Framework of "two-dimension three-element" coupling flow of real water and virtual water

Abstract: With the background of changing environment and fast economic globalization, the regional hydrology and water resource system is experiencing profound changes. Under this new situation, to solve the problem of water scarcity and imbalance water associated with water cycle process, only relying on the traditional water resource planning, regulating and management is not enough. The concept of virtual water widens the cognitive scope of hydrology and water resources and enriches the ways to cope with water-related issues. However, it is still not clear about how to construct an integrated scientific framework combining the virtual water theory with the traditional hydrology and water resource theory, and how to consider the new evolution law of water resources in the entire natural, economic and social systems. The paper firstly presented a basic framework of real water and virtual water coupling flow effect. The coupling flow regime between real water and virtual water was a new important characteristic of the natural-social water resource system in the context of modern environment. Secondly, from the perspective of historical evolution, this study discussed the developing process of the hydrology and water resource system in human society. There were mainly 3 phases in the evolution process of water resource system since the birth of human civilization. In ancient time (before Industrial Revolution in 1760s), when the productive force level was low and the human's influence on water resource system was small, the driving force of water resource system was almost the natural power (e.g., gravity, solar energy). Thus the water flow route of water resource system in this phase could be defined as "one-dimension one-element" flow. The "one-dimension" mainly referred to the real water and the "one-element" referred to that the water flowing path of water resource system was only in the natural cycling route. After Industrial Revolution, the productive force level was greatly improved, and the human's influence on water resource system was correspondingly enhanced. Therefore, the water flow route of water resource system during this time was defined as "one-dimension two-element" flow. Here the "two-element" referred to that the water flowing path of water resource system was not only in the natural cycling route, but also in artificial canal systems. Nowadays, with fast development of economic globalization and international trade, there is not only a huge amount of real water exchanged through large water project, but also a large amount of virtual water embedded in commodities transported by trade among different regions of countries. As a consequence, the water flow route in the water resource system in the new conditions was defined as "two-dimension three-element" (2D-3E) flow. Here the "two-dimension" referred to real water and virtual water and the "three-element" referred to that the water coupling flowing path of the new water resource system included 3 routes (i.e., real water flowing route, real water being transformed to virtual water route, and virtual water flowing route in society). According to the above analysis, our research depicted the 2D-3E flowing route's structure in detail based on the coupling mechanism of real water and virtual water. At last, a set of equations to quantitatively characterize the coupling flow process were proposed, which could be a good tool for the combined regulation and management of real water and virtual water. On the whole, a preliminary theory of real water and virtual water coupling flow regime is established.