MULTIPLE LINEAR REGRESSION (MLR) MODEL FOR PREDICTION POTENTIAL EVAPOTRANSPIRATION (ET0) الکلمات المفتاحية : نموذج التنبؤ، الانحدار الخطي المتعدد (MLR)، التبخر المحتمل للنتح (ET0)،

 for Prediction Potential Evapotranspiration (ET0)

Nabeel M. Bani Hani¹, Ahmad N. Al-Shadaidah², and Moawiya A. Haddad³

¹Water and Irrigation Program, National Center for Agricultural Research and Extension, P.O. Box 939, Baqa 19381, Jordan.

² Dept. plant production and protection, Faculty of Agricultural Technology, Al-Balqa Applied University, Al-Salt, 19117, Jordan.

³Dept. Nutrition and Food Processing, Faculty of Agricultural Technology, Al-Balqa Applied University, Al-Salt, 19117, Jordan.

ABSTRACT

Prediction Model for potential crop evapotranspiration (ETo) as dependent factor of three metrological stations extended along the Jordan Valley have been evaluated using multiple linear regression (MLR) model using Microsoft office excel. The observed ETo values used have been estimated by Penman Monteith equation. The average daily means meteorological data for period extended from 2001 till 2008 for DairAlla and Al Karama stations and from 2001 till 2006 for Sharhabeel station were used. The temperatures (T) (⁰C), relative humidity percentage (RH), wind speed (U) ms^-1 and solar radiation (RS) MJ s^-1 as independent variables collected from metrological station. The MLR model was applied for each station to determine one equation for each station. Also, average mean daily climatic data for three stations for the period extended from 2001 till 2006 were used to abstract one representative MLR equation for Jordan Valley. The root mean square error (RMSE) for Al karama , Dair Alla, Sharhabeel and overall stations MLR equations were; 0.143, 0.126, 0.165and 0.131, respectively. A strong positive linear correlation between ET₀ with T and Rs and the coefficient of determination (R²) are 0.82 and 0.953 respectively, and a weak positive linear correlation was found between ET₀ and U with R² value is 0.522, whereas a moderate negative linear correlation was found among ET₀ and RH with R² value is 0.725.

Keywords –prediction mode, multiple linear regression (MLR), Potential evapotranspiration (ET0),

INTRODUCTION

Jordan is located about 100 km from the south-eastern coast of the Mediterranean between latitudes 29º 11’ - 33º 22’ N and longitudes 34º 59’- 39º 12’ E. with a total area of about 89 210 km² with 9.5 Million population, is one of the most water scarce countries in the world with annual per capita share of fresh water not exceeding 145 m³ (Al-Bakri et al., 2013; DOS, 2016), and this amount is expected to decrease to 90 m³ in 2025 (Jordan, 2009). This fresh water supply shortage is mitigated by the supplemental use of reclaimed municipal waste water of inferior quality. Subsequently, soils in the Northern and Middle Jordan Valley (JV) have become partially irrigated with the reclaimed wastewater. In the South, saline well water is the major irrigation water resource.

Jordan Valley is a lowlands located in the western part of the country starts at Lake Tiberias in the north to the Dead Sea in the south. JV is a part of Great Rift Valley that extends from Syria to the African horn. The annual rainfall varies from 350 mm in northern part to 35 mm in southern part (Shatanawi et al., 2014, Bani Hani and Shatanawi, 2011). However, it is where the bulk of the country’s irrigated agricultural production occurs. Water is the most important environmental constrain determining agricultural productivity of fruit and vegetables in the Jordan Valley (Shatanawi et al., 2006). In 1962, a land reform program created thousands of small farms (3.5ha on average). The irrigated area in Jordan Valley is about 33,000 ha. The climate in Jordan Valley is typical arid, whereas rainfall occurred from November till April. Drip irrigation is already the common irrigation practice in the Jordan Valley (96% of farms) (Aken et al., 2007). The level of the Dead Sea falls each year by 0.85 meter due to extensive water use in the Jordan basin. Irrigated soils along the Jordan valley are showing signs of salinization since natural floods are no longer available to flush the irrigated land and leach salts (District 2450, 1997).

Soil formation is influenced by more than one parent material including recent alluvium occupying a narrow flood plain along the Jordan River and lacustrine (Lisan Marl) deposits overlaid by more than one layer of colluvial sediments transported as colluvial fans along the Eastern Escarpment edges. The moisture regime is Ustic in the north (N250 mm annual rainfall) and Aridic in the south. The temperature regime is Hyperthermic in the entire JV. Traditionally, the JV has been the principle fruit (mainly oranges and banana) and vegetable production basket of the country. A subtropical climate prevails in the JV with decreasing rainfall and increasing temperature in the southward direction. Such geographically-driven climate change evolved soils with decreasing pedogenic development in the same south ward direction. (Lucke et. al., 2013;Taimeh, 2014).

Hydrological parameters such as precipitation, evapotranspiration, soil moisture and ground water are likely to change with climate (Gleick, 1986) and the impact of climate change on evapotranspiration rate is important for hydrologic processes. Crop water requirements depend upon several climatic variables like rainfall, radiation, temperature, humidity and wind speed. Therefore, any change in climatic parameters due to global warming willalso affect evapotranspiration (Allen et al., 1998; Goyal, 2004).

Evaporation estimation Models based on meteorological variable were evaluated by many studies (Chang et. al., 2010; Almedeij, 2012). The modified Penman Monteith equation is recommended as a standard method to calculated potential evapotranspiration (Allen et al., 1998). However, to generalize this equation derived multiple linear model from variable metrological data (temperature, wind speed, relative humidity and/or solar radiation) needed to derive. Consequently, sometimes parameters are not available to determine potential evapotranspiration ET0 by Penman Monteith.

MATERIALS AND METHODS

Multiple Linear Regression (MLR) model was used to evaluate observed potential evapotranspiration (ET₀) calculated by Penman Monteith equation according to FAO 56 (Allen et al., 1998). The evaluation of observed (ET₀) as dependant variable and four mean daily climatic parameters namely; temperature in degree ⁰C (T), relative humidity percentage (RH%), wind speed at two meter height (U) in m/s, and solar radiation (Rs) in MJ s^-1. The data were collected from three metrological stations along the Jordan Valley (JV) extends 110 km from Lake Tiberias (220 m below sea level) in the north to the Dead Sea (405 m below sea level) in the south (Fig. 1). Distribution of metrological stations was representative to different agroclimatic zone along Jordan Valley. The difference in agroclimatic zone was related to site pedology, crop types, soil texture, soil salinity, irrigation water quality and/or quantity of rainfall, since irrigation water quality and cropping pattern adhered to the variation in the JV agroclimatic zones. In the Northern JV citrus orchards irrigated with fresh water from the King Abdulla Canal, while reclaimed waste water or fresh water mixed with reclaimed wastewater irrigating green house vegetable crops was the focus in the Middle JV (e.g. high-tech and protected agriculture). Saline ground water irrigating date palm, banana orchards, and open field vegetables represented most of the farms in the South JV (Abu Sharar et al., 2014).

Studied metrological stations were; sharhabeel in north (altitude of (32° 06َ 12ً N), and longitude of (35° 51َ 07ً E) at an elevation of 190 m below sea level), Dair Alla in middle, and Karama in south of Jordan Valley (a latitude 32^o12’N and longitude 35^o37’E). Metrological stations were constructed by National Center for Agricultural Research and Extension (NCARE) through Irrigation Management Information System (IMIS) which was supported by USDA/ARS. These stations serve an area cultivated with orchards, and nurseries. The Model was used for available average daily data from 2001 to 2008 for Dair Alla and Karama, whereas Sharhabeel from 2001 till 2006. Also, a determination of coefficient (R²) and Pearson correlation (R) among the observed ET₀ value with T, RH, U and Rs were calculated. Root mean square errors (RMSE) for each MLR equation of each station and for all over stations were estimated between observed and calculated ET₀ (Maheda and Patel, 2015)

Fig. 1. Jordan Valley Map

RESULT AND DISCUSSION

Due to the high temperatures in the Jordan valley and the low values of relative humidity the evaporation force of the climate was very high. The potential evaporation in the north was around 2100 mm/yeat increasing to about 2400 mm/year at the shores of the Dead Sea in the south (Salameh, 2001). Annual rainfall did not exceed 350 mm and the average temperature was 15 ⁰C in January and 30 ⁰C in August. However, these figures are not fixed along the 110 km Jordan Valley from north to south. In the extreme north where it was 2 to 3 km the valley width  rain fall 350 mm and the ET₀ about 1230 mm whereas further south (middle Jordan Valley) the valley became more wide (5 km), the climate became more arid (rain fall 280 mm and the ET₀ about 1370 mm) (Philippie, 2004). A straight-line relationship existed between each independent variable (T, RH, U, and RS) and the dependent variable (ET₀), for each metrological station.

The mean, minimum average and maximum average daily temperature (T) overall three stations were; 23.3, 12.8, and 33 ⁰C, respectively (Table 1), and a strong positive linear correlation between ET₀ with T with coefficient of determination (r²) 0.820 (Table 2) were observed. The highest coefficient of determination value (between ET₀ and T) was obtained in Sharhabeel (0.830), whereas the lowest value occurs in Al-Karama (0.807) (Table 2).

The mean, minimum average and maximum solar daily radiation (Rs) overall three stations were; 18.8, 9.5, and 28.0 MJ s^-1, respectively (Table 1), also a strong positive linear correlation between ET₀ with Rs with coefficient of determination (r²) 0.953 (Table 2). The highest coefficient of determination value was between ET₀ and Rs obtained in A-Karama (0.952), whereas the lowest value occurs in Sharhabeel (0.932) (Table 2).

The mean minimum average and maximum daily relative humidity (RH) overall three stations are; 50.7, 40.4, and 67.5 %, respectively and 6.47 standard deviation (Table 1), also a moderate positive linear correlation between ET₀ with RH with coefficient of determination (r²) 0.725 (Table 2). The highest coefficient of determination values between ET₀ and RH was obtained in Al-Karama and Shahabeel (0.750, 0.749, respectively), whereas the lowest value occured in Dair Alla(0.599) (Table 2).

The mean, minimum average and maximum daily wind speed (U) overall three stations are; 1.4, 1.0, and 1.9 m s^-1 respectively (Table 1), also a moderate positive linear correlation between ET₀ with U with coefficient of determination (r²) 0.522 (Table 2). The highest coefficient of determination values was between ET₀ and U obtained in Sharhabeel (0.673), whereas the lowest value occured in Dair Alla (0.075) (Table 2).

The mean, minimum average and maximum daily measured potential evapotranspiration (ET₀) overall three stations are; 4.32, 1.5, and 7.1 mm day^-1 respectively and 1.86 standard deviation (Table 1).

Reference evapotranspiration (ETo) is an essential component of irrigation water management as a basic input for estimating crop water requirements. Multiple approaches have been identified for ETo assessment but most of them were based on daily meteorological data provided by weather station networks that provide an accurate meteorological characterization (Cruz, 2014).

Table (1): Descriptive statistics for daily climatic parameters for studied metrological stations for periods extended from 2001 to 2008.

Table (2): Person correlation (r) and determination coefficient (r2) values, for ET0 with T, RH%, U and RS for studied metrological stations.                                                   

Obtaining PM–ET_o in the absence on of metrological data parameters (Rs, T, RH and U)   led to develop was approach including the use of generated weather data (Stöckle et al., 2004, Pereira et al., 2015) and, more often, replacement equations to the FAO–PM based on multiple regression analyses (El-Shafie et al., 2013). The agricultural researchers and extension agents can use assessed value of potential evapotranspiration in the same agricultural and metrological zone by using MLR equations.

             Multiple linear regressions models using mean average daily metrological data were used to derive linear generic equations with ET_o, (Cristea, 212): B0+B1*T+B2*RH+B3*U+B4*Rs

MLM equations were built to predict daily reference evapotranspiration for each site in Jordan Valley and for all over Jordan Valley for data from three metrological stations (Espino et al., 2016). 

Minimum root mean squared error (RMSE) and maximum correlation coefficient (R²) were calculated for MLR equation. The root mean square error (RMSE) for karama, Dair Alla,  Sharhabee and overall stations MLR equations were; 0.143, 0.126, 0.165 and 0.131, respectively. The R² were; 0.993, 0.995, 0.993 and 0.987 for Al Karama, Dair Alla, Sharhabeel and overall stations, respectively (Table 3) the same result was obtained by Kisi and Guven (2010), Perugu et al. (2013) and Sriram and Rashmi (2014) .

Stan et al. (2016) found multiple linear regressions by considering all meteorological parameters (air, relative humidity, moisture deficit, wind speed, precipitations and water temperature) with coefficient of determination of 0.86 in May for the aquatic plants evapotranspiration.

Table (3) Multiple Linear regression (LR) models

Accurate estimation of reference evapotranspiration (ET₀) is importance for many studies such as hydrologic water balance, irrigation system design and management, crop yield simulation, and water resources planning and management. Simple regression techniques sometimes provide adequate estimation of ET₀. The linear regression models developed in certain region can be applied in the region with similar climatic conditions for ET₀ estimation (Perugu et al., 2013). The potential to make such predictions is crucial in optimizing water resources management.

REFERENCES

1. Abu-Sharar T.M., Bani Hani N. and S. Al-Khader. 2014. Boron adsorption–desorption characteristics of irrigated soils in the Jordan Valley. Geoderma Regional.  2–3: 50–59.
2. Aken M. V., Courcier R, Venot J-P, Molle F. 2007. Historical Trajectory of a River Basin in the Middle East: The Lower Jordan River Basin (in Jordan). International Water Management Institute and French Regional Mission for Water and Agriculture.
3. Al-Bakri, J.T., Salahat, M., Suleiman, A., Suifan, M., Hamdan, M.R., Khresat, S., Kandakgi, T., 2013. Impact of climate and land use changes on water and food security in Jordan: implications for transcending “the tragedy of the commons”. Sustainability 5:725–748.
4. Allen RG, Pereira LS, Raes D and Smith M. 1998. Crop evapotranspiration: Guidelines for computing crop requirements. Irrigation and Drainage Paper 56, FAO. Rome. p. 300.
5. Almedeij J. 2012.  Modeling pan evaporation for Kuwait by multiple linear regressions. The Scientific World Journal. Volume 2012, Article ID 574742, 9 pages
6. Bani Hani N., and M. Shatanawi. 2011. Effect of Sustained Deficit Irrigation on Stem Water Potential of Navel Oranges in Jordan Valley. Journal of Agricultural Science and Technology. B1: 1152-1160.
7. Chang F. J., Chang L. C., Kao H. S. and G. R. Wu. 2010. Assessing the effort of meteorological variables for evaporation estimation by self-organizing map neural network,” Journal of Hydrology, vol. 384, no. 1-2, pp. 118–129.
8. Cristea N. 2012. Evaluation reference evapotranspiration and the effects of climate change and soil parameterization within distributed hydrologic models. A dissertation Doctor of Philosophy, University of Washington.
9. Cruz M. B. 214. New Techniques for Determining Reference Evapotranspiration. PhD thesis, UniveRsity of Córdoba.
10. Department of Statics (DOS) in Jordan. 2016. Population Report.
11. District 2450. 1997. A detailed summary of the water situation and potential solutions in Lebanon, Egypt, Jordan, Cyprus, Bahrain, UAE, Sudan, Armenia and Georgia. Water and sanitation Rotarian Action Group.  
12. El-Shafie, A., Alsulami, H., Jahanbani, H., Najah, A., 2013. Multi-lead ahead prediction model of reference evapotranspiration utilizing ANN with ensemble procedure. Stochastic Environ. Res. Risk Assess. 27 (6): 1423–1440.
13. Espino D. J., Charlesworth S. M., Momparler S.P. and Doménech I. A. 2016. Prediction of Evapotranspiration in a Mediterranean Region Using Basic Meteorological Variables. J. Hydrol. Eng. 10.1061/(ASCE)HE.1943-5584.0001485:1-11.
14. Gleick P. H. 1986. Methods for evaluating the regional hydrologic impacts of global climatic changes.” J Hydrol. 88:97–116.
15. Goyal R. K. 2004. Sensivity of evapotranspiration to global warming: a case study of arid zone of Rajasthan (India).  Agric Water Manag. 69: 1–11.
16. Jordan MowaI. 2009. Water for Life - Jordan's Water Strategy 2008-2022.
17. Kisi O. and Guven A., 2010. Evapotranspiration modeling using linear genetic programming technique. J. Irrig. Drain Eng. 136:715-723.
18. Lucke B., Ziadat F. and A. Taimeh, A., 2013. Soils of Jordan. Atlas of Jordan. p. 72-76.
19. Mahida H. R., and V N Patel. 2015. Impact of climatological parameteRs on reference crop evapotranspiration using multiple linear regression analysis. International Journal of Civil Engineering. 2(1):22-25.
20. Pereira L.S., Allen R.G., Smith M. and Raes D. 2015 Crop evapotranspiration estimation with FAO56: Past and future. Agricultural Water Management 147: 4–20.
21. Philippie V. J. 2004. Farming system in the Jordan River basin in Jordan: agronomical and economic description. MERA.
22. Perugu M. Singam A. J.,  Kamasani C. S. R. 2013. Multiple linear correlation analysis of daily reference evapotranspiration. Water Resour Manage. 27:1489–1500.
23. Salameh E. 2001. Sources of water salinities in the Jordan Valley are/Jordan. Acta hydrochim. hydrobiol. 29 (6–7): 329–362 329.
24. Shatanawi, M., Duqqah, M., and S. Naber. 2006. Agriculture and irrigation water policies toward improved water conservation in Jordan, Jordan Presentation at the 5^th Workshop of WASAMED Project on Harmonization and Integration of Water Saving Options, Convention and Promotion of Water Saving Policies and Guidelines, Malta.
25. Sriram A.V., and Rashmi C. N. 2014. Estimation of potential evapotranspiration by multiple linear regression method. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE).V11(2): 65-70.
26. Stan F. I., Neculau G., Zaharia L, Toroimac G. I. and, Mihalache S. 2016. Study on the evaporation and evapotranspiration measured on the Căldăruşani Lake (Romania). Procedia Environmental Sciences 32: 281 – 289.
27. Stöckle, C.O., Kjelgaard, J., Bellocchi, G., 2004. Evaluation of estimated weather data for calculating Penman–Monteith reference crop evapotranspiration. Irrig. Sci.23 (1), 39–46.
28. Taimeh, A., 2014. Soils of Jordan. Jordan University publication.