumption of maximization of application efficiency in effect states that losses due to deep percolation or runoff are equally weighted.

4.3 Intermediate analysis of field data

4.3.1 Inflow-outflow
4.3.2 Advance and recession
4.3.3 Flow geometry
4.3.4 Field infiltration

Individual measurement of these seven processes listed above (inflow, advance, recession, outflow, soil moisture deficit, surface volume, and infiltration) is time consuming and therefore expensive. A number of procedures have been developed for estimating one or more of the seven from an analysis of the others. These are called the intermediate evaluations. Of the seven parameters listed above, only the inflow hydrograph and soil moisture deficit must be known in all cases. The evaluation of the remaining data can be divided into the following intermediate evaluations.

4.3.1 Inflow-outflow

The flow through the field inlet onto the surface of the field can be measured to yield a hydrograph which, when integrated, determines the total volume of applied water. The inflows should be maintained at a steady rate. Tailwater runoff where not restricted with a dyke (outflow hydrograph) can be obtained in a similar manner. An example inflow-outflow hydrograph for a single furrow in northeastern Colorado, USA, is shown in Figure 41.

Figure 41. Inflow-outflow hydrographs from a furrow irrigation evaluation in Colorado, USA (from Salazar, 1977)

There are two useful parameters obtained from a comparison of inflow and outflow hydrographs. First, the integrated differences between the two hydrographs are an accurate measurement of the total volume of water infiltrating into the soil:

Vz = Vin - Vtw

in which Vz, Vin, and Vtw are the total volume of infiltration, inflow and runoff, respectively. The second parameter defined by the inflow-outflow hydrograph is the steady state or 'basic' infiltration rate. In Figure 41 the difference between the two hydrographs near the end of the irrigation is approximately .046 m3/min. If the basic intake rate, fo, in Eq. 15 can be defined at that point, it would be determined as follows:

fo = (Qin - Qout)/L (31)

= 0.046 m3/min/625 m = 0.000074 m3/min/m furrow

where Qin and Qout are the flow rates in m3/min onto and off the field near the steady state condition and L is the length in m. It should be noted that to assess fo accurately, the outflow hydrograph should be steady. In Figure 41, the outflow hydrograph shows a continual rise - which indicates that the first term in the right hand side of Eq. 15 is still a significant part of the total infiltration, and fo will be over-estimated. In these cases, it is essential to extend the irrigation test until inflow-outflow data near the time of cutoff are approximately constant.

4.3.2 Advance and recession

The intake opportunity time is the interval during which water will infiltrate at a specified location. It begins when the water flow first reaches the point (advance) and ends when the water eventually drains from the point (recession). Because infiltration is assumed to be uniform over the field, the variation in intake opportunity time is also an indication of application uniformity.

The time required for the water to advance to the end of the field length or to cover the field completely is an important consideration in managing surface irrigation systems. As will be seen in Section 5, the advance time dictates in large measure when the inflow must be terminated and it provides the time when field tailwater begins flowing from the field or when the field begins to pond. The advance trajectory does not have a concise mathematical description, but can be reasonably well approximated with the simple power function:


where x is the advance distance in m from the field inlet that is achieved in tx minutes of inflow, and p and r are fitting parameters. Elliott and Walker (1982) made several comparisons of Eq. 32 with more elaborate relationships and methods of fitting and concluded that the best results are achieved by a two-point fitting of the equation. The time of advance to a point near one-half the field length, t.5L, and the advance to the end, tL, can be simultaneously solved to define the empirical parameters, p and r:





An example use of these equations is shown in Figure 42 with the axes reversed to be consistent with the normal values of a time space trajectory.

Figure 42. Advance Data (Salazar, 1977)

For borders and basins, the undulations in the ground surface may have a major affect upon both advance and recession. The advancing front may be very uneven so rather than attempt to plot an average length of travel of the advancing front against time, the watered and dewatered area of the basin are plotted against time. To illustrate this type of analysis of advance-recession data, the basin field study reported by Kundu and Skogerboe (1980) can be examined. A basin 36.6 m wide and 36.6 m long was constructed immediately following land levelling. The soil was a silty clay loam. The basin was staked with a 6 x 6 m grid and irrigated with an inflow of 0.83 m3/min. Advance and recession contours drawn at different times during the tests are shown in Figures 43 and 44.

Figure 43. Advance contours for a basin evaluation (Kundu and Skogerboe, 1980)

Figure 44. Recession contours from basin evaluation (Kundu and Skogerboe (1980)

The data from the advance contours were plotted on a logarithmic scale in Figure 45 and were described by the following function:


in which Ax is the area wetted (m2) in tx minutes.

Figure 45. Basin advance data. (Kundu and Skogerboe, 1980)

The recession data could also be plotted as a function of cumulative time but the results would not be usable since the recession occurs over the field in a somewhat varied way. In order to determine the intake opportunity time, it is necessary to record the advance and recession data at each point in the grid. Table 5 summarizes the data in terms of the spatial grid.


Grid Row

Grid Column

















































4.3.3 Flow geometry

It is necessary to segregate the volume of water on the soil surface from the volume which has infiltrated into the soil during the advance phase in order to evaluate the field infiltration parameters. To do this it is necessary to describe mathematically the shape of the flow cross-section and the flow area. Probably the most useful flow equation is the Manning formula:


where Q is the discharge in m3/sec, A is the cross-sectional area of the flow in m2, R is the hydraulic radius in m, So is the slope of the hydraulic grade lines which is assumed to equal the field slope, if one exists, and n is a resistance coefficient.

The simplest case of Eq. 37 is the sloping border in which a width of one metre is taken as representative of the flow and the relation reduces to:


in which y is the depth of flow in m, and Q is the flow per unit width.

For basins the problem becomes slightly more complex because the field slope is zero. Under these conditions, it is often assumed that the slope of the hydraulic gradeline can be approximated by the depth at the field inlet, yo, divided by the distance over which the water surface has advanced. Equation 37 with this modification becomes:


where x is the advance distance at time tx, in m. Thus, the area of flow in a basin is time dependent during the advance phase and is continually changing. In sloping furrows and borders it is assumed constant with time.

The geometry of flow under furrow irrigation is difficult to describe. The furrow shape is continually changing because of erosion and deposition of soil as the water moves it along, but its typical shape ranges from triangular to nearly trapezoidal. In most cases, simple power functions can be used to relate the cross-sectional area and wetted perimeter with depth. Figure 46 shows a furrow cross-section developed from the profilometer described in Section 3. The simplest way to analyse these data is to first plot the cross-section as shown, then divide the depth into 10-15 equal increments and graphically or numerically integrate area and wetted perimeter. Table 6 summarizes the writer's analysis.

Figure 46. Typical furrow cross-section


Furrow Depth, y

Area, A

Perimeter, WP





































Assuming a power relation between depth and both area and perimeter, a twopoint fit of the data in Table 6 will determine the parameters:


at y = 5 cm A = 54.1 cm2 = 5.41 x 10-3 m2
at y = 10 cm A = 179.70 cm2 = 1.797 x 10-2 m2


a1 = .01797 / 101.732 = 3.331 x 10-4


at y = 5 cm WP = 21.632 cm = .2163 m
at y = 10 cm WP = 37.798 cm = .378 m


b1 = .378 / 10.805 = .05922

Equations 40 and 41 can be combined for the following expression for the hydraulic section in Eq. 37:



p2 = 1.667 - .667 * b2 / a2 = 1.3568



Then Eq. 37 is written:


The units of depth, area and perimeter can be measured in cm for Eqs. 40 and 41 and converted to metres Eq. 45. Note that in Eq. 44, p2 reduces to 1.667 and p1 is equal to 1.0 when applied to border flow conditions

4.3.4 Field infiltration

The most crucial and often the most difficult parameter to evaluate under the surface irrigation condition is infiltration. In general, a relatively large number of field measurements of infiltration is required to represent the average field condition. Methods which use a static water condition (such as ring infiltrometers) often fail to indicate the typically dynamic field condition. As a result there is a useful approach to obtain field representative infiltration functions based on the response of the field to an actual watering. This method determines the infiltration formula directly from the inflow-outflow and advance data, along with an assumption concerning the volume of water on the surface during the advance phase.

There are of course works like that of Merriam and Keller (1978) which propose other methods of estimating the parameters in an infiltration equation. These methods have the same objectives as the technique discussed below which is to define a relationship between soil-water contact time and infiltration that accurately reflects the mass balance of water in the field confines. For instance, Merriam and Keller (1978) propose an approach using inflow and outflow data to adjust a relationship derived from ring infiltrometer tests.

One should understand the fundamental processes that interact during the course of an irrigation event and apply methodologies that do not violate the nature of these processes. Figure 47 shows two infiltration curves plotted on loglog paper. They are typical of functions found from field data which can be simulated by a relationship such as Eq. 15 and have historically been approximated by relations like Eq. 13. If the evaluation is based on Eq. 13, it is only possible to describe accurately the field mass balance at the end of the advance phase. Potentially large errors will occur in estimating runoff as well as the final subsurface moisture distribution, depending on the relative 'linearity' of the infiltration process indicated on log-log paper. The larger the deviations of infiltration data from a linear relation after a logarithmic transformation, the more error that is inherent in using the wrong relationship for infiltration. The procedure discussed below is not free of the error, but it is not so burdened by a problem of structure.

Figure 47. Logarithmic plot of two infiltration functions differing only in the value of the exponent

Elliott and Walker (1982) and many colleagues before and after observed that a large number of point measurements of infiltration rates using blocked furrow and cylinder infiltrometers failed to provide a satisfactory projection of actual furrow advance or an accurate prediction of tailwater volume. These investigators concluded that perhaps a better and more effective evaluation would be to measure advance rates, hydraulic cross-sections and tailwater volumes and, from these data, deduce an average infiltration relationship.

The method suggested for defining infiltration from a field evaluation of the irrigation system is based on a two-point approximation to the mass balance of water on the field during the advance phase. The solution assumes the mathematical form of both the infiltration function (Eq. 15), and the advance trajectory (Eq. 32).

Utilizing these two assumptions, the volume balance equation can be written for any time


where Ao is cross-section area of flow at the inlet, m2, Qo is inlet discharge in m3/min/furrow or unit width, t is elapsed time since the irrigation started in min. Sz is the subsurface shape factor defined as:


The inlet cross-sectional flow area, Ao, can be computed using the uniform flow equation given in Ea. 45 rearranged as follows:


Values of the Manning roughness coefficient, n, range from about 0.02 for previously irrigated and smooth soil, to about 0.04 for freshly tilled soil, to about 0.15 for conditions where dense growth obstructs the water movement.

The 'two-point' method of evaluating the parameters in Eq. 15 begins by defining fo from the inflow-outflow hydrograph or by other means which will be noted in a following paragraph. Then Eq. 46 is written for two advance points using advance rate measurements to define the parameters in Eqs. 43 and 44. The two common points are the mid-distance of the field and the end of the field. Thus, for the mid-distance:


and for the end of the field:


where t.5L is advance time to one-half the field length in min, tL is advance time to the end of the field in min, and L is field length in m.

The unknowns in Eq. 49 and 50 are the parameters k and a. Solving these two equations simultaneously yields:






then Sz is found directly from Eq. 47 and the parameter k is found by:


Several approaches can be used for determining a value for fo in the infiltration equation. One method utilizes the data from blocked furrow or cylinder infiltrometer tests made the day before irrigation. After an infiltrometer test has been run for several hours (the time being dependent on soil type), the essentially constant rate of infiltration can be taken to be fo. If a runoff hydrograph is not measured, such as for a basin evaluation, it is suggested that Table 3 be used to define fo based on soil type.

4.4 System evaluation

4.4.1 Furrow irrigation evaluation procedure
4.4.2 Border irrigation evaluation
4.4.3 Basin irrigation evaluation

Field studies are necessary to define quantitatively the irrigation system performance in relation to not only the physical features of the system but also its design and management. Field analyses of the single irrigation may not clearly establish these relationships and, therefore, should be repeated at times when the soil, crop or operational characteristics have changed sufficiently to reveal the other facets of the irrigation system.

Three typical results of surface irrigation are illustrated in Figure 48. When the inflow is cut off too soon after the advance phase, the application at some point in the field may be inadequate to refill the root zone (curve a). Or the application may just satisfy the needs in the least watered areas (curve b). But most often, the applied depths exceed the target depth, Zreq at all locations (curve c). Large differences in economic, physical, social and operational conditions occur in surface irrigated systems. Consequently it is impractical to judge any of the three cases as good or bad since situations like the need for conservation or rainfall expectations make each regime one to utilize when the time calls for it. The suggested evaluation of performance is the numerical definition of the efficiency parameters described earlier tempered by a case by case professional judgement.

Figure 48. Three typical irrigation application patterns under surface irrigation (after Walker and Skogerboe, 1987)

The Typical Under-Irrigation Case

The Typical Complete-Irrigation Case

The Typical Over-Irrigation Case

4.4.1 Furrow irrigation evaluation procedure

A furrow evaluation would normally consist of activities before, during and after the irrigation. The pre-irrigation work is largely reconnaissance, equipment installation and soil moisture determination. During the irrigation, measurements of inflow, advance, runoff or ponding; and recession are made. Following the irrigation, furrow cross-sections can be determined as well as follow-up soil moisture sampling if desired. There are no formal rules for the evaluation since different personnel prefer their own order and technique. Merriam and Keller (1978) list some step by step procedures and give a convenient list of equipment and supplies that are needed.

Following the field evaluation, the next step is to determine the infiltration function and then, in conjunction with the recorded intake opportunity, the distribution of water applied to the root zone. The length should be subdivided into 10 or more increments and the cumulative intake computed for each increment by:

Zi = k [tr - (tx)i]a + fo [tr - ( tx)i] (55)

in which tx is the recession time in minutes if it is determined. If not, the time of cutoff, tco, is used in Eq. 55 in place of tx.

The results from Eq. 55 should then be plotted as in Figure 49 along with a line representing the application needed to refill the root zone deficit, Zreq which is the soil moisture deficit measured in the field. The plot can then be integrated graphically or numerically to define the components of application efficiency, deep percolation ratio, runoff ratio and requirement efficiency (or uniformity if desired).

4.4.2 Border irrigation evaluation

The analysis of border irrigation data follows the same procedures as for furrow irrigated systems. Advance, if irregular, should be contoured and analysed as previously indicated. Simplification can be made in using flow rate per unit width instead of total border flow if the advancing front is relatively uniform. The flow cross-section is rectangular. This analysis assumes a free-draining outflow condition. For ponded conditions arising from a dyked downstream boundary, the analysis follows the basin procedure.

In the evaluation of furrow systems, the infiltration during recession can often be considered negligible. For border systems, the infiltration during the recession period is significant and must be considered. Once the depletion and recession times (td and tr) have been determined, the distribution of water applied to the soil can be plotted and the performance measures evaluated as for furrow evaluation.

4.4.3 Basin irrigation evaluation

The estimates of basin application efficiencies are somewhat simplified by a small field slope and the prevention of runoff. Water first entering the basin would advance to the end dyke and then pond on the surface. As the water surface rises, it will approach a horizontal orientation. Thus, it can be seen that during the depletion and recession phases the surface water has little or no movement, and the subsurface profile is determined by adding the surface depths to the profile which developed during the advance phase. The application efficiency, deep percolation ratios and requirement efficiency can be found from the equations given earlier. The tailwater ratio is zero for basin irrigation.

4.5 General alternatives for improvement

The field evaluation should identify at least some modifications that will improve efficiency and uniformity. The easily identified problems such as applying too much or too little water, the poor distribution of infiltrated water over the field, excessive tailwater runoff or significant deep percolation losses should be evident. In planning to improve irrigation performance, it must be recognized that all of the parameters are interdependent. Therefore, when considering changes in inflow, time of cutoff, or field length, one must understand that the time of advance, infiltration, tailwater runoff and deep percolation will be affected simultaneously.

The flow rate used on an irrigated field will significantly affect the time of advance, the volume of runoff and the erosion hazard. Utilizing high flow rates will maximize the potential for tailwater losses (except for basin irrigation) and erosion, but minimize the time of advance and thereby the variation in opportunity time along the field length. In order to reduce the tailwater runoff from border or furrow systems, a high discharge rate can be used during the advance phase and then 'cut back' (reduced) for the wetting phase. Tailwater can be collected and reused as well.

For whatever discharge is being used, the ideal time of cutoff, tco, occurs when the infiltrated depth in the least watered portion of the field is equal to the irrigation requirement. Discharge and time of cutoff are the two operational hydraulic parameters, with tco being the easiest for the irrigator to modify. Again, the interdependence between inflow and cutoff time must be known in order to maximize the performance of a surface irrigation system.

Surface irrigation is critically dependent on the field topography. Undulations interrupt the flow of water and concentrate water in depressions. The high points tend to become saline. It is not a simple matter to apply the appropriate irrigation requirement, in fact, much greater depths are generally applied. Precision land levelling is an important aspect of improving the operation of surface irrigation systems, particularly for basins. Likewise, furrow preparation needs to yield channels of uniform depth and spacing. In short, land preparation should be considered an integral part of surface irrigation and not treated as an independent operation.

4.6 An example furrow irrigation evaluation

4.6.1 Field infiltration characteristics
4.6.2 Evaluation of system performance
4.6.3 Measures to improve performance

An evaluation was conducted on an existing furrow system during the first irrigation of the season. The field characteristics were found to be as follows. The soil was a sandy loam which gravimetric soil samples indicated had a soil moisture depletion averaging 9.5 cm prior to the irrigation. The field had a uniform slope of 0.0075 with 200 metre furrows spaced at 75 cm intervals across the field. The water supply to the field was a large tube-well capable of supplying water on demand.

Additional field measurements made during each evaluation were: (1) the furrow inflow hydrograph; (2) runoff hydrographs; (3) furrow shape shown in Figure 46 previously, and (4) the advance and recession trajectories. The furrow inflow was a steady value of 0.12 m3/min during both irrigations. The remaining data are tabulated on Tables 7 and 8. The inflow to the tests was stopped at 390 minutes.


Advance Distance

Advance Time

Recession Time




















Time Since Irrigation Started




































4.6.1 Field infiltration characteristics

Analyses of the infiltration function as defined by the behaviour of water movement in the furrow involves a five step procedure. For this evaluation, these steps are as follows:

i. Furrow inlet flow area, Ao, is computed from the Manning relation, Eq. 48, with the following data:

Qo = 0.12 m3/min (measured);
n = 0.04 (assumed);
p1 =.444 and p2 = 1.357 from subsection 4.3.3; and
So = the slope of 0.0075 (measured).


ii. The advance trajectory can be represented by a power function (Eq. 32). Using a two-point method based on the measured advance data:

x = 200 m at tx = 54.8 min
x = 112 m at tx = 18.0 min
r = log(200/112)/log(54.8/18) = 0.5208

Evaluation of the parameter p is not necessary.

iii. The basic intake rate, fo, is defined by Eq. 31 using:

Qin = m3/sec (measured); and
Qout = the steady state runoff, .00095 m3/sec (estimated from Table 8)
L = the field length, 200 m (measured).


fo = (.002 - .00095) * 60/200 = 0.000315 m3/min/m

iv. The values of k and a in the infiltration function, Eq. 15 are determined as follows. First, Eqs. 52 and 53 are defined:

and then from Eq. 51:

The subsurface shape factor sz, is described by Eq. 47:

Then, from Eq. 54:

k = 0.013367 / (.7622 * 54.8.532) = 0.00208 m3/mina/m

v. The final field evaluated infiltration function for the first irrigation is:

Z = 0.00213 r0.532 + 0.000315 r

4.6.2 Evaluation of system performance

Using the derived infiltration function and the measured opportunity time (a recession time minus advance time at each point), the water applied to the soil reservoir was calculated and plotted in Figure 49. Also plotted is the application required to replace the root zone deficit (requirement is the depth times the furrow spacing, i.e. .095 m * .75 m = 0.0713 m3/m). It can be ascertained graphically that both irrigations applied too much water, far more than enough to refill the root zone. Obviously in both cases the water requirement efficiency is 100 percent.

Figure 49. Distributions of applied wafer curing the two test irrigations

The application efficiency for the test can be computed from the relationship:


= 100 * (.0713 * 200) / (.002 * 60 *390) = 30.5%

The performance of the system during the evaluation was poor, about 70 percent of all water applied was wasted from the field as runoff or deep percolation. In order to identify improvements, these losses must be separated, either by integrating the applied distribution and computing the deep percolation ratio or by integrating the runoff hydrograph and computing the tailwater ratio. For this example, the latter is chosen to reflect more confidence in measured runoff than calculated infiltration. Figure 50 shows the runoff hydrograph. Using a trapezoidal integration, the runoff per furrow during the irrigation was 16.7 m3. The tailwater ratios were therefore:

TWR = 100 * 16.7 / (.002 * 60 * 390) = 35.7%

Figure 50. Runoff hydrographs during the two evaluations

To complete the performance picture, the deep percolation ratio for the first evaluation is:

DPR = 100 - Ea - TWR = 33.8% (57)

4.6.3 Measures to improve performance

Losses during the irrigation were almost evenly split between tailwater and deep percolation. The most obvious way to improve the performance of this system would be to cut the inflow off when the application at the lower end of the field was approaching the required depth. If the required intake opportunity time at the end of the field is calculated and added to the advance time, the cutoff time represented by their sum is approximately 180 minutes. If this would have happened, the total water applied to the field would have been reduced from 46.8 m3/furrow to 21.6 m3/furrow. The soil moisture deficit would still have been completely replenished (Ea = 100 percent), but the application efficiency would have been increased to about 66 percent. The DPR and TWR values would have been reduced to 11 percent and 20 percent respectively. Further improvements could be made by utilizing a cutback flow after the advance was completed or by adjusting the inflow rate (reducing it in this case would improve performance).

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