Nonlinear dynamics are basic to the characterization of many physical phenomena encountered in practice. Typically, we are given a time series of some observable(s) and the requirement is to uncover the underlying dynamics responsible for generating the time series. This problem becomes particularly challenging when the process and measurement equations of the dynamics are both nonlinear and noisy. Such a problem is exemplified by the case study of sea clutter, which refers to radar backscatter from an ocean surface. After setting the stage for this case study, the paper presents tutorial reviews of: 1) the classical models of sea clutter based on the compound K distribution and 2) the application of chaos theory to sea clutter. Experimental results are presented that cast doubts on chaos as a possible nonlinear dynamical mechanism for the generation of sea clutter. Most importantly, experimental results show that on timescales smaller than a few seconds, sea clutter is very well described as a complex autoregressive process of order four or five. On larger timescales, gravity or swell waves cause this process to be modulated in both amplitude and frequency. It is shown that the amount of frequency modulation is correlated with the nonlinearity of the clutter signal. The dynamical model is an important step forward from the classical statistical approaches, but it is in its early stages of development.

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[1] Precipitation events were examined at Fort Simpson, Northwest Territories, Canada, during the autumn and winter of 1998 and during the spring of 1999 with a variety of observational tools, including a polarimetric radar. This location is characterized by a relatively small amount of precipitation (annual average of 450 mm), with approximately half being in the form of snow. During the observational periods, precipitation was produced within multilayered cloud systems with heights ranging up to 10 km, and instances of light snow were associated with either low (<2.5 km) or high (up to 10 km) clouds. Precipitation over the observational periods was typically produced in banded structures, was sometimes reduced because of subcloud evaporation or sublimation, and in the winter was often in the form of individual crystals. A state-of-the-art weather forecasting model was often poor at simulating some of the critical features of the precipitation events, such as cloud top height and precipitation amount. In addition, it was shown that with the sensitive CloudSat radar, $17% of overpasses will be associated with the occurrence of detectable precipitation at Fort Simpson, but with the less sensitive Global Precipitation Measurement (GPM) radar, much of the precipitation will be undetected.

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