Inter-comparison of time series models of lake levels predicted by several modeling strategies R. Khatibi a , M.A. Ghorbani b,⇑ , L. Naghipour c , V. Jothiprakash d , T.A. Fathima d , M.H. Fazelifard b a Consultant Mathematical Modeller, Swindon, UK b Department of Water Engineering, Tabriz University, Tabriz, Iran c Department of Civil Engineering, Tabriz University, Tabriz, Iran d Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India article info Article history: Received 18 July 2013 Received in revised form 20 December 2013 Accepted 6 January 2014 Available online xxxx This manuscript was handled by K. Georgakakos, Editor-in-Chief, with the assistance of Attilio Castellarin, Associate Editor Keywords: Lake water level prediction Chaos theory ARIMA Neural networks Evolutionary methods Pluralism in modeling summary Five modeling strategies are employed to analyze water level time series of six lakes with different phys- ical characteristics such as shape, size, altitude and range of variations. The models comprise chaos the- ory, Auto-Regressive Integrated Moving Average (ARIMA) – treated for seasonality and hence SARIMA, Artificial Neural Networks (ANN), Gene Expression Programming (GEP) and Multiple Linear Regression (MLR). Each is formulated on a different premise with different underlying assumptions. Chaos theory is elaborated in a greater detail as it is customary to identify the existence of chaotic signals by a number of techniques (e.g. average mutual information and false nearest neighbors) and future values are pre- dicted using the Nonlinear Local Prediction (NLP) technique. This paper takes a critical view of past inter-comparison studies seeking a superior performance, against which it is reported that (i) the perfor- mances of all five modeling strategies vary from good to poor, hampering the recommendation of a clear- cut predictive model; (ii) the performances of the datasets of two cases are consistently better with all five modeling strategies; (iii) in other cases, their performances are poor but the results can still be fit- for-purpose; (iv) the simultaneous good performances of NLP and SARIMA pull their underlying assump- tions to different ends, which cannot be reconciled. A number of arguments are presented including the culture of pluralism, according to which the various modeling strategies facilitate an insight into the data from different vantages. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction Five different modeling strategies are used to investigate the variation in water levels of six lakes using their time series re- corded monthly and spanning from 58 to 109 years of data record. If lakes are closed systems, one expects that their water levels would display distinct patterns and probably would be predictable by any reasonable model. This pragmatic expectation is challenged by a comparison of the performance of different modeling strate- gies using different datasets from different lakes with different shapes and sizes. A study of this nature is of a practical significance as noted among others by Sen et al. (2000) that water levels play a significant role in management of fresh water supply, designing and planning of lakeshore structures and the environment. Model- ing is the key for the simulation of level variations and understand- ing their baseline and future states. There are various reasons for the importance of lake water lev- els, e.g. Hayshi and Kamp (2007) in studying hydrological pro- cesses in water balance of lakes, who note that ‘‘Certain types of plants require relatively high water levels, while others cannot tol- erate standing water. Therefore, water level change is considered a disturbance to many aquatic plants.’’ The balance between inputs and outputs of water is controlled by the hydrological processes and this gives rise to dynamic changes in water level that can be explained by simple equations. Water level changes may also be driven by surface winds leading to the setup of seiches as standing waves. There are other processes taking place within lakes that are driven by thermal currents and mixing processes creating physical movements in the body of lake waters but the amount of change in water level is often small. These important processes are studied by using Navier–Stokes equations and provide a deeper insight into the ongoing processes, see Rodi (1984), Hodges et al. (2000) for a review. The implementation of these models is only feasible by using expensive data and long computational times but this is not the case with yet another category of models, known as time series analysis, which make use of simple records of water levels http://dx.doi.org/10.1016/j.jhydrol.2014.01.009 0022-1694/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. Tel.: +98 411 3392786; fax: +98 411 3345332. E-mail address: m_Ali_ghorbani@ymail.com (M.A. Ghorbani). Journal of Hydrology 511 (2014) 1–16 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol Please cite this article in press as: Khatibi, R., et al. Inter-comparison of time series models of lake levels predicted by several modeling strategies. J. Hydrol. (2014), http://dx.doi.org/10.1016/j.jhydrol.2014.01.009