Neural Network Approach to Wave Height Prediction in the Apostle Islands. Michael Meyer

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1 Neural Network Approach to Wave Height Prediction in the Apostle Islands Michael Meyer The Sea Caves site in the Apostle Islands on Lake Superior is a popular destination for recreational kayakers. Kayakers depart from Meyers Beach which is approximately 1.5 miles from the actual Sea Caves site and paddle along the shore to the site to explore the Sea Caves. Wave height is an important consideration for kayakers deciding whether conditions are safe before departing but in the case of this location. Wave heights can range up to five feet at this location, and can be dangerous for kayakers. The actual Sea Caves site is not visible from the launch location and wave conditions can be very different between the two locations. To advise kayakers on conditions before they depart there is currently a kiosk that displays wave information gathered from a wave sensor deployed at the site. This sensor is being permanently removed, however, leaving a need for an alternative means of providing wave height data. The goal of this project to is to create a neural network means of predicting current wave heights at the sea caves site using data sources that are available in real time. There is some precedent for a neural network approach to wave height prediction including the work presented by Deo in Neural Networks for Wave Forecasting. In Incorporation of artificial neural networks and data assimilation techniques into a third-generation wind-wave model for wave forecasting Zhang explores configuring a neural network to use the output of a wave model as an input and, after being trained using historical model outputs as inputs and historical observed wave heights as targets, to output a more accurate wave height. The goal of this work, however, is to use as inputs the predictions of two models, along with weather and wave conditions recorded by a buoy and weather station, to output a wave height prediction that is more accurate than any individual model or wave height prediction method. There are several wave models running with accessible outputs that predict current wave heights on Lake Superior including a SWAN wave model of the Apostle Islands region of Lake Superior operated at the University of Wisconsin Madison and the wave height nowcast output from the NOAA Great Lakes Coastal Forecasting System. Additionally, wind (wind speed and direction) and air temperature data from a NOAA weather station located on Eagle Island, approximately 20 miles from the Sea Caves site, is available online in near real-time as well as wave height, wind, air and water temperature data from a buoy approximately 40 miles west in Lake Superior. Figure 1 shows the locations of the data sources relative to the project location. A neural network was calibrated to predict wave height based on the weather data and buoy data (without utilizing the predictions of the two models). A committee machine was then applied, treating the two models and the created neural network as independent experts, to determine a final wave height prediction.

2 Figure 1: Locations of weather and buoy data sources. The data used consisted of buoy, weather, and wave height (target) records from 2011 through Model predicted wave height records from 2015 through 2016 were also used. Records from 2011 through 2016 were used for neural network training, records from 2015 through 2016 were used for committee machine training, and records from 2017 were reserved for testing. A summary of the records and how they were used in creation of the network is included as Table 1. Year Weather data x Table 1: Summary of records used. Available Data GLERL model SWAN model x x x Function Neural network training Neural network training and committee machine training Number of records The neural network utilized a feature vector of 13 inputs. These included current wind speed from the buoy and weather station, wind speeds from both locations one through four hours prior, change in wind direction as measured at the Eagle Island station as compared to one and two hours prior, and the temperature difference between air and water as measured at the buoy. Given that the project location is near shore, generally waves generated by winds coming from the direction of open water are larger than waves generated by winds coming from the direction of the shoreline. This is because winds coming from open water have more water to act over, generating larger waves. Due to this fundamental difference in the relationship between the inputs and the target outputs depending on the wind direction, the wind direction value, as measured at Eagle Island, was used to separate the data into six bins, for each of which a different neural network was trained. This separation is illustrated in Figure 2. This x x x Testing 1384

3 approach, effectively creating a committee machine which separates the data based on knowledge of the process being modeled, is an application of the modular modeling described by Solomatine and Siek in Modular learning models in forecasting natural phenomena. An illustration of this network layout is shown in Figure 3. Figure 2: Illustrates the separation of records based on wind direction (measured in degrees). Figure 3: Neural network committee configuration. The system of neural networks each consisted a single hidden layer of 5 sigmoid neurons. This network configuration was found to produce the best results when tested against 5-5, 10, 10-10, 15, and 20 configurations. Network configurations were tested by running 100 network trainings for each configuration. For each training, the data was divided randomly, 70% training, 15% validation, 15% testing. The r² value of the network outputs for the test data (as compared to the target values) was recorded for each training and the mean and max values are reported in Table 2. The final six neural networks (one for each wind direction bin) used were created by selecting the top performing networks from the 100 network trainings for the single layer 5 neuron configuration.

4 Network configuration Mean r² to to to to to to Max r² 0 to to to to to to Table 2: Mean and max testing r² values after running 100 training iterations for each network configuration for each wind direction categorization. Highest values for each wind direction categorization are highlighted. Five neuron single layer network was chosen because it had the greatest number of highest mean r² results. The committee machine layer of the network utilized the outputs from the neural network and two models to generate a final network wave height prediction. The mean square error of each of these experts was computed for the six wind direction bins over the committee machine training data (2015 through 2016 records). The committee machine generates an output predicted wave height that is the average of the three expert wave height predictions weighted inversely proportionally to the mean square error of the expert for the given wind speed and wave height categorization as determined using the training data. Testing of this method was conducted by first generating neural network wave height predictions for the test data set. These outputs were then combined with the two model wave height predictions and were input into the committee machine described above to produce final wave height predictions. These predictions were evaluated against the target values. The results of this method are displayed in Table 3. It was found that, in terms of evaluating by root mean square error of the wave height prediction, the Committee Machine approach showed slightly better performance than either of the wave models or the neural network when evaluating over all wind speeds. Wind direction Nearual net GLERL Model SWAN model Committee 0 to to to to to to Total set Table 3: Root mean square error in feet of each of the three expert predictors and the Committee machine evaluated for each wind direction bin and over the total set.

5 The committee machine approach showed some marginal improvement in overall prediction performance over the models. It did not provide any significant improvement however. It is likely that the committee machine performance may improve if another variable was found that predicted the relative performance of the experts to be used in addition to wind direction. Improvement may also be possible if more data was found that would improve the performance of the neural net. References: M.C. Deo, A. Jha, A.S. Chaphekar, K. Ravikant, Neural networks for wave forecasting, In Ocean Engineering, Volume 28, Issue 7, 2001, Pages , ISSN , Solomatine, DP (Solomatine, D. P.); Siek, MB (Siek, M. B.), Modular learning models in forecasting natural phenomena, In Neural Networks 19 (2006) Pages Zhixu Zhang, Chi-Wai Li, Yok-Sheung Li, Yiquan Qi, Incorporation of artificial neural networks and data assimilation techniques into a third-generation wind wave model for wave forecasting, In Journal of Hydroinformatics Jan 2006, 8 (1) 65-76; DOI: /jh