The Relationship Between NDVI and Climate Factors at Different Monthly

sustainability

Article The Relationship between NDVI and Climate Factors at Diﬀerent Monthly Time Scales: A Case Study of Grasslands in Inner Mongolia, China (1982–2015)

Zhifang Pei 1,2 , Shibo Fang 2,3,*, Wunian Yang 1,*, Lei Wang 2, Mingyan Wu 1 , Qifei Zhang 4, Wei Han 5 and Dao Nguyen Khoi 6 1 College of Earth Science, Chengdu University of Technology, Chengdu 610059, China; [email protected] (Z.P.); [email protected] (M.W.) 2 State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China; [email protected] 3 Collaborative Innovation Centre on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science & Technology, Nanjing 210044, China 4 State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China; [email protected] 5 Shandong General Station of Agricultural Technology Extension, Jinan 250013, China; [email protected] 6 Faculty of Environment, University of Science, Vietnam National University Ho Chi Minh City, Ho Chi Minh City 700000, Vietnam; [email protected] * Correspondence: [email protected] (S.F.); [email protected] (W.Y.); Tel.: +86-10-6840-6142 (S.F.); +86-137-0800-5934 (W.Y.) Received: 22 November 2019; Accepted: 13 December 2019; Published: 17 December 2019

Abstract: There are currently only two methods (the within-growing season method and the inter-growing season method) used to analyse the normalized difference vegetation index (NDVI)–climate relationship at the monthly time scale. What are the differences between the two methods, and why do they exist? Which method is more suitable for the analysis of the relationship between them? In this study, after obtaining NDVI values (GIMMS NDVI3g) near meteorological stations and meteorological data of Inner Mongolian grasslands from 1982 to 2015, we analysed temporal changes in NDVI and climate factors, and explored the difference in Pearson correlation coefficients (R) between them via the above two analysis methods and analysed the change in R between them at multiple time scales. The research results indicated that: (1) NDVI was affected by temperature and precipitation in the area, showing periodic changes, (2) NDVI had a high value of R with climate factors in the within-growing season, while the significant correlation between them was different in different months in the inter-growing season, (3) with the increase in time series, the value of R between NDVI and climate factors showed a trend of increase in the within-growing season, while the value of R between NDVI and precipitation decreased, but then tended toward stability in the inter-growing season, and (4) when exploring the NDVI–climate relationship, we should first analyse the types of climate in the region to avoid the impacts of rain and heat occurring during the same period, and the inter-growing season method is more suitable for the analysis of the relationship between them.

Keywords: NDVI; climate factor; within-growing season; inter-growing season; Inner Mongolian grassland

1. Introduction Vegetation connects the water, the soil, the atmosphere and other natural substances, and plays a vital role in the terrestrial circulation of matter and energy [1–4]. Climate is the primary factor

Sustainability 2019, 11, 7243; doi:10.3390/su11247243 www.mdpi.com/journal/sustainability Sustainability 2019, 11, 7243 2 of 17 of vegetation change, especially temperature and precipitation, which have important influences on vegetation growth, distribution and carbon budget functions [5–7]. Nowadays, the changes of global climate and environment are obvious, and the phenomenon of climate anomalies has become prominent [8–12]. Climate change will inevitably cause variation in vegetation growth and affect vegetation dynamics and functions [3,13,14]. Therefore, to understand the evolution of vegetation and predict its change characteristics under future climate changes, it is very valuable to study the normalized difference vegetation index (NDVI)–climate relationship in-depth and reveal its internal relations. The vegetation index is usually used to indicate vegetation growth and ecosystem change [1]. The development of remote sensing technology makes it more efficient and convenient for us to obtain the characteristics of vegetation change [15]. Not only is NDVI simple and easy to obtain, but it also reflects the status of surface vegetation to a large extent and is widely used at present [16–19]. The existing NDVI time series data sets mainly include the SPOT (Systeme Probatoire d’ Observation de la Terre)/Vegetation NDVI, MODIS (Moderate–resolution Imaging Spectroradiometer) NDVI, and GIMMS (Global Inventory Monitoring and Modeling Studies) NDVI data sets, as well as others. These data sets have been commonly used to analyse the vegetation responses to climate on global and regional scales [20–23]. The NDVI–climate relationship at different scales has been well documented. At the global scale, NDVI is greatly affected by temperature, and the increase of vegetation activities in the Northern Hemisphere is mainly caused by a temperature increase [24–27]. Further, precipitation has a great influence on NDVI at the regional scale, especially in arid and semi-arid areas [28,29]. However, some areas are affected differently by climate factors at different times. In East Asia, the increase in vegetation cover before 1997 was mainly affected by the increase in temperature, while the change in precipitation after 1997 was the main factor for the decrease in vegetation cover [30]. The inter-annual variation of vegetation in Inner Mongolia is greatly affected by precipitation, while vegetation growth is affected by temperature and precipitation at the monthly time scale [31,32]. Due to the complex relationship between vegetation and climate, and the differences in spatiotemporal scale and vegetation type, analytical results may vary. The choice of a time scale is very important when analysing the NDVI–climate relationship. According to the literature, there are many studies on the relationship between them at annual or seasonal time scales [18,33,34]. However, vegetation has a cumulative effect on climate change [19,35–37], and at the annual or seasonal time scales, the influence of hydrothermal factors on vegetation is not clear enough, which cannot truly reflect the relationship between them [38,39]. At the monthly time scale, hydrothermal conditions have a more obvious effect on vegetation growth than other conditions [39], and the lag relation between them is also more obvious. Therefore, it may be more reasonable to explore the NDVI–climate relationship at the monthly time scale. At present, there are two different methods performed at the monthly time scale that explore the NDVI–climate relationship: one method calculates the correlation coefficients between them in all months in multiple growing seasons, and we call this method the within-growing season method [13,40–45], while the other method calculates the correlation coefficients between them in the same month in multiple growing seasons, and we call this method the inter-growing season method [10,17,46]. However, what are the differences between the two methods, and why do they exist? Which method is more suitable for the analysis of the relationship between them? This requires further analysis [47]. In view of the above problems, we took the Inner Mongolian grasslands as a case study and obtained the NDVI values (GIMMS NDVI3g) near the meteorological stations and meteorological data of the Inner Mongolian grasslands from 1982 to 2015, and the value of R between NDVI and climate factors was analysed at different time scales. The main aims are: (1) to understand the temporal changes in NDVI and climate factors and analyse the relationships between them, (2) to explore the NDVI–climate relationship by R and compare the differences in R between them at different monthly time scales, and (3) to analyse the change in R between NDVI and climate factors at multiple time scales Sustainability 20192020,, 1112,, 7243x FOR PEER REVIEW 33 of of 17 at multiple time scales and determine which method is more suitable for the analysis of the and determine which method is more suitable for the analysis of the relationship between them. This relationship between them. This study is expected to accurately explain the difference between NDVI study is expected to accurately explain the difference between NDVI and climate factors at different and climate factors at different monthly time scales, and to provide a reasonable analysis method for monthly time scales, and to provide a reasonable analysis method for revealing the NDVI–climate revealing the NDVI–climate relationship in the future. relationship in the future.

2. Materials Materials and and Methods

2.1. Study Study Area Area

Inner Mongolia (37◦°2244′0–53–53°2◦233′0 N, 97°1 97◦122′0––126126°0◦044′0 E)E) is is located located along along the the northern northern border border of of China, China, extending diagonally diagonally from from northeast northeast to to southwest southwest with with a narrow a narrow and and long long shape shape [34] [(Figure34] (Figure 1). The1). Thegrassland grassland in Inner in Inner Mongolia Mongolia has has a main a main area area of of 86.667 86.667 million million hectares, hectares, of of which which 68.18 68.18 million hectares areare e effeﬀectivective natural natural pastures, pastures, accounting accounting for for 27% 27% of of the the total total grassland grassland area area in China.in China It is. It the is thelargest largest grassland grassland and and natural natural pasture pasture region region in China. in China.

Figure 1. The spatial distribution of grassland types (left) (the inset map indicates where the study area is in China) and the elevations and average NDVI (the normalized diﬀerence vegetation index) values of the meteorological stations (right) in this study.

The climate of Inner Mongolia is dominated by continental monsoon climate. The annual average temperature is between 3.7 and 11.2 C, and the average temperature of the whole region is 6.2 C. − ◦ ◦ And the annual precipitation is between 150 and 400 mm and gradually decreases from east to west, with most precipitation occurring in June to August [10]. From East to West, the climate shows a zonal distribution. Accordingly, the grassland types of Inner Mongolia are divided into a meadow steppe to Figure 1. The spatial distribution of grassland types (left) (the inset map indicates where the study the west of the Daxinganling Mountains in eastern Inner Mongolia, a typical steppe in central Inner area is in China) and the elevations and average NDVI (the normalized difference vegetation index) Mongolia, and a desert steppe in central and western Inner Mongolia [44,48] (Figure1). values of the meteorological stations (right) in this study. 2.2. Data Sources The climate of Inner Mongolia is dominated by continental monsoon climate. The annual averageThe temperature GIMMS NDVI3g is between data were−3.7 and used 11.2 in the°C, study.and the GIMMS averageNDVI3g temperature data of are the global whole vegetation region is 6.2index °C. change And the data annual provided precipitation by the GIMMS is between group 150 of and NASA 400 mm (https: and//ecocast.arc.nasa.gov gradually decreases/ datafrom/ pub east/ togimms west,/3g.v1 with/ )[ most18]. precipitation And the dataset occurring has been in June preprocessed to August by[10]. radiometric From East correction, to West, the geometric climate showcorrections a zonal and imagedistribution. enhancement. Accordingly, GIMMS the NDVI3g grassland data types have of been Inner commonly Mongolia used are individed the study into of a meadowregional and steppe global to the vegetation west of change the Daxinganling because of the Mountains long time in series eastern and Inner wide Mongolia, coverage [26 a typical,49,50]. steppe in central Inner Mongolia, and a desert steppe in central and western Inner Mongolia [44,48] (Figure 1). Sustainability 2019, 11, 7243 4 of 17

In this study, we obtained GIMMS NDVI data from January 1982 to December 2015. To minimise the inﬂuence of clouds, atmosphere, and monthly phenology, the MVC (maximum value composite) method was adopted to synthesize the monthly scale data [4,51]. In studies of the NDVI–climate relationship, to maintain consistency with NDVI space, most studies use the spatial interpolation method to carry out the spatial interpolation of climate factors [10,16,17,52]. However, due to the large error of the interpolation itself, if the interpolation results are used for correlation analysis, the error may be further increased [53]. Thus, we selected representative meteorological stations for meadow steppes, typical steppes, and desert steppes for this study (Figure1). Among them, the meteorological stations in the meadow steppe include the Erguna, Yakeshi, Chenbarhu banner, Hailar and Ulagai stations; the meteorological stations in the typical steppe area include the Xin Barag left banner, East Ujumchin, Xilinhot, Xin Barag right banner, and Abaga banner stations. The meteorological stations in the desert steppe area include the Sonid left banner, Sonid right banner, Erenhot, Mandula, and Urad middle banner stations. To be consistent with the time range of the NDVI data, we also obtained the monthly average climate data (temperature and precipitation) of 15 representative meteorological stations from January 1982 to December 2015, which were derived from the monthly surface climate data set of the China Meteorological Data Sharing Service Platform (http://data.cma.cn/). In this study, the administrative region, land use and land cover data for China in 2015 and vegetation type data (1:1,000,000) were all derived from the Resource and Environment Science Data Center of the Chinese Academy of Sciences (http://www.resdc.cn).

2.3. Methods

2.3.1. Calculation of the NDVI Data at the Meteorological Stations Generally, a radius of 10 km around the meteorological station is eﬀective when the data are measured at stations [42,54]. In this study, in view of the spatial resolution of the NDVI data and the impact of agriculture or construction around meteorological stations, the NDVI value at 15 meteorological stations is calculated by the mean value of the 3 3 pixel centred over the × meteorological station [54]. Finally, we obtain NDVI data from 15 representative meteorological stations from January 1982 to December 2015.

2.3.2. Correlation Analysis between NDVI and Climate Factors In the study, R values were calculated to explore the NDVI–climate relationship. The R model is as follows [34]: Pn [(xi x)(yi y)] i=1 − − Rxy = s , (1) n n P 2 P 2 (xi x) (yi y) i=1 − i=1 − where Rxy is the Pearson correlation coefficients between variable x and variable y, with a value between 1 and 1, n is the sample size, x is the value of NDVI in the ith month, and y is the mean − i i monthly climate factors in the ith month, where x and y are the means of the two variables, respectively. In addition, we also test the significance of the correlation coefficients. In this study, we analysed the NDVI–climate relationship at two different monthly time scales. In the within-growing season, we took the NDVI monthly series (April to October) from 1982 to 2015 as a group of variables (238 samples) and the climate factor monthly series (April to October) as another group of variables (238 samples) and calculated the value of R between NDVI and climate factors. In the inter-growing season, we took the value of NDVI in April from 1982 to 2015 as one group of variables (34 samples) and the climate factors in April from 1982 to April 2015 as another group of variables (34 samples) and calculated the value of R between NDVI and climate factors in April. Sustainability 2019, 11, 7243 5 of 17

Similarly, the value of R between NDVI and climatic factors in May to October were also calculated. The above two methods were used to calculate the value of R in this study.

2.3.3. Lag Analysis between NDVI and Climate Factors Vegetation is sensitive to climate change, but under a specific environment, vegetation may also have some adaptability to climate change; that is, the NDVI–climate relationship may have a lag effect [35]. Lag correlation coefficients are used to analyse the lag period of NDVI response to climate change. The expression is as follows [55]:

R = max R0, R1, R2, , Rn 1, Rn , (2) { ······ − } where R is the lag correlation coeﬃcients, and n is the number of samples. R0, R1, R2, ... , Rn are the lag coeﬃcients of NDVI and the current month, NDVI and the previous month, NDVI and the previous 2 months, ... , NDVI and the previous n months, respectively. If R = Rn, the lag period of NDVI response to climate change is n months. In this study, we calculated the value of R between NDVI and current month climatic factors, NDVI and previous 1–3 month climatic factors, respectively, and so on.

3. Results

3.1. Temporal Changes in NDVI and Climate Factors We analysed the temporal changes in NDVI and climate factors (temperature and precipitation) in the grassland region from January 1982 to December 2015. Here, NDVI and climate factors of the grassland were obtained by averaging NDVI and climate factors data of 15 representative meteorological stations. The mean value of NDVI in the grassland showed obvious characteristics from 1982 to 2015 (Figure2). The range of change in NDVI in the area was small and maintained a stable ﬂuctuation. The multi-year average value of NDVI was 0.224, with the lowest value of 0.210 in 2007, and the highest value of 0.241 in 1998 (Figure2b). NDVI changed alternately every year, with the highest values appearing from June to September, and the lowest values appearing from December to February (Figure2a). In August, the monthly average value of NDVI reached 0.403, and grassland growth was generally good, while in February, the monthly average value of NDVI reached 0.098, and grassland growth was not good (Figure2b). The value of NDVI in the area was relatively high from April to October,Sustainability which 2020, 1 is2,usually x FOR PEER used REVIEW as the grassland growing season. 6 of 17

0.26 NDVI 12 0.466 0.24

10 0.387 NDVI 0.22

8 0.20 0.308 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 6 0.50 Year

Month 0.230 0.40 4 0.30 0.151 2 NDVI 0.20

0.072 0.10

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1990 1995 2000 2005 2010 2015 1985 Month Year (a) (b)

FigureFigure 2. Change in NDVI from 1982 to 20152015 inin thethe area:area: (aa)) monthlymonthly scales;scales; ((bb)) annualannual averageaverage scalescale (top)(top) andand monthlymonthly average average scale scale (bottom). (bottom).

There was a significant change in the average temperature from 1982 to 2015 in the area (Figure 3). Over 34 years, the annual average temperature fluctuated and increased, with an increase rate of 0.0401/a. The multi-year average temperature was 2.04 °C , the lowest value was 0.43 °C in 1985, and the highest value was 3.63 °C in 2007 (Figure 3b). Every year, a high temperature value appeared in June to August, and a low temperature value appeared in December to February (Figure 3a). For many years, the highest monthly average temperature was 21.60 °C in July, and the lowest value was −20.64 °C in January (Figure 3b).

4.00 Temperature (℃) 12 24.00 3.00 2.00 10

14.24 1.00 Temperature(℃) 8 0.00 4.48 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 6 30.00 Year

Month -5.28 15.00 4 -15.04 0.00 2 -15.00

-24.80 Temperature(℃) -30.00

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1985 1990 1995 2000 2005 2010 2015 Year Month

(a) (b)

Figure 3. Change in average temperature from 1982 to 2015 in the area: (a) monthly scales; (b) annual average scale (top) and monthly average scale (bottom).

There was also a significant change in the precipitation from 1982 to 2015 in the area (Figure 4). Over 34 years, annual precipitation showed a slight downward trend with a change rate of –0.335/a. The multi-year average value of precipitation was 255.99 mm, the highest value was 398.65 mm in 1998, and the lowest value was 177.58 mm in 2001 (Figure 4b). Every year, high precipitation appeared in June, July, and August, and precipitation in other months was relatively low (Figure 4a). For many years, precipitation was the most concentrated in July, with an average annual precipitation amount of 72.1 mm (Figure 4b). Sustainability 2020, 12, x FOR PEER REVIEW 6 of 17

0.26 NDVI 12 0.466 0.24

10 0.387 NDVI 0.22

8 0.20 0.308 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 6 0.50 Year

Month 0.230 0.40 4 0.30 0.151 2 NDVI 0.20

0.072 0.10

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1990 1995 2000 2005 2010 2015 1985 Month Year (a) (b)

Figure 2. Change in NDVI from 1982 to 2015 in the area: (a) monthly scales; (b) annual average scale Sustainability 2019, 11, 7243 6 of 17 (top) and monthly average scale (bottom).

There waswas aa signiﬁcantsignificant change change in in the the average average temperature temperature from from 1982 1982 to to 2015 2015 in in the the area area (Figure (Figure3). Over3). Over 34 years,34 years, the the annual annual average average temperature temperature ﬂuctuated fluctuated and and increased, increased, with with anan increaseincrease raterate of 0.04010.0401/a./a. The multi-yearmulti-year average temperature was was 2.042.04 ◦°CC,, the the lowestlowest valuevalue waswas 0.430.43 ◦°CC inin 1985,1985, andand thethe highest value was was 3.63 3.63 °C◦C in in 2007 2007 (Figure (Figure 3b3b).). Every Every year, year, a a high high temperature temperature value value appeared appeared in inJune June to toAugust, August, and and a alow low temperature temperature value value appeared appeared in in December December to February (Figure 3 3aa).). For For many years,years, the highest monthly average temperature was 21.6021.60 ◦°CC inin July, andand thethe lowestlowest valuevalue was −20.64 °CC in in January January (Figure 3 3bb).). − ◦

4.00 Temperature (℃) 12 24.00 3.00 2.00 10

14.24 1.00 Temperature(℃) 8 0.00 4.48 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 6 30.00 Year

Month -5.28 15.00 4 -15.04 0.00 2 -15.00

-24.80 Temperature(℃) -30.00

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1985 1990 1995 2000 2005 2010 2015 Year Month

(a) (b)

Figure 3. Change in average temperature fromfrom 19821982 toto 20152015 inin thethe area:area: (a)) monthlymonthly scales;scales; ((bb)) annualannual average scalescale (top)(top) andand monthly averageaveragescale scale (bottom).(bottom).

There was also a signiﬁcantsignificant change in the precipitation from 1982 to 2015 2015 in the area (Figure 4 4).). Over 34 years,years, annual precipitation showed a slight downward trend with a change rate of –0.3350.335/a./a. − TheThe multi-yearmulti-year average average value of precipitation precipitation was 255.99255.99 mm,mm, thethe highesthighest value waswas 398.65398.65 mmmm inin 1998,1998, andand the the lowest lowest value value was was 177.58 177.58 mm inmm 2001 in (Figure 2001 (Figure4b). Every 4b). year, Every high year, precipitation high precipitation appeared inappeared June, July, in June, and August,July, and and August, precipitation and precipitation in other months in other was months relatively was low relatively (Figure low4a). (Figure For many 4a). years,For many precipitation years, prec wasipitation the most was concentrated the most concentrated in July, with inan July, average with an annual average precipitation annual precipitat amountion of Sustainability 2020, 12, x FOR PEER REVIEW 7 of 17 72.1amount mm of (Figure 72.1 mm4b). (Figure 4b).

400.00 Precipitation (mm) 12 132.50 300.00

10 106.10 200.00

8 Precipitation(mm) 79.70 100.00 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 6 80.00 Year

Month 53.30 60.00 4 40.00 26.90 2 20.00

0.50 Precipitation(mm) 0.00

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1985

1990

1995

2000

2005 2010 2015 Month Year (a) (b)

Figure 4. Change in precipitation fromfrom 19821982 toto 20152015 in the area: ( a) m monthlyonthly scales;scales; ((b)) annual average scale (top)(top) and monthly averageaverage scalescale (bottom).(bottom).

Based on the above results, the temperature and precipitation in the area showed obvious periodic changes, and related to these periodic changes in rain and temperature, NDVI also showed periodic changes but with an obvious lag (Figure 5).

0.45 NDVI 25 80 Temperature (℃) 0.40 Precipitation (mm) 20 70 0.35 15 60 10 0.30 5 50 0.25 0 40 0.20 -5 30 0.15 -10 20 0.10 -15 0.05 -20 10 0.00 -25 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec -- Month

Figure 5. Monthly average changes in NDVI and climate factors in the area.

3.2. Correlation between NDVI and Climate Factors

Considering that the NDVI value of the grasslands in the study area was small in some months, the growing season (April to October) was selected to analyse the NDVI–climate relationship. Here, we analysed the value of R between them in all grassland type at different monthly time scales (i.e., in the within-growing season and the inter-growing season).

3.2.1. Correlation between NDVI and Climate Factors in the Within-Growing Season

We calculated the value of R between NDVI and climate factors near meteorological stations in the current month (1982–2015) (Figure 6). The value of R between them gradually decreased from East to West, and they were all significantly positively correlated. And the value of R between NDVI Sustainability 2020, 12, x FOR PEER REVIEW 7 of 17

400.00 Precipitation (mm) 12 132.50 300.00

10 106.10 200.00

8 Precipitation(mm) 79.70 100.00 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 6 80.00 Year

Month 53.30 60.00 4 40.00 26.90 2 20.00

0.50 Precipitation(mm) 0.00

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1985

1990

1995

2000

2005 2010 2015 Month Year (a) (b)

Figure 4. Change in precipitation from 1982 to 2015 in the area: (a) monthly scales; (b) annual average Sustainabilityscale (top2019) ,and11, 7243monthly average scale (bottom). 7 of 17

Based on the above results, the temperature and precipitation in the area showed obvious Based on the above results, the temperature and precipitation in the area showed obvious periodic periodic changes, and related to these periodic changes in rain and temperature, NDVI also showed changes, and related to these periodic changes in rain and temperature, NDVI also showed periodic periodic changes but with an obvious lag (Figure 5). changes but with an obvious lag (Figure5).

Figure 5. Monthly average changes in NDVI and climate factors in the area. Figure 5. Monthly average changes in NDVI and climate factors in the area. 3.2. Correlation between NDVI and Climate Factors 3.2. Correlation between NDVI and Climate Factors Considering that the NDVI value of the grasslands in the study area was small in some months, the growingConsidering season that (April the NDVI to October) value of was the selected grasslands to analyse in the study the NDVI–climate area was small relationship. in some months Here,, wethe analysedgrowing seasonthe value (April of R to between October) them wasin selected all grassland to analyse type the at diNDVIﬀerent–climate monthly relationship. time scales Here, (i.e., inwe the analysed within-growing the value seasonof R between and the them inter-growing in all grassland season). type at different monthly time scales (i.e., in the within-growing season and the inter-growing season). 3.2.1. Correlation between NDVI and Climate Factors in the Within-Growing Season 3.2.1. Correlation between NDVI and Climate Factors in the Within-Growing Season SustainabilityWe calculated 2020, 12, x the FOR value PEER ofREVIEW R between NDVI and climate factors near meteorological stations8 of in17 the currentWe calculated month (1982–2015)the value of (FigureR between6). The NDVI value and of climate R between factors them near gradually meteorolo decreasedgical stations from in and temperature were higher, indicating that temperature had a greater impact on grassland than Eastthe current to West, month and they (1982 were–2015) all signiﬁcantly (Figure 6). The positively value of correlated. R between And them the gradually value of R decreased between NDVI from did precipitation, especially over meadow steppes. andEast temperatureto West, and were they higher,were all indicating significantly that positively temperature correlated. had a greater And t impacthe value on of grassland R between than NDVI did precipitation, especially over meadow steppes.

1.0 1.0

0.8 0.887(MEAN) 0.8

0.752(MEAN) 0.6 0.6 0.607(MEAN) 0.632(MEAN) 0.588(MEAN)

0.4 0.4 0.518(MEAN) Correlation Coefficient Correlation 0.2 Coefficient Correlation 0.2

0.0 0.0 Meadow steppe Typical steppe Desert steppe Meadow steppe Typical steppe Desert steppe

(a) (b)

FigureFigure 6.6. TheThe valuevalue ofof RR betweenbetween NDVINDVI andand climateclimate factors factors (all(all grassland grassland type): type): ((aa)) temperaturetemperature and and ((bb)) precipitation.precipitation. All All coe coefficientsﬃcients were were signiﬁcant significant at atp p< < 0.05.0.05.

We also analysed the lag between NDVI and climate factors (Figure 7). NDVI was significantly affected by climate factors of the current month in the meadow steppe. However, NDVI was more sensitive to climate factors of the previous month than to those of the current month in the other two grassland types.

(a) Sustainability 2020, 12, x FOR PEER REVIEW 8 of 17

and temperature were higher, indicating that temperature had a greater impact on grassland than did precipitation, especially over meadow steppes.

1.0 1.0

0.8 0.887(MEAN) 0.8

0.752(MEAN) 0.6 0.6 0.607(MEAN) 0.632(MEAN) 0.588(MEAN)

0.4 0.4 0.518(MEAN) Correlation Coefficient Correlation 0.2 Coefficient Correlation 0.2

0.0 0.0 Meadow steppe Typical steppe Desert steppe Meadow steppe Typical steppe Desert steppe

(a) (b)

SustainabilityFigure2019, 6.11 The, 7243 value of R between NDVI and climate factors (all grassland type): (a) temperature and 8 of 17 (b) precipitation. All coefficients were significant at p < 0.05.

We alsoWe also analysed analysed the the lag lag between between NDVI NDVI and and climate factors factors (Figure (Figure 7).7 ).NDVI NDVI was was significantly signiﬁcantly aﬀectedaffected by climate by climate factors factors of of the the current current month month in the meadow meadow steppe. steppe. However, However, NDVI NDVI was wasmore more sensitivesensitive to climate to climate factors factors of of the the previous previous monthmonth than to to those those of of the the current current month month in the in other the other two two grasslandgrassland types. types.

Sustainability 2020, 12, x FOR PEER REVIEW 9 of 17 (a)

(b)

FigureFigure 7. The 7. T timehe time lag lag in Rin betweenR between NDVI NDVI andand climateclimate factors factors (all (all grassland grassland type): type): (a) temperature (a) temperature and (andb) precipitation. (b) precipitation. T0, T0 T1,, T1, T2, T2, and and T3 T3 representrepresent t temperatureemperature variables variables in the in theprevious previous 0–3 months, 0–3 months, respectively;respectively P0,; P1,P0, P1, P2, P2, and and P3 P3 represent represent precipitationprecipitation variables variables in in previous previous 0–3 0–3months, months, respectively respectively.. All coefficients were significant at p < 0.05. All coeﬃcients were signiﬁcant at p < 0.05.

3.2.2.3.2.2. Correlation Correlation between between NDVI NDVI and and Climate Climate FactorsFactors in in the the Inter Inter-Growing-Growing Season Season ComparedCompared to the to the value value of of R R between between NDVI NDVI and climate climate factors factors in inthe the within within-growing-growing season, season, the value of R in the inter-growing season were not as high, and there were positive and negative the value of R in the inter-growing season were not as high, and there were positive and negative correlations. In terms of temperature (Table 1), the temperature had a significant impact on the correlations.meadow In steppe terms in of April,temperature May and (Table October,1), the temperaturewhen the temperature had a signiﬁcant promoted impact the on growth the meadow of steppegrasslands. in April, In May April and and October, October, when there the was temperature a significant promotedpositive correlation the growth between of grasslands. temperature In April and the typical steppe, while there was a significant negative correlation between temperature and the typical steppe in June and August. However, the relationship between temperature and the desert steppe was not significant. In terms of precipitation (Table 1), precipitation in July had a significant impact on the meadow steppe, the typical grassland was sensitive to precipitation from May to July, of which July was the most sensitive, and precipitation had the most extensive impact on desert steppe, with August having the greatest impact.

Table 1. The value of R between NDVI and climate factors (all grassland type).

Grassland Climate April May June July August September October Type Factor Meadow Temperature 0.457 0.573 0.410 steppe Precipitation 0.431 Typical Temperature 0.408 −0.420 −0.440 0.389 steppe Precipitation 0.414 0.491 0.550 Desert Temperature −0.368 steppe Precipitation 0.515 0.436 0.532 0.542 All coefficients are significant at p < 0.05.

For all grassland type, we calculated the value of R between NDVI and climate factors of the current and previous months and took the month with the highest correlation coefficient (p < 0.05) as the lagged month (Figure 8). In terms of temperature, for the meadow steppe, NDVI was significantly Sustainability 2019, 11, 7243 9 of 17 and October, there was a significant positive correlation between temperature and the typical steppe, while there was a significant negative correlation between temperature and the typical steppe in June and August. However, the relationship between temperature and the desert steppe was not significant. In terms of precipitation (Table1), precipitation in July had a significant impact on the meadow steppe, the typical grassland was sensitive to precipitation from May to July, of which July was the most sensitive, and precipitation had the most extensive impact on desert steppe, with August having the greatest impact. For all grassland type, we calculated the value of R between NDVI and climate factors of the current and previous months and took the month with the highest correlation coefficient (p < 0.05) as the lagged month (Figure8). In terms of temperature, for the meadow steppe, NDVI was significantly affected by the temperature of the current month in April and May. For the typical steppe, NDVI was sensitive to the temperature of the current month in April, June, and August, while NDVI was significantly affected by the temperature of the previous month in July, September, and October. For the desert steppe, NDVI was sensitive to the temperature of the current month in April, while NDVI was mainly affected by the temperature of the previous month in September. In terms of precipitation, for the meadow steppe, NDVI was affected by the precipitation of the previous month in June and August. For the typical steppe, NDVI was sensitive to the precipitation of the current month in May and July, and NDVI was significantly affected by the precipitation of the previous month in June and August, whileSustainability NDVI 20 was20, 1 sensitive2, x FOR PEER to precipitationREVIEW of the previous two months in September and October.10 of 17 For the desert steppe, NDVI was sensitive to the precipitation of the current month in May, to the precipitationaffected by the of the temperature previous month of the current from June month to September, in April and and May. to the For precipitation the typical steppe, of the previousNDVI was twosensitive months to in the October. temperature of the current month in April, June, and August, while NDVI was significantly affected by the temperature of the previous month in July, September, and October. For the desert steppe,Table NDVI 1. The was value sensitive of R between to the NDVI temperature and climate of factors the current (all grassland month type).in April, while NDVI

wasGrassland mainly affectedClimate by the temperature of the previous month in September. In terms of April May June July August September October precipitation,Type for Factor the meadow steppe, NDVI was affected by the precipitation of the previous month in JuneMeadow and August.Temperature For the 0.457typical steppe, 0.573 NDVI was sensitive to the precipitation of the 0.410 current monthsteppe in May Precipitationand July, and NDVI was significantly affected 0.431 by the precipitation of the previous Typical Temperature 0.408 0.420 0.440 0.389 − − monthsteppe in June Precipitationand August, while NDVI 0.414 was sensitive 0.491 to precipitation 0.550 of the previous two months in SeptemberDesert andTemperature October. For the0.368 desert steppe, NDVI was sensitive to the precipitation of the current − monthsteppe in May,Precipitation to the precipitation of0.515 the previous 0.436 month 0.532 from June 0.542 to September, and to the precipitation of the previous twoAll months coeﬃcients in areOctober. signiﬁcant at p < 0.05.

Lagged month Lagged month Desertsteppe Desertsteppe 2 1

1 Typical steppe Typical

0 steppe Typical

GrasslandType GrasslandType

Meadow steppe Meadow steppe

April May June July April May June July August August Month October Month October September September (a) (b)

FigureFigure 8. 8The. The monthly monthly lags lags between between NDVI NDVI and and climate climate factors factors (all (all grassland grassland type): type) (a: )(a temperature) temperature andand (b ()b precipitation.) precipitation.

3.3.3. Change in the NDVI–Climate Relationship at Multiple Time Scales We analysed the change in R between NDVI and climate factors at multiple time scales (Figure 9). In the within-growing season, with the increase in time series, the value of R between NDVI and climate factors fluctuated slightly, but all of them showed increasing trends in all grassland types . The value of R between NDVI and temperature were always higher. The fluctuation in R between NDVI and temperature in the meadow steppe was the smallest, and the fluctuation in the desert steppe was largest, which may be due to the fact that the desert steppe is vulnerable to extreme climates or is greatly affected by non-climate factors.

1.0 1.0 1.0

0.9 0.9 0.9

0.884(MEAN) 0.887(MEAN) 0.8 0.88(MEAN) 0.873(MEAN) 0.8 0.8

0.7 0.7 0.7 0.758(MEAN) 0.752(MEAN)

0.739(MEAN) 0.742(MEAN)

Correlation Coefficient Correlation Correlation Coefficient Correlation 0.6 Coefficient Correlation 0.6 0.6 0.605(MEAN) 0.607(MEAN) 0.594(MEAN) 0.559(MEAN) 0.5 0.5 0.5 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015

(a) (b) (c) Sustainability 2020, 12, x FOR PEER REVIEW 10 of 17

affected by the temperature of the current month in April and May. For the typical steppe, NDVI was sensitive to the temperature of the current month in April, June, and August, while NDVI was significantly affected by the temperature of the previous month in July, September, and October. For the desert steppe, NDVI was sensitive to the temperature of the current month in April, while NDVI was mainly affected by the temperature of the previous month in September. In terms of precipitation, for the meadow steppe, NDVI was affected by the precipitation of the previous month in June and August. For the typical steppe, NDVI was sensitive to the precipitation of the current month in May and July, and NDVI was significantly affected by the precipitation of the previous month in June and August, while NDVI was sensitive to precipitation of the previous two months in September and October. For the desert steppe, NDVI was sensitive to the precipitation of the current month in May, to the precipitation of the previous month from June to September, and to the precipitation of the previous two months in October.

Lagged month Lagged month Desertsteppe Desertsteppe 2 1

1 Typical steppe Typical

0 steppe Typical

GrasslandType GrasslandType

Meadow steppe Meadow steppe

April May June July April May June July August August Month October Month October September September (a) (b)

Figure 8. The monthly lags between NDVI and climate factors (all grassland type): (a) temperature Sustainabilityand (b2019) precipitation, 11, 7243 . 10 of 17

3.3.3. Change in the NDVI–Climate Relationship at Multiple Time Scales 3.2.3. Change in the NDVI–Climate Relationship at Multiple Time Scales We analysed the change in R between NDVI and climate factors at multiple time scales (Figure 9). InWe the analysed within-growing the change season, in R betweenwith the NDVIincrease and in climate time series, factors the at value multiple of R time between scales NDVI (Figure and9). Inclimate the within-growing factors fluctuated season, slightly, with but the all increase of them in showed time series, increasing the value trends of R in betweenall grassland NDVI types and. climateThe value factors of R fluctuated between NDVIslightly, and but temperature all of them showed were always increasing higher. trends The in fluctuation all grassland in types.R between The valueNDVI of and R between tempera NDVIture in and thetemperature meadow steppe were was always the higher.smallest, The and fluctuation the fluctuation in R between in the NDVI desert andsteppe temperature was largest, in the which meadow may steppe be due was to the smallest,fact that andthe desertthe fluctuation steppe is in vulnerable the desert steppe to extreme was largest,climates which or is greatly may be affected due to by the non fact-climate that the factors. desert steppe is vulnerable to extreme climates or is greatly affected by non-climate factors.

1.0 1.0 1.0

0.9 0.9 0.9

0.884(MEAN) 0.887(MEAN) 0.8 0.88(MEAN) 0.873(MEAN) 0.8 0.8

0.7 0.7 0.7 0.758(MEAN) 0.752(MEAN)

0.739(MEAN) 0.742(MEAN)

0.8 0.8 0.8

0.7 0.7 0.7

0.6 0.6 0.6

0.632(MEAN) 0.5 0.611(MEAN) 0.5 0.576(MEAN) 0.581(MEAN) 0.588(MEAN) 0.5 0.588(MEAN) 0.586(MEAN) 0.568(MEAN) 0.4 0.4 0.4 0.52(MEAN) 0.522(MEAN) 0.518(MEAN) 0.463(MEAN)

0.3 0.3 0.3

Correlation Coefficient Correlation

Correlation Coefficient Correlation Coefficient Correlation 0.2 0.2 0.2

0.1 0.1 0.1 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015

(d) (e) (f)

FigureFigure 9. Change in R between NDVI and climate factors at multiple timetime scalesscales (the(the within-growingwithin-growing season):season): T Temperature:emperature: (a ()a ) meadow meadow steppe, steppe, (b ()b typical) typical steppe steppe,, (c) ( cdesert) desert steppe. steppe. Precipitation Precipitation:: (d) (meadowd) meadow steppe, steppe, (e) (typicale) typical steppe, steppe, (f) (desertf) desert steppe steppe.. All Allcoefficients coeﬃcients were were significant signiﬁcant at p at

DueDue toto abnormalabnormal climateclimate change, change, the the uncertainty uncertainty of of the the climate climate factors factors increased, increased, and and the the value value of Rof between R between NDVI NDVI and and climate climate factors factors were were not very not very significant significant in the in inter-growing the inter-growing season. season. The value The ofvalue R between of R between NDVI and NDVI precipitation and precipitation in July were in relatively July were significant. relatively To significant. analyse the To variation analyse in the R invariation the inter-growing in R in the seasoninter-growing with increasing season with time increasing series length, time we series used length, precipitation we used as precipitation an example toas analysean example the variationto analyse (Figure the variation 10). We (Fi foundgure 10). that We the found value ofthat R the between value NDVIof R between and precipitation NDVI and changedprecipitation steadily changed in the steadily meadow in steppe.the meadow However, steppe. the However, value of R the between value NDVIof R between and precipitation NDVI and decreasedprecipitation with decreased the increase with inthe the increase time series in the of time the typicalseries of steppe the typical and desertsteppe steppe, and desert which steppe, may havewhich been may due have to be moreen due uncertainty to more uncertainty caused by the caused increase by the in theincrease sample in number,the sample which number, caused which the correlationcaused the correlation degree to decrease. degree to Wedecrease. also found We also that found the change that the in change the correlation in the correlation coefficient coefficient became increasinglybecame increasingly smaller andsmaller tended and toward tended stability.toward stability.

1.0 1.0 1.0

0.9 0.9 0.9

0.8 0.8 0.8

0.7 0.7 0.7 0.834(MEAN)

0.785(MEAN) 0.6 0.6 0.767(MEAN) 0.6 0.729(MEAN)

0.5 0.5 0.5 0.578(MEAN) 0.581(MEAN) 0.532(MEAN)

0.4 0.4 0.55(MEAN) 0.4

Correlation Coefficient Correlation Correlation Coefficient Correlation 0.448(MEAN) 0.457(MEAN) Coefficient Correlation 0.426(MEAN) 0.431(MEAN) 0.3 0.3 0.3

0.2 0.2 0.2 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015

(a) (b) (c)

Figure 10. Change in R between NDVI and precipitation at multiple time scales (the inter-growing season): (a) meadow steppe, (b) typical steppe and (c) desert steppe. All coefficients were significant at p < 0.05.

4. Discussion

Vegetation growth is mainly driven by hydrothermal conditions. The synchronization of rainfall and temperature caused by the monsoon climate in China occurs in summer, and the high temperatures and abundance of precipitation in summer usually correspond with a high vegetation index. This kind of repetition over many years will inevitably result in high correlation between the two variables. In the within-growing season, the correlation coefficients obtained by this analysis method are a kind of pseudo correlation, which may not truly reflect the impact of water and heat conditions on vegetation, so this type of analysis should be carefully used in the future [47]. In the inter-growing season, the NDVI–climate relationship in different months was analysed separately, which can reduce the synchronization of rainfall and temperature and eliminate the possibility of false correlation [47], and the response of NDVI to hydrothermal conditions is different in different Sustainability 2020, 12, x FOR PEER REVIEW 11 of 17

0.8 0.8 0.8

0.7 0.7 0.7

0.6 0.6 0.6

0.632(MEAN) 0.5 0.611(MEAN) 0.5 0.576(MEAN) 0.581(MEAN) 0.588(MEAN) 0.5 0.588(MEAN) 0.586(MEAN) 0.568(MEAN) 0.4 0.4 0.4 0.52(MEAN) 0.522(MEAN) 0.518(MEAN) 0.463(MEAN)

0.3 0.3 0.3

Correlation Coefficient Correlation

Correlation Coefficient Correlation Coefficient Correlation 0.2 0.2 0.2

0.1 0.1 0.1 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015

(d) (e) (f)

Figure 9. Change in R between NDVI and climate factors at multiple time scales (the within-growing season): Temperature: (a) meadow steppe, (b) typical steppe, (c) desert steppe. Precipitation: (d) meadow steppe, (e) typical steppe, (f) desert steppe. All coefficients were significant at p < 0.05.

Due to abnormal climate change, the uncertainty of the climate factors increased, and the value of R between NDVI and climate factors were not very significant in the inter-growing season. The value of R between NDVI and precipitation in July were relatively significant. To analyse the variation in R in the inter-growing season with increasing time series length, we used precipitation as an example to analyse the variation (Figure 10). We found that the value of R between NDVI and precipitation changed steadily in the meadow steppe. However, the value of R between NDVI and precipitation decreased with the increase in the time series of the typical steppe and desert steppe, which may have been due to more uncertainty caused by the increase in the sample number, which caused the correlation degree to decrease. We also found that the change in the correlation coefficient became increasingly smaller and tended toward stability. Sustainability 2019, 11, 7243 11 of 17

1.0 1.0 1.0

0.9 0.9 0.9

0.8 0.8 0.8

0.7 0.7 0.7 0.834(MEAN)

0.785(MEAN) 0.6 0.6 0.767(MEAN) 0.6 0.729(MEAN)

0.5 0.5 0.5 0.578(MEAN) 0.581(MEAN) 0.532(MEAN)

0.4 0.4 0.55(MEAN) 0.4

Correlation Coefficient Correlation Correlation Coefficient Correlation 0.448(MEAN) 0.457(MEAN) Coefficient Correlation 0.426(MEAN) 0.431(MEAN) 0.3 0.3 0.3

0.2 0.2 0.2 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015 2008–2015 2000–2015 1992–2015 1982–2015

(a) (b) (c)

FigureFigure 10.10. ChangeChange inin RR betweenbetween NDVINDVI andand precipitationprecipitationat at multiplemultipletime time scales scales (the (the inter-growing inter-growing season):season): ((aa)) meadowmeadow steppe, steppe, ( b(b)) typical typical steppe steppe and and (c ()c desert) desert steppe. steppe All. All coe coefficientsﬃcients were were signiﬁcant significant at pat< p0.05. < 0.05.

4.4. Discussion

VegetationVegetation growth growth isis mainlymainly drivendriven byby hydrothermalhydrothermal conditions.conditions. The synchronizationsynchronization ofof rainfallrainfall andand temperature temperature caused caused by the by monsoon the monsoon climate climate in China in occurs China in occurs summer, in and summer, the high and temperatures the high andtemperatures abundance and of abundance precipitation of inprecipitation summer usually in summer correspond usually with correspond a high vegetation with a high index. vegetation This kindindex. of This repetition kind of over repetition many years over will many inevitably years will result inevitably in high resultcorrelation in high between correlation the two between variables. the Intwo the variables. within-growing In the within season,-growing the correlation season, the coe ffi correlationcients obtained coefficients by this obtained analysis by method this analysis are a kindmethod of pseudo are a kind correlation, of pseudo which correlation, may not which truly may reflect not the truly impact reflect of water the impact and heat of water conditions and heat on vegetation,conditions on so thisvegetation, type of analysisso this type should of analysis be carefully should used be incarefully the future used [47 in]. the In the future inter-growing [47]. In the season,inter-growing the NDVI–climate season, the relationshipNDVI–climate in direlationshipfferent months in different was analysed months separately, was analysed which canseparately, reduce thewhich synchronization can reduce the of rainfallsynchronization and temperature of rainfall and and eliminate temper theature possibility and eliminate of false the correlation possibility [47 of], andfalse the correlation response of[47] NDVI, and tothe hydrothermal response of conditionsNDVI to hydrothermal is different in conditionsdifferent months, is different so the in value different of R between them obtained by this analysis method may be more realistic for reflecting the response of NDVI to climate change. Here, we also analysed the influence of the synchronization of rainfall and temperature on the NDVI–climate relationship by increasing the time range of the growing season (Figure 11). The expansion of the range indicated that the phenomenon of rain and heat occurring during the same period was increasingly obvious. We can see that the value of R between NDVI and climate factors in all grassland types was also increasing. During the period from May to September, a lag between NDVI and climate factors was possible, resulting in a low value in R between them, and during the period from June to July, the NDVI–climate relationship was more significant, resulting in a higher value of R between them. However, most studies did not consider the phenomenon of water and heat synchronization when analysing the NDVI–climate relationship, so the results need to be verified [13,41,42,54]. In addition, in the study of the meteorological drought index, most studies did not take into account the phenomenon of rain and heat occurrence during the same period [56–59], and whether the meteorological drought index also had the same periodicity should be considered. So, when exploring the NDVI–climate relationship, we should first analyse the climate types of the region to avoid the impact of rain and heat occurrence during the same period. Sustainability 2020, 12, x FOR PEER REVIEW 12 of 17 months, so the value of R between them obtained by this analysis method may be more realistic for reflecting the response of NDVI to climate change. Here, we also analysed the influence of the synchronization of rainfall and temperature on the NDVI–climate relationship by increasing the time range of the growing season (Figure 11). The expansion of the range indicated that the phenomenon of rain and heat occurring during the same period was increasingly obvious. We can see that the value of R between NDVI and climate factors in all grassland types was also increasing. During the period from May to September, a lag between NDVI and climate factors was possible, resulting in a low value in R between them, and during the period from June to July, the NDVI–climate relationship was more significant, resulting in a higher value of R between them. However, most studies did not consider the phenomenon of water and heat synchronization when analysing the NDVI–climate relationship, so the results need to be verified [13,41,42,54]. In addition, in the study of the meteorological drought index, most studies did not take into account the phenomenon of rain and heat occurrence during the same period [56–59], and whether the meteorological drought index also had the same periodicity should be considered. So, when exploring the NDVI–climate relationship, we should first analyse the climate types of the region to avoid the impact of rain and heat occurrence during the same period. Sustainability 2019, 11, 7243 12 of 17

Erguna Month Erguna Month 1.0 7 0.8 7 6–7 6–7 6–8 6–8 0.8 5–8 0.6 5–8 5–9 5–9 0.6 4–9 4–9 4–10 0.4 4–10 0.4 Ulagai Yakeshi Ulagai Yakeshi 0.2 0.2

0.0 0.0

Hailar Hailar Chenbarhu banner Chenbarhu banner (a) (b)

Xin Barag left banner Month Xin Barag left banner Month 1.0 7 0.8 7 6–7 6–7 6–8 6–8 0.8 5–8 0.6 5–8 5–9 5–9 0.6 4–9 4–9 4–10 0.4 4-10 0.4 Xin Barag Xin Barag Abaga banner Abaga banner right banner 0.2 right banner 0.2

0.0 0.0

Xilinhot Xilinhot Sustainability 2020, 12, x FOR PEER REVIEWEast Ujumchin East Ujumchin13 of 17 (c) (d)

Sonid left banner Month Sonid left banner Month 1.0 7 0.8 7 6–7 6–7 6–8 6–8 0.8 5–8 0.6 5–8 5–9 5–9 0.6 4–9 4–9 4–10 0.4 4–10 Urad middle 0.4 Sonid right Urad middle Sonid right banner banner banner 0.2 banner 0.2

0.0 0.0

Mandula Mandula Erenhot Erenhot (e) (f)

FigureFigure 11. 11. ChangeChange in in R Rbetween between NDVI NDVI and and climate climate factors factors during during different different periods. periods. Temperature: Temperature: (a) meadow(a) meadow steppe, steppe, (c) typical (c) typical steppe, steppe, and ( ande) desert (e) desert steppe. steppe. Precipitation: Precipitation: (b) meadow (b) meadow steppe, steppe,(d) typical (d) steppe,typical steppe,and (f) desert and (f )steppe. desert steppe.All coefficients All coeffi werecients significant were significant at p < 0.05. at p < 0.05.

TheThe growth ofof vegetationvegetation is is the the result result of of various various factors factors [60 [,60,61]61], and, and climate climate factors factors play play a vital a vital role. roleRevealing. Revealing the NDVI–climate the NDVI–climate relationship relationship has been has challenging, been challenging and the, and relationship the relationship between bet themween is themobviously is obviously eﬀected effected by the scale. by the Atscale the. A long-termt the long scale,-term scale, climate climate determines determines the vegetation the vegetation type, type, and and the climate has experienced many large alternations between dry and wet conditions . Thus, today’s vegetation pattern was formed against the background of substantial climate changes [62]. At the short-term scale, vegetation and climate interact and undergo subtle changes, and the relationship between them is extremely complex and nonlinear [63]. At the regional scale, due to the influence of water and heat factors, the climate determines the distribution of vegetation, such as meadow steppe, typical steppe, and desert steppe, showing zonal characteristics. At the local scale, vegetation change is likely to be closely related to human activities [64,65]. In addition, changes in the non-climate environment, such as changes in the groundwater level and soil matrix, will affect the NDVI–climate relationship [66,67]. Therefore, to improve the prediction of NDVI response to future climate change, we should consider all kinds of uncertainty factors when analysing the NDVI– climate relationship.

5. Conclusions

In the study, taking Inner Mongolian grassland as an example, we analysed the temporal changes in NDVI and climate factors, and explored the differences in R between them at different monthly time scales and analysed the change in R between them at multiple time scales. The main conclusions are as follows:

(1) NDVI was affected by temperature and precipitation from 1982 to 2015 in the area, showing obvious periodic changes, and NDVI showed a certain time lag for climate factors. (2) The NDVI–climate relationship was quite different when comparing the within-growing season and the inter-growing season. NDVI had a high value of R with climate factors in the within- growing season, while the significant correlation between them was different in different months in the inter-growing season. (3) With the increase in time series, the value of R between NDVI and climate factors of all grassland types showed a trend of increase in the within-growing season, while the value of R between NDVI and precipitation decreased but then tended toward stability in the inter-growing season. (4) Due to the synchronization of rainfall and temperature, the correlation coefficients obtained by the within-growing season method were a kind of pseudo correlation, which may not truly reflect the impact of water and heat conditions on vegetation, so this method should be carefully Sustainability 2019, 11, 7243 13 of 17 the climate has experienced many large alternations between dry and wet conditions. Thus, today’s vegetation pattern was formed against the background of substantial climate changes [62]. At the short-term scale, vegetation and climate interact and undergo subtle changes, and the relationship between them is extremely complex and nonlinear [63]. At the regional scale, due to the inﬂuence of water and heat factors, the climate determines the distribution of vegetation, such as meadow steppe, typical steppe, and desert steppe, showing zonal characteristics. At the local scale, vegetation change is likely to be closely related to human activities [64,65]. In addition, changes in the non-climate environment, such as changes in the groundwater level and soil matrix, will aﬀect the NDVI–climate relationship [66,67]. Therefore, to improve the prediction of NDVI response to future climate change, we should consider all kinds of uncertainty factors when analysing the NDVI–climate relationship.

5. Conclusions In the study, taking Inner Mongolian grassland as an example, we analysed the temporal changes in NDVI and climate factors, and explored the diﬀerences in R between them at diﬀerent monthly time scales and analysed the change in R between them at multiple time scales. The main conclusions are as follows:

(1) NDVI was affected by temperature and precipitation from 1982 to 2015 in the area, showing obvious periodic changes, and NDVI showed a certain time lag for climate factors. (2) The NDVI–climate relationship was quite different when comparing the within-growing season and the inter-growing season. NDVI had a high value of R with climate factors in the within-growing season, while the significant correlation between them was different in different months in the inter-growing season. (3) With the increase in time series, the value of R between NDVI and climate factors of all grassland types showed a trend of increase in the within-growing season, while the value of R between NDVI and precipitation decreased but then tended toward stability in the inter-growing season. (4) Due to the synchronization of rainfall and temperature, the correlation coefficients obtained by the within-growing season method were a kind of pseudo correlation, which may not truly reflect the impact of water and heat conditions on vegetation, so this method should be carefully used in the future. In the inter-growing season, the NDVI–climate relationship in different months was analysed separately, which can reduce the impact of rain and heat in the same period and may be more realistic to reflect the relationship between them. So the inter-growing season method is more suitable for the analysis of the NDVI–climate relationship.

Global climate change is becoming increasingly intense, and extreme climate events are occurring more frequently. In view of the complex vegetation–climate relationship, it is always challenging to explore the relationship between them. Our ﬁndings will provide a reference for choosing a more scientiﬁc and reasonable way to study the NDVI–climate relationship in the future.

Author Contributions: Z.P., S.F., and W.Y. designed the study of the paper, contributed to the ideas, interpretation of the data, and manuscript writing; L.W. and W.H. contributed to data processing and manuscript modifying; M.W. and Q.Z. contributed to data processing and analysis; D.N.K. contributed to formal analysis. All authors contributed to the discussion and commented on the manuscript at all stages. Funding: This paper was supported by the National Key Research and Development Program of China (grant number 2018YFC1506500), the Fundamental Research Funds (grant number 2019Z010) and the National Natural Science Foundation of China (grant number 41671432). Acknowledgments: The authors sincerely thank the anonymous reviewers and the editors for their valuable comments and constructive suggestions. Conﬂicts of Interest: The authors declare no conﬂicts of interest. Sustainability 2019, 11, 7243 14 of 17

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