HYDROLOGICAL PROCESSES Hydrol. Process. 24, 2400–2404 (2010) Published online 24 March 2010 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/hyp.7642 A predictive model for well loss using fuzzy logic approach Abd¨ usselam Altunkaynak* Hydraulics Division, Civil Engineering Department, Istanbul Technical University, 34469 Istanbul, Turkey Abstract: Simple methods for calculating well losses are important for well design and optimization of groundwater source operation. Well losses arise from both laminar flow within the aquifer and turbulent flow within the well, and are often ignored in theoretical aquifer test analysis. The Jacob (1947) and Rorabaugh (1953) techniques for predicting well losses are widely used in the literature; however, inherent in these techniques are the assumptions of linearity, normality and homoscedascity. In the Rorabaugh technique, prior knowledge, or prediction of, the parameters A, C and n is required for calculation of well losses. Unfortunately, as of yet, no method for adequately obtaining these parameters without experimental data and linear regression exist. For these reasons, the Rorabaugh methodology has some practical and realistic limitations. In this paper, a fuzzy logic approach is employed in the calculation of well losses. An advantage of the fuzzy logic approach is that it does not make any assumptions about the form of the well loss functionality and does not require initial estimates for the calculation of well losses. Results show that the fuzzy model is a practical alternative to the Rorabaugh technique, producing lower errors (mean absolute error, mean square error and root mean square error) relative to observed data, for the case presented, comparatively to the Rorabaugh model. Copyright  2010 John Wiley & Sons, Ltd. KEY WORDS drawdown; prediction; fuzzy; groundwater; well loss Received 13 October 2009; Accepted 1 February 2010 INTRODUCTION Determination of well losses is fundamental for the design and operation of wells and pumping capacity. There have been many previous studies conducted to measure and to predict well losses. These studies have following several different approaches for correlating well losses with the governing physical processes (e.g. Jacob, 1947; Rorabaugh, 1953; Avci, 1992; Sen, 1995). Of these methods, one of the most common is the least square method or the so-called regression approach. While useful, these regression approaches have some restrictive assumptions, and require preprocess of the data to put it in proper form for the analysis to keep application results from leading to erroneous conclusions. The restrictive assumptions inherent in linear regression are listed as follows (Sen et al., 2003; Uyumaz et al., 2006; Altunkaynak, 2009). 1. Normality: Variables (Discharge, Q, Drawdown, s) or residuals which denote the deviations from mean value (Q i  Q) and (s i  s) should fit the normal distribution to solve regression equations. Where Q and s are mean values of discharge and drawdown, respectively. If the variables do not satisfy normality assumption, they should be transformed (logarithmic, square root, etc.) properly. 2. Homoscedasticity: It is known as homogeneity of variance. The distribution of function variances of the * Correspondence to: Abd¨ usselam Altunkaynak, Department of Civil and Environmental Engineering, University of Houston, 4800 Calhoun, Houston, Texas 77204-4003, USA. E-mail: aaltunka@mail.uh.edu variables (Q i  Q) and (s i  s) should be constant. Also all random variables should have the same finite variance. 3. Linearity: It is assumed that the underlying relationship between predictor and predicted variables (Q, s) fol- lows a straight line. Namely the relationship between Q and s should be linear. If the trend can not be rep- resented by a straight line, regression analysis will not represent it accurately. 4. Means of conditional distributions: For every Q i value, the mean of the calculated errors (s i  s) should be equal to zero. If it is not, the regression parameters will be biased estimates. 5. Autocorrelation: Each observation value of variables is independent from other observations. For instance, Q i or s i can not be predicted from Q i1 or s i1 . Also it is used to check the randomness in the data. 6. Lack of measurement error: It is assumed that Q i and s i include no measurement errors. Measurement errors lead to biased predictions. With a fuzzy logic approach, one can avoid these restrictive assumption mentioned above. Aquifer and well parameters are important to operation of groundwa- ter resources. Groundwater levels, drawdowns and dis- charges may change with time and space and be interre- lated with each other. For instance, drawdown inside the well is directly correlated to discharge. For this reason, it is necessary to determine an empirical well depen- dent drawdown–discharge relationship obtained from an individual well by measuring a series of discharges and corresponding drawdowns. Energy losses are directly Copyright  2010 John Wiley & Sons, Ltd.