American Journal of Engineering and Applied Sciences Original Research Paper Mapping of Temperature Trend Slope in Iran′s Zayanderud River Basin: A Comparison of Interpolation Methods 1 2 3 2 4 5 6 Ali Zahraei, Saeid Eslamian, Ali Saeidi Rizi, Neda Azam , Morteza Soltani, Mohammad Mousavi, Sona 7 Pazdar and Kaveh Ostad-Ali-Askari 1Department of Irrigation and Drainage Engineering, College of Abureyhan, University of Tehran, Tehran, Iran 2Department of Water Engineering, Isfahan University of Technology, Isfahan, Iran 3Department of Civil Engineering, Shahid Bahonar University of Kerman, Kerman, Iran 4Department of Architectural Engineering, Shahinshahr Branch, Islamic Azad University, Shahinshahr, Iran 5Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran 6Civil Engineering Department, Aghigh University, Shahinshahr, Isfahan, Iran 7Department of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran Article history Abstract: The spatial distribution of daily, nightly and mean temperature Received: 19-05-2018 trend in Iran′s Zayanderud river basin was carried out in this study by Revised: 05-02-2019 applying three approaches of interpolation including Inverse Distance Accepted: 24-06-2019 Weighting (IDW), Multiple Linear Regression (MLR) and integration of these two methods (IDW+MLR). In this paper, t-test and statistical Corresponding Author: measures including Mean Absolute Error (MAE), Root Mean Square Error Kaveh Ostad-Ali-Askari (RMSE), systematic Root Mean Square Error (RMSE s) and unsystematic Department of Civil Root Mean Square Error (RMSE u) were used to evaluate the performance Engineering, Isfahan of approaches. This study reveals that temperature trends are inversely (Khorasgan) Branch, Islamic correlated with the altitude. All three interpolation methods overestimate in Azad University, Isfahan, Iran the prediction of daily and mean temperature trend and underestimate in Emails: [email protected] estimating nightly temperature trend. Among three methods, IDW is the [email protected] most accurate and precise in predicting daily and mean temperature trends. IDW is the most accurate and IDW+MLR is the most precise method to estimate nightly temperature trend. The MLR method for estimating nightly, mean temperature trend and the IDW method for estimating daily temperature trend have the lowest systematic error. Keywords: Interpolation, Spatial Distribution, Temperature Trend, Ayanderud River Basin, Iran Introduction study of the spatial distribution of temperature variables is carried out using interpolation techniques and Geographic Climate change is one of the most interesting and Information Systems (GIS). There are several concerning issues for the scientist in recent decades interpolation methods including Spline, Kriging, Inverse which is taken into account for its significant impact Distance Weighting (IDW), Regression Analysis, etc. to on natural and social systems. International Panel on map spatial distribution hydrometeorological variables. Climate Change (IPCC) showed the temperature trend Among these methods, Kriging, Inverse Distance has been risen (0.65-1.06 °C and 0.85 on average) Weighting (IDW) and multiple linear regression (MLR) during 1880-2012 and it is predicted that it will are the most commonly used (Sluiter, 2009). Many studies increase to 1.5-2°C, by the end of the 21st century. have been conducted to compare the IDW and Kriging There are types of research focus on the analysis of methods, show the IDW method is simpler, quicker and temperature trend, including: Schِnwiese and Rapp no needs too much information. These researches exhibit Klein Tank and Kِnnen (2003); Brunetti et al . the same outcomes or better performance for the IDW ;(1997) (2000; 2004; 2006); Toreti et al . (2010); Wulfmeyer method (Jarvis and Stuart, 2001; Stahl et al ., 2006; and Henning-Müller (2006); Rebetez and Reinhard Valley et al ., 2005; Yunus, 2005; Weber and Englund, (2008); Chaouche et al . (2010); Zarenistanak et al . 1994; Gallichand and Marcotte, 1993; Dingman, 1994; (2014); Dastorani and Poormohammadi (2016). The Boman et al ., 1995; Brus et al ., 1996; Declercq 1996; © 2019 Ali Zahraei, Saeid Eslamian, Ali Saeidi Rizi, Neda Azam, Morteza Soltani, Mohammad Mousavi, Sona Pazdar and Kaveh Ostad-Ali-Askari. This open access article is distributed under a Creative Commons Attribution (CC-BY) 3.0 license. Ali Zahraei et al . / American Journal of Engineering and Applied Sciences 2019, 12 (2): 247.258 DOI: 10.3844/ajeassp.2019.247.258 Dirks et al ., 1998; Moyeed and Papritz, 2002). Yunus et al . basin. Then the performances of these methods are (2015) studied the IDW interpolation method and evaluated using statistical analysis. integration of the IDW and the MLR methods to evaluate the spatial distribution of temperature in Data and Methods Malaysia. They showed that the integrated method offers more reliable results. The IDW and Spline methods by Zayanderud River Basin integration with the regression models was assessed by Zayanderud river basin with an area of over 41,000 Kurtzman and Kadmon (1999) in Israel. In this study, square kilometers vitalizes around 3.5 million people of the statistical analysis was used to evaluation of the central Iran. Zayandehud River originates from the performance of the methods. The results indicated that the western basin and flows through Isfahan megacity, finally IDW method in the winter and the Spline method in the ends Gavkhooni wetland in the eastern basin (Fig. 1). summer make a more acceptable estimation for the Topographic features of the basin have led to temperature temperature variables. Also, the integration of these variations in different parts of the basin. The annual methods with the MLP method led to increasing the minimum, mean and maximum temperature of the basin accuracy in estimating extreme temperature variables. is 5.7, 13 and 20.5 respectively and the annual mean Made a comparison of the IDW, Kriging and Spline precipitation of the basin is 178 mm. Zayanderud river methods to prepare spatial distribution and generation of supplies urban, industrial, agricultural and environmental continuous data in Iraq. The results of the statistical demands of the basin but in recent years do not able to analysis indicated that the Kriging method has better meet all water requirements. Some studies show that performance. Huixia et al . (2011) using data of 38 stations increasing temperature in Zayanderud basin is one of the during 1960-2004 assessed the spatial interpolation by the effective factors in an imbalance between consumptions IDW, Kriging and MLR methods in Xinjiang Uygur and resources (Zareian et al ., 2015; Gohari et al ., 2013; Autonomous Region, China. They exhibited that Ahmadi et al ., 2015). integration of the IDW and the MLR methods, based on Data statistical analysis, results in more acceptable outcomes. Anis et al . (2006) compared the IDW and the MLR In this study, a data set of 37 stations in Zayanderud methods to generate a spatial distribution map for river basin and around it with long term maximum temperature variables. They figured out by integrating temperature (or daily temperature), mean temperature and minimum temperature (or nightly temperature) were these two methods, the precision of results in the summer studied. Monthly data during period 1951-2010 were and winter will increase. Bhowmik and Cabral (2011) collected from the meteorological organization and the compared the IDW, Spline and Kriging methods to ministry of energy and then were averaged to obtain interpolate temperature trend in Bangladesh by statistical annual data. All record lengths are more than 30 years measures. They showed that the IDW method is better in started from 1950s, 1960s, 1970s and 1980s and ended estimation to mean and minimum temperature trend with the year 2010. As the record length affect the whereas the Kriging method has a better performance for validity of trends all stations with a different record estimating maximum temperature trend. Pal and Al- length were considered (Githui, 2009). The location of Tabbaa (2010) studied the relation between temperature the stations is shown in Fig. 2. trend and physiographic parameters. They indicated that the changes in the temperature trend may vary in different Sen-Slope (SS) patterns. You et al . (2010) investigated variations of We evaluated the magnitude of the trend by applying temperature trend versus elevation in Tibetan Plateau of the Q Sen’s slope estimator developed by Sen (1968). At China. They revealed that there is a poor correlation first the slope of N pair of data are computed by: between elevation and annual temperature trends. Vuille and Bradley (2000) studied annual temperature trend in x− x Q=j i for k = 1,2,...., N (1) Tropical Andes. They indicated that temperature trend is k j− i associated with elevation and reported greatest trend at low elevations. In Equation (1), x and x are the data values at times j There are lots of studies on the interpolation methods to j i and i (j > i). The median of N value of Qk is Sen’s slope detect spatial distribution of temperature, while there is only which is computed as: little research conducted on the comparison and analysis of the interpolation methods to find spatial distribution of Q if N isodd temperature trend. In this study, three interpolation methods []N +1/ 2 including IDW, MLP and integration of these two methods = Q +Q Qmed N 2 (2) N + 2