Arab J Geosci DOI 10.1007/s12517-013-1263-0

ORIGINAL PAPER

Rapid evaluation of reference evapotranspiration in Northern China Shao-hua Zhao & Yong-hui Yang & Feng Zhang & Xin-xin Sui & Yun-jun Yao & Na Zhao & Qiuxiao Zhao & Chun-qiang Li

Received: 10 May 2013 / Accepted: 18 November 2013 # Saudi Society for Geosciences 2014

Abstract Due to the lack of adequate measurement of meteorological factors, the estimation of reference evapotranspiration (ET0) over a long period of time is difficult to estimate in many areas. Meteorological factors such as wind speed, sunshine hours, and relative humidity variously influence ET0—a key element for the quantification of agriculture water requirement. Due to less meteorological input requirement, the Thornthwaite and Hargreaves equations are the most common empirical methods used to estimate ET0. Thus, here in this S.
study, the two simple empirical methods are compared with the standard FAO-56 Penman–Monteith (FAO-56 PM) equation for the period 1966–2002 using 267 meteorological stations in Northern China. The Northern China study area is divided into three climatic regions, consisting of North China, Northeast China, and Northwest China. Linear regression analysis shows highly significant correlations (P <0.001) between the empirical and FAO-56 PM models in the three climatic regions. The analysis shows that the Thornthwaite method generally underestimates ET0. To more accurately estimate ET0, improved empirical models (based on the analyzed regression equations) are proposed and validated using 17 representative meteorological stations in the three climatic regions. The results suggest that of errors of both methods are small and therefore negligible. The mean absolute errors (MAEs) for the improved Thornthwaite method are 0.45, 0.39, and 0.41 mm day−1 with corresponding root mean square errors (RMSEs) of 0.57, 0.50, and 0.53 mm day−1 for the North China, Northeast China, and Northwest China climatic regions, respectively. Similarly, MAEs for the improved Hargreaves method in the three climatic regions are 0.27, 0.21, and 0.36 mm day−1 with RMSEs of 0.34, 0.30, and 0.44 mm day−1, respectively. The adjustments enhanced ET0 estimation accuracy significantly, which is the prediction performance of the user interface of the two methods. The better prediction enhances a more reliable discussion of the trends in ET0, precipitation, and wetness index. The apparent increase in drought after the mid-1980s is a major concern for food security in the study area.

Keywords Reference evapotranspiration . Meteorological factor . FAO-56 PM equation . Thornthwaite equation . Hargreaves equation

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Introduction Severe shortage of water resources is an increasingly limiting factor of industrial and agricultural production in arid/semiarid regions, where agriculture is by far the biggest water user (Fekri and Kasmaei 2013), for instance, in Northern China. It is therefore critical that in this region, crop water requirement is accurately estimated. Crop water consumption (or evapotranspiration demand) is widely estimated in relation to ET0 and crop coefficient (K c). This approach, proposed by the Food and Agriculture Organization of the United Nations (FAO), has been directly adopted or integrated into related models in crop water requirement studies (Doorenbos and Pruitt 1975; Allen et al. 1998; Abdel Kawy and Darwish 2013; Abdel Kawy and Abou El-Magd, 2013; El‐Shirbeny et al. 2013). The efforts have considerably enhanced the reliability of estimated ET0, is a critical element of crop production, efficient irrigation scheme and water resources management (Abdel Kawy 2012). ET0 can be estimated as a function of weather, whose approach includes physical and empirical or semiempirical methods (Penman 1948; Thornthwaite 1948; Monteith 1965; Priestley and Taylor 1972; Hargreaves 1974; Linacre 1977; Hargreaves et al. 1985; Qiu 1996). Accuracy and ease of use are two important requirements in developing ET0 estimation method (Dinpashoh 2006; Gao et al. 2007; Gavilán et al. 2006; Pereir and Pruitt 2004). Among the empirical methods for estimating ET0, the Thornthwaite and Hargreaves methods require the minimum input data (Thornthwaite 1948; Hargreaves et al. 1985). This makes the use of these methods highly convenient since proper meteorological data (e.g., sunshine hours, wind speed, and relative humidity) are largely lacking for many regions. The application of the Thornthwaite and Hargreaves equations requires localized calibration. The calibration or validation of one model with the results of another is a common practice in scientific studies (Allen et al. 1998; Itenfísu et al. 2003; Irmak et al. 2003). A number of studies have demonstrated the superiority of the Penman–Monteith equation over several other methods when compared with lysimeter data (Jensen et al. 1990; Lecina et al. 2003; López-Urrea et al. 2006a, b). Because of its superiority, FAO endorsed the Penman–Monteith equation as the standard for estimating ET0 and recommended the calibration and validation of other ET0 estimation methods against the FAO Penman– Monteith equation (Smith et al. 1991; Allen et al. 1998; Gavilán et al. 2006). Encouragingly enough, the FAO Penman–Monteith equation has performed strongly under a variety of climatic conditions (Allen et al. 1989; Smith 1991; López-Urrea et al. 2006b). The importance of adjusting or evaluating empirical equations in different local conditions has been discussed by Gavilán et al. (2006). Subsequently, several studies

have embarked on the adjustment of models for localized conditions around the globe in the last 40 to 50 years (Hargreaves et al. 1985; Hargreaves 1994; Willmott et al. 1985; Xu and Singh 2001; Hargreaves and Allen 2003; Pereir and Pruitt 2004). Although similar studies have been carried out in China (Li et al. 2002; Zhang et al. 2008), such studies are rare for Northern China where there are severe shortage of water resources. Liu et al. (2006) evaluated several empirical methods against the FAO-56 Penman–Monteith (FAO-56 PM) equation using data from limited weather stations in North China. Here in this study, we test the performance of the Thornthwaite and Hargreaves equations (both of which have low input requirement) through comparison and validation with the standard FAO-56 PM equation. The main objective of the study is to determine the regression equation that significantly improves the accuracy of ET0 estimated by the Thornthwaite and Hargreaves methods. The optimal regression equation is tested in Northern China, which comprises three climatic regions—North China, Northeast China, and Northwest China (Liu et al. 2012).

Materials and method Study area The area under study comprises Northern China which lies between latitudes 28° N and 53° N and longitudes 75° E and 132° E. The study area is divided into three climatic regions— North China, Northeast China, and Northwest China. The North China region generally covers Hebei and Shanxi Provinces, the Neimenggu Autonomous Region, and Tianjin and Beijing Municipalities. The Northeast China region covers Heilongjiang, Jilin, and Liaoning Provinces. The Northwest China region covers Shanxi, Gansu, Ningxia, and Qinghai Provinces and the Xinjiang Autonomous Region (Liu and Lin 2008; Liu et al 2012). Meteorological (monthly maximum and minimum air temperature, relative humidity, precipitation, wind speed, and sunshine hours) and geological (latitude, longitude, and elevation) data were collected from 284 weather stations for the period 1966–2002 (Fig. 1). Among these stations, 267 stations in the three climatic regions were used to compare the two empirical models (the Hargreaves and Thornthwaite models) with the standard (FAO-56 Penman– Monteith) model, which served as the basis on which the optimum regression models were developed and calibrated. Another 17 stations (representative of the North China, Northeast China, and Northwest China climatic regions) were then used to validate the regression models. Table 1 lists the details of the 17 stations used for validation. The meteorological data were provided by the Climatic Data Center (CDC), National

Arab J Geosci Fig. 1 The distribution of meteorological stations in the Northern China study area

Meteorological Information Center (NMIC) of China Meteorological Administration (CMA).

Thornthwaite equations for calculating ET0. The FAO-56 PM equation is quantified as follows (Allen et al. 1998):

Methods

ET0 ¼

FAO-56 PM method As the FAO-56 PM equation has been adopted by FAO as a standard for estimating ET0 (Allen et al. 1998), the equation was used in this study to verify the Hargreaves and Table 1 The geographical location of the 17 stations used in the validation of the regression models for optimizing the Hargreaves and Thornthwaite empirical equations

Lat latitude, Lon longitude, Elv elevation, NS number of stations, T/NSV number of stations used in the validation of total stations in a region

0:408ΔðRn − GÞ þ γ ð900=ðT þ 273ÞÞU 2 ðes − ea Þ ð1Þ Δ þ γ ð1 þ 0:34U 2 Þ

where ET0 is the reference evapotranspiration (millimeters per day), Δ is the slope of saturation vapor pressure versus air temperature curve (kilopascals per degree Celsius), R n is the daily net radiation (megajoules per square meter per day), G is the soil heat flux (megajoules per square meter per day), λ is

Station

Lat (°)

Lon (°)

Elv (m)

Location

NS

T/NSV

Region

Shijiazhuang Taiyuan Hailar Hohhot Xilinhot Tianjin – Bei'an Harbin Jiamusi Changchun Shenyang Xian Lanzhou Yinchuan Xining Urumqi Hetian

38.00 37.8 49.13 40.49 43.57 39.01 – 48.15 45.45 46.81 43.90 41.8 34.3 36.1 38.5 36.38 43.47 37.09

114.42 112.6 119.45 111.41 116.07 117.00 – 126.31 126.46 130.28 125.22 123.4 108.93 103.9 106.2 101.48 87.39 79.95

81 778 610 1,063 1,003 25 – 272 142 326 237 42 397 1,517 1,111 2,260 935 1,375

Hebei Shanxi Neimenggu

19 15 46

83/6

North China

Tianjin Beijing Heilongjiang

2 1 28

72/5

Northeast China

Jilin Liaoning Shanxi Gansu Ningxia Qinghai Xinjiang

21 23 14 26 9 29 51

129/6

Northwest China

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the psychrometric constant (kilopascals per degree Celsius), T is the mean air temperature at 2-m height (degrees Celsius), U 2 is the daily mean wind speed at 2-m height (meters per second), e s is the saturation vapor pressure (kilopascals), and e a is the actual vapor pressure (kilopascals). The soil heat flux (G ) is assumed to be zero at the calculated time step period (24 h). The parameters were calculated using the Allen et al. (1998) equations. In Eq. (1), monthly averages of air temperature, relative humidity, solar radiation, wind speed, and other climatic variables were used to estimate daily ET0 which were then multiplied by the number of days in each month to get monthly ET0 (millimeters·per month). Adjusted Thornthwaite equation The adjusted Thornthwaite method (ATW) proposed by Pereir and Pruitt (2004) and adopted in this study can be quantified as follows: ET0;i

8 < −415:85 þ 32:24TCi − 0:43TC2i ; TCi > 26  C ¼ 16ð10TCi =I Þa ; 0  C < TCi ≥ 26  C : 0; TCi ≤ 0

ð2Þ

Hargreaves equation (HG-1985) The Hargreaves equation is expressed as follows (Hargreaves and Samani 1985; Allen et al. 1998): ET0 ¼ 0:0023Ra ðT þ 17:8ÞðT max − T min Þ0:5

ð7Þ

where ET0 is the reference evapotranspiration (millimeters per day); R a is the daily value of extraterrestrial radiation in equivalent millimeter of water evaporation for a day (millimeters per day); T max, T min, and T are respectively the daily maximum, minimum, and mean air temperature (degrees Celsius); and the value 0.0023 is the Hargreaves and Samani (1985) empirical coefficient. Although daily ET0 estimations have been reported, this method performs best for weekly or longer prediction periods (Hargreaves and Allen 2003). In this study, R a for a given month (n) and latitude (L a , 0≤ L a ≤ 50° N) is estimated using the Kotsopoulous and Babajimopoulos (1997) equation (also see Dinpashoh 2006), expressed as follows: 

where ET0 is the reference evapotranspiration and TCi is the long-term effective temperature, defined by Pereir and Pruitt (2004) as   TCi ¼ 0:5k 3T max;i − T min;i ð3Þ where k =0.72 and the index i is the number of months, I is a thermal index imposed by the local normal climatic temperature (TCi ), and the exponent a is a function of I, quantified as follows: I¼

12   X 0:2TCi

1:514

;

TCi > 0  C

   2πJ 4πJ Ra ¼ M þ C 1 cos þ C 2 þ C 3 cos þ C4 12 12

ð8Þ

where J is the order of the months of the year, M = 14.9425 − 0.0098L a − 0.0098L a − 0.00175L 2a , C 1 = − 0.5801+0.1834L a −0.00066L 2a , C 2 =3.1365−0.00489L a + 0.000061L 2a , C 3 =0.597−5.36×10− 6L 3a , and C 4 =2.9588− 0.00909L a +0.00024L 2a . ET0 values of Eqs. (1), (2), and (6) are monthly averages in millimeters per day, which were converted into cumulative monthly ET0 values.

ð4Þ

n¼1

Evaluation method and a ¼ 6:75  10−7 I 3 − 7:71  10−5 I 2 þ 1:7912  10−2 I þ 0:49239

The performances of the models were evaluated by mean absolute error (MAE) and root mean square error (RMSE) analysis as follows (Willmott 1982):

ð5Þ MAE ¼ The correction factor C is a function of the duration of the day (d) and the number of days (N) in the month, quantified as follows: C¼

d N  12 30

ð6Þ

Then, the adjusted ET0 was computed by multiplying Eq. (2) by Eq. (6).

n 1X jE i − M i j N i¼1

ð9Þ

and sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1X RMSE ¼ ðE i − M i Þ2 N i¼1

ð10Þ

where E i and M i are respectively the estimated and measured variables and n is the sample size.

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Results and discussions FAO-56 PM, Thornthwaite, and Hargreaves ET0 Average monthly ET0 values for the 37 years were computed for each station from the recorded monthly meteorological data. Figure 2 plots the comparison of the results of the Thornthwaite and Hargreaves empirical methods with the standard FAO-56 PM method for each of the three climatic regions in the study area. Simple linear regression analyses show that the estimated ET0 by both the Thornthwaite and

a

d

280

280 240

Hargreaves ET0(mm)

Thornthwaite ET0(mm)

240 200 160 120 80

y = 0.871x + 8.1217 R² = 0.8775 ***

40

200 160 120 80

y = 1.0308x - 5.686 R² = 0.9324 ***

40

0

0 0

40

80

120

160

200

240

0

280

40

80

200

240

280

200

160 120 80 40

y = 0.8735x + 7.6797 R² = 0.8722 ***

160 120 80 40

y = 1.1313x - 7.2976 R² = 0.9492 ***

0

0 0

40

80

120

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0

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FAO56-PM ET0(mm)

FAO56-PM ET0(mm)

c

160

e

200

Hargreaves ET0(mm)

Thornthwaite ET0(mm)

b

120

FAO56-PM ET0(mm)

FAO56-PM ET0(mm)

f

320

320

280

280

240 200 160 120 80

y = 0.8459x + 3.8907 R² = 0.8575 ***

40 0

Hargreaves ET0(mm)

Thornthwaite ET0(mm)

Fig. 2 Plots of estimated ET0 by FAO-56 PM against that of the Thornthwaite and Hargreaves methods for the North China (a, d), Northeast China (b, e), and Northwest China (c, f) climatic regions

Hargreaves methods is high, but significantly correlated with that of the standard FAO-56 PM method (P <0.001). From Fig. 2, it is obvious that the Hargreaves method is more strongly correlated with FAO-56 PM than the Thornthwaite method is with FAO-56 PM (also see Garcia et al. 2004; Liu et al. 2006). Figure 2a–c also suggests that the Thornthwaite method highly underestimates ET0 in the arid/semiarid study area, which is consistent with the observations of several other studies (Stanhill 1961; Pruitt and Doorenbos 1977; Hashemi and Habibian 1979; Malek 1987; Garcia et al. 2004). Although Fig. 2 shows that the Hargreaves method also slightly

240 200 160 120 80

y = 1.0105x - 2.5175 R² = 0.9194 ***

40 0

0

40

80

120 160 200 240 280 320

FAO56-PM ET0(mm)

0

40

80

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FAO56-PM ET0(mm)

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underestimates ET0, as also noted by López-Urrea et al. (2006b) and Dinpashoh (2006), it performs better than the Thornthwaite method—see error analysis in Table 2. There are, however, clear voids of cloud in the Thornthwaite plot in Fig. 2b, which occur at about the 40mm (30–50) and 80-mm (70–90) ranges. It is, however, not clear if these voids have any influence on the performance of the Thornthwaite equation. Irrespectively, the results suggest that the Thornthwaite method which uses only air temperature is not too suitable for application at large scale where there could be significant changes in solar radiation. The significant differences in latitude, longitude, and elevation suggest the need for subdividing the region into smaller areas. On the other hand, this is not the case with the Hargreaves equation, because it also introduced the R a that reflects the extraterrestrial radiation, except for the air temperature. We suppose to introduced R a to estimate ET0 for embracing location and time factors. And it may also partly explain why the Hargreaves equation behavior is better than that of the Thornthwaite method.

Validation To improve ET0 estimation by the relatively simple methods, the Thornthwaite and Hargreaves equations were optimized using the regression equations in Fig. 2. A total of 17 weather stations representing the three climatic regions (six from North China, five from Northeast China, and six from Northwest China) were used to validate the accuracy of optimized models—see Table 1 for details. Comparisons of ET0 estimation between the adjusted methods and FAO-56 PM are

shown in Fig. 3. Good agreements between FAO-56 PM and adjusted results are obvious. Both MAE and RMSE analyses suggest a significant improvement in estimated ET0 by the adjusted methods (see Table 2). After adjustment, the Thornthwaite equation more favorably agrees with the standard FAO-56 PM equation. Error analysis shows a reduction in MAE from 0.75 mm day−1 (22.5 mm month−1) to 0.45 mm day−1 (13.5 mm month−1) for the North China climatic region, from 0.40 mm day−1 (12.0 mm month−1) to 0.39 mm day−1 (11.7 mm month−1) for the Northeast China climatic region, and from 0.50 mm day − 1 (15.0 mm month − 1 ) to 0.41 mm day−1 (13.3 mm·month−1) for the Northwest China climatic region. The corresponding RMSE drops from 0.93 mm day−1 (27.9 mm month−1) to 0.57 mm day−1 (17.10 mm month−1) for the North China climatic region, remains constant at 0.50 mm day−1 (15 mm month−1) for the Northeast China climatic region, and drops from 0.63 mm day−1 (18.9 mm month−1) to 0.53 mm day−1 (15.90 mm·month−1) for the Northwest China climatic region. Similarly after adjustment of the Hargreaves equation, MAE drops from 0.31 mm day − 1 (9.3 mm month − 1 ) to 0.27 mm day−1 (8.1 mm month−1) for the North China climatic region, from 0.32 mm day−1 (9.6 mm month−1) to 0.21 mm day−1 (6.3 mm month−1) for the Northeast China climatic region, and remains at 0.36 mm day − 1 (10.8 mm month−1) for the Northwest China climatic region. The corresponding RMSE also drops from 0.38 mm day−1 (11.4 mm month−1) to 0.34 mm day−1 (10.2 mm month−1) for the North China climatic region, from 0.37 mm day−1 (11.1 mm month−1) to 0.30 mm day−1 (9.0 mm month−1) for the Northeast China climatic region, and from 0.45 mm day−1

Table 2 Details of error analysis on the calibrated and unmodified model performances in the studied three climatic regions Method

Thornthwaitea

Hargreavesb

Calibrated Model

8 < −416:85 þ 32:48TCi − 0:43TC2i ; TCi > 26  C ET0;i ¼ 16:12ð10TCi =I Þa þ 2:12; 0  C < TCi < 26  C : 8 2:12; TCi ≤0 < −413:97 þ 32:19TCi − 0:43TC2i ; TCi > 26  C ET0;i ¼ 15:98ð10TCi =I Þa þ 1:30; 0  C < TCi < 26  C : 8 1:30; TCi ≤0 < −413:45 þ 32:68TCi − 0:44TC2i ; TCi > 26  C ET0;i ¼ 16:22ð10TCi =I Þa þ 8:05; 0  C < TCi < 26  C : 8:05; TCi ≤0 ET0 =0.0021R a (T +17.8)(T max −T min)0.5 +10.83 ET0 =0.0019R a (T +17.8)(T max −T min)0.5 +9.69 ET0 =0.0021R a (T +1.8)(T max −T min)0.5 +9.07

MAE (mm day−1)

RMSE (mm day−1)

Cal

Unm

Cal

Unm

0.45

0.75

0.57

0.93

North China

0.39

0.40

0.50

0.50

Northeast China

0.41

0.50

0.53

0.63

Northwest China

0.27 0.21 0.36

0.31 0.32 0.36

0.34 0.30 0.44

0.38 0.37 0.45

North China Northeast China Northwest China

Cal calibrated model run, Unm unmodified model run a

Calculated TCi, I, and a are as described in “Adjusted Thornthwaite equation”

b

Calculated R a , T, T max, and T min are as described in “Hargreaves equation (HG-1985)”

Climatic region

Arab J Geosci

d

200

Calibrated Hargreaves ET0(mm)

a Calibrated Thornthwaite ET0(mm)

Fig. 3 Comparisons of estimated ET0 by the adjusted Thornthwaite and Hargreaves methods with that of the FAO-56 PM method for the North China (a, d), Northeast China (b, e), and Northwest China (c, f) climatic regions

160

120

80

40

0

0

40

80

120

160

200

160

120

80

40

0

200

0

FAO56-PM ET0(mm)

e

160

120

80

40

0

0

40

80

120

Calibrated Hargreaves ET0(mm)

Calibrated Thornthwaite ET0(mm)

160

120

80

40

40

80

120

160

FAO56-PM ET0(mm)

(13.5 mm month−1) to 0.44 mm day−1 (13.2 mm month−1) for the Northwest China climatic region. Compared with the unadjusted models, the maximum MAE and RMSE after adjustment decrease respectively by ∼40 and ∼39 % for the Thornthwaite equation. In fact, Garcia et al. (2004) noted that the unadjusted

200

80

40

0

40

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FAO56-PM ET0(mm)

f

0

160

120

0

160

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0

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FAO56-PM ET0(mm)

c

80

FAO56-PM ET0(mm)

Calibrated Hargreaves ET0(mm)

Calibrated Thornthwaite ET0(mm)

b

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FAO56-PM ET0(mm)

Thornthwaite equation underestimates ET0 by up to 50 % for measured grass and crop evapotranspiration in arid/semiarid regions. Because the Thornthwaite equation is developed primarily for humid climate and also neglects air saturation deficit, it generally significantly underestimates ET 0 in arid/semiarid climate

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(Stanhill 1961; Pruitt and Doorenbos 1977; Garcia et al. 2004). Also after adjustment, the maximum average MAE and RMSE decrease respectively by ∼34 and ∼19 % for the Hargreaves equation. This is similar to the relative error of ∼25 % reported by López-Urrea et al. (2006b). Also, Gavilán et al. (2006) reported 60 and 15 % drops, respectively, in MAE and RMSE after calibration of the Hargreaves equation. There is, however, no improvement in estimated ET0 by the adjusted Thornthwaite method for the Northeast China climatic region. Similarly, the Hargreaves method shows no improvement after adjustment for the Northwest China climatic region. As Northeast China is a semiarid to semihumid climate region, the adjusted Thornthwaite method is more suitable for application in the region. Also, the estimated ET0 by the unadjusted Hargreaves method is similar to that of the FAO-56 PM method for the Northwest China climatic region, suggesting that there is no need for further adjustment. The close fit of the Hargreaves method with FAO-56 PM for Northwest China shows its suitability for application in arid/semiarid regions (Dinpashoh 2006). The errors of the adjusted methods are nearly twice those reported by Cai et al. (2007) for the Northeast and North China regions. This could be due to the fact that Cai et al. (2007) used data from only two stations for a period of 15 years, grossly lacking spatial and temporal representation of the regions. Irrespectively, the errors of the two adjusted methods are still considered minimal and therefore acceptable. The analysis in Table 2 suggests that errors of the Hargreaves equation are less than those of the Thornthwaite equation. While the Thornthwaite equation only needs temperature as input, the Hargreaves equation uses effects of temperature, radiation, elevation, and latitude as input. The Hargreaves method is therefore superior over the Thornthwaite method in terms of estimating ET0. Trend analysis of ET0 and precipitation Based on the monthly meteorological data, estimated ET0 values by the FAO-56 PM method and precipitation were averaged for each year to get the general trend for the 37 years (Fig. 4). From Fig. 4, it is obvious that ET0 for Northwest China is highest, followed by that for North China and then Northeast China. This trend reflects the differences in the climatic regions where annual average temperature and wind speed are highest for Northwest China and lowest for Northeast China. In North China, ET0 decreases from 1966 to 1990 before slightly rebounding through 2002. In Northeast China, ET0 decreases from 1966 to 1994 before slightly rebounding through 2002. In fact, for both North China and Northeast China, ET0 generally declines, coincident with precipitation trend. This

Fig. 4 Variations in ET0 and precipitation during 1966–2002 in the North China (a), Northeast China (b), and Northwest China (c) climatic regions

suggests that precipitation is a critical consideration for ET0 in these regions. In Northwest China, ET0 increases from 1966 to 1973, decreasing through 1992 and then slightly rebounds through 2002. Precipitation is lowest

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in Northwest China (fluctuation within 300 mm) and highest in Northeast China. For the three climatic regions, precipitation generally increases from 1966 to 1982 before decreasing through 2002 (Fig. 4). The ratio of precipitation to ET0, also named the wetness index (Allen et al. 1998), reflects the probable occurrence of drought in a given region. The wetness indices or draught probabilities in the three climatic regions are plotted in Fig. 5. It is obvious in Fig. 4 that the wetness index is highest for Northeast China (with 0.7 fluctuation) and lowest for Northwest China (with 0.3 fluctuation). This trend is mainly driven by the high rainfall in Northeast China as against the low rainfall in Northwest China. The wetness index also increases from 1966 to 1985 before decreasing through 2002 in all the three climatic regions. It then implies an increasing tendency of drought in the Northern China study area (Ma and Fu 2006). The increasing incidence of drought in the Northern China region is of major concern which continues to attract the attention of researchers, farmers, and decision makers.

Conclusions Both the two empirical approaches used in this study for estimating ET0 require limited meteorological data input. The approaches are evaluated using data from 267 meteorological stations distributed across Northern China. The results show that the estimated monthly ET0 by the Thornthwaite and Hargreaves equations is significantly correlated with that of the FAO-56 PM equation (the standard equation). The Thornthwaite and Hargreaves equations are adjusted with linear regression models for optimum ET0 estimation. A total of 20 stations are used to verify the performances of the adjusted models. Stronger agreements are observed between the results of the adjusted models with the standard FAO-56 PM model. By this measure, the adjusted empirical models more accurately estimate ET0 than the unadjusted ones. Thus, the adapted regression models well complement the Thornthwaite and Hargreaves equations for better estimation of ET0 in the Northern China study area. The study also shows that the Hargreaves equation is more reliable than the Thornthwaite equation for estimating ET0 in arid climate. The study further shows that the Thornthwaite approach generally underestimates ET0 in the Northern China study area. Although the approach adopted in this study is not entirely innovative, it has a practical application in the study area where there is increasing water shortage. The study could lay the basis for a more accurate estimation of ET0 in Northern China with limited meteorological

Fig. 5 Variations of wetness index during 1966–2002 in the North China (a), Northeast China (b), and Northwest China (c) climatic regions

data. The use of temperature or in combination with radiation data alone to accurately estimate ET0 could positively influence efficient water management strategies in especially arid/semiarid region. This is because temperature is among the most commonly available meteorological data in the world today.

Arab J Geosci Acknowledgments We deeply appreciate the financial support of the National Natural Science Foundation of China (41101313, 41201331) and MOST (2010CB951002). We are also thankful for the insightful comments raised by the editors and anonymous reviewers during the review process.

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