A mathematical meta-model for assessing the self-sufficient water resources carrying capacity across different spatial scales in Iran

Hydrological modeling, water accounting assessments, and land evaluations are well-known techniques to carry out water resources carrying capacity (WRCC) assessments at multiple spatial levels. Using the results of an existing process-based model for assessing WRCC from very fine to national spatial scales, we propose a mathematical meta-model, i.e., a set of easily applicable simplified equations to assess WRCC as a function of high-quality agricultural lands for optimistic to realistic scenarios. These equations are based on multi-scale spatial results. Scales include national scale (L0), watersheds (L1), sub-watersheds (L2), and water management hydrological units (L3). Applying the meta-model for different scales could support spatial planning and water management. This method can quantify the effects of individual and collective behavior on self-sufficient WRCC and the level of dependency on external food resources in each area. Carrying capacity can be seen as the inverse of the ecological footprint. Hence, using publicly available data on the ecological footprint in Iran, the results of the proposed method are validated and give an estimation of lower and upper bounds for all biocapacity of the lands. Moreover, the results confirm the law of diminishing returns in the economy for the carrying capacity assessment across spatial scales. The proposed meta-model could be considered a complex manifest of land, water, plants, and human interaction for food production, and it could be used as a powerful tool in spatial planning studies.