Water Resour Manage DOI 10.1007/s11269-014-0782-0
Analysis of the Effect of Missing Weather Data on Estimating Daily Reference Evapotranspiration Under Different Climatic Conditions M. Majidi & A. Alizadeh & M. Vazifedoust & A. Farid & T. Ahmadi
Received: 9 August 2013 / Accepted: 25 August 2014 # Springer Science+Business Media Dordrecht 2015
Abstract Numerous equations exist for estimating reference evapotranspiration (ETo). Relationships were often subject to rigorous local calibration, hence having limited global validity. The Penman–Monteith (P − M) equation is widely perceived as the best equation for estimating daily and monthly ETo in all climates. The main shortcoming of the P − M equation is that it requires numerous weather data that may not always be available. This study evaluates the methods to estimate missing data in the context of their influence on the performance of the ETo equations. The performance of other ETo equations under missing data are also compared. ETo equations are ranked individually in semi − humid and semi − arid climates based on their accuracy. Results indicate that the P − M equation is more sensitive in semi − arid climate than semi − humid climate under missing data conditions. The accuracy of the P − M equation under these conditions increases remarkably if any available relationships between dew point and minimum temperatures and also long–term average wind speed for each station are exploited. Finally, the minimum data requirements necessary for adequate performance of the P − M equation are air temperature for semi − humid climates, air temperature and wind speed for semi − arid climates, and the availability of a relationship between dew point and minimum temperature, especially for semi − arid climate. In absence of the satisfaction of such minimum requirements, the Hargreaves–Samani equation is preferable for semi − humid climates and the Hargreaves equation modified by Droogers and Allen (2002) for semi − arid climates. Keywords Missing weather data . ETo equations . Dew point temperature . Wind speed
1 Introduction Water scarcity issues are a major problem in many parts of the world affecting quality of life, the environment, industry, and the economies of developing nations. This can be attributed to M. Majidi (*) : A. Alizadeh : A. Farid : T. Ahmadi Water Engineering Department, Faculty of Agriculture, Ferdowsi University of Mashhad, Mashhad, Iran e-mail:
[email protected] M. Vazifedoust Water Engineering Department, Faculty of Agriculture, University of Guilan, Guilan, Iran
M. Majidi et al.
climate change, increasing demand for freshwater by the competing users in different sectors and more importantly the environmentally induced problems such as desertification and overexploitation of the existing water resources (Pereira 2005). Irrigated agriculture accounts for about 70 % of the available fresh water globally (Fischer et al. 2006). Dependency on water for future crop production has become a major constraint for sustainable food production in the developing countries, e.g., in Iran, more than 90 % of food production is from irrigated areas with about 90 % of annual extractable water getting allocated to agriculture (Esmaeili and Vazirzadeh 2009). In such circumstances, it is necessary to improve crop productivity and agricultural water management. One of the most important and key factors in agricultural water management and increasing crop productivity is the accurate estimation of plant water requirements. The urgent need to develop a standard, precise and globally acceptable method of estimating reference evapotranspiration for accurate computation of crop water requirements has been stressed by many authors (Doorenbos and Pruitt 1975; Doorenbos and Kassam 1979; Chiew et al. 1995; Allen et al. 1998; Xu and Singh 2002). Many of these models are subject to local calibration which restricts their implementation for other area and hence their global applicability. Due to the higher performance of FAO–56 Penman–Monteith (P–M) model in different parts of the world when compared with other models, it has been accepted as the sole method of computing reference evapotranspiration from meteorological data (Jensen et al. 1990; Allen et al. 1998; Hess 1998; Ravelli and Rota 1999; Zhao et al. 2005; Garcia et al. 2006; Gavilán et al. 2006; Abghari et al. 2012; Perugu et al. 2013; Kisi and Cengiz 2013). Many other studies have confirmed the superiority of this equation (Ventura et al. 1999; Pereira and Pruitt 2004; Lopez– Urrea et al. 2006; Gavilán et al. 2007; Trachkovich and Kolakovich 2009b). The P–M equation can be used globally without any local calibrations due to its physical basis and it is a well documented equation that has been tested using a variety of lysimeters (Trachkovich and Kolakovich 2009a, c). The main shortcoming of the P–M equation is that it requires a data input of numerous weather variables that are not always available for many locations such as developing countries, since automatic weather stations are not available in most cases. This makes it very difficult to conveniently estimate reference evapotranspiration in such countries. To overcome this problem, Allen et al. (1998) recommend procedures to estimate the parameters of the FAO–56 P–M equation when some weather data were missing. The absence of weather data also can be overcome by using other ETo equations or models with fewer weather data requirements (Rahimikhoob et al. 2012, 2013; Rahimikhoob 2014; Ababaei 2014; Citakoglu et al. 2014). The most important weather data which have been regularly investigated are solar radiation, wind speed and vapor pressure data. Where sunshine data are lacking, the difference between the maximum and minimum temperature can be used successfully for the estimation of solar radiation (Hargreaves et al. 1985a; Allen 1996). So far, a few studies have been conducted for calculating reference evapotranspiration when vapor pressure and wind speed data are missing. Trachkovich and Kolakovich (2009c) recommended using local default wind speed and minimum temperature when wind speed and vapor pressure data were not available. However, these procedures may not be applicable in all climates. Hence, the behaviour of the P–M method in various climates under missing data conditions is still unknown. Previous studies mostly focused on monthly time step for adopting the appropriate ETo equation in limited data condition. However, daily weather data are necessary for real–time irrigation scheduling. Therefore, there is an urgent need to evaluate more logical scenarios for estimating daily reference evapotranspiration under missing data conditions. The main concern of this research was to shed light on the question which equation estimates ETO most accurately under missing
Analysis of the Effect of Missing Weather Data on Estimating Daily
data and different climatic conditions. Thus, an attempt was made to compare and evaluate behavior of the conventional reference evapotranspiration methods under missing data and alternative procedures to estimate this missing data. The main objectives of this study were i) ranking the most appropriate models to achieve the reliable estimation of reference evapotranspiration in different climatic conditions under missing weather data, and ii) determining the best alternative approaches to estimate the missing data.
2 Material and Methods 2.1 Study Area and Datasets The study area is located between 30°31′ N to 38° 14′ N latitude and 56°03′ E to 61°16′ E longitude with semi–arid to semi–humid climate. The fifteen weather stations selected for this study are located in Southern, Razavi and Northern Khorasan Provinces, Iran. For each station daily climatic data was recorded since its installation. The characteristics and long–term mean value of weather data for each station are given in Table 1. 2.2 Estimating Missing Solar Radiation Data Solar radiation is rarely measured at the most weather stations (Trachkovich and Kolakovich 2009c). However, sensors used in pyranometers and net radiometers are very sensitive and expensive and they deteriorate rapidly in comparison with other sensors (Llasat and Snyder 1998). Hence, this parameter is frequently estimated using the Angstrom equation (Allen et al. 1998; Trachkovich and Kolakovich 2009c). n Ra ð1Þ Rs ¼ a þ b N Table 1 Weather stations description Station
Climate
Altitude (m)
Latitude (°N)
Temperature (°C)
Relative humidity (%)
Rainfall (mm)
Wind Speed at 2 m height (m/s)
Mashhad
Semi humid
992.22
36° 16′
14.20
55.10
255.04
1.58
Quchan
Semi humid
1287.00
37° 10′
12.85
55.51
311.08
1.22
Chenaran
Semi humid
1176.00
36° 32′
13.46
48.20
208.12
2.25
Bojnord
Semi humid
1112.00
37° 28′
13.33
58.91
270.00
1.71
Nishabur
Semi humid
1213.00
36° 16′
14.42
48.46
236.63
0.84
Torbat–e Heydarieh
Semi humid
1450.80
35° 16′
14.30
46.96
274.40
1.46
Gonabad
Semi arid
1056.00
34° 21′
17.32
37.70
143.90
1.40
Sabzevar
Semi arid
972.00
36° 13′
17.47
41.08
189.56
2.43
Sarakhs
Semi arid
235.00
36° 33′
17.90
47.68
187.37
1.60
Kashmar
Semi arid
1109.70
35° 12′
17.78
39.00
204.11
1.08
Birjand
Semi arid
1491.00
35° 25′
16.50
36.64
170.41
1.96
Ferdows
Semi arid
1293.00
34° 10′
17.23
36.24
146.78
1.82
Qaen
Semi arid
1432.00
33° 43′
14.37
37.84
175.00
1.88
Torbat–e Jam
Semi arid
950.40
35° 15′
15.68
45.38
174.66
2.94
M. Majidi et al.
where Rs is the solar radiation (MJm−2 day−1), n is the sunshine hours (h day−1), N is the daylight hours (h day−1) and Ra is the extraterrestrial radiation (MJm−2 day−1). In this study, the sunshine data are used as substitute for the measured solar radiation data and it is known as the standard procedure when there is no measured radiation data (Allen et al. 1998; Todorovic 1999; Vanderlinden et al. 2004; Nandagiri and Kovoor 2006; Cai et al. 2007). The difference between maximum and minimum temperature could be used to estimate solar radiation in which sunshine data are not available (Hargreaves et al. 1985a): Rs ðT Þ ¼ 0:16 ðT max −T min Þ0:5 Ra
ð2Þ
where Rs(T) is the solar radiation estimated from air temperature differences (MJm−2 day−1), Tmax and Tmin are the maximum and minimum air temperature (°C), respectively. 2.3 Estimating Missing Vapor Pressure Data The determination of actual and saturation vapor pressure values is necessary to estimate the deficit vapor pressure. Note that it is difficult to measure the actual vapor pressure accurately. Therefore, the actual vapor pressure usually can be derived from the dew point temperature. In the absence of dew point temperature, the estimate of actual vapor pressure can be made by assuming minimum air temperature is equal to dew point temperature (Jensen et al. 1990; Kimball et al. 1997). Substituting minimum daily temperature with dew point, actual vapor pressure is specified as follows: 17:27 T min ð3Þ VPðT min Þ ¼ 0:611 exp T min þ 237:2 where VP(Tmin) is the actual vapor pressure obtained from minimum air temperature (kPa). Equation 3 is suitable for humid climates and may not be applicable in arid climates. Therefore, in this study the relationship between dew point and minimum temperatures was firstly extracted for each station, each climate and the whole study area. Then, based on obtained relationships the dew point values were calculated via minimum temperature and then substituted in Eq. 3 instead of Tmin. 2.4 Estimating Missing Wind Speed Data Wind speed is one of the least easily estimated and least available parameters needed for estimating ETO (Trachkovich and Kolakovich 2009b, c). Three approaches were used to estimate missing wind speed data. First, considering long–term average wind speed value of each station instead of daily wind speed data. Second, using estimated long–term average wind speed value of entire study area instead of daily wind speed. Third, substituting default world wind speed of 2 m/s in lieu of daily wind speed. 2.5 ETO Estimation Equations The equations for estimating ETO are given in Table 2. 2.6 Application of Equations Under Missing Data Condition ETO calculation under missing data condition needs utilizing wide variety of approaches to estimate required data. Thus, various scenarios were defined in which one or more data
Analysis of the Effect of Missing Weather Data on Estimating Daily Table 2 ETO equations used in this study Method
Thornthwaite
Equation
Symbol in this paper 0
1
B C 10T B C ET o ¼ 16N 360 @ 12 A 1:514 ∑ ð0:2T k Þ
12
0:016 ∑ ð0:2T k Þ1:514 þ 0:5
THORNT
k¼1
k¼1
Hargreaves–Samani
ETo,hair =0.0023×0.408×Ra ×(Tavg +17.8)×TD0.5
HARG 1
Hargreaves modified by ET o;har;Tra ¼ 0:0023 0:408 Ra ðT max −T min Þ0:424 T max þT min Trajkovic (2007) þ 17:8
HARG 2
Hargreaves modified by ETo,har,D;A =0.0013×0.408×Ra ×(Tavg +17)× (TD−0.0123P)0.76 Droogers and Allen (2002)
HARG 3
Blaney – Criddle
ETo =p(0.46Tavg +8.13)
BLANY C
Turc
ETo =0.013×(23.88×Rs +50)×Tavg ×(Tavg +15)−1
TURC 1
Turc modified by Trachkovich and Kolakovich (2009a, b, c) Jensen – Haise modified
ETo =Cu0.013×(23.88×Rs +50)×Tavg ×(Tavg +15)−1 Cu =−0.0211×U22 +0.1109×U2 +0.9004 ETo =CT ×(Tavg −Tx)×0.408Rs 1 CT ¼ h þ 365 45−ð137 Þ ðes;max −es;min Þ h T x ¼ −2:5−0:14 es;max −es;min 500 max þ429:41 es;max ¼ exp 19:08T T max þ237:3 min þ429:41 es;min ¼ exp 19:08T T min þ237:3
TURC 3
ETo =CT ×(Tavg −Tx)×KT ×0.408Ra ×TD0.5 S 0:5 K T ¼ 0:075 TD h i
JH 3
2
Penman–Monteith
ET o ¼ 0:408ΔðRn −GÞ
þγ
900 U VPD ðT avg þ273Þ 2 Δþγ ð1þ0:34U 2 Þ
JH 1
PM
ETO = reference evapotranspiration (mm day−1 ), Δ = slope of the saturation vapor pressure curve (kPa °C –1 ), Rn = net radiation (MJ m−2 day−1 ), G = soil heat flux (MJ m−2 day−1 ), γ = psychometric constant (kPa °C−1 ), T = mean monthly air temperature (°C), Tavg = mean air temperature (°C), U2 = average 24–h wind speed at 2 m height (m s−1 ), VPD = vapor pressure deficit (kPa)., N = maximum possible duration of sunshine (hours), n = actual duration of sunshine (hours), Tx = mean air temperature in the xth month (°C); x=1, 2,. . . 12., Tmax = maximum air temperature (°C), Tmin = minimum air temperature (°C), Ra = extraterrestrial radiation (MJ m−2 day−1 ), h = altitude of location (m)
intentionally omitted and estimated via the mentioned procedures. Finally, after substituting estimated data by the measured ones in ETO equations, the obtained values are evaluated based on the P − M equation using complete data. Missing data were dew point (Td) (or vapor pressure), wind speed and solar radiation. Equation 2 was used to estimate solar radiation. Four strategies were used for substituting dew point data including i) applying Tmin instead of Td, ii) estimating Td by Tmin for each station, iii) estimating Td by Tmin for each climate, and v) estimating Td by Tmin for the whole study area. Three strategies were used to substitute missing wind speed data including i) applying long–term average value of each station, ii) applying long–term average value of whole study area, and iii) applying the value of 2 m/s (world mean wind speed). Finally, 57 scenarios enlisted in Table 4 were developed from the combination of the mentioned approaches.
M. Majidi et al.
2.7 Evaluation Criteria The weighted root mean square difference (WRMSD) and the model efficiency (ME) criteria are used to compare and evaluate estimated ETO values via the mentioned equations. The WRMSD is determined as follows (Jensen et al. 1990): WRMSD ¼ 0:7 ð0:67RMSD þ 0:33ARMSDÞ þ 0:3 ð0:67RMSDP þ 0:33ARMSDP Þð4Þ where the RMSD and the altered RMSD are calculated by following equations and p stands for the pick month (Trachkovich and Kolakovich 2009a): 2 M 30:5 X 2 ET −ET PM ;FULL;i eq;i 7 6 6 i¼1 7 7 RMSD ¼ 6 ð5Þ 6 7 M 4 5 2
M X
ET PM;FULL;i −ET eq;i 6 6 i¼1 ARMSD ¼ 6 6 M 4
2
30:5 7 7 7 7 5
ð6Þ
where ET PM;FULL is the mean estimated ETO value by the P–M equation with complete data, M is the total number of observations and b is the regression line slope between the observed and estimated values of ETO through the P–M equation (b=ETPM,FULL/ETeq). The RMSD and ARMSD values are calculated for all months and for the peak month, separately. The WRMSD values indicate the ability of equations to accurately estimate reference evapotranspiration during all months (47 % weight, i.e., the coefficient 0.7 × 0.67), the ability to accurately estimate peak ETO (20 % weight, i.e., the coefficient 0.3 × 0.67), and the ability to be adjusted using a linear multiplier (33 % weight) (Trachkovich and Kolakovich 2009a). Therefore, the ETO equations were ranked based on these criteria. Additionally, the model efficiency (ME) was used to measure efficiency of the applied ETO equation (Nash and Sutcliffe 1970): M X
Efficiency ¼ 1−
ET PM ;FULL;i −ET eq;i
2
i¼1 M X
ET PM ;FULL;i −ET eq;m
2
ð7Þ
i¼1
A model efficiency of 90 % represents a satisfactory level of the model or the equation of interest. The values between 80 and 90 % show good efficiency, whereas the values under 80 % provide no satisfactory level of the model (Chauhan and Shrivastava 2009).
3 Results and Discussion 3.1 Estimation of Dew Point (Td) and Minimum Temperature (Tmin) Estimation process was carried out for all historical values of dew point (Td) and minimum temperature (Tmin) at all weather stations. The obtained relationships for each station, stations with similar climate and the whole area were shown in Table 3.
Analysis of the Effect of Missing Weather Data on Estimating Daily Table 3 Dew point (Td) and minimum air temperature (Tmin) calibration equations Station/Area
Calibration equation
Mashhad
T d ¼ −15:63213 0:966986−eð0:043926T min Þ
Coefficient of Standard determination deviation 0.971
0.981
0.975
0.942
ð0:74344T min −1:68437Þ
0.975
0.875
ð0:836769T min −1:09511Þ
0.990
0.753
0.918
1.275
0.971
0.944
ð0:669343T min −1:07688Þ ð1þ0:011145T min þ0:000509T 2min Þ
Quchan
Td ¼
Chenaran
Td ¼
Bojnord
Td ¼
Nishabur
2 3 Td =−1.16367+0.5788×Tmin −0.02098×Tmin +0.00057×Tmin
ð1þ0:01105T min þ0:00142T 2min Þ ð1þ0:0086638T min þ0:00038T 2min Þ
2 Torbat–e Heydarieh Td =−1.78206+0.560582×Tmin −0.006562×Tmin
Gonabad
2 Td =−2.11895+0.363633×Tmin −0.1312×Tmin +0.000594× 3 Tmin
0.953
0.905
Sabzevar
2 3 Td =−2.6515+0.49454×Tmin −0.00952×Tmin +0.00023×Tmin
0.972
0.825
Sarakhs
2 3 Td =−0.90573+0.8236×Tmin −0.0374×Tmin +0.000993×Tmin
0.942
1.230
Kashmar
2 3 Td =−3.00173+0.54158×Tmin −0.0132Tmin +0.00038×Tmin
0.961
0.981
Birjand
2 3 Td =−3.718+0.360147×Tmin −0.00553×Tmin +0.000304×Tmin 0.952 ð0:016448174T nib Þ 0.779 T d ¼ −18:393086 1:147525−e
0.884
2 Td =−3.44302+0.435606×Tmin −0.002234×Tmin 2 3 Td =−1.72416+0.73095×Tmin −0.04048×Tmin +0.00122×Tmin 2 3 Td =−2.1674+0.5043×Tmin −0.01694×Tmin +0.000485×Tmin 2 3 Td =−1.1459+0.6982×Tmin −0.016727×Tmin +0.00029×Tmin 2 3 Td =−2.4981+0.51495×Tmin −0.01705×Tmin +0.00057×Tmin
0.964
0.924
0.940
1.245
0.970
0.866
0.978
0.844
0.963
0.885
Ferdows Qaen Torbat–e Jam Entire area Semi humid climate Semi arid climate
0.964
3.2 Ranking ETO Estimation Equations As mentioned before, ETO equations were evaluated in the 57 defined scenarios of missing or available required data. Different defined scenarios were individually ranked for each climate condition based on WRMSD (George et al. 2002; Jensen et al. 1990 and Trachkovich and Kolakovich 2009a) and shown in Table 4. The result strongly supports performance of the P − M equation even in the absence of the complete data due to its physical base (Fischer et al. 2006; Jensen and Haise 1963; Martinez–Cob and Tejero–Juste 2004; Trachkovich and Kolakovich 2009a, b, c and Turc 1961). The comparison of WRMSD values for the P–M scenarios indicated that the P–M equation gave better results in the semi–humid climate rather than semi–arid climate under missing data condition. It can be concluded that the P–M equation showed more sensitivity to missing data in the semi–arid climates. The model efficiency (ME) values of P–M scenarios also indicated the satisfactory level of the P–M equation under missing data. Table 4 also confirmed better performance of the Hargreaves, Jensen–Haise and Blaney–Cridle equations in the semi–humid climate. The results showed that whenever solar radiation or sunshine hour data (PM1) were missing, the P–M equation gave quite good estimation close to ETO estimated values through the P–M equation with complete data (PMFull), in both semi–humid and semi–arid climates (WRMSD and ME for semi–humid and semi–arid climate conditions were 0.14, 0.12 mm/day, 99.5 and 99.7 %, respectively). These results were quite similar for each station and the whole study area as well. It is noteworthy that Eq. 2 revealed good efficiency to estimate missing solar radiation data. When the daily wind speed (U) data was not available, the P–M equation
Using dew point temperature relationship for each station
Using minimum temperature instead of dew point temperature for missing vapor pressure data
Description
Penman–Monteith
Eto equation
0.44 0.44 0.46 0.46
Rs, VP, U* Rs, VP, U** Rs, VP, U*** VP
PM21
PM22
PM23
PM24
0.29
0.44
VP, U***
0.58
Rs, VP, U***
PM15
PM20
0.61
Rs, VP, U**
PM14
VP, U**
0.65
Rs, VP, U*
PM13
PM19
0.59
VP, U***
PM12
0.27
0.62
VP, U**
PM11
0.42
0.66
VP, U*
PM10
VP, U*
0.47
Rs, U***
PM9
Rs, VP
0.46
Rs, U**
PM8
PM18
0.44
Rs, U*
PM7
PM17
0.45
Rs, VP
PM6
0.19
0.45
U***
PM5
VP
0.45
U**
PM4
PM16
0.45 0.43
VP U*
PM3
1.06
1.13
1.09
1.03
1.12
1.08
1.02
1.04
1.02
1.03
1.00
0.96
1.02
0.99
0.95
1.13
1.09
1.03
0.94
1.12
1.07
1.02
0.93
1.01
ME
97.50
94.51
95.64
96.94
95.17
95.93
97.31
98.12
99.14
94.49
93.84
93.10
94.02
93.12
92.35
94.45
95.61
96.95
96.26
95.00
95.81
97.24
95.66
99.50
Rank
6
30
26
14
17
18
10
4
2
36
38
41
37
40
42
31
28
15
19
22
21
11
24
1
WRMSD
0.29
0.98
0.86
0.73
0.77
0.88
0.71
0.39
0.34
1.21
1.18
1.14
1.11
1.13
1.12
0.80
0.86
0.73
0.85
0.77
0.84
0.71
0.83
0.12
1.04
1.00
1.00
1.02
1.05
1.00
1.02
1.05
1.05
0.89
0.87
0.89
0.90
0.89
0.89
1.05
1.00
1.02
0.87
1.05
1.00
1.02
0.87
1.00
ETqi/ETPm,FULL
ETqi/ETPm,FULL
WRMSD 0.15
Semi–arid
Semi–humid
PM2
Rs
Missing data
PM1
Name
Table 4 Summary of statistics and ranking of ETO equations under various missing data scenarios and climate condition
98.19
84.94
90.37
94.09
91.72
89.73
94.26
96.95
97.62
80.85
82.23
83.69
83.88
82.80
83.54
91.13
90.36
94.11
89.38
91.67
90.73
94.24
89.36
99.74
ME
Rank
2
38
29
14
18
37
11
7
4
45
43
42
39
41
40
24
32
16
28
19
27
12
25
1
M. Majidi et al.
Using dew point temperature relationship for each climate condition
Using dew point temperature relationship for whole area
Description
Table 4 (continued)
0.46 0.47 0.45 0.48 0.50 0.29 0.42 0.43 0.43 0.44 0.45 0.46
VP, U* VP, U** VP, U*** Rs, VP, U* Rs, VP, U** Rs, VP, U*** VP Rs, VP VP, U* VP, U** VP, U*** Rs, VP, U* Rs, VP, U** Rs, VP, U***
PM26
PM27
PM28
PM29
PM30
PM31
PM32
PM33
PM34
PM35
PM36
PM37
PM38
PM39
0.57
1.50 1.55 1.46
–
– Rs –
HARG 3
TURC 1
TURC 2
Hargreaves modified by Droogers and Allen (2002)
Turc
TURC 3
0.85
–
HARG 2
Hargreaves modified by Trajkovic (2007)
Turc modified by Trachkovich and
0.45
–
HARG 1
0.22
0.37 0.41
Rs, VP
PM25
Semi–humid
Missing data
Name
Hargreaves–Samani
Eto equation
1.15
1.11
1.10
1.11
1.05
0.86
1.13
1.09
1.03
1.12
1.08
1.02
1.04
1.03
1.17
1.12
1.06
1.16
1.11
1.05
1.07
85.67
86.42
88.90
90.73
96.08
85.76
94.63
95.78
96.80
95.27
96.07
97.32
97.55
98.86
93.02
94.86
96.61
93.87
95.34
97.36
95.79
50
56
53
35
46
23
29
22
16
13
12
9
5
3
34
33
20
32
27
8
7
1.35
1.44
1.42
0.70
1.45
0.87
0.80
0.86
0.73
0.79
0.86
0.71
0.38
0.33
0.80
0.86
0.74
0.79
0.87
0.72
0.35
1.12
1.06
1.08
1.00
0.92
0.76
1.05
1.00
1.02
1.05
1.00
1.02
1.05
1.06
1.04
0.99
1.01
1.04
0.99
1.01
1.04
Semi–arid
86.47
86.97
89.42
92.69
89.72
71.97
91.09
90.34
94.06
91.08
90.11
94.22
96.99
97.64
91.18
90.27
93.93
91.13
90.01
94.07
97.57
49
55
54
8
56
36
23
30
15
20
34
10
6
3
22
33
17
21
35
13
5
Analysis of the Effect of Missing Weather Data on Estimating Daily
0.70 0.78
Rs –
JH 3
JH 2
Jensen–Haise modified
0.82 0.62
3.63
– –
1.47
Rs, U***
TURC 10
–
1.41
U**
TURC 9
BLANEY C
1.49
Rs, U*
TURC 8
JH 1
1.43
U***
TURC 7
Blaney–Criddle
1.50
Rs, U**
TURC 6
Jensen–Haise
1.45
U*
THORNT
1.51
Rs
Semi–humid
TURC 5
Missing data
TURC 4
Name
Thornthwaite
Kolakovich (2009a, b, c)
Eto equation
0.68
0.67
0.67
0.67
0.67
0.66
0.67
0.66
0.65
0.65
0.19
1.29
90.09
88.41
89.65
87.90
89.22
87.40
90.25
88.40
87.69
85.66
66.51
83.53
44
43
39
45
57
51
47
52
48
54
49
55
0.86
0.82
0.70
1.18
2.77
1.34
1.32
1.36
1.34
1.38
1.36
1.37
0.78
0.79
0.77
0.79
0.77
0.78
0.76
0.78
0.75
0.76
0.29
1.10
Semi–arid
77.29
76.82
76.61
76.13
75.96
75.47
76.52
76.18
73.79
73.27
59.11
80.13
31
25
9
44
57
47
46
51
48
53
50
52
Rs=Missing solar radiation data (Eq. 2 was used as alternative method to estimate Rs), VP=Missing vapor pressure data (dew point temperature), U*=Using long–term average of wind speed of each station for missing wind speed. U**=Using long–term average of wind speed of whole area for missing wind speed. U***=Using U=2 m/s for missing wind speed
Description
Table 4 (continued)
M. Majidi et al.
Analysis of the Effect of Missing Weather Data on Estimating Daily
gave reliable results using long–term average wind speed value, especially in semi–humid climate. However, the modified Hargreaves by Droogers and Allen (2002) and Jensen–Haise equations gave better results in semi–arid climate in the absence of wind speed data. The P–M equation was not applicable if the dew point temperature data were not available in both semi– arid and semi–humid climates. In fact, application of minimum temperature instead of missing dew point temperature, as recommended by Trachkovich and Kolakovich (2009c), decreased the accuracy of the P–M equation. However, the P–M equation gave the most accurate results if the relationship between Tmin and Td (Table. 3) used to estimate missing dew point temperature. It can be concluded that the air temperature and dew point temperature data (measured or estimated using the recommended relationships) were the minimum required data necessary to successfully use the P–M equation in the semi–humid climate. Otherwise, the Hargreaves–Samani equation (Hargreaves and Samani 1985b) gave better results. On the other hand, in semi–arid climate the air temperature, dew point temperature data (measured or estimated using the recommended relationships) and also the long–term average wind speed value were necessary to successfully use the P–M equation. Otherwise, the modified Hargreaves (HARG3) and Jensen–Haise (JH1) equations are preferred. It can be seen from Table 4 that the P–M equation mostly tended to overestimate ETO in the semi–humid climates, while; in the semi–arid climates, the P–M equation produced mixed results but severely underestimated ETO which related to the scenarios consisting missing vapor pressure data. The Hargreaves–Samani equation overestimated ET O by 5 % in semi–humid climates. The ET O was underestimated by 0.3 % when using the modified Hargreaves equation in semi–arid climate. The Turc and Thornthwaite equations severely underestimated ETO in both semi–humid and semi–arid climates. The comparison of WRMSD values also indicated that using minimum temperature to estimate missing vapor pressure data has the highest negative influence on the performance of the P–M equation. Effect of missing wind speed data was less than missing vapor pressure data. Moreover, missing solar radiation data had the smallest effect on the accuracy of P–M equation. The Blaney–Criddle, Turc and Thornthwaite equations were ranked last in both climates due to their poor results. 3.3 Effect of Missing Data The effect of missing weather data on ETO estimations using the P–M equation were investigated here. 3.3.1 Effect of Missing Solar Radiation Data The results showed that the effect of missing solar radiation data was negligible on ETO estimates using the P–M equation. This equation gave accurate results when RS (only missing data) was calculated using Eq. 2 based on the minimum and maximum temperature in both semi–humid and semi–arid climates. 3.3.2 Effect of Missing Vapor Pressure (VP) Data The results showed that the P–M equation gave accurate estimations of ETO using estimated vapor pressure from the relationships between dew point and minimum temperatures for each station (PM16), each climate (PM32) and the whole study area (PM24) in semi–humid climates. If dew point and minimum temperature relationship was not available, the
M. Majidi et al.
Hargreaves–Samani equation was preferred to estimate ETO (Fig. 1) and the P–M equation is not suitable and applicable in semi–humid climate. The effect of adopting estimated dew point temperature to calculate ETO by the P–M equation was shown in Fig. 1. In this figure, mean WRMSD values of scenarios including missing vapor pressure data were presented. According to this figure, the accuracy of the P–M equation became less than the Hargreaves–Samani equation in condition of missing vapor pressure data. The highest WRMSD values for these scenarios revealed that the accuracy of the P–M equation decreased when number of missing data increased. Regarding to Fig. 1, the Hargreaves–Samani gave better result for ETO estimation in semi–humid climate, when vapor pressure data and relationship between minimum and dew point temperature were not available. Figure 2 showed the effect of missing vapor pressure data on the ETO estimates in semi–arid climate. Estimation of ETO using the relationship between dew point and minimum temperatures for each station (PM16) and each climate (PM32) gave more accurate results. As shown in Fig. 2 the effect of using estimated dew point temperature is more severe in semi–arid climate compared to semi–humid climate. Since the accuracy of the Penman–Monteith equation was reduced without vapor pressure data and relationship between minimum and dew point temperature, applying the modified Hargreaves equation (HARG3) was preferred. As discussed earlier, the P–M equation provided accurate estimation of ETO in the semi–arid climate if only missing vapor pressure data estimated by the relationship between dew point and minimum
Fig. 1 Effect of the relationship between dew point and minimum temperature on the accuracy of ETO estimations by the P–M equation in semi–humid climate
Analysis of the Effect of Missing Weather Data on Estimating Daily
Fig. 2 Effect of the relationship between dew point and minimum temperature on the accuracy of ETO estimations by the P–M equation in semi–arid climate
temperatures. Therefore, it is strongly recommended to estimate dew point temperature using this relationship to achieve accurate estimation of ETO. 3.3.3 Effect of Missing Wind Speed Data As stated earlier, three strategies were proposed to estimate missing wind speed data. The results showed that adopting long–term average wind speed value of each station (Us) was the best method to estimate ETO using P–M equation when wind speed data was not available (PM3) (Table. 4). Fig. 3 revealed that the wind speed had a crucial effect on the accuracy of ETO estimates by the P–M equation. Regarding to this figure, adopting long–term average wind speed value of each station instead of missing wind speed, produced relatively good results even if other weather data were not available. Therefore, the long–term average wind speed value of each station or the whole area was adequate to successfully use the P–M equation in semi–humid climate and missing wind speed data conditions. The application of default wind speed of 2 m/s instead of missing wind speed was not recommended due to its poor result. While, in the semi–arid climate using the modified Hargreaves equation (HARG3) provided more accurate estimates of ETO compared to the P–M equation when wind speed was missing (Fig. 4). Hence, there is no appropriate alternative to
M. Majidi et al.
Fig. 3 Effect of missing wind speed data and its alternative methods on the accuracy of ETO estimations by the P–M equation in semi–humid climate
replace the wind speed to apply in the P–M equation when it is not available in semi–arid condition. 3.3.4 Simultaneous Effect of Missing Solar Radiation, Vapor Pressure and Wind Speed Data In the semi–humid climate, the P–M equation provided the accurate estimation of ETO when there was a relationship between dew point and minimum temperatures (at any spatial scale) even if the wind speed and solar radiation data were missing. Otherwise, the Hargreaves–Samani equation (HARG1) was the best method for estimating ETO. While, in the semi–arid climate, the P–M equation has no applicability if the wind speed, solar radiation and vapor pressure data were missing simultaneously. The P–M equation was suggested if the maximum missing data were solar radiation and vapor pressure estimated from the relationship between dew point and minimum temperatures. Otherwise, the modified Hargreaves equation (HARG3) gave more accurate estimates of ETO (WRMSD =0.69 mm/day; ME=92.69 %).
4 Conclusions In this study, an attempt was made to evaluate the most appropriate methods for estimating ETO under missing data using various scenarios of weather data and ETO
Analysis of the Effect of Missing Weather Data on Estimating Daily
Fig. 4 Effect of missing wind speed data and its alternative method on the accuracy of ETO estimations by the P–M equation in semi–arid climate
equations. Some equations including Thornthwaite, Hargreaves, Blaney–Criddle (based on temperature data), Turc and Jensen–Haise (based on solar radiation data) were used to estimate ETO and compared with the P–M equation results as a standard using WRMSD criteria. The summarized conclusions of this study were presented in Table 5. This table shows which equation and alternative procedures could be used to achieve accurate ETO under missing data condition. Based on our results in this study, following concluding remarks can be made: i. It is strongly recommended to use the relationship between minimum and dew point temperature for estimating missing vapor pressure data for both semi–humid and semi–arid climates due to the highest effect of missing vapor pressure data on ETO estimates by the P–M equation. Otherwise, applying the Hargreaves–Samani in semi–humid and the modified Hargreaves by Droogers and Allen (2002) and Jensen–Haise equations in semi–arid climates were preferred. ii. It is strongly recommended using long–term average wind speed value of each station or the whole area as an alternative for missing wind speed in semi–humid climate. Unfortunately, there was no alternative method to estimate missing wind speed in semi–arid climate. Therefore, the modified Hargreaves equation by Droogers and Allen (2002) and Jensen–Haise equations were recommended to estimate ETO.
Modified Hargreaves by Droogers and Allen (2002) Modified Hargreaves by Droogers and Allen (2002)
Hargreaves–Samani
Penman–Monteith
Penman–Monteith
Penman–Monteith*
Hargreaves–Samani
Hargreaves–Samani
Vapor pressure (dew point temperature)
Wind speed
Solar radiation and Vapor pressure (dew point temperature)
Solar radiation and wind speed
Vapor pressure (dew point temperature) and wind speed
Solar radiation, Vapor pressure (dew point temperature) and wind speed
Penman–Monteith
Modified Hargreaves by Droogers and Allen (2002) Modified Hargreaves by Droogers and Allen (2002) Modified Hargreaves by Droogers and Allen (2002)
Penman–Monteith** Penman–Monteith***
Penman–Monteith
Modified Hargreaves by Droogers and Allen (2002)
Penman–Monteith
Penman–Monteith
Penman–Monteith
Penman–Monteith
Penman–Monteith
Penman–Monteith
***Only when the calibrated dew point temperature and the long–term average of wind speed value of each station used for missing vapor pressure and wind speed, respectively
**Only when the calibrated dew point temperature of each station or each climate used for missing vapor pressure data
*Only when the long–term average of wind speed value of each station used for missing wind speed
Modified Hargreaves by Droogers and Allen (2002)
Modified Hargreaves by Droogers and Allen (2002)
Modified Hargreaves by Droogers and Allen (2002)
Modified Hargreaves by Droogers and Allen (2002)
Penman–Monteith
Penman–Monteith
Penman–Monteith Penman–Monteith
Penman–Monteith
Penman–Monteith
NONE
Semi–humid
Semi–arid
Semi–humid
Semi–arid
Using dew point and minimum temperature relationship
Without dew point and minimum temperature relationship
Solar radiation
Missing data
Table 5 The appropriate ETO equations for various missing data scenarios and climate condition
M. Majidi et al.
Analysis of the Effect of Missing Weather Data on Estimating Daily
iii. Effect of missing solar radiation on the P–M ETO estimation is negligible. It indicated that estimating solar radiation using minimum and maximum temperature gave accurate results.
Acknowledgments The authors would like to thank the anonymous reviewers for their precious and insightful comments and suggestions that greatly improved the quality of this manuscript.
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