What is Stochasticity

In hydrology, two modeling approaches have been prevalent: deterministic and stochastic. The ‘permanent’ nature of the Earth, ocean, and the atmosphere and the ‘cyclical’ nature of the associated mechanisms support the deterministic approach. The ‘highly irregular and complex’ nature of hydrologic processes and our ‘limited ability to observe’ the details favor the stochastic approach. In view of these, the question of whether a deterministic approach or a stochastic approach is better is meaningless. Indeed, for most hydrologic systems and processes, both the deterministic approach and the stochastic approach are complementary to each other and, thus, an approach that can couple these two and serve as a middle-ground would often be the most appropriate. ‘Chaos theory’ can offer such a coupled deterministic-stochastic approach, since its underlying concepts of nonlinear interdependence, hidden determinism and order, sensitivity to initial conditions are highly relevant in hydrology. The last two decades have witnessed numerous applications of chaos theory in hydrology. The outcomes of these studies are encouraging, but many challenges also remain. This chapter is intended: (1) to provide a comprehensive review of chaos theory applications in hydrology; and (2) to discuss the challenges that lie ahead and the scope for the future.