May 17, 2013 - 2 School of Civil and Water Resources Engineering, Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia. 3 Department of Earth and Environment, Florida International University, Miami, FL, USA. Abstract:.
HYDROLOGICAL PROCESSES Hydrol. Process. 28, 2945–2960 (2014) Published online 17 May 2013 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/hyp.9844
A simple temperature method for the estimation of evapotranspiration Temesgen Enku1,2 and Assefa M. Melesse3* 1
2
Ethiopian Institute of Water Resources, Addis Ababa University, Addis Ababa, Ethiopia School of Civil and Water Resources Engineering, Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia 3 Department of Earth and Environment, Florida International University, Miami, FL, USA
Abstract: Accurate estimation of evapotranspiration (ET) is essential in water resources management and hydrological practices. Estimation of ET in areas, where adequate meteorological data are not available, is one of the challenges faced by water resource managers. Hence, a simplified approach, which is less data intensive, is crucial. The FAO-56 Penman–Monteith (FAO-56 PM) is a sole global standard method, but it requires numerous weather data for the estimation of reference ET. A new simple temperature method is developed, which uses only maximum temperature data to estimate ET. Ten class I weather stations data were collected from the National Meteorological Agency of Ethiopia. This method was compared with the global standard PM method, the observed Piche evaporimeter data, and the well-known Hargreaves (HAR) temperature method. The coefficient of determination (R2) of the new method was as high as 0.74, 0.75, and 0.91, when compared with that of PM reference evapotranspiration (ETo), Piche evaporimeter data, and HAR methods, respectively. The annual average R2 over the ten stations when compared with PM, Piche, and HAR methods were 0.65, 0.67, and 0.84, respectively. The Nash–Sutcliff efficiency of the new method compared with that of PM was as high as 0.67. The method was able to estimate daily ET with an average root mean square error and an average absolute mean error of 0.59 and 0.47 mm, respectively, from the PM ETo method. The method was also tested in dry and wet seasons and found to perform well in both seasons. The average R2 of the new method with the HAR method was 0.82 and 0.84 in dry and wet seasons, respectively. During validation, the average R2 and Nash–Sutcliff values when compared with Piche evaporation were 0.67 and 0.51, respectively. The method could be used for the estimation of daily ETo where there are insufficient data. Copyright © 2013 John Wiley & Sons, Ltd. KEY WORDS
evapotranspiration; air temperature; Penman–Monteith method; Hargreaves method; new simple temperature method; Ethiopia
Received 23 April 2012; Accepted 20 August 2013
INTRODUCTION Evapotranspiration (ET) is one of the main components of the hydrologic cycle, and its accurate estimation is essential in agricultural and hydrological practices. In tropical regions of the world, ET is the mechanism via which large volumes of water are circulated between the land–water surface and atmosphere. ET has always been difficult to measure, especially on an ecosystem or watershed spatial scale with a desired level of accuracy. Unlike rainfall and river flow, which can be directly measured, ET is usually estimated on the basis of mass transfer, energy transfer, or water budget methods. Traditional measurements of evaporation by pan evaporation method and lysimeter are mainly for
*Correspondence to: Assefa M. Melesse, Department of Earth and Environment, Florida International University, Miami, FL, USA. E-mail: melessea@fiu.edu
Copyright © 2013 John Wiley & Sons, Ltd.
smaller-scale applications and experimental studies. Such methods are also based on assumptions and can be labour and cost intensive. More recently, micrometeorological methods, such as energy balance Bowen ratio and eddy covariance, have found widespread application to measure actual evaporation and have improved our understanding of the evaporation process (Drexler et al., 2004). These methods are also expensive to run because the initial cost and cost of maintaining the monitoring program can be high. There are different ET estimation methods that are developed and are being used in different regions of the world. Some methods work well in an area where they have been developed. When such approaches are tested in other climatic conditions, their performance is poor. The Penman–Monteith reference evapotranspiration (PM ETo) is the only globally accepted method, which performs well in many climatic conditions in the world. Many of the methods available are data intensive, or the data they require are not easily available in developing counties.
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Food and Agriculture Organization of the United Nations (FAO) published a manual in 1998 for estimating crop water requirements (Allen and Pereira, 1998) using the FAO-56 PM. The FAO-56 PM approach is a physically based approach, which requires measurements of numerous weather data including maximum and minimum air temperature, maximum and minimum relative humidity, solar radiation (or sunshine hours), and wind speed at height of 2 m. The main limitation for widely using the globally accepted FAO-56 PM method is the numerous required data that are not available at many weather stations. The quality of these numerous data is also another problem. Solar radiation data are always lacking reliability. Average 24-h wind speed at 2-m height also has a questionable quality. Relative humidity measurement by electronic sensors is commonly full of errors. But maximum temperature is largely and easily available in many regions of the world. In regions where there are insufficient data, a simple temperature method, which requires only temperature data, is important for the estimation of reference ET. The objective of this study was not to develop a new method, which replaces FAO-56 PM, but to develop a new simple temperature method that uses only maximum temperature for areas where other climatic parameters are not available at the desired scale. The FAO-56 PM will be used as a standard method in the development of this new temperature method. The performance of the model in comparison with that of the well-known methods will be assessed. The ability of the new model to capture the seasonality of ET will be also studied. This new simple temperature method could be used in areas where there are insufficient weather data. The specific objectives are to (1) develop an air temperature-based method for estimating ET, (2) evaluate the performance of the new approach by comparing it with the most commonly used complex ET method (PM) and simple but widely used approach (Hargreaves (HAR) method), (3) evaluate the seasonal variation of simulated ET using dry and wet season temperature data, and (4) validate the performance of the new approach with observed Piche evaporimeter data collected from different parts of Ethiopia, representing different agroclimatological regions.
STUDY AREA AND DATA Ethiopia is found in the Horn of Africa; it lies between about 3–15 N and 33–48 E. There is high altitude difference in the country, which ranges from an elevation of about 116 m below sea level, in the Dallol depression of the Afar region, to an elevation of about 4620 m above sea level at Ras Dashen, in the Semien Mountains in the northern part of the country. Because of this high altitude Copyright © 2013 John Wiley & Sons, Ltd.
difference, there is high spatial variability of temperature, whereas seasonal variability of temperature is relatively low. Ethiopia is subdivided into five climatic regimes: moist, dry sub-humid, semi-arid, arid, and hyper-arid regimes. The Ethiopian National Meteorological Agency defines three seasons in Ethiopia: rainy season (June–September), dry season (October–January), and short rainy season (February–May). Camberlin (1997) reported that the Indian monsoon activity is a major cause for summer rainfall variability in the East African Highlands. The rainfall season over the study area starts in June and ends in October. Majority of the study area receives rain during this summer season (locally called Kiremit). The rest of the time, it remains relatively dry and hot. The spatial variability of rainfall attributed to altitudinal differences is substantial. For this study, meteorological data were collected from the National Meteorological Agency of Ethiopia. Five to 15 years of data were collected from ten class I stations distributed over Ethiopia. The data collected from the stations include the following: daily maximum and minimum temperature, daily maximum and minimum relative humidity, sunshine hours, and wind speed at 2 m. The elevation of these stations ranges from about 1146 m at Dire Dawa to 2446 m at Debre Markos. The mean annual temperature in these stations ranges from 16.8 C at Debre Markos to 25.7 C at Dire Dawa. The stations are chosen because they represent majority of the climatic regions and different ecosystems in Ethiopia, and they cover majority of the latitudes in Ethiopia. These stations lie within 6 N and 12.3 N latitudes (Figure 1 and Table I). For this study, ten class I stations with different climatic settings distributed over Ethiopia have been selected. The rainfall distribution follows altitude; Dire Dawa has the lowest elevations and very hot and dry climatic setting, which receives the lowest mean annual rainfall of 661 mm with standard deviation of 163.6 mm among the stations (Table II). On the other hand, Debre Markos has the highest elevation and relatively cold climatic setting, which receives higher annual rainfall of about 1477 mm with standard deviation of 447.6 mm with extended unimodal type of rainfall. The Bahir Dar station receives the highest rainfall among the stations considered with medium altitude having unimodal rainfall characteristics. Awassa and Arba Minch are located in the rift valley region of Ethiopia with bimodal rainfall characteristics, and Dire Dawa represents lowlands and hot climatic settings. Whereas the Addis Ababa station represents the central highlands, the Debre Markos and Bahir Dar stations represent north and northwest highlands of Ethiopia. The detailed characteristics of the stations are shown Table I. Referring to the mean temperature, Dire Dawa and Arba Minch are the hottest stations with mean temperature of 25.7 and 23.8 C, respectively, whereas Debre Markos is the coldest among the stations with mean Hydrol. Process. 28, 2945–2960 (2014)
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Figure 1. Location map of the study area
Table I. Background information of stations Location
Rainfall (mm)
Station name
Latitude
Longitude
Altitude (m)
Addis Ababa Adet Arba Minch Awassa Ayehu Bahir Dar Dangila Debre Markos Dire Dawa Gondar Motta
8.59 11.27 6.04 7.04 10.65 11.36 11.25 10.33 9.36 12.3 11.06
38.48 37.49 37.04 38.3 36.78 37.24 36.83 37.72 41.52 37.25 37.88
2386 2179 1207 1750 1771 1800 2116 2446 1180 2128 2417
Mean
Std. dev.
Kiremit
1219 1262 883 996 1196 1527 1662 1477 661 1174 1177
188.6 187.5 162.7 128.4 133.2 156.6 273.7 447.6 163.6 79.5 160.9
75.3 82 41.3 55 79.8 93.4 85 81 57 79.9 82.1
temperature of 16.8 C. The Addis Ababa and Motta stations are also colder stations with mean temperature of 17.1 C. The details are also shown in Table I. The station names, their respective locations, and data periods are shown in Table I. Short period missed data were filled by simple averaging, whereas longer periods of missed data were discarded from further analysis in this study during the calibration period. However, during the validation period, missed data were totally discarded from Copyright © 2013 John Wiley & Sons, Ltd.
% of rainfall Belg
Rainfall type
Temperature Mean
Std. dev.
No. of years
21.8 14.5 51.6 33.9 18.1 6.5 12.9 15.2 34 11.5 13.5
Bimodal Unimodal Bimodal Bimodal Unimodal Unimodal Unimodal Unimodal Bimodal Unimodal Unimodal
17.1 18.5 23.8 20.1 20.3 19.8 17.2 16.8 25.7 20.5 17.1
1.6 1.8 1.5 1.4 2.1 2.1 1.8 1.7 2.8 2 1.8
11 6 15 11 5 14 13 10 11 8 8
further analysis. The distributions of the meteorological stations over the study area are shown in Figure 1. Weather data were analysed with statistics of (minimum, first quartile, median, third quartile, and maximum) values of each data collected. The historical minimum temperature was recorded at the Ayehu station with the value of 3.5 C among the stations, whereas the minimum mean temperature was at the Dangila station with value of 9.2 C and standard deviation of 3.4 C. The historical maximum Hydrol. Process. 28, 2945–2960 (2014)
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Table II. Data statistics of weather variables Data statistics Station and period Addis Ababa (1995–2005)
Adet (2003–2008)
Arba Minch (1997–2005)
Awassa (1995–2005)
Ayehu (2004–2008)
Bahir Dar (1998–2008)
Dangila (1996–2008)
Debre Markos (2002–2011)
Dire Dawa (1995–2005)
Gondar (2004–2008)
Motta (2004–2008)
Weather variables
Mean
Std. dev.
Minimum
First quartile
Median
Third quartile
Maximum
Tmax Tmin RH SS WS Tmax Tmin RH SS WS Tmax Tmin RH SS WS Tmax Tmin RH SS WS Tmax Tmin RH SS WS Tmax Tmin RH SS WS Tmax Tmin RH SS WS Tmax Tmin RH SS WS Tmax Tmin RH SS WS Tmax Tmin RH SS WS Tmax Tmin RH SS WS
23.8 10.3 58.8 6.7 0.6 26.4 10.7 58.4 7.4 0.7 30.4 17.2 62.1 7.3 0.6 27.4 12.9 66.5 7.3 0.8 28.1 12.5 67.0 7.0 0.6 27.2 12.7 57.6 8.0 0.9 25.1 9.2 66.9 7.2 0.9 22.9 10.6 56.6 7.2 1.2 32.4 19.1 51.2 8.5 1.6 27.4 13.6 50.9 7.5 1.3 21.2 11.9 75.8 7.1 1.3
2.3 2.4 15.1 3.1 0.3 2.8 2.6 18.0 2.6 0.3 2.6 2.1 11.4 3.0 0.3 2.5 2.7 11.2 2.8 0.4 3.5 3.5 15.7 2.8 0.3 2.5 3.0 15.4 2.8 0.4 2.7 3.4 17.7 2.8 0.3 2.8 1.9 21.6 3.2 0.4 2.8 3.3 12.0 2.5 0.9 2.9 2.1 20.2 2.7 0.4 1.3 1.5 7.0 2.8 0.3
14.5 0 24 0.0 0.0 16.5 0 17 0 0.0 22.2 8.4 29 0 0 19 0 32 0.0 0.0 17.0 3.5 31 0.0 0.0 18.6 2.5 22 0 0.0 15.8 0.6 7 0 0.0 13 0 7 0 0.0 20.5 4.5 24 0 0.0 17.5 0 13 0 0.0 15.5 0 37 0 0.0
22.3 9 46 4.2 0.3 24.5 9 44 5.8 0.5 28.6 16.2 54 5.4 0.4 25.6 11.2 58 5.4 0.6 25.2 10.8 53 4.9 0.5 25.5 10.6 45 6.2 0.5 23.2 6.5 54 5.3 0.7 20.8 9.5 38 4.7 1.0 30.8 17.4 44 7.8 1.0 25.2 12.5 34 5.6 1.1 20.5 11 72 5.4 1.1
23.8 10.8 58 7.2 0.5 26 11 61 8 0.7 30.3 17.5 63 8.1 0.57 27.5 13.4 69 7.9 0.7 28.1 13.5 66 7.4 0.6 27 13.4 58 8.9 0.9 25 10 71 7.8 0.9 23 11 54 7.6 1.2 32.8 19.8 50 9.5 1.4 27.5 13.5 47 8.1 1.3 21.5 11.7 76 7.6 1.3
25.3 12 72 9.5 0.7 28.5 12.5 73 9.5 0.9 32.2 18.6 70 9.8 0.78 29.2 15 74 9.7 1.0 30.8 15.0 82 9.6 0.8 29 14.8 71 10.2 1.1 27 12 82 9.6 1.1 25 12 78 10.1 1.4 34.6 22.1 59 10.5 2.2 29.5 14.9 70 9.9 1.5 22 12.7 80 9.4 1.5
30.5 16.6 97 11.9 5.4 32.6 17.2 97 11.7 2.6 37.5 24.3 100 11.4 1.87 34 19.5 100 11.6 5.9 35.5 20.6 99 11.2 2.3 33.8 22 94 11.8 3.1 32 16.5 99 11.7 2.9 29.7 16 100 12 3.8 39 27 97 11.8 5.2 34.4 21 91 11.6 3.7 23.8 16 95 11.1 2.2
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temperature of 39 C was recorded at Dire Dawa with mean maximum temperature of 32.4 C and standard deviation of 2.8 C. The mean maximum sunshine hour was at Dire Dawa, whereas the mean minimum was at Addis Ababa with values of 8.5 and 6.7 h and standard deviations of 2.5 and 3.1 h, respectively. The details of all these weather data statistics are shown in Table II.
THEORY AND METHODS Penman–Monteith method
The FAO-56 PM is a physically based approach, which requires measurements of air temperature, relative humidity, solar radiation (or sunshine hours), and wind speed. ETo is the potential ET from a reference surface of a hypothetical green grass of uniform height, 0.12 m, well watered and actively growing and has a constant albedo of 0.23 with fixed surface resistance of 70 s m1 (Allen and Pereira, 1998). After the aerodynamic resistance, ra = 208/u2, and the surface resistance, rs = 70 s m1, are estimated, for such a reference crop, the PM equation can be rewritten as follows: ETo ¼
900 0:408ΔðRn GÞ þ g Tþ273 u2 ðes ea Þ Δ þ gð1 þ 0:34u2 Þ
(1)
where ETo is reference evapotranspiration (mm day1); Rn is the net radiation at the crop surface (MJ m2 day1); G is soil heat flux density (MJ m2 day1), assumed zero on daily basis; T is mean daily air temperature at 2-m height ( C); u2 is wind speed at 2-m height (m s1); es is saturation vapour pressure (kPa); ea is actual vapour pressure (kPa); es = ea is saturation vapour pressure deficit (kPa); Δ is slope of vapour pressure curve (kPa C1); and g is psychrometric constant (kPa C1). The FAO-56 PM combination equation (Equation (1)) was proposed as the sole standard method for estimating ETo and for evaluating other equations (Allen et al., 1994a, b; Slavisa, 2005). It has been proved that this equation could overcome the shortcomings of the previous methods and provided more consistent values in different regions of the world (Liu et al., 1997; Ventura et al., 1999; Du et al., 2000; Rana and Katerji, 2000; Dingman, 2002; Nandagiri and Kovoor, 2005; Temesgen et al., 2005; Bois et al., 2008). Penman–Monteith sensitivity analysis
A sensitivity analysis is an important technique to improve one’s understanding of the dominant climatic variables in the estimation of ETo in an area of interest. ETo is a measure of evaporative power of the atmosphere, which could be estimated from the meteorological data only. ‘In humid climate, ETo provides an upper limit for Copyright © 2013 John Wiley & Sons, Ltd.
actual ET and in an arid climate it indicates the total available energy for actual ET’ (Gong et al., 2006). A sensitivity analysis of the inputs incoming solar radiation, air temperature, relative humidity, and wind speed to PM ETo was carried out. These variables were increased and decreased by 10%, 20%, and 30% from the monthly average values for each run. To understand the sensitivity of the input variables, minimum and maximum temperature and relative humidity, averages of air temperature and relative humidity, and their amplitudes were calculated (Bois et al., 2008). In this analysis, it was assumed that the maximum and minimum temperature were to increase and decrease simultaneously. For the computations of net radiation, solar angles at the 15th day of each month were assumed. Monthly sensitivity analysis was carried out at the Bahir Dar station in the year 2007, and the results are presented. Simple temperature method
In this study, the FAO-56 PM method was used as a standard method for the development of a new simple temperature method that uses only maximum temperature for the estimation of ETo. This study was based on the sensitivity analysis result of ET over the study area (Temesgen, 2009). Part of the sensitivity analysis is presented in this paper, which shows that PM ETo is almost equally sensitive to solar radiation and air temperature. Solar radiation-based ET models such as those of Abtew (1996) and the modified Makkink (De Bruin, 1981) were performing well in the estimation of ET over the area. This has called to develop a simple temperature method that could perform as good as the radiation methods. Temperature data are easily available than solar radiation data in Ethiopia. It is this sensitivity analysis result, which led to the development of a new simple empirical temperature method, that uses only maximum temperature data for the estimation of ET. Abtew’s (1996) simple equation was defined as follows: ET ¼ k
Rs l
(2)
where ET is evapotranspiration (mm day1), Rs is the incoming solar radiation (MJ m 2 day 1 ), k is a coefficient with a value of 0.53, and l is a conversion constant. In developing the new method, Rs was replaced by Tmax, as incoming solar radiation and temperature were equally sensitive to PM ETo, and the constants k and l were replaced by a new coefficient k. Finally, the new simple empirical temperature method, which we named ‘Enku’s simple temperature method’, was developed as follows: Hydrol. Process. 28, 2945–2960 (2014)
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— 10 4 11 — 11 — 8 — 5 6 — — 0.56 0.48 0.49 — 0.51 — 0.58 — 0.38 0.57 0.51 — 0.69 0.61 0.58 — 0.65 — 0.72 — 0.75 0.67 0.67 — 0.88 0.86 0.88 — 0.85 0.91 0.87 — 0.74 0.85 0.86 1 1.0 3.6 5.7 2 3.85 2.5 1 3.2 2.65
PM, Penman–Monteith; HAR, Hargreaves; NS, Nash–Sutcliff; AME, absolute mean error; RMSE, root mean square error.
0.85 — 0.9 0.87 0.88 0.81 0.88 0.83 — 0.75 0.83 0.84 — 6 4 3 — 4 2 3 — 3 3 — — 0.64 0.55 0.52 — 0.47 0.66 0.54 — 0.57 0.63 0.57 — 0.23 0.51 0.47 — 0.68 0.2 0.64 — 0.65 0.56 0.49 Addis Ababa Adet Arba Minch Awassa Ayehu Bahir Dar Dangila Debre Markos Dire Dawa Gondar Motta Average
840 950 1260 1050 1180 1000 930 720 1170 960 720 —
0.61 — 0.54 0.58 0.68 0.61 0.67 0.71 0.67 0.74 0.67 0.65
0.52 — 0.41 0.31 0.25 0.47 0.5 0.57 0.66 0.67 0.5 0.49
0.4 — 0.52 0.44 0.52 0.44 0.43 0.45 0.54 0.44 0.48 0.47
0.51 — 0.65 0.55 0.65 0.56 0.53 0.59 0.7 0.54 0.59 0.59
1.7
11 10 6 11 5 11 — 13 11 5 5 —
— 0.6 0.6 0.63 — 0.72 0.62 0.72 — 0.71 0.62 0.65
— 0.52 0.44 0.41 — 0.37 0.54 0.4 — 0.45 0.5 0.45
No. of years R2 R2 R2 No. of years AME RMSE NS R2 R2
NS
% No. of AME RMSE Error years
Validation Calib. Station
Hargreaves method
The Hargreaves and Samani (1985) equation is a wellknown temperature-based method for the estimation of
NS
Validation Calib.
Valid.
Performance with HAR
where ETo is the reference evapotranspiration (mm day1); n = 2.5, which can be calibrated for local conditions; k is the coefficient, which can be 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, could be approximated as k = 48 * Tmm 330 for combined wet and dry conditions, k = 73 * Tmm 1015 for dry seasons, and k = 38 * Tmm 63 for wet seasons, where Tmm ( C) is the long term daily mean maximum temperature for the seasons under consideration. The daily mean temperature was used to estimate ETo and was found not able to simulate the amplitudes. Our study also compared the ETo simulation with the Hargreaves method, which uses average daily temperature as an input for ETo simulation. The coefficients of this new method were first calibrated using the global standard PM ETo method as a true value of ET. With these calibrated coefficients, the new method was compared with the PM ETo as well as the Piche evaporimeter data from the stations. This new method was also compared with the known temperature method. The comparison of the new method with the HAR method uses the coefficient of determination (R2). This is because the HAR method also required local calibration of the coefficient over the study area. The performance of the method was validated with different data set from 2 to 6 years of data at different stations as shown in Table III. The method was also validated at the Adet station, a station not used for calibration, using 6 years of data after computing the coefficient (k) from the mean maximum temperature data of other stations. The method was also compared with the observed Piche evaporimeter data. Four to 11 years of observed Piche evaporimeter data were collected from six stations. A Piche evaporimeter is described that has only one evaporative surface, is constructed from inexpensive plastic tubing, and from which water loss is measured gravimetrically. In validating the new method with the Piche data, the millilitre form of the Piche observed data was converted to millimetre depth, considering the net disk evaporating area. This conversion was carried out for ease of comparison. The performance of the new method was compared with the observed Piche data with coefficient of determination (R2) and Nash–Sutcliff (NS) efficiency. In this comparison, all missed data were discarded from further analysis.
Performance with PM
(3)
Coeff. k
ðT max Þn k
Table III. Model performance comparison for the combined seasons
ETo ¼
Performance with Piche evaporator
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daily ETo. This method requires daily maximum and minimum air temperature, and extraterrestrial solar radiation data. The extraterrestrial solar radiation is computed from the information on latitudes of the study site and Julian day of the year. The Hargreaves and Samani (1985) equation is defined as follows: ETo ¼ 0:0023ðTmax Tmin Þ0:5 ðTm 17:8ÞRa
(4)
where ETo is daily reference evapotranspiration (mm day1), Tmax is daily maximum temperature ( C), Tmin is daily minimum temperature ( C), Tm is daily mean temperature ( C), and Ra is the daily extraterrestrial solar radiation (mm day1).
Figure 3. Comparison of long-term means of the new method versus PM ETo
Figure 2. Sensitivity analysis of PM ETo to input variables for 4 months in different seasons Copyright © 2013 John Wiley & Sons, Ltd.
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Figure 4. Combined dry and wet season comparison of the new method with PM
RESULTS AND DISCUSSION Sensitivity analysis
Sensitivity analysis of the input variables of PM ETo was carried out in the year 2007 at the Bahir Dar station Copyright © 2013 John Wiley & Sons, Ltd.
(Temesgen, 2009). The result of sensitivity analysis showed that solar radiation was found to be the most sensitive weather variable independent of the seasons of the year. PM ETo was also comparably sensitive to air temperature as solar radiation. Wind speed was found to be least sensitive. Hydrol. Process. 28, 2945–2960 (2014)
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Figure 5. Combined comparison of new method with Piche evaporimeter data
Gong et al. (2006) explained that sensitivity of ETo to the input variables varies with seasons unlike our findings at the Bahir Dar station, where variation of weather variables over years was minimum. The detailed weather variables at the stations and their statistics are shown in Table II. A simple but practical way of presenting a sensitivity analysis is to plot relative changes of weather variables against changes in PM ETo by using a graph. The sensitivity analysis result at the Bahir Dar station for some of the months in the year 2007, representing different seasons, is shown in Figure 2. Combined dry and wet seasons
The result of the simple new temperature model was compared with that of the global standard PM ETo method and the well-known HAR temperature method at all ten stations. In semi-arid areas such as Dire Dawa, Arba Minch, and Ayehu, where the mean annual maximum temperature is higher, that is, 32.4, 30.4, and 28.1 C, respectively, the coefficient k is required to be as large as 1260 to provide better results. In areas where the Copyright © 2013 John Wiley & Sons, Ltd.
mean annual maximum temperature is lower, about 23 C, the coefficient k was found to be as low as 720 for the method to provide better results. The comparison was made with R2, NS efficiency, root mean square error (RMSE), absolute mean error (AME), and annual percentage error of the new method with the PM ETo. The R2 of the new method, when compared with that of PM ETo, was as high as 0.74 at the Gondar station. The annual average R2 over the ten stations were 0.65 and 0.84 when compared with PM and HAR methods, respectively. The NS efficiency of the method when compared with that of the PM ETo was as high as of about 0.67 at the Gondar and Dire Dawa stations. Using the averages of the ten stations, the method could simulate the PM ETo estimate with an average NS efficiency of 0.49. It is shown that the HAR method overestimates daily ETo when compared with PM ETo, which indicates that local calibration of the HAR coefficients is required. The R2 of the new method with the HAR temperature method was as high as 0.9 at the Arba Minch station and as low as 0.75 at the Gondar station (Table III). Referring the performance indicators of R2 and NS efficiency, the Hydrol. Process. 28, 2945–2960 (2014)
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Figure 6. Combined dry and wet season comparison of the new method with the HAR
new method was able to perform better at the Gondar station with R2 = 0.74, NS = 0.67, RMSE = 0.54 mm, AME = 0.44 mm, and annual percentage error = 1% when compared with the PM ETo (Table III). These results were repeated during the validation period, and better results Copyright © 2013 John Wiley & Sons, Ltd.
were observed at some of the stations during the validation period (Table III). At the Adet station, the method was validated after computing the coefficient k from the mean maximum temperature data. The method was able to estimate PM ETo Hydrol. Process. 28, 2945–2960 (2014)
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Table IV. Dry and wet season model comparisons Performance when compared with PM Dry Station and period Addis Ababa (1995–2005) Arba Minch (1997–2005) Awassa (1995–2005) Ayehu (2004–2008) Bahir Dar (1998–2011) Dangila (1996–2008) Debre Markos (2004–2008) Dire Dawa (1995–2005) Gondar (2004–2008) Motta (2004–2008) Average
Performance with HAR R2
Wet
Coeff. k
R2
NS
AME RMSE Coeff. k
850 1300 1150 1300 1020 980 730 1150 1000 730 —
0.51 0.62 0.52 0.61 0.6 0.65 0.61 0.65 0.65 0.65 0.61
0.37 0.52 0.32 0.49 0.52 0.6 0.55 0.5 0.63 0.57 0.51
0.39 0.49 0.36 0.32 0.39 0.34 0.36 0.42 0.36 0.42 0.39
0.51 0.61 0.45 0.42 0.5 0.44 0.46 0.53 0.46 0.54 0.49
770 1200 1000 950 940 820 620 1170 940 610 —
R2
NS
AME RMSE
Dry
Wet
0.63 0.52 0.66 0.64 0.57 0.57 0.56 0.42 0.6 0.59 0.58
0.63 0.42 0.48 0.63 0.57 0.55 0.53 0.4 0.59 0.44 0.52
0.3 0.49 0.41 0.27 0.3 0.3 0.33 0.59 0.33 0.34 0.37
0.85 0.91 0.84 0.83 0.81 0.84 0.83 0.75 0.75 0.83 0.82
0.85 0.91 0.92 0.83 0.87 0.79 0.84 0.84 0.87 0.67 0.84
0.38 0.6 0.53 0.33 0.38 0.38 0.41 0.76 0.41 0.47 0.47
PM, Penman–Monteith; HAR, Hargreaves; NS, Nash–Sutcliff; AME, absolute mean error; RMSE, root mean square error.
with R2 = 0.6, RMSE = 0.64 mm, and AME = 0.52 mm. The performance of the method was tested in terms of R2 and NS with the Piche evaporation data at the Adet, Motta, Debre Markos, Bahir Dar, and Arba Minch stations using 4–11 years of daily data. The new method was able to reproduce the observed Piche evaporation data with average R2 and NS of 0.67 and 0.51, respectively (Table III). The long-term time series averages of PM and the new method ETo estimates at different stations were also compared in terms of R2 and NS at the stations. The analysis found R2 and NS of 0.98 and 0.97, respectively (Figure 3). The mean maximum temperature is the function of incoming solar radiation and is also highly correlated with the altitudes of the stations in the area. The coefficient of determination between mean maximum temperature and stations altitude was as high as 0.91. The calibrated coefficient k of the new method was also strongly correlated with the altitude of the stations (R2 of 0.81). Hence, the coefficient k could also be estimated from altitude data with comparable results, as k = 0.37h + 1700, where h is elevation above mean sea level (m). Generally, the method was able to estimate annual ETo with an annual average error of
