Temporal and spatial variations in reference evapotranspiration (ET0) and aridity index (AI) can be used as important indexes for understanding climate change and its effects on ecosystem stability. Thus, in this work, we comprehensively investigated 71 meteorological stations in Northeast China from 1965 to 2017 to analyze the spatial-temporal variation and trend of ET0 and AI using the nonparametric Mann–Kendall test, the linear regression, and the Morlet wavelet methods. The results elucidated that ET0 for Northeast China as a whole exhibited a decrease at a rate of −1.97 mm/yr, AI declined at a rate of −0.01/yr during 1965–2017, and approximately 94% stations showed a decrease trend. Spatially, the high values of AI and ET0 were primarily at the western part of the study area except for the Heilongjiang province, and the stations showing low values were mainly distributed in the central and eastern part. The decreasing trends for AI were more obvious in the eastern part compared with the western part over the study region. The abrupt changes in AI occurred in 2005 and 2007, whereas only one abrupt change for ET0 occurred in 1995. For annual ET0, there were periods of 3, 7, 11, and 15 yr, and there existed periods of 1, 7, 11, and 13 yr for annual AI. The correlation coefficients implied wind speed and precipitation were the dominant meteorological factors resulting in the ET0 and AI decrease, respectively. Additionally, the change of the Indian summer monsoon index (ISMI) may also contribute to the weakened AI in the study area. Nevertheless, further investigation is still required to clarify the mechanisms for AI and ET0 variations in the future.

1. Introduction

The Fourth Assessment Report (AR4) provided by the Intergovernmental Panel on Climate Change (IPCC) pointed that the variation of global climate could reach an unprecedented rate in the 21st century [1, 2]. Under a warming climate, especially extreme climate events, including extreme rainfall, heat waves, floods, and droughts, would occur more frequently [2]. Additionally, climate extremes can cause great economic losses in different parts of the world [35], and the extreme climate events were generally more significant to natural and human systems than their mean values [6]. Thus, climate extremes have already been extensively investigated, and studies in certain regions worldwide, such as Africa [7, 8], Asia [912], Europe [13, 14], and North America [15, 16]. These works have come to the conclusion that the obvious changes in temperature extremes and the spatial variations in precipitation extremes are associated with the global warming. Additionally, reference evapotranspiration (ET0), defined as the potential evapotranspiration of a hypothetical surface of green grass of uniform height, was one of the most important hydrological variabilities for agricultural irrigation and regional hydrologic cycle [1719], which was a significant hydrological process for water cycle. Therefore, better understanding of the changes of ET0 was a major component in local hydrological research [20]. A majority of studies have verified the effect of climate variation on ET0 and obtained fruitful results. The ET0 showed a decreasing trend in all seasons, particularly in Northwest and southeast China during 1954–1993 [21], which could be attributed to the sunshine, solar radiation, and wind speed variations. Similarly, it was found that global ET0 decreased at a rate roughly between −1 and −5 mm/yr [2224], and the same tends of ET0 were also found in Taoer River Basin, Yangtze River Basin, and Tibetan Plateau [2527]. Nevertheless, it was reported that the aridity index (AI), frequently used to predict model scenarios that assess the extreme dry events, would benefit some agricultural areas [28], but AI has not been extensively employed except for Northwest China [20] and part of Tibetan Plateau [28], and the obtained results displayed that AI had a similar decreasing trend in Northwest China and significantly decreased by 0.04/10 yr in the central and eastern part of Tibetan Plateau from 1960 to 2012.

Northeast China located in high latitudes is a sensitive area of climate change, especially in the central and western regions in the way of rain, and is also an important area of grain production in China. Therefore, for the purpose of studying the characteristics of change of AI and ET0 in northeast of China from 1965 to 2017, we collected the long-term and available daily meteorological data. This paper aimed to provide scientific basis for decision making regarding rational planning of regional agricultural production and evaluating water resources, by analyzing the spatial and temporal characteristics of ET0 and AI, which could play a vital role in understanding the effect of global warming over the study region.

2. Materials and Methods

In this section, we firstly give some essential information, such as natural conditions in the study region and dataset regarding the selected meteorological stations. Secondly, equations for calculating ET0 and AI that have been extensively used were described in detail. Thirdly, in order to better analyze the characteristic of temporal variations of ET0 and AI in Northeast China, the Mann–Kendall (M-K) method was introduced for assessing the temporal data trend and abrupt change in AI and ET0. Meanwhile, the method of Morlet wavelet was given and described, which was applied to evaluate the ET0 and AI periodicity change.

2.1. Study Area

Northeast China (38°40′–53°34′N and 115°05′–135°02′E) is a geographical region of China (Figure 1). It mainly includes three administrative regions: Heilongjiang province, Jilin province, and Liaoning province, with a total area of around 1.24 × 106 km2. Northeast China is a major manufacturing base for agriculture, forestry, grassland farming, and industry. The study region belongs to continental monsoon climate, and it is a relatively sensitive region of variations in climate under global climate models [29]. The annual mean temperature is from 4.7 to 10.7°C, with seasonal average temperature ranging from 14.7 to 23.8°C in summer and from −27.7 to 2.5°C in winter. The annual range of air temperature is even high up to 40°C. The length of time for which snow covers the ground can last for six months in certain regions [30]. The annual rainfall showed a decrease from the southeast (1000 mm) to the northwest (300 mm), and it has an irregular seasonal precipitation distribution [31], which primarily occurred in summer and autumn.

2.2. Data Sources

In the present work, daily mean wind speed, temperature (maximum, minimum, and mean temperature), mean relative humidity, precipitation, and sunshine duration from 71 meteorological stations in Northeast China from 1965 to 2017 were obtained from the China Meteorological Information Center (Figure 1, Table 1; available at http://data.cma.cn). The selected stations are uniformly distributed in the study region, particularly in Jilin and Liaoning provinces. 27 stations are in the Heilongjiang province, 23 in Liaoning province, and 21 in Jilin province. The starting time of all the stations was in 1950s (Table 1). However, the time series dataset of some stations was discontinued and missing during 1950–1963; thus, we used monitoring data from 1965 to 2017 in this study. The data we used here have been subjected to strictly control the data quality and homogenization, and procedures [3235]. Moreover, the Multivariate ENSO Index (MEI), the Pacific Decadal Oscillation (PDO), the Western North Pacific Monsoon Index (WNPMI), and the Indian Summer Monsoon Index (ISMI) were provided by the National Oceanic and Atmospheric Administration-Cooperative Institute for Research in Environmental Sciences (available at https://www.esrl.noaa.gov/psd/).

2.3. Reference Evapotranspiration and Aridity Index

The Penman–Monteith method is applied to estimate ET0 from hypothetical reference grass with a height of 0.12 m, a defined surface resistance of 70 sm−1, and an albedo of 0.23 [32]. The PM56 expression applied for reference evapotranspiration (ET0) equation [32] is given aswhere Rn represents the net radiation at the ground surface (MJ/(m2·d)), G stands for the ground heat flux (MJ/(m2·d)), T denotes the air temperature at a height of 2 m (m/s), γ stands for the psychrometric constant (kPa/°C), U2 means the wind speed at 2 m height (m/s), es stands for the saturation vapor pressure (kPa), ea is actual vapor pressure (kPa), and Δ stands for the slope of the saturated water-vapor pressure to air temperature curve (kPa/°C). Detailed calculation of Rn,G, γ, es, ea, and Δ can be found in [36].

AI was defined for distinguishing the differences between precipitation and evapotranspiration through potential evapotranspiration [37]. The description can measure the degree of arid in certain regions. In the present work, AI can be computed as follows and it has been successfully applied to evaluate the arid degree [20]:where P represents the monthly total precipitation (yearly) and ET0 stands for the monthly reference evaporation (yearly).

2.4. Mann–Kendall Test

M-K test, famous for Kendall’s tau test developed by [38, 39], is a nonparametric check for evaluating the significance of a trend for environmental data [40, 41], which was extensively adopted in studying trend detection [42, 43]. The null hypothesis H0 is that, in a sample of data {xi, i= 1, 2, …, n}, xi means independent and identically distribution. The hypothesis H1 means a monotonic trend. The statistic S of Kendall’s tau is calculated as follows:where xj is the sequential data value and n means the length of data series.

Mann [39] and Kendall [38] have reported that when n ≥ 8, the statistic S means naturally distributed with zero (E(S) = 0) and the variance is defined aswhere tm represents the number of ties of extent m. The standardized test Zc is calculated bywhere Zc stands for the test statistics. When |Zc| > Z1−α/2, where Z1−α/2 is the standard normal deviates and α stands for the significance for this test. Mann–Kendall index is widely applied in analyzing changes of climate data [28, 44, 45]. Temporal data show no changing trend when the value of M-K index is 0, and temporal data tend to increase when M-K index is greater than 0, whereas data tend to decrease when M-K index is less than 0.

Moreover, the M-K test was employed to test abrupt changes in AI and ET0 in Northeast China [46].

2.5. Morlet Wavelet Method

Wavelet transform is an important method to analyze the frequency, intensity, time, and duration of the changes in a time series [27] by showing the localized time and frequency in formation. The wavelet transform has been frequently used to the fields regarding climatic change and hydrological research. In this work, according to Torrence and Compo [47], the Morlet wavelets were extensively adopted [35, 48, 49]. The Morlet wavelet function iswhere s represents the wavelet scale; ω means the frequency; H(ω) is the heaviside step function, H(ω) = 1 if ω > 0, H(ω) = 0 otherwise; and ω0 means the nondimensional frequency, thus taken to be 6 to meet the adoptability condition [50].

3. Results and Discussion

3.1. Temporal Variation of Meteorological Variables

The yearly and seasonal average temperature exhibited an increase in Northeast China, at the rate of 0.38°C/10 yr () in recent 50 years [51], similar to the findings reported by Lu et al. [52]; Li et al. [34], and Zhang et al. [30] in Songhua River Basin, Southwestern China, and Heilongjing Province. There was a clear decreasing trend in annual precipitation during 1960–2009 in the Songhua River Basin [53]. An obvious peak appeared in July in monthly distribution in Northeast China, and the maximum was 151 mm/month, which is remarkably higher than that occurred in preceding months where the values did not exceed 10 mm/month. Summer precipitation from June to August accounted for about 66% of the total precipitation [54]. The sunshine time and growing season (April to September) presented the declined trend, especially in the Songnen Plain, midwest of Jilin province, and west part of Liaohe Plain in recent decades [31]. Meanwhile, the wind speed and relative humidity likewise presented decreasing trend, and the precipitation as an important climate parameter that influences the ET0 and AI also decreased during 1965–2017 exhibiting a trend of −0.65 mm/yr.

3.2. Annual Variations of ET0 and AI

The regional average values of ET0 in Northeast China during 1965 to 2017 were shown in Figure 2. The average of annual total ET0 from 1965 to 2017 was 611 mm, and the maximum (680 mm) appeared in 1982 and the minimum appeared in 2017. Linear regression displayed that the annual average ET0 in the study area presented a decrease trend at a rate of −1.97 mm/yr (Figure 2(a)), and this trend of annual ET0 was similar to the results obtained in North China and Pearl River Basin [11, 54, 55]. However, the observed annual ET0 greatly declined at the rate of −3.09 mm/yr in arid area of Northwest China in the past 54 years [29], and the decline rate was about 1.5 times higher than that estimated in Northeast China. Huo et al. [20] concluded that the contribution of wind speed to the ET0 decrease was more than that of other meteorological factors in arid area in Northwest China. As mentioned above, the average annual temperature increased over the study region, whereas the annual ET0 showed a declined trend, suggesting the existence of paradox because an increase in temperature usually leads to upward ET0. Nevertheless, effect of increasing temperature was offset by obviously declining the wind speed and relative humidity. For example, both the annual wind speed and relative humidity presented decreasing trends at the rate of −0.012 m·s−1/yr and −0.05%/yr in the study area, respectively. The correlation coefficient between wind speed and ET0 was high with a value up to 0.682, followed by relative humidity (0.601) and sunshine duration (0.551), indicating that wind speed and relative humidity were two main climatic factors responsible for the variation of ET0 in the study region. The precipitation decreased at the rate of 0.65 mm/yr over the study region and was the main meteorological factor resulting in downward AI due to the high correlation coefficient (0.710), which was followed by wind speed (correlation coefficient = 0.583).

Besides, we also investigated the trends of ET0 in three provinces over Northeast China, including Liaoning, Jilin, and Heilongjiang provinces. The results exhibited that the trend of ET0 was consistently decreasing with the whole study region, at the rate of −2.50 mm/yr, −1.63 mm/yr, and −1.76 mm/yr, respectively (Figures 2(b)2(d)). Obviously, the most pronounced decreasing trend occurred in Heilongjiang province over Northeast China, and it has contributed approximately to 42% of ET0 decrease in Northeast, which had two different phases, mainly divided by the change point in 1989 (Figure 6). The ET0 was higher during 1961–1989 compared with the entire period and presented the volatile downward trend, whereas ET0 showed significantly declined trend during 1990–2017. It revealed that Northeast China tended to be wetter in recent two decades. The statistical tendency of annual average AI in Northeast China is shown in Figure 3. The highest AI value was observed in 1978 (0.19), and the lowest value appeared in 2010 (−1.18). The annual AI had an insignificant declined trend at a rate of about −0.01/yr from 1965 to 2017, and the linear trend of AI was statistically nonsignificant (Figure 3(a)), as well as the three provinces of Northeast China likewise showed statistically decreased trends at the rate of −0.0085/yr, −0.0064/yr, and −0.0129/yr, respectively. The decline trend rate for Heilongjiang province was the largest of all and contributed to 46% for Northeast China. It was consistent with Northwest China and Loess Plateau region, which implied that Northeast China tended to be wetter; this was probably due to the decrease of annual wind speed, sunshine time, and ET0 over Northeast China.

3.3. Interdecadal Changes of ET0 and AI

For the purpose of investigating the temporal variation characteristics in ET0 and AI in Northeast China during the past 53 years, the interdecadal change trends were analyzed by probability distribution functions (PDFs). Figure 4 displayed the PDFs of the occurrence of annual ET0 and AI in the past 53 years. The ET0 presented an increasing trend from the 1960s to the 1970s, then decreased in the 1980s, and displayed a decreasing rapidly trend in 1990s to the period of 2000–2017, which was consistent with previous study results [28]. Moreover, AI exhibited a positive tendency from the 1960s to the 1970s and presented a rapid decreasing trend in 2000s.

3.4. Spatial Distributions of ET0 and AI

To better understand the spatial distributions of the ET0 and AI in Northeast China, the Zc value was calculated by the M-K test. Figures 5(a) and 5(c) display the average value and the tendency of ET0 and AI over Northeast China from 1965 to 2017. As is shown in Figure 5(a), most stations with high ET0 were distributed in the west of the study region except for Heilongjiang province, while the stations with low values of ET0 were primarily located in the central and eastern part. The regions that displayed maximum (814.92/mm) of ET0 appeared at Chaoyang station in Liaoning province, and the minimum (403.96/mm) appeared in Heihe station, exhibiting large variations in the average value of ET0 in the study area. The obvious difference between the two stations mentioned above can be mainly attributed to the temperature [56]. These stations with low values of ET0 were primarily located in mountainous areas and with a high normalized difference vegetation index [57]. Additionally, the estimated ET0 in Liaoning province was generally much higher than that of the other two provinces. Figure 5(b) presents spatial patterns for the trend of ET0 over Northeast China during 1965–2017. Remarkably, considerable stations showed a decreasing tendency for ET0, and the proportions of meteorological stations with negative trends were approximately 94% (94% statistically significant), which was consistent with the results in Yangtze River Basin and Tibetan Plateau [25, 27]. Moreover, only four meteorological stations exhibited an increasing trend for ET0 and these four stations primarily distributed in mountain areas in Jilin and Liao provinces, and just one station had shown statistical significant positive trend. Figure 5(c) shows that the distribution of AI stations with higher values was mainly in the western part of Northeast China, which was similar to that of ET0, indicating that the western region was dryer than other regions in the study area. The highest value was observed at Tongyu station in Jilin province, and the lowest value was at Kuandian station in Liaoning province. Figure 5(d) shows spatial patterns of trends for AI during 1965–2017, and a large amount of stations presented a decreasing trend for AI on the whole study area. Moreover, around 85% of the stations were at the significant level. Contrarily, only four stations showed an increasing trend with no statistically significant positive trend, the four station mainly in Liaoning and Jilin provinces, and the obtained results was in agreement with the Northwest China [20]. The results suggested Northeast China generally tended to be wetter under global warming, which may be primarily attributed to the topography and increasing vegetation [57].

3.5. Abrupt Change Analysis

Abrupt changes estimated by the M-K method reflected remarkable variation in trends for the target series. Figure 6 shows the test results of ET0 and AI in Northeast China during 1965–2017. There was only one abrupt change in annual ET0, and abrupt point in 1995 was at the 0.01 significance level. The ET0 showed an interdecadal oscillation before 1995 and then presented a significant declined trend. There were two abrupt changes in the whole change process of time sequence for AI, mainly in 2005 and 2007, significant at 0.01 level. The abrupt change was relatively smaller in 2005, while there was a sudden decline trend, consequently, and thus an abrupt point in 2007 for AI.

3.6. Period Analysis and Climate Teleconnection to the Annual AI

To further estimate the ET0 and AI variations, we apply the Morlet wavelet transforms to yearly time series of the AI and ET0. Figures 7 and 8 show the time-frequency characteristics in real part of the Morlet wavelet method for the ET0 and AI in Northeast China from 1965 to 2017. In these two figures, (a) represents annual ET0 time series employed for this analysis. (b) represents local wavelet power spectrums of (a). The black contour designated at 5% significance level against red noise and the cone of influence (COI) is shown using a thin black curve. (c) represents Fourier power spectrums of ET0 and AI (solid). The dashed line was the 95% confidence spectrum. (d) represents scale-averaged wavelets over the 2- to 8-year band for ET0 and AI (solid). The dashed line was at 95% confidence level. For annual ET0, it existed periods of 3, 7, 11, and 15 yr that were not significant (Figures 7(b) and 7(c)). There also existed periods of 1, 7, 11, and 13 yr for AI, and only 1 yr period was significant (95% confidence level) (Figures 8(b) and 8(c)). Obviously, the period with significant mean variance of ET0 was inline with that of AI.

Large-scale climate oscillations play vital roles in regional climate change and water resource cycling. So, it was significant to clarify if the AI and ET0 had relationship with the MEI, PDO, WNPMI, and ISMI. Thus, these correlation coefficients among indexes mentioned above were analyzed. As shown in Figure 9, obviously, the MEI, PDO, WNPMI, and ISMI were all positively correlated with AI. These selected indexes displayed increasing trends in Northeast China during the 1965–2017. Overall, the increasing trend for AI with ISMI was the most remarkable of all the indexes and significant at the 0.05 level, which suggested a remarkable impact of the ISMI on AI. The lower R values were presented between AI and MEI, PDO, and WNPMI, indicating that the effect of the three selected indexes on AI was not significant. In recent decades, climatic anomaly and extreme climatic event in Asia [2] may affect the correlation between AI and the indexes. However, apart from the climate elements and natural oscillations, anthropogenic forcing induced by human activities should be paid attention as well [58, 59]. Besides, deforestation and urbanization are also potential factors that influence the AI. Therefore, it remains a long way to go for adequate understanding of the influence of climate oscillations, meteorological factors and human activities on AI as well as ET0, which needs further investigation in the ongoing research.

4. Conclusions

According to the collected dataset from 71 meteorological stations over Northeast China from 1965 to 2017, the spatial and temporal variations of the AI and ET0 were investigated. The average of annual total ET0 was 611.43 mm between 1965 and 2017, presenting a decreased trend of −1.97 mm/yr. The trends of ET0 across all the observatories exhibited similar decreasing trends, at the rates of −2.50 mm/yr, −1.63 mm/yr, and −1.76 mm/yr, respectively. Annual AI also showed nonsignificant slightly declined trends, at a rate of about −0.01/yr during 1965–2017; the decline rate of Heilongjiang province was the largest of all and contributed to 46% for Northeast China. The analysis of PDFs indicated that the ET0 has an increasing trend from 1960s to 1970s and then decreased in the 1980s, as well as it displayed a rapidly decreasing trend in 1990s to the period of 2000–2017. AI showed a positive tendency from the 1960s to the 1970s but displayed a rapid decrease in 2000s. Considerable stations with high values of ET0 were mainly in the western part of the study area except for Heilongjiang province, and most stations with low values were primarily suited in the central and eastern part, which was generally consistent with the AI over the study area. Moreover, there were two abrupt changes in the whole change process of time sequence for AI, primarily in 2005 and 2007, and abrupt point of ET0 happened in 1995. There were periods of 3, 7, 11, and 15 yr that were nonsignificant trends. Meanwhile, there existed periods of 1, 7, 11, and 13 yr, for AI, and 1 yr period that was significant at 95% confidence level. Consequently, the results of this research estimated climate drought over past decades and addressed the possible causes. However, further investigation is still required to clarify the mechanisms of variability in AI and ET0 over Northeast China in the future.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.


This work was partially supported by the National Key Research and Invention Program of the Thirteenth (2017YFC0504702); The Science and Technology Service Network Initiative Project of Chinese Academy of Sciences (KFJ-STS-ZDTP-036); National Natural Science Funds of China (41771220); Natural Science Foundation of Shaanxi Province (2018JM4020); The Fundamental Research Funds for the Central Universities (GK201803047, GK201903075, GK201703051, GK201903071).