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Application of Artificial Neural Network (ANN) to improve forecasting of sea level
Ocean & Coastal Management 55 (2012) 101e110
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Ocean & Coastal Management journal homepage: www.elsevier.com/locate/ocecoaman
Application of Artificial Neural Network (ANN) to improve forecasting of sea level Alessandro Filippo a, *, Audálio Rebelo Torres Jr. b, Björn Kjerfve c, d, André Monat e a Departamento de Oceanografia Física, Faculdade de Oceanografia, Universidade do Estado do Rio de Janeiro e UERJ, Rua São Francisco Xavier, 524, 4o andar, bloco E, sala 4017, Rio de Janeiro, RJ, Brazil b Departamento de Meteorologia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil c World Maritime University, S-201 24 Malmö, Sweden d Departments of Geography/Oceanography, Texas A&M University, College Station, TX, USA e Programa de Pós Graduação ESDI, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history: Available online 1 October 2011
To improve on forecasting of tidal water level beyond harmonic analysis requires the incorporation of meteorological variables in the analysis. This suggests the use of Artificial Neural Networks (ANN) as an optimum tool to train and translate the combined influence of meteorological and astronomical forcing to predict sea level variations and reduce the margin of error of close to 50% (from 26% to 12%). To accomplish this, the ANN was trained by using hourly time series of atmospheric pressure, wind, and harmonically derived tides for 1982 as input data and hourly time series of measured tides as output data. The meteorological data were obtained from São Sebastião (SP) and Ponta da Armação (RJ), and the sea level data from Cananéia (SP) and Ilha Fiscal (RJ). Data gaps in the time series were interpolated based on FFT analysis. To forecast water levels, the 1983 meteorological time series was used as input data, and compared the resulting water level outputs to the water level measurements for the same period. The ANN served as a very good forecasting tool for sea level variability. In the case of Cananéia, with several meteorological data gaps, the comparison was less successful as compared to the Ilha Fiscal results, besides this, there is a local influence of the estuary flows, a variable not considered that could answers for the remaining 12% of the correlation. The coefficient of correlation between predicted and measured water level time series at Cananéia was 0.88 and at Ilha Fiscal 0.98. This kind of improvement can be used for port terminals and marinas, for handling incoming and outgoing ships and boats more safely through the navigation channels in the estuaries. It is applicable and useful information for decision makers in management activities in the coastal area. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The influence of meteorological phenomena in the oceanographic parameters is one of the most interesting point to study about the atmosphereeocean interaction, especially in coastal environments, places of high population density and economic importance. Nowadays, the sea level changes are much discussed as a consequence of the global warming and storm waves. Littoral erosion and floods are examples of coastal problems that authorities deal and the prediction of the sea level variation, based on meteorological events prediction, is a helpful information to coastal management. In this paper, we highlight the importance of better prediction of sea level fluctuations.
* Corresponding author. E-mail address: amfi[email protected] (A. Filippo). 0964-5691/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ocecoaman.2011.09.007
The most commonly used technique to predict sea level variation is harmonic analysis (Franco, 1988), which permits forecast of tidal variations due to a locally modified response to astronomical forcing. Harmonic analysis is a powerful prediction tool but, in fact, sea level variations often differ significantly from predictions. The main reason is that harmonic prediction does not include variations due to meteorological forcing. A way of inserting the action of meteorological forcings in the forecast process is the utilization of Artificial Neural Networks (ANN), which it can translate and learn the relation between the behavior of the meteorological and the sea level variables. ANN consists of two steps, i.e. (i) definition of the architecture, and (ii) a learning algorithm to improve on the performance. The performance of the ANN improves with training (Rauber, 1998). The learning algorithm generalizes on the statistical behavior and memorizes the ledge of the ANN through the application of weights. A model based on ANN has two degrees of freedom, (i) the definition on the net type to solve the problem in consideration, and (ii) the algorithm to train the net. In
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a mathematical model of the neuron (NIBS, 2003), the effects of synapses are represented by weights, which modulate the effect of the associated input signals, and the nonlinear characteristics exhibited by neurons are represented by a transfer function that is usually a sigmoid function (NIBS, 2003). The neuron impulse is computed as the weighted sum of the input signals, transformed by the transfer function. The learning capability of an artificial neuron is achieved by adjusting the weights in accordance to the chosen learning algorithm, usually by a small amount DWj ¼ asXj where a is called the learning rate and s the momentum rate. The psychologist Frank Rosenblatt proposed the “Perceptron,” a pattern recognition device with learning capabilities in 1958 (NIBS, 2003), since then, the hierarchical neural network has been the most widely studied form of network structure. Widrow and Hoff (1960), Kohonen (1972, 1990), Hopfield (1982), Sarle (1996), Ivarsson (1998) and others developed studies on ANN that enhanced it uses as a powerful tool along the time. A hierarchical neural network is one that links multiple neurons hierarchically. When a signal is entered into the input layer, it is propagated to the next layer by the interconnections between the neurons. Simple processing is performed on this signal by the neurons of the receiving layer prior to its being propagated on to the next layer. So, in our case of interest, the signals of wind, atmospheric pressure and astronomic tide are processed and interconnected, and related to observed sea level signals. This process is repeated until the signal reaches the output layer completing the processing for this signal. ANN has not been used in large scale in oceanography and meteorology, yet. It is much used at financial and economic areas.
French et al. (1992) used ANN to predict rainfall intensity. Mase (1995) and Mase et al. (1995) applied the ANN algorithm to assess the stability of the armor units and the rubble-mound breakwater. Fernandes et al. (1995) has used a Multilayer Perceptron to make a forecasting exercise to allow an empirical comparison between the ANN model and the traditional structural time series or unobservable components model with the annual rainfall index from Fortaleza city, CE, Brazil. Deo and Naidu (1999) and Tsai et al. (1999) applied ANN models to estimate the wave’s forces acting on the structures and wave heights. Maier and Dandy (2000) have investigated the application of ANN for forecasting water resource variables. Hsieh and Pratt (2002) had used ANN to recover tidal field data. Recently, Lee and Jeng (2002) and Lee (2004) applied ANN for forecast the tide oscillations, but they did not considerate the meteorological influence. The objective of this study is to demonstrate how to predict sea level variations due to a combination of astronomical and meteorological forcing using an Artificial Neural Network (ANN), which is an efficient prediction tool. In the case of this study, our expectations are to improve the sea level forecasts giving the knowledge of meteorological and calculated astronomical tide (by the harmonic analysis) behavior to the neural network, at the same time period, obtaining results as close to real observed values as possible. 2. Study area The study area is situated along the southeastern coast of Brazil between latitude 22 300 S and 25 300 S and longitude 42 300 W and 48 000 W (Fig. 1). Sea level data were obtained from two stations,
Fig. 1. Locations of the two tide stations used for the analysis. Depths in meters.
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Table 1 Locations and data used for the ANN analysis. The data were obtained from Diretoria de Hidrografia e Navegação (DHN) of the Brazilian Navy. The period of all data is from 1-Jan-1982 to 31-Dec-1983. Stations
Longitude W
Latitude S
Type of data
N
% Good data
Cananéia São Sebastião
47.93 45.35
25.02 23.36
Ilha Fiscal Ponta da Armação
43.17 43.16
22.90 22.90
Sea level Atm. Pressure Wind Sea level Atm. Pressure Wind
17520 5444 5588 17520 5470 5818
100.0 93.2 95.7 100.0 93.7 99.6
with a float instrument type, Cananéia and Ilha Fiscal (Table 1), for the analysis. Frequent passages of westerly waves and cold fronts are typical of the region. Generally, these systems form over the Pacific Ocean, move eastward until they reach the Andes, and then turn toward the northeast along the east coast of South America. Such frontal systems often propagate along the coast between 40 S and 20 S, although they can reach latitudes as low as 13 S during the austral summer (Kousky, 1979). On the average, 3e6 frontal systems passes per month throughout the year between 20 S and 34 S, implying 5e10 days between passages. Oliveira (1986) shows that the frequency of occurrence of frontal systems tends to decrease toward the equator and to increase during the austral winter. The fewest frontal systems occur in February (3 per month) and the maximum in October (5 per month). The Mid-Atlantic continental shelf of South America is affected by winds from different directions as a result of the passage of frontal systems. Stech and Lorenzzetti (1992) estimated that the displacement speed of the cold fronts toward the northeast is approximately 500 km day1. Winds in the warm sector have a mean speed of 5 m s1 and rotate from northeasterly to a northwesterly wind direction (anticyclonic gyre) with the approach of the cold front. In the cold sector, northeastward winds have a mean speed of 8 m s1 and switch from a southwesterly to northeasterly direction with 24 h after passage of a cold front (Filippo, 2003). The inner shelf is occupied mainly by Coastal Water, which tends to be vertically homogeneous due to mixing processes caused by wind stress and tidal shear.
Fig. 2. Energy spectrum in frequency of the observed series (Wx), the series with gaps filled by the average (Wxm) and with zeros (Wxz).
Fig. 3. Original series (Wx), filtered of the original (Wxf) and filtered of the original with gaps fulfilled by zeros (Wxzf) and by the average (Wxmf).
3. Methodology The used data for this study was hourly sea level time series from Cananéia e SP and Ilha Fiscal e RJ stations, and time series of wind and atmospheric pressure every 3 h from São Sebastião e SP and Ponta da Armação e RJ station in the period from 01-Jan-1982 to 31-Dec-1983. Each station data set was analyzed separated to observe and preserve the local characteristics, following the methods bellow. The used program to design the ANN and run the predictions was the Statistica Neural Networks Release 4 from Statsoft Inc. (StatSoft, 2000b). The most common method used nowadays is the harmonic constants method, which takes into account the local astronomical influences. The strategy is to give that knowledge for the neural network, including the calculated astronomical tide as input data of the network. a. Treatment of the Tidal data The sea level data of the two stations were plotted and analyzed as to spurious values due to simple handling mistakes or the tide
Fig. 4. Observed and filtered series of the wind component Wx using the average to fulfill gaps.
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Fig. 5. Observed and filtered series of the wind component Wy using the average to fulfill gaps.
gauge’s bad operation. The criterion used to determinate of the limits for these spurious values was established regarding the values band (H) contained among percentiles of 25% and 75% of the samples. To reduce the data to the variation around the average level, the respective averages were subtracted of the original series. Then, the series was used to calculate the local harmonic constant, and then to calculate the astronomic tide using the PACMARE software developed by Franco (Franco and Harari, 1987; Franco, 1988). This astronomic tide is used as input data. The spectral analysis of the level of the sea, atmospheric pressure and of wind data series was accomplished by the application of (FFT), using as input parameters: Hanning window 4096 and overlaping 10. b. Treatment of the meteorological data These data also received treatment regarding spurious values, using the same adopted criterion. To certify which the best interpolation method for gaps is for the data series to be applied in to the ANN analysis were accomplished two tests. The first consisted in perform gaps with zeros and to do the interpolation via Fast Fourier Transformed (FFT), who consists in calculate the absolute of FFT,
Fig. 7. The Selected network design for the Ilha Fiscal station data.
conceding the complex part of the series and doing a filtration putting zeros on the frequencies that is wished eliminate, in function of the largest gap period. Following, it calculates the inverse of FFT of the modified series and obtains itself a compatible percolated series with for original. The second test consisted in perform gaps with the average of the series and to do the same interpolation via FFT. To accomplish the tests was used only a part of the series of wind (component Wx) which did not introduce gaps. Gaps were induced artificially and filled by zeros and by the average, forming the series Wxz and Wxm, respectively. The Fig. 2 shows the frequency spectrum of the series Wx, Wxm and Wxz. We can observe the biggest likeness among spectrums of the original series (Wx) and the fulfilled by the average (Wxm), mostly noted at the low frequencies. The Fig. 3 shows the percolated and interpolated series Wxf, Wxmf, Wxzf and the original series Wx. We can note that the series Wxzf was more distant from the series Wx and Wxf in the period when the fulfilling was made (marked with ellipses). The series of Wxmf represents better the tendency of the percolated original curve (Wxf). Thus, we opted by the utilization of the percolated series resulted from interpolation via FFT with fulfilling of gaps by the average. The series of the wind components would be the most problematic once that by the sense inversion, the average was next of zero, not there being a difference accentuated input fulfill with zeros or with the average. This does not occur with the series of atmospheric pressure, whose values vary very above of the zero,
Table 2 The Network sensibility analysis of the individual input variables.
Fig. 6. Observed and filtered series of the atmospheric pressure using the average to fulfill gaps.
Cananéia #
Pressure
WX
WY
Harm_pre
Rank Error Ratio I. Fiscal # Rank Error Ratio
3 0.1872 1.0123
2 0.2049 1.1080
4 0.1847 0.9990
1 0.3943 2.1322
4 0.1713 0.9994
2 0.1722 1.0045
3 0.1720 1.0036
1 0.3455 2.0158
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Fig. 8. Comparison between the observed sea level and predicted sea level by the neural network curves, for the March of 1983. Ilha Fiscal Station.
come in 1001 and 1030 hPa, being more indicated same to perform gaps with the average. Gaps of the series of the wind components in the axis X and Y (Wx and Wy), of the atmospheric pressure were, so, fulfilled with the average and submitted to the interpolation via FFT. Like result, the series filtered for all parameters were obtained, which are shown in the Figs. 4e6, to follow. After this treatment, another interpolation was done in order to convert the 3-hourly series into an hourly one so that it could be compared to the hourly tide series. The function CUBIC SPLINE from the MatLab program was used to make the interpolation (The MathWorks, 2000) and was compared with the original series characteristics. c. The neural network designing and training To find the best network to traduce the meteorological influence over the tide, we used the Intelligent Problem Solver and network sets wizard-style Statistica Neural Network function that can walk the user through the necessary analysis steps and make “intelligent” choices for the individual parameters.
The input data was the interpolated atmospheric pressure, X and Y wind direction components data series, and the calculated astronomical tide. The output data was the observed tide data series (with meteorological effects). A network is successful at regression if it makes predictions more accurate than a single estimate. The simplest way to construct an estimate, given training data, is to calculate the mean of the training data, and use that mean as the predicted value for all previously unseen cases. The average expected error from this procedure is the standard deviation of training data. The aim in using a regression network is therefore to produce an estimate that has a lower standard deviation for the prediction error than the standard deviation of the training data. The Statistica Neural Networks Program automatically calculates the mean and standard deviation of the training and verifications subsets, when the entire data set is run. It also calculates the mean and standard deviation of the prediction errors. The ratio of the prediction to data standard deviations is displayed; if this is 1.0, then the network does no better than a simple average. A lower ratio indicates a better estimate. The standard Pearson-R correlation between the actual and predicted outputs is displayed. A correlation of 1.0 does not
Fig. 9. Comparison between the observed sea level and predicted sea level by the neural network curves, for April/may of 1983. Ilha Fiscal Station.
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Fig. 10. Comparison between the observed sea level and predicted sea level by the neural network curves, for July/August of 1983. Ilha Fiscal Station.
necessarily indicate a perfect prediction (only a prediction which is perfectly linearly correlated with the actual outputs), although in practice the correlation coefficient is a good indicator of performance (StatSoft, 2000a). There are two kinds of experiments that could be done. The first is to design a neural network based on a set of one data station and try to use it for the other. So we could find a general neural network that could be used for prediction at other locations. The second is to design a neural network for each station. We chose in following the first experiment type, once it would be more practical to have a ready neural network, whose adaptation to a new place would be accomplished through training with previous local data. Once adapted, the neural network would be capable to accomplish forecasts. The first experiment step was done using the tide and meteorological data of Ilha Fiscal station to design the neural network. It was used an 8640 5 matrix data, being the first 4 columns the input data and the last one the output. The period considered was from 1-Jan-1982 to 26-Dec-1982, because the last days of December had lot of gaps of meteorological data of this station. From this, 70% was used by the program for training, 15% for
verification and 15% for test. The neural network was design and trained, than was used to forecast the meteorological tide for the year of 1983. Giving sequence to the experiment, we used the Cananéia’s tide and meteorological observed series data and the calculated astronomical tide for training the neural network. It resulted on a 7896 5 matrix data, being the first 4 columns (pressure, Wx, Wy, astronomical tide) the input data and the last column (observed tide) the output one. The considered period was from 1Feb-1982 to 26-Dec-1982. The absence of the January of 1982 was caused by a large gap of meteorological data of this station. Finished the training, we used the neural network to forecast the meteorological tide for the year of 1983. 4. Results During the design step, 32 networks were tested, 5 retained. The best network found between the 5 retained had O.K. performance (regression ratio ¼ 0.4084, correlation ¼ 0.9128, error ¼ 0.1390). Hiesh and Pratt (2002) found correlation coefficient ¼ 0.9716 and error ¼ 0.0996 using a partially recurrent network studying
Fig. 11. The coherence between the observed tide and predicted by the neural network curves for Ilha Fiscal station, 1983.
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Fig. 12. Comparison between the observed sea level and predicted sea level by the neural network curves, for February of 1983. Cananéia Station.
a self-recovery of surface elevations problem. The selected network has the following design shown on Fig. 7. This figure shows that the 4 input variables had significant influence in the process. The hour and day variables were not take account in the network design for the training step, once they have had take account during the harmonic astronomic tide prediction, which was used as input variable. The test for designing the network indicates that the more important variables into the process to generate meteorological observed tide were pressure, Wx, Wy and astronomic tide. The Table 2 shows the relative importance of the individual input variables rank. It is an investigation of how the network’s performance is affected if any of variables would be excluded. The importance of the variable in the process increases as the error increases. We can observe that the calculated harmonic constants prediction is the most important input variable in the process, followed by the X wind component Wx. There is a difference between the Cananéia and Ilha Fiscal’s stations rank. The atmospheric pressure is less important at Ilha Fiscal’s ANN, while the Wy is less important at Cananéia’s ANN. This difference could be a local response, once the Wy wind component is perpendicular to the coast at the entrance of Guanabara Bay, facilitating the entrance
and exit of water inside of the bay, where the Ilha Fiscal station is situated. The forecast results of the designed ANN for the year of 1983 had a good performance, compared to the observed data of Ilha Fiscal station. The Figs. 8, 9 and 10 show the both curves, predicted and observed, for different periods along the year. The major error between the curves was 0.25 m, and the correlation coefficient was 0.98, what can be confirmed by the coherence graphic shown on Fig. 11. We can notice that even at spring or neap tides the behavior of the curves is very close. The following sections will outline the basic formatting rules for mathematical symbols and units. For the Cananéia station, the forecast results to the 1983 period was not so good as the Ilha Fiscal station, although had a good performance, too. The neap tide period shows the major differences between the curves as shown on Figs. 12, 13 and 14. The coherence between the curves was 0.88, little lower than the Ilha Fiscal coefficient, and more irregular (Fig. 15). 5. Discussions The chosen area for the study possesses an intense activity in the atmosphere, with meteorological events of large, meso and
Fig. 13. Comparison between the observed sea level and predicted sea level by the neural network curves, for August of 1983. Cananéia Station.
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Fig. 14. Comparison between the observed sea level and predicted sea level by the neural network curves, for September of 1983. Cananéia Station.
micro scales presence. The passage of cold fronts along the coast and the deriving implications of this process, as change in the pressure gradient and in the speed and direction of the winds, they contribute in the transference of energy for the sea surface, generating variations not contemplated in the current methods of tide forecast. The overall performance of the ANN in the use for predicts the meteorological tide using atmospheric pressure, wind and calculated harmonic tide data was good. The Table 3 shows the comparison of the correlation coefficients between the ANN method and the classical harmonic constants method to estimate the sea level variation. We can observe that the coefficients obtained by the ANN method are greater than the harmonic constants. Once the ANN method uses the calculated harmonic constants method curve as an input data, we can clearly see that they are complementary and the ANN method is an improvement to estimate the sea level fluctuations as close as the actual fluctuation. In the analysis of the harmonic constants, there is the mathematical translation of the influence of the stars, mainly of the Sun and of the Moon, through
the combination of their respective forces of gravitational attraction with their respective rotation movements around of the Earth. In this process, the date, the hour and the place have importance to determine the position of the stars in relation to the wanted place and to calculate their influences. However, all the variability generated by the meteorological events induces to great differences in the forecast done by this method when compared to the observed real variability, about 26% in Cananéia and 31% in the Fiscal Island (Table 3). With the use of ANN, those meteorological effects are incorporate for the net and computed in the accomplishment of the forecast, reducing the margin of error, about 12% for Cananéia and 2% for Fiscal Island. The relevance of the good meteorological input dates is notorious. We can see the ANN response under not so good data had also not so good results. The meteorological data of Cananéia region were not as good as the Ilha Fiscal ones, even for training or forecasting. They have to be treated as described on the Methodology to cover more frequent little gaps. Besides, the fact of the Cananéia station is located inside of an estuary, whose fresh water flow is significantly able to influence the local sea level (Bernardes, 2001), it is possible that the absence of
Fig. 15. The coherence between the observed tide and predicted by the neural network curves for Cananéia station, 1983.
A. Filippo et al. / Ocean & Coastal Management 55 (2012) 101e110 Table 3 Comparison of the correlation coefficients between the observed tide curve and the predicted curves by the Harmonic constants and ANN methods for Cananéia and Ilha Fiscal stations. Period of 1983. Method
Cananéia e 1983
Ilha Fiscal e 1983
Harmonic constants ANN
0.74 0.88
0.69 0.98
this variable as input data reflects to smallest efficiency of the neural network forecast to this place. This reflects on the better correlation coefficient found to the Ilha Fiscal results, whose fresh water flow is insignificant (8 times smaller) regarding the tide prism (Kjerfve et al., 1997). The analysis of the variability of the local sea level had one gain when assimilated the characteristic behavior of the local meteorology and combined it with the characteristic behavior of the local harmonic components through the ANN. Oliveira et al. (2009), using NCEP/NCAR reanalysis data to predict sea level variation due storm surges at same area with ANN, founded a similar results, obtaining a observed and predicted data correlations of 99.06% for Cananéia e SP and 99.45% for Ponta da Armação e RJ stations. This is in accordance with our results, being the differences due to source of our data of input that were measurements of coastal stations and not of points in the grid of the NCEP reanalysis set. Other experiments can be done to try to get better, even, the tide forecasts, using ANN of different types. In a close future, studies can be accomplished using results of the winds fields and of atmospheric pressure gradient from forecast models, as input data of the net, besides the tide forecast for the classic method of the harmonic constants. This, in an attempt of foreseeing the meteorological tide, with base in preterits meteorological data through the training, but projecting forward with base in foreseen meteorological data, that can come to happen, or not. Nowadays, the good reliability of the atmospheric models forecasts has a horizon of 3 days, what restricts the sea level forecast horizon for the same period. Thus, the more the precision of the atmospheric models, better will be the result of the tide forecast by ANN.
6. Conclusion The main conclusions are: a) The ANN use as a tide prediction tool had a good performance, reaching values very close to the observed registered values; b) The ANN tool is complementary to the Harmonic constants method, once its results are used as input data and, improved by meteorological input data, makes better predictions; c) The input data quality is fundamental to make predictions with ANN, once it is sensible to little variations. It can be clearly seen in Cananéia’s case. Its meteorological data had a great number of little gaps along the series comparing to the Ilha Fiscal series. The Cananéia’s correlation coefficient was 0.88, while the Ilha Fiscal’s was 0.98. d) This smaller correlation coefficient in Cananéia could also have been caused by the influence of the local fluvial flow contribution, which is significant. It could be one more input variable in the network that would explain the variation of the local sea level, once that there is no limit for the number of input variables in an ANN. e) With ANN’s utilization, the meteorological effects are incorporated by the network and computed in the accomplishment of the forecast, decreasing the difference margin in terms of
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correlation coefficient for about 12% to Cananéia and 2% to Fiscal Island. This kind of improvement on the forecast of sea level variation can be used for port terminals and marinas, for handling incoming and outgoing ships and boats more safely through the navigation channels in the estuaries. Although there is still no consensus among researchers about the increasing frequency of storms and storm surges, the consensus is that, when the sea level is higher, the destructive capacity of a storm on the coast is much higher. It is useful information for decision makers in activities in the coastal area, especially in the face of global climate change that is associated with the variation of sea level.
Acknowledgments Our acknowledgments to Diretoria de Hidrografia e Navegação e DHN, of Brazilian Navy to give access to sea level and meteorological data. And also to Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES for the scholarship funds during the doctoral graduation. Our special gratefulness to Carlos Jansen Siqueira Neto for his aid in the final art of illustrations. References Bernardes, M.E.C., 2001. Circulação estacionária e estratificação de sal em canais estuarinos parcialmente misturados: simulação com modelos analíticos. Instituto Oceanográfico, Universidade de São Paulo, p. 162. Deo, M.C., Naidu, C.S., 1999. Real time wave forecasting using neural networks. Ocean Engineering 26, 101e303. Fernandes, L.G.L., Portugal, M.S., Navaux, P.O.A., 1995. Previsão de Séries de Tempo: Redes Neurais Artificiais e Modelos Estruturais. Filippo, A., 2003. Variabilidade do nível do mar em função de eventos meteorológicos de baixa freqüência. Departamento de Geoquímica Ambiental, Universidade Federal Fluminense - UFF, 100. Franco, A.S., 1988. Tides: Fundamentals, Analysis and Prediction, second ed.. Fundação Centro Tecnológico de Hidráulica (FCTH), 249 pp. Franco, A.S., Harari, J., 1987. Computer programs for tidal data cheking, correction, analysis and prediction by harmonic method. Relatório Interno 16, 1e65. French, M.N., Krajewski, W.F., Cuykendall, R.R., 1992. Rainfall forecasting in space and time using a neural network. Journal of Hydrology 37, 435e446. Hopfield, J.J., 1982. Neural networks and physical systems with emergent collective computational abilities. National Academy of Science, USA, 2554e2558. Hsieh, B.B., . Pratt, T.C., 2002. Field Data Recovery in Tidal System Using Artificial Neural Networks. http://www.iahr.org/elibrary/beijing_proceedings/Theme_F/ FIELD%20DATA%20RECOVER Available online from. Ivarsson, P.H., 1998. Multivariate Nonlinear Time-Series Prediction of Foreign Exchange Rate Returns Using Genetic Algorithms and Artificial Neural Networks. Institute of Theoretical Physics, Chalmers University of Technology, p. 60. Kjerfvé, B., Ribeiro, C.H.A., Dias, G., Filippo, A., Quaresma, V.S., 1997. Oceanographic characteristics of an impacted coastal bay: Baía de Guanabara, Rio de Janeiro, Brazil. Continental Shelf Research 17, 1609e1643. Kohonen, T., 1972. Correlation matrix memories. IEEE C-21, 353e359. Kohonen, T., 1990. The self-organizing map. IEEE. Kousky, V.E., 1979. Frontal influences on northeast Brazil. Mon. Weather Rev. 107, 1140e1153. Lee, T.L., 2004. Back-propagation neural network for long-term tidal predictions. Ocean Engineering 31, 225e238. Lee, T.L., Jeng, D.S., 2002. Application of artificial neural networks in tide-forecasting. Ocean Engineering 29, 1003e1022. Maier, H.R., Dandy, G.C., 2000. Neural networks for predicting and forecasting of water resources variables: a review of modelling issues and applications. Environmental Modelling & Software 15, 101e104. Mase, H., 1995. Evaluation of artificial armor layer stability by neural network method. In: 26th Congress of IAHR, London. IAHR, pp. 341e346. Mase, H., Sakamoto, M., Sakai, T., 1995. Neural network for stability analysis of rubble-mound breakwaters. Journal of Waterways 121, 294e299. Nibs, 2003. NeuroForecasterÒ with GENETICA Net Builder. User’s Guide. Eletronic Source. http://www.kdiscovery.com/index.htm#DownLoadCorner. Oliveira, A.S., 1986. Interações entre sistemas frontais na América do Sul e convecção na Amazônia, Instituto de Pesquisas Espaciais. INPE. de Oliveira, M.M.F., Ebecken, N.F.F., de Oliveira, J.L.F., Nunes, L.M.P., 2009. Predição da Variação Extrema do Nível do Mar relacionada a tempestades severas
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utilizando Redes Neurais Artificiais. Revista da Sociedade Brasileira de Redes Neurais (SBRN) 7 (1), 19e29. Rauber, T.W., 1998. Redes Neurais Artificiais. I Escola Regional de Informática da Sociedade Brasileira de Computação - Regional RJ/ES, Nova Friburgo, RJ - Vitória, E.S. Sociedade Brasileira de Computação, 268. Sarle, W.S., 1996. In: Measurement Theory: Frequently Asked Questions, fourth ed.. Disseminations of the International Statistical Applications Institute, ACG Press, 61e66 pp. StatSoft, 2000a. Release 4. StatSoft Inc.. StatSoft, 2000b. Neural Networks with STATISTICA. High Performance Statistical Software. StatSoft Inc.. Stech, J.L., Lorenzzetti, J.A., 1992. The response of the South Brazil bight to the passage of wintertime cold fronts. Journal Geophysical Research 97, 9507e9520. The MathWorks, I, 2000 6.0. Tsai, C.P., Lee, T.L., Chu, L.H., 1999. Forecasting of wave time series using backpropagation neural network. Journal of the Chinese Institute of Civil and Hydraulic Engineering 11, 589e596.
Widrow, B., Hoff, M.E., 1960. Adaptive Switching Circuits 1960 WESCON Convention Record, New York.
List of abbreviations ANN: Artificial Neural Network DHN: Diretoria de Hidrografia e Navegação da Marinha do Brasil a: the learning rate s: the momentum rate R: correlation coefficient FFT: Fast Fourier Transform Wx, Wy: wind components relative to the X (zonal) and Y (meridional) Wxf, Wyf: filtered wind components relative to the X (zonal) and Y (meridional) Wxmf, Wymf: filtered wind components relative to the X (zonal) and Y (meridional) with gaps filled with the respective mean Wxzf, Wyzf: filtered wind components relative to the X (zonal) and Y (meridional) with gaps filled with zeros
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Ocean & Coastal Management journal homepage: www.elsevier.com/locate/ocecoaman
Application of Artificial Neural Network (ANN) to improve forecasting of sea level Alessandro Filippo a, *, Audálio Rebelo Torres Jr. b, Björn Kjerfve c, d, André Monat e a Departamento de Oceanografia Física, Faculdade de Oceanografia, Universidade do Estado do Rio de Janeiro e UERJ, Rua São Francisco Xavier, 524, 4o andar, bloco E, sala 4017, Rio de Janeiro, RJ, Brazil b Departamento de Meteorologia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil c World Maritime University, S-201 24 Malmö, Sweden d Departments of Geography/Oceanography, Texas A&M University, College Station, TX, USA e Programa de Pós Graduação ESDI, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history: Available online 1 October 2011
To improve on forecasting of tidal water level beyond harmonic analysis requires the incorporation of meteorological variables in the analysis. This suggests the use of Artificial Neural Networks (ANN) as an optimum tool to train and translate the combined influence of meteorological and astronomical forcing to predict sea level variations and reduce the margin of error of close to 50% (from 26% to 12%). To accomplish this, the ANN was trained by using hourly time series of atmospheric pressure, wind, and harmonically derived tides for 1982 as input data and hourly time series of measured tides as output data. The meteorological data were obtained from São Sebastião (SP) and Ponta da Armação (RJ), and the sea level data from Cananéia (SP) and Ilha Fiscal (RJ). Data gaps in the time series were interpolated based on FFT analysis. To forecast water levels, the 1983 meteorological time series was used as input data, and compared the resulting water level outputs to the water level measurements for the same period. The ANN served as a very good forecasting tool for sea level variability. In the case of Cananéia, with several meteorological data gaps, the comparison was less successful as compared to the Ilha Fiscal results, besides this, there is a local influence of the estuary flows, a variable not considered that could answers for the remaining 12% of the correlation. The coefficient of correlation between predicted and measured water level time series at Cananéia was 0.88 and at Ilha Fiscal 0.98. This kind of improvement can be used for port terminals and marinas, for handling incoming and outgoing ships and boats more safely through the navigation channels in the estuaries. It is applicable and useful information for decision makers in management activities in the coastal area. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The influence of meteorological phenomena in the oceanographic parameters is one of the most interesting point to study about the atmosphereeocean interaction, especially in coastal environments, places of high population density and economic importance. Nowadays, the sea level changes are much discussed as a consequence of the global warming and storm waves. Littoral erosion and floods are examples of coastal problems that authorities deal and the prediction of the sea level variation, based on meteorological events prediction, is a helpful information to coastal management. In this paper, we highlight the importance of better prediction of sea level fluctuations.
* Corresponding author. E-mail address: amfi[email protected] (A. Filippo). 0964-5691/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ocecoaman.2011.09.007
The most commonly used technique to predict sea level variation is harmonic analysis (Franco, 1988), which permits forecast of tidal variations due to a locally modified response to astronomical forcing. Harmonic analysis is a powerful prediction tool but, in fact, sea level variations often differ significantly from predictions. The main reason is that harmonic prediction does not include variations due to meteorological forcing. A way of inserting the action of meteorological forcings in the forecast process is the utilization of Artificial Neural Networks (ANN), which it can translate and learn the relation between the behavior of the meteorological and the sea level variables. ANN consists of two steps, i.e. (i) definition of the architecture, and (ii) a learning algorithm to improve on the performance. The performance of the ANN improves with training (Rauber, 1998). The learning algorithm generalizes on the statistical behavior and memorizes the ledge of the ANN through the application of weights. A model based on ANN has two degrees of freedom, (i) the definition on the net type to solve the problem in consideration, and (ii) the algorithm to train the net. In
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a mathematical model of the neuron (NIBS, 2003), the effects of synapses are represented by weights, which modulate the effect of the associated input signals, and the nonlinear characteristics exhibited by neurons are represented by a transfer function that is usually a sigmoid function (NIBS, 2003). The neuron impulse is computed as the weighted sum of the input signals, transformed by the transfer function. The learning capability of an artificial neuron is achieved by adjusting the weights in accordance to the chosen learning algorithm, usually by a small amount DWj ¼ asXj where a is called the learning rate and s the momentum rate. The psychologist Frank Rosenblatt proposed the “Perceptron,” a pattern recognition device with learning capabilities in 1958 (NIBS, 2003), since then, the hierarchical neural network has been the most widely studied form of network structure. Widrow and Hoff (1960), Kohonen (1972, 1990), Hopfield (1982), Sarle (1996), Ivarsson (1998) and others developed studies on ANN that enhanced it uses as a powerful tool along the time. A hierarchical neural network is one that links multiple neurons hierarchically. When a signal is entered into the input layer, it is propagated to the next layer by the interconnections between the neurons. Simple processing is performed on this signal by the neurons of the receiving layer prior to its being propagated on to the next layer. So, in our case of interest, the signals of wind, atmospheric pressure and astronomic tide are processed and interconnected, and related to observed sea level signals. This process is repeated until the signal reaches the output layer completing the processing for this signal. ANN has not been used in large scale in oceanography and meteorology, yet. It is much used at financial and economic areas.
French et al. (1992) used ANN to predict rainfall intensity. Mase (1995) and Mase et al. (1995) applied the ANN algorithm to assess the stability of the armor units and the rubble-mound breakwater. Fernandes et al. (1995) has used a Multilayer Perceptron to make a forecasting exercise to allow an empirical comparison between the ANN model and the traditional structural time series or unobservable components model with the annual rainfall index from Fortaleza city, CE, Brazil. Deo and Naidu (1999) and Tsai et al. (1999) applied ANN models to estimate the wave’s forces acting on the structures and wave heights. Maier and Dandy (2000) have investigated the application of ANN for forecasting water resource variables. Hsieh and Pratt (2002) had used ANN to recover tidal field data. Recently, Lee and Jeng (2002) and Lee (2004) applied ANN for forecast the tide oscillations, but they did not considerate the meteorological influence. The objective of this study is to demonstrate how to predict sea level variations due to a combination of astronomical and meteorological forcing using an Artificial Neural Network (ANN), which is an efficient prediction tool. In the case of this study, our expectations are to improve the sea level forecasts giving the knowledge of meteorological and calculated astronomical tide (by the harmonic analysis) behavior to the neural network, at the same time period, obtaining results as close to real observed values as possible. 2. Study area The study area is situated along the southeastern coast of Brazil between latitude 22 300 S and 25 300 S and longitude 42 300 W and 48 000 W (Fig. 1). Sea level data were obtained from two stations,
Fig. 1. Locations of the two tide stations used for the analysis. Depths in meters.
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Table 1 Locations and data used for the ANN analysis. The data were obtained from Diretoria de Hidrografia e Navegação (DHN) of the Brazilian Navy. The period of all data is from 1-Jan-1982 to 31-Dec-1983. Stations
Longitude W
Latitude S
Type of data
N
% Good data
Cananéia São Sebastião
47.93 45.35
25.02 23.36
Ilha Fiscal Ponta da Armação
43.17 43.16
22.90 22.90
Sea level Atm. Pressure Wind Sea level Atm. Pressure Wind
17520 5444 5588 17520 5470 5818
100.0 93.2 95.7 100.0 93.7 99.6
with a float instrument type, Cananéia and Ilha Fiscal (Table 1), for the analysis. Frequent passages of westerly waves and cold fronts are typical of the region. Generally, these systems form over the Pacific Ocean, move eastward until they reach the Andes, and then turn toward the northeast along the east coast of South America. Such frontal systems often propagate along the coast between 40 S and 20 S, although they can reach latitudes as low as 13 S during the austral summer (Kousky, 1979). On the average, 3e6 frontal systems passes per month throughout the year between 20 S and 34 S, implying 5e10 days between passages. Oliveira (1986) shows that the frequency of occurrence of frontal systems tends to decrease toward the equator and to increase during the austral winter. The fewest frontal systems occur in February (3 per month) and the maximum in October (5 per month). The Mid-Atlantic continental shelf of South America is affected by winds from different directions as a result of the passage of frontal systems. Stech and Lorenzzetti (1992) estimated that the displacement speed of the cold fronts toward the northeast is approximately 500 km day1. Winds in the warm sector have a mean speed of 5 m s1 and rotate from northeasterly to a northwesterly wind direction (anticyclonic gyre) with the approach of the cold front. In the cold sector, northeastward winds have a mean speed of 8 m s1 and switch from a southwesterly to northeasterly direction with 24 h after passage of a cold front (Filippo, 2003). The inner shelf is occupied mainly by Coastal Water, which tends to be vertically homogeneous due to mixing processes caused by wind stress and tidal shear.
Fig. 2. Energy spectrum in frequency of the observed series (Wx), the series with gaps filled by the average (Wxm) and with zeros (Wxz).
Fig. 3. Original series (Wx), filtered of the original (Wxf) and filtered of the original with gaps fulfilled by zeros (Wxzf) and by the average (Wxmf).
3. Methodology The used data for this study was hourly sea level time series from Cananéia e SP and Ilha Fiscal e RJ stations, and time series of wind and atmospheric pressure every 3 h from São Sebastião e SP and Ponta da Armação e RJ station in the period from 01-Jan-1982 to 31-Dec-1983. Each station data set was analyzed separated to observe and preserve the local characteristics, following the methods bellow. The used program to design the ANN and run the predictions was the Statistica Neural Networks Release 4 from Statsoft Inc. (StatSoft, 2000b). The most common method used nowadays is the harmonic constants method, which takes into account the local astronomical influences. The strategy is to give that knowledge for the neural network, including the calculated astronomical tide as input data of the network. a. Treatment of the Tidal data The sea level data of the two stations were plotted and analyzed as to spurious values due to simple handling mistakes or the tide
Fig. 4. Observed and filtered series of the wind component Wx using the average to fulfill gaps.
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Fig. 5. Observed and filtered series of the wind component Wy using the average to fulfill gaps.
gauge’s bad operation. The criterion used to determinate of the limits for these spurious values was established regarding the values band (H) contained among percentiles of 25% and 75% of the samples. To reduce the data to the variation around the average level, the respective averages were subtracted of the original series. Then, the series was used to calculate the local harmonic constant, and then to calculate the astronomic tide using the PACMARE software developed by Franco (Franco and Harari, 1987; Franco, 1988). This astronomic tide is used as input data. The spectral analysis of the level of the sea, atmospheric pressure and of wind data series was accomplished by the application of (FFT), using as input parameters: Hanning window 4096 and overlaping 10. b. Treatment of the meteorological data These data also received treatment regarding spurious values, using the same adopted criterion. To certify which the best interpolation method for gaps is for the data series to be applied in to the ANN analysis were accomplished two tests. The first consisted in perform gaps with zeros and to do the interpolation via Fast Fourier Transformed (FFT), who consists in calculate the absolute of FFT,
Fig. 7. The Selected network design for the Ilha Fiscal station data.
conceding the complex part of the series and doing a filtration putting zeros on the frequencies that is wished eliminate, in function of the largest gap period. Following, it calculates the inverse of FFT of the modified series and obtains itself a compatible percolated series with for original. The second test consisted in perform gaps with the average of the series and to do the same interpolation via FFT. To accomplish the tests was used only a part of the series of wind (component Wx) which did not introduce gaps. Gaps were induced artificially and filled by zeros and by the average, forming the series Wxz and Wxm, respectively. The Fig. 2 shows the frequency spectrum of the series Wx, Wxm and Wxz. We can observe the biggest likeness among spectrums of the original series (Wx) and the fulfilled by the average (Wxm), mostly noted at the low frequencies. The Fig. 3 shows the percolated and interpolated series Wxf, Wxmf, Wxzf and the original series Wx. We can note that the series Wxzf was more distant from the series Wx and Wxf in the period when the fulfilling was made (marked with ellipses). The series of Wxmf represents better the tendency of the percolated original curve (Wxf). Thus, we opted by the utilization of the percolated series resulted from interpolation via FFT with fulfilling of gaps by the average. The series of the wind components would be the most problematic once that by the sense inversion, the average was next of zero, not there being a difference accentuated input fulfill with zeros or with the average. This does not occur with the series of atmospheric pressure, whose values vary very above of the zero,
Table 2 The Network sensibility analysis of the individual input variables.
Fig. 6. Observed and filtered series of the atmospheric pressure using the average to fulfill gaps.
Cananéia #
Pressure
WX
WY
Harm_pre
Rank Error Ratio I. Fiscal # Rank Error Ratio
3 0.1872 1.0123
2 0.2049 1.1080
4 0.1847 0.9990
1 0.3943 2.1322
4 0.1713 0.9994
2 0.1722 1.0045
3 0.1720 1.0036
1 0.3455 2.0158
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Fig. 8. Comparison between the observed sea level and predicted sea level by the neural network curves, for the March of 1983. Ilha Fiscal Station.
come in 1001 and 1030 hPa, being more indicated same to perform gaps with the average. Gaps of the series of the wind components in the axis X and Y (Wx and Wy), of the atmospheric pressure were, so, fulfilled with the average and submitted to the interpolation via FFT. Like result, the series filtered for all parameters were obtained, which are shown in the Figs. 4e6, to follow. After this treatment, another interpolation was done in order to convert the 3-hourly series into an hourly one so that it could be compared to the hourly tide series. The function CUBIC SPLINE from the MatLab program was used to make the interpolation (The MathWorks, 2000) and was compared with the original series characteristics. c. The neural network designing and training To find the best network to traduce the meteorological influence over the tide, we used the Intelligent Problem Solver and network sets wizard-style Statistica Neural Network function that can walk the user through the necessary analysis steps and make “intelligent” choices for the individual parameters.
The input data was the interpolated atmospheric pressure, X and Y wind direction components data series, and the calculated astronomical tide. The output data was the observed tide data series (with meteorological effects). A network is successful at regression if it makes predictions more accurate than a single estimate. The simplest way to construct an estimate, given training data, is to calculate the mean of the training data, and use that mean as the predicted value for all previously unseen cases. The average expected error from this procedure is the standard deviation of training data. The aim in using a regression network is therefore to produce an estimate that has a lower standard deviation for the prediction error than the standard deviation of the training data. The Statistica Neural Networks Program automatically calculates the mean and standard deviation of the training and verifications subsets, when the entire data set is run. It also calculates the mean and standard deviation of the prediction errors. The ratio of the prediction to data standard deviations is displayed; if this is 1.0, then the network does no better than a simple average. A lower ratio indicates a better estimate. The standard Pearson-R correlation between the actual and predicted outputs is displayed. A correlation of 1.0 does not
Fig. 9. Comparison between the observed sea level and predicted sea level by the neural network curves, for April/may of 1983. Ilha Fiscal Station.
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Fig. 10. Comparison between the observed sea level and predicted sea level by the neural network curves, for July/August of 1983. Ilha Fiscal Station.
necessarily indicate a perfect prediction (only a prediction which is perfectly linearly correlated with the actual outputs), although in practice the correlation coefficient is a good indicator of performance (StatSoft, 2000a). There are two kinds of experiments that could be done. The first is to design a neural network based on a set of one data station and try to use it for the other. So we could find a general neural network that could be used for prediction at other locations. The second is to design a neural network for each station. We chose in following the first experiment type, once it would be more practical to have a ready neural network, whose adaptation to a new place would be accomplished through training with previous local data. Once adapted, the neural network would be capable to accomplish forecasts. The first experiment step was done using the tide and meteorological data of Ilha Fiscal station to design the neural network. It was used an 8640 5 matrix data, being the first 4 columns the input data and the last one the output. The period considered was from 1-Jan-1982 to 26-Dec-1982, because the last days of December had lot of gaps of meteorological data of this station. From this, 70% was used by the program for training, 15% for
verification and 15% for test. The neural network was design and trained, than was used to forecast the meteorological tide for the year of 1983. Giving sequence to the experiment, we used the Cananéia’s tide and meteorological observed series data and the calculated astronomical tide for training the neural network. It resulted on a 7896 5 matrix data, being the first 4 columns (pressure, Wx, Wy, astronomical tide) the input data and the last column (observed tide) the output one. The considered period was from 1Feb-1982 to 26-Dec-1982. The absence of the January of 1982 was caused by a large gap of meteorological data of this station. Finished the training, we used the neural network to forecast the meteorological tide for the year of 1983. 4. Results During the design step, 32 networks were tested, 5 retained. The best network found between the 5 retained had O.K. performance (regression ratio ¼ 0.4084, correlation ¼ 0.9128, error ¼ 0.1390). Hiesh and Pratt (2002) found correlation coefficient ¼ 0.9716 and error ¼ 0.0996 using a partially recurrent network studying
Fig. 11. The coherence between the observed tide and predicted by the neural network curves for Ilha Fiscal station, 1983.
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Fig. 12. Comparison between the observed sea level and predicted sea level by the neural network curves, for February of 1983. Cananéia Station.
a self-recovery of surface elevations problem. The selected network has the following design shown on Fig. 7. This figure shows that the 4 input variables had significant influence in the process. The hour and day variables were not take account in the network design for the training step, once they have had take account during the harmonic astronomic tide prediction, which was used as input variable. The test for designing the network indicates that the more important variables into the process to generate meteorological observed tide were pressure, Wx, Wy and astronomic tide. The Table 2 shows the relative importance of the individual input variables rank. It is an investigation of how the network’s performance is affected if any of variables would be excluded. The importance of the variable in the process increases as the error increases. We can observe that the calculated harmonic constants prediction is the most important input variable in the process, followed by the X wind component Wx. There is a difference between the Cananéia and Ilha Fiscal’s stations rank. The atmospheric pressure is less important at Ilha Fiscal’s ANN, while the Wy is less important at Cananéia’s ANN. This difference could be a local response, once the Wy wind component is perpendicular to the coast at the entrance of Guanabara Bay, facilitating the entrance
and exit of water inside of the bay, where the Ilha Fiscal station is situated. The forecast results of the designed ANN for the year of 1983 had a good performance, compared to the observed data of Ilha Fiscal station. The Figs. 8, 9 and 10 show the both curves, predicted and observed, for different periods along the year. The major error between the curves was 0.25 m, and the correlation coefficient was 0.98, what can be confirmed by the coherence graphic shown on Fig. 11. We can notice that even at spring or neap tides the behavior of the curves is very close. The following sections will outline the basic formatting rules for mathematical symbols and units. For the Cananéia station, the forecast results to the 1983 period was not so good as the Ilha Fiscal station, although had a good performance, too. The neap tide period shows the major differences between the curves as shown on Figs. 12, 13 and 14. The coherence between the curves was 0.88, little lower than the Ilha Fiscal coefficient, and more irregular (Fig. 15). 5. Discussions The chosen area for the study possesses an intense activity in the atmosphere, with meteorological events of large, meso and
Fig. 13. Comparison between the observed sea level and predicted sea level by the neural network curves, for August of 1983. Cananéia Station.
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Fig. 14. Comparison between the observed sea level and predicted sea level by the neural network curves, for September of 1983. Cananéia Station.
micro scales presence. The passage of cold fronts along the coast and the deriving implications of this process, as change in the pressure gradient and in the speed and direction of the winds, they contribute in the transference of energy for the sea surface, generating variations not contemplated in the current methods of tide forecast. The overall performance of the ANN in the use for predicts the meteorological tide using atmospheric pressure, wind and calculated harmonic tide data was good. The Table 3 shows the comparison of the correlation coefficients between the ANN method and the classical harmonic constants method to estimate the sea level variation. We can observe that the coefficients obtained by the ANN method are greater than the harmonic constants. Once the ANN method uses the calculated harmonic constants method curve as an input data, we can clearly see that they are complementary and the ANN method is an improvement to estimate the sea level fluctuations as close as the actual fluctuation. In the analysis of the harmonic constants, there is the mathematical translation of the influence of the stars, mainly of the Sun and of the Moon, through
the combination of their respective forces of gravitational attraction with their respective rotation movements around of the Earth. In this process, the date, the hour and the place have importance to determine the position of the stars in relation to the wanted place and to calculate their influences. However, all the variability generated by the meteorological events induces to great differences in the forecast done by this method when compared to the observed real variability, about 26% in Cananéia and 31% in the Fiscal Island (Table 3). With the use of ANN, those meteorological effects are incorporate for the net and computed in the accomplishment of the forecast, reducing the margin of error, about 12% for Cananéia and 2% for Fiscal Island. The relevance of the good meteorological input dates is notorious. We can see the ANN response under not so good data had also not so good results. The meteorological data of Cananéia region were not as good as the Ilha Fiscal ones, even for training or forecasting. They have to be treated as described on the Methodology to cover more frequent little gaps. Besides, the fact of the Cananéia station is located inside of an estuary, whose fresh water flow is significantly able to influence the local sea level (Bernardes, 2001), it is possible that the absence of
Fig. 15. The coherence between the observed tide and predicted by the neural network curves for Cananéia station, 1983.
A. Filippo et al. / Ocean & Coastal Management 55 (2012) 101e110 Table 3 Comparison of the correlation coefficients between the observed tide curve and the predicted curves by the Harmonic constants and ANN methods for Cananéia and Ilha Fiscal stations. Period of 1983. Method
Cananéia e 1983
Ilha Fiscal e 1983
Harmonic constants ANN
0.74 0.88
0.69 0.98
this variable as input data reflects to smallest efficiency of the neural network forecast to this place. This reflects on the better correlation coefficient found to the Ilha Fiscal results, whose fresh water flow is insignificant (8 times smaller) regarding the tide prism (Kjerfve et al., 1997). The analysis of the variability of the local sea level had one gain when assimilated the characteristic behavior of the local meteorology and combined it with the characteristic behavior of the local harmonic components through the ANN. Oliveira et al. (2009), using NCEP/NCAR reanalysis data to predict sea level variation due storm surges at same area with ANN, founded a similar results, obtaining a observed and predicted data correlations of 99.06% for Cananéia e SP and 99.45% for Ponta da Armação e RJ stations. This is in accordance with our results, being the differences due to source of our data of input that were measurements of coastal stations and not of points in the grid of the NCEP reanalysis set. Other experiments can be done to try to get better, even, the tide forecasts, using ANN of different types. In a close future, studies can be accomplished using results of the winds fields and of atmospheric pressure gradient from forecast models, as input data of the net, besides the tide forecast for the classic method of the harmonic constants. This, in an attempt of foreseeing the meteorological tide, with base in preterits meteorological data through the training, but projecting forward with base in foreseen meteorological data, that can come to happen, or not. Nowadays, the good reliability of the atmospheric models forecasts has a horizon of 3 days, what restricts the sea level forecast horizon for the same period. Thus, the more the precision of the atmospheric models, better will be the result of the tide forecast by ANN.
6. Conclusion The main conclusions are: a) The ANN use as a tide prediction tool had a good performance, reaching values very close to the observed registered values; b) The ANN tool is complementary to the Harmonic constants method, once its results are used as input data and, improved by meteorological input data, makes better predictions; c) The input data quality is fundamental to make predictions with ANN, once it is sensible to little variations. It can be clearly seen in Cananéia’s case. Its meteorological data had a great number of little gaps along the series comparing to the Ilha Fiscal series. The Cananéia’s correlation coefficient was 0.88, while the Ilha Fiscal’s was 0.98. d) This smaller correlation coefficient in Cananéia could also have been caused by the influence of the local fluvial flow contribution, which is significant. It could be one more input variable in the network that would explain the variation of the local sea level, once that there is no limit for the number of input variables in an ANN. e) With ANN’s utilization, the meteorological effects are incorporated by the network and computed in the accomplishment of the forecast, decreasing the difference margin in terms of
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correlation coefficient for about 12% to Cananéia and 2% to Fiscal Island. This kind of improvement on the forecast of sea level variation can be used for port terminals and marinas, for handling incoming and outgoing ships and boats more safely through the navigation channels in the estuaries. Although there is still no consensus among researchers about the increasing frequency of storms and storm surges, the consensus is that, when the sea level is higher, the destructive capacity of a storm on the coast is much higher. It is useful information for decision makers in activities in the coastal area, especially in the face of global climate change that is associated with the variation of sea level.
Acknowledgments Our acknowledgments to Diretoria de Hidrografia e Navegação e DHN, of Brazilian Navy to give access to sea level and meteorological data. And also to Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES for the scholarship funds during the doctoral graduation. Our special gratefulness to Carlos Jansen Siqueira Neto for his aid in the final art of illustrations. References Bernardes, M.E.C., 2001. Circulação estacionária e estratificação de sal em canais estuarinos parcialmente misturados: simulação com modelos analíticos. Instituto Oceanográfico, Universidade de São Paulo, p. 162. Deo, M.C., Naidu, C.S., 1999. Real time wave forecasting using neural networks. Ocean Engineering 26, 101e303. Fernandes, L.G.L., Portugal, M.S., Navaux, P.O.A., 1995. Previsão de Séries de Tempo: Redes Neurais Artificiais e Modelos Estruturais. Filippo, A., 2003. Variabilidade do nível do mar em função de eventos meteorológicos de baixa freqüência. Departamento de Geoquímica Ambiental, Universidade Federal Fluminense - UFF, 100. Franco, A.S., 1988. Tides: Fundamentals, Analysis and Prediction, second ed.. Fundação Centro Tecnológico de Hidráulica (FCTH), 249 pp. Franco, A.S., Harari, J., 1987. Computer programs for tidal data cheking, correction, analysis and prediction by harmonic method. Relatório Interno 16, 1e65. French, M.N., Krajewski, W.F., Cuykendall, R.R., 1992. Rainfall forecasting in space and time using a neural network. Journal of Hydrology 37, 435e446. Hopfield, J.J., 1982. Neural networks and physical systems with emergent collective computational abilities. National Academy of Science, USA, 2554e2558. Hsieh, B.B., . Pratt, T.C., 2002. Field Data Recovery in Tidal System Using Artificial Neural Networks. http://www.iahr.org/elibrary/beijing_proceedings/Theme_F/ FIELD%20DATA%20RECOVER Available online from. Ivarsson, P.H., 1998. Multivariate Nonlinear Time-Series Prediction of Foreign Exchange Rate Returns Using Genetic Algorithms and Artificial Neural Networks. Institute of Theoretical Physics, Chalmers University of Technology, p. 60. Kjerfvé, B., Ribeiro, C.H.A., Dias, G., Filippo, A., Quaresma, V.S., 1997. Oceanographic characteristics of an impacted coastal bay: Baía de Guanabara, Rio de Janeiro, Brazil. Continental Shelf Research 17, 1609e1643. Kohonen, T., 1972. Correlation matrix memories. IEEE C-21, 353e359. Kohonen, T., 1990. The self-organizing map. IEEE. Kousky, V.E., 1979. Frontal influences on northeast Brazil. Mon. Weather Rev. 107, 1140e1153. Lee, T.L., 2004. Back-propagation neural network for long-term tidal predictions. Ocean Engineering 31, 225e238. Lee, T.L., Jeng, D.S., 2002. Application of artificial neural networks in tide-forecasting. Ocean Engineering 29, 1003e1022. Maier, H.R., Dandy, G.C., 2000. Neural networks for predicting and forecasting of water resources variables: a review of modelling issues and applications. Environmental Modelling & Software 15, 101e104. Mase, H., 1995. Evaluation of artificial armor layer stability by neural network method. In: 26th Congress of IAHR, London. IAHR, pp. 341e346. Mase, H., Sakamoto, M., Sakai, T., 1995. Neural network for stability analysis of rubble-mound breakwaters. Journal of Waterways 121, 294e299. Nibs, 2003. NeuroForecasterÒ with GENETICA Net Builder. User’s Guide. Eletronic Source. http://www.kdiscovery.com/index.htm#DownLoadCorner. Oliveira, A.S., 1986. Interações entre sistemas frontais na América do Sul e convecção na Amazônia, Instituto de Pesquisas Espaciais. INPE. de Oliveira, M.M.F., Ebecken, N.F.F., de Oliveira, J.L.F., Nunes, L.M.P., 2009. Predição da Variação Extrema do Nível do Mar relacionada a tempestades severas
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A. Filippo et al. / Ocean & Coastal Management 55 (2012) 101e110
utilizando Redes Neurais Artificiais. Revista da Sociedade Brasileira de Redes Neurais (SBRN) 7 (1), 19e29. Rauber, T.W., 1998. Redes Neurais Artificiais. I Escola Regional de Informática da Sociedade Brasileira de Computação - Regional RJ/ES, Nova Friburgo, RJ - Vitória, E.S. Sociedade Brasileira de Computação, 268. Sarle, W.S., 1996. In: Measurement Theory: Frequently Asked Questions, fourth ed.. Disseminations of the International Statistical Applications Institute, ACG Press, 61e66 pp. StatSoft, 2000a. Release 4. StatSoft Inc.. StatSoft, 2000b. Neural Networks with STATISTICA. High Performance Statistical Software. StatSoft Inc.. Stech, J.L., Lorenzzetti, J.A., 1992. The response of the South Brazil bight to the passage of wintertime cold fronts. Journal Geophysical Research 97, 9507e9520. The MathWorks, I, 2000 6.0. Tsai, C.P., Lee, T.L., Chu, L.H., 1999. Forecasting of wave time series using backpropagation neural network. Journal of the Chinese Institute of Civil and Hydraulic Engineering 11, 589e596.
Widrow, B., Hoff, M.E., 1960. Adaptive Switching Circuits 1960 WESCON Convention Record, New York.
List of abbreviations ANN: Artificial Neural Network DHN: Diretoria de Hidrografia e Navegação da Marinha do Brasil a: the learning rate s: the momentum rate R: correlation coefficient FFT: Fast Fourier Transform Wx, Wy: wind components relative to the X (zonal) and Y (meridional) Wxf, Wyf: filtered wind components relative to the X (zonal) and Y (meridional) Wxmf, Wymf: filtered wind components relative to the X (zonal) and Y (meridional) with gaps filled with the respective mean Wxzf, Wyzf: filtered wind components relative to the X (zonal) and Y (meridional) with gaps filled with zeros