Learning from data for wind–wave forecasting

LEARNING FROM DATA FOR WIND–WAVE FORECASTING BY AHMADREZA ZAMANI, DIMITRI SOLOMATINE, AHMADREZA AZIMIAN & ARNOLD HEEMINK

BASIC OVERVIEW Location of study conducted : Caspian Sea. The problem associated with these models is to forecast significant wave heights for several hours ahead using buoy measurements. Models are based on artificial neural network (ANN) and instance-based learning (IBL). To capture the wind–wave relationship at measurement sites, these models use the existing past time data describing the phenomenon in question. Three feed-forward ANN models have been built for time horizon of 1h, 3h and 6 h with different inputs.

BASIC OVERVIEW The other six models are based on IBL method for the same forecast horizons. Instance-based learning or memory-based learning is a family of learning algorithms that, instead of performing explicit generalization, compare new problem instances with instances seen in training, which have been stored in memory. Instance-based learning is a kind of lazy learning. Experiments show that the ANNs yield slightly better agreement with the measured data than IBL. ANNs can also predict extreme wave conditions better than the other existing methods.

INTRODUCTION The sea state can be described with a wave spectrum, which represents the wave energy density per frequency and direction. By means of energy-balance equation the evolution of wave spectrum can be computed in space and time and hence wave forecasting could be obtained in the region of study. Presently WAM, Wave Watch III & SWAN are well-known mathematical-based models which are used in the most meteorological centers. When such models are used, preparation of meteorological data and heavy computer processing is a challenging job.

WHY ANN? These methods are based on the analysis of all data characterizing the system under study to find an unknown mapping or dependencies between the systems input and output from the available data. Puca et al. (2001) designed a neural network approach to the problem of recovering lost data in a network of marine buoys. *Weighted k-nearest neighbors (k-NN) and locally weighted regression (LWR) with Gaussian kernel were used. Another method used in the present work is known as average mutual information (AMI) method. AMI measures the dependence between the two random variables.

STUDY AREA Two sets of meteorological and wave data have been used in this study. Wind and wave data was collected by a 3-m diameter discuss shape buoy. This buoy deployed by Khazar Exploration and Production COmpany (KEPCO) at two different locations (A) and (B) situated in the southern part of the Caspian Sea. Location (A) is near the beach but location (B) is far from the coast. The water depth at these locations is 15 and 800m, respectively. The period of data collection at location (A) is from November 20,2005 to April 9, 2006 and at location (B) is from October 11, 2006 to May 2, 2007. Fortunately during these periods buoy collected data continuously and without any gaps in transmitting of data.

DETERMINATION OF INPUTS Intuitively, mutual information measures the information that A and B share. It measures how much knowing about one of these variables reduces our uncertainty about the other variable. For two statistically independent random variables the average mutual information (AMI) score is zero. Also if the random variables are strongly related, the AMI score would take a high value. From this figure it is clear that the value of AMI at location (B) is higher than that at location (A). This means that more substantial information about the wave data is included in the wind field at location (B). On the other hand due to the boundary and sea bed effects at location (A) which is close to the coast, the wave system will be affected by other parameters which are not included in the wind information.

SELECTION OF INPUTS A compromise approach has been chosen: the data was divided into two parts in such a way that both blocks of data would have extreme events of similar nature. For all the experiments the latest 400 observation were selected for testing the models, and the rest of the data was used for their training—this ensured both blocks have at least one extreme event for both locations. Still, this has not ensured very similar statistical properties of the two-data subsets because of seasonal effect. For example most of training set in location (A) belongs to winter while the test period is in the spring (see Fig. 2). This situation has implications on the way models are trained.

MODEL TRAINING For evaluation of models, a three-layer feed-forward ANN with sigmoid transfer function for hidden layer and linear transfer function for output layer have been selected. The network with five neurons in the hidden layer appeared to be the best model for both the locations. The stopping criteria were one of the following: minimum error in validation set mean square error in training reaching threshold of 0.0001 or the number of epochs reaching 2500

CONCLUSION This presented results show how the data-driven models could be effectively used to perform the short term wind–wave forecasting. A number of models were built and their inputs were selected by analyzing the AMI that gave some insight into the dependency of input and output parameters in the measurement locations. The selected case studies at shallow water (location A) and deep water (location B) showed that all models perform much better in deep waters. The presented research was aimed at investigating the possibilities of the data-driven methods. The results obtained could have been better if we would have had more data for the considered locations, and especially if there would be data available for the other locations in the Caspian Sea..

Learning from data for wind–wave forecasting

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Learning from data for wind–wave forecasting