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A Coupled Numerical and Artificial Neural Network Model for Improving Location Specific Wave Forecast
Applied Ocean Research 59 (2016) 483–491
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Applied Ocean Research journal homepage: www.elsevier.com/locate/apor
A Coupled Numerical and Artificial Neural Network Model for Improving Location Specific Wave Forecast S.N. Londhe a,∗ , Shalaka Shah a , P.R. Dixit a , T.M. Balakrishnan Nair b , P. Sirisha b , Rohit Jain a a
Vishwakarma Institute of Information Technology, Pune, India Indian National Centre for Ocean Information System (Ministry of Earth Sciences), “Ocean Valley”, Pragathi Nagar (BO), Nizampet (SO) 500090, Hyderabad, India b
a r t i c l e
i n f o
Article history: Received 6 April 2016 Received in revised form 2 June 2016 Accepted 5 July 2016 Keywords: Wave forecasting Numerical model’s wave forecasts Artificial neural network (ANN) Indian national centre for ocean information services (INCOIS)
a b s t r a c t As more than a quarter of India’s population resides along the coastlines, it is of utmost importance to predict the significant wave height as accurately as possible to cater the needs of safe and secure life. Presently Indian National Centre for Ocean Information Services (INCOIS) provides wave height forecasts on regional as well as local level ranging from 3 hours to 7 days ahead using numerical models. It is evident from numerical model forecasts at specific locations that the significant wave heights are not predicted very accurately. The obvious reason behind this is the ‘wind’ used in these models as a forcing function is itself forecasted wind (ECMWF wind (European Centre for Medium-range Weather Forecasting)) and hence many times the forecasts, differ very largely from the actual observations. These models work on larger grid size making it as major impediment in employing them particularly for location specific forecasts even though they work reasonably well for regional level. Present work aims in reducing the error in numerical wave forecast made by INCOIS at four stations along Indian coastline. For this ‘error’ between forecasted and observed wave height at current and previous time steps was used as input to predict the error 24 hr ahead in advance using ANN since it has been effectively used for wave forecasting (univariate time series forecasting in general) since last two decades or so. This predicted error was then added or subtracted from numerical wave forecast to improve the prediction accuracy. It is observed that numerical model forecast improved considerably when the predicted error was added or subtracted from it. This hybrid approach will add to the usefulness of the wave forecasts given by INCOIS to its stake holders. The performance of improved wave heights is judged by correlation coefficient and other error measures like RMSE, MAE and CE. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Earth System Science Organization – Indian National Centre for Ocean Information Services (ESSO-INCOIS), Hyderabad delivers quantitative ocean state forecast (OSF) to the Indian coast, from the year 2008 onwards by issuing forecasts of vital ocean parameters like significant wave height, remotely generated waves (swells) and ocean surface winds, seven days in advance and at 3-hourly interval with daily updates. Additionally ESSO-INCOIS is issuing high wave alerts under extreme events, as forecasted by numerical models. These alerts give information about significant wave height, swell
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (S.N. Londhe), [email protected] (P.R. Dixit). http://dx.doi.org/10.1016/j.apor.2016.07.004 0141-1187/© 2016 Elsevier Ltd. All rights reserved.
wave height, wave period, wave direction and ocean surface winds. High wave alerts are issued in English as well as local languages so that the users can easily understand and start the preparedness. Most of the users utilize these forecasts as guidance for their daily operational activities and to ensure safe navigation at sea [3]. Apart from this the forecast is being sent to the Non-Governmental Organizations (NGOs) in the coastal areas who perform the dissemination through FM Radio and Village Information Centres [41]. Being the sole operational ocean state forecast agency for the north Indian Ocean, ESSO-INCOIS gives high-wave alerts/warnings during high wave conditions. The numerical models require exogenous data inputs and work on larger gird size making it as major impediment in employing them particularly for location specific forecasts even though they work reasonably well for regional level. It can be observed from Fig. 1 that the forecast given by numerical models are not very
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Fig. 1. Wave plot showing the observed and forecasted wave heights by INCOIS (www.incois.gov.in).
accurate and there is a scope for improving the forecast. For the current study it was thought of to obtain the error between the observed and forecasted values of the wave heights at particular locations and to predict these errors for the desired future time step. These errors were then added or subtracted to the forecasts made by the numerical models, in an effort toimprove their accuracy particularly for specific locations. The numerical models already take into consideration the physics of the underlying process involved and thus, the authors thought of using soft computing tools for the modeling of these errors. Soft computing techniques which do not require a priori knowledge of the underlying phenomenon and can give meaningful solutions by using the readily available measured data and their antecedent values, can therefore be employed to bridge the gap between these wave forecasts and observed values by developing a wave forecast improving model using the error between the observed and forecasted wave values. The last two decades of the twentieth century witnessed a surge of publications in the area of modelling hydrodynamics using the soft computing technique of Artificial Neural Networks (ANNs). ANN is now an established technique in the field of Hydraulic Engineering as well as coastal and Ocean Engineering as evident from a plethora of publications in the journals of international repute. Therefore, it is proposed to use Artificial Neural Networks (ANNs) as a modeling tool in the present study. 2. Details of the Tools Used 2.1. MIKE 21 SW model The ESSO-INCOIS uses operational MIKE21 SW (Spectral Waves) model for significant wave height (SWH) forecasting over the entire Indian coastal region covering the Arabian Sea (AS), Bay of Bengal (BOB) and North Indian Ocean. MIKE21 SW is a third generation spectral wind wave model, based on unstructured meshes, and is developed by Danish Hydraulic Institute. The model simulates growth, decay and transformation of wind generated waves and swells in offshore and coastal areas. The use of unstructured mesh enhances accuracy of the wave model near the complex areas of the coastline. SW model is based on flexible mesh and therefore is particularly applicable for wave analysis both on regional and local scales which is very important in simulating cyclone generated wave fields [39]. Model simulates the wave growth by the action of wind, non-linear wave–wave interaction, dissipation due to white-capping, bottom friction and depth induced wave breaking, refraction and shoaling due to depth variations, wave–current interaction and the effect of time varying water depth.
Description of all source functions and the numerical methods used in the model are elaborated in Sørensen et al. [42]. In the present study, SW model domain from 60◦ S–30◦ N; 30◦ –120◦ E is used. Many recent studies show that swells from the southern Indian Ocean significantly modify the wave climate in north Indian Ocean [39,40]. Hence, the domain was extended up to 60◦ S so that swells generated at southern ocean were properly simulated by numerical model For the model runs, the mesh resolution was chosen to be 0.130 along the Indian coast, 0.400 for the BOB and AS and a coarse resolution of 10 for the southern ocean. Bathymetry data from etopo2 (2 min gridded global relief data) and etopo5 (5 min gridded global relief data) were used in this study. Readers are referred to [37], for more information on etopo2 and etopo5. 2.2. Artificial Neural Networks An artificial neural network (ANN) works like a biological neural network of the human brain and provides mathematical models for cognition [15]. It is a soft computing tool which treats the human brain as its role model and mimics the ability of the human mind to effectively employ modes of reasoning and/or pattern recognition that is approximate rather than exact. The mapping of input and output to the required accuracy is done by using an iterative procedure for minimizing the error between the observed and network predicted variables (outputs). The calibration (‘training’ as per ANN terminology) is done on a set of data using a training algorithm which minimizes the error and makes the network ready to face the unseen data kept aside for testing the model. The ANN is now an established technique in modeling water flows and therefore most of readers are well versed with the terminology and working of ANN. Hence detail information of its working is avoided in the current paper. The readers can refer text books like Bose and Liang [5], Wasserman [46] and research papers by The ASCE Task Committee [44], Maier and Dandy [24] and Dawson and Wilby [7] for understanding the preliminary concepts and working of ANN. 3. Literature Review The technique of ANN has been successfully used since the last two decades for the forecasting of wave heights.The previous attempts to forecast significant wave heights (SWHs) can be divided into various categories. The first category represents temporally univariate models, in which current and previous SWHs are used to forecast the SWHs a few hours to a few days in advance as
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Fig. 2. Map showing study area along Indian coastline.
done by Deo et al. [9], Deo and Naidu [11], Deo and Kirankumar [8], Agrawal and Deo [1], Makarynskyy [26], Makarynskyy et al. [29], Balas et al. [4], Makarynskyy et al. [30], Makarynskyy et al. [31], Makarynskyy [27], Mandal and Prabhaharan [34], Londhe and Panchang [21], Makarynskyy and Makarynska [28], Jain and Deo [18], Mirikitani [36], Ozger [38], Dixit et al. [12]. The next category represents cause-effect models in which the forcing function viz. wind mostly has been used to forecast SWHs as can be seen in the works done by Deo et al. [10], Altunkaynak and Ozger [2], Mandal et al. [35], Malekmohamadi et al. [33], Mahjoobi et al. [23], Swerpel et al. [43], Zamini et al. [47], Mahjoobi and Mossabeb [22], Herman et al. [16], Etemad-Shahidi and Mahjoobi [13], Tsai and Tsai [45], Kamranzad et al. [19] and Malekmohamadi et al. [32]. Furthermore, there were publications that aimed at improving the power of numerical models which include works done by Krasnopolsky et al. [20], Makarynskyy and Makarynskaa [25], Zhang et al. [48], Mahjoobi et al. [23], and Gunaydin [14]. Makarynskyy [27] attempted to improve numerical model accuracy for wave buoys on the western coast of Portugal. He first calculated the error between the observed SWH value and numerically predicted SWH value and developed a univariate time series ANN model to forecast the error in advance using the previous values of error used as inputs. The results showed considerable improvement in prediction accuracy of numerical models. This study concluded that these developments, which rely on ANNs, can aid in more reliable and efficient operation of physics-based wave forecasting systems. Thus, for the present work a methodology similar to the one followed by Makarynskyy [27] was adopted. The earlier works mentioned above were particularly targeted towards forecasting significant wave heights (SWHs) few hours to few days in advance using either previously measured SWHs or wind. However none of these models were actually applied to any particular location in real time mode ‘as has been done in the present work’ therefore becoming more or less a “proof of concept” type of work. In this particular work, the error between the observed wave heights and predictions by numerical models was forecasted for
a lead time of 24 hours at four wave buoys along the coastline of India and then the forecasted errors were added or subtracted to the numerical model forecasts to improve their results. More importantly, the model developed is actually connected to INCOIS server wherein it works for 8 times a day, 7 days a week since the last 7 months (at Ratnagiri).
4. Study Area and Data Used The present work was done at four buoy locations along the coastline of India. The three locations were Ratnagiri, Pondicherry, Gopalpur and Kollam which can be seen in Fig. 2. Ratnagiri is a port city on the Arabian Sea coast in Ratnagiri District in the southwestern part of Maharashtra, India. The district is a part of Konkan division of Maharashtra. It is located at 16.98◦ N 73.3◦ E. It has an average elevation of 11 m. The data used for this port consisted of wave heights(both measured by wave buoy and forecasted by numerical model) at a regular intervals of 3 hours over a time span for 3 years, that is, 2011–2013. Pondicherry is situated on the east coast of Tamil Nadu and is more or less a flat land with no hills and forests. It is located at 11.93◦ N 79.78◦ E. Pondicherry’s average elevation is 3 m. The data used for this port consisted of wave heights at a regular intervals of 3 hours over a time span for 4 years (both measured by wave buoy and forecasted by numerical model), that is, 2011–2014. Gopalpur is a town on the Bay of Bengal coast in Ganjam district in the southern part of Odisha. It is located at 19.27◦ N 84.92◦ E. Gopalpur’s average elevation is 1 m. The data used for this port consisted of wave heights at a regular intervals of 3 hours over a time span of 3 years (both measured by wave buoy and forecasted by numerical model), that is, 2013–2015. Kollam or Quilon, formerly Desinganadu, is an old seaport and city on the Laccadive Sea coast in Kerala, India on Ashtamudi Lake. It is located at 8.88◦ N 76.60◦ E. Kollam’s average elevation is 3 m. The data used for this port consisted of wave heights at a regular intervals of 3 hours over a time span of 2 years (both measured by wave buoy and forecasted by numerical model), that is, 2013–2014.
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Fig. 4. AMI plot for input selection at Ratnagiri.
numerical model forecasts 24 hr ahead the corresponding ‘errors’ must be predicted 24 hr in advance. This was achieved by developing Artificial Neural Network models for particular stations. Fig. 3 explains the working principle of Artificial Neural Network technique (ANN) for the prediction of errors. Fig. 3. Methodology for formation of datasets.
5.2. Input Selection
5. Model formulation 5.1. Methodology As mentioned above, the data of significant wave heights forecasted by numerical model (Provided by INCOIS) and the measured wave heights from 2011 and 2013 (3 years) at Ratnagiri, from 2011 to 2014 (4 years) at Pondicherry, from 2013 to 2015 (3 years) at Gopalpurand from 2013 to 2014 (2 years) at Kollam was used in the present work. The difference between the observed and forecasted wave height is the ‘error’ which is necessarily to be minimized to improve the location specific wave forecast at both these locations. As maximum as the reduction in this error, the maximum accuracy can be achieved in forecasting the waves. To improve the numerical model prediction at a particular lead time, this ‘error’ should be predicted for that particular lead time. In the same regards, time series of calculated ‘errors’ was used to predict the corresponding error at particular lead time (24 hr ahead). Thus to improve the
The input time series to be used for the training and testing in the soft computing tool were decided with the help of Average Mutual Information (AMI). Mutual information measures the information that any two variables 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 AMI is zero. Also if the random variables are strongly related, the AMI score would take a high value. For the present study, the AMI was calculated between the output (24 hr ahead error) and inputs (error at previous time steps). A graph was then plotted between the values of AMI vs the corresponding time step. The plot for AMI at Ratnagiri is shown in Fig. 4 as an example. A conclusion was reached upon to use 9 previous values of data as input for Ratnagiri, Gopalpur and Kollam models and 4 previous values of data as input for Pondicherry models as the value of AMI at this time step was 50% of the maximum AMI, as per the amount of uncertainty reduction that was required. That is, for output at time‘t’ at Ratnagiri, the input data set will start from t-24 and go back 9 steps for 24 hr forecast.
Fig. 5. Wave plot for 24 h forecast at Ratnagiri.
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Fig. 6. Wave plot for 24 hr forecast at Pondicherry.
Fig. 7. Wave plot for 24 hr forecast at Gopalpur.
Fig. 8. Wave plot for 24 hr forecast at Kollam.
5.3. Model Formulation Once the datasets were ready, the models to predict the errors at 24 hr ahead lead time were developed. 70% of the data from the total
data set of errors was used to train the model while remaining 30% data was used for validation (15%) and testing (15%) to develop each model. The transfer functions used were ‘log-sigmoid’ and ‘linear’ between 1 st (input) and 2nd (hidden) layer and 2nd (hidden) and
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Table 1 Model formulation and ANN model details for all stations. Ratnagiri Model for 24 hr ahead Pondicherry Model for 24 hr ahead Gopalpur Model for 24 hr ahead Kollam Model for 24 hr ahead
Input t-24, t-21, t-18, t-15, t-12, t-9, t-6, t-3, t (total 9 inputs)
Output t + 24 (24hr ahead predicted error)
Architecture of ANN models 9:1:1 LM, 0–1, mse, logsig-purelin, 30 epochs
Input t-9, t-6, t-3, t (total 4 inputs)
Output t + 24 (24hr ahead predicted error)
Architecture of ANN models 4:1:1 LM, 0–1, mse, logsig-purelin, 30 epochs
Input t-24, t-21, t-18, t-15, t-12, t-9, t-6, t-3, t (total 9 inputs)
Output t + 24 (24hr ahead predicted error)
Architecture of ANN models 9:8:1 LM, 0–1, mse, logsig-purelin, 35 epochs
Input t-24, t-21, t-18, t-15, t-12, t-9, t-6, t-3, t (total 9 inputs)
Output t + 24 (24hr ahead predicted error)
Architecture of ANN models 9:1:1 LM, 0–1, mse, logsig-purelin, 15 epochs
3rd (output) layer respectively for all the cases. The algorithm used was Levernberg Marquardt (LM). The fitness criterion was the mean squared error (mse). The hidden neurons were fixed by trial and error. Table 1 presents the input- output and architectural details (Input neurons: Hidden Neurons: Output neurons) of these models. These predicted errors were then added or subtracted from the numerical model forecasts of respective lead times and forecasts done by numerical models for 24 hr ahead lead time were improvised (corrected). Subsequently these improvised forecasts were compared with the observed wave heights (by the wave rider buoys at these locations) to perceive the model competency the results of which are discussed in the next section.
6. Results and Discussion All the models were tested with unseen inputs and the errors were forecasted for the respective lead times at the station. The numerical model forecasts were then improvised by using these predicted errors as mentioned in model formulation. The accuracy in forecasting the significant wave heights was then judged by the correlation coefficient (r) between the observed and improvised wave heights, scatter plots between the same and the wave plots. Additionally other error measures such as root mean squared error (RMSE), Mean absolute error (MAE) and coefficient of efficiency (CE) as suggested by The ASCE Task Committee [44] between the observed and improvised wave heights and the observed and forecasted wave heights were also calculated. Readers are referred to Dawson and Wilby [7] for their formulae. Additionally, two more error measures were calculated to judge the accuracy of the models, namely, scatter index and Bias. Scatter index (SI) is a standard metric for wave model inter-comparison [6]. Essentially, it is a normalized measure of error that takes into account the observed wave height. Lower values of the SI are an indication of a better forecast. Bias refers to the tendency of a measurement process to over- or under-estimate the value of a parameter. Table 2 presents the model assessment done using coefficient of correlation, RMSE, MAE, CE, Scatter Index and Bias for all the four stations followed by a detailed statistical analysis in Table 3. Figs. 5–8 show the wave plots for observed, forecasted and improvised forecasts, at Ratnagiri, Pondicherry, Gopalpur and Kollam respectively. Also, Figs. 9–12 give the scatter plots for the predicted and corrected wave heights for Ratnagiri, Pondicherry, Gopalpur and Kollam respectively. From the figures it is evident that the improvised values of wave forecasts are giving results better as compared to the forecast made by numerical models as is seen even by the values of error measures in Table 2 and the detailed statistical analysis in Table 3. The scatter plots of all the four models show that the scatter for corrected wave heights is more balanced as compared to the scatter for the numerical model predictions.
Fig. 9. Scatter plot for 24 hr forecast at Ratnagiri.
Fig. 10. Scatter plot for 24 hr forecast at Pondicherry.
7. Real Time Implementation of ANN Models The Ratnagiri model developed for correction in 24 hour ahead forecast as mentioned above is automated and connected to the INCOIS online server, for functioning in real time operational mode since October 2015. The model runs daily and gives values of wave forecast one day in advance. The wave plot and scatter plot for the time period from October 2015 to December 2015 for Ratnagiri are
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Table 2 Error measures for all four stations (Offline models in testing). Forecast Interval
r RMSE MAE CE Scatter Index Bias
Ratnagiri
Pondicherry
Gopalpur
Kollam
Observed and Numerical model
Observed and Improvised
Observed and Numerical model
Observed and Improvised
Observed and Numerical model
Observed and Improvised
Observed and Numerical model
Observed and Improvised
0.93 0.45 0.36 0.56 0.24 −0.36
0.96 0.17 0.01 0.93 0.16 −0.01
0.79 0.24 0.17 0.24 0.23 −0.17
0.87 0.14 0.03 0.75 0.18 −0.02
0.89 0.34 0.30 −0.14 0.19 −0.30
0.90 0.14 0.02 0.80 0.18 −0.02
0.68 0.27 0.05 0.39 0.14 0.05
0.83 0.19 0.004 0.69 0.10 0.004
Table 3 Detailed statistical analysis of models developed in offline mode (Testing). Statistical Parameter Ratnagiri
Mean Standard Deviation Max Min Skewness Kurtosis
Pondicherry
Gopalpur
Kollam
Observed Numerical Model
Improvised Observed Numerical Model
Improvised Observed Numerical Model
Improvised Observed Numerical Model
Improvised
1.12 0.69 2.73 0.26 0.56 −1.25
1.13 0.66 2.84 0.30 0.62 −1.08
0.77 0.25 2.06 0.34 1.49 3.25
0.79 0.32 1.80 0.33 1.20 0.68
1.85 0.31 2.58 1.24 −0.02 −1.03
1.47 0.55 3.15 0.75 0.79 −0.52
0.74 0.28 2.11 0.23 1.37 2.50
Fig. 11. Scatter plot for 24 hr forecast at Gopalpur.
0.92 0.24 2.06 0.46 1.36 2.74
0.77 0.32 1.87 0.37 1.11 0.64
1.08 0.32 2.13 0.68 1.21 1.00
1.86 0.35 2.88 1.19 0.07 −0.84
1.81 0.16 2.23 1.38 −0.44 0.12
Fig. 12. Scatter plot for 24 hr forecast at Kollam.
Fig. 13. Real time implementation of Ratnagiri Model (Oct 2015–Dec 2015).
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Acknowledgement The authors would also like to thank INCOIS, Hyderabad (Indian National Centre for Ocean Information Services, Ministry of earth sciences, Govt. of India.) for funding the research project under the Ocean State forecasts Scheme (OSF). References
Fig. 14. Scatter plot for 24 hr forecast for Ratnagiri Operational Model (Online mode). Table 4 Statistical analysis of Ratnagiri operational model (Online Model). Error Measure
Observed and Numerical Model
Observed and ANN Corrected
Coefficient of Correlation RMSE Scatter Index Bias
0.71 0.27 0.24 −0.22
0.78 0.12 0.19 0.015
shown in Figs. 13 and 14 respectively. From the wave plot it can be observed that the values for wave forecast given by ANN models are closer to the actual observed wave heights, as compared to the results given by the numerical models. Also, the scatter plot for the corrected wave heights (by ANN) is well distributed along the best fit line as opposed to the numerical model scatter, which shows overpredicted values at certain places. Furthermore, a detailed statistical analysis for the operational model at Ratnagiri is given in Table 4. From the statistical analysis also it is clear that the results from the improvised ANN models were working a shed better than the numerical model. The model for Pondicherry, Gopalpur and Kollam is submitted to INCOIS out of which Pondicherry is also automated and connected to the INCOIS server as in case of Ratnagiri and models for the remaining two stations are in the process of automation. 8. Conclusion This paper portrays the use of neural network technique for improving the wave forecasts at four wave buoys along the Indian Coastline. The forecast done by the numerical model for a lead time of 24 h was improvised (corrected) by adding or subtracting the ‘errors’ which were forecasted by the use of neural network technique. It is evident from the above mentioned results that there is an elevated improvement in the 24 hr forecast at all the four locations and hence it can be said that the use of ANN is worthwhile in similar kind of research works in improvising the forecasting accuracy. This approach will definitely be a significant addition to the usefulness for the wave forecasts to INCOIS and its stake holders. High correlation coefficient (‘r’) and coefficient of efficiency (CE) values and low RMSE, MAE, scatter index and biasvalues proves the proficiency of new hybrid technique of NNT and hence it is pretty clear that this technique can be explored further in analogous class of research area.
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Applied Ocean Research journal homepage: www.elsevier.com/locate/apor
A Coupled Numerical and Artificial Neural Network Model for Improving Location Specific Wave Forecast S.N. Londhe a,∗ , Shalaka Shah a , P.R. Dixit a , T.M. Balakrishnan Nair b , P. Sirisha b , Rohit Jain a a
Vishwakarma Institute of Information Technology, Pune, India Indian National Centre for Ocean Information System (Ministry of Earth Sciences), “Ocean Valley”, Pragathi Nagar (BO), Nizampet (SO) 500090, Hyderabad, India b
a r t i c l e
i n f o
Article history: Received 6 April 2016 Received in revised form 2 June 2016 Accepted 5 July 2016 Keywords: Wave forecasting Numerical model’s wave forecasts Artificial neural network (ANN) Indian national centre for ocean information services (INCOIS)
a b s t r a c t As more than a quarter of India’s population resides along the coastlines, it is of utmost importance to predict the significant wave height as accurately as possible to cater the needs of safe and secure life. Presently Indian National Centre for Ocean Information Services (INCOIS) provides wave height forecasts on regional as well as local level ranging from 3 hours to 7 days ahead using numerical models. It is evident from numerical model forecasts at specific locations that the significant wave heights are not predicted very accurately. The obvious reason behind this is the ‘wind’ used in these models as a forcing function is itself forecasted wind (ECMWF wind (European Centre for Medium-range Weather Forecasting)) and hence many times the forecasts, differ very largely from the actual observations. These models work on larger grid size making it as major impediment in employing them particularly for location specific forecasts even though they work reasonably well for regional level. Present work aims in reducing the error in numerical wave forecast made by INCOIS at four stations along Indian coastline. For this ‘error’ between forecasted and observed wave height at current and previous time steps was used as input to predict the error 24 hr ahead in advance using ANN since it has been effectively used for wave forecasting (univariate time series forecasting in general) since last two decades or so. This predicted error was then added or subtracted from numerical wave forecast to improve the prediction accuracy. It is observed that numerical model forecast improved considerably when the predicted error was added or subtracted from it. This hybrid approach will add to the usefulness of the wave forecasts given by INCOIS to its stake holders. The performance of improved wave heights is judged by correlation coefficient and other error measures like RMSE, MAE and CE. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Earth System Science Organization – Indian National Centre for Ocean Information Services (ESSO-INCOIS), Hyderabad delivers quantitative ocean state forecast (OSF) to the Indian coast, from the year 2008 onwards by issuing forecasts of vital ocean parameters like significant wave height, remotely generated waves (swells) and ocean surface winds, seven days in advance and at 3-hourly interval with daily updates. Additionally ESSO-INCOIS is issuing high wave alerts under extreme events, as forecasted by numerical models. These alerts give information about significant wave height, swell
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (S.N. Londhe), [email protected] (P.R. Dixit). http://dx.doi.org/10.1016/j.apor.2016.07.004 0141-1187/© 2016 Elsevier Ltd. All rights reserved.
wave height, wave period, wave direction and ocean surface winds. High wave alerts are issued in English as well as local languages so that the users can easily understand and start the preparedness. Most of the users utilize these forecasts as guidance for their daily operational activities and to ensure safe navigation at sea [3]. Apart from this the forecast is being sent to the Non-Governmental Organizations (NGOs) in the coastal areas who perform the dissemination through FM Radio and Village Information Centres [41]. Being the sole operational ocean state forecast agency for the north Indian Ocean, ESSO-INCOIS gives high-wave alerts/warnings during high wave conditions. The numerical models require exogenous data inputs and work on larger gird size making it as major impediment in employing them particularly for location specific forecasts even though they work reasonably well for regional level. It can be observed from Fig. 1 that the forecast given by numerical models are not very
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Fig. 1. Wave plot showing the observed and forecasted wave heights by INCOIS (www.incois.gov.in).
accurate and there is a scope for improving the forecast. For the current study it was thought of to obtain the error between the observed and forecasted values of the wave heights at particular locations and to predict these errors for the desired future time step. These errors were then added or subtracted to the forecasts made by the numerical models, in an effort toimprove their accuracy particularly for specific locations. The numerical models already take into consideration the physics of the underlying process involved and thus, the authors thought of using soft computing tools for the modeling of these errors. Soft computing techniques which do not require a priori knowledge of the underlying phenomenon and can give meaningful solutions by using the readily available measured data and their antecedent values, can therefore be employed to bridge the gap between these wave forecasts and observed values by developing a wave forecast improving model using the error between the observed and forecasted wave values. The last two decades of the twentieth century witnessed a surge of publications in the area of modelling hydrodynamics using the soft computing technique of Artificial Neural Networks (ANNs). ANN is now an established technique in the field of Hydraulic Engineering as well as coastal and Ocean Engineering as evident from a plethora of publications in the journals of international repute. Therefore, it is proposed to use Artificial Neural Networks (ANNs) as a modeling tool in the present study. 2. Details of the Tools Used 2.1. MIKE 21 SW model The ESSO-INCOIS uses operational MIKE21 SW (Spectral Waves) model for significant wave height (SWH) forecasting over the entire Indian coastal region covering the Arabian Sea (AS), Bay of Bengal (BOB) and North Indian Ocean. MIKE21 SW is a third generation spectral wind wave model, based on unstructured meshes, and is developed by Danish Hydraulic Institute. The model simulates growth, decay and transformation of wind generated waves and swells in offshore and coastal areas. The use of unstructured mesh enhances accuracy of the wave model near the complex areas of the coastline. SW model is based on flexible mesh and therefore is particularly applicable for wave analysis both on regional and local scales which is very important in simulating cyclone generated wave fields [39]. Model simulates the wave growth by the action of wind, non-linear wave–wave interaction, dissipation due to white-capping, bottom friction and depth induced wave breaking, refraction and shoaling due to depth variations, wave–current interaction and the effect of time varying water depth.
Description of all source functions and the numerical methods used in the model are elaborated in Sørensen et al. [42]. In the present study, SW model domain from 60◦ S–30◦ N; 30◦ –120◦ E is used. Many recent studies show that swells from the southern Indian Ocean significantly modify the wave climate in north Indian Ocean [39,40]. Hence, the domain was extended up to 60◦ S so that swells generated at southern ocean were properly simulated by numerical model For the model runs, the mesh resolution was chosen to be 0.130 along the Indian coast, 0.400 for the BOB and AS and a coarse resolution of 10 for the southern ocean. Bathymetry data from etopo2 (2 min gridded global relief data) and etopo5 (5 min gridded global relief data) were used in this study. Readers are referred to [37], for more information on etopo2 and etopo5. 2.2. Artificial Neural Networks An artificial neural network (ANN) works like a biological neural network of the human brain and provides mathematical models for cognition [15]. It is a soft computing tool which treats the human brain as its role model and mimics the ability of the human mind to effectively employ modes of reasoning and/or pattern recognition that is approximate rather than exact. The mapping of input and output to the required accuracy is done by using an iterative procedure for minimizing the error between the observed and network predicted variables (outputs). The calibration (‘training’ as per ANN terminology) is done on a set of data using a training algorithm which minimizes the error and makes the network ready to face the unseen data kept aside for testing the model. The ANN is now an established technique in modeling water flows and therefore most of readers are well versed with the terminology and working of ANN. Hence detail information of its working is avoided in the current paper. The readers can refer text books like Bose and Liang [5], Wasserman [46] and research papers by The ASCE Task Committee [44], Maier and Dandy [24] and Dawson and Wilby [7] for understanding the preliminary concepts and working of ANN. 3. Literature Review The technique of ANN has been successfully used since the last two decades for the forecasting of wave heights.The previous attempts to forecast significant wave heights (SWHs) can be divided into various categories. The first category represents temporally univariate models, in which current and previous SWHs are used to forecast the SWHs a few hours to a few days in advance as
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Fig. 2. Map showing study area along Indian coastline.
done by Deo et al. [9], Deo and Naidu [11], Deo and Kirankumar [8], Agrawal and Deo [1], Makarynskyy [26], Makarynskyy et al. [29], Balas et al. [4], Makarynskyy et al. [30], Makarynskyy et al. [31], Makarynskyy [27], Mandal and Prabhaharan [34], Londhe and Panchang [21], Makarynskyy and Makarynska [28], Jain and Deo [18], Mirikitani [36], Ozger [38], Dixit et al. [12]. The next category represents cause-effect models in which the forcing function viz. wind mostly has been used to forecast SWHs as can be seen in the works done by Deo et al. [10], Altunkaynak and Ozger [2], Mandal et al. [35], Malekmohamadi et al. [33], Mahjoobi et al. [23], Swerpel et al. [43], Zamini et al. [47], Mahjoobi and Mossabeb [22], Herman et al. [16], Etemad-Shahidi and Mahjoobi [13], Tsai and Tsai [45], Kamranzad et al. [19] and Malekmohamadi et al. [32]. Furthermore, there were publications that aimed at improving the power of numerical models which include works done by Krasnopolsky et al. [20], Makarynskyy and Makarynskaa [25], Zhang et al. [48], Mahjoobi et al. [23], and Gunaydin [14]. Makarynskyy [27] attempted to improve numerical model accuracy for wave buoys on the western coast of Portugal. He first calculated the error between the observed SWH value and numerically predicted SWH value and developed a univariate time series ANN model to forecast the error in advance using the previous values of error used as inputs. The results showed considerable improvement in prediction accuracy of numerical models. This study concluded that these developments, which rely on ANNs, can aid in more reliable and efficient operation of physics-based wave forecasting systems. Thus, for the present work a methodology similar to the one followed by Makarynskyy [27] was adopted. The earlier works mentioned above were particularly targeted towards forecasting significant wave heights (SWHs) few hours to few days in advance using either previously measured SWHs or wind. However none of these models were actually applied to any particular location in real time mode ‘as has been done in the present work’ therefore becoming more or less a “proof of concept” type of work. In this particular work, the error between the observed wave heights and predictions by numerical models was forecasted for
a lead time of 24 hours at four wave buoys along the coastline of India and then the forecasted errors were added or subtracted to the numerical model forecasts to improve their results. More importantly, the model developed is actually connected to INCOIS server wherein it works for 8 times a day, 7 days a week since the last 7 months (at Ratnagiri).
4. Study Area and Data Used The present work was done at four buoy locations along the coastline of India. The three locations were Ratnagiri, Pondicherry, Gopalpur and Kollam which can be seen in Fig. 2. Ratnagiri is a port city on the Arabian Sea coast in Ratnagiri District in the southwestern part of Maharashtra, India. The district is a part of Konkan division of Maharashtra. It is located at 16.98◦ N 73.3◦ E. It has an average elevation of 11 m. The data used for this port consisted of wave heights(both measured by wave buoy and forecasted by numerical model) at a regular intervals of 3 hours over a time span for 3 years, that is, 2011–2013. Pondicherry is situated on the east coast of Tamil Nadu and is more or less a flat land with no hills and forests. It is located at 11.93◦ N 79.78◦ E. Pondicherry’s average elevation is 3 m. The data used for this port consisted of wave heights at a regular intervals of 3 hours over a time span for 4 years (both measured by wave buoy and forecasted by numerical model), that is, 2011–2014. Gopalpur is a town on the Bay of Bengal coast in Ganjam district in the southern part of Odisha. It is located at 19.27◦ N 84.92◦ E. Gopalpur’s average elevation is 1 m. The data used for this port consisted of wave heights at a regular intervals of 3 hours over a time span of 3 years (both measured by wave buoy and forecasted by numerical model), that is, 2013–2015. Kollam or Quilon, formerly Desinganadu, is an old seaport and city on the Laccadive Sea coast in Kerala, India on Ashtamudi Lake. It is located at 8.88◦ N 76.60◦ E. Kollam’s average elevation is 3 m. The data used for this port consisted of wave heights at a regular intervals of 3 hours over a time span of 2 years (both measured by wave buoy and forecasted by numerical model), that is, 2013–2014.
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Fig. 4. AMI plot for input selection at Ratnagiri.
numerical model forecasts 24 hr ahead the corresponding ‘errors’ must be predicted 24 hr in advance. This was achieved by developing Artificial Neural Network models for particular stations. Fig. 3 explains the working principle of Artificial Neural Network technique (ANN) for the prediction of errors. Fig. 3. Methodology for formation of datasets.
5.2. Input Selection
5. Model formulation 5.1. Methodology As mentioned above, the data of significant wave heights forecasted by numerical model (Provided by INCOIS) and the measured wave heights from 2011 and 2013 (3 years) at Ratnagiri, from 2011 to 2014 (4 years) at Pondicherry, from 2013 to 2015 (3 years) at Gopalpurand from 2013 to 2014 (2 years) at Kollam was used in the present work. The difference between the observed and forecasted wave height is the ‘error’ which is necessarily to be minimized to improve the location specific wave forecast at both these locations. As maximum as the reduction in this error, the maximum accuracy can be achieved in forecasting the waves. To improve the numerical model prediction at a particular lead time, this ‘error’ should be predicted for that particular lead time. In the same regards, time series of calculated ‘errors’ was used to predict the corresponding error at particular lead time (24 hr ahead). Thus to improve the
The input time series to be used for the training and testing in the soft computing tool were decided with the help of Average Mutual Information (AMI). Mutual information measures the information that any two variables 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 AMI is zero. Also if the random variables are strongly related, the AMI score would take a high value. For the present study, the AMI was calculated between the output (24 hr ahead error) and inputs (error at previous time steps). A graph was then plotted between the values of AMI vs the corresponding time step. The plot for AMI at Ratnagiri is shown in Fig. 4 as an example. A conclusion was reached upon to use 9 previous values of data as input for Ratnagiri, Gopalpur and Kollam models and 4 previous values of data as input for Pondicherry models as the value of AMI at this time step was 50% of the maximum AMI, as per the amount of uncertainty reduction that was required. That is, for output at time‘t’ at Ratnagiri, the input data set will start from t-24 and go back 9 steps for 24 hr forecast.
Fig. 5. Wave plot for 24 h forecast at Ratnagiri.
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Fig. 6. Wave plot for 24 hr forecast at Pondicherry.
Fig. 7. Wave plot for 24 hr forecast at Gopalpur.
Fig. 8. Wave plot for 24 hr forecast at Kollam.
5.3. Model Formulation Once the datasets were ready, the models to predict the errors at 24 hr ahead lead time were developed. 70% of the data from the total
data set of errors was used to train the model while remaining 30% data was used for validation (15%) and testing (15%) to develop each model. The transfer functions used were ‘log-sigmoid’ and ‘linear’ between 1 st (input) and 2nd (hidden) layer and 2nd (hidden) and
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Table 1 Model formulation and ANN model details for all stations. Ratnagiri Model for 24 hr ahead Pondicherry Model for 24 hr ahead Gopalpur Model for 24 hr ahead Kollam Model for 24 hr ahead
Input t-24, t-21, t-18, t-15, t-12, t-9, t-6, t-3, t (total 9 inputs)
Output t + 24 (24hr ahead predicted error)
Architecture of ANN models 9:1:1 LM, 0–1, mse, logsig-purelin, 30 epochs
Input t-9, t-6, t-3, t (total 4 inputs)
Output t + 24 (24hr ahead predicted error)
Architecture of ANN models 4:1:1 LM, 0–1, mse, logsig-purelin, 30 epochs
Input t-24, t-21, t-18, t-15, t-12, t-9, t-6, t-3, t (total 9 inputs)
Output t + 24 (24hr ahead predicted error)
Architecture of ANN models 9:8:1 LM, 0–1, mse, logsig-purelin, 35 epochs
Input t-24, t-21, t-18, t-15, t-12, t-9, t-6, t-3, t (total 9 inputs)
Output t + 24 (24hr ahead predicted error)
Architecture of ANN models 9:1:1 LM, 0–1, mse, logsig-purelin, 15 epochs
3rd (output) layer respectively for all the cases. The algorithm used was Levernberg Marquardt (LM). The fitness criterion was the mean squared error (mse). The hidden neurons were fixed by trial and error. Table 1 presents the input- output and architectural details (Input neurons: Hidden Neurons: Output neurons) of these models. These predicted errors were then added or subtracted from the numerical model forecasts of respective lead times and forecasts done by numerical models for 24 hr ahead lead time were improvised (corrected). Subsequently these improvised forecasts were compared with the observed wave heights (by the wave rider buoys at these locations) to perceive the model competency the results of which are discussed in the next section.
6. Results and Discussion All the models were tested with unseen inputs and the errors were forecasted for the respective lead times at the station. The numerical model forecasts were then improvised by using these predicted errors as mentioned in model formulation. The accuracy in forecasting the significant wave heights was then judged by the correlation coefficient (r) between the observed and improvised wave heights, scatter plots between the same and the wave plots. Additionally other error measures such as root mean squared error (RMSE), Mean absolute error (MAE) and coefficient of efficiency (CE) as suggested by The ASCE Task Committee [44] between the observed and improvised wave heights and the observed and forecasted wave heights were also calculated. Readers are referred to Dawson and Wilby [7] for their formulae. Additionally, two more error measures were calculated to judge the accuracy of the models, namely, scatter index and Bias. Scatter index (SI) is a standard metric for wave model inter-comparison [6]. Essentially, it is a normalized measure of error that takes into account the observed wave height. Lower values of the SI are an indication of a better forecast. Bias refers to the tendency of a measurement process to over- or under-estimate the value of a parameter. Table 2 presents the model assessment done using coefficient of correlation, RMSE, MAE, CE, Scatter Index and Bias for all the four stations followed by a detailed statistical analysis in Table 3. Figs. 5–8 show the wave plots for observed, forecasted and improvised forecasts, at Ratnagiri, Pondicherry, Gopalpur and Kollam respectively. Also, Figs. 9–12 give the scatter plots for the predicted and corrected wave heights for Ratnagiri, Pondicherry, Gopalpur and Kollam respectively. From the figures it is evident that the improvised values of wave forecasts are giving results better as compared to the forecast made by numerical models as is seen even by the values of error measures in Table 2 and the detailed statistical analysis in Table 3. The scatter plots of all the four models show that the scatter for corrected wave heights is more balanced as compared to the scatter for the numerical model predictions.
Fig. 9. Scatter plot for 24 hr forecast at Ratnagiri.
Fig. 10. Scatter plot for 24 hr forecast at Pondicherry.
7. Real Time Implementation of ANN Models The Ratnagiri model developed for correction in 24 hour ahead forecast as mentioned above is automated and connected to the INCOIS online server, for functioning in real time operational mode since October 2015. The model runs daily and gives values of wave forecast one day in advance. The wave plot and scatter plot for the time period from October 2015 to December 2015 for Ratnagiri are
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Table 2 Error measures for all four stations (Offline models in testing). Forecast Interval
r RMSE MAE CE Scatter Index Bias
Ratnagiri
Pondicherry
Gopalpur
Kollam
Observed and Numerical model
Observed and Improvised
Observed and Numerical model
Observed and Improvised
Observed and Numerical model
Observed and Improvised
Observed and Numerical model
Observed and Improvised
0.93 0.45 0.36 0.56 0.24 −0.36
0.96 0.17 0.01 0.93 0.16 −0.01
0.79 0.24 0.17 0.24 0.23 −0.17
0.87 0.14 0.03 0.75 0.18 −0.02
0.89 0.34 0.30 −0.14 0.19 −0.30
0.90 0.14 0.02 0.80 0.18 −0.02
0.68 0.27 0.05 0.39 0.14 0.05
0.83 0.19 0.004 0.69 0.10 0.004
Table 3 Detailed statistical analysis of models developed in offline mode (Testing). Statistical Parameter Ratnagiri
Mean Standard Deviation Max Min Skewness Kurtosis
Pondicherry
Gopalpur
Kollam
Observed Numerical Model
Improvised Observed Numerical Model
Improvised Observed Numerical Model
Improvised Observed Numerical Model
Improvised
1.12 0.69 2.73 0.26 0.56 −1.25
1.13 0.66 2.84 0.30 0.62 −1.08
0.77 0.25 2.06 0.34 1.49 3.25
0.79 0.32 1.80 0.33 1.20 0.68
1.85 0.31 2.58 1.24 −0.02 −1.03
1.47 0.55 3.15 0.75 0.79 −0.52
0.74 0.28 2.11 0.23 1.37 2.50
Fig. 11. Scatter plot for 24 hr forecast at Gopalpur.
0.92 0.24 2.06 0.46 1.36 2.74
0.77 0.32 1.87 0.37 1.11 0.64
1.08 0.32 2.13 0.68 1.21 1.00
1.86 0.35 2.88 1.19 0.07 −0.84
1.81 0.16 2.23 1.38 −0.44 0.12
Fig. 12. Scatter plot for 24 hr forecast at Kollam.
Fig. 13. Real time implementation of Ratnagiri Model (Oct 2015–Dec 2015).
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Acknowledgement The authors would also like to thank INCOIS, Hyderabad (Indian National Centre for Ocean Information Services, Ministry of earth sciences, Govt. of India.) for funding the research project under the Ocean State forecasts Scheme (OSF). References
Fig. 14. Scatter plot for 24 hr forecast for Ratnagiri Operational Model (Online mode). Table 4 Statistical analysis of Ratnagiri operational model (Online Model). Error Measure
Observed and Numerical Model
Observed and ANN Corrected
Coefficient of Correlation RMSE Scatter Index Bias
0.71 0.27 0.24 −0.22
0.78 0.12 0.19 0.015
shown in Figs. 13 and 14 respectively. From the wave plot it can be observed that the values for wave forecast given by ANN models are closer to the actual observed wave heights, as compared to the results given by the numerical models. Also, the scatter plot for the corrected wave heights (by ANN) is well distributed along the best fit line as opposed to the numerical model scatter, which shows overpredicted values at certain places. Furthermore, a detailed statistical analysis for the operational model at Ratnagiri is given in Table 4. From the statistical analysis also it is clear that the results from the improvised ANN models were working a shed better than the numerical model. The model for Pondicherry, Gopalpur and Kollam is submitted to INCOIS out of which Pondicherry is also automated and connected to the INCOIS server as in case of Ratnagiri and models for the remaining two stations are in the process of automation. 8. Conclusion This paper portrays the use of neural network technique for improving the wave forecasts at four wave buoys along the Indian Coastline. The forecast done by the numerical model for a lead time of 24 h was improvised (corrected) by adding or subtracting the ‘errors’ which were forecasted by the use of neural network technique. It is evident from the above mentioned results that there is an elevated improvement in the 24 hr forecast at all the four locations and hence it can be said that the use of ANN is worthwhile in similar kind of research works in improvising the forecasting accuracy. This approach will definitely be a significant addition to the usefulness for the wave forecasts to INCOIS and its stake holders. High correlation coefficient (‘r’) and coefficient of efficiency (CE) values and low RMSE, MAE, scatter index and biasvalues proves the proficiency of new hybrid technique of NNT and hence it is pretty clear that this technique can be explored further in analogous class of research area.
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