Present and future of hydrology

Xiao-fang RUI*, Ning-ning LIU, Qiao-ling LI, Xiao LIANG

College of Hydrology and Water Resources, Hohai University, Nanjing 210098, P. R. China

Present and future of hydrology

Xiao-fang RUI*, Ning-ning LIU, Qiao-ling LI, Xiao LIANG

College of Hydrology and Water Resources, Hohai University, Nanjing 210098, P. R. China

The complexities of hydrological phenomena, the causes that lead to these complexities, and the essences and defects of reductionism are analyzed. The driving forces for the development of hydrology and the formation of branch subjects of hydrology are discussed. The theoretical basis and limitations of existing hydrology are summarized. Existing misunderstandings in the development of the watershed hydrological model are put forward. Finally, the necessity of the expansion of hydrology from linear to nonlinear is discussed.

hydrological phenomenon; hydrological theory; hydrological method; hydrological model; reductionism; nonlinear

1 Introduction

Hydrology is the study of hydrological cycle process, their temporal and spatial variations, and the interaction between water and other subsystems, such as the ecology, environment, and society, in the Earth system. One of the core scientific problems in hydrology is the principle of formation and evolution of runoff from rainfall. Hydrology is an important support subject for the prevention of flood and drought disasters, sustainable use of water resources, and protection of ecology and the environment. It is also essential to engineering construction for water conservancy, energy sources, and transportation. We recognize that hydrology is a profound subject. This paper describes our understanding of hydrology in five parts: the complexities of hydrological phenomena and defects of reductionism, the branches of hydrology and driving forces for the development of hydrology, the hydrological methods and limitations of existing theories, the development trends of watershed hydrological models and their existing misunderstandings, and the necessity of hydrological expansion from linear to nonlinear.

2 Complexities of hydrological phenomena and defects of reductionism

Hydrological phenomena are the products of interactions between atmospheric processes and land surface conditions (Rui and Jiang 2010). The same temporal and spatial distributionsof rainfall falling over different land surfaces of watershed will generate different flood processes and hydrological time series; different temporal and spatial distributions of rainfall falling over the same land surface of watershed will also generate different flood processes and hydrological time series. According to the current level of understanding, the complexities of hydrological phenomena have the following characteristics. First, the temporal and spatial variations of hydrological phenomena have both deterministic and non-deterministic characteristics. The latter is more obvious in many cases. Second, the deterministic performance of hydrological phenomena has both periodic and non-periodic characteristics. The latter consists of causality and tendency. Third, the non-deterministic performance of hydrological phenomena may be expressed as randomness, grey characteristics, fuzziness, mutability, chaos characteristics, etc. Randomness consists of pure randomness, stationary randomness, and non-stationary randomness. Fourth, hydrological phenomena have broad spatial and temporal spans. The temporal and spatial variability is very large in many cases. Fifth, the non-similarity of hydrological phenomena at different scales is very large. Finally, compared with weather phenomenon, hydrological phenomena are more sensitive to human activities.

The six characteristics mentioned above show that hydrological phenomena are very complex. However, due to the limitations of human understanding, the complexities of hydrological phenomena may not be fully revealed. Therefore, when the law of hydrology is discussed through reductionism (Chang 2008), it will sometimes run into a stone wall.

Reductionism is an approach to understanding the nature of complex things by reducing them to simpler parts. The application of reductionism to analysis of river flood wave movement can be regarded as quite successful; its application to analysis of the formation of rainfall-runoff basically can be regarded as successful. However, when applying it to analysis of temporal and spatial variations in the hydrological cycle and long-term evolution of runoff, we run into a stone wall. Because the hydrological cycle is a complex system consisting of multiple paths and multiple scales, it is almost impossible to attain a thorough understanding using the theory of reductionism. Therefore, it is necessary to look for other ways to solve such problems. The biggest challenge is selecting proper mathematical and physical tools to describe such a complex system completely.

3 Branches of hydrology and driving forces for development of hydrology

The Earth system is composed of four spheres. Atmospheric science is the study of the atmosphere, geological science is the study of the lithosphere, biological science is the study of the biosphere, and water science, consisting of hydrology and oceanography, is the study of the hydrosphere. As an independent subject, hydrology may be of a junior generation. But it has been developing rapidly over the last half-century. It has become an extensive subject system with many branch subjects (Rui 2004). According to the water studied (Fig. 1), it canbe classified into watershed hydrology, river hydrology, lake and reservoir hydrology, groundwater hydrology, estuarine and coastal hydrology, wetland hydrology, glacier hydrology, hydrometeorology, eco-hydrology, and global hydrology. According to practical applications of hydrology (Fig. 2), it can be classified into engineering hydrology, bridge hydrology, urban hydrology, agricultural hydrology, forest hydrology, water resources hydrology, and environmental hydrology. According to the interdisciplinarity or research methods (Fig. 3), it can be classified into dynamic hydrology, systematic hydrology, stochastic hydrology, computational hydrology, digital hydrology, geographical hydrology, hygrometry, hydrological informatics, experimental hydrology, and isotope hydrology.

Fig. 1 Classification of hydrology according to water studied

Fig. 2 Classification of hydrology according to practical applications of hydrology

Fig. 3 Classification of hydrology according to interdisciplinarity or research methods

As with any other subject, the driving force for the development of hydrology falls into three categories. The first is curiosity, which is a natural potential of humans. Their curiosity about hydrological phenomena has always existed. Zongyuan Liu, who lived in the Tang Dynasty, was curious about the phenomena of runoff generation and concentration. His articleTian Duigives an original description of runoff formation on repletion of storage. In 1674, the French researcher Perreault became curious about the quantitative relationship between annual rainfall and annual runoff of the Seine River Basin, and concluded that the annual runoff in this basin was equal to 1/6 of the annual rainfall (Biswas 1972). In 1961, the British researcher Penman expressed his curiosity about rainfall-runoff with the question “What happens to the rain?” (Singh and Woolhiser 2002) It can be said that science could not originate without curiosity.

The second is the needs of economic development. Engineering hydrology developed rapidly from the 1930s to 1940s. Water resources hydrology and environmental hydrology began to develop after the 1970s. The rise of eco-hydrology research has occurred over the last 20 years. All of these are the requirements of economic society development.

The third is the seeking of the truth. In the process of scientific research, truth-seeking is driven by scientific discussion and scientific critical spirit. The process of scientific discussion and criticism is the process of seeking the truth. Dunne put forward a new theory of runoff in the 1970s, which was based on his criticism of the original Horton runoff theory (Kirkby 1979). The reason why Cunge (1969) found the hydraulic basis of the Muskingum method in 1969 is that he deeply believed that a theoretical link existed between hydrologic andhydraulic methods, since flood routing problems could be solved using both of them. These examples all indicate that people did contribute to the scientific development in the process of seeking the truth.

These three driving forces, which promote the development of hydrology, exist objectively and complement one another.

4 Hydrological methods and limitations of existing theories

The development of a subject needs driving forces; effective and skillful methods are also indispensable. Subject development and subject methodologies are mutually reinforcing. The innovation of subject methodologies greatly contributes to the prosperous development of a subject. On the other hand, the subject development effectively promotes the development of methodologies and the emergence of better methods. We think we can summarize hydrological methods in two levels: thinking methodology and research methodology. Thinking methodology refers to the thought used to examine the hydrological phenomena and reveal their laws. It is mainly demonstrated in its application to the dialectical relations between macro and micro, statistics and cause, aggregation and disaggregation, linear and nonlinear, physical laws and constitutive relations, physical processes and applied mathematical processes, and modeling and forecasting. Research methodology refers to the method used to express the revealed hydrological law and to meet the purpose of application. The specific research methodologies of hydrology generally include the observation methods used to examine the hydrological phenomena and the analysis methods used for expressing their own laws. The observation of hydrology generally includes field observation by setting up stations, scientific investigation, and scientific experiments. The analysis of hydrology includes deductive reasoning and mathematical modeling. Hypothesis, conjecture, and analogy are the analytical tools commonly used in hydrological research.

There have been many attractive research cases during the long history of hydrology (Rui 2003). These cases indicate that research methodology plays an important role in promoting the development of a subject. Exploring and refining these cases not only inspires people’s spirit of scientific innovation, but also carries forward dialectics of nature.

The development of hydrology has generally gone through four stages so far (Chen 2004; Xu and Li 2010). By reviewing the development process of hydrology, it is not difficult to find that some theories that support existing hydrology have mainly been formed over the last 100 years, especially since the 1930s. In addition to the basic physical laws such as the mass conservation law, energy conservation law, momentum conservation law, law of thermodynamics, and diffusion law, there are lots of hypotheses (Rui et al. 2007, 2012a) (1) assuming that the global hydrological cycle is a closed system, (2) assuming that hydrological factors are uniform over a certain spatial area, (3) assuming that changes of hydrological factors are uniform within a limited period, (4) assuming that the hydrologicalfactors meet the requirements of superposition and uniformity, (5) assuming that a threshold effect exists, (6) assuming that hydrological factors have random independence, (7) assuming a stationary time series, and (8) assuming that there are reproducibility and similarity.

The rationality and applicability of the hypotheses listed above cannot be generalized. Some of them can be approximately verified via experiments or measured data. For example, under certain conditions they approximately show superposition, multiple proportions, a threshold effect, and temporal and spatial distribution uniformity. However, under other conditions there may exist large errors and these hypotheses cannot even be used. Others are mainly verified via speculation. For example, the assumptions such as independent randomness, stationary randomness, reproducibility, and similarity still cannot be verified in reality.

The existing theories of hydrology can meet the requirements of hydrology for the development of an economic society despite the problems mentioned above.

With a higher demand of hydrology for the development of an economic society and the pursuit of scientific truth, more questions are raised about the rationality of existing hydrological theories and their accuracy. The voices asking for improvement in hydrology theory grow louder and louder.

5 Development trends of watershed hydrological models and their existing misunderstandings

Watershed hydrological models are the product of hydrology and computer technology. The emergence of watershed hydrological models was a landmark in the history of hydrology. According to Singh and Woolhiser (2002), there are hundreds of watershed hydrological models in the world. Seventy of them have great practical value, and 15 models are popular. The Xin’anjiang model developed by Renjun Zhao is one of them. Watershed hydrological models have gradually become important tools for exploring the hydrological law and solving the water issues emerging in economic development. Research on watershed hydrological models is generally concerned with the basic scientific questions of hydrology, which are how to improve accuracy and how to better simulate and predict what happens to the rain. The facts of the development of watershed hydrological models over the last 30 years show that the general trends of their development are (Rui et al. 2012b) (1) from lumped, dispersed models to distributed models; (2) from black boxes and conceptual models to physically based models; (3) from considering the deterministic characteristic or the random characteristic only to considering the both; (4) from only simulating the formation of runoff to integrating flow, convergence, sediment, and water quality; and (5) from a traditional way to the way based on a digital watershed.

We are willing to put forward several notable problems existing in the process of research and application of watershed hydrological models (Rui et al. 2012b). First, developing and applying watershed hydrological models are the only goals in the process of hydrologicalstudies, and this results in exaggerating its role and neglecting the mechanisms of hydro-physical processes. Second, hydrological models developed under certain conditions are misused. The hydrological models developed abroad are used anywhere, but their specific conditions of application are neglected. Third, optimization methods are aimlessly used to calibrate model parameters. The model structure and physical meaning of parameters are neglected, and thereby the equifinality existing among parameters is also ignored. Fourth, attention is paid to fitting historical data but the verification of prediction is neglected. Many research reports or papers declare success in simulating one or a few flood events, and do not publish the model parameters or undertake any reasonable analysis. Finally, the illusion of good fitting results is artificially created. For example, the flow duration curve instead of the chronological order process is used to express simulation results. Furthermore, parameters are verified according to the calculation results of empirical formulas.

6 Necessity of hydrological expansion from linear to nonlinear

The thinking way can be classified into linear and nonlinear thinking in philosophy. Linear thinking is based on the mechanistic worldview, while nonlinear thinking is based on a complex worldview.

Linear thinking is the thinking of the linear system. The basic nature of the linear system is that the change of the initial state will lead to any subsequent state change proportionally. Nonlinear thinking (Yi 1995) emerged with nonlinear science and examines the world from the view of totality, process, and evolution. In nonlinear thinking, people find a more realistic picture, an open, evolving, and complex world instead of a decisive, simple, and harmonious pattern created by Newton and Einstein. The world is regarded as a holistic complex system, in which summation of partial functions does not equal the overall function. Furthermore, a number of interrelated factors do not meet the principle of superposition, but have the characteristics of being non-equilibrium, being non-uniform, aperiodicity, asymmetry, non-integrability, irreversibility, and discontinuity.

In the history of science development, linear thinking plays an important role in exploring natural laws, which can be used to solve practical problems. It promotes the development of science, technology, and social productivity effectively. However, when scientific research gradually goes deeper into the ecosystem, the Earth system, the universe system, and the social system, linear thinking is not the best way to understand facts and solve problems. In fact, many natural phenomena, including hydrological phenomena, are not as simple as linear thinking describes. They are complex systems including deterministic and non-deterministic elements. Both reversible and irreversible processes can be found in these complex systems. Following the course of hydrologic development, people find the reality mentioned above. Although linear thinking helps to basically solve some scientific problems such as flood wave movement and the formation of runoff, it cannot help to solve the problems of droughts andfloods, which are caused by temporal and spatial variations in the global hydrological cycle. Although the accuracy of short-term flood forecasting can be basically met, the dilemma of use and abandonment of long-term flood forecasting results cannot be resolved.

Of course, there is no unbridgeable gap between linear thinking and nonlinear thinking. Therefore, the change from linear to nonlinear does not mean abandonment of linearity. It means that the foundation of linearity should be more consolidated. Linear thinking is not only an effective tool for solving some hydrological problems in the future, but also an important tool for approaching nonlinear thinking gradually (Rui et al. 2008a, 2008b).

Hydrology needs to develop from linear to nonlinear. It is a historical necessity. It will be very difficult to achieve nonlinearity in the research of hydrology, but it has great promise (Menabde et al. 2001; Fleurant et al. 2006).

7 Conclusions

Hydrological phenomena are very complex phenomena of nature. Hydrology is the study of hydrological phenomena: their occurrence, development, and evolution. The main task of hydrology is to investigate the long-term evolutionary law of hydrological time series and the mechanism of catchment runoff generation. Hydrology has been becoming an extensive subject system with many branch subjects over more than 300 years, which fully shows its colorful intension and extension. Present achievements in hydrology are mainly based on the theories of linearity and reductionism. However, hydrology has become incapable of fully satisfying economic development under certain conditions, limited by these theories. We believe that from linear to nonlinear and introduction of the holistic theory will be the development tendencies of hydrology.

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(Edited by Yun-li YU)

This work was supported by the National Natural Science Foundation of China (Grant No. 41130639).

*Corresponding author (e-mail:jiangguol@hotmail.com)

Oct. 8, 2011; accepted Apr. 20, 2012