Forecasting daily lake levels using artificial intelligence approaches

Abstract

Accurate prediction of lake-level variations is important for planning, design, construction, and operation of lakeshore structures and also in the management of freshwater lakes for water supply purposes. In the present paper, three artificial intelligence approaches, namely artificial neural networks (ANNs), adaptive-neuro-fuzzy inference system (ANFIS), and gene expression programming (GEP), were applied to forecast daily lake-level variations up to 3-day ahead time intervals. The measurements at the Lake Iznik in Western Turkey, for the period of January 1961–December 1982, were used for training, testing, and validating the employed models. The results obtained by the GEP approach indicated that it performs better than ANFIS and ANNs in predicting lake-level variations. A comparison was also made between these artificial intelligence approaches and convenient autoregressive moving average (ARMA) models, which demonstrated the superiority of GEP, ANFIS, and ANN models over ARMA models.

Introduction

Lake water level forecasting at various time intervals using the records of past time series is an important issue in water resources planning (engineering, etc.). Variations in lake level are complex outcomes of many environmental factors, such as precipitations, direct and indirect runoffs from neighbor catchments, evaporation from free water body, air and water temperature, and interactions between the lake and the low lying aquifers. Although it is possible to identify sophisticated models taking into consideration the aforementioned parameters, it is preferable that a model which simulates lake-level variations based on previously recorded lake levels be available for research as well as practical purposes.

Recently, the use of artificial intelligence (AI) techniques has been accepted as an appropriate tool for modeling complex nonlinear phenomena in hydrology and water resources systems, leading to widening of their applications. In this context, artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS), and genetic programming (GP) methods have been widely applied. Recent investigations have used the capabilities of ANNs in modeling water resource variables (e.g., American Society of Civil Engineers (ASCE) Task Committee on Application of Artificial Neural Networks in Hydrology, 2000, Kisi, 2004a, Kisi, 2004b, Kisi, 2006a, Kisi, 2006b, Kisi, 2009, Wu and Chau, 2010). A review of all ANN studies in water resources engineering is beyond the scope of this paper and only some most relevant studies will be addressed here. Jain et al. (1999) applied ANN for predicting reservoir inflow and operations. Deo and Naidu (1999) applied ANNs to wave forecasting. More and Deo (2003) used ANNs for wind forecasting. Makarynskyy et al. (2004) used ANN to predict hourly sea-level variations for the following 24 h as well as for half-daily, daily, 5-daily, and 10-daily average sea levels. Ondimu and Murase (2007) applied ANN to forecast reservoir level. Makarynska and Makarynskyy (2008) used ANN to predict hourly sea-level variations with warning times from 1 to 5 days. Cimen and Kisi (2009) applied SVM and ANN models in modeling lake-level fluctuations.

ANFIS is a combination of an adaptive neural network and a fuzzy inference system. The parameters of the fuzzy inference system are determined by the NN learning algorithms. Since this system is based on the fuzzy inference system, reflecting amazing knowledge, an important aspect is that the system should be always interpretable in terms of fuzzy IF–THEN rules. ANFIS is capable of approximating any real continuous function on a compact set to any degree of accuracy (Jang et al., 1997). ANFIS identifies a set of parameters through a hybrid learning rule combining backpropagation gradient descent error digestion and a least-squared error method. There are two approaches for fuzzy inference systems, namely the approach of Mamdani (Mamdani and Assilian, 1975) and the approach of Sugeno (Takagi and Sugeno, 1985). The neuro-fuzzy model used in this study implements Sugeno’s fuzzy approach (Takagi and Sugeno, 1985) to obtain the values for the output variable from those of input variables. Here, ANFIS has some input variables (previously recorded lake levels) and one output, lake level at the following day(s).

Chang and Chen (2001) applied a counterpropagation fuzzy-neural network modeling approach to real-time streamflow predictions. Keskin et al. (2004) used fuzzy models to estimate daily pan evaporation in Western Turkey. Kazeminezhad et al. (2005) applied ANFIS to forecast wave parameters in Lake Ontario and found ANFIS superior to the Coastal Engineering Manual methods. Kisi (2006c) investigated the ability of ANFIS techniques to improve the accuracy of daily evaporation estimation. Kisi and Ozturk (2007) used ANFIS computing techniques for evapotranspiration estimation. Bae et al. (2007) applied weather forecasting information and neuro-fuzzy techniques for predicting monthly dam inflow. Hong and White (2009) introduced a dynamic neuro-fuzzy local modeling system for complex dynamic hydrological modeling. Chang and Chang (2009) applied neuro-fuzzy techniques for prediction of water level in reservoirs. Ozger and Yildirim (2009) used ANFIS to determine turbulent flow friction coefficients. Shiri et al. (2011) used ANFIS for predicting short-term operational water levels.

Genetic programming, first proposed by Koza (1992), as a generalization of genetic algorithm (GA) (Goldberg, 1989), employs a “parse tree” structure for the search of its solutions. This technique has the capability for deriving a set of explicit formulations that rule the phenomenon, to describe the relationship between the independent and the dependent variables using various operators.

Babovic et al. (2001) applied GP for modeling risks in a water supply. Drecourt (1999) and Savic et al. (1999) applied GP to 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 to suspended sediment, and found it to perform better than conventional rating curve and multilinear regression techniques. Guven and Gunal (2008) predicted the local scour downstream the hydraulic structures, using a GP approach. Ustoorikar and Deo (2008) used the GP for filling up gaps between data of wave heights. Gaur and Deo (2008) applied the GP for real-time wave forecasting. Londhe (2008) presented a soft computing approach by using ANNs and GP for real-time estimation of missing wave heights. Ghorbani et al. (2010) applied GP to forecast sea water-level variations in Hillarys Boat Harbor and compared the results with those of ANNs, which showed the feasibility of GP in modeling time series analysis. Shiri and Kisi (2011) compared GEP to ANFIS for predicting groundwater table depth fluctuations and found GEP to be better than ANFIS in this regard.

The present study investigates the abilities of GP (i.e., gene expression programming, GEP), ANFIS, and ANN and conventional autoregressive moving average (ARMA) techniques to forecast daily lake levels, three time steps ahead. The subsequent parts of this paper are organized as follows: the second section deals with describing the used dataset as well as the applied techniques including GEP, ANFIS, and ANN. The third part presents the applied statistical measures for model analysis, followed by the fourth section including results and discussions. Finally, the last section provides the concluding remarks of the present study.