Time-lagged response of vegetation dynamics to climatic and teleconnection factors

Catena 189 (2020) 104474

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Time-lagged response of vegetation dynamics to climatic and teleconnection factors

T

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Jing Zhaoa, Shengzhi Huanga, , Qiang Huanga, Hao Wangb, Guoyong Lengc,d, Wei Fanga a

State Key Laboratory of Eco-Hydraulic in Northwest Arid Region of China, Xi’an University of Technology, Xi’an 710048, China State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China, Institute of Water Resources and Hydropower Research, Beijing 100038, China c Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China d Environmental Change Institute, University of Oxford, Oxford OX1 3QY, UK b

A R T I C LE I N FO

A B S T R A C T

Keywords: Climate changes Vegetation dynamics Time-lag effect Soil moisture Large-scale modes of climate variability

Understanding vegetation dynamics and its response to climate changes is important for revealing the mechanisms of terrestrial ecosystem behaviour, predicting future vegetation growth, and thus guiding environmental management. The Jing River Basin (JRB) and the Beiluo River Basin (BLRB), two typical ecoenvironmentally vulnerable regions on the Loess Plateau in China, were selected as case study regions. Based on longterm Normalized Difference Vegetation Index (NDVI) datasets, the time-lag relationships between NDVI and climatic factors (precipitation/temperature) as well as teleconnection factors (large-scale modes of climate variability and solar activity) were revealed. Additionally, ridge regression models were established to quantitatively explore the response of vegetation dynamics to climate change. Results indicate that: (1) NDVI in autumn showed significantly increasing trend (p < 0.01), whereas that in spring and summer was insignificant; (2) there was a time-lag of more than one month between spring/winter NDVI and precipitation/temperature behaviour, and summer NDVI exhibited no lag with temperature but a one month lag with precipitation; (3) regarding the time-lag effects, precipitation was the driving factor of NDVI variations in spring, whereas sunspots dominated NDVI variations in autumn; (4) when time-lagged teleconnection factors were considered, the explanation of the climate effect on the vegetation dynamics in three seasons all relatively increased by > 95%, which indicates that the prediction accuracy of NDVI was significantly improved; (5) in summer, time-lagged climatic and teleconnection factors explained < 20% of NDVI variations, whereas when soil moisture and base flow were considered, the explanation of NDVI changes in the JRB and BLRB relatively increased by 37.4% and 65.1%, respectively. These findings highlight that considering the time-lag effect of climatic and teleconnection factors has important significance for the accurate monitoring of underlying surface dynamics under changing environment.

1. Introduction As a crucial element of terrestrial ecosystems, vegetation plays an indispensable role in influencing climate systems and regulating carbon cycles, energy exchange between the atmosphere and the land surface via the process of evapotranspiration, photosynthesis and surface albedo (Wen et al., 2017; Potter et al., 2008; Guan et al., 2018). Previous studies have demonstrated that 20% of the Earth’s surface is covered by vegetation, and the vegetation growth is highly sensitive to interannual climate variability (Daham et al., 2018; Xiao et al., 1995; Piao et al., 2006). Therefore, monitoring vegetation dynamics and quantifying the response of vegetation growth to climate has become a hot issue in the

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study of global change, which is of great significance to understand the behaviour mechanisms of vegetation ecosystem (Peng et al., 2012; Yu, 2000; Suzuki et al., 2007). The IPCC Fifth Assessment Report documented that the mean global surface temperature exhibited an increase of 0.85 °C over the period 1880–2010 (IPCC, 2013). As a result, the duration and frequency of precipitation was evidently affected, which led to frequent extreme climate events (Wallace, 2014; Yu et al., 2015; Yang and Yang, 2012; Xu et al., 2010; Huang et al., 2017; Dai et al., 2020; Guo et al., 2020; Han et al., 2019). Recently, the dynamics of vegetation and the coupled relationships between vegetation and climatic factors, especially precipitation and temperature, have been well explored based on the

Corresponding author. E-mail address: [email protected] (S. Huang).

https://doi.org/10.1016/j.catena.2020.104474 Received 9 April 2019; Received in revised form 9 January 2020; Accepted 14 January 2020 0341-8162/ © 2020 Elsevier B.V. All rights reserved.

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J. Zhao, et al.

loessial soil, which has led to the serious ecological fragility of the region (Zheng et al., 2012; Han et al., 2010; Zhao et al., 2020). In addition, a warming and drying trend of the climate conditions on the Loess Plateau has been reported over the past five decades (Wang et al., 2017), which may theoretically limit the vegetation growth due to the reduction of available water and thus aggravate water and soil loss. However, Xie et al. (2016) and Ma et al. (2019) found that both the vegetation cover and gross primary productivity (GPP) showed a significantly increasing trend on the Loess Plateau, and this increasing trend is inextricably linked to global warming which prolongs the growing season in spring and autumn and influences primary production. Therefore, the response of terrestrial ecosystems to climate change on the Loess Plateau exhibits a comparatively complex sensitivity. The Jing River Basin (JRB) and Beiluo River Basin (BLRB) are two typical basins on the Loess Plateau which characterized by extremely fragile ecological environments and sparse vegetation coverage. Therefore, evaluating the vegetation dynamics and quantifying the time-lag responses of vegetation dynamics to climatic and teleconnection factors in these two basins is of great significance for deeply understanding the response of vegetation activities to climate, and thus providing a theoretical basis for predicting future interactions of terrestrial ecosystems and climate change and restoring the ecological environment. In detail, the primary objectives of this study are: (1) to investigate the time-lag effects of climatic and teleconnection factors on vegetation dynamics and then determine the primary climate-driven factors of seasonal vegetation dynamics; (2) to quantitatively analyze the relationship of vegetation dynamics in response to climatic and teleconnection factors.

Normalized Difference Vegetation Index (NDVI) (Zhao et al., 2019; Fang et al., 2019). Fang et al. (2004) indicated that the vegetation coverage has significantly increased in almost all regions in China during 1982–1999, and this was mainly attributed to the increase of temperature and precipitation. For arid and semi-arid region, Xu et al. (2008) and Cao et al. (2014) showed that the inter-annual changes of vegetation were sensitive to precipitation because the lack of precipitation may limit vegetation growth. However, Sun et al. (2015a,b) found a stronger connection between temperature and NDVI than precipitation in northern China. It is well known that vegetation growth tends to respond to climate only when climate variations exceed the tolerance of vegetation (Wang and Alimohammadi, 2012). Therefore, a time-lag effect may exist between vegetation growth and climate. In recent decades, several studies have related NDVI to time-lag effects of climate during the growing season. For example, Ning et al. (2015) revealed a 1-month time-lag between precipitation and vegetation growth on the Northern Loess Plateau. Gu et al. (2018) found that vegetation exhibited various timelag responses to climatic factors in the Red River Basin, which is an important international river in China and Southeast Asia. However, the above studies mainly focus on the impacts of previous single-month precipitation and temperature on vegetation growth, and did not consider the influence of accumulated precipitation and average temperature in previous months, thus failing to fully capture the relevant characteristics between vegetation growth and climatic factors. Due to the diversity of vegetation ecosystem behaviours in different seasons, the time-lag relationship between climatic factors and vegetation growth in the entire growing season is more complicated. However, most previous studies on the time-lag responses based on monthly or mean growing season NDVI data tend to exaggerate or diminish the time-lag effects, which is not conducive to determining the lag. Therefore, more attention should be paid to the study of the timelag effects of vegetation growth in response to both previous single months and cumulative climatic factors at seasonal scales. In addition, there is increasing evidence that large-scale climate oscillations and solar activity play crucial roles in vegetation growth at both global and regional scales (Cho et al., 2014; Gouveia et al., 2008; Li et al., 2016; Jaksic, 2001). Particularly, teleconnection between vegetation dynamics and the Arctic Oscillation (AO), Pacific Decadal Oscillation (PDO), El Niño/Southern Oscillation (ENSO) and sunspots (hereafter teleconnection factors) has become a hot topic over decades (Huang et al., 2015; Guo et al., 2019). Li et al. (2016) demonstrated that the winter AO atmospheric mode had an effect on modulating the vegetation behaviours in spring over the northern high latitudes. Jaksic (2001) found that El Niño exhibited a strong impact on terrestrial ecosystems in western South America. Shi et al. (2018) explored the relationship between PDO index and NDVI over the Tibetan Plateau and found a significant negative correlation between them. Liu et al. (2018) noted that sunspots influenced vegetation activity via climatic factors in China during 1982–2012. However, few studies have directly investigated the statistical time-lag relationships between the teleconnection factors and vegetation dynamics with consideration of seasonal heterogeneity. Moreover, the major driving factors of seasonal vegetation dynamics have not been clearly detected. Therefore, the lagged linkages of the climatic and teleconnection factors on vegetation dynamics were investigated in the present study to explore how the climatic and teleconnection factors influence vegetation behaviour. Moreover, physical mechanisms that lead to the asynchronous linkages between precipitation/ temperature/AO/PDO/ENSO/sunspots and vegetation dynamics have rarely been investigated, and thus the present study also aims to quantify the time-lagged impact of climatic and teleconnection factors on vegetation dynamics. The Loess Plateau has experienced the most serious soil and water erosion in the world due to severe vegetation degeneration and the wide distribution of two highly erodible soil types, loessial soil and dark

2. Study area and data collection 2.1. Study areas The JRB (106.2°E–109.1°E, 34.8°N–37.4°N) and BLRB (107.2°E–109.1°E, 34.8°N–37.4°N), two typical arid and semi-arid regions on the Loess Plateau, were selected as the study areas (Fig. 1). As the second-level tributary of the Yellow River Basin (YRB), the JRB and BLRB cover areas of approximately 4.54 × 104 km2 and 2.69 × 104 km2, respectively. The JRB belongs to the temperate semi-humid continental monsoon climate area with a mean annual precipitation of 545 mm. The BLRB is situated in the temperate semi-arid continental monsoon climate area with a mean annual precipitation of 514 mm. The regional mean temperature in the coldest month ranges from −3°C to −1°C, whereas that in the hottest month varies from 23 °C to 26 °C (Zhao et al., 2015). Overall, the two basins are characterized by abundant precipitation and high air temperature in summer and by rare precipitation and low air temperature in winter (Huang et al., 2014; Ren et al., 2020). Loessial soil and dark loessial soil are highly erosive and widely distributed in the study area (Liu et al., 2018a,b). Due to the seasonal heterogeneity of precipitation on the Loess Plateau, nearly 60% of the annual precipitation is concentrated in the flood season (from June to September). Therefore, the occurrence frequency of water loss and soil erosion is very high, which makes the JRB and BLRB sediment-laden basins with nearly 2.6 × 108 t/year and 0.96 × 108 t/year of sediment transported into the YRB, respectively (Xin et al., 2011). Correspondingly, the ecological environment in the two basins is extremely fragile and the vegetation coverage is sparse. 2.2. Data sources The Normalized Difference Vegetation Index (NDVI) data (1982–2010) from the US National Oceanic and Atmospheric Administration’s (NOAA) Advanced Very High Resolution Radiometer (AVHRR) was used to explore vegetation dynamics and its relationship with climate change (https://nex.nasa.gov/nex/ projects/1349/). In 2

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Fig. 1. Location of the Jing River Basin and Beiluo River Basin.

3. Methodology

the present study, the seasonal maximum NDVI values were chosen to represent the seasonal NDVI time series. Moreover, due to the poor vegetation coverage in winter, only spring (May), summer (August) and autumn (September) seasons were considered in the present study (Chen et al., 2008). In addition, the simulated gridded monthly soil moisture and base flow data during 1982–2010 based on the Variable Infiltration Capacity (VIC) model in China was used in this study. All the gridded NDVI, soil moisture and base flow data were spatially processed into watershed-averaged values for use. Daily temperature (°C) and precipitation (mm) spanning 1982–2010 were collected from 8 meteorological stations in the JRB and BLRB. The meteorological data were provided by the National Climate Center (NCC) of the China Meteorological Administration (CMA). The few missing data, which were < 0.1% of the total data, were interpolated based on the values from neighbouring stations. Additionally, the double-mass curve method was applied to check the consistency of the reconstructed data, and the results indicated that all the daily precipitation and air temperature data adopted in the study were consistent. Based on the results from individual meteorological stations, the regional temperature and precipitation of the JRB and BLRB were calculated by the Thiessen polygon method on the ArcGIS platform (Faisal and Gaffar, 2012). Additionally, Monthly Arctic Oscillation (AO), Pacific Decadal Oscillation (PDO), ENSO and sunspot data from 1982 to 2010 were also employed in this study. Monthly AO and PDO indexes were obtained from the NOAA National Climatic Data Center (http://www.cpc.ncep. noaa.gov/products/precip/CWlink/daily_ao_index/ao_index.html) and the Tokyo Climate Center (http://ds.data.jma.go.jp/tcc/tcc/products/ el niño/decadal/pdo.html), respectively. Trenberth (1997) proposed that the Niño 3.4 region was the most sensitive to the initiation, duration, dissipation and magnitude of ENSO events, and region Niño 3.4 data acquired from the NOAA Earth System Research Laboratory were used in this study as an index of ENSO behaviour (http://www. esrl.noaa.gov/psd/data/correlation/nina34.data) (Trenberth 1997; Philippon et al., 2014; Asoka and Mishra, 2015). Sunspot numbers were used as an index of solar activity, and the dataset collected from the NOAA’s National Geophysical Data Center (NGDC) was chosen (https:// www.esrl.noaa.gov/psd/gcos_ wgsp/Timeseries/SUNSPOT/).

3.1. The modified Mann-Kendall (MMK) trend test The original Mann-Kendall (MK) test, recommended by the World Meteorological Organization, is a popular non-parametric method for analysing trends of hydrometeorological variables such as precipitation, temperature and streamflow (Zhao et al., 2015). However, the MK trend test is based on uncorrelated data, and test results tend to be affected by the persistence of time series. Hamed and Rao (1998) proposed the modified Mann-Kendall method that uses the lag-i autocorrelation to remove the persistence. In this study, the MMK test was applied to detect the trends of NDVI and climatic factors at the 95% significance level. 3.2. Partial correlation analysis Partial correlation is a statistical measure of the direction and strength of a linear relationship between two variables X and Y while eliminating the disturbed impacts from the controlling covariates Z (Xu, 2002). In this study, partial correlation analysis was applied to explore the vegetation-climate interaction (Guarracino et al., 2010; Wu et al., 2015). The partial correlation coefficient is defined as:

RXY ·Z =

RXY − RXZ × RYZ 2 2 (1 − RXY ) × (1 − RYZ )

(1)

where RXY ∙ Z refers to the partial correlation coefficient between X and Y, with Z as the controlled variable, and RXY , RXZ and RYZ refer to the Pearson correlation coefficients between X and Y, X and Z, and Y and Z, respectively. In statistics, the partial correlation coefficient ranges from −1 to 1, with higher absolute values indicating a stronger correlation. The significance of the partial correlation was accessed by the t-test. 3.3. Time-lag effects analysis Climate change will inevitably lead to changes in vegetation only when it accumulates beyond the carrying capacity of the environment or the tolerance of vegetation, indicating that there is a time lag in the 3

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bias (Kumar, 1975). In addition, the multicollinearity problem is mitigated by augmenting the main diagonal elements of the correlation matrix by small positive quantities (Mason and Brown, 1975). Consider the standard model for multiple linear regression:

response of vegetation dynamics to climate. Previous studies showed that the lagging months of NDVI responses to regular climatic factors (precipitation/temperature) were < 3 months (Chen et al., 2014; Ning et al., 2015), whereas the teleconnection factors (AO, PDO, sunspots and ENSO) had a strongly controlling effect on vegetation growth at an annual scale (Detsch et al., 2016; Li et al., 2017a,b). Therefore, in this study, the lagging months of NDVI responses to regular climatic factors and teleconnection factors were chosen as 0–3 months and 0–11 months, respectively. Firstly, the partial correlation coefficient between NDVI and climatic as well as teleconnection factors for each specific lagging month was computed; then, the lagging month corresponding to the maximum partial correlation coefficient was chosen as the lag time for NDVI responses to climatic and teleconnection factors.

Y = Xβ + e

where Y is a n × 1 matrix representing the observed values, X is the corresponding n × p full Rank (matrix of rank p) matrix that contains the values of P predictor variables, β is a p × 1 vector of unknown coefficients, and e is an n × 1 vector of normally distributed random errors. The least squares estimate of β is as follows:

β ̂ = (X ′X )−1X ′Y

The cross-wavelet analysis developed by Hudgins et al. (1993) is an effective method in examining the linkage between two time series in a comprehensive way compared to traditional methods (such as Fourier transform). Specially, combined with cross spectrum analysis and wavelet transform, the cross-wavelet transform can not only detect the correlations between two time series, but also reflect their phase structure and local characteristics in both time and frequency domains (Torrence and Compo, 1998; Hudgins and Huang, 1996). The cross wavelet transform of the two time series x n and yn is expressed as W XY = W X W Y ∗, where * is their complex conjugation. The cross-wavelet power is|W XY |. The complex argument arg (W xy ) can be regarded as the local relative phase between x n and yn in time–frequency field. The theoretical distribution of the cross-wavelet power of the two time series with their background power spectra PkX and PkY is expressed as follows: ⎜

Z (p) Wn X (s ) WnY ∗ (s ) Pk X Pk Y < p⎞ = ν ν σX σY ⎠

(4)

When there is a multicollinearity problem between the independent variables of the regression model, the absolute value of X ′X is approximately zero (|X ′X | ≈ 0 ), which makes the parameter β ̂ very unstable in the multiple linear regression analysis. At this point, if the least square method is continued to be used for estimation, the mean square error ofβ ,̂ which can be represented ̂ ̂ will become unusually large asMSE (β ) = E (β − β )′ (β ̂ − β ) , (Beckstead, 2012). However, if a positive constant matrix kI (k > 0) is added to X ′X matrix, then X ′X + kI is much less likely to be singular than X ′X , which means that X ′X + kI is much less likely to be equal to 0. Ridge regression is based on adding a biasing constant k to the diagonal elements of Eq. (3) as follows:

3.4. The cross-wavelet transform

D⎛ ⎝

(3)

β (̂ k ) = (X ′X + kI )−1X ′Y = (X ′X + kI )−1X ′Xβ ,̂ k ⩾ 0

(5)

where k is the ridge parameter and I is the identity matrix. β ̂(k ) is a linear transformation of the least square estimate. Note that β ̂(k ) is a biased estimate of β , and the mean square error of ̂ β (k ) can be obtained as follows:

⎟

(2)

MSE (β (̂ k )) = E [(β ̂(k ) − β )′ (β ̂(k ) − β )] = (X ′X + kI )−1X ′Xβ

where Z ν (p) is the confidence level related with the probability p for a probability distribution function defined by the square root of the two χ 2 distributions (Grinsted et al., 2004).

(6)

The ridge regression (β (̂ k ) ) has a smaller mean squared error in comparison with the least squares regression, that is, MSE ̂ The suitable value for k can be obtained by cross(β ̂(k ) ) < MSE(β ). validation.

3.5. Ridge regression model

4. Results

The multiple linear regression model has been widely used to evaluate the impacts of climate changes on vegetation dynamics. However, the MLR requires that all the climate variables be independent which is not suitable in the present study (Mekanik et al., 2013). To solve the multicollinearity problem between variables, the ridge regression model (RR) proposed by Hoerl and Kennard (1970) was applied. The purpose of ridge regression is to reduce the high variances of the estimated coefficients at the expense of incurring some

4.1. Trends of NDVI and climate factors The interannual variation of NDVI in the JRB and BLRB were shown in Fig. 2. Generally, the NDVI values during 1982–2010 in the BLRB (the average value is 0.39) were much higher than those in the JRB (the average value was 0.33). There was noticeably increasing trend in

Fig.2. The interannual NDVI variations in the JRB and BLRB from 1982 to 2010. 4

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Table 1 The trends of seasonal NDVI, P and T in the JRB and BLRB. Season

Spring Summer Autumn

JRB

Table 2 The correlation coefficients between NDVI and P/T.

BLRB

Basins

NDVI

P

T

NDVI

P

T

0.8 1.4 4.1**

−1.0 0.3 0.8

2.6 ** 3.6** 2.2*

0.1 1.2 3.3**

−0.8 −0.7 0.9

3.0** 2.1* 0.9

JRB

Note: P and T denote precipitation and temperature, respectively; “*” and “**” represent significant at 95% and 99% confidence level, respectively.

annual NDVI in the JRB and BLRB from 1982 to 2010. As illustrated in Fig. 2, the NDVI series was divided into two distinct stages. During 1982–1999, NDVI exhibited an overall increasing trend with fluctuation, and the increasing rate in the JRB and BLRB was 0.7 × 10–3/yr and 0.6 × 10-3/yr, respectively. However, during 2000–2010, NDVI in the two basins increased sharply with the rate of 3.1 × 10-3/yr and 3.5 × 10-3/yr, respectively, which was approximately 5 times the rate in 1982–1999. The NDVI variations indicated that vegetation coverage of the JRB and BLRB experienced a significant amelioration from 1982 to 2010, especially after the large-scale implementation of the “Grain For Green” (GFG) program on the Loess Plateau in 1999 (Li et al., 2017a,b; Zhao et al., 2017). This finding was consistent with that of Yan et al. (2018) and Sun et al. (2015a,b). The MMK trend test was applied to obtain the trend of NDVI, precipitation and temperature, and the results were exhibited in Table 1. At the seasonal scale, NDVI exhibited a statistically significant increasing trend in autumn (p < 0.01). In spring and summer, NDVI had an insignificant positive trend (p > 0.05). This conveyed that the increase of annual NDVI in the JRB and BLRB was generally attributed to the increase of autumn NDVI. Precipitation in the JRB and BLRB exhibited a non-significant changing trend in three seasons (p > 0.05), while temperature in the two basins showed a significantly increasing trend at the 95% confidence level in the three seasons except for autumn in the BLRB. Overall, the JRB has experienced a hotter and drier spring climate, and the BLRB has a hotter and drier spring and summer climates during 1982–2010.

BLRB

Period (month)

0 1 2 3 0–1 0–2 0–3 1–2 1–3 2–3 0 1 2 3 0–1 0–2 0–3 1–2 1–3 2–3

NDVI-P

NDVI-T

Spring

Summer

Autumn

Spring

Summer

Autumn

0.17 0.46* 0.17 0.28 0.37* 0.44* 0.43* 0.49** 0.47* 0.18 0.18 0.34 0.33 0.09 0.32 0.42* 0.38* 0.47* 0.44* 0.29

0.14 0.29 −0.10 −0.14 0.29 0.28 0.20 0.20 0.10 −0.16 −0.07 0.26 −0.24 −0.14 0.11 0.00 −0.05 0.03 −0.02 −0.23

0.27 0.37* 0.14 0.04 0.45* 0.42* 0.39* 0.35 0.32 0.05 −0.01 0.02 0.01 −0.11 0.00 0.02 −0.03 0.02 −0.04 −0.10

−0.04 0.19 0.30 −0.03 0.06 0.27 0.17 0.38* 0.24 0.13 0.11 0.33 0.31 0.18 0.30 0.42* 0.37 0.44* 0.37 0.23

−0.15 −0.04 0.04 −0.12 −0.10 0.01 0.02 0.08 0.04 −0.06 −0.17 0.12 0.08 −0.15 −0.02 0.05 −0.01 0.16 0.06 −0.11

0.25 0.18 0.21 0.35 0.33 0.32 0.44* 0.24 0.40* 0.35 −0.06 −0.02 0.13 0.07 −0.05 0.00 0.02 0.04 0.07 0.10

Note: 0 represent climatic variables in the current month; 1, 2, and 3 represent climatic variables in the previous 1, 2 and 3 month, respectively; The correlation coefficients were calculated between NDVI and P/T; 0–1, 0–2, 0–3, 1–2, 1–3 and 2–3 represent climatic variables over the previous 0–1, 0–2, 0–3, 1–2, 1–3 and 2–3 months, respectively; The correlation coefficients were calculated between NDVI and the cumulative P/T; “*” and “**” represent significant at 95% and 99% confidence level, respectively.

partial correlation coefficients between the NDVI and precipitation/ temperature for particular temporal scales were calculated (Table 2). Generally, NDVI was more correlated with precipitation than that with temperature in the JRB and BLRB. This might be attributed to the arid and semi-arid climate conditions of the Loess Plateau, which resulted in the influence of precipitation on vegetation was greater than that of temperature on vegetation. Moreover, correlation coefficients of individual seasons showed that spring NDVI exhibited the strongest positive relationship with precipitation/temperature. This finding suggested that spring NDVI increased with increasing amounts of precipitation and rising temperature. In autumn, NDVI had a significant positive correlation with precipitation/temperature in the JRB, while a weak correlation in the BLRB. However, summer NDVI exhibited weak correlation with precipitation and temperature, especially with temperature. Taking the gradients corresponding to the maximum coefficient as the lag time, Table 2 showed that the time-lag effects between NDVI and precipitation/temperature varied across seasons. In spring, NDVI

4.2. Time-lagged response of NDVI to precipitation/temperature variations Changes in vegetation coverage and climate conditions are inextricably linked in the arid and semi-arid regions. According to Fig. 3, NDVI and precipitation/temperature variations showed similar temporal variations before June, indicating that NDVI was sensitive to precipitation/temperature in the first half of the year. However, in the latter half of the year, NDVI response to precipitation/temperature showed a certain time lag. To further explore the time-lag relationship between NDVI and precipitation/temperature in the study areas, the

Fig. 3. Monthly NDVI, precipitation and temperature in the JRB and BLRB during 1982–2010. 5

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effects on the vegetation growth exceeded 6 months in the JRB but < 6 months in the BLRB. Positive correlations between PDO and NDVI were found in almost all lag periods, which implies that the PDO had a certain role in promoting the vegetation growth especially in autumn when the strongest correlations occurred. In addition, the strength of the time-lagged relationship between autumn NDVI and PDO was weaker than that of the correlations with no time lag, which implies that PDO variation in the same season may be more important to vegetation growth. Unlike the positive correlations between NDVI and PDO, sunspots had negative effects on NDVI. Moreover, the most significant relationship between sunspots and NDVI appeared in autumn for the two- and three-month lag that existed in the JRB and BLRB, respectively. Summer NDVI had the greatest correlation with Niño3.4 in the same season, and no lag effects were detected, whereas spring NDVI had apparent lag effects with Niño3.4 for 2 months and 11 months in the JRB and BLRB, respectively. Similarly, significantlylagged correlations were found between autumn NDVI and Niño3.4, with a 10-month delay. Generally, the associations between PDO/sunspots and vegetation growth were stronger than those between AO/ Niño3.4 with vegetation growth in the study areas. Based on the above, the optimum lag time between vegetation cover and teleconnection factors was obtained and is exhibited in Table 3. In spring, AO was the dominant factor compared with the other three teleconnection factors in the JRB and BLRB. PDO and Niño3.4 showed the strongest connection with summer NDVI in the JRB, whereas AO exhibited the most significant influence on summer NDVI in the BLRB. The leading factors of autumn vegetation variations in the JRB are PDO and sunspots, and sunspots alone for the BLRB. Combined with the teleconnection factors, a deep understanding of the climatic system’s impact on seasonal vegetation growth has been obtained.

responded to precipitation/temperature in the previous 1–2 months, demonstrating that the time-lag of NDVI to precipitation and temperature was 1–2 months in both the JRB and the BLRB. And spring NDVI was more correlated with precipitation (R = 0.49, p < 0.01 in the JRB; R = 0.47, p < 0.05 in the BLRB) than with temperature (R = 0.38, p < 0.05 in the JRB; R = 0.44, p < 0.05 in the BLRB). The vegetation cover in autumn in the JRB exhibited the strongest correlation with precipitation and temperature in the previous 0–1 months and 0–3 months, respectively. The NDVI in the BLRB showed a certain time-lag effect related to precipitation and temperature in autumn, with the lag time exceeding one month. Similar with spring NDVI that was alternatively regulated by precipitation and temperature, autumn NDVI in the JRB was more correlated with precipitation (R = 0.45, p < 0.05) than with temperature (R = 0.44, p < 0.05). However, autumn NDVI in the BLRB was more correlated with temperature (R = 0.13, p > 0.05) than with precipitation (R = -0.11, p > 0.05). Different with autumn NDVI that showed significant correlations with precipitation and temperature in the JRB, autumn NDVI in the BLRB displayed an insignificant correlation in the BLRB. As indicated by previous studies (Zhou et al., 2001; Wen et al., 2018; Zhang et al., 2013), rising spring and autumn temperature would elongate growing season, benefit carbon assimilation, and increase biomass growth and vegetation production. And these effects were further confirmed by the positive correlation between NDVI and spring temperature as well as autumn temperature. The NDVI exhibited a 1-month time lag to precipitation in summer, indicating that the vegetation growth in the study regions mainly depended on the precipitation in the previous month. However, the highest negative correlation between NDVI and temperature occurred with no time-lag effects in summer, that is, vegetation growth was obviously inhibited by the temperature in the same month in summer. In addition, summer NDVI was more correlated with precipitation (R = 0.29, p > 0.05 in the JRB; R = 0.26, p > 0.05 in the BLRB) than with temperature (R = -0.15, p > 0.05 in the JRB; R = 0.-0.17, p > 0.05 in the BLRB). Different with summer precipitation that did not show significant trend in the study areas, summer temperature showed a significant increasing trend. Therefore, high temperature in summer would lead to the acceleration of evaporation, thus prohibiting vegetation growth. These effects were confirmed by the negative correlation between NDVI and summer temperature.

5. Discussion 5.1. Possible physical mechanisms for the correlation between NDVI and P/ T NDVI on the Loess Plateau increased significantly during 1982 to 2010, especially in autumn. Similar results have been found by Zhao et al. (2017) and Li et al. (2017a,b). As demonstrated by previous studies, vegetation growth is closely related to changes of precipitation and temperature (Roerink et al., 2003; Chu et al., 2019; Piao et al., 2006). To further reveal the relationship between NDVI and precipitation/temperature, the cross-wavelet analysis was adopted. For the sake of brevity, only the results of the JRB were presented in Fig. 5. The color bar meant the energy density and the 95% confidence level against red noise is shown as a thick contour. The arrow represents the phase relationship between factor 1 (like precipitation/temperature) and factor 2 (like NDVI). Particularly, the arrow “→” denotes that the variations of factor 2 and 1 are synchronous; “↓” indicates that the variation of factor 2 lags behind that of factor 1 with one fourth of resonant period; “←” implies that the variation of factor 2 lags behind that of factor 1 with a half resonant period; and “↑” shows that the variation of factor 2 lags behind that of factor 1 with three fourths of resonant period (Shao, 2013). It can obviously be observed from Fig. 5 (A) that the interaction between NDVI and precipitation occurred in the period of 9–14 months and 1–3 months during 1982–2010. In the period of 9–14 months, NDVI and precipitation had significantly positive phase relationships. However, in the period of 1–3 months, the positive and negative phases were staggered, indicating that precipitation had both positive and negative impacts on vegetation in the period of 1–3 months, which was consistent with the results in Table 2. Fig. 5 (B) indicated that the strong interaction between NDVI and temperature also took place in the period of 9–14 months and significantly positive relationship existed between NDVI and temperature during 1982–2010. Moreover, it has been documented that the response of vegetation

4.3. Lag-linkage between vegetation growth and teleconnection factors The large-scale modes of climate variability and solar activity (AO, PDO, sunspots and ENSO) which highly correlated with precipitation and temperature in the study area could indirectly affect vegetation cover. Revealing the correlations between NDVI and teleconnection factors helps to further explore the teleconnection effect on the vegetation cover in the JRB and BLRB. The partial correlation coefficients between NDVI and teleconnection factors in the same month were presented in Fig. 4. The correlation between AO and NDVI was weak and negative in all the three seasons. Non-significant positive correlations were found between NDVI and PDO in spring and summer, whereas autumn NDVI exhibited a significantly positive relationship with PDO at the 99% confidence level. Similarly, sunspots showed remarkable correlation with NDVI in autumn compared with spring and summer. Correlation coefficients of NDVI response to ENSO were weak in the study areas, and the strongest correlation occurred in summer. Given time delays between variations in AO/PDO/ENSO/sunspots and the consequent effects on vegetation growth, time-lag effects might occur. Therefore, the lag-correlations between the 4 teleconnection factors and NDVI were detected in three seasons (Fig. 4). Preliminary results indicated that different teleconnection factors had varied timelag effects on vegetation growth in different seasons. At seasonal scales, NDVI exhibited fluctuating correlations with AO for the selected lag time scales, and the correlation values illustrated that the best time-lag 6

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Fig.4. Lagged Correlation coefficients between seasonal NDVI and AO/PDO/ ENSO/Sunspots. Note: 0 represent climatic variables in the current month, and 1, 2, …,11 represent climatic variables in the previous 1, 2,…, 11 month, respectively.

In this study, we also confirmed that vegetation growth responded to precipitation/temperature varied seasonally, which was in agreement with the results revealed by Mohammat et al. (2013) and Piao et al. (2006). In spring and autumn, the temperature rise leads to the increase of soil temperature and accelerates the rate of biochemical processes of plant, thus changing the phenological phase and prolonging the growing season of vegetation, and then increasing biomass production and vegetation coverage (Damberg and AghaKouchak, 2014; Mulder et al., 2017; Slot et al., 2014). Moreover, the increase of autumn precipitation in the study area indicates that the water supply is increased, which is more conducive to photosynthesis and thus affects the biomass production. In summer, the climate is characterized by high temperature and abundant rainfall due to maritime air advection and prevailing easterly and southeasterly winds. The high temperature may rise beyond the optimum temperature for photosynthesis, which results in the enhancement of transpiration and the decrease of soil moisture and thus inhibits vegetation growth (Yan et al., 2013). In addition, higher temperature in summer leads to increased respiration in plants, which in turn affects net primary production by depleting the organic matter (Lu et al., 2018). Consequently, the summer

growth to climatic factors has temporal lags due to the characteristics of climatic and soil conditions in the arid and semi-arid region. Therefore, vegetation growth may not be primarily driven by current climatic conditions, and earlier climatic conditions may have the greatest impact on vegetation growth (Wu et al., 2015; Wen et al., 2018; Ning et al., 2015). The lag effects between NDVI and precipitation/temperature were further confirmed by the sloping arrow in Fig. 5. As shown in Table 2, almost all the time-lag effects of precipitation/temperature were stronger than those with no lag, which indicates the significance of antecedent precipitation and temperature for vegetation growth. Additionally, the results also demonstrated that precipitation was the driving factor for NDVI alteration on the Loess Plateau, which coincides well with previous research in the arid and semi-arid regions (Cao et al., 2014; Du et al., 2016; Zhao et al., 2017). The time lag response of vegetation growth to precipitation was because soil was the direct water source for vegetation growth and the water content of soil directly affected the growth and development of vegetation. Precipitation can replenish soil water, which is absorbed by plant through roots and then transported to leaves for photosynthesis, thus increasing chlorophyll and making it reflected by vegetation index (NDVI).

Table 3 Time lag of NDVI response to climatic and teleconnection factors. Basins

JRB

BLRB

Influencing factors

P T AO PDO sunspots Niño3.4 P T AO PDO sunspots Niño3.4

Spring

Summer

Autumn

Lag time

Correlation coefficients

Lag time

Correlation coefficients

Lag time

Correlation coefficients

1–2 1–2 11 10 10 2 1–2 1–2 2 1 10 11

0.49** 0.38* −0.33 0.18 −0.21 −0.22 0.47* 0.44* 0.42* −0.12 −0.25 −0.12

1 0 11 3 11 0 1 0 2 2 11 0

0.29 −0.15 0.25 0.28 −0.24 −0.28 0.26 −0.17 −0.44* 0.20 −0.25 −0.16

0–1 0–3 7 0 2 10 3 2 6 0 3 10

0.45* 0.44* −0.24 0.49** −0.49** 0.33 −0.11 0.13 0.33 0.33 −0.50** 0.28

Note: “*” and “**” represent significant at 95% and 99% confidence level, respectively. 7

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Fig. 5. The cross wavelet transforms between monthly NDVI series and climatic factors in the JRB: (A) NDVI and precipitation; (B) NDVI and temperature.

monthly ENSO and NDVI in the JRB. A significant positive relation was found between ENSO and NDVI in the JRB with a 9–14 months’ resonant period during 1982–2010. Meanwhile, the arrow in Fig. 6 had a larger tilt Angle than that in Fig. 5, indicating that the lag time of NDVI's response to PDO and ENSO was longer than to precipitation and temperature. This finding suggested that PDO and ENSO events may have played important roles in the variation of vegetation in the JRB. In addition, Fig. 7 displays the cross wavelet transform between the PDO/ENSO events and precipitation/temperature in the JRB. PDO and ENSO events have exhibited statistically positive correlations with precipitation and temperature with a 9–14 months’ resonant period in 1982–2010. Therefore, by influencing regional climatic conditions, the large-scale modes of climate variability affected vegetation growth on the Loess Plateau with time lags and these time lags are longer than precipitation and temperature (Li et al., 2017a,b; Rishma and Katpatal, 2016). The large-scale modes of climate variability change atmospheric circulation via rain belt movement and water vapour transport and thus affect regional hydrological factors. For example, ENSO can redistribute heat and water vapour by changing large-scale air flow on the surface and small-scale ocean circulation, like Hadley and Walker circulation, which thus significantly affects annual and monthly temperature and precipitation (Yeh et al., 2014). Being different from ENSO events, PDO

temperature exhibited a negative relationship with NDVI. The JRB and BLRB are located in arid and semi-arid region, and approximately twothirds of the annual precipitation is concentrated in summer, which promotes vegetation growth. Our finding is in accordance with that of Sun et al. (2015a,b). The partial correlation coefficient between NDVI and precipitation in summer was significantly lower than that in spring and autumn, mainly because the vegetation growth enters a stable state in summer, and the vegetation growth is less dependent on precipitation. However, sufficient precipitation in summer enabled irrigation and precipitation to meet the needs of vegetation growth, and the impact of precipitation on vegetation growth was thus weakened.

5.2. Possible physical mechanisms for the correlation between NDVI and the large-scale modes of climate variability In order to further explore the influence mechanism of the largescale modes of climate variability and solar activity (AO, PDO, sunspots and ENSO) on vegetation growth, the cross-wavelet analysis was utilized. The correlations between the PDO/ENSO and NDVI were exhibited in Fig. 6 (only the results of the JRB were presented). It can be seen from Fig. 6 (A) that monthly NDVI and PDO were positively correlated with a 9–14 months’ resonant period during 1982–2010 in the JRB. Similarly, Fig. 6 (B) exhibits the cross wavelet transform between

Fig. 6. The cross wavelet transforms between monthly NDVI series and large-scale modes of climate variability in the JRB: (A) NDVI and PDO; (B) NDVI and ENSO. 8

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Fig. 7. The cross wavelet transforms between large-scale modes of climate variability and precipitation/temperature in the JRB: (A) PDO and precipitation; (B) PDO and temperature; (C) ENSO and precipitation; (D) ENSO and temperature.

is the sea surface temperature (SST) of the Pacific Ocean fluctuates over 10-year period (Mantua and Hare, 2002). Only two full PDO cycles occurred in the past century: cool PDO phase during 1890–1924 and 1947–1976, and warm PDO phase during 1925–1946 and 1977–1990 s (Limsakul and Singhruck, 2016). PDO and precipitation/temperature correlated with each other during the 1982–2010 (Fig. 7), implying PDO warm phase was profoundly associated with the interannual/ decadal change pattern of regional climate variables, such as temperature and precipitation, and thus significantly affects the interannual and seasonal changes of vegetation growth by its control on regional climate (Zhang et al., 2017). Solar activity such as sunspot is known to have 11-year periodicity and can affect the solar radiation intensity (Balasubramaniam and Henry, 2016; Zhu and Jia, 2018). The seasonal solar radiation directly supplies the energy needed for water surface evaporation, and the warm and wet air flow formed by water evaporation will change the moisture content in the atmosphere and thus impact the distribution characteristics of precipitation, which then affects the vegetation in different seasons (Dong et al., 2017). In addition, it has been reported that solar radiation enables photosynthesis for carbon fixation, which thus provides the essential conditions for the carbon sequestration (Wu et al., 2015). Moreover, solar activity has strong influences on the largescale modes of climate variability, and the significant correlation was mainly concentrated in 0.25a-11a periodicity (Dong et al., 2017). Therefore, the solar energy will be transmitted to precipitation and temperature via the large-scale climatic phenomena. For example, ENSO can act as a medium and transmit the energy of sunspot movement to the regional climate via the “west Pacific subtropical high-east Asian circulation-water vapour movement” (Zhou et al., 2013). Consequently, solar activity displays indirect influences on vegetation dynamics via its impact on precipitation and temperature (Velasco and Mendoza, 2008). In general, the large-scale atmospheric circulation affects seasonal vegetation dynamics via regulating regional climate. Solar activity energy can transfer to large-scale atmospheric circulation and then to regional climate, which will indirectly affect seasonal vegetation dynamics. However, all the correlations between seasonal vegetation dynamics and large-scale atmospheric circulation as well as solar activity show a certain lag time that is longer than that between seasonal

vegetation dynamics and temperature/precipitation due to the energy transfer process.

5.3. Explanation of vegetation growth response to climate and teleconnection change Based on the time-lag relationships between NDVI and the P/T/AO/ PDO/ENSO/sunspot series, the seasonal ridge regression model (RR) was developed for three scenarios: 1) ignoring the time-lag effects of climate on vegetation growth; 2) considering P/T time-lag effects; 3) considering P/T/AO/PDO/ENSO/sunspot time-lag effects. As illustrated in Fig. 8, the ridge regression model performance, in terms of the determination coefficient (R2) values, varied for different scenarios and different basins across seasons. Ignoring the time-lag effects of the JRB, the explanations of precipitation and temperature to vegetation growth were only 6.1%, 6.0% and 2.9% in spring, summer and autumn, respectively. However, under the same conditions, the climatic effects on vegetation growth in the BLRB were only 1.4%, 1.4% and 0.2% in spring, summer and autumn, respectively. When the time-lag effects of precipitation and temperature were considered, the explanation of vegetation growth by precipitation and temperature in the JRB was obviously increased to 20.6%, 10.5% and 23.3% in spring, summer and autumn, respectively. Moreover, the p-value was < 0.05 in spring and < 0.01 in autumn, which indicates that the ridge regression model had a better performance than that without considering the time-lag effects. For the BLRB, 24% of the spring vegetation growth was explained by time-lagged precipitation and temperature, whereas the weak connection between NDVI and climatic factors was characterized by low determination coefficient (R2) values in summer and autumn with 0.03 and 0.02, respectively. Then, the ridge regression model was established based on the time-lag effects of the large-scale atmospheric circulation patterns (AO/PDO/ENSO) and sunspot events on vegetation cover, in which an evident improvement of the determination coefficients was discovered. It can be discerned through Fig. 8 that with respect to the time-lag effects, multiple climatic indices can exactly depict the vegetation growth in spring and autumn, with an average explanation of 47% and that the models exhibited the best performance compared with the other two scenarios. Consequently, a distinct regularity was found that the more climatic and teleconnection factors 9

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Fig. 8. The determination coefficient (R2) and significance of the multiple linear regression model between NDVI and climatic factors for the period 1982–2010. The blue bars, green bars and yellow bars represent the results which ignore the time-lag effects, only considered the P/T time-lag effects and considered the P/T/AO/ PDO/Sunspots/ Niño3.4 time-lag effects, respectively. “*” and “**” represent significant at the 95% and 99% confidence level, respectively.

time-lag effects were diverse across the seasons. Spring NDVI showed the strongest correlation with the previous 1–2 month’s accumulated precipitation. The previous 1-month’s precipitation and the previous 2month’s AO were the major factors that influenced the summer vegetation growth in the JRB and BLRB, respectively. The PDO in the same period and sunspots in the previous 2 months showed the most evident impact on autumn vegetation growth in the JRB, whereas the previous 3-month’s sunspot levels were the key factors for autumn vegetation growth in the BLRB. The results obtained by the multiple linear regression models revealed that precipitation and temperature explained < 10% of the vegetation growth without containing the time-lag effects. When the lag effects of precipitation and temperature were included, the interpretations for all three seasons obviously increased. Moreover, when the time-lagged teleconnection factors were considered, the explanation relatively increased by above 95% in the three seasons, especially in summer and autumn in the BLRB, which relatively improved > 200%. Therefore, the time-lag effects of multiple climatic factors should not be neglected in the study of vegetation growth responses to climate change. Finally, this study provides a new thought in investigating vegetation growth at seasonal scales under changing environment. The results help to reveal the interaction between vegetation dynamics and climate change.

were included in the model, the better the simulation performance obtained. This finding was congruent with that of Wu et al. (2015) and Jong et al. (2013). Moreover, a prominent temporal heterogeneity existed in the study areas: a better explanation of climate effects on vegetation was detected in spring and autumn. However, for the summer NDVI prediction, a weak connection was detected between climate changes and vegetation dynamics, indicating that climate condition was not the only limitation affecting summer vegetation growth in the Loess Plateau. Three causes may explain the weak connection. Firstly, precipitation had been well preserved in the soil in the months leading up to summer, which resulted in high soil moisture in the summer in the study areas that could counteract the effect of climate change on vegetation growth. However, Xu et al. (2014) proposed that in the quaternary aquifer region, the groundwater level has a direct influence on vegetation growth in the YRB. Evidently, the base flow is also an indispensable factor that affects vegetation growth in summer. On the basis of the previous analysis of vegetation growth response to lagged P/T/AO/PDO/ENSO/sunspots, base flow and soil moisture simulated by the VIC model were considered in the ridge regression model to further characterize the effects of climate changes on summer vegetation growth. Compared with the results in Fig. 8, we found that the explanations of summer vegetation growth in the JRB and BLRB increased to 28.1% and 20.3%, respectively. Therefore, the interpretation of summer vegetation growth by climate changes was improved in the JRB and BLRB when soil moisture and base flow were taken into account. In addition, frequent rainstorms were mostly concentrated in summer, which could cause serious soil erosion in Loess Plateau regions characterized by loose soil. Therefore, the effects of climate on vegetation growth were weakened during summer.

Acknowledgements This research was jointly funded by the National Key Research and Development Program of China (grant number 2017YFC0405900), the National Natural Science Foundation of China (grant number 51709221), the Planning Project of Science and Technology of Water Resources of Shaanxi (grant numbers 2015slkj-27 and 2017slkj-19), the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (China Institute of Water Resources and Hydropower Research) (grant number IWHR-SKLKF201803).

6. Conclusions Investigation of time-lag effects of climate on vegetation response is of great significance for better understanding the vulnerability of ecological environments to climate change, especially on the Loess Plateau with its very fragile ecological environment. Generally, climate conditions in the study areas were characterized by an insignificantly drier and significantly warmer trend during 1982 to 2010. Accordingly, the vegetation coverage exhibited an obvious upward tendency due to the extension of the growing season and the enhancement of photosynthesis caused by rising temperature. In this study, the partial correlation method was applied to explore the time-lag relationship between NDVI and climatic and teleconnection factors, and the driving factors of vegetation variations were thus determined. The dominant factors of vegetation growth considering the

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