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© 2020 Conscientia Beam. All Rights Reserved. 

ESTIMATING REFERENCE EVAPOTRANSPIRATION BY HARGREAVES AND 
BLANEY-CRIDDLE METHODS IN HUMID SUBTROPICAL CONDITIONS 

 

 

 Muhammad 
Hafeez1+ 
Zia Ahmad Chatha2 
Alamgir Akhtar Khan3 
Allah Bakhsh4  
Abdul Basit5 
Fatima Tahira6 

 

1Department of Agricultural Engineering, Faculty of Agricultural Sciences 
and Technology, Bahauddin Zakariya University, Multan, Pakistan. 

 
2Department of Food Engineering, Faculty of Agricultural Engineering, 
UAF, Faisalabad, Pakistan. 

 
3Department of Agricultural Engineering, MNSUA, Multan, Pakistan. 

 
4,5Department of Botany, Ghazi University, Dera Ghazi Khan, Pakistan. 

 
6Department of Mathematics, Institute of Southern Punjab, Multan, 
Pakistan. 

 
 

 
(+ Corresponding author) 

 ABSTRACT 
 
Article History 
Received: 21 January 2020 
Revised: 25 February 2020 
Accepted: 30 March 2020 
Published: 27 April 2020  
 

Keywords 
Blaney-Criddle 
Hargreaves 
Humid subtropical 
ETo 
Islamabad 
Kakul 
Pakistan. 

 
Various methods are available to predict reference evapotranspiration (ETo) but the 
Penman-Monteith (PM) ETo method has been considered to be the most accurate ETo 
method to determine ETo. The PM ETo method can be solved by various weather 
parameters like atmospheric temperature, wind velocity, moisture content and net solar 
radiations. There are many weather stations in the world that have no complete set of 
weather parameters to predict ETo by applying PM ETo method. So alternative ETo 
methods like Hargreaves (HG) and Blaney-Criddle (BC)  ETo methods are used which 
need only a fewer number of weather parameters. In this paper, two ETo methods, HG 
and BC are compared with PM ETo method in humid subtropical climatic conditions of 
Islamabad and Kakul (Abbottabad) weather stations. The study indicate that HG ETo 
method overestimated PM ETo method by 23.78% at Islamabad weather station and 
28.47% at Kakul station. The BC ETo method overestimated PM ETo method by 
37.93% at Islamabad weather station and by 22.68% at Kakul weather station. The 
dissimilarity of HG ETo method with PM  ETo method with RMSE was 1.09 mm/day 
at Islamabad weather station and 1.17 mm/day at Kakul  weather station. The 
dissimilarity of BC ETo method with PM ETo method has Root Mean Square Error 
(RMSE) of 2.86 mm/day at Islamabad weather station and 1.48 mm/day at Kakul 
weather station.  
 

Contribution/Originality: The objective of this investigation is to compare ETo by HG and BC ETo methods 

with PM ETo method in humid subtropical climatic conditions of Pakistan. 

 

1. INTRODUCTION 

The usage of high calorie and meat-intensive food consumption are estimated to approximately twice by 2050 

due to increasing of population to fulfill the diet security in the next decades, significant variations in agricultural 

water management are needed [1]. From January to April in 2010, a severe sacristy occur in southwest China, 

which thread more than sixty million public and produced greater than 23.66 billion financial fatalities [2]. In 

distinction to the increasing requirement on irrigated yield, water for agriculture has been decreased due to regular 

Current Research in Agricultural Sciences 
2020 Vol. 7, No. 1, pp. 15-22. 
ISSN(e): 2312-6418 
ISSN(p): 2313-3716 
DOI: 10.18488/journal.68.2020.71.15.22 
© 2020 Conscientia Beam. All Rights Reserved. 

 
 
 

 
 
 

 

 
 
 
 

https://orcid.org/0000-0002-3262-7014
https://www.doi.org/10.18488/journal.68.2020.71.15.22


Current Research in Agricultural Sciences, 2020, 7(1): 15-22 

 

 
16 

© 2020 Conscientia Beam. All Rights Reserved. 

scarcities and struggle for water reservoirs among the different users [3]. The pure water has been considered as 

precious as blue gold and it is designed to be the most serious concern of the present era [4]. Pakistan lies in arid to 

semi-arid region where average annual rainfall is 254 to 356 mm against a potential demand (of water for maximum 

crop production) of 1778 mm. This gap between the demands and supplies is met through applying irrigation. 

Moreover, the country is facing threat of rapidly increasing population with the annual growth rate of 2.05 percent. 

It has been observed that water availability for agriculture is expected to decline globally to 62 percent by 2020 as 

was available (72%) in 1995 and from 87% to 73% in developing countries [5]. Land and water are two important 

factors, which are required for agricultural development and strong economy of a country. Pakistan is facing the 

problem of water scarcity and the demand of water for irrigation is also increased due to mounting demand of food 

and fiber [6]. As a result of increasing demand for water resources due to population growth, urbanization, and 

irrigated agriculture, optimizing the use of the limited available water especially in crop production systems is 

becoming more critical each year. Therefore, in order to manage and conserve increasingly scarce water resources, 

it is important to examine various methods that increase water use efficiency and reduce the excessive application of 

water. The knowledge of crop evapotranspiration (ET) is one of the most important factors in understanding crop 

water use, irrigation scheduling, proper water resources management, crop production, and water conservation. 

Generally, the estimation of crop ET involves calculating reference crop ET (ETo), and then multiplying the ETo 

by an appropriate crop coefficient [7]. ETo is defined as the evapotranspiration rate at which water would be 

removed from a reference surface where water is not limited or a limited factor [8]. The widely used ETo method , 

which have been developed to estimate ETo is Penman-Monteith ETo method as concluded by large number of 

studies including Allen, et al. [8]; Walter, et al. [9]; Howes, et al. [10]; Gurski, et al. [11]; Akumaga, et al. [12]; 

De Fraiture and Wichelns [13] and Gundalia and Dholakia [14]. Three significant practices (soil, plant and 

weather data based) applied for estimation of accurate irrigation schedule are soil, plant and weather data based, but 

weather data based practice has got consideration among the researchers because this practice requires no extra 

high value and specific detectors to calculate humidity of soil, atmospheric temperature and leaf area index [15]. 

Reference Evapotranspiration (ETo) is an important element of water-cycle of agricultural systems [16]. The 

exact figures about ETo rate are very significant for the weather data dependent practices to be used [17]. There 

are various ETo methods for the estimation of ETo. i-e Penman-Monteith (PM) ETo method [8] Blaney-Criddle 

ETo method [18] Priestley-Taylor (PT) ETo method [19] and Hargreaves –Samani ETo method [20] but the 

global researchers has accepted PM ETo as the most accurate method because of its accurate results when 

compared with other ETo methods  in various climatic regions of the world [21]. Many researches have proved the 

correctness of the Penman-Monteith ETo method [8] when comparing it with lysimeter measurements 

particularly for daily ETo estimations [22]. The PM ETo method is widely used as the standard ETo method for 

estimating ETo [23]. The PM ETo method requires numerous meteorological variables for effective application 

which may be unavailable or missing in some locations, especially in developing countries [24]. Therefore, 

alternative approaches that require less weather parameters input are needed. The objective of this investigation is 

to compare ETo by HG and BC ETo methods with PM ETo method in humid subtropical climatic conditions of 

Pakistan. 

 

2. MATERIALS AND METHODS 

2.1. Experimental Area and Data Collection 

The GPS (Global Positioning System) coordinates of Islamabad are 33.6844o N and 73.o479o E and elevation of 

540 meters. The weather of Islamabad has a humid subtropical climate conditions. The GPS (Global Positioning 

System) Coordinates of Kakul (Abbottabad) are 34.1833o N and 73.2500o E and height of 1308 meters. Kakul has a 

humid subtropical climate conditions.  



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The mean monthly weather data of 10-years (2000-2009) of Islamabad weather station and 10-years (2001-

2010) of Kakul weather stations is used to compare ETo by HG and BC ETo methods with the PM ETo method as 

stated in the Table 1. 

 
Table-1. Geographical coordinates and climate of metrological stations used in the study. 

Station Latitude Longitude Elevation (m) Climate 

Islamabad 33.6844° N 73.0479° E 540 Humid subtropical 
Kakul 34.1833o N 73.2500 o E 1308 Humid subtropical 

 

 

2.2. Evapotranspiration Estimation Methods 

2.2.1. Estimation of ETo by Penman-Monteith Method 

Allen, et al. [8] presented the Penman–Monteith (PM) method as: 

                      (1) 

Where, ETo is the reference crop evapotranspiration (mm d−1) by PM ETo method ; Δ is the slope of the 

saturation vapor pressure function (kPa (°C)−1 );  Rn is the net radiation (MJ m−2 day−1); G is the soil heat flux 

density (MJ m−2 day−1); T is the mean air temperature (°C); U2 is the average 24-hour wind speed at 2-meter height 

(m s−1); (es-ea) is the vapor pressure deficit (kPa); and γ is the psychometric constant (kPa °C−1). The computation of 

all data required for the calculation of ETo followed the method suggested by Allen, et al. [8]. 

 

2.3. Estimation of ETo by Hargreaves Method 

ETo calculated by applying Hargreaves ETo Method [20] is given as: 

HG (Tmax-Tmin) (0.5)       (2) 

Where, ETo HG is in mm day-1 and Tmean is mean monthly air temperatures (0C). A coefficient of 0.408 is used 

to convert MJm-2 day -1 into mmd-1 as concluded by Allen, et al. [8]  and 0.0023 is the original coefficient of the HG 

ETo method as suggested by Hargreaves and Samani [20]. 

Due to the small number of climatic data requirement, it is often applied under conditions where less climatic 

data is available, and especially, when only air temperatures are available [25]. 

 

2.4. Estimation of ETo by Blaney-Criddle Method 

The original model as described by Blaney and Criddle [18] is: 

 

 = a+b [                                         (3) 

Where,  

) – n                                       (4) 

b = 0.82-0.0041(RHmin) +1.07 (n/N)+0.066(ud)-0.006 (RHmin) (n/N)-0.0006 (RHmin) (ud)         (5) 

with T being the mean monthly temperature (°C) and p the monthly percentage of the annual daytime hours. 

 

 

 

 



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© 2020 Conscientia Beam. All Rights Reserved. 

2.5. Evaluation Criteria 

In this study, the root mean square error (RMSE), percentage error of estimate (PE), mean bias error (MBE) 

and coefficient of determination (R2) are used for the evaluation of ETo methods. The RMSE, PE, MBE and R2 are 

defined in Equations 6, 7, 8 and 9. 

 

                                                               (6)                  

                                                                                                  (7) 

                                                                                        (8)   

                            (9) 

 

Where, 

 Pi are predicted values and Oi are observed values,  are the average values of Pi and Oi, and n is the 

total number of data. 

 

3. RESULTS AND DISCUSSION 

3.1. Comparison at Islamabad Station 

The HG and BC ETo methods are compared with PM ETo method for monthly ETo assessments in humid 

sub-tropical climatic region of Islamabad. The HG ETo method indicated overestimation of  ETo by 23.78% as 

compared to the PM ETo method at Islamabad weather station as shown in Figure 1 (a) and also in Table 2. The 

overestimation of ETo by HG ETo method in humid subtropical region is similar as concluded by Droogers and 

Allen [26]; Rojas and Sheffield [27] and Ashraf, et al. [28]. The BC ETo method indicated an overestimation of 

ETo by 37.93% as compared to the PM ETo method at Islamabad weather station as shown in Figure 1 (b) and also 

in the Table 2. The overestimation of ETo by BC ETo method as compared with the PM ETo method in humid 

subtropical climatic region is similar as stated by Tabari, et al. [29].  

 
Table-2. Summary results of HG and BC ETo methods compared with PM ETo method at Islamabad station. 

Sr.no Station Method RMSE R2 %Error Mean SD MBE 

1 Islamabad Hargreaves 1.09 0.98 23.78 4.49 1.8 -1.097 
2 Islamabad Blaney-Criddle 2.86 0.94 37.93 5.51 3.65 -2.092 

 

 



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© 2020 Conscientia Beam. All Rights Reserved. 

 

 

Figure-1. Monthly comparison of ETo _ PM with (a) HG and (b) BC at Islamabad station. 

 
Figure-2. Monthly comparison of ETo _ PM with HG and BC at Islamabad station. 

 

The statistical results indicate that HG ETo method  overestimate ETo as compare to the PM ETo method at 

Islamabad weather station with R2 0.98, MBE of -1.097 and RMSE of 1.09 mm/day as shown in the Table 2. The 

BC ETo method show overestimation of ETo when compare with PM ETo method at Islamabad weather station 

with R2 0.94, MBE of -2.092 and RMSE of 2.86 mm/day, as shown in Table 2.    

 

3.2. Comparison at Kakul Station 

The HG ETo and BC ETo methods are compared with PM ETo method in humid subtropical climatic 

conditions of Kakul (Abbottabad) weather station. The statistical results show that the HG ETo method 

overestimated ETo by 28.47% as compare to the PM ETo method at Kakul weather station as shown in Figure 3 

(a). The overestimation of ETo by HG ETo method in humid subtropical climatic conditions  are similar as 

concluded by Dinpashoh [30]; Droogers and Allen [26]; Rojas and Sheffield [27] and Ashraf, et al. [28]. The BC 

ETo method also show overestimation of ETo by 22.68% as compare to PM ETo method at Kakul station Figure 3 

(b). The overestimation of ETo by BC method under humid subtropical conditions is similar as concluded by 

Tabari, et al. [29]. 

 

 
 

Figure-3. Monthly comparison of ETo _ PM with (a) HG and (b) BC at Kakul station. 

 



Current Research in Agricultural Sciences, 2020, 7(1): 15-22 

 

 
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© 2020 Conscientia Beam. All Rights Reserved. 

 
Figure-4. Monthly comparison of ETo _ PM with HG and BC at Kakul station. 

 
Table-3. Summary results of hargreaves and blaney-criddle methods compared with penman-monteith method at kakul station. 

Sr.no Station Method RMSE R2 %Error Mean SD MBE 

1 Kakul Hargreaves 1.17 0.98 28.47 3.86 1.68 -1.10 
2 Kakul Blaney-Criddle 1.48 0.95 22.68 3.57 2.55 -0.81 

 

 

The statistical results which indicate that the HG ETo method overestimated PM ETo method with RMSE of 

1.17 mm/day, MBE of -1.10 and R2 0.98 at Kakul station in humid subtropical climatic conditions as shown in 

Table 3. The BC ETo method also overestimate PM ETo method with RMSE of 1.48 mm/day, MBE of -0.81 and 

R2  0.95 at Kakul station in humid subtropical climatic conditions as shown in Table 3. 

 

4. CONCLUSION 

This study is conducted to compare the accuracy HG ETo  BC ETo methods against PM ETo method in 

humid sub-tropical climatic conditions  of Islamabad and Kakul regions. The results of both the ETo methods are 

obtained on the basis of statistical analysis. The statistical analysis averagely show over all twelve months 

overestimation of ETo by HG and BC ETo methods as compared to the PM ETo method. The PM ETo method is 

considered as the standard ETo method all over the world due to its accurate ETo estimation as concluded by 

Gundalia and Dholakia [14]; Afzaal, et al. [31]; Trajkovic, et al. [32] that’s why in present study this ETo method 

is taken as standard method for the comparison of both HG and BC ETo methods. The comparison show that  both 

HG ETo method and BC ETo method indicate overestimation of ETo as compared to the PM ETo method at 

Islamabad and Kakul weather stations. 

 

Funding: This study received no specific financial support.    
Competing Interests: The authors declare that they have no competing interests.  
Acknowledgement: The authors would like to thank Pakistan Meterological Department, 
Lahore and Peshawar for providing the climatic data records used in this research. 

 

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