Abstract

In most parts of the world, pan evaporation decreases with increased air temperature rather than increases, which is known as the “evaporation paradox.” The semiarid Loess Plateau, which is sensitive to global climate change and ecological variations, has a unique warming and drying climate. The authors of this study consider whether pan evaporation shows the same decreasing trend in this unique environment. Meteorological observations of the typical semiarid Dingxi in the Loess Plateau from 1960 to 2010 were used to analyze the variation in pan evaporation and its responses to climatic factors. It was found that the pan evaporation has increased considerably over the past 50 yr, which does not support the evaporation paradox proposed in previous studies. A multifactor model developed to simulate the independent impacts of climate factors on pan evaporation indicated that the temperature, humidity, wind speed, and low cloud cover variations contributed to pan evaporation by 46.18%, 25.90%, 2.48%, and 25.44%, respectively. The increased temperature, decreased relative humidity, and decreased low cloud cover all caused an increase in pan evaporation, unlike many parts of the world where increased low cloud cover offsets the effects of increased temperature and decreased relative humidity on pan evaporation. This may explain why the evaporation paradox occurs. If all relevant factors affecting pan evaporation are considered, it is possible the paradox will not occur. Thus in warm and drying regions, the increased pan evaporation will lead to increasingly arid conditions, which may exacerbate drought and flood disaster occurrences worldwide.

1. Introduction

Evaporation is an important component of the land surface water balance (Zhang and Wang 2007) and also the main process removing surface water. Its temporal and spatial variation affects the availability of water resources and its utilization by vegetation for growth and crop yield. There are two critical processes that are linked through evaporation: surface liquid water is vaporized consuming heat energy, and moisture is transported to the atmosphere by air movement, a complex dynamic interaction between water and energy. Heat is a precondition for evaporation, and nearly half of the solar radiation energy absorbed by the earth is consumed by evaporation (Trenberth et al. 2009). Thereby, increased air temperature is bound to change the surface and atmospheric thermal conditions, causing variations in the spatial and temporal distributions of evaporation.

However, the actual surface evaporation is influenced not only by surface energy and atmospheric motion but also by soil moisture availability. The former is the energy and environmental demand for evaporation, and the latter is the material supply. Usually, energy and environmental conditions play key roles, but sometimes the soil moisture limitation can completely dominate the effect of energy and micrometeorological conditions and outweigh the influence of other factors. This occurrence is particularly prominent in arid and semiarid areas characterized by drought (Liu et al. 2010). As a result of the influence of soil water limitation in these areas, land surface evaporation does not always demonstrate a consistent response to increased air temperature. Pan evaporation is very similar to the potential evaporation; both are a measure of atmospheric evaporation demand (Zhang et al. 2011). Pan evaporation represents free water surface evaporation without water limitation. It is usually influenced by near-surface atmospheric motion, which is a micrometeorological condition, and is also mainly controlled by solar radiation. Pan evaporation therefore behaves similarly to the potential evaporation and responds more clearly to climate change than actual surface evaporation with prominent effects of increased air temperature (Scheff and Frierson 2014; Fu and Feng 2014; Sherwood and Fu 2014).

Because of the exacerbating effects of global warming, much attention has been given to the response characteristics of pan evaporation to increased air temperature in recent years. Initially, it was theoretically speculated (Roderick and Farquhar 2002; Zuo et al. 2005) that as the earth’s surface warms, the surface energy used in evaporation should increase and the water cycle should accelerate, leading to further pan evaporation. However, large numbers of international studies (Peterson et al. 1995; Chattopadhyay and Hulme 1997; Quintana-Gomez 1998; Golubev et al. 2001; Hobbins et al. 2004) have shown that pan evaporation decreases significantly under a background of increased air temperature in most parts of the world, including America (Golubev et al. 2001; Hobbins et al. 2004; Lawrimore and Peterson 2000), Russia (Peterson et al. 1995), India (Chattopadhyay and Hulme 1997), Italy (Moonen et al. 2002), China (Thomas 2000; Liu et al. 2004), Venezuela (Quintana-Gomez 1998), Australia (Roderick and Farquhar 2004), New Zealand (Roderick and Farquhar 2005), and many other areas. However, it showed an increasing trend in a few regions such as Israel (Cohen et al. 2002) and Iran (Tabari and Marofi 2011). In short, most observations support the conclusion that pan evaporation decreases under conditions of increased air temperature. This conclusion seems to be contrary to expectations and is commonly known as the “evaporation fallacy” or “evaporation paradox” in the academic world (Brutsaert and Parlange 1998). There are various explanations for this phenomenon. One of the most accepted explanations is that global warming increases cloudiness, weakens sunshine intensity, and diminishes heat quantity for evaporation, thus decreasing the pan evaporation (Chattopadhyay and Hulme 1997; Roderick and Farquhar 2002; Liu et al. 2006). Moreover, researchers have demonstrated that low cloud cover in most parts of the world has significantly increased because of the enhanced atmospheric water holding capacity from increased air temperature (Liu et al. 2008). However, realization of this increased capacity requires sufficient water available for evaporation, which may be lacking in arid environments.

The Loess Plateau is the world’s largest area of loess deposits (Zhang et al. 2009). It is not only a transition area from inland arid climate zone to the monsoon climate zone, but also the major coupling region in China of the winter monsoon and summer monsoon. Because the region is geographically vast, short-term fluctuations and long-term changes in regional climate are very prominent. Because of the Loess Plateau’s location and ecological vulnerability, the region is more sensitive to climate change than many other regions of the world. In recent years, the warming and drying climate trend is prominent across the semiarid Loess Plateau (Zhang et al. 2013; Huang et al. 2008; Huang et al. 2016b). This trend may suggest that there will be reduced instances of low cloud cover in the future, which is opposite to the observations in most parts of the world that have shown increased low cloud cover and precipitation (Liu et al. 2006). With this unique climate change response, it is unknown whether pan evaporation in this region will follow the usual significant decreasing trend. In addition, the question remains as to whether the evaporation paradox really exists. If pan evaporation increases with increased air temperature in the Loess Plateau, this would suggest that the evaporation paradox is not inevitable and may support previous studies that inferred that increased low cloud cover was the main reason for reduced pan evaporation in arid areas (Brutsaert and Parlange 1998; Roderick and Farquhar 2002). However, if the change trend in pan evaporation is similar to that in most other places of the world, it would suggest that the reason for the decreasing pan evaporation trend under increased air temperature is not as simple as currently thought.

Previous studies have devoted little attention to changes in pan evaporation across the Loess Plateau. Moreover, because of the inconsistency of equipment, more detailed and thorough research is required to determine relatively objective and credible pan evaporation change features. Because pan evaporation is simultaneously affected by multiple factors (including temperature, sunshine, wind speed, low cloud cover, and atmospheric humidity), it can be difficult to isolate the independent effects of the different climatic factors on pan evaporation. At present the recent change trends of pan evaporation over recent decades and the mechanisms by which pan evaporation responds to increased temperature in this particular region are still unknown. These unknowns restrict the development of solutions for important issues such as drought monitoring technologies and exploitation of water resources.

In view of these uncertainties, we analyzed the pan evaporation trend across the typical semiarid area of the Loess Plateau using homogenization processed meteorological observations at the Dingxi Station from 1960 to 2010. We consider how pan evaporation responds to increased air temperature and other climate factor variations and discuss whether the evaporation paradox really exists. This study gives us an objective understanding of the contribution of climatic factors to pan evaporation variations and the role of climate change in this process, thus providing a scientific basis for further climate change and drought mitigation research.

2. Study area and research data

This study uses conventional meteorological data from 1960 to 2010 from the Dingxi Station in the semiarid Loess Plateau, China. The station is located in the suburb of Dingxi in Gansu (35°35′N, 104°37′E) and is part of the elevation extended area of the Loess Plateau with an altitude of 1896.7 m, an average annual rainfall of approximately 386 mm, and an annual pan evaporation of approximately 1200 mm. As shown in Fig. 1, the west of the Loess Plateau, near the Qinghai–Tibet Plateau, is a transition zone from the north China monsoon to the northwest arid region. Dingxi Station is located in this semiarid climate zone with a typical hilly landscape, which well represents the climate of the Loess Plateau. The surface of the station is flat and consistent with the surrounding landscape. In the prevailing wind direction, there is only farmland surrounding the station and no high-rise buildings and trees are present.

Fig. 1.

The (a) altitude and (b) climate of the Dingxi Station region.

Fig. 1.

The (a) altitude and (b) climate of the Dingxi Station region.

The specific observations include pan evaporation measured by a small evaporation dish (diameter 20 cm) and an E601 large evaporation dish (diameter 61.8 cm), low cloud cover, precipitation, sunshine, temperature, wind speed, and relative humidity. The average air temperature, relative humidity, and wind speed were observed at 0200, 0800, 1400, and 2000 Beijing time (BJT), and pan evaporation, low cloud cover, and sunshine were recorded only once per day. Precipitation was measured at 0800 and 2000 BJT. The evaporation dish is simply composed of a cylindrical container with an open top and a device that can measure the water required to return to the initial tick mark. The small dish and the E601 large dish are the current routine evaporation measurement equipment in China. During the period of 1960–84, a small evaporation dish was used at Dingxi Station. During 1985–2001, both types of dishes were used from May to September, while only the small dish was used in other months. After 2002, pan evaporation was measured with only the large dish from May to September and only with the small dish in the other months.

To unify the small and large dish evaporation data, both types of pan evaporation observations were compared during the overlapping periods (from May to August of 1985–2001) (Fig. 2a). Clear differences were found between these two datasets; pan evaporation from the small dish is much greater than that from the large dish, with a correlation slope of 0.574 and a RMSE of 3.4 mm. However, these differences are merely systematic biases, and there is a good correlation between the two series with a correlation coefficient of 0.81. To utilize and unify the data from 2002 to 2010, the data of the large pan for May to September were corrected to small pan evaporation (Table 1).

Fig. 2.

Comparison of large and small dish evaporation (a) before and (b) after correction.

Fig. 2.

Comparison of large and small dish evaporation (a) before and (b) after correction.

Table 1.

The fit of the modeled linear relationship between large and small pan evaporation.

The fit of the modeled linear relationship between large and small pan evaporation.
The fit of the modeled linear relationship between large and small pan evaporation.

The fit of the linear relationship between the large and small dishes can be given as follows, based on the comparison of the overlapping periods (from May to September of 1985–2001):

 
formula

where and are the pan evaporation (mm) with the large and small dish of the ith month, respectively, and αi is the correction coefficient of the ith month. We corrected the large pan evaporation with Eq. (1). To check whether the difference is statistically significant, the comparison of the pan evaporation before and after correction is shown in Fig. 2b. The deviation between the corrected small pan evaporation and large pan evaporation of the overlapping periods has been reduced, with the fitting line slope increased to 0.9617 and the standard error reduced to 1.72 mm. To test whether the revised data were significantly different, we used the Mann–Whitney test. The result shows that there were no significant differences between the pan evaporation time series before and after correction (Table 2).

Table 2.

Summary of the Mann–Whitney hypothesis test results. Asymptotic significances are displayed; the significance level is 0.05.

Summary of the Mann–Whitney hypothesis test results. Asymptotic significances are displayed; the significance level is 0.05.
Summary of the Mann–Whitney hypothesis test results. Asymptotic significances are displayed; the significance level is 0.05.

The revised pan evaporation is homogenized and meets the technical requirements of pan evaporation trend analysis. This means that the correction coefficients are reliable and can be used in correcting the large pan evaporation from 2002 to 2010. There is no sudden change at the critical point of 2001–02 and the correction is feasible and effective. Therefore, we can obtain the complete small pan evaporation from 1960 to 2010 (Table 3).

Table 3.

After correction, all evaporation data are combined into small pan evaporation. “Small” represents small pan evaporation, and “large” represents large pan evaporation.

After correction, all evaporation data are combined into small pan evaporation. “Small” represents small pan evaporation, and “large” represents large pan evaporation.
After correction, all evaporation data are combined into small pan evaporation. “Small” represents small pan evaporation, and “large” represents large pan evaporation.

There is no long-term observation of radiation because the Dingxi Station is not a solar radiation station. Therefore, sunshine duration is applied to analyze the relationship of radiation with pan evaporation.

Because pan evaporation, low cloud cover, and sunshine hours are measured only once per day, the temperature, wind speed, precipitation, and relative humidity were also converted into daily averages. To compare the pan evaporation of different regions of the world, all data were normalized.

3. Pan evaporation trends

Studies have found that the evaporation paradox has been observed in most parts of the world (Brutsaert and Parlange 1998). We consider whether pan evaporation follows the same decreasing trend with increasing temperature in a semiarid area. Figure 3 shows the standardized pan evaporation changes in the semiarid region with the results of studies conducted in other regions worldwide (Xie et al. 2008; Liu et al. 2011; Liu et al. 2013; Shi et al. 2008; Oguntunde et al. 2012; Padmakumari et al. 2013; Da Silva 2004). We found that pan evaporation in the semiarid Loess Plateau showed a unique and significant upward trend, with a normalized value from approximately −1 to 1. Although they have different time-length series, pan evaporation in other regions of the world exhibited clear decreasing trends. This result indicates that pan evaporation trends are not entirely consistent in the context of increased air temperature; it may decrease in most areas but can increase in some areas. Therefore, pan evaporation trends are not determined entirely by increased air temperature, and the evaporation paradox may not always occur.

Fig. 3.

Comparison of standardized pan evaporation trends in the semiarid Loess Plateau with other regions worldwide (10-yr moving average).

Fig. 3.

Comparison of standardized pan evaporation trends in the semiarid Loess Plateau with other regions worldwide (10-yr moving average).

Previous studies (Zuo et al. 2005; Hobbins et al. 2004; Lawrimore and Peterson 2000; Brutsaert and Parlange 1998; Roderick and Farquhar 2002; Liu et al. 2008) have analyzed the reasons behind the variations of climate factors relevant to pan evaporation. We next consider whether the temporal trend of pan evaporation in the Loess Plateau is also affected by the unique climate in this area.

Figure 4 shows the average temperature, relative humidity, wind speed, sunshine, precipitation, and low cloud cover changes in this region in comparison with other regions of the world. It shows that over the last few decades, temperature has significantly increased, but relative humidity, precipitation and low cloud cover have significantly decreased, while wind speed and sunshine duration are oscillating but increasing overall. The changes in temperature and relative humidity are consistent with those in some other regions of the world, but relative humidity has decreased considerably more than in the other regions. Low cloud cover and precipitation show a decreasing trend, which is opposite to that in the other regions. Although the trends of wind speed and sunshine are not entirely opposite to those in other regions, they show antiphase relationships. This indicates that pan evaporation may show an opposite increasing trend in response to increased air temperature in this region when compared with locations worldwide because climate factors (such as precipitation, low cloud cover, wind speed, and sunshine) follow significantly different patterns across the Loess Plateau than in other locations. This is especially true for relative humidity, which decreased more substantially. Thus, the increase of pan evaporation in the semiarid Loess Plateau during the past 50 yr was most likely caused primarily by reduced low cloud cover, increased wind speed and sunshine, and significantly reduced relative humidity, rather than by temperature increases alone.

Fig. 4.

Comparison of standardized average (a) temperature, (b) relative humidity, (c) wind speed, (d) sunshine hours, (e) daily low cloud cover, and (f) annual precipitation trends in the semiarid Loess Plateau and other regions worldwide (10-yr moving average).

Fig. 4.

Comparison of standardized average (a) temperature, (b) relative humidity, (c) wind speed, (d) sunshine hours, (e) daily low cloud cover, and (f) annual precipitation trends in the semiarid Loess Plateau and other regions worldwide (10-yr moving average).

Of course, the climate factors are not entirely independent. For example, precipitation, low cloud cover, and sunshine hours are interrelated; and reduced precipitation, low cloud cover, and increased sunshine, which have the same climate significance and represent the drought trend, belong to a chain reaction to some extent. In principle, the regional drought trend may be the main cause of the increased pan evaporation in the semiarid Loess Plateau.

4. The influence mechanism of pan evaporation variation

In addition to the temporal variation in pan evaporation, we examined the functional responses of pan evaporation to individual climatic conditions.

Figure 5 gives the variations of pan evaporation at different temperatures, relative humidity, wind speed, and low cloud cover change ranges based on observational data. Average pan evaporation was calculated when the meteorological elements changed within certain ranges. Figure 5 shows that the higher the temperature and wind speed, the larger the pan evaporation. With the increased temperature, the differences between pan evaporation ranges correspondingly increase. When temperature changes from 20°–25°C to 25°–30°C, the pan evaporation changes by approximately 2.9 mm. However, with increased wind speed, the differences between pan evaporation ranges are less clear. Additionally, the pan evaporation is small when there is enhanced low cloud cover. When the low cloud cover increases, the differences between the pan evaporation ranges become smaller. There are no significant changes in pan evaporation from low cloud cover of 7–8 to the range of 8–9. Changes in pan evaporation with relative humidity are more complex, and it is not a linear relationship. When relative humidity varies from 15%–30% to 30%–45%, pan evaporation reaches its maximum value (7.0 mm) and when relative humidity shifts to lower or higher ranges, pan evaporation decreases. When relative humidity is nearly saturated (90%–100%), pan evaporation is only approximately 1.1 mm. This complexity occurs because humidity is not only the influencing factor but also the outcome of pan evaporation, and is thus also related to the air temperature conditions.

Fig. 5.

Distribution characteristics of pan evaporation for different (a) temperature, (b) relative humidity, (c) wind speed, and (d) low cloud cover ranges.

Fig. 5.

Distribution characteristics of pan evaporation for different (a) temperature, (b) relative humidity, (c) wind speed, and (d) low cloud cover ranges.

However, the variations of pan evaporation in different climatic factors at different ranges of values cannot completely represent the independent variation of pan evaporation with climate factors. This is because the characteristics of variation in response to any climatic factor are in fact affected by several other changing climatic elements. Based on the distribution characteristics in Fig. 5, we broadly infer that pan evaporation remains unchanged in the temperature range of 5°–20°C, relative humidity range of 15%–60%, wind speed range of 2–4 m s−1, and low cloud cover range of 5–7, which indicates that changes to climatic factors within these ranges have little effect on pan evaporation. Therefore, when any three factors change within these ranges, it can be assumed that the pan evaporation changes can be affected by the final factor and have little to do with the other three factors.

Figure 6 shows the respective effects of temperature range, relative humidity, wind speed, and low cloud cover on pan evaporation when the other three climate factors change within a specific range. Pan evaporation has a relatively good correlation with temperature, relative humidity, and low cloud cover with correlation coefficients of 0.83, 0.67, and 0.53, respectively (Fig. 6). Pan evaporation increases significantly with increasing temperature at a rate of approximately 0.29 mm °C−1, but it decreases with increasing relative humidity and low cloud cover at reduction rates of 1.50 mm 10%−1 and 0.34 mm yr−1. The relationship between pan evaporation and wind speed is relatively distinct. There is only a slight increase [0.7 mm (1 m s−1)−1] in pan evaporation with increasing wind speed. The influence mechanism of temperature on pan evaporation is relatively easy to understand and has been considered in several previous studies (Peterson et al. 1995; Brutsaert and Parlange 1998). Increased relative humidity leads to a reduction of the humidity gradient between the land and atmosphere, which inhibits surface water vapor from being transported to the atmosphere, resulting in a more unfavorable environment for pan evaporation and thus reducing pan evaporation. Contrary to the role of relative humidity, increased wind speed will enhance the transmission and diffusion capacity of water vapor, which is conducive to pan evaporation and thus causes an increase in pan evaporation. Increased low cloud cover leads to a decrease in sunlight intensity and reduces input of the heat needed to instigate pan evaporation, which will also lead to a reduction in pan evaporation.

Fig. 6.

Effects of (a) temperature, (b) relative humidity, (c) wind speed, and (d) low cloud cover on daily pan evaporation when the other climatic factors change within a specific range.

Fig. 6.

Effects of (a) temperature, (b) relative humidity, (c) wind speed, and (d) low cloud cover on daily pan evaporation when the other climatic factors change within a specific range.

Before the model fitting, all data used for analysis were tested with the Kolmogorov–Smirnov test and accordance with the normal distribution. Figure 7 shows the frequencies and normal distribution curves of different meteorological elements. Equation (2) gives the multifactor fitting formula between pan evaporation and temperature, relative humidity, wind speed, and low cloud cover based on the relationship between pan evaporation and the different climatic factors:

 
formula

where E is the annual average daily pan evaporation (mm) and is the 50-yr average of the annual average daily pan evaporation; T is the annual average daily temperature (°C) and is the 50-yr average of the annual average daily temperature; e is the annual average daily relative humidity (%) and is the 50-yr average of the annual average daily relative humidity; u is the annual average daily wind speed (m s−1) and is the 50-yr average of the annual average daily wind speed; and c is the annual average daily low cloud cover and is the 50-yr average of the annual average daily low cloud cover. The multifactor formula can be used to represent the combined effect of climate factors on pan evaporation. As seen from this relationship, the coefficients of low cloud cover and relative humidity are negative, and the coefficients of temperature and wind speed are positive, which is in accordance with the impacts of these climatic factors on pan evaporation. Moreover, the influence coefficients of relative humidity and temperature are larger than those of low cloud cover and wind speed, with the coefficient of wind approximately one order of magnitude smaller.

Fig. 7.

The frequency and normal distribution curve of all data used for the fitting analysis.

Fig. 7.

The frequency and normal distribution curve of all data used for the fitting analysis.

Figure 8 shows the comparison of pan evaporation trends for the estimated and measured values and the corresponding correlation scatterplot. The estimated values are consistent with the observation values because the two curves are significantly similar (Fig. 8). The variation values are 0.0139 mm yr−1 and 0.0161 mm yr−1 and the correlation coefficient and standard error are 0.85 and 0.17 mm, respectively, and the relative error is approximately 5%. This result indicates that the multifactor fitting formula is able to reflect the relationship of pan evaporation with temperature, relative humidity, wind speed, and low cloud cover and that it can be used in simulation experiments.

Fig. 8.

(a) Comparison of measured and estimated pan evaporation trends, and (b) the corresponding correlation scatterplot.

Fig. 8.

(a) Comparison of measured and estimated pan evaporation trends, and (b) the corresponding correlation scatterplot.

5. The contribution of different climate factors to pan evaporation

To analyze the contributions of different climatic factors to changes in pan evaporation, we first need to isolate the independent impact of each factor on pan evaporation. The key process is a simulation using the multifactor fitting Eq. (2), assuming that three factors in Eq. (2) remain unchanged (defined as the average in 1960) and estimating the pan evaporation change by varying only the last factor. Figure 9 shows the independent changes of pan evaporation caused by temperature (Fig. 9a), humidity (Fig. 9b), wind speed (Fig. 9c), and low cloud cover (Fig. 9d) variations while the other three factors remain constant. For the last 50 yr, if only temperature changes, pan evaporation will increase by approximately 0.30 mm. If only wind speed changes, pan evaporation will only increase slightly. If only relative humidity changes, pan evaporation will increase by approximately 0.17 mm. If only low cloud cover changes, pan evaporation will also increase by approximately 0.19 mm. Clearly, all climate factors, not just increased air temperature alone, have had significant impacts on pan evaporation over the past 50 yr, which is consistent with the previous analysis.

Fig. 9.

Change in pan evaporation caused by (a) temperature, (b) humidity, (c) wind speed, and (d) low cloud cover changes while the other three factors listed are held constant.

Fig. 9.

Change in pan evaporation caused by (a) temperature, (b) humidity, (c) wind speed, and (d) low cloud cover changes while the other three factors listed are held constant.

As Fig. 10 shows, the air temperature contributes the most, followed by relative humidity and low cloud cover. The contribution of temperature is relatively large and the contribution of wind speed is almost negligible. This quantitative analysis shows that the direct effect of increased temperature can indeed cause an increase in pan evaporation, and in principle there should be no evaporation paradox. Because the reduced pan evaporation caused by increased low cloud cover offset the increased pan evaporation due to the temperature increase and relative humidity decrease in many parts of the world, the true effect of the temperature increase on pan evaporation was thus obscured. In the semiarid Loess Plateau, both increases in temperature and decreases in low cloud cover cause an increase in pan evaporation, and the reduced relative humidity also significantly increases pan evaporation. Therefore, not only the actual effect of temperature but also the combined influences of climatic factors significantly influence pan evaporation. The combined contribution of low cloud cover and relative humidity is over 50%, approximately equivalent to the contribution of temperature changes. Therefore, the dominant factors remain low cloud cover and relative humidity, which is consistent with explanations proposed in previous literature (Brutsaert and Parlange 1998; Roderick and Farquhar 2002).

Fig. 10.

Contribution rates of daily average temperature, relative humidity, wind speed, and low cloud cover to pan evaporation changes over the past 50 yr.

Fig. 10.

Contribution rates of daily average temperature, relative humidity, wind speed, and low cloud cover to pan evaporation changes over the past 50 yr.

In principle, the temperature, relative humidity, and low cloud cover variations are all possible effects of global warming, but the temperature increase is the most direct response and follows the same trends worldwide but at different magnitudes. Low cloud cover and relative humidity changes are indirect effects of global warming, and they act differently worldwide because of the complex responses of atmospheric moisture to climate change. There are many places where low cloud cover and relative humidity are significantly reduced, especially in arid and semiarid regions, while in general, local low cloud cover increases and relative humidity decreases slightly. In other words, there is a general increase in air temperature and wet trend of humidity and precipitation in many parts of the world, but there are also some places (e.g., arid and semiarid areas) that express increased air temperature and drying trend of humidity and precipitation. For these two distinctly different response characteristics to global warming, there are two different pan evaporation trends; pan evaporation is decreased in warm and humid regions and increased in warming and drying regions. The semiarid Loess Plateau area typically falls into the latter category.

It is worth noting that these response characteristics of pan evaporation to climate change form a positive feedback mechanism. In warming and dry regions, the lower precipitation will lead to reduced cloud cover, thus leading to increased radiation and increased pan evaporation, which will in turn increase aridity and alter the local water cycle. However, in warming and humid regions, the situation is opposite; arid areas are increasingly arid and humid areas are increasingly humid, which may exacerbate occurrences of drought and flood disasters worldwide. This inference is consistent with some current observations (Sun et al. 2005).

6. Conclusions and discussion

Through systematic bias correction of pan evaporation measurements from different instruments over the past 50 yr, relatively homogenized observations were obtained that meet the needs of technical analysis of pan evaporation changes in the semiarid Loess Plateau.

Semiarid regions may be the most sensitive areas to global changes because of their fragile ecosystems (Rotenberg and Yakir 2010). The climate change of Dingxi in the semiarid Loess Plateau shows a unique trend. Standardized pan evaporation significantly increased over the past 50 yr, which is significantly different from most other parts of the world. In addition to changes in temperature, the changes of the other climate factors affecting pan evaporation, including precipitation, low cloud cover, wind speed, and sunshine, were also generally contrary to the trends in most other parts of the world. In particular, relative humidity reduces more significantly than in most other areas. Therefore, the evaporation paradox should not necessarily exist in this region.

We found that pan evaporation is significantly affected by climate change in the semiarid Loess Plateau. It increases markedly with increasing temperature independently at a rate of approximately 0.29 mm °C−1; however, with increasing relative humidity and low cloud cover, pan evaporation reduces independently at rates of 1.50 mm (10%)−1 and 0.34 mm yr−1. As seen from the multifactor fitting relationship, the coefficients of low cloud cover and relative humidity are negative, and the coefficients of temperature and wind speed are positive. Moreover, the influence coefficients of relative humidity and temperature are larger than those of low cloud cover and wind speed, with the coefficient of wind speed approximately one order of magnitude smaller than that of low cloud cover. The formula used in this study was able to reflect the relationships between pan evaporation and temperature, relative humidity, wind speed, and low cloud cover, and the simulations are consistent with the observed values. The simulation experiments of single climatic factors that influence pan evaporation showed that temperature, relative humidity, wind speed, and low cloud cover changes caused increases of approximately 0.30, 0.17, 0.02, and 0.19 mm in pan evaporation over the last 50 yr, and the contribution rates were 46.18%, 25.90%, 2.48%, and 25.44%, respectively. Thus, air temperature contributes the most, followed by relative humidity and low cloud cover. The combined contribution of low cloud cover and relative humidity is greater than that of temperature. The wind speed and pan evaporation are positively related. Roderick et al. (2007) pointed out that the decrease of the wind speed is the main factor causing the decreased pan evaporation in most parts of the world. However, in the current study, the wind speed growth rate is 0.031 m s−1 decade−1. The change is small and it is not as sensitive as other factors to pan evaporation (Figs. 4 and 5). Thus the contribution of wind speed was minimal (only 2.48%).

In many parts of the world, increased low cloud cover happens to offset the increased pan evaporation because of temperature increase and relative humidity decrease, but in the semiarid Loess Plateau, the increased temperature and relative humidity and decreased low cloud cover all caused an increase in pan evaporation and thus significantly enhanced the impact of increased temperature. We found that the warming trend was particularly enhanced in the boreal cold season (November–March) over semiarid regions showing a temperature increase of 1.53°C as compared with the global annual mean temperature increase of 1.13°C found over land by Huang et al. (2012). Therefore, the increased pan evaporation caused by temperature in semiarid regions may be considered more significant. The most probable reason for the apparent evaporation paradox in many regions of the world is the fact that pan evaporation is a complex process for which expectations based on single factors can lead to seemingly paradoxical observations; for example, decreased pan evaporation with global warming. If all relevant factors affecting pan evaporation are considered (air temperature, cloud cover, humidity, wind speed, soil moisture and subsequent evaporation of the surrounding region, etc.) there might not appear to be any paradox.

Temperature, relative humidity, and low cloud cover changes are all influenced by global warming, but temperature exhibits basically the same trend worldwide. Low cloud cover and relative humidity change significantly on a regional basis, and relative humidity reduced more significantly in the Loess Plateau than in other regions. Thus, pan evaporation is reduced in most warm and humid regions and increased in warming and drying regions, such as the semiarid Loess Plateau. The Bet Dagan in Israel (Cohen et al. 2002) and Hamedan in Iran (Tabari and Marofi 2011), where pan evaporation is increasing, are also located in semiarid climates. These positive feedback mechanisms may cause humid areas to become more humid and arid areas to become increasingly arid. Huang et al. (2016a) showed that the area in transition from semiarid (subhumid–humid) to arid (semiarid) is much larger than that in transition from arid (semiarid) to semiarid (subhumid–humid); therefore, more semiarid (subhumid–humid) regions are likely to become drier.

Acknowledgments

We acknowledge Dengrong Lu and Zhihong Hui from the Meteorological Bureau of Gansu, Information Center, for providing meteorological data for this article. We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript. Funding was provided by the Key Program of the National Natural Science Foundation of China (Grants 41630426 and 40830957) and the National Key Basic Research Program of China [2013CB430200 (2013CB430206)].

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