Irrigation is the primary management practice that is utilized to increase crop yields (or to permit crop production) in semiarid and arid climates. In addition, irrigation is used to stabilize crop yields when rainfall is unreliable in subhumid and humid climates.

Including irrigation depths (IR) in the ratios of DM production or marketable yield (Y) to transpiration (T) or evapotranspiration (ET) is necessary when making both engineering and economic decisions, to determine the optimal irrigation depths. The difference between both kinds of ratios is due first, to the fact that all of the water evapotranspirated by a crop does not come from irrigation and, second, that all of the water applied by irrigation is not evapotranspirated by the soil-plant set.

Far fewer studies [73] have expressed the relationship of yield to applied irrigation amount. Water-production functions relating seasonal irrigation depth and crop yield have been derived for several crops by polynomial regression analyses [74]. The relation of irrigation to crop production is essentially site specific [75].

Evidence exists that the function of yield applied IR is convex in shape, in contrast to the linear shape of the yield ET function [76]. The linear [ Y = f (ET)] and the convex [ Y = f (IR)] functions coincide up to a point and then diverge as the amount of applied water increases [77]. The difference between the two curves is the non-ET portion of applied water. The relationship between DM or Y and IR depends mainly on the ET function (DM/ET or Y/ET), the irrigation salinity, and the irrigation hydrology determined by the partitioning of ET and T from IR as influenced by irrigation uniformity.

Crop yields typically are related to seasonal ET and seasonal IR as shown in Fig. 5.40 [77]. In a given season, the available soil water at planting (ASWP) and the effective rainfall (Pe) supply the crop with water to reach its dryland yield level. The applied-water yield relationship may be roughly linear up to approximately 50% of full irrigation [64].

For larger depths of applied water, the function begins to curve. Deep percolation increases with additional applied water. If the increase in applied water is associated with higher irrigation frequencies, larger evaporation may occur. The irrigation system will become less efficient as water use approaches full irrigation.

Tangent with slope

0 10 20 30 40 50 SEASONAL IRRIGATION DEPTH IR (cm)

Tangent with slope

LU 8

LU 8

cc 4

0 10 20 30 40 50 SEASONAL IRRIGATION DEPTH IR (cm)

cc 4

ET from

FIELD WATER SUPPLY (cm)

Figure 5.40. Processes leading to reductions in plant growth and grain yields due to excessive soil water. Source: Adapted from [77].

Because Y response to applied IR is a diminishing-return function, it follows that, at some point on this curve, further water application cannot be justified economically

In irrigated agriculture, the uneveness (nonuniformity) with which water infiltrates the root zone is determined mainly by the spatial variability of irrigation water application and on the variability of hydrologic soil properties [78]. The yield of a given crop, grown during a specific season in a certain field and under certain management and cultivation conditions, is also spatially variable because it is assumed to be directly dependent on the spatially variable water infiltration [79]. Unfortunately, none of the known irrigation systems are able to apply water with perfect uniformity. Because of this lack of uniformity, part of the surface is adequately irrigated but other parts are not. In the areas receiving an excess of water, the price of pumping can increase, yields may decline and mineral nutrients may be leached from the soil. This leaching of fertilizers represents an economic loss of applied resources, lowering of yields, and pollution of groundwater. In areas receiving insufficient irrigation water, a drop in yield can be noticed along with a poor use of fertilizers, which are not used by crops even though the whole water volume is retained in the rhizosphere.

Uneven irrigation or soil infiltration variability can produce nonlinear yield ET functions even though the basic yield function is exactly linear.

The economic implications of nonuniform irrigation application on crop yield and profit maximization have been analyzed by various researchers. Results are critically influenced by the nature of the water/yield relations postulated for the crop species. Results show that conventional economic analyses ignoring infiltration uniformities underestimate optimal levels of applied water, often substantially.

Seginer [80] offered a comprehensive review describing a general approach to economic optimization of sprinkler irrigation systems.

Warrick et al. [81] showed methods for calculating the performance parameters of irrigation systems for each of the theoretical water distribution functions: normal, lognormal, uniform and specialized power. They noticed that matching raw data to theoretical functions can better estimate parameters than the direct use of raw data.

Orgaz etal. [82] assumed that water distribution in a sprinkler system could be fitted to a uniform function. They therefore formulated a relation that allows estimation of production depletion on the basis of different gross water applications from the irrigation system [83]. The application to sprinkler injection is given in Section 5.4. Similar approaches to drip injection are proposed by Anyoji and Wu [84].

A study by de Juan et al. [85] provides a general methodology for analyzing the effects of infiltration uniformity on crop yield, optimum water application, and profit. The results show that conventional economic analyses, which ignore infiltration uniformities, underestimate the optimum level for the applied water. Further developments are given in other studies [86, 87].

The continued use of simple statistical models of crop-yield response to applied irrigation water could be replaced by process-orientated models in which individual components can be evaluated and analyzed. As the development of comprehensive crop-growth models increases, the irrigation economic analyses and real-time irrigation decisions can be accomplished with expert systems that rely on crop simulation.

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