purposes. From a practical point of view, they enable predictions and/or simulations; that is, they are a means to an end. In addition, however, parameterizations encapsulate our understanding of the physical interactions among disparate scales and processes. From this point of view, parameterizations are a route to understanding.
It is a truism of dynamical systems theory that simple component processes can combine in a coupled nonlinear system to yield unexpected emergent behaviors, through feedback among the components. The computational simulation models in wide current usage would seem rife with such possibilities, yet they usually are configured to maximize stability and minimize surprises. This is partly due to a prudent conservatism, but it does avoid the central issue of unexpected emergent behaviors. Because the large models can only have a small portion of their possible behaviors explored, an essential companion activity is discovering and fully understanding a suite of artfully conceived, elegant, minimally constructed models of canonical emergent behaviors germane to the atmosphere and ocean. Some examples of such elegant models are low-order geochemical box (i.e., well-mixed reservoir) models and oscillator models for El Niño-Southern Oscillation and paleoclimatic cycles, as well as more fluid-dynamical models for turbulent boundary layers, synoptic weather life cycles, and the turbulent equilibrium of a zonal baroclinic jet. Many more canonical models for relevant emergent behaviors are needed if our field is ever to come to trust and understand the abundant but complicated evidence from simulation models and measurements.
It is possible to conceive of a purely empirical route to parameterization in which understanding is only required at the level of asserting that the process can be represented in terms of large-scale variables and identifying which of those variables the process in question should depend on. The specific relationship between these variables and the process would be determined purely by experiment. Although such an empirical method may be possible, it would no doubt prove cumbersome. Moreover, not adequately understanding the physical processes would make it less robust, and it likely would be less satisfying intellectually. This highlights the intimate connection between understanding and parameterization, which can be regarded as an embodiment of a set of physical hypotheses. The most satisfying parameterizations start out with an understanding of the importance of the process to be parameterized, followed by an elegant hypothesis about the relationship