Quantitative Analysis of the Impact of Meteorological Factors on Reference Evapotranspiration Changes in Beijing, 1958–2017

The effects of meteorological factors on reference evapotranspiration (ET0) are variable on different time scales, although research tends to focus only on certain time scales. Therefore, using the meteorological data from 1958 to 2017 of Beijing, China, ET0 values over the last 60 years were calculated using Penman–Monteith method. The variation in ET0 values was thus analyzed against four meteorological factors over different time scales. The sensitivity of ET0 to these factors was assessed using a sensitivity coefficient, while the contribution of each factor to ET0 change was quantified by combining this sensitivity coefficient with the factor’s relative change rate over multiple time scales. The results showed that the sensitivity coefficient of relative humidity over different time scales were all negative, while the sensitivity coefficients of net radiation, temperature and wind speed were mostly positive. The main sensitivity factors of ET0 on different time scales varied. On annual time scales, the main factors were relative humidity and temperature. Over annual time scales, relative humidity and net radiation alternated as the main sensitivity factor; while over interannual time scales, the most sensitive factor was relative humidity during 1958–1979 and net radiation thereafter. The contribution of these four meteorological factors to ET0 also fluctuated greatly on intra-annual time scales. On daily time scales, the contributions of temperature and wind speed at the start and end of the year were large, while net radiation and relative humidity were dominant mid-year. On monthly to seasonal time scales, the contributions of these four meteorological factors to ET0 were notable. The contribution of relative humidity was largest in spring and autumn; net radiation was dominant in summer, while temperature and wind speed were dominant in winter. This research on the temporal variability of ET0 response factors is of great significance for understanding regional climate change.


Introduction
Evapotranspiration refers to the key hydrological process of water vapor escaping from the land surface to the atmosphere, which occurs between vegetation, soil or open water and the atmosphere [1,2] Reference evapotranspiration (ET 0 ) is defined as the maximum evapotranspiration of a hypothetical underlying surface of green grass 0.12 m in height, actively growing and adequately watered, with fixed surface resistance and albedo values of 70 m/s and 0.23, respectively [3,4]. ET 0 is considered one of the most important hydrological variables for scheduling irrigation systems because it affects the water and energy balance between land and air, and must be considered when calculating actual The study area is situated in Beijing (39.4°-41.6° N; 115.7°-117.4° E), with an average elevation of 43.5 m (Figure 1). It has a temperate semi-arid continental monsoon climate. The multi-year average temperature, wind speed and relative humidity are 12.1 °C, 1.2 m/s and 52%, respectively. There are 2502 h of annual sunshine, the effective accumulated temperature over 10 °C is 4730 °C, and the average daily solar net radiation is 171 W/m 2 . There are 185 frost-free days throughout the year on average. The annual rainfall and average evaporation are 540 mm and 1021 mm, respectively. More than 80% of the annual rainfall occurs from June to September. The soil is mainly sandy loam, suitable for the growth of various crops. A wheat-corn rotation is the traditional cultivation system in Beijing. With this system, the annual crop water requirement is 876 mm, 453 mm of which is for winter wheat and 423 mm for summer corn [39,40]. Historical daily meteorological data from 1958 to 2017, including sunshine hours, T, RH and U, were obtained from China Meteorological Science (http://cdc.cma.gov.cn).

Calculation of Reference Evapotranspiration
The Penman-Monteith (P-M) equation, recommended by Food and Agricultural Organization guidelines (FAO-56), was used to calculate ET0 values [3]: where ET0 is the reference evapotranspiration (mm d −1 ); ∆ is the slope of the saturated vapor pressure pressure curve; is the surface net radiation (MJ/m 2 /d); is the surface soil heat flux (MJ/m 2 /d), could be neglected at daily scale [3]; is the psychrometric constant(kPa°C − 1 ); T is the daily average temperature (°C); is the wind speed at 2 m height (m/s); is the saturated vapor pressure (kPa); and is the actual vapor pressure (kPa).

Sensitivity Analysis
A sensitivity coefficient was used to quantify the influence of each meteorological factor on ET0. This coefficient is the ratio between the variations in ET0 and the change rate of each meteorological factor [25,41,42], defined as: x x x ET (2) where Sx is the sensitivity coefficient of a given meteorological factor, x; and ΔET0 and Δx are the variable amounts of ET0 and meteorological factor x, respectively. A positive or negative Sx represents

Calculation of Reference Evapotranspiration
The Penman-Monteith (P-M) equation, recommended by Food and Agricultural Organization guidelines (FAO-56), was used to calculate ET 0 values [3]: where ET 0 is the reference evapotranspiration (mm d −1 ); ∆ is the slope of the saturated vapor pressure curve; Rn is the surface net radiation (MJ/m 2 /d); G is the surface soil heat flux (MJ/m 2 /d), could be neglected at daily scale [3]; γ is the psychrometric constant(kPa • C −1 ); T is the daily average temperature ( • C); U is the wind speed at 2 m height (m/s); e s is the saturated vapor pressure (kPa); and e a is the actual vapor pressure (kPa).

Sensitivity Analysis
A sensitivity coefficient was used to quantify the influence of each meteorological factor on ET 0 . This coefficient is the ratio between the variations in ET 0 and the change rate of each meteorological factor [25,41,42], defined as: where S x is the sensitivity coefficient of a given meteorological factor, x; and ∆ET 0 and ∆x are the variable amounts of ET 0 and meteorological factor x, respectively. A positive or negative S x represents an increase or decrease in ET 0 , as the meteorological factor increases or decreases, respectively. Meanwhile, the absolute value of S x reflects the degree of sensitivity to that factor.

Determination of Contributions
Multiplying the sensitivity coefficient of a single meteorological factor by its relative change rate over multiple years indicates the contribution rate of the factor to the change in ET 0 . A positive value indicates that the change related to this selected factor causes an increase in ET 0 , making a positive contribution. A negative value indicates that the change in the selected factor causes a decrease in ET 0 , making a negative contribution.
where RC x is the multiannual relative variation rate of x; n is a given year; Trend x is the meteorological trend of x and reflects the variation of a given meteorological factor on the selected space scale over multiple years; av x is the multiannual mean value; and Con x is the contribution rate of the meteorological factor x to ET 0 variation. The contribution rate of each meteorological factor is accumulated to obtain the total contribution to the change in ET 0 , as follows: where Con RN , Con T , Con RH and Con U represent the contribution rates of RN, T, RH and U to ET 0 variation, respectively; and Con represents the total contribution rate of these meteorological factors to ET 0 variation.
where G RN , G T , G RH and G U represent the average contributions of RN, T, RH, and U to ET 0 variation, respectively; and G sum represents the total contribution of these four meteorological factors to ET 0 variation.

Interannual Variations
The main meteorological factors and ET0 changes from 1958 to 2017 are shown in Figure 3. At interannual scales, the fluctuations of U were the largest, while fluctuations of RN were the smallest. The RN, RH and U decreased at rates of 0.16 (MJ/m 2 /d)/10a, 1.47%/10a and 0.04 (m/s)/10a, respectively. Meanwhile, T and ET0 increased at rates of 0.41 °C/10a and 7.77 mm/10a over the study period. The ranking of the four climate factors and ET0 changes as follows ET0 > T > RN > U> RH. Significance test results show that at a significant level of 0.05, the four climate factors and ET0 show significant changes. The five factors are fitted with a linear function, and the ranking of correlation coefficients is RN> T> RH> U> ET0.

Interannual Variations
The main meteorological factors and ET 0 changes from 1958 to 2017 are shown in Figure 3. At interannual scales, the fluctuations of U were the largest, while fluctuations of RN were the smallest. The RN, RH and U decreased at rates of 0.16 (MJ/m 2 /d)/10a, 1.47%/10a and 0.04 (m/s)/10a, respectively. Meanwhile, T and ET 0 increased at rates of 0.41 • C/10a and 7.77 mm/10a over the study period. The ranking of the four climate factors and ET 0 changes as follows ET 0 > T > RN > U > RH. Significance test results show that at a significant level of 0.05, the four climate factors and ET 0 show significant changes. The five factors are fitted with a linear function, and the ranking of correlation coefficients is

Intra-Annual Variations in Sensitivity Coefficients
The daily sensitivity coefficient changes for each of the four meteorological factors in Beijing over the past 60 years are in shown in Figure 4. The sensitivity coefficients of RN, T, RH, and U were 0.217-0.847, 0.101-0.507, 0.337-1.015 and 0.059-0.510, respectively. Over the course of 1 year, the T sensitivity coefficient had two peaks and two valleys, with an approximately symmetrical distribution. The RH sensitivity coefficient first decreased and then increased over the year, with a zigzag distribution. The U sensitivity coefficient first decreased and then increased over the year. Meanwhile, the RN sensitivity coefficient first increased and then decreased, with a single-peak distribution. Table 1 shows rates of change of the four meteorological factors on monthly to seasonal scales. The annual trend in T was positive, while the annual trends in RN, RH (except for January) and U Water 2020, 12, 2263 8 of 16 were negative. These values suggest that, on monthly scales, T increased each month, while RN, RH (except January) and U (except July, August and September) decreased each month in the past 60 years. T increased the most in March and the least in June, having an annual change rate varying from 0.228 • C/10a to 0.647 • C/10a. RH increased only in January and decreased in all other months (especially in March), having an annual change rate varying from −2.9%/10a to 0.4%/10a. U increased only in July, August and September and decreased in all other months, having an annual change rate varying from −0.130 (m/s)/10a to 0.084 (m/s)/10a. RN decreased most in January and least in August, having an annual change rate varying from −0.420 (MJ/m 2 )/10a to −0.012 (MJ/m 2 )/10a. Meanwhile, the biggest and the smallest RN values were recorded in June and January, respectively. ET 0 decreased in January and June, but increased in all other months, with the largest increase in March and the largest decrease in June. The annual change rate of ET 0 varied from −2.076 mm/10a to 2.826 mm/10a.  zigzag distribution. The U sensitivity coefficient first decreased and then increased over the year. Meanwhile, the RN sensitivity coefficient first increased and then decreased, with a single-peak distribution.  Table 1 shows rates of change of the four meteorological factors on monthly to seasonal scales. The annual trend in T was positive, while the annual trends in RN, RH (except for January) and U were negative. These values suggest that, on monthly scales, T increased each month, while RN, RH (except January) and U (except July, August and September) decreased each month in the past 60 years. T increased the most in March and the least in June, having an annual change rate varying from 0.228 °C/10a to 0.647 °C/10a. RH increased only in January and decreased in all other months (especially in March), having an annual change rate varying from −2.9%/10a to 0.4%/10a. U increased only in July, August and September and decreased in all other months, having an annual change rate varying from −0.130 (m/s)/10a to 0.084 (m/s)/10a. RN decreased most in January and least in August, having an annual change rate varying from −0.420 (MJ/m 2 )/10a to −0.012 (MJ/m 2 )/10a. Meanwhile, the biggest and the smallest RN values were recorded in June and January, respectively. ET0 decreased in January and June, but increased in all other months, with the largest increase in March and the largest decrease in June. The annual change rate of ET0 varied from −2.076 mm/10a to 2.826 mm/10a.
It can be seen that ET0 was the most sensitive to RH and RN on monthly and seasonal scales, but the ranking of sensitivity varied in different months and seasons (Table 1). On monthly scales, during November-February, the sensitivity of ET0 to the four climatic factors was as follows: RH > U > RN > T. In March, this ranking became RH > RN > U > T; in April, May and June it was RN > T > RH >U; in July, August and September, it was RN > RH > T> U, while in October, it was RH > RN > T> U. On seasonal scales, the sensitivity of ET0 to the four climatic factors also varied. In spring, the ranking was RN > T > RH > U; in summer, this ranking became RN > RH > T> U; in autumn, it was RH > RN > T> U; and in winter, it was RH > U > RN > T. According to annual averages, ET0 was most sensitive to RH, followed by RN and T, and was least sensitive to U (Table 1).  It can be seen that ET 0 was the most sensitive to RH and RN on monthly and seasonal scales, but the ranking of sensitivity varied in different months and seasons (Table 1). On monthly scales, during November-February, the sensitivity of ET 0 to the four climatic factors was as follows: RH > U > RN > T. In March, this ranking became RH > RN > U > T; in April, May and June it was RN > T > RH > U; in July, August and September, it was RN > RH > T > U, while in October, it was RH > RN > T > U. On seasonal scales, the sensitivity of ET 0 to the four climatic factors also varied. In spring, the ranking was RN > T > RH > U; in summer, this ranking became RN > RH > T > U; in autumn, it was RH > RN > T > U; and in winter, it was RH > U > RN > T. According to annual averages, ET 0 was most sensitive to RH, followed by RN and T, and was least sensitive to U (Table 1).

Interannual Variation of Sensitivity Coefficients
The interannual variations of the sensitivity coefficients of the four meteorological factors in Beijing from 1958 to 2017 are shown in Figure 5. Over the last 60 years, the sensitivity coefficients of RH and RN have declined at rates of −2.2%/10a and −0.009 (MJ/m 2 /d)/10a, respectively. Meanwhile, the sensitivity coefficients of T and U have increased at rates of 0.007 • C/10a and 0.015 (m/s)/10a, respectively. These changes indicate that the positive sensitivity of ET 0 to both RH and RN has decreased, while its positive sensitivity to T and U has increased. The sensitivity coefficients of RN, T, RH and U were 0.555, 0.408, −0.572 and 0.244, respectively, with the ranges of 0.489-0.662, 0.374-0.434, −0.453-0.783 and 0.170-0.305. The sensitivity coefficients of T, U and RN varied slightly, while the sensitivity coefficient of RH fluctuated markedly.
Beijing from 1958 to 2017 are shown in Figure 5. Over the last 60 years, the sensitivity coefficients of RH and RN have declined at rates of −2.2%/10a and −0.009 (MJ/m 2 /d)/10a, respectively. Meanwhile, the sensitivity coefficients of T and U have increased at rates of 0.007 °C/10a and 0.015 (m/s)/10a, respectively. These changes indicate that the positive sensitivity of ET0 to both RH and RN has decreased, while its positive sensitivity to T and U has increased. The sensitivity coefficients of RN, T, RH and U were 0.555, 0.408, −0.572 and 0.244, respectively, with the ranges of 0.489-0.662, 0.374-0.434, −0.453-0.783 and 0.170-0.305. The sensitivity coefficients of T, U and RN varied slightly, while the sensitivity coefficient of RH fluctuated markedly.
From 1958 to 1979, the sensitivity coefficient of RH increased from −0.47 to −0.71, then decreased to 0.50 in 1981, and has continued to slowly decline. The turning point for this decline in the RH sensitivity coefficient occurred in 1979. On an annual scale, ET0 showed strongest sensitivity to RH and RN. From 1958 to 1963, RN was the most sensitive factor; while from 1964 to 1978, the most sensitive factor was RH; and then from 1979 to 2017, RH and RN were alternately the most sensitive factors affecting ET0.

Daily Time Scales
At daily time scales, the contributions of the four meteorological factors to ET0 are shown Figure  6. These factors made contributions on ET0 that typically varied between −2 and 4 mm. According to the average contributions of these four factors on a daily basis, the ranking of their contributions was T > RH > RN > U. However, the contribution of T fluctuated greatly in mid to late February, mainly because positive and negative distributions of T were relatively symmetrical over the study period, yielding a small mean value for T, when derived from Formulas (3) to (6). Because there were singular points in the contribution from T, the net contributions of RH and RN were greater than T. Clearly, the contributions of T and U at the start and end of the year were large, while contributions of RN and RH were dominant mid-year.

Daily Time Scales
At daily time scales, the contributions of the four meteorological factors to ET 0 are shown Figure 6. These factors made contributions on ET 0 that typically varied between −2 and 4 mm. According to the average contributions of these four factors on a daily basis, the ranking of their contributions was T > RH > RN > U. However, the contribution of T fluctuated greatly in mid to late February, mainly because positive and negative distributions of T were relatively symmetrical over the study period, yielding a small mean value for T, when derived from Formulas (3) to (6). Because there were singular points in the contribution from T, the net contributions of RH and RN were greater than T. Clearly, the contributions of T and U at the start and end of the year were large, while contributions of RN and RH were dominant mid-year.

Daily Time Scales
At daily time scales, the contributions of the four meteorological factors to ET0 are shown Figure  6. These factors made contributions on ET0 that typically varied between −2 and 4 mm. According to the average contributions of these four factors on a daily basis, the ranking of their contributions was T > RH > RN > U. However, the contribution of T fluctuated greatly in mid to late February, mainly because positive and negative distributions of T were relatively symmetrical over the study period, yielding a small mean value for T, when derived from Formulas (3) to (6). Because there were singular points in the contribution from T, the net contributions of RH and RN were greater than T. Clearly, the contributions of T and U at the start and end of the year were large, while contributions of RN and RH were dominant mid-year.   Table 2 shows the contributions of the four meteorological factors to ET 0 on monthly and seasonal scales. The contribution of T to the change in ET 0 was positive, the contribution of RN to the change in ET 0 was negative, while the contribution of RH to the change in ET 0 was negative in January and positive for all other months. The contribution of U to the change in ET 0 was positive in July, August and September, and negative for other months. Specifically, in December and January, U contributed the most to ET 0 change, with contributions of −4.66 and −6.16 mm, while RN contributed the least to ET 0 change, with contributions of −0.65 and −0.22 mm, respectively. In February and April, T contributed most to ET 0 change, with contributions of 7.38 and 11.17 mm, while RN contributed least to ET 0 change, with contributions of −1.26 and −2.93 mm. In March, May, August, October and November, the contributions of RH to ET 0 change were greatest, with contributions of 13.92, 9.62, 13.62, 7.96 and 5.58 mm, respectively. On monthly scales, the ranking of the average contributions of the four meteorological factors to ET 0 was RH > RN > T > U.

Monthly and Seasonal TIME Scales
On seasonal scales, the contributions of T and RH to ET 0 were positive for all four seasons, while the contributions of U to ET 0 change was negative in all other seasons, but only in summer was positive. From spring to winter, the maximum meteorological factors contributing to ET 0 change were RH, RN, T, and U, with contributions of 36.51, −49.67, 23.29 and 15.52 mm respectively. On seasonal scales, the average contributions of the four meteorological factors to ET 0 were ranked: RH > RN > T > U, which was consistent with monthly scales.
Clearly, there was a difference between the total contributions of the four meteorological factors to ET 0 change on both monthly and seasonal scales. This is because the calculation of ET 0 change was characterized by the product of climate tendency and research year. However, meteorological factors are not a single linear change, the climate tendency does not reflect the changes in these meteorological factors. Therefore, the variation in ET 0 calculated using this method becomes large. Notably, the differences between total contributions of meteorological factors and the change in ET 0 on smaller than seasonal scales reflect the accumulation of differences in shorter cycles over the long term.

Discussion
Based on the daily data for meteorological variables in Beijing from 1958 to 2017, the ET 0 for different time scales was calculated by using the P-M formula recommended by the FAO-56. The characteristics of change of the four main meteorological factors and ET 0 were quantified using climate trends. The dynamic changes of these four meteorological factors led to an increase in ET 0 of 7.766 mm/10a in Beijing, which is within the range of values reported in many former studies (5.9-19.3 mm) [43][44][45]. The differences in rates obtained in these studies likely reflect different study periods, having different ET 0 ranges and trends.
Generally, the changes in sensitivity coefficients varied depending on the time scale considered. On daily scales, the sensitivity coefficients fluctuated markedly, and were derived for each variable. Suat et al. [46] found that the wind speed sensitivity coefficient fluctuated greatly, while the changes in the sensitivity coefficients of the other three meteorological factors (T max , T min and R s ) were smaller in eight regions in the United States. We found that RH was most sensitive to ET 0 at the start and end of the day, while RN was the most sensitive factor in the middle of the day, which is consistent with the results of Hupet et al. [47], Liu et al. [48] and Zhao et al. [45]. On a monthly scale, ET 0 was most influenced by RH from October to March, while RN played the biggest role in other months. Liu et al. [43] found that relative humidity was the most important factor in March, August, October, November and December, but in July it was sunshine. On seasonal scales, ET 0 was most sensitive to RN in spring and summer, but to RH in autumn and winter. On annual scales, sensitivity coefficients of RH and RN decreased gradually, while those of T and U increased gradually. For 1958-1982, the RH sensitivity coefficient was far larger than the sensitivity coefficients of any other meteorological factor. After 1982, its influence declined sharply, leading to RH and RN being alternately the most sensitive meteorological factor, ET 0 was not sensitive to U. The magnitudes and trends of the sensitivity coefficients were closely related to variations of the meteorological factors and the structure of the ET 0 partial differential equation incorporating these meteorological factors. The sensitivity factors varied over all time scales, although they fluctuated more obviously on shorter time scales.
At present, research on the contribution of meteorological factors to changes in ET 0 remains scarce. Zhao et al. [45] found that the VPD contributed greatly to the annual ET 0 change. Conversely, Huan et al. [37] reported that the wind speed was the major contributor to ET 0 change. On a monthly scale, Kang et al. [36] found that T, U and RH contributed the most to monthly ET 0 change; only T contributed to the change of ET 0 in winter and spring, while wind speed and humidity influenced ET 0 in summer and on an annual scale. Yin et al. [41] found that U and sunshine hours were the main meteorological factors controlling changes in ET 0 in China, with minor contributions from RH and T. However, most research focuses only on certain time scales and does not consider the response of meteorological factors to ET 0 changes at different time scales. Meanwhile, the quantitative analysis of the impact of meteorological factors on ET 0 changes is imperfect in Beijing under different time perspectives.
In this study, we found that the contributions of the four meteorological factors on different time scales to the ET 0 change reflected the magnitude of their sensitivity coefficients and their relative rates of change. On daily scales, the contributions of T and U at the start and end of the day were larger than those of RN and RH in the middle of the day. On monthly scales, the rate of ET 0 change in December and January was 0.24 and −0.40 mm/10a, respectively. The U sensitivity coefficient in these 2 months was second only to the RH sensitivity coefficient, while the relative U change rate was second only to the relative T change rate, which resulted in U contributing most to ET 0 change in these months. In February and April, ET 0 increased at 0.82 and 1.67 mm/10a, respectively. T contributed most to the ET 0 changes in these months because of its relatively high change rate in February and large sensitivity coefficient in April. In March, May, August, October and November, RH contributed the most to ET 0 change. The value of the RH sensitivity coefficient and the relative change rates of ET 0 were high, with rates of 2.83, 0.91, 1.86, 0.76 and 0.20 mm/10a in these months. In June, July and September, ET 0 changed at rates of −2.08, 0.31 and 0.65 mm/10a, respectively. RN contributed greatly to ET 0 change in these months, linked to a large RN sensitivity coefficient and a relatively high change rate. On seasonal scales, the contribution of RH was the largest in spring and autumn, RN in summer, and U and T in winter. In spring and autumn, although the RH sensitivity coefficients were lower than the RN sensitivity coefficients, its relative rates of change were higher. This led RH to become the main contributing factor to ET 0 change in spring and autumn. In summer, the RN sensitivity coefficient was much larger than all other factors, making it the main contributing factor to ET 0 change in this season. In winter, although the T and U sensitivity coefficients were small, their relative change rates were high, so their contributions to ET 0 change were the greatest. Thus, the rise in ET 0 in Beijing has been caused mainly by the decrease in RH and increase in T over the long term. Concurrently, the decrease in U and RN hinders further rise in ET 0 in Beijing, with RN being the most inhibitory in summer.
A limitation of this research is that the application of contribution rate analysis method was only done for Beijing; therefore, the scale should be expanded in future work. Additionally, Gong et al. [27] noted that the ET 0 response to climate change will differ by region and season because of the large spatiotemporal variability of the sensitivity coefficients. The characteristics of the relative change rate of meteorological factors are also closely related to the spatiotemporal scale, which leads to variability in the main ET 0 control factors on different time scales. Thus, an important focus area for research will be analyzing the contribution of meteorological factors to changes in ET 0 on larger spatial scales and different temporal scales.

Conclusions
In this paper, we qualitatively characterize the sensitivity factors to ET 0 under different time perspectives, also quantitatively analysis of the impact of meteorological factors on ET 0 changes by combining sensitivity coefficient with the factor's relative change rate over multiple time scales in Beijing. On the one hand, determining the main control factors of changes in ET 0 will provide a theoretical basis for water resources regulation, irrigation system design and crop water management in Beijing, on the other hand, exploring the temporal variability of ET 0 response factors is of great significance for understanding regional climate change. The main conclusions are as follows: (1) Over the last 60 years, RH, U and RN values have all declined, and only T has continued to rise.
The rise in T and decline in RH are the main reasons underlying the ET 0 increase. However, the decline in U and RN hinder further increases of ET 0 in Beijing, with RN being the most inhibitory in summer. Determining the main control factors of ET 0 change on different time scales will provide a theoretical basis for water resources regulation, irrigation system design and crop water management in Beijing. (2) The variations of sensitivity coefficients of the four meteorological factors over different time scales has resulted in variation in the main sensitivity factor affecting ET 0 . Over the course of 1 year, the sensitivity coefficients of four meteorological factors fluctuated greatly, with RH and RN being alternately the most sensitive factor. Between 1958 and 1979, RH was the most sensitive factor, but it has since become RN. (3) The contributions of the four meteorological factors to ET 0 varied on different time scales, reflecting their annual fluctuations. The contributions of T and U were large at the start and the end of the year, while the contributions of RH and RN were dominant mid-year. On interannual scales, the main contributing factors were RH and T. (4) A limitation of this research is that the application of contribution rate analysis method was only done for Beijing, also, the ET 0 response to climate change will differ by region and season because of the large spatiotemporal variability of the sensitivity coefficients and relative change rate. Thus, an important focus area for research will be analyzing the contribution of meteorological factors to changes in ET 0 on larger spatial scales and different temporal scales. Meanwhile, it is worth noting that the applicability of the contribution rate method in different climate zones still needs to be discussed.