Rainfall erosion is a major cause of inducing soil degradation, and rainfall patterns have a significant influence on the process of sediment yield and nutrient loss. The mathematical models developed in this study were used to simulate the sediment and nutrient loss in surface runoff. Four rainfall patterns, each with a different rainfall intensity variation, were applied during the simulated rainfall experiments. These patterns were designated as: uniform-type, increasing-type, increasing- decreasing -type and decreasing-type. The results revealed that changes in the rainfall intensity can have an appreciable impact on the process of runoff generation, but only a slight effect on the total amount of runoff generated. Variations in the rainfall intensity in a rainfall event not only had a significant effect on the process of sediment yield and nutrient loss, but also the total amount of sediment and nutrient produced, and early high rainfall intensity may lead to the most severe erosion and nutrient loss. In this study, the calculated data concur with the measured values. The model can be used to predict the process of surface runoff, sediment transport and nutrient loss associated with different rainfall patterns.

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In arid and semi-arid irrigated croplands, the excessive accumulation of soluble salts in the root zone is an extensive problem that seriously limits crop yield and water productivity (WP). To avoid affects the yield potential of crops, the application of extra irrigation for leaching of excessive salts from the root zone was required. Quantitative knowledge of effects of the irrigation water salinity and leaching fraction (LF) on the relative yield (RY) and the unit water productivity of crop evapotranspiration (UWP ET) and the unit water productivity of irrigation water (UWP I) were becoming gradually important. This article provided theoretical models for estimating the UWPs (UWP ET and UWP I) and optimizing leaching fraction according to irrigation water salinity. In the present study, eight levels of irrigation water salinity (ECw = 0.25, 0.50, 0.75, 1, 2, 3, 4, and 5 dS/m) and 39 levels of LF values ranging from 0.04 to 0.80 were set and tested to assessing their effects on the RY and UWPs for four typical crops (barley, bean, wheat, and maize) with different salt tolerance levels. Almost every curve determined between the UWPs and LFs for the four crops had an inflection point. It was indicated that the UWP ET and UWP I could be maximized by optimizing the LF under different irrigation water salinities. Furthermore, the linear regression relationships were established to estimate the maximum values of UWPs and their corresponding optimal LFs for four crops by using the irrigation water salinity. Moreover, the theoretical models for estimating the UWPs were validated by data of wheat from previous literature, and the models could be suitable with acceptable relative errors when LFs ranging from 0.07 to 0.17.

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The Leaf Area Index (LAI) strongly influences crop biomass production and yields. The variation characteristic of LAI and the development of crop growth models can provide a theoretical basis for predicting crops’ water consumption, fruit quality and yields. This paper analyzes the relationship between measurements of aboveground grape biomass and trends in LAI and dry biomass production in grapes grown in the Turpan area. The LAI changes in grapes were estimated using the modified logistic model, the modified Gaussian model, the log-normal model, the cubic polynomial model, and the Gaussian model. Universal models of LAI were established in which the applied irrigation quota was applied to calculate the maximum LAI. The relationship between the irrigation quota and biomass production, yields, and the harvest index was investigated. The developed models could accurately predict the LAI of grapevines grown in an extremely arid area. However, the Gaussian and cubic polynomial models produced less accurate results than the other models tested. The Michaelis–Menten model analyzed the relationship between biomass and LAI, providing a numerical method for predicting dynamic changes in grapevine LAI. Moreover, the crop biomass increased linearly with the irrigation quota for quotas between 6375 and 13,200 m3/hm. This made it possible to describe the grape yield and harvest index with a quadratic polynomial function, which increases during the early stages of the growing season and then decreases. The analyses of the relationship between yield and harvest index provide important theoretical insights that can be used to improve water use efficiency in grape cultivation and to identify optimal irrigation quotas.