Path Analysis in Identification of Dominant Effective Meteorological Parameters on ET0 in East Azarbaijan

Document Type : Full length article


1 Associate Professor of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

2 PhD in Climatology (Climate Change), University of Tabriz, Tabriz, Iran


Reference potential evapotranspiration (ET0) is one of the main elements of hydrologic cycle which can be estimated from weather data. This element can be used in calculating crop water requirements, scheduling irrigation systems, preparing input data to hydrological water-balance models, regional water resources assessment, and planning and management of water in a region and/or basin. The use of ET0 permits a physically realistic characterization of the effect of the microclimate in a field on the evaporative transfer of water from the soil-plant system to the atmosphere. It provides a measure of the integrated effects of radiation, wind speed, temperature and humidity on evapotranspiration. The long-term mean ET0 value in a certain timescale (month, season or year) can be changed during the recent decades in a given station. By decreasing ET0, crop water demand decreases. Conversely, by increasing ET0 the crop water requirements can also increase accordingly. Therefore, it can be suggested that change in the rates of ET0 due to climate change would have great importance for agriculturalists and water decision makers. On the other hand, accurate estimation of ET0 is crucial in improving the irrigation efficiency in a region. Many climatic parameters impacted the ET0 value in a single site. On the other hand, these parameters are correlated to each other.  
Materials and methods
The climatic data from the synoptic stations with at least 20 years of continuous records in East Azarbaijan province were gathered from the Islamic Republic of Iran Meteorological Organization (IRIMO). The obtained data are including maximum air temperature (Tmax), minimum air temperature (Tmin), wind speed in 10 m height (U), maximum relative humidity (RHmax), minimum relative humidity (RHmin), and duration of sunshine hours (n). The well-known FAO-PM56 method was used to calculate the ET0. There are many methods for ET0 estimation. The Penman–Monteith (PM) method is recommended as the standard by the United Nations Food and Agriculture Organization (UNFAO) and has gained worldwide acceptance and received much research interests. The PM equation has been widely used in ET0 estimation. However, this method needs more meteorological data which is not available in many regions. This led scientists to use other methods which do not need more parameters. Among the empirical methods which estimate ET0 using less climatic parameters are Hargreaves, Tornth-Wait, Belaney-Criddle and Priestley–Taylor. Unfortunately, outputs of these models are not accurate in all the sites. Therefore, for using these simple empirical models the calibration process should be done as well. Therefore, the following issues need urgent study: (1) selection of as few dominant meteorological variables as possible in meteorological parameters affecting ET0, and (2) universal application of an established model in more regions.
The alternative method namely Multiple Linear Regression (MLR) can be used to estimate the ET0. In order to evaluate the performance of the MLR method, some measures were calculated by comparing the results of MLR with FAO56-PM method. These measures are the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Nash–Sutcliffe Efficiency (NSE), and the coefficient of determination (R2). Then, the correlation coefficients (ryxi) calculated for the ET0 time series (y) and each of the meteorological parameters (xi). Then, the partial correlation coefficients (rij) are calculated for the explanatory variables (xi and xj) as well. Both of the direct and indirect effects of each climatic parameter on ET0 were evaluated by path analysis. These effects are denoted by P and Rdc, respectively. By solving the Eq. 6, the elements of P (direct effect of xi on y or ET0) are obtained. By multiplying the obtained P vector (direct effects) on  , we calculated the indirect effect of xi through the xj on ET0. This process is repeated for all the selected sites.
Path analysis was first proposed in 1921 as a mathematical and statistical method by the geneticist Sewell Wright. Nowadays, the method is broadly used in agriculture and energy demands to reveal direct or indirect relationships between some morphological characters. However, information is available on the use of this technique to evaluate the factors affecting ET0. Given the fact that all the meteorological variables are strongly correlated and ultimately lead to multi-collinearity, traditional trend and correlation analyses cannot quantify the interactions among the meteorological factors when filtering the suitable parameters.
Path analysis is a type of multivariate statistical analysis for studying relationships among variables. It can reveal the strength of the effects of independent variables on a dependent variable. Path analysis can determine direct and indirect effects of independent variables on the dependent variable; multi-collinear independent variables resulted from their own strong correlations, and optimal regression equations without unnecessary independent variables. The path coefficient is a type of standard partial regression coefficient (without units) that expresses causalities among related variables. It is also a directional correlation coefficient between independent and dependent variables. This analysis was conducted for each of the selected stations in East Azarbaijan province, Iran. To do this, we initially calculated the correlation coefficients between each of the climatic parameters and ET0 time series. Similarly, correlation coefficients matrix between the climatic parameters affecting ET0 was obtained for each of the stations.  
Results and discussion
The results of this research showed that the values of MAPE obtained for the stations were between 0.433 and 0.874. However, the R2 values were between 0.972 and 0.9953. Similarly, the RMSE were between 0.042 (mm/day) and 0.982 (mm/day), and the obtained MAE values were between 0.033 and 0.057. It was also found that the wind speed at the stations namely Tabriz, Jolfa, Sarab, Sahand, Maragheh and Mianeh had significant correlation (at the 0.01% level) with ET0. The strongest correlation was related to the station Ahar, which was between ET0 and the wind speed (at the 0.01% level). The results of path analysis showed that the maximum value of P (direct effects of meteorological parameters on ET0 belonged to the wind speed). The P values of wind speed in the stations Tabriz, Julfa, Sahand, Sarab, Maragheh, and Mianeh were equal to 0.637, 0.787, 0.877, 0.578, 0.850, and 0.780, respectively. In the station Ahar, the highest value of the P observed belong to the Tmax (equal to 0.398).  
Accurate estimation of ET0 is very important from the view of optimal water management in any region. Wind speed was found to be the dominant direct climatic parameter due to having the largest value of the P. In general, it can be concluded that the causal analysis method can be considered as an effective way to investigate the direct and indirect effects of meteorological parameters on ET0. Overall, it is more reasonable to apply path analysis method to evaluate dominant meteorological parameters of the ET0 in direct and indirect ways. The further research can be oriented in analysis on why dominant factors vary with meteorological stations. Development of other soft computing techniques calculated ET0 using the climatic methods (such as firefly algorithm, artificial neural networks, support vector regression, and genetic expression programming) and comparing their accuracy with that of the MLR are recommended for further studies.


اسدزاده، ف.؛ کاکی، م. و شکیبا، س. (1396). بررسی و تحلیل روند تبخیر و تعرق گیاه مرجع با استفاده از آزمون اسپیرمن در ایستگاه‏های سینوپتیک استان کردستان، تحقیقات منابع آب ایران، 13(۱): شماره‏ 1، ۲۱۶-۲۲۲.
جهان‏بخش‏ اصل، س.؛ موحد ‏دانش، ع. ا. و مولوی، و. (1380). تحلیل مدل‏های برآورد تبخیر- تعرق برای ایستگاه هواشناسی تبریز، مجلة دانش کشاورزی، ‏ 11(۲): ۵۱-66.
سیفی، ا.؛ میرلطفی، م. و ریاحی، ح. (1389). توسعة مدل ترکیبی رگرسیون چندگانه‏- تحلیل مؤلفه‏ها و عامل‏های اصلی (MLR-PCA) در پیش‏بینی تبخیر- تعرق مرجع؛ مطالعة موردی: ایستگاه کرمان، نشریة آب و خاک، 24(۶): ۱۱۸۶-1196.
کردوانی، پ. و قلعه‏ای، م.ح. (1392). تخمین مقادیر تبخیر- تعرق مرجع با استفاده از مدل فائو پنمن 56 در حوضة رودخانة آیدوغموش، فصل‏نامة علمی‏- پژوهشی اکوبیولوژی تالاب، دانشگاه آزاد اسلامی اهواز، 5(۱۵): ۱۵-22.
جعفری، م. و دین‏پژوه، ی. (1395). ارزیابی مدل رگرسیون چندمتغیرة تیغه‏ای در برآورد تبخیر از تشت، نشریة علوم و مهندسی آبیاری، 40(۱): ۸۳-97.
Asadzadeh, F.; Kaki, M. and Shakiba, S. (2017). Trend analysis of reference evapotranspiration in the synoptic sites of Kurdistan Province using Spearman’s test, Iran-Water Resources Research, 13(1): 222-256. In Persian.
Balan, B.; Mohaghegh, S. and Ameri, S. (1995). State- of- art- in permeability determination from well log data: Part 1- A comparative study, Model Development, SPE Technical Report 30978: 17-25.
Cai, J.; Liu, Y.; Xu, D. and Shi, B. (2008). Sensitivity analysis on water deficit indicator of winter wheat based on path analysis theory, J. Hydraul. Eng., 39(1): 83-90.
Dewey, D.R. and Lu, K.H. (1959). A correlation and path-coefficient analysis of components of crested wheatgrass Seed Production, Agronomy Journal, 51(9): 515-518.
Foster, G. and Rahmstorf, S. (2011). Global temperature evolution 1979-2010, Environmental Research Letters, 6(4): 044022.
Hatch, U.; Jagtap, S.; Jones, J. and Lamb, M. (1999). Potential effects of climate change on agricultural water use in the southeast US., J. Am. Water Resour., 35: 1551-1561.
Huber, M. and Knutti, R. (2011). Anthropogenic and natural warming inferred from changes in earth's energy balance, Nature Geosciences, 5(1): 31-36.
Jacobsen, S.E.; Jensen, C.R. and Liu, F. (2012). Improving crop production in the arid Mediterranean climate, Field Crop Res., 128: 34-47.
Jafari, M. and Dinpashoh, Y. (2015). Evaluation of multiple ridge regression model to estimation of pan evaporation, Journal of Irrigation Science and Engineering, 40(1): 83-97. In Persian
Jarvis, P.G. and McNaughton, K. (1986). Stomatal control of transpiration: Scaling up from leaf to region, Adv. Ecol. Res., 15: 1-49.
Jahanbakhsh, S.; Rezaee Banafshe, M.; Esmaeelpour, M. and Tadayoni, M. (2012). The evaluation of potential evapotranspiration estimation models and its spatial distribution in the Southern Basin of Aras River, Journal of Geography and Planning, 16(40): 25-46. In Persian.
Kardavani, P. and Qalehe, M.H. (2013). Estimating the reference evapotranspiration values by using FAO-56PM in Aydoghmush River basin, Journal of Wetland Ecobiology, 5(1): 15-22. In Persian.
Khdkar, D.D.; Singh, P.K.; Bhakar, S.R.; Kothari, M.; Jain, H.K. and Mudgal, V.D. (2016). Modeling of Reference Evapotranspiration using Regression Techniques, International Journal of Agriculture Sciences, 8(26): 3529-3532.
Liu, Y.; Yu, M.; Ma, X. and Xing, X. (2016). Estimating models for reference evapotranspiration with core meteorological parameters via path analysis, Hydrology Research, 48(6): 1-15.
Mahida, H.R. and Patel, V.N. (2015). Impact of climatological parameters on reference crop evapotranspiration using multiple linear regression analysis, SSRG International Journal of Civil Engineering (SSRG-IJCE), 2(1): 22-25.
Malik, A. and Kumar, A. (2015). Pan evaporation simulation based on daily meteorological data using soft computing techniques and multiple linear regression, Water Resources Management, 29: 1859-1872.
Manikumari, N. and Vinodhini, G. (2016). Regression models for predicting reference evapotranspiration, International Journal of Engineering Trends and Technology (IJETT), 38(3): 134-139.
Nam, W.H.; Hong, E.M. and Choi, J.Y. (2015). Has climate change already affected the spatial distribution and temporal trends of reference evapotranspiration in South Korea? Agric, Water Manag, 150: 129-138.
Peng, Q.; Guanxin, Zh. and Xu, Y.J. (2017). Spatiotemporal changes of reference evapotranspiration in the highest-latitude region of china, Water, 9(7): 493; Doi:10.3390/w9070493.
Seifi, A.; Mirlatifi, S.M. and Riahi, H. (2011). Developing a combined model of multiple linear regression-principal component and factor analysis (MLR-PCA) for estimation of reference evapotranspiration (Case Study: Kerman Station), Journal of Water and Soil, 24(6): 1186-1196. In Persian.
Silva, H.J.F.D.; Santos,  M.S.D.;  Junior, J.B.C.;  Spyrides, M.H.C. (2016). Modeling of reference evapotranspiration by multiple linear regression. Journal of Hyperspectral Remote Sensing. 6(1): 44-58.
Wever, L.A.; Flanagan, L.B. and Carlson, P.J. (2002). Seasonal and interannual variation in evapotranspiration, energy balance and surface conductance in a northern temperate grassland, Agr. Forest. Meteorol., 112: 31-49.
Xing, X.; Liu, Y.; Zhao, W.G.; Kang, D.G.; Yu, M.  and Ma, X. (2016). Determination of dominant weather parameters on reference evapotranspiration by path analysis theory, Computers and Electronics in Agriculture, 120: 10-16.
Yu, S.W.; Zhu, K.J. and Zhang, X. (2012). Energy demand projection of China using a path-coefficient analysis and PSO-GA approach, Energy Convers. Manage, 53(1): 142-153.
Zakizadeh, M.; Esmaeilzadeh Moghaddam, M. and Kahrizi, D. (2010). Study on genetic variation and relationship between plant characteristics and grain yield in long spike bread wheat (Triticum Aestivum L.) genotypes using multivariate analysis, Iranian Journal of Crop Science, 12: 18-30.
Zhang, B.Z.; Xu, D.; Liu, Y.; Li, F.S.; Cai, J.B. and Du, L.J. (2016). Multi-scale evapotranspiration of summer maize and the controlling meteorological factors in north China, Agric. Forest Meteorol., 216: 1-12.
Zhang, X.S.; Yan, Y.l . and Hu, Z.H. (2017). Using path analysis to identify impacting factors of evapotranspiration at different time scales in farmland, Chinese Journal of Agro-meteorology, 38(4): 201-210.