Develop Evaporation Model Using Multiple Linear Regression in the Western Desert of Iraq –Horan Valley

Evaporation is a main element of the hydrologic cycle, it is considered a key factor in the management of water resources for arid and semi-arid regions. Estimating water loss through evaporation is essential for modeling, surveying and managing many hydrological and water resource systems projects [1-8]. In general, evaporation data is significantly less easily obtainable than rainfall data.

Evaporation is a variable that combines or incorporates the effects of many elements of the atmosphere, such as temperature, humidity, rainfall, solar radiation and wind speed [9, 10]. The evaporation increases with high wind speed, max temperatures and low humidity [7].

Potential evaporation is the potential or ability of the atmosphere to remove water from a surface if there is no limit to the water availability [11, 12]. Potential evaporation is the most commonly used variable, while actual evaporation is the amount of water removed by evaporation from that surface [13, 14].

Evaporation estimates are required for a variety of problems in water resource management, hydrology, river flow forecasting, land resources planning, agricultural, forestry, irrigation management, and ecosystem modeling.

Reservoir locations will be limited in arid areas with flat terrains, and reservoirs will likely be shallow and have large surface areas. In such cases evaporation can cause large amounts of water to be lost [15, 16]. As a result, estimating the evaporation losses will be crucial in evaluating the design and operation of these reservoirs. The measurement of evaporation in the open environment is difficult and is usually done by proxy and models can be useful for evaporation prediction methods.

The application of the multiple linear regression (MLR) technique for evaporation studies helps to penetrate the hidden interrelationships among different parameters in catchments arid regions and developed model to best predict the processes of evaporation [17]. The models developed from meteorological data involve empirical relationships to some extent, these models may give reliable results when applied to climatic conditions [14]. The use of formulas or mathematical models that can predict evaporation from available climate data is therefore assertive and can provide more precise results than the calculated evaporation [18-21]. These models had been widely used by several researchers to estimate evaporation based on meteorological parameters like [1, 9, 13, 19, 20, 22-25].

Cahoon et al. [26] and Fennessey and Vogel 1996 [27] used regression methods to create models for regional monthly average evaporation in the United States as a function of publicly available factors including temperature, longitude, and elevation. Hanson [28] investigated the daily evaporation on three sites on the watershed in southwest Idaho India. The study pointed to daily pan evaporation estimated by mean temperature and solar radiation, the correlation coefficients (r) were obtained between 0.84 to 0.90. Almedeij [25] investigated the evaporation in Kuwait state and reported that the correlation of evaporation with temperature was 0.94, RH was -0.92 and wind speed was 0.74. Almedeij [1] develop an evaporation model arid region using a monthly period of 23 years (1993-2015). The study showed that evaporation values, ranged between 0.1 to 40 mm/day, from January – July within this period.

The significance of this study emerged through the fact that accurately measuring evaporation is a difficult task, especially in arid regions. As a result, using equations or statistical models to predict pan evaporation from available meteorological data may provide more accurate results. The main aim of this study was to develop a monthly predict evaporation model using multiple linear regression that can be used to estimate monthly evaporation in arid regions and identify the internal relationships between the independent variables that contribute to the prediction of evaporation.

Monthly climate data such as temperature (T), evaporation (E), relative humidity (RH), wind speed (WS) and solar brightness (SS) for the period 2000-2017 are provided from Iraqi Meteorological Organization Seismology (IMOS) in Baghdad presents six weather stations namely Ramadi, Haditha, Anah, Qaim, Rutba and Nakheb (see Figure 2).

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Figure 2. Locations of the climatic station around the study area

Prediction accuracy analysis typically requires the estimation of errors between observed and predicted values. Five performance indicators were used in the current study such as root mean square error (RMSE), normalized absolute error (NAE), coefficient of determination (R²), Nash-Sutcliffe efficiency (NSE) and mean average percentage error (MAPE). NAE and RMSE should reach zero for a successful pattern, while NSE and R² should be closer to one [7].

$\mathrm{R}^{2}=\left(\frac{\sum_{i-1}^{N}\left(P_{i}-\bar{P}\right)\left(O_{i}-\bar{O}\right)}{N . S_{\text {pred }} \cdot S_{o b s}}\right)^{2}$            (2)

$R M S E=\sqrt{\frac{1}{N-1} \sum_{i-1}^{N}\left(P_{i}-\mathrm{O}_{i}\right)^{2}}$        (3)

$\mathrm{NAE}=\frac{\sum_{i=1}^{n}|\mathrm{Pi}-\mathrm{Oi}|}{\sum_{i=1}^{n} \mathrm{Oi}}$       (4)

$\operatorname{MAPE}=\frac{1}{\mathrm{~N}} \sum_{\mathrm{i}=1}^{\mathrm{n}}\left|\frac{O i-\mathrm{Pi}}{O \mathrm{i}}\right| * 100$         (5)

$\mathrm{NSE}=1-\left[\frac{\sum_{\mathrm{i}=1}^{\mathrm{N}}\left(O \mathrm{i}-\mathrm{P}_{\mathrm{i}}\right)^{2}}{\sum_{\mathrm{i}=1}^{\mathrm{N}}(O \mathrm{i}-\overline{\mathrm{O}})^{2}}\right]$            (6)

MLR modelling (stepwise and backward method) was conducted to find an evaporation predictive equation using climatic variables, such as T, WS, SS and RH. Table 4 shows the variables selection using the stepwise and backward methods for two groups depending on the p-value 0.05, group 1 includes E as dependent variable and T, WS, RH and SS as independent variables and Group 2 included E as dependent variable and T, WS and SS as independent variables.

Group 1: Three models were generated using stepwise method, model 1 select the SS variable only (R²=0.821), model 2 were select T and SS variables (R²=0.849) and model 3 select T, WS and SS variables (R²=0.855). The Backward method generated two models, model 1 select all independent variables T, WS, RH and SS (R² =0.855), model 2 were selected T, WS and SS variables (R²=0.855) and this indicate that RH has no predictive effect on evaporation.

Group 2: The stepwise and backward results for group 2 that got similar results for group 1 as shown in Table 4 which confirms that the model consisting of T, WS and SS is the best model that generated using stepwise and backward regression method which gave adjusted R²=0.855. Based on the above it can be concluding the most significant parameters that can used to carry out the best fit prediction monthly evaporation model in arid regions were temperature (T), wind speed (WS) and sunshine (SS).

Performance indicators criteria were used to evaluate the accuracy of the MLR evaporation developed model (see Table 5).

Table 5. Performance Indicators for Evaporation validation model

By comparing the MLR evaporation developed a model with the most common evaporation models commonly used in arid regions such as Kharufa and Khosla model. This model had been widely used by researchers to study evaporation and water balance modeling. Table 6 shows the performance indicators for the above models, the following inferences have been made. For MLR evaporation developed model R² was 0.937 while Kharufa and Khosla model were 0.90 and 0.85 respectively. Thus, in terms of this indicator, MLR performed the best. Moreover, the values of the error measures, namely RMSE and NAE for MLR evaporation developed model were 36.3 and 0.123, Kharufa model 71.22 and 0.241 and Khosla model was and 173.7 and 0.581 respectively. Therefore, in terms of these two indicators, the MLR evaporation developed model performed the best. The remaining accuracy measures NSE and MAPE for MLR evaporation developed model were 0.936 and 17.83, Kharufa model 0.754 and 28.79 and Khosla model was 0.463 and 51.10 respectively. In terms of these two indicators, MLR performed the best.

Table 6. Comparison of performance between Evaporation MLR model and Kharufa and Khosla model

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Figure 5. Scatter plot of observed dataset with MLR evaporation developed model using validation dataset

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Figure 6. Scatter plot of observed dataset with Kharufa model using validation dataset

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Figure 7. Scatter plot of observed dataset with Khosla model using validation dataset

Based on the foregoing, indicates that the results of performance indicators of the MLR developed evaporation model in the current study outperform all performance indicators and prove to be better than the aforementioned models (see Figure 5, Figure 6 and Figure 7).

The authors would like to acknowledge the contribution of the University of Anbar (WWW.uoanbar.edu.iq) via their prestigious academic staff in supporting this research with all required technical and academic support and also the authors are grateful to the Meteorological Organization Seismology of Iraq (IMOS)-Climatological Division, for providing the relevant data of pan evaporation, temperature, relative humidity, wind speed and sunshine.