Irrigation Notes

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California State University, Fresno, California 93740-0018

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January 1988

Irrigation Systems and Water Application Efficiencies

By Kenneth H. Solomon

Water application efficiency is an irrigation concept that is very important both in system selection and design and in irrigation management. The ability of an irrigation system to apply water uniformly and efficiently to the irrigated area is a major factor influencing the agronomic and economic viability of the farming enterprise.

Attainable water application efficiencies vary greatly with irrigation system type and management, but the following ranges give some idea of the efficiencies that may be achieved with reasonable design management as shown in Table 1.

Irrigation efficiency can be divided into two components: water losses and uniformity of application. If either the water losses are large, or application uniformity is poor, efficiency will be low. Although both components of efficiency are influenced by system design and management, losses are predominantly affected by management, while uniformity is predominantly affected by system design.

Table 1. Water Application Efficiencies

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Type of System	Attainable Efficiencies
Surface Irrigation
Basin	80 - 90%
Border	70 - 85%
Furrow	60 - 75%
Sprinkler Irrigation
Hand Move or Portable	65 - 75%
Traveling Gun	60 - 70%
Center Pivot & Linear Move	75 - 90%
Solid Set or Permanent	70 - 80%
Trickle Irrigation
With Point Source Emitters	75 - 90%
With Line Source Products	70 - 85%

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WATER LOSSES

Over-watering is probably the most significant cause of water loss in any irrigation system. No matter how well the system is designed, if more water is applied than can be beneficially used by the crop, efficiency will suffer. Thus, proper irrigation scheduling is important if high efficiencies are to be achieved. Other types of possible water losses are specific to the type of irrigation system used.

Aside from over-watering, the major losses associated with surface irrigation systems are direct evaporation from the wet soil surface, runoff losses, and seepage losses from water distribution ditches. Direct evaporation losses can be important when irrigating young orchard crops. Runoff losses can be virtually eliminated with return flow systems that capture the runoff water and direct it back to the originating field, or to other fields. The amount of seepage loss from unlined ditches will depend on soil characteristics and the extent of the ditch network, but may range from 10 to 15% of the supplied water. Seepage losses are eliminated with lined canals or pipe distribution systems.

The primary losses associated with sprinkler irrigation (other than those due to over-watering) are direct evaporation from wet soil surfaces, wind drift and evaporation losses from the spray, system drainage and leaks. Evaporation from the soil surface will depend upon irrigation frequency and the extent of bare soil between the plants to be irrigated. These losses can be high in young orchards. Some of the water "lost" to wind drift and evaporation from the sprinkler spray is not actually lost, since it substitutes for crop transpiration. Net losses in this case may be as low as 2-3%, to as high as 15-20% under extreme adverse conditions. Well maintained sprinkler systems should have leak and drainage losses below 1%, but poorly managed systems have shown losses of near 10%.

If not over-irrigated, trickle system losses should be low. Though a relatively small portion of the soil surface is wetted, the irrigation frequency is high, so there will be some loss due to evaporation from wet soil. With good management, losses due to leaks, system drainage, and flushing of filters and lateral lines should not exceed 1%.

IRRIGATION UNIFORMITY

Ideally, an irrigation system would apply water in a completely uniform manner, so that each part of the irrigated area receives the same amount of water. Unfortunately, there seems to no way achieve this. Even natural rainfall is not completely uniform. So the phrase "irrigation uniformity" actually refers to the variation or non-uniformity in the amounts of water applied to locations within the irrigated area. Significant effort in irrigation system design and management is directed towards dealing with problems related to irrigation uniformity, or the lack of it.

Whenever water is applied with less than perfect uniformity, some parts of the crop will receive more water than others. If the irrigation system is operated so that the part of the crop receiving the most water has its requirement met, then the remainder of the crop will be over-irrigated. Thus, a non-uniform irrigation unavoidably results in some degree of under- or over-watering.

Irrigation uniformity is related to crop yields through the agronomic effects of under- and over-watering. Insufficient water leads to high soil moisture tension, plant stress and reduced crop yields. Excess water may also reduce crop yields below potential levels through mechanisms such as leaching of plant nutrients, increased disease incidence or failure to stimulate growth of commercially valuable parts of the plant.

Irrigation uniformity is also linked to the efficiency with which agricultural resources are used. To the extent that non-uniformity results in the application of excess water, several water related resources are lost:

· The excess water itself;

· Energy for pumping the excess water;

· Fertilizers, either applied with the irrigation water or leached by the excess water;

· Other chemicals which may be applied with or washed away by the water;

· Investment losses due to the extra capacity designed into the irrigation and drainage systems to carry the excess water.

To the extent that non-uniformity causes crop yields to fall below potential levels, agricultural inputs applied in anticipation of full yields are wasted.

Because irrigation uniformity relates to crop yield and the efficient use of resources, engineers regard it as an important factor to be considered in the selection, design and management of irrigation systems. Various measures of uniformity are used as indices of performance by which, for example, sprinklers and sprinkler spacings are judged. Uniformity plays a similar role in decisions regarding other types of irrigation systems. In surface irrigation design, limits on factors like flow rates or furrow length are set so that non-uniformity in the water application will not be excessive. Hydraulic limitations on pipe networks for trickle and sprinkler irrigation are similarly determined.

MEASURES OF IRRIGATION UNIFORMITY

There are many measures of irrigation uniformity in use, and a discussion of all of them is beyond the scope of this paper. Two commonly used measures will be presented here to facilitate comparisons in some later examples. The first is the Uniformity Coefficient (UC) proposed by J.E. Christiansen in 1942.

UC = 100(1-[D/M])

where

UC = Uniformity Coefficient (%)

D = Average Absolute Deviation of Irrigation Amounts

M = Average of Irrigation Amounts

The second measure is the Distribution Uniformity (DU), proposed in one form or another by various workers.

DU = 100 (1-[LQ/M])

where

DU = Distribution Uniformity (%)

LQ = Average of the Lowest 1/4 of the Irrigation Amounts
M = Average of Irrigation Amounts

These two uniformity measures are (approximately) related by the equations:

UC = (0.63)(DU) + 37

DU = (1.59)(UC) - 59

Christiansen developed UC to measure the uniformity of sprinkler systems, and it is most often applied in sprinkler irrigation situations. UC has been occasionally applied to other forms of irrigation, though. DU has been applied to all types of irrigation systems. In trickle irrigation, it is also known as Emission Uniformity (EU). It has been applied to sprinkler situations under the name of Pattern Efficiency (PE).

UNIFORMITY AND SYSTEM ECONOMICS

Irrigation systems can be designed to apply water with varying degrees of uniformity. A number of techniques can be used in the design of a system to increase its uniformity. For pressurized systems, these techniques include using larger pipe sizes to minimize pressure differences due to friction losses, using pressure regulators to minimize pressure differences due to elevation differentials, using close sprinkler spacings, or trickle emitters with low manufacturing variations. All such techniques will increase the cost of the system, and in general, the cost of the irrigation system goes up with the uniformity of application (for a particular type of irrigation system).

But since higher uniformities mean higher irrigation efficiencies, there are some savings associated with the higher uniformity systems, notably savings in water and energy costs. Sometimes these savings can offset the increased cost of the system. I would like to illustrate this situation using a trickle irrigation example developed by R.J. Kunde ("Life Cycle Costs Resulting from Various Design Emission Uniformities," Proceedings of the 3rd International Drip/Trickle Irrigation Congress, Volume II, pages 859-866).

This example is based on a series of trickle system designs for an 80 acre vineyard, using sound engineering practice and actual costs for 1985 in the San Joaquin Valley of California. Mr. Kunde compared investment costs, water costs and power costs for 9 designs ranging in DU from 80 to 94% (this corresponds roughly to a UC range of from 87 to 96%). The results of Mr. Kunde's analysis are shown in table 2. Costs are given in 1985 US dollars. The investment costs were converted to equivalent annual costs using a Capital Recovery Factor of 0.1598 (15% interest rate, and 20 year investment period).

Initial investment costs increase with DU, while water and power costs decrease. These trends are general, and are to be expected in any agricultural area. The present example is based on the relatively low water cost of 1.2 cents per cubic meter, and power costs of 8 cents per kilowatt hour. The water and power cost savings amount to roughly US $1.40 per acre/year for each percentage point of DU improvement, more than enough to pay back the increased cost of higher DUs. In agricultural areas with higher water costs, the savings due to improved efficiencies would be even higher. For this example, the lowest total annual cost occurs with the highest DU (94%).

Table 2. Irrigation Equipment, Water and Power Costs for a Range of Distribution Uniformities

------------Annual Costs Per Acre---------

Distribution Uniformity (DU)	Initial Cost ($/acre)	Investment ($/acre/yr)	Power ($/acre/yr)	Water ($/acre/yr)	Total ($/acre/yr)
94%	809	129.26	19.34	36.23	184.83
92%	798	127.52	20.73	37.01	185.26
90%	800	127.88	22.89	37.84	188.61
88%	795	127.06	23.91	36.69	189.66
86%	788	125.98	25.76	39.59	191.33
84%	780	124.66	27.84	40.54	193.04
82%	775	123.77	30.14	41.53	195.44
80%	774	123.63	32.59	42.56	198.78

CROP RESPONSE TO WATER AND UNIFORMITY

The response of a crop to applied water can be summarized in a water yield function. This equation is used to calculate the yield from the seasonal water application. It is convenient to express both yield and applied water in relative or dimensionless terms. Relative yield (y) is defined as the ratio of actual yield to maximum yield, and relative applied water (w) is defined as the ratio of actual applied water to that amount corresponding to maximum yields. If w is taken to include effective rainfall and soil moisture stored at the beginning of the season, the yield function will be fairly general and can be representative of more than one location or year. If the yield function is adjusted so that w refers only to the water applied by the irrigation system, the significance of various irrigation options is more apparent, though some generality is lost. The shape of the yield function also depends on the irrigation frequency, but it is generally assumed that a yield function is valid for most "reasonable" irrigation schedules.

A particular yield function for sugar cane is given below. It is based on data from a number of sources, and assumes that rainfall and soil moisture stored in the rootzone at the beginning of the season amount to 20% of the water necessary for maximum yield, and that sensitivity to excess is relatively low.

y(w) = 0.05 + 2.47w - 2.19w2 + 0.77w3 - 0.10w4

where

y(w) = Relative Sugar Cane Yield corresponding to an irrigation application w

w = Relative Seasonal Irrigation Application

Table 3 shows how relative sugar cane yield changes with the relative seasonal irrigation application.

Because plants respond to water, they respond to how uniformly the water is applied. Suppose, for example, that sugar cane is irrigated so that 60% of the area receives the yield maximizing amount of water (w=1.00), but that for 20% of the area w=0.75, and that for the remaining 20% of the area, w=1.25. You would naturally expect the overall yield to be the weighted average yield from these particular irrigation amounts:

Table 3. Relative Sugar Cane Yield for Differing Relative Irrigation Amounts

Relative Irrigation	Relative Sugar Cane Yield
w	y
0.25	0.54
0.50	0.83
0.75	0.96
1.00	1.00
1.25	0.98
1.50	0.92
1.75	0.85

Relative Yield = (20%)[y(0.75)] + 60%)[y(1.00)] + (20%)[y(1.25)]

Relative Yield = (20%)[0.96] + (60%)[1.00] + (20%)[0.98]

Relative Yield = 0.99

The small degree of non-uniformity in the water application causes only a 1% decrease in yield. But suppose the irrigation is much less uniform: for 35% of the area w=0.50; for 30% of the area w=1.00; and for 35% of the area w=1.50. In this case,

Relative Yield = (35%)[y(0.55)] + (30%)[y(1.00)] +(35%)[y(1.50)]

Relative Yield = (35%)[0.83] + (30%)[1.00] + (35%)[0.92]

Relative Yield = 0.91

The larger degree of non-uniformity causes a 9% decrease in yields. The general formula for estimating crop yields from non-uniform irrigation is:

Relative Yield = (P1)[y(w1)] + (P2)[y(w2)] +...+ (Pi)[y(wi)] +...

where P1, P2,...Pi are the percentages of the area that receive relative irrigation amounts w1, w2,...,wi..., and y(wi) is the relative yield associated with wi by the yield function. In this way the crop response to various degrees of non-uniformity can be estimated.

Based on the yield function given previously, the relationship between uniformity and sugar cane yield is calculated (Table 4). It is assumed that the irrigation amounts are normally distributed.

Similar calculations can be done with yield functions for other crops and circumstances to evaluate the yield influence of irrigation uniformity.

Table 4. Influence of Uniformity on Sugar Cane Yield

Uniformity Coefficient UC	Sugar Cane Relative Yield
100%	1.00
95%	1.00
90%	0.99
85%	0.98
80%	0.97
75%	0.95
70%	0.93
65%	0.90
60%	0.86
55%	0.82
50%	0.77

Irrigation efficiency is important not only for the conservation of agricultural resources, it can have important implications in terms of system design and cost, operational costs, and crop yields.

REFERENCES

Heermann DF and Kohl RA. 1980. Fluid Dynamics of Sprinkler Systems. In: Design and Operation of Farm Irrigation Systems, ME Jensen (ed), ASAE, St. Joseph, MI, pp 583-618.

Keller J. 1976. Irrigation Scheduling and Efficiency. Proceedings, Rain Bird Seminars Relating to Irrigation Decision Making, Rain Bird, Glendora, CA, pp 85-95.

Kunde RJ. 1985. Life Cycle Costs Resulting from Various Design Emission Uniformities. Proceedings, 3rd International Drip/Trickle Irrigation Congress, November 18-21, Fresno, CA, Volume II, pp 859-866.

Solomon KH. 1983. Irrigation Uniformity and Yield Theory. PhD dissertation, Department of Agricultural and Irrigation Engineering, Utah State University, Logan UT, 287 p.

Solomon KH. 1987. Sprinkler Irrigation Uniformity. Extension Bulletin No. 247, Food & Fertilizer Technology Center, Tapei City, Taiwan, Republic of China.


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