# High-Precision Combined Tidal Forecasting Model
## 1 Introduction  
Tide is the periodic rising and falling of the sea level, and its fluctuations largely influence human lifestyle. Accurate real-time recording of tide level information is essential for ship navigation safety, the development and utilization of marine resources, and marine disaster mitigation and prevention [1]. Therefore, a simple and efficient tidal prediction method is urgently required. Based on their underlying prediction principles, tidal prediction methods are classified into traditional and intelligent prediction models. Traditional tidal prediction models are mainly based on harmonic analysis [2; 3]. Harmonic analysis for tide prediction was pioneered by [PERSON] in 1866, which was subsequently improved by [PERSON], who formulated the equilibrium tide theory. [PERSON] determined the harmonic analysis constants by least-squares fitting the observed tidal data [4]. [PERSON] smoothed the harmonic analysis constants by passing them through a Kalman filter [5]. After hundreds of years of development, harmonic analysis continues to be widely used in tidal prediction; however, this model only considers the astronomical tidal level affected by the tide-generating forces. Other environmental factors such as wind, pressure, and seabed topography, which exert nonlinear effects on the tidal level, are ignored. If the tide level is predicted by harmonic analysis alone, a large prediction error is incurred, which can be verified in Section 3.2.2 of this paper. Harmonic analysis also requires long-term historical data of tidal levels, which are generally precluded by the high cost of on-site monitoring equipment [6]. In today's artificial intelligence era, data prediction is performed by increasingly intelligent models. Owing to their strong adaptive learning ability and nonlinear-mapping ability, neural networks arenow widely used in tidal prediction. Many researchers have combined neural networks with related intelligent algorithms in their tidal prediction models, with much success. The first prediction of diurnal and semidiurnal tides by an artificial neural network was attempted by [PERSON] et al. [7]; [PERSON] et al. [8] proposed an adaptive neuro-fuzzy inference system for sea level prediction, which accounts for the tidal forces and thermal expansion of the ocean; and [PERSON] et al. [9] developed a 24 h tidal prediction model based on a neural network, and applied it to the New Mangalore tidal station on the west coast of the Indian Ocean. However, neural networks generally require a large amount of training data, are easily trapped into local optima, lack universal applicability, etc. Support vector machines (SVM) have been widely used in prediction because they provide good nonlinear fitting with small input data volumes and are strongly generalizable [10]. [PERSON] et al. [11] successfully forecasted the families and subfamilies of G-protein coupled receptors by an SVM-based approach; [PERSON] et al. [12] combined an SVM with a Hidden Markov model, and hence proposed a new framework of vehicle collision prediction; and [PERSON] et al. [13] hybridized the SVM model with graded resolution, and predicted the surface roughness during abrasive water-jet machining. [PERSON] et al. [14] proposed an evolutionary hybrid system composed of an exponential smoothing filter, the Autoregressive Integrated Moving Average Model (ARIMA), autoregressive (AR) linear models, and an SVR model, which has been proven to have good prospects in the forecasting field. Given this diversity of applications, the prospects of SVM in tidal prediction are high. Nevertheless, tidal prediction by SVM has rarely been reported. To exploit these prospects, the current study proposes a tidal prediction model based on harmonic analysis and an autoregressive integrated moving-average-SVM for Regression (ARIMA-SVR): The model uses the typical time-series-processing model ARIMA and the SVR, with an excellent nonlinear-data regression performance, to predict the residual sequence generated by the prediction of harmonic analysis.