Agricultural Water Optimal Allocation Using Minimum Cross-Entropy and Entropy-Weight-Based TOPSIS Method in Hetao Irrigation District, Northwest China

Abstract

Affected by the temporal and spatial changes of natural resources, human activities, and social economic system policies, there are many uncertainties in the development, utilization, and management process of irrigation district agricultural water resources, which will increase the complexity of the use of irrigation district agricultural water resources. Decision makers find it challenging to cope with the complexity of fluctuating water supplies and demands that are critical for water resources’ allocation. In response to these issues, this paper presents an optimization modeling approach for agricultural water allocation at an irrigation district scale, considering the uncertainties of water supply and demand. The minimum cross-entropy method was used to estimate the parameters of hydrologic frequency distribution functions of water supply and demand, which are the basis for agricultural water resources’ optimal allocation and the evaluation of water resources’ carrying capacity in the Hetao Irrigation District. Interval Linear Fractional Programming was used to find water availability, shortage, and use efficiency in different irrigation areas of the Hetao Irrigation District (HID) under different scenarios. The denominator of fractional planning is the environmental goal, and the numerator is the economic goal; so, the objective function of fractional programming is the utility rate required in the post-optimization analysis. Future water availability and shortage scenarios are adopted consistent with the Representative Concentration Pathways’ (RCPs’) framework, and future water use scenarios are developed using the Shared Socioeconomic Pathways’ (SSPs’) framework. Results revealed that under SSP1, the annual water consumption increased from 30 billion m3 to 60 billion m3, almost doubling in Urad. The annual water consumption under SSP2 and SSP3 increased slightly, from 30 billion m3 to about 50 billion m3. The amount of water available for well irrigation in Urad decreased from 300 to 250 billion m3, while the amount of water available for canal irrigation in Urad remained at 270 billion m3 from 2010 s to 2030 s, only dropping to 240 billion m3 in 2040 s. The entropy-weight-based Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method was applied to evaluate agricultural water resources’ allocation schemes because it can avoid the subjectivity of weight determination and can reflect the dynamic changing trend of irrigation district agricultural water resources’ carrying capacity. The approach is applicable to most regions, such as the Hetao Irrigation District in the Upper Yellow River Basi with limited precipitation, to determine water strategies under the changing environment.