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Trend analysis of the ET from 1948 to 2018
To reveal the ET trend in the 71 years from 1948 to 2018 in the study area, we extracted the ET in the study area throughout this period from the GLDAS data, calculated the Z value of each pixel throughout this period with the TFPW-MK test method, and generated an ET change trend distribution map with the Z value of each pixel.
First, we adopt the annual ET of each pixel as the statistical value to establish the 71-year time series. The trend of each pixel from 1948 to 2018 is analysed to examine the general trend of the ET in China and its spatial distribution characteristics. Then, we select the ET of each pixel in each month from January to December as the statistical value, establish 12-month time series over the 71-year study period, and analyse the trend in each month over the 71 years from January to December to examine the influence of the month on the ET change trend in China.
Trend analysis of the ET over the years
First, we analyse the annual ET trend of each pixel throughout this period, and Fig. 1 shows the distribution of the Z value reflecting this trend.
According to the obtained statistics, there are approximately 15258 pixels in the study area, of which 13662 pixels exhibit Z values larger than 0, accounting for approximately 89.5% of all pixels. The other pixels with Z values smaller than 0 account for approximately 10.5% of all pixels. This shows that the overall trend in most regions of China since 1948 is an increasing trend, and only a small part exhibits a decreasing trend. Figure 1 shows that the regions where ET has significantly decreased are distributed across parts of Western China and the two islands in southern China, while the ET in most other regions exhibits a relatively significant growth trend.
Figure 1 shows that the ET change trend in Western China is quite different. The change trends in most areas are consistent with the overall ET change trend in China, showing a significant upward trend. The ET in a small part of the area (the red area in the figure), namely, the western Qiangtang Plateau and its surrounding areas, exhibits a significant downward trend. The Qiangtang Plateau is the main body of the Qinghai-Tibet Plateau in southwestern China. Most of the plateau is above 4600 metres above sea level. It is a typical area with very harsh climate conditions and an extremely fragile ecological environment in China. The environmental characteristics are mainly exemplified by a dry and cold climate, windy conditions, and abundant surface sand areas, sparse vegetation and a low ecological capacity49. Since the 1950s, the western Qiangtang Plateau has increasingly become arid with global changes50, and the precipitation in the southern surrounding area has decreased significantly51.These factors together led to the most obvious ET decreasing trend on the western Qiangtang Plateau and its surrounding areas in Southwest China. The reason for the significant increase in ET in Western China is basically the same as the reason for the increase in ET in the other parts of China, namely, climate change and human activities. Climate change is mainly due to the increase in precipitation17 and the increase in warming and aridification in most parts of China, which has greatly increased the temperature and relative humidity52. However, the increase in human activities is primarily caused by the fact that since 2000, the state has heavily invested in ecological restoration and has successively implemented a number of major ecological environmental protection and construction projects, such as returning farmland to forestland and grassland, returning grazing land to grassland, natural forest protection, and forest system protection projects. With the implementation of the above ecological projects, the vegetation conditions in certain areas have been improved53, and the areas where the ET has notably increased are mainly located in areas with a high vegetation cover54.
Figure 1

Spatial-temporal trend of the ET in China from 1948 to 2018.

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When the absolute Z value is greater than or equal to 2.32, the confidence level is 99%, and when it is greater than 1.64 but less than 2.32, the confidence level is 95%. When the absolute Z value is greater than 1.28 but less than 1.64, the confidence level is 90%. Table 1 lists the proportion of the number of pixels in each distribution interval of the Z value. The Z value in 63% of all pixels is greater than 2.32, and the areas covered by these pixels have a 99% chance of exhibiting an increasing trend. Analogously, the areas with Z values greater than 1.28, accounting for 89.7% of all pixels, have a 90% chance of exhibiting an increasing trend. All of these statistics indicate that in China, the ET in most regions exhibits a very obvious increasing trend.
Table 1 Confidence level of the Z value and pixel proportion.
Full size table

Variation trend of ET with the different months
From January to December, solar radiation changes with the time, temperature, precipitation and other meteorological elements, and ET also changes over time55. To reveal the ET trend with the month, we calculated the ET trend of each pixel throughout the 71-year period from January to December. Figure 2 shows a distribution map of the Z value reflecting this trend.
Figure 2 reveals that the ET trend in China varies greatly with the change in months, and many regions show the most or least obvious increasing trend (or decreasing trend) at different times. The details are as follows:
(1)
In Northeast China, especially the Middle-Lower Yangtze Plain and the eastern Tibetan Plateau, the ET increasing trend is the most obvious in April and the least obvious in January and December.

(2)
On the North China Plain, the ET increasing trend is the most obvious in March, and the ET decreasing trend is the most obvious in November and December.

(3)
On the Yunnan-Guizhou Plateau and Chiang-nan Hilly Region, ET increased the most from June to August and decreased the most in January.

(4)
The increasing trend on the Inner Mongolia Plateau is the most obvious in February and March and the least obvious in August.

(5)
Compared to the other months, the increasing trend on the western Tibetan Plateau from May to September is more obvious. However, the annual ET increasing trend is not obvious, but the decreasing trend is very obvious.

(6)
The decreasing trend in January and December in Northwest China is obvious, and the increasing trend in the other months is obvious.

(7)
The annual ET trend in the Tarim Basin and its surrounding areas is an obvious increasing trend. However, the ET trends in the east and west of the Tarim Basin are obviously different. In August and September, the west of the Tarim Basin reaches the maximum value of the ET trend, while the east of the Tarim Basin exhibits the most obvious decreasing trend.

In general, the ET trend in Northeast China varies greatly from month to month. The ET in most areas of Northeast China mainly increases from March to October, while the ET mainly decreases from December to February. This is related to the concentrated distribution of the forest areas in the Greater Khingan Mountains and Changbai Mountains in Northeast China. The ET in forest ecosystems is the highest. From March to October every year, plants are subject to the growing season, the vegetation is lush, transpiration and evaporation occur vigorously, and ET is on the rise. From December to February of the following year, plants are in the declining or non-growing season. Moreover, due to the low temperature, energy and stomatal conductance levels, the ET values reveal a downward trend54.
The variation trend of the ET in southern China, northwestern China, and northern China is also relatively obvious. The ET from June to August mainly reveals an upward trend, and the ET mainly shows a downward trend from September to May of the following year. This is mainly related to the temperature and precipitation. Between June and August, the temperature and precipitation increase, and the ET is also very notable; from September to May of the following year, the temperature drops, and the precipitation and ET also decrease56.
However, the ET in most parts of Southwest China exhibits a downward trend in almost all months, but it is also observed that the area with a decreasing trend in winter is relatively large, while that in summer is relatively small. The main reason why the ET in each month decreases is that this region is located on the Qiangtang Plateau, an alpine and cold region with an altitude higher than 4600 metres, which has a unique natural environment and climatic conditions51. Drought and precipitation reduction are the leading factors of the ET decrease50,51, , and the ET throughout the whole year mostly presents a downward trend. Moreover, the monthly changes in the climate of the Qiangtang Plateau are very obvious, with distinct cold and wet seasons. Generally, the period from May to September is the warm, rainy and less windy season, but the period from October to April of the following year is the cold, dry, and windy season50, and the area with an ET decreasing trend from May to September shrinks, while the area with an ET decreasing trend from October to April expands.
Figure 2

Spatial-temporal trend of the monthly ET in China from 1948 to 2018.

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According to the monthly change trend, we calculated the proportion of the number of pixels with an increasing trend, i.e., those pixels with Z values greater than 0. Figure 3 shows the calculation results. The figure shows the ET trend in China with the change in months.
Figure 3 shows that in January, only 57.95% of the study area exhibited an increasing trend, which quickly increased to over 76.0% in February, reaching a maximum value in May, after which it began to decrease. However, the area increased in September, rising to 81.81%, and then continued to decrease, until it reached a minimum value in December, similar to January. On the whole, the proportion of (Z >0) from January to December was ( >50%), and all months of the year were dominated by a growth trend, and from January to May, the pixels with (Z >0) increased, with a total increase of 29.65%. The growth rate was the highest from January to February, with a total increase of 18.05%, accounting for 60.88% of the increase, indicating that the area where the ET was on the rise from January to February exhibited the fastest growth, and the number of pixels with (Z >0) reached a maximum value of 87.60% in May, after which it decreased. There was a small fluctuation in the middle of September, but an overall decrease was still observed, and the rate of decrease increased, with a total decrease of 30%, reaching a minimum value of 57.60% in December, which was still higher than 50%. From Fig. 3,we can deduce that the number of pixels with an increasing trend in the study area was the largest in May and the smallest in December and January. In particular, the region in the study area with an increasing trend was the largest in May and the smallest in December. In all months of the year, more than half of the pixels exhibited an increasing trend, which also indicates that in regard to the study area, the annual ET trend was still dominated by an increasing trend, which is consistent with the finding from Fig. 1.
Figure 3

Proportion of pixels with an increasing trend over the 12 months.

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Figure 2 does not directly show the monthly fluctuation in the ET trend of each pixel from January to December. Standard deviation analysis of the 12 subgraphs of Fig. 2 is conducted, and Fig. 4 is obtained. The standard deviation can be adopted to analyse the dispersion of the Z value of each pixel from January to December, and based on Fig. 4 we can determine the monthly fluctuation in the ET trend.
Figure 4

Standard deviation distribution of the monthly ET trend in China.

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Figure 4 shows that in the dark blue parts, i.e., in Northeast China, West China, Northwest China and South China , a large variation occurs, especially in the border area of Northeast China and a small number of pixels in Northwest China, where the standard deviation exceeds 4.5, indicating that the ET trend in these regions is greatly affected by the months. In regard to the light blue parts of the map, such as the northwest Tarim Basin, Tianshan Mountains and its surrounding areas, east Tibet Plateau and middle Inner Mongolia Plateau, the impact of the month is relatively small.
Coefficient of variation analysis
Through statistical analysis of the ET CV in time and space, the dispersion of ET in time and space can be analysed, and the stability of the ET fluctuation in time and space can then be determined.
Spatial distribution of the time series CV of ET
The time series CV of ET from 1948 to 2018 is calculated for each pixel, and Fig. 5 is obtained.
Figure 5

Spatial distribution of the time series CV of ET.

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Figure 5 shows that the ET CV of each pixel in China from 1948 to 2018 shows a trend of gradually decreasing from northwest to southeast. The ET in northern China is more discrete than that in the south, and the ET in the west is more discrete than that in the east. The higher the dispersion degree is, the more unstable the ET in these regions is over the 71-year period. The lower the dispersion degree is, the more stable the change in ET is.
In summary, from 1948 to 2018, the variation in ET in northern China was more severe than that in southern China, and the variation in ET in Western China was more severe than that in eastern China. The ET in the surrounding areas of the Tarim Basin in northwestern China revealed the most dramatic changes, and the ET changes in most parts of East China remained the most stable.
Time fluctuation in the spatial distribution CV of ET
From 1948 to 2018, the CV of the yearly ET spatial distribution in the study area was calculated to analyse the fluctuation in the ET spatial variation over time. Figure 6 shows a linear graph based on the 71 CV yearly values, from which we can observe the changes in the spatial variation from 1948 to 2018. Moreover, we also calculated the SD and mean from 1948 to 2018. To facilitate a comparison of the change trends of the SD and mean with the change trend of the CV, we mapped the SD and mean to the range of the CV, [0.55, 0.67], and accordingly plotted a line graph of the SD and mean.
Figure 6

Time fluctuation in the spatial distribution CV of ET.

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In Fig. 6, the yellow solid line is the change curve of the SD over time, and the blue solid line is the variation line of the CV over time. The blue solid line reveals that the change in the spatial distribution CV over time from 1948 to 2018 can be roughly divided into two stages: 1948–2001 and 2002–2018. The red dotted line is the mean value of the CV in each year in the two stages. The following is a description of these two stages:
The first stage: 1948–2001. During this period, the CV value of ET fluctuated within a high range, ranging from 0.61 to 0.67, and the average value was approximately 0.63, but the fluctuation range in most years was approximately 0.62 to 0.65, and the change was relatively small. Among them, the CV of ET in 1959 and 2000 was relatively small, indicating that the ET in the study area in these two years remained relatively uniform, while the CV in the other years (such as 1951, 1965, and 1986) were relatively large, indicating that the ET in the study area varied greatly in these years. However, on the whole, the CV in each year in this stage was larger than that in the second stage, indicating that the spatial difference in ET in the study area in this stage was large, and the overall ET was uneven.
The second stage: 2002–2018. Figure 6 shows that the CV began to decrease in 2002, and it decreased to a minimum value of 0.55 in 2003. Thereafter, up to 2018, the value of the CV fluctuated within a low range, ranging from 0.55 to 0.62, with an average value of 0.58, which is a decrease of 0.05 over the first stage value. Although it reached a maximum value of 0.62 in the second stage in 2018, the value was smaller than the average value in the first stage , indicating that the CV in this stage was generally smaller than that in the first stage. Notably, the difference in ET between the various regions in the study area decreased in 2002, and the ET in China became more even. According to the change curve of the average ET, the average ET in China began to increase in 2002. Although fluctuations occurred, the average ET also fluctuated within a relatively high range. This is consistent with the research results of Bing Longfei7, namely, after 2000, the annual ET greatly exceeded the previous ET level. Combined with the decrease in the CV value, this shows that after 2002, the ET in the various regions of China started to increase. The main reason for this result is that the state invested heavily in ecological restoration in 2000 and successively implemented a number of major ecological environmental protection and construction projects, such as returning farmland to forestland and grassland, returning grazing land to grassland, natural forest protection and shelterbelt system projects53. After 2002, good results were achieved, and vegetation conditions were improved, while the regions with a notably increased ET primarily occurred in those regions with an improved vegetation cover54. Therefore, after 2002, the ET in all regions in China began to increase, and the CV began to decrease.
By comparing the SD line chart and the CV line chart, it is observed that the trend of these two lines in the first stage and the second stage is basically the same, but after the first stage, the CV exhibits a decrease, the SD does not change, and there is an increasing trend after 2002. However, the SD is an absolute indicator. When the sample mean level is different, an absolute difference index cannot be considered in a comparative analysis57, while the CV measures the degree of variation between samples with different units or with a large difference in the mean. Here, the annual average ET value constantly changes, and it is more accurate to adopt the CV to compare the dispersion degree between the different regions within the study area.
In other words, the annual ET spatial difference within the study area was relatively large from 1948 to 2001, and the annual ET in the study area was very uneven. After 2002, the annual spatial difference decreased, and in 2003, the spatial distribution of the ET in the study area was the most uniform.
Future trend analysis of ET
The variation in ET in the study area from 1948 to 2018 has been previously analysed. This section assesses the future ET variation in China, i.e., whether the future ET variation in the study area will follow the trend from 1948 to 2018. This is evaluated with the Hurst index. The value range of the Hurst index is between 0 and 1. If the Hurst index is larger than 0.5, this indicates that the future trend will follow the original trend. The closer the Hurst index is to 1, the stronger the continuity is. If the Hurst index is smaller than 0.5, this indicates that the future trend will contradict the original trend. If the Hurst index is equal to 0.5, this indicates that the future trend is uncertain and not related to the original trend. Figure 7 shows a map of the distribution based on the calculated Hurst index of each pixel.
Figure 7

Spatial distribution of the Hurst index from 1948 to 2018.

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According to the calculated Hurst index of each pixel, only 26 pixels in Fig. 7 have a Hurst index smaller than 0.5, no pixels exhibit a Hurst index equal to 0.5, and most of the pixels in the study area reveal a Hurst index larger than 0.5. This implies that in the future, the vast majority of the study area will continue the trend from 1948 to 2018, as shown in Fig. 1. In terms of the possibility of this continuity, the number of pixels with a Hurst index larger than 0.9 accounts for approximately 23.2% of all pixels, and the number of pixels with a Hurst index between 0.8 and 0.9 accounts for approximately 36.8% of all pixels, while the number of pixels with a Hurst larger than 0.8 accounts for approximately 60% of all pixels. These results indicate that it is very possible for these pixels to continue the current trend in the future. Especially in Northeast China, South-Central China and West China, the Hurst index values are all close to 1, and the ET trend in these regions exhibits a notable continuity. For example, according to Fig. 1, it is found that the ET in Northeast China has a strong increasing trend from 1948 to 2018. Combined with the Hurst index analysis results in Northeast China, as shown in Fig. 7, it is concluded that in the future, the ET in Northeast China will increase more than that in the other regions. More

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