Forecasting Caspian Sea level changes using satellite altimetry data (June 1992–December 2013) based on evolutionary support vector regression algorithms and gene expression programming

Highlights

• Caspian Sea level changes are predicted using artificial intelligent approaches.

• Using promising SVM and GEP approaches as satisfactory forecasting models

• Using time series obtained by satellite altimetry as available high-quality data

Abstract

Sea level forecasting at various time intervals is of great importance in water supply management. Evolutionary artificial intelligence (AI) approaches have been accepted as an appropriate tool for modeling complex nonlinear phenomena in water bodies. In the study, we investigated the ability of two AI techniques: support vector machine (SVM), which is mathematically well-founded and provides new insights into function approximation, and gene expression programming (GEP), which is used to forecast Caspian Sea level anomalies using satellite altimetry observations from June 1992 to December 2013. SVM demonstrates the best performance in predicting Caspian Sea level anomalies, given the minimum root mean square error (RMSE = 0.035) and maximum coefficient of determination (R² = 0.96) during the prediction periods. A comparison between the proposed AI approaches and the cascade correlation neural network (CCNN) model also shows the superiority of the GEP and SVM models over the CCNN.

Introduction

Accurate predictions and a reliable foresight of sea level behavior have always been important in water resource management scenarios. The analysis of the long-term and short-term sea level fluctuations is especially important because it potentially affects the natural processes occurring in the basin and influences the infrastructure built along coastlines (Llovel et al., 2011, Kisi et al., 2012, Milne and Peros, 2013). Sea level variations are complex outcomes of different site-specific geographical and meteorological variables, including precipitation, runoff, evaporation, temperature, water salinity, and the interaction between surface water and low-lying aquifers, which differ throughout the area. Although sea level monitoring is essentially useful as an applied and a fundamental policy on water management strategies, anticipation of future conditions, both in the short term and in the long term, is necessary at certain times to make reliable hydrological and water management decisions. Regarding different contributors, accurate measurements and analyses by conventional approaches are still difficult to achieve and may suffer from large uncertainties (Talebizadeh and Moridnejad, 2011). Computer-intensive statistical methods have improved modeling approaches for time series data in water resources (e.g., American Society of Civil Engineers (ASCE) Task Committee on Application of Artificial Neural Networks in Hydrology, 2000, Renssen et al., 2007, Ghorbani et al., 2010, Ozyavas et al., 2010, Kisi et al., 2012). Most conventional techniques for sea level prediction are based on the extrapolation of linear trends, where nonlinear time series and irregular changes, such as the El Niño/Southern Oscillation, cannot be satisfactorily fitted. Artificial intelligence (AI) techniques, such as artificial neural network (ANN), decision tree techniques, and fuzzy network, have been developed and are being used to model complex nonlinear phenomena in hydrology and water resource engineering (e.g., More and Deo, 2003, Huang et al., 2006, Wu and Chau, 2010, Kisi et al., 2012, Imani et al., in press). Recently, neural network methodologies, namely, support vector machines (SVMs) and gene expression programming (GEP), have been introduced as applied forecasting techniques in time series analysis (e.g., Kim, 2003, Yu et al., 2006, Guven and Gunal, 2008, Rajasekaran et al., 2008, Ghorbani et al., 2010). The learning algorithms of SVMs, developed by Vapnik et al. (1997), are described specifically by the capacity control of the decision function, the kernel functions, and the sparsity of the solution (Cristianini and Taylor, 2000). SVMs are resistant to the over-fitting problem and thus demonstrate highly generalized performance in solving various time series forecasting cases. Unlike most of the traditional neural network models, which implement the empirical risk minimization principle, SVMs implement the structural risk minimization principle, which seeks to minimize the upper bound of the generalization error rather than minimize the training error (Tay and Cao, 2001). The main advantages of SVMs are being effective in high-dimensional spaces even when the number of dimensions is greater than the number of samples and comprising a subset of training points called support vectors as well as different kernel functions, which can be specified for the decision function. The traditional ANNs have considerable subjectivity in model architecture, whereas the learning algorithm of SVMs automatically decides the model architecture (number of hidden units). Moreover, traditional ANN models do not emphasize the generalization performance, whereas the main characteristic of SVMs is to address this subject in a rigorous theoretical setting (Vapnik, 1992, Haykin, 2003). Despite well-documented studies in other fields, the applications of SVM in hydrology are few. Sivapragasam et al. (2001) conducted one-lead-day rainfall and runoff forecasting using SVM, with preprocessing input data by singular spectrum analysis, resulting in a high-dimensional input space. Tripathi et al. (2006) applied SVM in the statistical downscaling of precipitation at a monthly timescale where the effectiveness of the approach is indicated by its application in meteorological subdivisions in India. Lins et al. (2013) presented a year-ahead prediction procedure based on sea surface temperature (SST) data of previous periods using SVMs. The proposed procedure was conducted based on the seasonal and intraseasonal features of SST. To the best of our knowledge, no study has used SVM in sea level time series prediction. Although the algorithm of SVMs automatically determines the model architecture, GEP is based on data alone to establish the structure and parameters of the model (e.g., Koza, 1992, Ferreira, 2006). GEP may generally be defined as an evolutionary algorithm for computer programs composed of multiple parse trees referred to as expression trees (ETs). GEP is based on the relationship between datasets, followed by model building to describe these connections. The advantage of the genetic programming (GP) approach over ANNs in developing climate change studies is that it provides efficient and transparent modeling results (Ferreira, 2006). Genetic programs are generally robust applications of optimization algorithms using statistical procedures to imitate nature. In this approach, a combination of mathematical expressions is derived to describe the relationship between different variables using operators, such as mutation, recombination, and evolution (Banzhaf et al., 1998). The comprehensibility of GEP models provides lower risk of over-fitting of training data and a way to improve the generalization of resulting models. In addition, the unique and multigenic nature of GEP allows evolution of highly complex programs composed of several subprograms the (Ferreira, 2001a, Ferreira, 2001b).

Only a few applications of GEP can be classified into the field of water and ocean engineering (e.g., Gaur and Deo, 2008, Ustoorikar and Deo, 2008). Drecourt (1999), Savic et al. (1999), Liong et al. (2002), and Aytek and Alp (2008) applied GP in rainfall–runoff modeling. Harris et al. (2003) used GP to predict velocity in compound channels with vegetated flood plains. Aytek and Kisi (2008) applied GP in suspended sediments and observed that GP is better than the conventional rating curve and multilinear regression techniques. Gaur and Deo (2008) applied GP in real-time wave forecasting.

Thus, the main focus of the present study is to predict Caspian Sea level anomalies using altimetric measurements from the TOPEX/Poseidon (T/P), Jason-1 (J-1), and Jason-2/OSTM (J-2) satellite missions from June 1992 to December 2013 by following new approaches, namely, SVMs and GEP, which have not been applied for satellite-based sea level analysis. Then, the proposed models are compared with the ANN-based approach.