Responses of vegetation yield to precipitation and reference evapotranspiration in a desert steppe in Inner Mongolia, China

Drought, which restricts the sustainable development of agriculture, ecological health, and social economy, is affected by a variety of factors. It is widely accepted that a single variable cannot fully reflect the characteristics of drought events. Studying precipitation, reference evapotranspiration (ET 0 ), and vegetation yield can derive information to help conserve water resources in grassland ecosystems in arid and semi-arid regions. In this study, the interactions of precipitation, ET 0 , and vegetation yield in Darhan Muminggan Joint Banner (DMJB), a desert steppe in Inner Mongolia Autonomous Region, China were explored using two-dimensional (2D) and three-dimensional (3D) joint distribution models. Three types of Copula functions were applied to quantitatively analyze the joint distribution probability of different combinations of precipitation, ET 0 , and vegetation yield. For the precipitation—ET 0 dry—wet type, the 2D joint distribution probability with precipitation≤245.69 mm/a or ET 0 ≥959.20 mm/a in DMJB was approximately 0.60, while the joint distribution probability with precipitation≤245.69 mm/a and ET 0 ≥959.20 mm/a was approximately 0.20. Correspondingly, the joint return period that at least one of the two events (precipitation was dry or ET 0 was wet) occurred was 2 a, and the co-occurrence return period that both events (precipitation was dry and ET 0 was wet) occurred was 5 a. Under this condition, the interval between dry and wet events would be short, the water supply and demand were unbalanced, and the water demand of vegetation would not be met. In addition, when precipitation remained stable and ET 0 increased, the 3D joint distribution probability that vegetation yield would decrease due to water shortage in the precipitation—ET 0 dry—wet years could reach up to 0.60–0.70. In future work, irrigation activities and water allocation criteria need to be implemented to increase vegetation yield and the safety of water resources in the desert steppe of Inner Mongolia.