Neural Network Characterization of Geophysical Processes With Circular Dependencies

This paper describes a method for training neural networks to learn circular dependencies. Variables with circular structure (e.g., time of day, day of year, and Earth location) appear in many different contexts within geoscience and remote sensing. Some common representations of circular variables (e.g., time of day in hours) can introduce discontinuities or topological distortions in estimation problems. They do not necessarily prevent a neural network from learning a relationship with circular dependencies. However, using topologically appropriate representations of circular variables can reduce the complexity necessary for a neural network to accurately learn such a relationship despite possibly increasing the number of inputs thereby reducing training times. In this paper, neural networks are trained to learn fictitious geophysical functions of time of day, of geolocation, and of time of year. In all three examples, using topologically appropriate representations of time and geolocation instead of conventional representations as inputs significantly reduced rms errors. Neural networks are also trained to learn the variations of air temperature observations with time of day and day of year, and one-month averages of sea surface temperature with geolocation. The improvement achieved by using topologically appropriate representations was limited by a natural random behavior in the data. However, there is a small but significant improvement in estimating the sea surface temperatures. Using the topologically appropriate representations of circular data when training the neural networks could be important in global Earth science remote sensing contexts, where significant diurnal, seasonal, or geographical variations exist. The studies presented also suggest the development of a more general framework for training neural networks that considers the topology of variables.