Experimental Simulation of Water Level Fluctuations using the Genetic Expression Programming (GEP)

1. Water level variations are highly sensitive to many environmental factors, such as lunar and solar gravitational attraction, waves and currents, atmospheric pressure and wind forcing, as well as many other dynamic presumably nonlinear and interconnected physical variables. Prediction of future water level heights in the coastal environment is of great importance for the protection of low-lying region's residents, for monitoring and prediction of changes in fishery and marine ecosystems. Different methods are used for water level prediction including time series analysis, fuzzy logic, neuron fuzzy, genetic programming, artificial neural networks, and recently, chaos theory [1]. Since the 1990s, time series methods employing the Genetic Expression Programming (GEP), Artificial Neural Network (ANN) and fuzzy logic methods have become viable, giving rise to the publication of many scientific studies [2]. This paper aims the application of GEP and ANN models to forecast sea level time series, which are data-driven modeling approaches.2. Methodology2.1. Study area and data: In this study, water level data was obtained from the Local Water Organization of Tabriz, Iran. Figure 1 shows the Urmia Lake located at latitude 40.35° North and longitude 13.44° East. Daily sea-water level measurements from January 1997 to July 2008 were used for training and validation of GEP and ANN models. The range of recorded values is from 1272.55 m (Jul, 2008) to 1277.77 m (June, 1997) with respect to above sea level. However, in a normal year, the range of level fluctuations does not exceed 87 cm. The initial time series data of was levels was obtained at a daily interval.2.2. Genetic expression programming: The GEP is similar to Genetic Algorithm (GA) but employs a “parse tree” structure for the search of its solutions, whereas the GA employs bite strips. The technique is truly a “bottom up” process, as there is no assumption made on the structure of the relationship between the independent and dependent variables but an appropriate relationship is identified for any given time series [3]. The relationship can be logical statements or it is normally a mathematical expression, which may be in some familiar mathematical format or it may assemble a mathematical functions in a completely unfamiliar format [4].3. Results and discussion3.1. Time series plots of predicted and observed values: Both the GEP and the ANN models were implemented using the recorded data at Urmia Lake, Iran. The record covering the years from 1997 to 2008 was divided into the period from 1997 to 2006 to train model and from 2007 to 2009 to verify it. GeneXpro software was used to implement the GEP model with the initial parameters. Fig. 1 show the recorded and simulated values and their scatter plot.Table 1 shows the results of each model. It can be seen that the Genetic Programming in general have smaller RMSE values than the Artificial Neural Network model for validation period and the correlation coefficient is high for the Genetic Expression Programming is higher than ANN model.Table 1. Statistical analysis of forecasted values with GEP and ANN methods R2 RMSE(m) Model0.997 0.0136 Genetic Programming0.996 0.0156 Artificial Neural Network4. The GEP and ANN were used for forecasting water level variations in Urmia Lake, Iran. This study used GeneXpro and the results were compared with those from the ANNs by Qnet software. The mathematical modeling techniques for the analysis of time series were diversifying and this paper compared the performance of two such techniques. The GEP seemed to perform marginally better for most of the cases. The results seemed to support the emerging consensus that a single modeling technique is unlikely to render the solution. Instead, a set of solutions using different parameters and different simulation techniques is likely to identify the variability of the problem and the solution should be conditioned by the variability.