Keywords: wave analysis, wave statistics, neural networks, operational waves, wind waves.

Almost any civil engineering activity in the ocean calls for the knowledge of wind generated gravity waves at the location of interest. Various government as well as private agencies over the world, like the National Institute of Ocean Technology of India and the National Data Buoy Center of U.S.A., have initiated ambitious wave data collection programs. Availability of large-scale direct wave observations as a result can be expected to fast replace the conventional wave prediction methods based on use of wind and many other met-ocean parameters, especially when point predictions rather than spatial ones are required.

This paper discusses performance of five wave data based forecasting schemes, which are based on analysis of the observed time history of waves. They include the Auto-Regressive Neural Networks (ARNN), Kalman Filter, Auto- Regressive Integrated Moving Average (ARIMA), Auto-Regressive Moving Average (ARMA) and Auto-Regressive (AR) models. The ARNN is a highly generalized form of conventional stochastic time series models where no a priori assumption on data properties is made, because of which it can operate even under the environment of non-stationarity and measurement errors. Kalman Filter is also a versatile stochastic time series model, which is free from any restriction on data characteristics like stationarity and error-free measurements. Auto Regressive Integrated Moving Average (ARIMA) and Auto Regressive Moving Average (ARMA) models represent the non-stationary and stationary time series, respectively. In the current study AR model of order 2 was found to be sufficient because still higher order models did not result in any further improvement in the results. Similarly commonly used ARMA and ARIMA models of the first order were employed in preference to their higher versions.

A wave rider buoy was deployed at the site off Goa in India for a period of 16 months starting from May 1983 and short-term (3-hourly) wave records numbering 2661 were collected. These data formed the basis of investigation reported herein.

Forecasting of significant wave heights was attempted over leading times of 3, 6, 12 and 24 hours on the basis of all models described in the previous section by suitably forming mean wave height series over the required intervals. The results of forecasting were compared with the actual observations, that were not involved in model calibrations, by

1. plotting time series,
2. drawing scatter diagrams,
3. evaluating correlation coefficient, and
4. estimating average absolute deviation.

Generally all rising and falling trends in the observed time series were picked up by the predicted series and their scatter was well dispersed around the line of exact match. The correlation coefficient had the highest value for the case of 3-hour ahead forecasting and its magnitude reduced as the forecasting interval increased to 24 hours. Similarly the average absolute deviation increased with the increase in leading time from 3 to 24 hours. When it came to lower leading times of 3 or 6 hours, ARNN was the most accurate, while Kalman Filter performed relatively better for longer leading times of 12 and 24 hours- ahead forecasting. ARIMA, ARMA and AR are highly dependent on model forms and the specific input-output relationship assumed therein a priori seems to become too restrictive to simulate the natural and complex phenomenon of wave occurrences. ARNN was most accurate for lower forecasting interval, but it was not so when compared with Kalman Filter for higher intervals. This appears to be so because of the lower number of training patterns available to calibrate it at higher forecasting durations. It therefore seems that the highly generalized ARNN works most satisfactorily for the problem under consideration provided sufficient number of examples are available to train the network. When this is not the case Kalman Filter could be a preferable choice, which produces equally accurate results for 3, 6 and 12 hour cases and does not seem to be too dependent on quantum of calibration data.

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