Predicting Reference Evaporation for the Ethiopian Highlands

Water is likely the most limiting factor in increasing agricultural production in large parts of Africa. Reference evaporation (ET0) is a key hydrological parameter to use efficiently the scarce supply. Several methods are available for predicting reference evaporation, but the accuracy of any of the methods has not been established for the Ethiopian highlands. The objective of this study is, therefore, to select the best methods for calculating the reference evaporation ET0. For the section, meteorological data of the Bahir Dar station were used, because all data needed for this study including the Class A pan Evaporation were recorded on a daily basis. Pan evaporation was considered as the best estimator of the reference evaporation. The results showed that the FAOPenman Monteith (using solar radiation, wind speed, temperature and relative humidity) and Enku method (using only maximum daily temperatures) have acceptable daily ET0 ranges and predicted to Class A pan evaporation with correlation coefficients greater than 90% in a monthly basis. Next best was the Thornthwaite’s method with correlation coefficient of 89% with pan evaporation. Piche methods performed relatively well with correlation coefficient of greater than 70%. Blaney-Criddle, Priestley & Taylor, and Hargreaves performed the poorest in predicting pan evaporation. These methods should be recalibrated for local condition and therefore not recommended for use in the Ethiopian highlands. In summary, the FAO-Penman Monteith is recommended for locations where the input data are available; otherwise, the Enku method using maximum daily temperature is best for estimating the reference evaporation.


Introduction
Throughout Africa, good quality water is being recognized as a finite resource that is in short supply-limiting development in many cases [1]. The Blue Nile basin is one of areas in Africa of extreme water scarcity: nearly 150 million people are dependent on the Blue Nile river with a discharge of less than 85 billion m 3 [2] [3]. Understandably, careful assessment of the use of water needs to be made because in the future, it will be increasingly important to match the supply (i.e., excess rainfall) in the Ethiopian highlands with the demand by irrigation systems, industry, and population in the basin. Estimating reference evaporation provides fundamental information on water abstraction in the highlands and downstream when used in combination with crop coefficients [4].
Estimating reference evaporation (ET 0 ) has taken many forms ranging from direct measurement to indirect methods employing meteorological measurements.
One of the direct measurements is the Class A evaporation pan. The pan evaporation can be related to reference evaporation with coefficients developed by Pereira et al. [5] and Allen et al. [6]. The disadvantage of Class A evaporation pans are only their availability at a few locations in developing countries. Indirect methods are, therefore, a good alternative and range from locally developed, empirical relationships to physically based energy-and mass-transfer models [7]. The meteorological data required vary with the type of indirect methods. The Penman and Priestley and Taylor methods require most meteorological data and the Penman is generally considered as the most accurate one [8] [9] [10] [11] [12], but as for the Class A pan data, the required data is only collected at few meteorological stations. Thornthwaite Mather, which is used frequently in Ethiopia, needs fewer climatic data (temperature and sunshine hour). The Hargraves, Blaney-Criddle, and Enku (locally developed) need only temperature to estimate the reference evaporation. Finally, methods that use the measurements of a Piche evaporimeter to calculate the reference evaporation were developed by [13] and [14].
Reference evaporation is defined by Meyer [4] as the rate of evaporation from a hypothetical crop with an assumed crop height of 12 cm and fixed canopy resistance of 70 s m −1 and an albedo of 0.23 and would give the same evaporation rate as envisioned by Smith et al. [9] of an extensive surface of green actively growing completely shading the ground and not short of water. It is of course difficult to replicate the conditions that define the reference evaporation. Several methods have been used to validate the direct and indirect methods. In the literature, these validation methods are divided in four categories. The first category uses the evaporation measured with Class A pan [15] [16] [17]. Other studies employ the ET 0 of FAO-Penman Monteith for validation [7] [10] [11] [18] [19] [20] [21].
Limited experimental studies have used the ET 0 calculated from Piche data for validation [19]. The final method used for validation of calculated reference evaporation are lysimeters [22] [23] [24] [25] but these are expensive to construct and operate and therefore not available in most developing countries.

A. A. Adem et al. Journal of Water Resource and Protection
Agronomists and hydrologists have little guidance [15] [26] to choose among the many available methods to estimate reference evaporation in the Ethiopian highlands where the density of weather station is low [27] [28] and often only measure temperature and precipitation. The objective of this study is, therefore, to select the most accurate method for estimating reference evaporation for the Ethiopian highlands. The Bahir Dar meteorological station was chosen for this study because as the only station in the Ethiopian highlands, all the meteorological variables were measured required for calculating the reference evaporation for all the methods considered. The data recorded on a daily basis included maximum and minimum temperature, relative humidity, wind speed, and sunshine hours and evaporation measured with the Piche and Class A pan.

Site Description and Data Set
The Ethiopian highlands is the region in Ethiopia above 1500 m and covers a total area of 537,000 km 2 (43% of Ethiopia) [29] [30]. It constitutes more than half of all the highland areas of Africa [31]. Most of the area of the highlands is cultivated land and land degradation is a major threat. One of the main rivers is the Blue Nile with a watershed of 180,000 km 2 . It has a monsoonal climate with rainfall varying between 800 and 3000 mm per year and evapotranspiration between 1400 and 1681 per year [32]. The major rain phase for the highlands of Ethiopia is between June and September.
One of the difficulties in the Ethiopian highlands is that pan evaporation data is measured only at the Bahir Dar Station for long period. It is located 2.2 km from Lake with latitude of 11˚35'59" and longitude of 37˚21'36". The elevation is 1805 m ( Figure S1 in the Supplementary Material). The station has more than 30 years of data but Pan Evaporation started only in 2005 (  Pan-Pereira methods were used for validation of the rest of the empirical models.

Reference Evaporation: Description of the Selected Methods
Since the Penman has not been validated for the Ethiopian highlands, the Class A pan data using coefficients proposed by Pereira et al. [5] and Allen et al. [6] are used as the direct measure of reference evaporation against which the calcu- from meteorological data. It has been recommended as the standard method for computation of the reference evapotranspiration. The method considers all parameters that govern energy exchange and corresponding latent heat flux and requires air temperature, relative humidity, sunshine intensity/hour, wind speed data and elevation as input parameters.
The modified Penman-Monteith equation can be written as [6]: where; 1 s a r r where; r s is surface resistance [s m −1 ] which is 70 s m −1 for the grass reference surface, r a is aerodynamic resistance which helps to determine the transfer of heat and water vapor from the evaporating surface into the air above the canopy.
where the subscript m indicates the months 1, 2, 3, …, 12, T m is the monthly mean temperature (˚C), I is the heat index for the year, given by: where, i m is monthly values of heat index and a is empirical coefficient defined as where ET 0 is reference crop evapotranspiration (mm/day) averaged over the month T mean = mean daily temperature (˚C), and p is mean daily percentage of annual daytime hours and varies between 0.26 and 0.29 for Bahir Dar.

6) Enku's Simple Temperature Method (ENKU)
The new simple empirical temperature method, which was named by "Enku's simple temperature method", was developed [19] and tested in Ethiopia with Penman Montieth reference Evaporation and the Piche Evaporimeter. The equation is: where ET 0 is the reference evapotranspiration (mm day −1 ); n = 2.5 for the Lake Tana area; k is the coefficient, which is calibrated for local conditions ranging from about 600 for lower mean annual maximum temperature areas to 1300 for higher mean annual maximum temperature areas. The coefficient, k, was found

7) Pan Methods
The evaporation rate from Class A Pans filled with water is easily obtained. In the absence of rain, the amount of water evaporated during a period (mm/day) corresponds with the decrease in water depth. Pans provide a measurement of the integrated effect of radiation, wind, temperature and humidity on the evaporation from an open water surface [6].
There are two types of Pan Models to estimate reference evaporation. a) Pereira Model (PAN-P) According to Pereira et al. [5], the reference evaporation, ET 0 from pan data calculated with: b) Allen Model (PAN-A) As Allen et al. [6], ET 0 from pan data calculated with: The pan coefficient K 2 for Class A pan with green fetch can be found as [6]: where F is fetch or distance of the reference grass (m) and RH is the relative humidity in percent.

8) Piche Methods
The Piche evaporimeter is a type of atmometer used to measure the rate of evaporation from a wet disc of absorbent paper. It is used mainly in hot, dry climates where water loss through evaporation must be observed regularly. Since the results are dependent on wind speed past the disc, as well as the wet bulb saturation deficit, it is almost essential to expose the evaporimeter inside a meteorological screen [14] [38] [39].
There are two types of Piche models used in this study to estimate evapotranspiration.

a) Stanhill Method (PI-S)
Stanhill [13] suggested that it may be possible to estimate the second term in Penman's equation from available sheltered Piche evaporation data (E pi ) as follows. where; where f(u) is an aerodynamic wind function and (e s − e a ) is the difference between saturated vapour pressure and actual vapour pressure in hPa, evaluated at mean air temperature and at 2 m above the ground or water surface.
The equivalent to the wind function of Penman [40] is where u is the wind speed in m s −1 at 2 m elevation, and a, and b, are empirical coefficients. Penman [40], Penman [41] suggested using values equivalent to 1 and 0.537 for a, and b, respectively for a short grass cover when u is measured in Adam and Ahmed [14] showed that the ratio of Penman estimated and Piche evaporation have relation with relative humidity exponentially. That is: where a and b are constants that can be find from the exponential relation and the RH humidity in percent

Methods of Data Analysis
The collected meteorological data for Bahir Dar (2005Dar ( -2015 was of good quality with less than 5% of missing data. A simple arithmetic mean was used to determine the missing data. Reference evaporation was computed at daily and monthly time step using the 10 methods listed above after data preparation. In addition, we compared the calculated reference evaporation with the ten methods using three techniques: visual inspection, descriptive statistics and sta- In this study, every single model was correlated with the pan ET 0 s to assess the model performances and standard error. Pearson's correlation and root mean square error (RMSE) equations were used for this purpose.
The formula for the Pearson product moment correlation coefficient, r, is: The equation for the standard error of the predicted y is: where x and y are the sample means.
A sensitivity analysis was carried out to evaluate the percentage response of calculated ET 0 to selected weather variables. Changes of model outputs and their variability induced by change in weather variables were evaluated. The change in variables was analyzed for values 25% above and 25% below the mean value.
Mann Kendall trend test was used to indicate whether there are trends in the ET 0 computed using the ten methods. Non-parametric Mann Kendall Trend Test is useful to examine the temporal variation trend. It is based on the significance of differences, not directly on the random values. Therefore the trend that's been determined is less affected by outliers [42]. The nonparametric Mann-Kendall trend test has been applied in many studies to identify whether monotonic trends exist in hydro-meteorological data such as temperature, rainfall and stream flow [43]. The Mann Kendall Trend Test, S is calculated by using the equation below where x j and x i are the sequential data value and j greater than i, N is the length of the data set.
As indicated in Mann [44] and Kendall and Stuart [46], when N ≥ 8, the distribution of S approaches the Gaussian form with mean E(S) = 0 and variance Var(S) given by: (24) where: t i is the number of ties of length m.
The statistic S is then standardized (Z), and its significance can be estimated from the normal cumulative distribution function.
The positive Z value indicates an increasing trend while a negative Z value indicates a decreasing trend. When testing two sided trends at a selected level of significance a, the null hypothesis (H 0 ) of no trend is rejected if the absolute value of Z is greater than Z a/2 where a represents the chosen significance level (5% with Z 0.025 = 1.96).

Reference Evaporation: Calculated Values
The reference evaporation, ET 0 , was calculated for a daily and monthly time step.
In Figure 1, as an example, the 2005 ET 0 for the ten methods are depicted. Values calculated for the other years are shown in tabular form in Table S2  Seasonally, the reference evaporation of each of the methods is greater during the dry phase from February to May when the temperature is high and there are few clouds than during the rain phase from June to September when it is cloudy and less warm (Figure 1, Figure 2). In addition, the reference evaporation decreases in December and January for some of the methods (Figure 1, Figure 2) due to cloudiness caused by of easterlies carrying moisture from Arabian Sea.
In equatorial countries like Ethiopia, the difference in sunshine duration between months is minimal and the difference in ET 0 is due to cloud cover mainly and temperature and relatively humidity secondly. This is different from temperate climates where the day length is the primary factor that determines the magnitude of the reference evaporation during the year.   (2)), HAR is Hargraves (Equation (5)), TH is Thornthwaite (Equation (9)), BC is Blaney-Criddle (Equation (10)), ENKU is the Enku's simple temperature method (Equation (11)), PAN-P is the Pan-Pereira (Equation (12)), PAN-A is the Pan-Allen (Equation (14)), PI-S is the Piche-Stanhill (Equation (16)) and PI-ADAH is the Piche-Adam and Ahmed (Equation (20)).   Figure 3 showed that the year to year variation in reference evaporation was small, indicating that the amount of rainfall and soil moisture have little or no effect on the loss of water in the atmosphere.

Reference Evaporation: Comparing the Methods
The data in Figure 2 are further summarized in Figure 4 where the monthly averaged reference evaporation, ET 0 , of each of the 10 methods for the eleven years   (10)), by monthly varying constants and calibrating these, the model will fit much better [48]. The modified Blaney-Criddle Equation becomes in this way similar to the Enku method (Equation (11)). Interestingly, in Figure 4 has shown that during the rain phase starting in May (when the first rains fell) through September (when the rains ended), the reference evaporation, ET 0 , calculated with the three indirect methods (the FAO-Penman Monteith, the Thornthwaite and the Enku methods) compared well with the direct measurement of both pan evaporation methods and the Piche evaporimeter using coefficients proposed by Adam and Ahmed [14].
During the rain phase when precipitation exceeds evaporation, the condition of a well-watered surface on which the reference evaporation is based is similar to that in the Ethiopian highlands. So, during the wet phase the direct and indirect  In addition to plotting the averaged reference evaporation, ET 0 , in Figure 5, it is also of interesting to investigate the variation in the reference evaporation for each of the 10 methods. Therefore, the maximum, minimum, mean, lower and upper quartile of the long term daily reference evaporation for the period are shown in Rácz et al. [15] stated that methods having smallest RMSE have the lowest systematic error in predicting ET 0 .

Sensitivity Analysis
In the sensitivity analysis, we looked the relative effect on reference evaporation of a 25% change in temperature, sunshine hours, relative humidity and wind speed ( Figure 6, Figure S2). As expected, an increase in temperature increased reference evaporation (Figure 6). For the indirect methods (Enku, Thornthwaite and Hargreaves methods), the reference evaporation increased the same percentage or more as the temperature. The direct methods were the least sensitive to the change in temperature. Changing sunshine hours, relative humidity and wind speed did not change or increased the reference evaporation with the exception that an increase in relatively humidity for the FAO-Penman Monteith and an increase in winds Speed for both pan methods decreased the reference evaporation ( Figure S2).

Trend Analysis
The trend analysis results of the reference potential evaporation obtained by applying the Mann-Kendall method is shown in Table 3. To our surprise despite our short 11-year record, there were strong trends for the majority of the 10   Priestly and Taylor methods that was ill suited for the Ethiopian highlands was an exception. Thus, since these methods were directly based on measured meteorological data (two only on temperature) it clearly indicates that the climate is changing in the Ethiopian Highlands. In other words, since three of the indirect methods were primarily based on temperature, it is getting warmer fast in Bahir Dar! Finally, the Piche methods that not directly depend on the measured standard indicated that the reference evaporation was decreasing.

Conclusions
Ten methods to predict the reference evaporation were tested for the Ethiopian where P atmospheric pressure [kPa], and Z elevation above sea level [m] The net radiation (R n ) is the difference between the incoming net shortwave radiation (R ns ) and the outgoing net long wave radiation (R nl ): where ω s is the sunset hour angle in radians