3. Results and discussion

#### 3.1. Estimation of ET using Penman-Monteith method

The Penman-Monteith method is the main approach recommended internationally to estimate ET; it requires the use of meteorological parameters, such as radiation, air temperature, relative humidity, and wind speed. These parameters might be difficult to obtain and measure in many meteorological stations, with the exception of temperature. Using Taiwan as an example, only a few meteorological stations had complete data of all meteorological parameters, and still there were missing data in the observation materials. Yeh et al. [13] evaluated the ET difference between the Penman-Monteith method and evaporation pan in southern Taiwan. They used six meteorological stations in the southern part of Taiwan as case studies and collected meteorological data over a span of 15 years from 1990 to 2004 to estimate ET and ET of evaporation pans. In addition, a coefficient of evaporation pans was established. The results showed that the Penman-Monteith method and evaporation pan were highly correlated. Therefore, this study used longterm meteorological data from 1961 to 2013 from Tainan Weather Station provided by Central Weather Bureau for estimation. The estimation results calculated using the Penman-Monteith method were taken as the standard, which were named PM1. In cases where radiation data were missing or incomplete, Eq. (3) was used for substitution, which was called PM2. When wind speed data were missing or incomplete, the average wind speed of 1.83 m s<sup>1</sup> in Taiwan was used for calculation [15], which was called PM3. Eq. (2) was used for substitution in cases where relative humidity data were missing or incomplete, which was named PM4. Finally, when radiation, wind speed, and relative humidity data were all missing, all of the above substitutes were used, which was called PM5. Statistical methods of MBE, RMSE, and R2 were applied to this study. In addition, the four models, namely PM2, PM3, PM4, and PM5, were used to estimate ET, and the results were compared with those of model PM1.

The characteristics of the ET at Tainan Weather Station estimated using different models are shown in Table 1. This demonstrates that maximum values are mainly concentrated in July, while minimum values are primarily concentrated in January or December. The average value was within the range of 3.42–3.61 mm/day. In addition, the ET estimated by PM models at Tainan Weather Station is shown in Figure 2, and the results indicate that the trend of each PM model was roughly the same as that of PM1. The comparison results between each PM model and PM1 are shown in Figure 3. This suggests that ET was underestimated by PM2 from July to September, while it was overestimated during other months; PM3 underestimated ET in


Table 1. Various scenarios for calculating evapotranspiration using the Penman-Monteith method (mm d<sup>1</sup> ).

Figure 2. Comparison of monthly mean values of the Penman-Monteith method from various scenarios.

3. Results and discussion

10 Current Perspective to Predict Actual Evapotranspiration

3.1. Estimation of ET using Penman-Monteith method

estimate ET, and the results were compared with those of model PM1.

The characteristics of the ET at Tainan Weather Station estimated using different models are shown in Table 1. This demonstrates that maximum values are mainly concentrated in July, while minimum values are primarily concentrated in January or December. The average value was within the range of 3.42–3.61 mm/day. In addition, the ET estimated by PM models at Tainan Weather Station is shown in Figure 2, and the results indicate that the trend of each PM model was roughly the same as that of PM1. The comparison results between each PM model and PM1 are shown in Figure 3. This suggests that ET was underestimated by PM2 from July to September, while it was overestimated during other months; PM3 underestimated ET in

Scenarios Min. Min. (month) Max. Max. (month) Mean Standard deviation

PM1 2.26 January 4.72 July 3.54 0.92 PM2 2.35 January 4.55 July 3.61 0.85 PM3 2.22 January 4.78 July 3.58 0.95 PM4 2.15 December 4.56 July 3.42 0.89 PM5 2.24 December 4.38 July 3.49 0.81

Table 1. Various scenarios for calculating evapotranspiration using the Penman-Monteith method (mm d<sup>1</sup>

).

The Penman-Monteith method is the main approach recommended internationally to estimate ET; it requires the use of meteorological parameters, such as radiation, air temperature, relative humidity, and wind speed. These parameters might be difficult to obtain and measure in many meteorological stations, with the exception of temperature. Using Taiwan as an example, only a few meteorological stations had complete data of all meteorological parameters, and still there were missing data in the observation materials. Yeh et al. [13] evaluated the ET difference between the Penman-Monteith method and evaporation pan in southern Taiwan. They used six meteorological stations in the southern part of Taiwan as case studies and collected meteorological data over a span of 15 years from 1990 to 2004 to estimate ET and ET of evaporation pans. In addition, a coefficient of evaporation pans was established. The results showed that the Penman-Monteith method and evaporation pan were highly correlated. Therefore, this study used longterm meteorological data from 1961 to 2013 from Tainan Weather Station provided by Central Weather Bureau for estimation. The estimation results calculated using the Penman-Monteith method were taken as the standard, which were named PM1. In cases where radiation data were missing or incomplete, Eq. (3) was used for substitution, which was called PM2. When wind speed data were missing or incomplete, the average wind speed of 1.83 m s<sup>1</sup> in Taiwan was used for calculation [15], which was called PM3. Eq. (2) was used for substitution in cases where relative humidity data were missing or incomplete, which was named PM4. Finally, when radiation, wind speed, and relative humidity data were all missing, all of the above substitutes were used, which was called PM5. Statistical methods of MBE, RMSE, and R2 were applied to this study. In addition, the four models, namely PM2, PM3, PM4, and PM5, were used to

January, February, and December, and it was overestimated in the remaining months; ET was underestimated by PM4 in all months; PM5 underestimated ET in June, July, August, September, October, and December and overestimated ET in other months.

In this study, the estimated ET of PM2, PM3, PM4, and PM5 models were compared with that of the PM1 model using the statistical methods of MBE, RMSE, and R<sup>2</sup> . Statistical verification

Figure 3. Monthly evapotranspiration comparison between the PM1 and the calculated values by using the various scenarios. (a) PM2; (b) PM3; (c) PM4; (d) PM5.

results of MBE showed that the MBE value was within the range of 0.12 to 0.07 mm d<sup>1</sup> , while the value of RMSE ranged from 0.09 to 0.31 mm d<sup>1</sup> . There is slight overestimation in PM2 and PM3. In contrast, there is slight underestimation in PM4 and PM5. In addition, R<sup>2</sup> was optimal in PM3 based on the statistical verification results. Therefore, according to the calculation results of MBE, RMSE, and R<sup>2</sup> , the PM3 model had the optimal performance. Given the above comparison, the results of this study showed that wind speed had little effect on the assessment of ET with the Penman-Monteith method as the standard (PM1), which was similar to the conclusion drawn by Jabloun et al. [25]. The results obtained by Popova et al. [26] using the global average wind speed of 2 m s<sup>1</sup> were similar to PM1 as well. In addition, compared to missing radiation or wind speed data, the absence of relative humidity data exerted a larger impact on the estimation of ET when Penman-Monteith method was used.

### 3.2. The results of ET estimation using different empirical formulas

Compared with other meteorological parameters, namely radiation, relative humidity, and wind speed, temperature is relatively easy to obtain. Apart from that, radiation can be accurately measured, and yet existing measurement methods are unable to acquire precise wind speed data, especially in dry areas where the error would be relatively larger. Because the mixed evaluation methods, such as the Penman-Monteith method, require many meteorological parameters, there are some difficulties in the funding, maintenance, and construction of meteorological stations, making it difficult to acquire certain data. Therefore, it is essential to develop ET estimation methods that require fewer or a single meteorological parameter [27]. A number of scholars have proposed various methods or experiential formulas and compared them to the Penman-Monteith method in the hope of finding a relatively simple method and experiential formula to measure ET [28]. This study selected six radiation-based methods and four temperature-based methods to explore their applicability in the study area.

#### 3.2.1. Estimation of monthly average ET using radiation-based methods

According to the radiation-based estimation methods that are used internationally, this study selected six methods, including Makkink [4], Turc [16], Jensen and Haise [17], Priestley and Taylor [5], Doorenbos and Pruitt [18], and Abtew [19]. A commonly used statistical mean error percentage was applied to the estimation so as to discuss the basic statistical differences. The data recorded by Tainan Weather Station from 1961 to 2013 were substituted into the formula, and the results are shown in Table 2. This demonstrates that minimum values were mainly concentrated in December and January, while maximum values were primarily concentrated in July. The mean value indicated a significant underestimation in ET calculated by the Makkink method, with an average value of 2.99 mm d<sup>1</sup> and an error percentage of 15.5%. The results of the Turc method showed a slight overestimation, with an average value of 3.66 mm d<sup>1</sup> and an error percentage of 3.4%. ET was significantly overestimated by the Jensen-Haise method, with a mean value of 5.16 mm d<sup>1</sup> and an error percentage of 45.8%. The results of the Priestley-Taylor method suggested an overestimation, with an average value of 3.96 mm d<sup>1</sup> and an error percentage of 11.9%. ET calculated by the Doorenbos-Pruitt method was the closest to the mean value of the Penman-Monteith method, with an average value of 3.43 mm d<sup>1</sup> and an


Table 2. Performance evaluation of the radiation-based methods against Penman-Monteith (mm d<sup>1</sup> ).

results of MBE showed that the MBE value was within the range of 0.12 to 0.07 mm d<sup>1</sup>

PM2 and PM3. In contrast, there is slight underestimation in PM4 and PM5. In addition, R<sup>2</sup> was optimal in PM3 based on the statistical verification results. Therefore, according to the

the above comparison, the results of this study showed that wind speed had little effect on the assessment of ET with the Penman-Monteith method as the standard (PM1), which was similar to the conclusion drawn by Jabloun et al. [25]. The results obtained by Popova et al. [26] using the global average wind speed of 2 m s<sup>1</sup> were similar to PM1 as well. In addition, compared to missing radiation or wind speed data, the absence of relative humidity data exerted a larger

Compared with other meteorological parameters, namely radiation, relative humidity, and wind speed, temperature is relatively easy to obtain. Apart from that, radiation can be accurately measured, and yet existing measurement methods are unable to acquire precise wind speed data, especially in dry areas where the error would be relatively larger. Because the mixed evaluation methods, such as the Penman-Monteith method, require many meteorological parameters, there are some difficulties in the funding, maintenance, and construction of meteorological stations, making it difficult to acquire certain data. Therefore, it is essential to develop ET estimation methods that require fewer or a single meteorological parameter [27]. A number of scholars have proposed various methods or experiential formulas and compared them to the Penman-Monteith method in the hope of finding a relatively simple method and experiential formula to measure ET [28]. This study selected six radiation-based methods and four temperature-based methods to explore their applicability

According to the radiation-based estimation methods that are used internationally, this study selected six methods, including Makkink [4], Turc [16], Jensen and Haise [17], Priestley and Taylor [5], Doorenbos and Pruitt [18], and Abtew [19]. A commonly used statistical mean error percentage was applied to the estimation so as to discuss the basic statistical differences. The data recorded by Tainan Weather Station from 1961 to 2013 were substituted into the formula, and the results are shown in Table 2. This demonstrates that minimum values were mainly concentrated in December and January, while maximum values were primarily concentrated in July. The mean value indicated a significant underestimation in ET calculated by the Makkink method, with an average value of 2.99 mm d<sup>1</sup> and an error percentage of 15.5%. The results of the Turc method showed a slight overestimation, with an average value of 3.66 mm d<sup>1</sup> and an error percentage of 3.4%. ET was significantly overestimated by the Jensen-Haise method, with a mean value of 5.16 mm d<sup>1</sup> and an error percentage of 45.8%. The results of the Priestley-Taylor method suggested an overestimation, with an average value of 3.96 mm d<sup>1</sup> and an error percentage of 11.9%. ET calculated by the Doorenbos-Pruitt method was the closest to the mean value of the Penman-Monteith method, with an average value of 3.43 mm d<sup>1</sup> and an

while the value of RMSE ranged from 0.09 to 0.31 mm d<sup>1</sup>

impact on the estimation of ET when Penman-Monteith method was used.

3.2. The results of ET estimation using different empirical formulas

3.2.1. Estimation of monthly average ET using radiation-based methods

calculation results of MBE, RMSE, and R<sup>2</sup>

12 Current Perspective to Predict Actual Evapotranspiration

in the study area.

,

. There is slight overestimation in

, the PM3 model had the optimal performance. Given

error percentage of 3.1%. The results of the Abtew method showed a slight overestimation, with an average value of 3.68 mm d<sup>1</sup> and an error percentage of 4.0%.

The trend of monthly average ET at Tainan Weather Station calculated by various radiation-based methods were all consistent with that of the Penman-Monteith method, which was taken as the standard, as shown in Figure 4. As shown in Figure 5, the monthly average ET was underestimated by the Makkink method, with an error percentage ranging from 16.9 to 13.7%; the Turc method slightly overestimated all the monthly average ET, with an error percentage of 1.1 to 11.1%; and the monthly average ET was significantly overestimated by the Jensen-Haise method. Especially in summer, the overestimation was far more significant, and the error percentage was up to 54.2%. The results of the Priestley-Taylor method suggest underestimation only in December and January, and overestimation in other months, with an error percentage of 4.4 to 17.2%. The Doorenbos-Pruitt method slightly underestimated ET in May, August, and September, while in other months ET was overestimated with an error percentage ranging from 11.7 to 16.8%. Compared with the Penman-Monteith method, ET was overestimated by the Abtew method, and the error percentage was within the range of 4.7 to 19%. The above results suggest that the Doorenbos-Pruitt method was the least biased in estimating ET, while the Jensen-Haise method was the most biased.

Figure 4. Monthly evapotranspiration computed by the Penman-Monteith method and six radiation-based methods.

Figure 5. Monthly evapotranspiration comparison between the Penman-Monteith method and the calculated values by using the radiation-based methods ((a) Makkink; (b) Turc; (c) Jensen-Haise; (d) Priestley-Taylor; (e) Doorenbos-Pruit; (f) Abtew).

In addition, three statistical methods, namely MBE, RMSE, and R2 , were used in this study to compare the estimation results of the Makkink, Turc, Jensen-Haise, Priestley-Taylor, Doorenbos-Pruitt, and Abtew methods with the Penman-Monteith method. The statistical verification results of MBE indicated that the value of MBE was within the range of 0.55 to 0.41 mm d<sup>1</sup> and the value of RMSE ranged from 0.23 to 1.78 mm d<sup>1</sup> . Figure 6(a) shows that the Makkink method underestimated ET, and the MBE value was 0.55. Furthermore, the other five methods, Turc, Jensen-Haise, Priestley-Taylor, Doorenbos-Pruitt, and Abtew methods, all overestimated ET, and the MBE values were respectively 0.12, 1.62, 0.41, 0.49, and 0.14. In particular, the overestimation of the Jensen-Haise method was the most significant. Figure 6(b) suggests that all six methods overestimated ET, and the values of RMSE were respectively 0.60, 0.23, 1.78, 0.55,

Figure 6. (a) MBE and (b) RMSE for evapotranspiration comparison between the Penman-Monteith method and six radiation-based methods.

In addition, three statistical methods, namely MBE, RMSE, and R2

and the value of RMSE ranged from 0.23 to 1.78 mm d<sup>1</sup>

14 Current Perspective to Predict Actual Evapotranspiration

compare the estimation results of the Makkink, Turc, Jensen-Haise, Priestley-Taylor, Doorenbos-Pruitt, and Abtew methods with the Penman-Monteith method. The statistical verification results of MBE indicated that the value of MBE was within the range of 0.55 to 0.41 mm d<sup>1</sup>

Figure 5. Monthly evapotranspiration comparison between the Penman-Monteith method and the calculated values by using the radiation-based methods ((a) Makkink; (b) Turc; (c) Jensen-Haise; (d) Priestley-Taylor; (e) Doorenbos-Pruit; (f) Abtew).

(e) Doorenbos-Pruit (1977) (f) Abtew (1996)

(a) Makkink (1957) (b) Turc (1961)

(c) Jensen-Haise (1963) (d) Priestley-Taylor (1972)

method underestimated ET, and the MBE value was 0.55. Furthermore, the other five methods, Turc, Jensen-Haise, Priestley-Taylor, Doorenbos-Pruitt, and Abtew methods, all overestimated ET, and the MBE values were respectively 0.12, 1.62, 0.41, 0.49, and 0.14. In particular, the overestimation of the Jensen-Haise method was the most significant. Figure 6(b) suggests that all six methods overestimated ET, and the values of RMSE were respectively 0.60, 0.23, 1.78, 0.55,

, were used in this study to

. Figure 6(a) shows that the Makkink

0.53, and 0.37. Evapotranspiration was most significantly overestimated by the Jensen-Haise method as well. The statistical results showed that R2 was within the range of 0.90–0.97. Therefore, judging from the statistical results of MBE, RMSE, and R2 , the Turc method was optimal at the Tainan Weather Station, followed by the Abtew method; the method with the worst performance was the Jensen-Haise method. Previously, Tabari et al. [29] used 31 methods to evaluate ET at a meteorological station named Rasht in a humid area of Iran. The results showed that, compared to the Penman-Monteith method, the Jensen-Haise method severely overestimated ET with a relative error of about 30%. It was also found to significantly overestimate ET in this study area, and the relative errors were respectively around 59 and 48%. Such overestimation also occurred in the humid regions of Serbia [30] and Florida of the USA [31].

#### 3.2.2. Estimation of monthly average ET using temperature-based methods

Among the temperature-based methods that are commonly used internationally, this chapter selected four methods, including Thornthwaite [20], Blaney and Criddle [21], Hamon [22], and Linacre [23]. To begin with, the commonly used statistical mean value and error percentage were used for estimation; then this chapter discusses the basic statistical error. After the data recorded by Tainan Weather Station from 1961 to 2013 were substituted into the formulas to calculate the daily ET, the average monthly ET was calculated with month as the unit, and the results are shown in Table 3. At the Tainan Weather Station, minimum values were mainly concentrated in January and maximum values were primarily concentrated in July. The mean value suggests that the Thornthwaite method severely underestimated ET, with a mean value of 1.95 mm d<sup>1</sup> and an error percentage of 44.9%. The Blaney-Criddle method significantly underestimated ET as well. Its mean value was 1.61 mm d<sup>1</sup> and the error percentage was 54.5%. The Hamon method underestimated ET, with a mean value of 2.72 mm d<sup>1</sup> and an error percentage of 23.2%. Evapotranspiration was overestimated by the Linacre method, with a mean value of 4.05 mm d<sup>1</sup> and an error percentage of 14.4%.

This chapter compared the ET of Tainan Weather Station as calculated by the temperaturebased methods with that of the Penman-Monteith method, and the results are as shown in Figure 7. The trends of the Thornthwaite, Hamon, and Linacre methods were consistent with the Penman-Monteith method, while Blaney-Criddle method suggested otherwise. The monthly average ET at Tainan Weather Station estimated by the temperature-based estimation methods was compared with Penman-Monteith method, as shown in Figure 8. Evapotranspiration was underestimated by Thornthwaite method, with an error percentage of 70.4 to 31.1%. The maximum error occurred in March and April. The Blaney-Criddle method underestimated monthly average ET, and the error percentage was within the range of 60.6 to 38.9%. Evapotranspiration was also underestimated by the Hamon method. The underestimation in winter was insignificant, with an error percentage of 23.5 to 18.1%. In May, the percentage reached its maximum. The Linacre method overestimated the monthly average ET. The error percentage ranged from 5.1 to 23.9% and reached maximum value in November. In light of the above results, the error percentage of Thornthwaite method was the largest.

This study used three statistical methods, namely MBE, RMSE, and R2 , to compare ET at the Tainan Weather Station estimated by the Thornthwaite, Blaney-Criddle, Hamon methods with that of the Penman-Monteith method. The value of MBE ranged from 1.93 to 0.51 mm d<sup>1</sup> and RMSE was within the range of 0.63–2.08 mm d<sup>1</sup> . The statistical results of R2 indicated that


Table 3. Performance evaluation of the temperature-based methods against Penman-Monteith (mm d<sup>1</sup> ).

3.2.2. Estimation of monthly average ET using temperature-based methods

16 Current Perspective to Predict Actual Evapotranspiration

with a mean value of 4.05 mm d<sup>1</sup> and an error percentage of 14.4%.

This study used three statistical methods, namely MBE, RMSE, and R2

Penman-Monteith 2.26 January 4.72 July 3.54 0.92 Thornthwaite (1948) 0.67 January 3.25 July 1.95 1.02 Blaney-Criddle (1959) 1.38 January 1.86 July 1.61 0.32 Hamon (1961) 1.85 January 3.61 July 2.72 0.80 Linacre (1977) 2.80 January 4.96 July 4.05 0.82

Table 3. Performance evaluation of the temperature-based methods against Penman-Monteith (mm d<sup>1</sup>

and RMSE was within the range of 0.63–2.08 mm d<sup>1</sup>

Among the temperature-based methods that are commonly used internationally, this chapter selected four methods, including Thornthwaite [20], Blaney and Criddle [21], Hamon [22], and Linacre [23]. To begin with, the commonly used statistical mean value and error percentage were used for estimation; then this chapter discusses the basic statistical error. After the data recorded by Tainan Weather Station from 1961 to 2013 were substituted into the formulas to calculate the daily ET, the average monthly ET was calculated with month as the unit, and the results are shown in Table 3. At the Tainan Weather Station, minimum values were mainly concentrated in January and maximum values were primarily concentrated in July. The mean value suggests that the Thornthwaite method severely underestimated ET, with a mean value of 1.95 mm d<sup>1</sup> and an error percentage of 44.9%. The Blaney-Criddle method significantly underestimated ET as well. Its mean value was 1.61 mm d<sup>1</sup> and the error percentage was 54.5%. The Hamon method underestimated ET, with a mean value of 2.72 mm d<sup>1</sup> and an error percentage of 23.2%. Evapotranspiration was overestimated by the Linacre method,

This chapter compared the ET of Tainan Weather Station as calculated by the temperaturebased methods with that of the Penman-Monteith method, and the results are as shown in Figure 7. The trends of the Thornthwaite, Hamon, and Linacre methods were consistent with the Penman-Monteith method, while Blaney-Criddle method suggested otherwise. The monthly average ET at Tainan Weather Station estimated by the temperature-based estimation methods was compared with Penman-Monteith method, as shown in Figure 8. Evapotranspiration was underestimated by Thornthwaite method, with an error percentage of 70.4 to 31.1%. The maximum error occurred in March and April. The Blaney-Criddle method underestimated monthly average ET, and the error percentage was within the range of 60.6 to 38.9%. Evapotranspiration was also underestimated by the Hamon method. The underestimation in winter was insignificant, with an error percentage of 23.5 to 18.1%. In May, the percentage reached its maximum. The Linacre method overestimated the monthly average ET. The error percentage ranged from 5.1 to 23.9% and reached maximum value in November. In light of the above results, the error percentage of Thornthwaite method was the largest.

Tainan Weather Station estimated by the Thornthwaite, Blaney-Criddle, Hamon methods with that of the Penman-Monteith method. The value of MBE ranged from 1.93 to 0.51 mm d<sup>1</sup>

Min. Min. (month) Max. Max. (month) Mean Standard deviation

, to compare ET at the

).

. The statistical results of R2 indicated that

Figure 7. Monthly evapotranspiration computed by the Penman-Monteith method and four temperature-based methods.

Figure 8. Monthly evapotranspiration comparison between the Penman-Monteith method and the calculated values by using the temperature-based methods ((a) Thornthwaite; (b) Blaney-Criddle; (c) Hamon; (d) Linacre).

it was within the range of 0.36–0.83. As shown in Figure 9(a), the results of Thornthwaite, Blaney-Criddle, and Hamon methods suggest underestimation, and the values of MBE were 1.58, 1.93, and 0.82, respectively. Results of the Linacre method, however, indicated overestimation with an MBE of 0.51. Figure 9(b) suggests overestimation in Thornthwaite,

Figure 9. (a) MBE and (b) RMSE for evapotranspiration comparison between the Penman-Monteith method and four temperature-based methods.

Blaney-Criddle, Hamon, and Linacre methods, with RMSE values of 1.63, 1.31, 1.15, and 1.12, respectively. In summary, according to the statistical results of MBE, RMSE, and R2 , the Linacre method was optimal for estimating ET at the Tainan Weather Station, followed by the Hamon method. The Blaney-Criddle method was the least fit.

According to relevant studies and literature, Fontenot [32] declared that for meteorological stations near the coast, the Linacre method overestimated ET by 18.46% compared to the Penman-Monteith method. It was also pointed out that this method could be greatly affected by the dew point temperature. Compared with the Penman-Monteith method, the results of Thornthwaite, Hamon, and Blaney-Criddle methods all suggest underestimation, as these three temperaturebased formulas all took daylight hours into consideration. In spite of the high temperature, the results would still be lower than the actual amount when daylight hours were insufficient, causing underestimation. Even if the daylight hours were insufficient, ET still occurred. The results of this study show that the Blaney-Criddle method underestimated ET in Tainan because it is strongly influenced by the annual daylight percentage of every month. Cruff and Thompson [33] used the Thornthwaite and Blaney-Criddle methods to estimate ET in the desert areas of the southwestern United States, and the results suggested underestimation as well.

This study compared the results of radiation-based methods with that of Penman-Monteith method and discovered that the empirical formulas of radiation-based methods were better than those of temperature-based methods. In addition, the errors of ET calculated by temperature-based methods were larger than those of the radiation-based methods. The reason is as follows: it is most likely that temperature is the only meteorological parameter used in empirical formulas of temperature-based methods. Therefore, it could be easily affected by the data of meteorological station, which would easily cause inaccuracy. Such a conclusion is similar to that of Lu et al. [34], Sentelhas et al. [8], and Gebhart et al. [35]. Moreover, the estimation results of Tukimat et al. [36] in Malaysia showed that three radiation-based methods, namely Makkink [4], Turc [16], and Priestley and Taylor [5], were more accurate than two temperature-based methods, the Thornthwaite [20] and Blaney and Criddle [21] methods. In terms of temperature-based estimation methods, many scholars have found that ET was underestimated by the Thornthwaite [20] method in humid areas compared to the Penman-Monteith method. For instance, the results of Alkaeed et al. [37] in Fukuoka of Japan, Trajkovic and Kolakovic [30] in six meteorological stations of Balkan Peninsula, and Sentelhas et al. [8] in Ontario of Canada, all showed the same conclusion. Some scholars, however, have pointed out that compared with the Penman-Monteith method, the performance of R2 in the Thornthwaite [20] method was worse, and yet its trend was consistent with the Penman-Monteith method. The evaluation of ET conducted by [36] in Kedah of Malaysia suggested same result.
