Vegetation Dynamics and Climate from A Perspective of Lag-Effect: A Study Case in Loess Plateau, China

Abstract

With global warming, the law of climate change is more and more complex, so it is of great significance to analyze the response mechanism of vegetation change to climate change. The Loess Plateau (LP) is a vulnerable area, but we must explore the mechanism between climate and vegetation for decision-makers to make adequate plans to better govern this population-intensive but ecological-fragile area. Our study analyzed the vegetation variation in a long-term period from 1982 to 2015 and its relationship with precipitation and temperature. We innovatively leverage the weighted time-lag method to detect the different contributions of a specific climatic factor from different months to vegetation growth. Moreover, we used such weighted accumulated climatic factors to find the relationships between precipitation/temperature and different types of vegetation. The main findings are as follows: (i) For different degrees of temperature and precipitation, different vegetation has different performance characteristics in different months from 1982 to 2015. Moreover, precipitation is the major driver of vegetation growth in the LP. (ii) The response of vegetation possesses some time-lag effect on climate and exhibits spatial heterogeneity in the LP, which may be related to the characteristics of different climate zones and different vegetation. (iii) The effect of the same climatic factor on different vegetation accounts for a certain proportion of different months in the LP. Climate possesses a cumulative effect in three months on vegetation and different climatic factors have different time lags to the same vegetation type. It has a complicated interaction between vegetation growth and climate change. This paper uses the weighted time-lag method to investigate the relationship between vegetation growth and climatic factors, whilst considering how the time-lag effect can explain the changes that occur in the process of vegetation growth to a large extent.

1. Introduction

Global warming has quietly impacted the terrestrial ecosystem over the last hundred years, with a series of problems affecting the environment change such as temperature increases, glacier ablation, sea-level rise [1,2,3,4], etc. Vegetation is very important for terrestrial ecosystems and is the hub that connects the atmosphere, soil, and water [5,6,7], which is a significant part of the hydrological cycle, biochemical cycle, as well as global energy cycle [8,9]. To explore the mechanisms of the effect of climate change on vegetation growth is crucial to learn the progress of ecosystem dynamics so that decision-makers can rely on such knowledge to make adequate plans to better trade-off the demand of supply of ecosystem services, especially in those ecological-fragile regions. Loess Plateau (LP) is such a vulnerable area, providing types of ecosystem services to around 100 million Chinese people, which comprises abundant species, alternative ecosystems, and different climate zones. Therefore, studying the response of vegetation to climate change and the continuous change in vegetation growth can provide a rich theoretical foundation for decision-making in the LP and demonstrate a study case for studying the ecological environment changes in other regions [10,11,12,13]. More and more researchers have analyzed the vegetation dynamic changes. The interaction between climate change and vegetation growth is a very complex process [14,15,16,17,18,19,20]. For example, Xin et al. [21] explored the spatio-temporal variation of vegetation, and the results showed that the vegetation changes were caused by combining human activities and climate change on LP. Sun et al. [22] analyzed the temporal variations and spatial distribution of vegetation in the past three decades in LP while assessing the relationships between human activities, climatic factors, and vegetation. Meanwhile, many kinds of research that illustrated the impact of climate change on vegetation growth do not occur synchronously [23]. The most likely impact is the effect of earlier climatic conditions, the phenomenon commonly referred to as the time-lag effect [24,25,26]. Moreover, the time-lag effect of climate change on different vegetation is different [27,28]. Considering the time-lag effect can enhance the correlation between temperature, precipitation, and vegetation, which can explore the influencing mechanism of climate change on vegetation growth to a certain extent [26,29,30,31,32].

Some scholars discovered vegetation response has some time-lag effect to climatic factors, and different vegetation has different degrees of response to climate in different regions [14,33,34,35,36,37,38]. Therefore, we should analyze the time-lag effect of temperature and precipitation on vegetation growth [8,39,40,41,42]. Anderson et al. [43] discovered diverse vegetation types and climatic factors can show diverse time-lag effects when studying the relationship between vegetation and atmospheric variables (precipitation, radiation, and aerosol optical depth) in Amazonia. Zhou et al. [31] explored the response mechanism of vegetation change to the climate in Central Asia from 1982 to 2011, the results illustrated no time lag from 1982 to 1991, however, 1–3 months’ time lag after 1992. Bunting et al. [44] found that woodland and shrubland had strong correlations with climate change and that the delay time is 6–12 months, while grassland had a short lag of about 3–6 months. The time-lag effect of vegetation to climate may be affected by the time scale adopted and linked to the biological mechanism of the vegetation itself. For example, deep-rooted vegetation may have a longer memory mechanism for precipitation changes [45], but from a quantitative perspective, the response time of vegetation to precipitation is difficult to determine [46]. A number of studies demonstrated that vegetation has a three-month time lag to climate change in the current month [8,26,32,36,47]. Based on this, we assume that vegetation growth primarily impacts the cumulative effects of climate change during the current month and the first three months.

Due to the different regional characteristics of the LP, different vegetation may impact different degrees of human and natural factors, which can be divided into natural vegetation (such as woodland, grassland, and sparse vegetation) and artificial vegetation. Climate change plays an important role in natural vegetation growth, while human activities affect the growth of artificial vegetation more often [48,49]. The research focuses on the effects of climate change on natural vegetation. The Normalized Difference Vegetation Index (NDVI) is commonly applied to detect the effect of climate change on vegetation and is a good indicator of the biophysical parameters of various vegetation [39,50,51,52,53,54,55]. Therefore, NDVI was used to characterize vegetation changes in this paper. On the basis of the temperature, precipitation, and NDVI from 1982 to 2015 of the LP, we study the cumulative effects of climatic conditions on vegetation.

In this paper, we innovatively adopted the weighted time-lag method to uncover the different contributions of a specific climatic factor from different months to vegetation growth. Assuming a maximum time-lag effect of three months, this paper studies the effects of different vegetation on different climatic factors, and how different weights can obtain the degree of effect of climatic factors on vegetation at different months. Our study will comprehensively consider the response time of vegetation growth to climatic factors to better explore and study the time-lag effect of climatic factors on vegetation during the growing season. Therefore, the study objectives include (i) studying the relationship between climate change and vegetation growth in the past 32 years in LP, and (ii) proving the time-lag effect of different climatic factors on different natural vegetation growth during the growing season to uncover the dynamic changes. In view, the time-lag effect is very essential for vegetation growth and terrestrial ecosystem balance, and it could also help us reveal the interaction between climate and vegetation.

2. Materials and Methods

2.1. Study Area

The LP (100°54′ E–114°33′ E and 33°43′ N–41°16′ N) locates in the upper and middle reaches of the Yellow River and has an area of about 640,000 km² in China. The altitude is above 800–3000 m. Our study area is one of the four plateaus in China. It has a complex landform, rich geological environment, serious soil erosion, and fragile ecological environment [56]. The annual mean temperature range is 3.6–14.3 °C. The average annual precipitation range is 150–750 mm and exhibits significant spatiotemporal differences. The climate zone in the LP is mainly composed of three typical types: arid, semiarid, and semi-humid regions (Figure 1).

2.2. Datasets and Pre-Processing

We used the NDVI to represent vegetation growth. The dataset was the third generation Global Inventory Monitoring and Modeling System (GIMMS NDVI3g). The GIMMS NDVI3g comes from NOAA’s Advanced Very High-Resolution Radiometer (AVHRR) data with 1/12° spatial resolution and 16-day temporal resolution which possesses a high spatial resolution, and long-time intervals, as well as high accuracy, from 1982 to 2015. A maximum value composite (MVC) method [57] was used to obtain the monthly NDVI data by alleviating the atmospheric effects of clouds and aerosols. The formula is:

$$NDV{I}_m=\mathrm{Max}\left(NDV{I}_{m1},NDV{I}_{m2}\right)$$

(1)

where NDVI_m represents the NDVI value for the m month, NDVI_m1 is the NDVI value for the first 15 days of the m month, NDVI_m2 is the NDVI value in the last 15 days of the m month. To avoid the impact of extreme weather in winter and early spring on vegetation, we choose the growing season (from April to October) to study.

The paper used monthly total precipitation and mean temperature from 52 meteorological stations on the LP. The surface climate dataset from the Chinese Climate Academic and Science Dataset (http://cdc.cma.gov.cn/) accessed on 15 May 2020. The study uses the method of Inverse Distance Weighting (IDW) for interpolation to get a climate raster dataset with identical spatial and temporal resolutions as the NDVI data.

Land-cover product is from Moderate-resolution Imaging Spectroradiometer (MODIS) products (MCD12C1) for statistical analysis, which includes 17 general land cover types. Our study focuses on the three main types of natural vegetation, mixed forests, grasslands, and barren or sparsely vegetated. Moreover, we filter out the vegetation-type-unchanged pixels from 2001 to 2015 since this is the overlap between the period we studied and the period that MODIS product covered. At the same time, we sampled the raster from 0.05° to 1/12° by the k-nearest neighbor algorithm. Figure 2 shows the patterns of land cover types, climate zones, and meteorological stations in the LP.

2.3. Methods

2.3.1. Weighted Time-Lag Method

In the existing related studies, most scholars only considered the response time of vegetation growth to climatic factors at a specific period of time but ignored the cumulative effects of climatic factors in previous months. Sun et al. [22] introduced a weighted time-lag method to uncover the relationship between climate change and vegetation. They thought that vegetation is mainly influenced by the cumulative effects of climate in the first three months and the current month. Assuming temperature and precipitation are independent of each other, the linear regression analysis is applied to demonstrate the time-lag effect of climatic factors on vegetation growth monthly. In this paper, T is for the current month, T-1 is for the previous one month, T-2 is for the previous two-month, and T-3 is for the previous three-month forward. T-month NDVI was affected by the combined effects of climatic factors of T, T-1, T-2, and T-3. The effect of each month on T-month NDVI is unknown, so different weights are given to each month: w_T, w_T-1, w_T-2, and w_T-3. The selection of w_T, w_T-1, w_T-2 and w_T-3 needs to satisfy two conditions: (1) w_T, w_T-1, w_T-2 and w_T-3 takes a value between [0.0, 1.0], and its sampling interval is SI = 0.1 (SI ≤ 1.0); (2) w_T + w_T-1 + w_T-2 + w_T-3 = 1. From the above schemes, there are 286 scenarios for weight selection, so there is a total of 286 results.

2.3.2. Linear Regression Analysis of the NDVI Data and Climate Variables

The paper uses linear regression to study the relationship between climatic factors (temperature and precipitation) and NDVI in growing seasons from 1982 to 2015 in the LP. The T-month NDVI was regressed with the T, T-1, T-2, and T-3 months’ temperature or precipitation for each of the 286 scenarios. The relationship between climatic factors and NDVI is as follows in Formula (2):

$$\{\begin{array}{l}NDV{I}_{i,j}\left(k\right)=a_{i,j}\left(k\right)\cdot Pr{e}_{i,j}\left(k\right)+b_{i,j}\left(k\right)\\ NDV{I}_{i,j}\left(k\right)=c_{i,j}\left(k\right)\cdot Te{m}_{i,j}\left(k\right)+d_{i,j}\left(k\right)\end{array}$$

(2)

where k represents the month of the growing season in the long-term sequence from 1982 to 2015. $NDV{I}_{i,j}\left(k\right)$ refers to the NDVI value of (i, j) pixel in k months. $Pr{e}_{i,j}\left(k\right)$ refers to total precipitation at (i, j) in k month, $Te{m}_{i,j}\left(k\right)$ refers to the mean temperature at (i, j) in k months. $a_{i,j}\left(k\right)$ and $b_{i,j}\left(k\right)$ are the slope as well as the intercept of NDVI and precipitation at pixel (i, j) in k month, $c_{i,j}\left(k\right)$ and $d_{i,j}\left(k\right)$ are slope and intercept of NDVI and temperature at pixel (i, j) in k month. The correlation coefficient has studied the correlation between NDVI and climatic factors and analyzes the conditions of spatial distribution. The formula is as follows:

$$R_{xy}=\frac{{\displaystyle \sum _{i=1}^n\left[\left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)\right]}}{\sqrt{{\displaystyle \sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}}}$$

(3)

where R_xy represents the correlation coefficient between the variable x and y, and $\overline{y}$ are the average of the two variables, and n represents the sample number. The i represents one month in the growing season. The R_xy range value is [−1.0, 1.0]. The correlation is becoming stronger as the R_xy gets closer to 1 or −1, while the correlation is becoming weaker as the R_xy gets closer to 0.

Through the weighted time-lag method, we can obtain 286 types of correlation coefficients for precipitation and temperature, respectively. Using the principle of the MVC method, the maximum value of the corresponding 286 types of pixels in all raster maps is extracted to obtain a maximum correlation coefficient raster map with the formula:

$$R_m=\{\begin{array}{c}\max \left|{\displaystyle \sum _{i,j=1}^n{R}_{xy,ij}}\right|,R_{xy,ij}>0\\ -\max \left|{\displaystyle \sum _{i,j=1}^n{R}_{xy,ij}}\right|,R_{xy,ij}<0\end{array}$$

(4)

$$R_{\max }=\{\begin{array}{c}\max \left|R_{m,ij}\right|,R_{m,ij}>0\\ -\max \left|R_{m,ij}\right|,R_{m,ij}<0\end{array}$$

(5)

where R_m is the correlation coefficient with the strongest correlation of the corresponding pixel regression in 286 scenarios, R_xy,ij is the correlation coefficient of corresponding pixels obtained by pixel-by-pixel regression of 286 schemes. R_max represents the maximum correlation coefficient among all corresponding image elements. To avoid human impact on vegetation as much as possible, this study focused on three types of natural vegetation, mixed forest, grasslands, and barren or sparsely vegetated, to study.

3. Results

3.1. Spatial Patterns of Relationship between NDVI and Precipitation/Temperature in Different Months

To illustrate the features of natural vegetation changes and analyze the major climatic driving factors of vegetation growth on the LP, we used the weighted time-lag method to weight precipitation and temperature for different months and then used NDVI to operate regression analysis on precipitation and temperature to obtain the corresponding correlation coefficients from April to October. Figure 3 and Figure 4 demonstrated the spatial patterns of the correlation coefficients between precipitation and temperature and the corresponding NDVI, respectively. The green areas indicate a positive correlation, and the red areas represent a negative correlation. The Loess Plateau crosses three climatic zones, and it can be seen that there is obvious spatial heterogeneity in the effects of different climatic factors on vegetation in different climatic zones.

Generally, the effect of precipitation on vegetation growth is positive and has different degrees of effect on vegetation growth in different months in Figure 3. As the growing season comes, precipitation has an increasingly strong effect on vegetation growth. To obtain the effects of different climatic zones on vegetation growth in the Loess Plateau, the effects of precipitation on vegetation growth under different climatic zones were counted in

Table 1. Correlation statistics of precipitation and NDVI under different climate zones.

Climate Region	Statistical Correlation	April	May	June	July	August	September	October
Arid	R > 0, p > 0.05	20.05%	38.84%	21.30%	19.12%	26.31%	19.44%	33.31%
	R > 0, p < 0.05	19.97%	27.88%	51.84%	63.32%	62.41%	74.37%	57.52%
	R < 0, p < 0.05	23.41%	6.97%	11.90%	8.39%	2.35%	2.35%	2.27%
	R < 0, p < 0.05	36.57%	26.31%	14.96%	9.17%	8.93%	3.84%	6.90%
	Rmax	0.85	0.68	0.83	0.83	0.81	0.77	0.69
Semiarid	R > 0, p < 0.05	37.57%	41.98%	38.24%	21.64%	23.88%	14.84%	22.43%
	R > 0, p < 0.05	32.01%	32.95%	44.66%	70.07%	59.61%	82.07%	66.78%
	R > 0, p < 0.05	5.11%	2.68%	3.69%	2.96%	5.56%	0.58%	2.52%
	R > 0, p < 0.05	25.31%	22.39%	13.42%	5.34%	10.95%	2.52%	8.28%
	Rmax	0.92	0.73	0.73	0.82	0.77	0.79	0.72
Semi-humid	R > 0, p < 0.05	30.46%	37.32%	34.94%	38.78%	31.01%	40.65%	36.40%
	R < 0, p < 0.05	27.30%	31.53%	28.66%	33.58%	27.60%	30.19%	29.64%
	R > 0, p < 0.05	12.31%	12.65%	17.81%	9.78%	20.69%	9.06%	8.81%
	R > 0, p < 0.05	29.93%	18.49%	18.59%	17.86%	20.69%	20.11%	25.16%
	Rmax	0.42	0.47	0.63	−0.51	−0.59	0.65	0.45

. The results showed that the NDVI response to precipitation was higher in arid and semiarid areas than in semi-humid areas. For arid regions, precipitation was mainly negatively correlated with the vegetation index in April, while the other months were mainly positively correlated. For both semiarid and semi-humid regions, precipitation had a positive effect on vegetation within the growing season. The maximum correlation coefficients between NDVI and precipitation appeared in semiarid regions, the correlation between NDVI and precipitation was poor in semi-humid regions, and the maximum correlation coefficients were negative in July and August. The above results indicate that the influence of precipitation on vegetation growth has obvious spatial variability, and different climatic zones have different influences on vegetation growth in the Loess Plateau.

In contrast to precipitation, the correlation between NDVI and temperature on the Loess Plateau during the 1982–2015 growing season showed significant differences in different months (Figure 4), and the significance percentages were lower than for precipitation. In contrast to precipitation, the correlation between NDVI and temperature on the Loess Plateau during the 1982–2015 growing season showed significant differences in different months, and the significant percentages were lower than for precipitation. At the beginning of the growing season, the temperature was highly significant for vegetation in semiarid and semi-humid regions and was higher than in arid regions (

Table 2. Correlation statistics of temperature and NDVI under different climate zones.

Climate Region	Statistical Correlation	April	May	June	July	August	September	October
Arid	R > 0, p > 0.05	47.30%	43.30%	23.96%	28.76%	34.53%	17.32%	18.97%
	R > 0, p < 0.05	36.88%	21.53%	6.89%	16.46%	24.04%	4.94%	4.86%
	R > 0, p < 0.05	2.51%	8.93%	27.88%	12.30%	16.91%	49.53%	37.85%
	R < 0, p < 0.05	13.31%	26.23%	41.27%	42.48%	24.51%	28.21%	38.32%
	Rmax	0.85	0.68	−0.70	−0.56	−0.57	−0.64	−0.64
Semiarid	R > 0, p < 0.05	17.37%	32.29%	30.52%	28.60%	38.59%	18.98%	30.62%
	R > 0, p < 0.05	78.01%	49.99%	14.10%	6.51%	17.75%	12.51%	24.14%
	R > 0, p < 0.05	1.12%	5.56%	25.36%	18.70%	13.47%	30.27%	12.91%
	R > 0, p < 0.05	3.50%	12.16%	30.02%	46.19%	30.19%	38.24%	32.33%
	Rmax	0.92	0.77	0.71	−0.77	−0.77	−0.72	−0.71
Semi-humid	R > 0, p < 0.05	14.99%	32.99%	25.35%	29.54%	38.51%	19.43%	42.29%
	R < 0, p < 0.05	69.29%	37.96%	14.60%	5.06%	9.40%	2.82%	30.95%
	R > 0, p < 0.05	4.28%	12.51%	25.89%	21.85%	15.43%	28.04%	8.81%
	R > 0, p < 0.05	11.44%	16.55%	34.16%	43.55%	36.66%	49.71%	17.96%
	Rmax	0.74	0.61	−0.59	−0.63	−0.71	−0.62	0.61

). At the same time, significance diminished in the middle of the growing season and picked up again towards the end of the growing season, at which point it was higher in arid regions than in semi-humid and semiarid regions. In addition, different climatic zones show different patterns of temperature effects on vegetation. The study describes the impact of climatic factors on vegetation on the LP and gives us a better understanding of the extent to which different climatic factors affect vegetation growth.

3.2. Relationship between Different Vegetation Types and Precipitation/Temperature

Climatic factors have different effects on different vegetation types (Figure 5, Figure 6 and Figure 7). In order to study the effect of climatic factors on different vegetation types, we counted the percentage of positive and negative correlations for mixed forests, grasslands, and barren or sparsely vegetated at a significance level of p < 0.05. Mixed forests show different responses to different climatic factors (Figure 5). The effect of temperature on mixed forests was positive correlations in April, May, August, and October, which were 80.00%, 85.71 %, 66.67%, and 90.91%, respectively. The effect of temperature on NDVI in June and July were mainly negatively affected, and the average negative correlation ratio was 72.67%, and positive and negative comparably in September. This could be because evaporation increases along with the increase in temperature in the summer, so the temperature is mainly a suppressive effect on mixed forests. For precipitation, at the beginning of the growing season, snow can seep into the soil and excessive moisture can inhibit vegetation growth in winter [6,58]. The response of mixed forests to precipitation was negative in April and October. May, June, and September are mainly positively correlated, while the positive and negative correlations in July and August were comparable. The demand for vegetation for precipitation increases due to temperatures higher in summer. We can tell that there is sufficient water supply; however, the capacity for vegetation to absorb water is limited [59].

The impact of temperature and precipitation on grasslands growth show differences in different months (Figure 6), where the temperature has a positive effect on grasslands in April and May, and the proportions were 86.34% and 74.16%, respectively. The temperature shows negative effects for July, September, and October, and the positive and negative correlations in June and October were comparable. The precipitation contributes a positive effect on grasslands. Therefore, precipitation appears to be the main driver of grasslands growth in the LP [34].

Barren or sparsely vegetated belong to the arid regions of LP. In Figure 7, barren or sparsely vegetated areas appear a positive correlation with temperature in April, and August, and a negative correlation in all other months. The effect of precipitation on barren or sparsely vegetated was positively correlated during the growing season. The statistical results indicate that temperature suppressed growth in the barren or sparsely vegetated region, whereas precipitation mainly promoted its growth.

The impacts of temperature and precipitation on different vegetation types show heterogeneity in time and space. At the beginning of the growing season, the correlation coefficients between mixed forests and grasslands to temperature were higher than precipitation, and they were mainly positively correlated (

Table 3. Maximum correlation coefficients of NDVI and precipitation for different vegetation types.

Vegetation Type	4	5	6	7	8	9	10
mixed forests	0.55	0.57	0.57	−0.49	−0.59	−0.46	0.52
grasslands	0.92	0.73	0.83	0.83	0.81	0.79	0.72
barren or sparsely vegetated	0.85	0.58	0.66	0.73	0.78	0.74	0.56

). We attribute this to the fact that the green plants rely on surrounding temperature as thermal energy to regulate internal biogeochemical processes, thereby further regulating vegetation growth and development [60]. However, the correlation coefficient between barren or sparsely vegetated and precipitation was higher than the temperature in the arid regions and was positive. This is due to the lack of water in arid regions and precipitation contributes to vegetation growth. Grasslands are mainly located in arid and semiarid regions and therefore have a good correlation with precipitation (

Table 4. Maximum correlation coefficients of NDVI and temperature for different vegetation types.

Vegetation Type	4	5	6	7	8	9	10
mixed forests	0.74	0.61	−0.53	−0.46	−0.48	−0.40	0.61
grasslands	0.92	0.77	0.71	−0.77	−0.77	−0.72	−0.71
barren or sparsely vegetated	0.85	0.54	−0.61	−0.55	−0.57	−0.55	−0.63

).

3.3. The Time-Lag Effect of Different Climatic Factors on Different Vegetation

The latest method, weighted time-lag, is used to analyze the response time of vegetation to climate factors. The time-lag effect of temperature and precipitation on the diverse vegetation types is shown in Figure 8 and Figure 9, where T represents the current month, T-1 represents the last month, T-2 represents the last second month, and T-3 represents the third month ahead of the current month. The horizontal axis represents different months, and the vertical axis represents the proportion contributed by the climatic factors in each month. The effects of precipitation and temperature on vegetation growth in different months are different in the statistical analysis. The temperature in the last three months (T-3, T-2, T-1) showed a larger impact in the current month on vegetation growth in Figure 8. The temperature in the last three months had proportions of 77.99%, 77.53%, and 79.18% in p < 0.05, respectively, for the current month of barren or sparsely vegetated, grasslands and mixed forests. As shown in Figure 9, different vegetation showed a greater impact of precipitation in the last three months, except for the precipitation in the T month of April, which had a greater impact on the growth of barren or sparsely vegetated. Overall, the precipitation in the last three months had proportions of 78.07%, 81.54%, and 76.83% in p < 0.05, respectively, for the current month of mixed forests, grasslands, and barren or sparsely vegetated. The research results can illustrate the fact that climate change has a significant time-lag effect on vegetation. Based on the above analysis, different vegetation types showed a different time lag to the identical climatic factor, and the identical vegetation type has different delay rules to different climatic factors. Thus, when studying the response regularity of vegetation to climate change, we should take the appropriate time scale to consider the time-lag effect to better understand their relationship.

4. Discussion

Vegetation growth is influenced by two major driving factors: one is climate-related factors [61,62,63,64] that offer essential environmental conditions to vegetation growth, and the other is disturbances owing to natural factors and human activities, for example, land-use change, agricultural irrigation, forest development, and so on [65,66,67,68,69]. Our study mainly focuses on the natural part—the time-lag effects of climatic factors on natural vegetation during the growth process. The relationships between climatic factors and NDVI show differences on the spatio-temporal scale in the LP [26]. Precipitation often positively contributes to vegetation growth, but it is negatively correlated with vegetation at the early time of the growing season (see April in Figure 3) [31,59,70]. The effect of temperature on vegetation is mainly positive in April and May, and the negative relationship is from June to September. At the early time of the growing season, the temperature increase can promote vegetation growth [71,72]; however, it decreases soil moisture by rising the evaporation in the middle of vegetation growth so that it restricts vegetation growth [73,74,75,76,77]. Figure 5, Figure 6 and Figure 7 illustrate that the impact of precipitation on vegetation growth is greater than temperature [78]. The positive correlation of barren or sparsely vegetated and grasslands with precipitation was higher than that of mixed forests. The Loess Plateau is in the arid and semi-arid climate zone, so vegetation growth relies on the intensity and duration of precipitation, where precipitation is the major driving factor affecting vegetation growth [21,79,80,81]. Xin et al. [21] analyzed the response of vegetation to human activities and climate change on the LP. The study shows temperature increases can accelerate soil surface evapotranspiration to potentially exacerbate soil drying. Therefore, the temperature has an obvious inhibiting effect on vegetation growth. Meanwhile, water conditions have proven to be a driving factor in the growth of vegetation, precipitation plays a crucial role in the spatial distribution of vegetation on the LP.

Many studies have accepted the conclusion that there is a certain time lag in vegetation growth to climatic factors [14,26,36,82,83,84]. The study uses the weighted time-lag method to investigate the relationship between climatic factors and natural vegetation. We found that different climatic factors show different lag effects on diverse vegetation types (Figure 8 and Figure 9). Overall, the effect of climate change on vegetation growth was in the last three months. The study found climatic factors have 3 months’ time-lag at least on vegetation growth since we only used three months as the maximum, as per previous studies [26,32]. However, extending the maximum to more months is expected in the future study since in some cases (see grassland in May in Figure 8 for example), the furthest past month can be the main part contributing to vegetation. The climate has a time-lag effect on vegetation growth and such a time lag exhibits different contribution from different months. Therefore, we suggest that we should consider the different contributions of a climatic factor from more months to the vegetation growth in future research so that we can better reveal the relationships between climate and vegetation.

In addition to the precipitation and temperature discussed in this study, climatic factors such as snowfall and radiation intensity can also affect vegetation growth. How to distinguish the degree of effect of different drivers remains a question for further research. Moreover, social impact, especially policy impact, is also a key to driving vegetation growth. A number of deforestation and various restoration policies in recent years also have crucial influences on vegetation growth to study on LP. Our study provides domain knowledge that can support decision-making in new policies to trade-off the demand and supply of these ecosystem services. Consequently, we need more field monitoring and proving to quantitatively evaluate the interaction between land management practices and climate change, and whether human activities have some effect.

5. Conclusions

The study adopted the method of a weighted time lag to explore the response time of different vegetation types to climatic factors. Moreover, we used linear regression to analyze the impact of monthly total precipitation and the mean temperature on vegetation growth. The result showed that different vegetation types show different responses to temperature and precipitation in different months and the effect of temperature on vegetation was greater than that of precipitation at the early time of the growing season. In general, precipitation was the main driving factor affecting vegetation growth in the LP. The study found that the lag of precipitation and temperature on vegetation growth occupies a certain proportion in different months. The statistics show a greater impact mainly in the last three months. All in all, considering the time-lag effects of three months can well explain vegetation change. Analyzing the response time of vegetation growth to climate change could better help the worker to study and predict the effect of climate change on LP ecosystems in the future. Our study improves our cognition of the complex response of vegetation to climatic factors from a new perspective.