Characterizing multiscale effects of climatic factors on the temporal variation of vegetation in different climatic regions of China

Vegetation dynamics are sensitive to climatic warming and are affected by individual or combined climatic factors at different temporal scales with different intensities. Previous studies have unraveled the relationships between vegetation dynamics and individual climatic factors; however, it is unclear whether the effects of single or combined climatic factors on vegetation dynamics are dominant for different temporal scales, vegetation types, and climatic regions. The objective of this study was to explore scale-specific univariate and multivariate controls on vegetation over the period 1982–2015 using bivariate wavelet coherence (BWC), multivariate wavelet coherence (MWC), and multidimensional empirical mode decomposition (MEMD). The results indicated that significant vegetation dynamics were located mainly at scales of 1, 0.5, and 0.3 years. Vegetation variations were divided into seasonal (≤ 1 year), short-term (1–4 years), medium-term (4–8 years), and long-term (> 8 years) scales. The combined explanatory powers of seven climatic factors on the vegetation were greater at the short-term and long-term scales, whereas individual climatic factors, such as precipitation or temperature, might affect vegetation dynamics in some climatic regions at the seasonal and medium-term scales. The combined effect of climatic factors in the grassland of the Tibetan Plateau (TP) and the temperate grassland of Inner Mongolia (TGIM) were the greatest, which were 65.06% and 59.53%, respectively. The explanatory powers of climate on crop dynamics in both temperate humid and subhumid Northeast China and the TP were around 47%, whereas the controls of climate on crops in both the TGIM and the temperate and warm-temperate desert of Northwest China were around 39%. Cropland farming practices could alleviate the spatial variation of the relationships between climate and vegetation while enhancing the temporal difference of their relationships. Additionally, the dominant influencing factor among different regions varied greatly at the medium-term scale. Collectively, the results might provide an alternative perspective for understanding vegetation evolution in response to climatic changes in China.


Introduction
Vegetation, a primary component of the terrestrial ecosystem, plays an important role in mitigating soil erosion, regulating terrestrial carbon balance, and providing food for living beings (Ding et al. 2020;Liu et al. 2018;Tong et al. 2016). Moreover, vegetation serves as a sensitive indicator for climatic changes in the ecological environment (Sun et al. 2015). Therefore, understanding of vegetation dynamics and its relationship with climatic factors are necessary for reducing uncertainty in exploring vegetation feedback to global warming and accurately evaluating terrestrial carbon cycles (Chuai, 2020).
Previous studies related to vegetation dynamics and its relationship with long-term series of climatic factors from regional to global spatial scales have been performed, especially with the assistance of a satellite-based normalized difference vegetation index (NDVI) (Li, 2020), which has been widely used in monitoring vegetation dynamics and exploring relationships between vegetation and climate change (He et al. 2012;Zewdie et al. 2017;Zhang et al. 2016). Most of these studies have focused on the original temporal scale without considering that climatic variables exert an effect on vegetation with different intensities at different temporal scales and different times (Rathinasamy et al. 2019). Thus, quantifying scale-and temporal-specific climatic driving factors on vegetation variability is necessary for unraveling vegetation response to climate change.
The scale-dependent variation of climatic factors or the scale-specific relationships between vegetation and individual climatic factors have been explored using ensemble empirical mode decomposition (EEMD) (Qi et al. 2019), the wavelet transform (Liu and Menzel 2016), or the combination of moving windows and the linear correlation method (Ning et al. 2019). However, the mechanism of vegetation response to climatic variables is complex and may be concurrently affected by climatic factors. Although the relative importance of mixed climatic factors was quantified using traditional methods, such as multivariate regression analysis (Liu et al. 2018) and the residual trend method (Sun et al. 2015), the neutralization effect at different scales and times may mislead the interpretation of vegetation variations. Meanwhile, previous studies (Gao et al. 2020;Liu and Menzel 2016;Zhao and Hu 2020) have reported that the mechanism of vegetation response to climate differs with climatic region and vegetation type. Therefore, temporal scales, climatic regions, and vegetation types should be considered when exploring the effect of combined climatic factors on vegetation growth.
Based on bivariate wavelet coherence (BWC), Hu and Si (2016) proposed a multivariate wavelet coherence (MWC) method that can be used to detect more multivariate relationships in the temporal scale domain than general multivariate methods because of its ability to identify localized multivariate relationships. The MWC method has been used widely in areas such as hydrology (Gu et al. 2020), soil science (Centeno et al. 2020), environmental science (Zhao et al. 2018), climate , and economics (Sen and Chaudhury 2019) for untangling scale-specific and localized multivariate relationships for both spatial and temporal series of data irrespective of stationarity or non-stationarity. Because of its wide applicability, we expect that the MWC method can be used in ecological science to explore scale-specific and localized effects of multiple climatic factors on vegetation distribution. Thus, we hypothesize that the response of vegetation to climatic factors differs with temporal scale, climatic condition, and vegetation type, which might be identified by wavelet methods including BWC and MWC. Additionally, previous studies indicated that multivariate empirical mode decomposition (MEMD) could also be applied to explore multivariate relationships in the spatial and frequency domain (Hu et al. 2014;Zhu et al. 2019). Therefore, the MEMD method could be used to compare results with the MWC method regarding the relationship between multiple climatic factors and the vegetation index.
China has a land area of approximately 960 × 10 4 km 2 covering approximately 50° of latitude and 62° of longitude and has extremely diverse climatic conditions (Bai et al. 2020). To disentangle the relations between climate and vegetation across China, different climatic regions were partitioned. The objective of this study was to explore the single or mixed climatic factors on the vegetation growth under different temporal scales, climatic regions, and vegetation types. Specifically, univariate relationships between monthly NDVI measurements and single climatic factors were explored using BWC; multivariate relationships between NDVI measurements and combined climatic factors were characterized by MWC and proved by MEMD.

Study area
Based on the climatic indexes of active accumulated temperature, aridity, and frost-free period, China can be divided into seven climatic regions (Zhao 1983), including temperate humid and subhumid Northeast China (THSNC1), warmtemperate humid and subhumid North China (WHSNC2), subtropical humid Central and South China (SHCSC3), tropic humid South China (THSC), the temperate grassland of Inner Mongolia (TGIM4), the temperate and warmtemperate desert of Northwest China (TWDNC5), and the Tibetan Plateau (TP6). In this study, the THSC region was combined with the SHCSC3 region because of the small area of THSC and the similar variations of vegetation in both regions. These six climatic regions are shown in Fig. 1a, and the corresponding climatic indices are shown in Table 1. The aridity index gradually increased from east to west, whereas the active accumulated temperature and frost-free period gradually increased from north to south in the east of China.

Data sources
From 1982 to 2015, a total of 2,474 meteorological stations across China collected data measurements-including daily temperature, precipitation, sunshine duration, relative humidity, and wind speed-from the Climatic Data Center, National Meteorological Information Center (https:// data. cma. cn/).  After eliminating the meteorological stations with deficient data, monthly mean temperature (MT), highest temperature (HT), lowest temperature (LT), accumulated precipitation (AP), sunshine duration (SSD), relative humidity (RH), and wind speed (WS) were obtained from each station. The NDVI was derived from Global Inventory Modeling and Mapping Studies (GIMMS) and obtained from Advanced Very High Resolution Radiometer (AVHRR) sensors on board National Oceanic and Atmospheric Administration (NOAA) satellites boarded on the advanced very high resolution radiometer (AVHRR) sensor (https:// ecoca st. arc. nasa. gov/ data/ pub/ gimms/). The meteorological stations where the highest quality of the NDVI accounted for more than 85% of the measurements (quality flags for 1982-2015) were selected, and their monthly NDVI data from 1982 to 2015 were extracted. Annual Moderate Resolution Imaging Spectroradiometer (MODIS) Land Cover Type (MCD12Q1) data layers for China from 2001 to 2015 were obtained from the Level-1 and Atmosphere Archive and Distribution System (LAADS) (https:// ladsw eb. modaps. eosdis. nasa. gov/). Only meteorological stations where land cover type did not change from 2001 to 2015 were retained in this study. Because the meteorological stations were located mostly in grasslands or croplands, only two vegetation types were considered (Fig. 1b).
Based on vegetation type, 564 meteorological stations located in grasslands and croplands were selected. The spatially averaged time series of the NDVI, MT, HT, LT, AP, SSD, RH, and WS were calculated over the period 1982-2015, corresponding to two vegetation types in six climatic regions.

Bivariate wavelet coherence (BWC) and multivariate wavelet coherence (MWC)
MWC between the response variable Y and predictor variables X ( X = [X 1 , X 2 , … , X m ] ) at the scale-time (or scalelocation) domain ( s, τ ) is defined as : When only one variable (X 1 ) is included in X, Eq. (2) is the equation for BWC, which is expressed as where ↔ ↔ w X,X (s, ) is a series of the smoothed auto-and cross-wavelet power spectra for multivariable X, which is expressed as is the smoothed auto-wavelet power spectra for response variable Y. Both BWC and MWC are calculated using the Monte Carlo method at a 95% significance level (Grinsted et al. 2004). A detailed description of BWC can be found in previous studies (Grinsted et al. 2004), and a detailed description of MWC can be found in Hu and Si (2016).

Multivariate empirical mode decomposition (MEMD)
MEMD is a multivariate extended empirical mode decomposition (EMD) algorithm. To overcome the disadvantage of generating different intrinsic mode function (IMF) numbers among multivariate temporal data, MEMD could align common IMFs present within multivariate data. The detailed procedures of MEMD can be found in other publications (Hu et al. 2013; Rehman and Mandic 2010).

Data processing
The local wavelet spectra of the NDVI for two vegetation types in six climatic regions were calculated to assess the NDVI variations. BWC between the NDVI and each individual climatic factor, MWC between the NDVI and the combined climatic factors, and the percentage area of significant coherence (PASC) (Hu et al. 2017;Zhu et al. 2016) were calculated to assess the relative effect of controlling factors on the NDVI. Meanwhile, MEMD, combined with the squared multiple correlation coefficient, was performed for the multivariate temporal series. The scales of each IMF for the NDVI and climatic factors were calculated using the Hilbert transform, and the mean scales were obtained to represent the characteristic scales. The variance contribution of each IMF to the total variation in the NDVI was calculated as the ratio of the variance of each IMF to the variance of the original temporal series of the NDVI. (3)

Relationships between NDVI and climatic factors at the temporal scale of 1 month
The Pearson correlation coefficients between the NDVI and climatic factors in six climatic regions and two vegetation types are presented in Table 2. Obviously, temperature and precipitation had consistently positive correlations with vegetation growth. The duration of sunshine and relative humidity also had a significantly positive effect on vegetation, whereas wind speed had significantly negative relationships with the NDVI except in the TP6 climatic region. The dominant climatic factors under different regions and vegetation types were similar, and temperature was most closely correlated with the NDVI across China.

Local variation of NDVI in the domain of time and scale
There were distinguishable seasonal patterns across the multiple temporal scales in the local wavelet spectrum of the NDVI (Fig. 2). The variation of the NDVI around the 1-year scale was discerned for the two vegetation types in the six climatic regions. Meanwhile, the seasonality patterns of significant variation around the 0.5-year scale were detected for grasslands and croplands in the THSNC1, TGIM4, and TP6 regions. A discernable pattern around the 0.3-year scale was found in the WHSNC2 and SHCSC3 croplands. Additionally, significant variations around the 0.5-and 0.3year scales were entangled with one another after 1995 in SHCSC3 croplands. However, seasonal patterns at a scale of less than 1 year were not detected at all in TWDNC5.

Univariate control of climatic factor on the NDVI by BWC
Scale-and temporal-specific correlations between the NDVI and single climatic factors in grasslands are shown in Fig. 3. BWC between the NDVI and HT or LT is not presented because of similar relationships between the NDVI and AT or HT or LT. BWC between a single climatic factor and the NDVI were significant around the 1-year scale except for relations between the NDVI and SSD in SHCSC3 and for relations between the NDVI and SSD or RH or WS in TP6.
The effect of precipitation on the NDVI around the 0.5-year scale was greater than that of temperature for grasslands in the THSNC1, WHSNC2, TGIM4, and TP6 regions. Meanwhile, the interannual effects of precipitation on vegetation were also detected locally or universally in the WHSNC2, TGIM4, TWDNC5, and TP6 grasslands.
Overall, significant correlations existed in the relationships between the NDVI and climatic factors. Therefore, the controls of climatic factors on vegetation could be divided into four temporal scales, including ≤ 1 year (seasonal), 1-4 years, 4-8 years, and > 8 years. The influential strength of each individual climatic factor on grass growth is shown in Table 3. For the ≤ 1-year scale, precipitation played a leading role in grassland activity across China except in the TWDNC5 region. For the 1-4-year scale, precipitation controlled grass growth in TGIM4 and TWDNC5, whereas temperature was the main factor in the rest of China. For the 4-8-year and > 8-year scales, the dominant factors varied among MT, AP, RH, and SSD in different climatic regions. However, the impact of precipitation on grass growth was noticeable at all scales across all of China.
BWC between the NDVI and single climatic factors in croplands is shown in Fig. 4. The relationships between single climatic factors and the NDVI were captured by significant wavelet coherence at temporal scales of 0.5, 1, 4, and 8 years. The impact of each individual climatic factor on crop growth is shown in Table 4. For the ≤ 1-year scale, precipitation had a predominantly positive effect on crop growth

Scale-and temporal-specific multivariate control of climatic factors on the NDVI by MWC
To compare the effect of individual climatic factors on the NDVI, the MWC method was used to explore the combined effect of climatic factors on the NDVI. Obviously, the climatic factors offered a clear explanation for the NDVI variations around scales of 1 and 0.5 years (Fig. 5). Although the explanatory capacity of single climatic factors on grass growth was limited in the SHCSC3 region, combined climatic factors could prominently improve the explanatory capacity on vegetation growth at the 1-4-year and > 8-year scales.
The PASC of MWC between the NDVI and combined climatic factors for grasslands and croplands are shown in Table 5. Obviously, the mixed effect of climatic factors could slightly increase the control of single climatic factors on vegetation growth at the ≤ 1-year and 1-4-year scales in most regions and could obviously improve the effect of single climatic factors at the > 8-year scale. However, the combined effect was limited in the 4-8-year scale, with improved effects observed only in TGIM4 and TP6 grasslands and TWDNC5 croplands, where the combined effects at the ≤ 1-year scale were weaker than that of a single climatic driver. It is worth pointing out that the combined effects of climatic factors on vegetation dynamics were greater than that of single climatic factors at the overall temporal scale. In summary, the leading factor for grass variation at the ≤ 1-year scale was precipitation for the TGIM4 and TP6 regions, and for the other regions, it was combined climatic factors; at the 4-8-year scale, it was RH, precipitation, SSD, combined climatic factors, precipitation, and combined climatic factors, respectively, for the six climatic regions; at the 1-4-year and > 8-year scales, it was combined climatic factors. For crop growth, the dominant factors at the ≤ 1-year scale were RH for TGIM4 and WS for TWDNC5; and they were a combination of climatic factors for the other regions; at the 4-8year scale, they were HT, WS, precipitation, HT, combined factors, and LT, respectively, for the six climatic regions;  The PASC of combined climatic factors ranged from 37 to 65% at the overall temporal scale in grasslands, and the effects in different regions were ranked as follows: SHCS C3 < TWDNC5 < THSNC1 < WHSNC2 < TGIM4 < TP6.
The PASC of the combined climatic factors at the overall temporal scale in croplands ranged from 39% in TGIM4 and TWDNC5 to 45% in WHSNC2 and SHCSC3 and 47% in THSNC1 and TP6. Therefore, considering the explanatory power of climate, the agricultural production areas can be classified into four regions as follows: WHSNC2-SHCSC3,   TGIM4-TWDNC5, THSNC1, and TP6. The variation of the PASC among different climatic regions was obviously lower for croplands than for grasslands, whereas the variation of the PASC among different temporal scales was greater for croplands than for grasslands.

Comparison of MWC and MEMD
The components of the NDVI from MEMD indicated that MEMD had the advantage to extract information on large trends (see Supplementary Fig. S1 and Fig. S2). The averaged scales of the NDVI and climatic factors and the variance contribution of each IMF towards original variance of the NDVI were calculated (see Supplementary Table S1). The shortest scale was 0.99 years, represented by IMF1, which contributed a majority variance of more than 80%. This agrees with the results analyzed by the wavelet transform, which showed that the majority of NDVI variations occurred at a scale of around 1 year (Fig. 2).
Coefficients of determination between each scale component of the NDVI and climatic factors at the corresponding scales demonstrated that the control of climatic factors on the NDVI was the greatest at temporal scales around 1 year and > 8 years (see Supplementary Fig. S3), which were similar to the results from MWC. However, temperature played a dominant role around the 1-year scale across China when using MEMD, whereas precipitation had the leading effect at the ≤ 1 year scale in most climatic regions when using MWC.

Vegetation variation at different temporal scales
The impact of land cover change on vegetation growth is complicated because it depends not only on the intensity but also on the type of land cover change (Gao et al. 2020). In this study, the land types during 1982-2000 were not considered because of the major shift in land use types that has taken place since 2000, such as urbanization, which caused a conversion from cropland to construction land, and the Grain for Green program, which caused a conversion from cropland to forest. Thus, to precisely evaluate the vegetationclimate variation at multiple temporal scales, the land types maintained from 2001 to 2015 were extracted in this study to minimize the heterogeneity of anthropogenic factors on vegetation.
The local variation of grass and crop NDVIs were significant around the 1-year scale across all of China from 1982 to 2015. The variation of vegetation around the 1-year scale was also observed by Liu et al. (2016). In the study, the significant variations of the NDVI around the 0.3-and 0.5-year scales were also detected at a 68% confidence level. Thus, the temporal scale of the significant variation of the NDVI was 1 year followed by 0.5 and 0.3 years, depending on the climatic regions and vegetation types. The significant variation of the NDVI at the 0.5-year scale could be perceived across China except in SHCSC3 grasslands, WHSNC2 croplands, and TWDNC5 grasslands and croplands. Because of the intensity of economy-driven anthropologic factors, frequent human activity in the southeast of China (Hou et al. 2015) might lead to the indiscernibility of patterns around the < 1-year scale in SHCSC3 grasslands. In WHSNC2 croplands, the variation around the 0.5-year scale was insignificant, whereas the variation around the 0.3-year scale was significant. The results might be related to the cropping system of winter wheat and spring maize (or summer maize) uniformly applied in this area (Yan, 2020). In the TWDNC5 region, because it had the lowest NDVI value across the whole year and the driest climatic conditions (Zhao and Hu 2020), the vegetation growth did not display seasonal variations at the < 1 year scale. Notably, the seasonal pattern around the 0.5-year scale was prominent in the THSNC1, TGIM4, and TP6 regions, which might be attributed to the difference between the vegetation season and the non-vegetation season (Zhou, 2020). The mingled seasonal patterns at the 0.5-and 0.3-year scales in SHCSC3 croplands might be attributed to the mixed cropping system of double-rice cropping and rice-wheat cropping after 1995 (Wu et al. 2013;Zhang et al. 2015). Therefore, vegetation variation was dominant at the 1-year scale across all of China, and variation at the 0.5-year scale was found in temperate areas and the Tibetan Plateau with a distinct difference between the vegetation season and non-vegetation season of a single year, and significant variation at the 0.3year scale was found generally in croplands in the major crop-producing areas of Southeast China (WHSNC2 and SHCSC3) that have multiple cropping systems.

Effect of single climatic factor on the NDVI at multiple temporal scales
Previous studies reported that precipitation, temperature, solar radiation, and relative humidity were significantly correlated with vegetation growth in China (Sun 2020;Yang and Zhang 2014;Zhao and Hu 2020). The climatic factors, MT, HT, LT, AP, SSD, RH, and WS, were selected in the present study. We observed that the correlation between temperature and vegetation was positive at the > 0.5-year scale and was negative at the ≤ 0.5-year scale. Temperature exerted either a dominantly positive or negative effect on vegetation growth at some scales, which is in agreement with previous observations in Southwest China (Liu and Menzel 2016). The noticeable positive relationships between temperature and vegetation at scales greater than 0.5 years might be attributed to more carbohydrate consumption and, subsequently, enhancement of persistent daytime photosynthesis, which resulted from nighttime warming optimizing both the root and leaf respiration of plants (Yuan, 2020). The negative effects of temperature on vegetation at scales less than 0.5 years were probably associated with shorttime limited water availability , which resulted from increasing evaporation because of an increase in highest temperature, constrained photosynthetic activities and aggravated plant respiration, and, thus, inhibited plant growth. Therefore, temperature exerted different effects on vegetation growth at different temporal scales. Precipitation had a pronounced positive effect on vegetation growth around the 1-year scale, which was different from the results from Southwest Germany (Liu and Menzel 2016), which might be attributed to the different climatic conditions between Germany and China. However, the positive correlation between precipitation and the NDVI was observed in the Yangtze River and Yellow River Basin at some temporal scales . Although precipitation was not the greatest influencing factor for grass growth based on the Pearson correlation coefficient, it played a leading role across all of China at overall temporal scales and seasonal scales except in the TWDNC5 region. Precipitation was not the leading factor for grass growth at the seasonal scale (≤ 1 year) in TWDNC5, but it had a critical effect at the 1-4-year and 4-8-year scales and overall temporal scale. In the TGIM4 region, precipitation had a critical effect on grass growth at all temporal scales, which was consistent with a previous finding that water availability dominated grass productivity in the region (Zhao and Hu 2020). For cropland at the seasonal scale (≤ 1 year), precipitation also played a leading role in major crop-producing areas (THSNC1, WHSNC2, and SHCSC3) and TP6, and RH had the dominant effect on crop productivity in TGIM4. In the TWDNC5 region, precipitation seemed to exert the dominant influence on crop growth only at the 4-8-year scale, probably because irrigation activities in the area disorganized crop-precipitation relations, and the interannual variation of precipitation is greater than its intra-annual variation (Linscheid et al. 2020), which resulted in the leading effect at the 4-8-year scale.
It is worth pointing out that SSD, which is related to solar radiation, was positively related with grass growth across the 1-year scale except for in the SHCSC3 and TP6 regions, whereas it had an unstable effect on vegetation dynamics at other temporal scales. The local negative effect of SSD on vegetation might be related to increased evaporation, where the increase of SSD caused water losses, further preventing plant growth. In SHCSC3, SSD did not have stable relationships with grass conditions around the 1-year scale, which might be because of the discrepancy between SSD and the critical factor of temperature. The higher temperature resulted from being closer to the equator and the lower SSD. In TP6, SSD was slightly correlated with grass at the 1-year scale, which agrees with a previous finding (Zhao and Hu 2020) that SSD offers less of an explanation in alpine grasslands than in temperate grasslands. The result might be attributed to the complex topology in TP6, which resulted in large variations in SSD.
Compared with precipitation, RH had relatively weak effects on the vegetation growth, especially in TP6. The complex topology in TP6, which makes the spatial distribution of climatic conditions much more heterogeneous, resulted in the varied mechanism of vegetation-climate dynamics. Meanwhile, the response of alpine grass to climate, which was distributed in TP6, was different from the response in temperate grasslands. The slightly weak effect of relative humidity on crop productivity in THSNC1 might be attributed to the irrigation activities for crops in the area.
WS exerted a negative influence on vegetation productivity at the 1-and 0.5-year scales, especially with the distribution of strong wind in temperate regions and the Tibetan Plateau. The noticeable impact of WS on vegetation growth was probably due to the mechanical destruction and excessive transpiration of plants resulting from strong winds (Gardiner et al. 2016), which is extremely injurious to plants. However, positive relationships between WS and vegetation were also observed in some localized times, because wind can increase turbulence in the atmosphere and the availability of CO 2 , thereby increasing photosynthesis (Konrad et al. 2021). Unfortunately, the effect of WS on vegetation dynamics was not captured by the Pearson correlation coefficient in the TP6 region.
We concluded that precipitation played a crucial role in affecting the seasonal variation of vegetation productivity, which resulted from the prominent effect around the 0.5year scale, and temperature played a leading role in affecting the variation of vegetation at the 1-4-year scale. Thus, the leading single factor is annual oscillation of temperature, combined with the 0.5-year intra-annual dominance of precipitation. For the 4-8-year and > 8-year scales, the dominant factor on vegetation varied with climatic regions and vegetation types, which implied that the mechanisms by which vegetation responds to a single climatic factor varied among different regions and vegetation types at these temporal scales.

Combined effect of climatic factors on the NDVI at multiple temporal scales
Our results showed that the interaction effects of multiple climatic factors on vegetation dynamics were stronger than the effect of individual climatic variables on the NDVI at a scale of > 8 years. Such long-term climate variation may occur in the form of periodic atmospheric fluctuations (Linscheid et al. 2020), which might result in the long-term variation of the NDVI. The combined climatic controls on the NDVI were evaluated in previous studies. For example, Qu (2020)  In our study, the explanatory capability of a combination of climatic factors on grass growth was ranked as follows: SHCSC3 < TWDNC5 < THSNC1 (or WHSNC2) < TGIM4 < TP6. In terms of the effects on crop growth, it was ranked as TGIM4 (or TWDNC5) < WHSNC2 (or SHCSC3) < THSNC1 (or TP6). The results indicated that socioeconomic condition is related to the dynamics of grass growth except in TWDNC5, which had the lowest NDVI values (Yao et al. 2019). The lesser variation of explanatory power among different regions demonstrated that tillage activities in cropland alleviated the spatial difference of climate-vegetation dynamics and strengthened its temporal difference. Meanwhile, the greatest variation at the 4-8-year scale implied that the climatic regions and vegetation types cannot be neglected in the analysis of vegetation growth at these temporal scales.

Comparison of MWC and MEMD on the multivariate relationships in ecology
The vegetation-climate relationships at around the 1-year scale and at the > 8-year scale were dominant, which were similar for both MWC and MEMD. The results demonstrated that both MWC and MEMD could disentangle the dominant temporal scales of NDVI variation. However, the discrepancy of dominant factors at the seasonal scale among MEMD and MWC might be attributed to the shortage of vegetation-climate relations at the 0.5-year scale for MEMD, where precipitation had a dominant effect on vegetation. MEMD can partition original series into limited temporal scales and generally attributed dominant variance to the seasonal process in ecology, which was consistent with findings from previous studies where IMFs decomposed by EMD contained more variation in the seasonal cycle and less modulation in the interannual temporal scales for the NDVI (Linscheid et al. 2020). In addition, other methods, such as multiple regression or local correlation methods, should be integrated into MEMD for yielding the combined scale-specific effect of climate on vegetation or for obtaining their localized multivariate relationships. Our results indicated that the residue decomposed by MEMD could represent the trend of vegetation growth. Although both MWC and MEMD could capture significant vegetation-climate relations at temporal scales of around 1 year and > 8 years, the distinctions between the two methods should be mastered and the appropriate one applied depending on the situation. This study paves the way for better understanding the scale-specific, localized, temporal heterogeneity of vegetation growth response to climate variability, and the temporal evolution of vegetation dynamics at different climatic regions should be explored in the future.

Conclusion
The following conclusions were drawn: (1) Vegetation variation at the 1-year scale could be captured across all of China; vegetation variation at the 0.5-year scale was displayed in temperate areas and the Tibetan Plateau with distinct differences between the vegetation season and non-vegetation season of a single year, and significant variation at the 0.3-year scale generally took place in the major crop-producing areas of Southeast China (WHSNC2 and SHCSC3) that have multiple cropping systems.

Declarations
Ethics approval Not applicable.

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Conflict of interest
The authors declare no competing interests.