Does Time–Space Symmetry Exist in Relationship Between Regional Vegetation Patterns and Budyko Shape Parameter Governing Annual Water Balance?

Abstract

The parsimony of the Budyko water balance model has prompted its extensive use for analyzing climate–vegetation–water interactions. Existence of time–space symmetry in the Budyko model, governing the hydrological predictions across both temporal (short-term annual) and spatial (long-term mean annual) domains, has enabled its application in ungauged basins through use of space-for-time substitution (SFTS). However, time–space symmetry in the relationship between the Budyko shape parameter and in vegetation changes has not been well studied. The Budyko curve, which varies spatially across regions due to differences of vegetation, also varies temporally as vegetation evolves over time. Here, we investigate this problem in a representative basin with several sub-catchments, which includes sensitivity to vegetation dynamics and climate change using two shape parameters (n₁ and n₂) and the vegetation cover, M. Interestingly, time–space symmetry was found between M/Φ and n₁/Φ or exp(−n₂)/Φ, compared to just M versus n separately (which produces asymmetry), implying a coupled ecohydrological adjustment mechanism between vegetation functioning and hydrological structure co-regulated in response to climatic constraints counteracting the effects of spatio-temporal heterogeneity on water balance partitioning. Our study proposes a novel and streamlined ecohydrological model within the time–space equivalence hypothesis and recognizes that the symmetry/asymmetry is crucial for accurate SFTS application.