Depending on the production function, irrigation water cost function and the sale price of yield, previously, lengthy mathematical expressions have been developed to estimate the optimal levels of water used in deficit irrigation, that would maximize yield (W m), under water limiting (W w), and under land limiting (W l) and the amount of water that leads to income equal to income of W m when land is limited (W el), and that leads to farm income equal to farm income of W m when water is limited W ew. Therefore, in this paper, firstly the previous lengthy expressions for (W el) and (W ew) were simplified. Secondly, simple expressions for both (W el) and (W ew) were derived under presence of rainfall. Thirdly, very simple mathematical relations between (W m & W l) and (W m & W w) were derived in order to determine much easier expressions than those previously derived for W el , and W ew respectively, with and without rainfall.

No abstract

The laboratory tests carried out 12 tests to follow the advance of wetting front at appropriate times during the wetting and redistribution phases as a resulting of water application from a single linear trickle source or two linear trickle sources with a certain spacing to soil profile. These data are used to express with an estimating relationships for the wetting pattern produced by single linear trickle source and two linear trickle sources during wetting and redistribution phases. The study showed that there is a significant correspond between the wetting pattern of the measured and the estimated by the experimental equations. The wetting pattern increases with the decreasing of spacing between the two linear trickle sources, and this increase is regular along the wetting front or the surrounding of the wetting pattern, and this increase in the vertical direction of the wetting pattern is more in sandy loam soil than in silty clay soil and vice versa in the horizontal direction, when compare among the wetting patterns at the end of the wetting phase and the redistribution phase at a total time of 72 hours.

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The performance of irrigation systems can be evaluated by criteria which show the efficient use of on-farm water distribution. The different distribution of infiltration depths in the soil may give the same value of application uniformity coefficient; therefore the present study considered the distribution uniformity coefficient of the useful infiltration depths in the root zone as part of the evaluation criteria. The considered criteria was expressed as a function of both application adequacy and the application uniformity of infiltration depths. The derived function is applicable for linear and natural distribution of infiltration depths.