A Copula Function–Monte Carlo Method-Based Assessment of the Risk of Agricultural Water Demand in Xinjiang, China

Agricultural water resources in Xinjiang, China, face significant supply and demand contradictions. Agricultural water demand risk is a key factor impacting water resource management. This study employs the copula function (CF) and Monte Carlo (MC) methods to evaluate agricultural water demand risk at 66 stations in Xinjiang. The evaluation is based on the marginal distributions of precipitation (PR) and reference evapotranspiration (RET). The findings classify Xinjiang’s precipitation–evapotranspiration relationship into three types: evapotranspiration, precipitation, and transition. Regions south of the Tianshan Mountains (TMs) primarily exhibit evapotranspiration characteristics. The Ili River Valley and areas north of the TMs display precipitation characteristics. Other areas north of the TMs have transitional characteristics. Both annual precipitation and RET in Xinjiang follow the Generalized Extreme Value (GEV) distribution. The Frank CF effectively describes the coupling relationship between precipitation and RET, revealing a negative correlation. This negative correlation is stronger north of the TMs and weaker to the south. The agricultural water demand risk in Xinjiang varies significantly across regions, with the precipitation–RET relationship being a crucial influencing factor. The demand index (DI) for agricultural water decreases as the risk probability (RP) increases. The stability of the DI is greatest in evapotranspiration-type regions, followed by transition-type, and weakest in precipitation-type regions. When the RP is constant, the DI decreases in the order of evapotranspiration, transition, and precipitation types. This study quantifies the spatial pattern of agricultural water demand risk in Xinjiang. The advantage of the CF–MC method lies in its ability to assess this risk without needing crop planting structures and its ability to evaluate spatial variations. However, it is less effective in areas with few meteorological stations or short monitoring periods. Future efforts should focus on accurately assessing water demand risk in data-deficient areas. The findings are crucial for guiding the regulation and efficient use of agricultural water resources in Xinjiang.