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Районирования территории и оценка репрезентативности расчетных методов величины эвапотранспирации для условий аридного климата
Поступила 02.11.201 7 г.
© Махмуд Мохамед Али Абдель-Азим, Али Габер Махмуд
Университет Файюма, г. Файюм, Арабская Республика Египет
Аннотация. Эталонная эвапотранспирация (ЕТо) является жизненно важным фактором в управлении водными ресурсами и их планировании. Для различных климатических регионов и по имеющимся данным разработаны различные методы оценки. Поэтому надежность таких методов зависит от климатических условий. В настоящем исследовании оцениваются четыре метода, основанные на температурных данных: методы FAO Блэйни-Кридла (BC), Тюрка, Дженсен-Хейза и Харгривза (HG), и два методов, основанных на радиационном балансе: ФАО-радиация (FAO-rаd) и Пристли-Тейлора (РТ) по сравнению с методом FAO-PM. Оценка проволилась для аридных условий Ливии. Для выбора наилучшего метода опредления величины ЕТо были рассчитаны процентная ошибка оценки (РЕ), среднеквадратичная ошибка (Ш5Е) и средняя ошибка смещения (МВЕ). Полученные значения ЕТо (FAO-PM и среднемесячное значение наилучших оценок величины ЕТо) были использованы для составления карт пространственной изменчивости ЕТо с помощью метода Кригинга. Статистический анализ полученных результатов показал, что уравнение Тюрка хорошо подходит для северной части исследуемой территории, которые включают територии в Налуте, Зуаре, Мосрате, Сырте, Шахате, Дерне, Тюбрюке, Хоне, Гале и Гагбубе. Для южной части исследоуемой территории подходят следующие зависимости: уравнение HG для Опари и Тазибру, уравнение BC для Куфры и Гадамеса, уравнение FAO-Rad для Себхи; уравнение JH для Гхаты.
Ключевые слова. Эвпотранспирация, аридный климат, метод Пенмана-Монтейта (FAO-PM), крининг.
Mapping and evaluation of reference évapotranspiration methods under arid conditions
Received on Nowember 02, 2017
© Mahmoud Mohamed Ali Abdel-Azim, Ali Gaber Mahmoud
University Of Fayoum, Arab Republic of Egypt
Abstract. Reference evapotranspiration (ETo) is a vital factor in water resources managing and planning. Various estimation methods have been developed for different climatic regions and according to the available data. Therefore, the reliability of such methods depends upon climatic conditions. The present investigation evaluates four temperature based methods: FAO Blaney-Criddle (BC), Turc, Jensen-Haise (JH) and Hargreaves (HG), and two radiation based methods: FAO-radiation (FAO-rad) and Priestley-Taylor (PT) in comparison with the FAO-PM method under arid conditions of Libya. In order to select the best ETo method, the percentage error of estimate (PE), the root mean square error (RMSE), and mean bias error (MBE) were calculated. The obtained ETo values (FAO-PM and the average of best-estimated monthly ETo) were utilized to generate spatial distribution maps of ETo with the aid of Kriging technique. Statistical analysis of the obtained results revealed that, Turc equation fitted well for the northern part of the study area, which include Nalut, Zuara, Mosrata, Sirt, Shahat, Derna, Tubruk, Hon, Galo and Gagbub. While for southern zone, HG equation performed better for Opari and Tazirbu, BC equation for Kufra and Ghadames, FAO-Rad equation for Sebha; and JH equation for Ghat.
Keywords. Evapotranspiration, arid climate, FAO Penman-Monteith method (FAO-PM), kriging
Introduction. Reference
evapotranspiration (ETo) is the synchronized transpiration and
evaporation processes in a soil-plant system (Tabari et al., 2011). ETo has a great importance in irrigation scheduling,
Ekologiya & Stroitelstvo | № 1, 2018 | DOI 39
together with climatological and hydrological studies (Sentelhas et al., 2010). Several methods have been developed to estimate ETo and they vary in required climatic-data. For many regions and climatic conditions, the Penman-Monteith method (P-M) has proved to be the best method and gives consistent ETo values (Allen et al. 2005, 2006). Thus, it is widely applied in various fields, among which are agronomy and irrigation management (Alexandris et al. 2006; Landeras et al, 2008; Du, et al., 2010; Hassanli, et al., 2010; Sentelhas et al. 2010).
In case of limited data required for P-M method, especially in the developing countries, significant attention has been paid to the evaluation of simple ETo methods and their application. The FAO-Penman-Monteith method (P-M) has proved of superior performance (Jensen et al. 1990; Allen et al. 1998; Abdelhadi et al., 2000; Hargreaves and Allen 2003; LopezUrrea et al., 2006; Gavilan et al., 2007 ; Trajkovic and Kolakovic, 2009 ; Martinez Thepadia, 2010). Therefore, the P-M method was used in this study to evaluate the reliability of the other ETo estimating methods. P-M method uses temperature, relative humidity, wind speed and solar radiation/sunshine to estimate ETo. The main limitation of the P-M method is the necessity for various weather data parameters (i.e., air temperature, humidity, wind speed, and solar radiation) which might be not available. Such limitation may exist particularly in developing countries (Droogers and Allen, 2002; Gocic and Trajkovic 2010; Maeda et al. 2011; Tabari et al. 2011). This is because of the difficulties in setting-up of weather stations, their maintenance and expenses (Sentelhas et al. 2010). One way to overcome such problem, is to utilize the ETo equations that require fewer meteorological parameters, several methods are developed to estimate ETo. But the simpler methods might give inconsistent ETo values (George et al., 2002; Xu and Singh, 2002; Lu et al., 2005; Temesgen et al., 2005; Nandagiri and Kovoor, 2006). Therefore, simpler equations must be evaluated against the P-M method or lysimetric measurements in order to find out the most suitable ETo method for each region where weather data are inadequate to apply the P-M method (Trajkovic and Kolakovic, 2009).
The present work was carried out to assess the performance of six simple ETo methods that require less readily available data against the P-M method in order to select the most suitable method to estimate ETo values in Libya. Maps representing the distribution of the ETo values and their relation to elevation above sea level is performed.
Materials and methods. The present investigation was carried out in the country of Libya (area of 1,760,000 km2) with a Mediterranean Coastline of nearly 1,800 kilometers. Seventeen
meteorological stations were selected to represent the different regions of the country. Figure 1 shows the distribution of chosen stations (as a point map); the geographic characteristics of these stations are presented in Table 1.
10°0'0"E 15°0'0"E 20°0'0"E 25°0'0"E
10°0'0"E 15°0'0"E 20°0'0"E 25°0'0"E
Figure 1. Study area and location of the weather stations.
The climatic data of the study area showed that the monthly mean-temperature varies from 12 to 30 °C. While the relative humidity ranges between 15 to 60 % (Figure 2).
Reference évapotranspiration ( ETo ) calculations. Seven different methods were used to estimate (ETo) at the studied seventeen locations. Applied methods were classified into their major methods as follows; a) one combination method [1- FAO 56-Penman-Monteith (PM)], b) four temperature methods [2- FAO Blaney-Criddle (BC), 3- Turc, 4- Jensen-Haise (JH) and 5- Hargreaves (HG)]; c) two radiation methods [(6-FAO radiation (FAO-Rad), and 7- Priestley Taylor (PT)].
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Table 1
Location, elevation, latitude and longitude of the studied meteorological stations
-■-T- mean -*-RH
Station Name
Nalut
Zoara
Tripoli
Mosrata
Sirt
Shahat
Derna
Tubruk
Ghadame
s
Sebha
Hon
Galo
Gagbub
Opari
Ghat
Tazirbu
Kufra
Elevation (m) (Above sea level)
621 3 81 32 13 649 26 50 346 432 263 45 01 463 692 261 436
Latitude (Degrees
and Minutes)
31° 32° 32° 32° 31° 32° 32° 32° 30° 27° 29° 29°
25° 25° 24°
52' 53' 40' 19' 12' 48' 47' 06' 06' 01' 07' 01'
29 45' 26° 36'
08° 40° 13°
Longitude (Degrees
and Minutes)
10°
12° 13° 15° 16° 21° 22° 23° 09° 14° 15° 21° 24° 12° 10° 21° 23°
59' 05' 09' 03' 35' 53' 35' 56' 29' 27' 57' 32' 32' 47' 09' 05' 18'
■g 15
I .„
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month
Figure 2. Average mean temperature and relative humidity in Libya.
The combination methods for ETo estimation depends upon recorded temperature, relative humidity, wind speed and solar radiation or sunshine. If such data are available, the P-M method ranked the first to estimate (ETo) between all other combination methods. As mentioned above, FAO 56-PM method was selected in this study to be the reference method. The equations of each method are presented in Table 2
35
65
30
60
25
55
20
50
45 ®
40
Table 2
Methods and equations used to estimate reference evapotranspiration (ETo)
Method Equation Explication
Combination method
FAO 56-PM 0.408 Д(Д„ - G)+y 90°273 u2 (e, - ea ) ETo - ( mean + ) Д + /.(1 + 0.34 .?У2 ) Tmax: maximum air temperature. Tmin : minimum air
Temperature methods temperature.
BC ETo = a+ bB* P (0. 4 6 T + 8 . 1 3 ), wind speed. Rn: net radiation.
a - 0.0043.RHmn - n / N-1.41 Rs: solar radiation.
TURC ETo - 0.013 Tmean (R + 50) (T«„ +15) s if RH > 50 % ETO - 0.013 Tmean (R + 50 )f 1 + (50 ~ Ш )1 (Tmean + 15)' ' \ 70 J if RH < 50 % n: actuel Daily Sunshine duration (hours). N: maximum possible daily sunshine hours. ea: actual vapor pressure. es: saturation vapor pressure (kPa). es - ea: saturation vapour pressure deficit [kPa]. RHmin: minimum relative humidity.
JH ETo - CT (T - Tx )R S
HG ETo = 0№23RAjTD(Tmean + 17.8) RH: relative humidity. G: soil heat flux density
Radiation methods (MH/ml per day).
FAO-Rad ETo - a + b\ Д R I 1Д + Г s ) A: slope vapour pressure curve [kPa °C-1]. y. psychrometric constant
PT ETo - a 1 Д jRn - G) я(д + ГУ n ' [kPa °C-1].
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Statistical analysis. In order to evaluate ETo values using the different methods in comparison with FAO P-M method. Data of all methods were tested on basis of the following statistical parameters (El-Mageed, T.A.A. and El-Wahed, M.A., 2014).
Percentage error of estimates (PE) calculated by the following equation:
ETo values calculated by different methods PE = ---.
ETo value calculated by P-M method
To evaluate The RMSD criterion was used to compare the estimated ETo values by different methods and P-M ETo method. The RMSD was selected as an appropriate ranking criterion because of the fact that this statistical parameter indicates the ability of equations and adjusted equations to accurately estimate reference evapotranspiration during all months (Trajkovic and Kolakovic, 2009:
"(V n ,[PM(ETo) - ETo RMSD = -(---e
d ]2)
where n - total number of observations. Mean bias error (MBE):
Xn_jPM(ETo) - EToestimated ] .
MBE -
MBE =
Z", [PM( ETo) - EToetim*ud ]
According to these statistical parameters, the criteria used to select the best method is to have the smallest
absolute deviation value. The criteria applied to select the more suitable method was associated with the smallest absolute deviation value obtained.
GIS application. Elevation Data. The digital elevation model (DEM) used in this study is the SRTM (NGA SRTM «finished» 3arcsec) data, which was retrieved freely from
https://lpdaac.usgs.gov. Then, it was clipped to the boundary of the study area.
Geostatistical analysis. Kriging analysis was applied to generate the ETo maps of the study area. Where the point map of the stations was utilized in geostatistical analysis to generate spatial distribution maps of ETo. Where one map was generated to represent the ETo values of the P-M method. On the other hand, the estimated ETo values for each station based on the relevant best-method were used to generate ETo map for the study area.
Results and discussion. Evaluation of estimation methods. For the studied stations, the monthly ETo values were estimated using the tested seven equations. Then, the obtained values from the six simple ETo method were compared with that values of P-M method. The calculated statistical parameters i.e., PE, MBE and RMSD for all methods in each station as compared to the P-M method are given in Table 3.
Table 3
Summary statistics of PE, MBE and RMSD and best ETo estimation method
for the studied locations
n
n
Best method:
Station Based on PE Based on RMSD Based on MBE
PE RMSD MBE
Nalut Turc 1 BC 0.46 Turc 0.02
Zoara Turc 1.01 HG 0.20 Turc -0.05
Tripoli HG 1.01 Turc 0.42 HG -0.05
Mosrata PT 0.98 Turc 0.21 PT 0.07
Sirt Turc 1.01 Turc 0.22 Turc -0.03
Shahat Turc 1.01 Turc 0.07 Turc -0.01
Derna PT 0.99 Turc 0.35 PT 0.04
Tubruk Turc 1.02 Turc 0.21 Turc -0.09
Ghadames BC 1.02 BC 0.41 BC -0.10
Sebha FAO-Rad 1 FAO-Rad 0.33 FAO-Rad 0.02
Hon Turc 1.01 Turc 0.45 Turc -0.05
Galo Turc 1.02 Turc 0.49 Turc -0.11
Gagbub BC 1 HG 0.20 BC 0.00
Opari HG 1.07 HG 0.37 HG -0.35
Ghat Turc 1.05 Turc 0.60 JH 0.16
Tazirbu HG 1.1 HG 0.49 HG -0.48
Kufra BC 1.03 FAO-Rad 0.45 BC -0.21
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As shown in Table 3, most of the best methods exceeded ETo values estimated by the P-M method. The overview of all results revealed that the
Turc and B-C methods perform better among the stations. The selection of the best method was done according to the values of PE, MBE and RMSD statistical parameters. Thus, for each station, the method having best values in two or three statistical parameters were assigned as the best method. Furthermore, generally, the study area could be divided into two zones; Northern and Southern ones (Figure 3).
10°0'0"E 15°0'0"E 20°0'0"E 25°0'0"E
™c pt BC V*- TURC y^SrURC ) N k
WL TURC fc
FAO RAtt^
' HARG
\ N TURC turc ♦ ♦ Northern Zone
FAO RAD
HARG ♦
• Southern Zone HARG
URC ♦ FAO RAD ♦
♦ Station
Elevation (m) M High : 2195
Low: -55 250 125 0 250 Km
10-0'0-E 15°0'0"E 20°0'0"E 25"0'0"E
Figure 3. ETo zones and the best ETo methods overlaid on DEM of the study area
(A) Northern zone: which extended from the coastal line towards south including the following locations: Nalut, Zuara, Mosrata, Sirt, Shahat, Derna, Tubruk, Hon, Galo and Gagbub where the best method was Turc, while for Tripoli the best method was HG.
(B) Southern zone: as for Opari and Tazirbu, the best method was HG; BC for Kufra and Ghadames; FAO-Rad for Sebha; and JH for Ghat. The poor performance of the J- H method obtained in this study is in a good agreement with the results found in Serbia (Trajkovic and Kolakovic 2009), Florida (Irmak et al. 2003a, b) and Iran (Tabari et al. 2011).
ETo Mapping. Values of evapotranspiration estimated by the P-M method and by the best method for each station were interpolated using ordinary kriging to generate ETo maps of the study area, Figure 4. As shown in Figure 4a, the ETo
value ranges from 3.4 to 7.1 (mm day-1), while in case of the best methods (Figure 4b) ETo ranges between 3.4 and 7.4 (mm day-1), and generally, ETo value increases from north to south. This could be resulted as the distribution of mean air-temperature that also increases towards south.
1IWE liWE 20'0'0"E 25'0'0"E _I_I_I_I_
-1-I-1-1-
1IWE liWE 20'0'0"E 25'0'0"E
a
10°0'0"E 15'0'0"E 20°0'0"E 25'0'0"E
N ► A
•
ETo (mm/day)
■ 3.4-4.5 4.5-5.5 5.5-6.5 250 125 0 250 Km
6.5-7.4
-1-1-1-1-
KT'O'CE 15E0'0"E 20°0,0"E 25E0,0"E
b
Figure4. Spatial distribution of ETo (mm day-1) in the study area: a — using P-M method; b — most reliable estimation method for each station
Conclusion
Seven methods were applied to estimate reference evapotranspiration using weather data from seventeen stations separated at whole Libya. The FAO P-M method was used as the standard of comparison for evaluating the other six methods for all stations. It was concluded that there are two regions
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of different climatological
characteristics namely: Region (1): Nalut, Zuara, Mosrata, Sirt, Shahat, Derna, Tubruk, Hon, Galo and Gagbub where the most reliable method was Turc. Region (2): Opari and Tazirbu with HG as best method, BC for Kufra and Ghadames, FAO-Rad for Sebha; and JH for Ghat. Furthermore, the estimated ETo values by P-M method and by the best method for each location were interpolated to generate ETo maps of the study area which could be employed in various decisions at regional scale. Finally, realized ETo equations can be used according the meteorological data availability for each region.
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Дополнительная информация
Сведения об авторах:
Махмуд Мохамед Али Абдель-Азим, кандидат технических наук; кафедра агроинже-нерии факультета сельского хозяйства; Университет Файюма; г. Файюм, Арабская Республика Египет; e-mail: mma12@fayoum.edu.eg.
Али Габер Махмуд, кафедра почвоведения и водных ресурсов факультета сельского хозяйства; Университет Файюма; г. Файюм, Арабская Республика Египет. T^n 0 В этой статье под лицензией Creative Commons Attribution 4.0 International License, которая разрешает копирование, распространение, воспроизведение, исполнение и переработку материалов статей на любом носителе или формате при условии указания автора(ов) произведения, защищенного лицензией Creative Commons, и указанием, если в оригинальный материал были внесены изменения. Изображения или другие материалы третьих лиц в этой статье включены в лицензию Creative Commons, если иные условия не распространяются на указанный материал. Если материал не включен в лицензию Creative Commons, и Ваше предполагаемое использование не разрешено законодательством Вашей страны или превышает разрешенное использование, Вам необходимо получить разрешение непосредственно от владельца(ев) авторских прав.
Для цитирования: Махмуд М.А., Али Г.М. Районирования территории и оценка репрезентативности расчетных методов величины эвапотранспирации для условий аридного климата // Экология и строительство. - 2018. - № 1. - C. 39-45.
Additional Information
Information about the authors:
Mahmoud Mohamed Ali Abdel-Azim, candidate of technical sciences, Agricultural Engineering Department, Faculty of Agriculture; University Of Fayoum; University zone, Fayoum, Arab Republic of Egypt; e-mail: mma12@fayoum.edu.eg.
Ali Gaber Mahmoud Soil and Water Department, Faculty of Agriculture; University Of Fayoum; University zone, Fayoum, Arab Republic of Egypt.
T^n 0 This article is licensed under a Creative Commons Attribution 4.0 International License, i^Wm which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Crea tive Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
For citations: Mahmoud M.A., Mahmoud A.G. Mapping and evaluation of reference evapotranspiration methods under arid conditions // Ekologiya i stroitelstvo. - 2018. - № 1. - Р. 39-45.
Mahmoud Mohamed Ali Abdel-Azim, candidate of technical sciences, Agricultural Engineering Department, Faculty of Agriculture; University Of Fayoum; University zone, Fayoum, Arab Republic of Egypt; e-mail: mma12@fayoum.edu.eg.
Ali Gaber Mahmoud Soil and Water Department, Faculty of Agriculture; University Of Fayoum; University zone, Fayoum, Arab Republic of Egypt.
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
For citations: Mahmoud M.A., Mahmoud A.G. Mapping and evaluation of reference evapotranspiration methods under arid conditions // Ekologiya i stroitelstvo. - 2018. - № 1. - Р. 39-45.
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