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Journal of Resources and Ecology >

2021 , Vol. 12 >Issue 5: 609 - 619

DOI: https://doi.org/10.5814/j.issn.1674-764x.2021.05.004

Human Activities and Ecological Security

Spatio-temporal Pattern of Surface Albedo in Beijing and Its Driving Factors based on Geographical Detectors

  • LIU Qinqin , 1, 2 ,
  • TIAN Yichen 2 ,
  • YIN Kai 2 ,
  • ZHANG Feifei 2 ,
  • YUAN Chao 2 ,
  • YANG Guang , 2, *
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  • 1. University of Chinese Academy of Sciences, Beijing 100049, China
  • 2. Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100101, China
*YANG Guang, E-mail:

LIU Qinqin, E-mail:

Received date: 2021-01-08

  Accepted date: 2021-04-02

  Online published: 2021-11-22

Supported by

The Major Project of High Resolution Earth Observation System(06-Y30F04-9001-2022)

The National Natural Science Foundation of China(41471423)

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Abstract

Surface albedo directly affects the radiation balance and surface heat budget, and is a crucial variable in local and global climate research. In this study, the spatial and temporal distribution of the surface albedo is analysed for Beijing in 2015, and the corresponding individual and interactive driving forces of different explanatory factors are quantitatively assessed based on geographical detectors. The results show that surface albedo is high in the southeast and low in the northwest of Beijing, with the greatest change occurring in winter and the smallest change occurring in spring. The minimum and maximum annual surface albedo values occurred in autumn and winter, respectively, and showed significant spatial and temporal heterogeneity. LULC, NDVI, elevation, slope, temperature, and precipitation each had a significant influence on the spatial pattern of albedo, yielding explanatory power values of 0.537, 0.625, 0.512, 0.531, 0.515 and 0.190, respectively. Some explanatory factors have significant differences in influencing the spatial distribution of albedo, and there is significant interaction between them which shows the bivariate enhancement result. Among them, the interaction between LULC and NDVI was the strongest, with a q-statistic of 0.710, while the interaction between temperature and precipitation was the weakest, with a q-statistic of 0.531. The results of this study provide a scientific basis for understanding the spatial and temporal distribution characteristics of surface albedo in Beijing and the physical processes of energy modules in regional climate and land surface models.

Key words： albedo; spatio-temporal distribution; explanatory factors; geographical detectors

Cite this article

LIU Qinqin , TIAN Yichen , YIN Kai , ZHANG Feifei , YUAN Chao , YANG Guang . Spatio-temporal Pattern of Surface Albedo in Beijing and Its Driving Factors based on Geographical Detectors[J]. Journal of Resources and Ecology, 2021 , 12(5) : 609 -619 . DOI: 10.5814/j.issn.1674-764x.2021.05.004

1 Introduction

Surface albedo is a non-dimensional parameter defined as a ratio of surface-reflected radiation to incident radiation (Ranson et al., 1991; Russell et al., 1997). It is one of the most critical parameters in surface energy budget studies, and its temporal and spatial changes are closely related to global climate change and regional weather systems (Dickinson, 1983; Richardson et al., 2013). Therefore, understanding the spatial and temporal distribution of surface albedo and its influencing factors can provide not only a powerful reference for simulating environmental climate change but also a theoretical basis for the parameterization of surface albedo models.
Surface albedo is usually determined by the land cover type and, as such, changes in land use can have strong influences on surface albedo (Bounoua et al., 2002; Liu et al., 2015; Liu et al., 2019). It is also affected by many factors, including solar elevation angle, surface roughness, normalized difference vegetation index (NDVI), meteorological factors, soil moisture, etc. (Govaerts et al., 2008; Loarie et al., 2011; Xiao et al., 2011; He et al., 2014). In previous studies, the linear regression method was usually used to analyze the correlations between surface albedo and driving factors (Yang et al., 2020). However, because of the complex process of the surface albedo responses to driving factors, the inflexible statistical linear models may not be able to accurately describe the internal relationships between the two variables. Spatial heterogeneity is a common feature of ecological geographical phenomena. Studies have shown that the spatio-temporal distribution of surface albedo display distinct geographical differences (Zhang et al., 2010; Nikolaos and Nektarios, 2015). The traditional linear analysis method usually only unifies the relationships between independent variables and dependent variables, and lacks the consideration of spatial heterogeneity of the variables. Geographical detectors are a set of statistical methods which can detect spatial stratified heterogeneity (SSH) and reveal the driving forces behind them. The central premise of these methods is the assumption that if the sum of the variances of the subregions is less than the total regional variances, then spatial differentiation exists. If an independent variable has an important influence on a dependent variable, the spatial distributions of the independent and dependent variables should be similar (Wang et al., 2010; Wang et al., 2016).
Geographical detectors were first used in health studies to determine the environmental factors associated with neural tube defects in new-borns and earthquake deaths (Liao et al., 2010; Hu et al., 2011; Wang et al., 2012). This approach can be used to measure and characterise the spatial heterogeneity of a target variable (Golkar et al., 2018; Malahlela et al., 2019), assess the degree of coupling between two variables, and investigate the interaction between two explanatory variables forced by a response variable (Yuan et al., 2019). Studies have applied geographical detectors to identify the driving factors of PM2.5 pollution (Lou et al., 2016; Yang et al., 2018; Ding et al., 2019), the driving force analysis of the spatial and temporal distribution of urban expansion (Wang et al., 2019; Yan et al. 2020), the impact of new transportation modes on population distribution (Wang et al., 2018), and many other relationships. Factor detector and interaction detector were used to detect that cumulative temperature, soil salinity and their interactions were the key factors affecting winter wheat yield (Chu et al., 2019). The interaction detector has shown that the interaction between economic activities and the urban environment has the greatest influence on the temperature of the Yangtze River Delta region (Zhou et al., 2020). The stratification heterogeneity of traffic accidents in Shenzhen was found by using geographical detector, and the results of factor detector showed that the influencing factors of fatalities and injuries are different (Zhang et al., 2020).
Since 2010, geographical detectors have been increasingly used in studies of natural, humanistic, economic and other factors with spatial heterogeneity. However, the detection of factors affecting the distribution of surface albedo using geographical detectors remains limited. To address this gap, this study sought to analyse the spatio-temporal distribution of surface albedo in Beijing in 2015 using the Global Land Surface Satellite (GLASS) albedo products. Based on the geographical detectors approach, the following explanatory factors of surface albedo were detected: land use and land cover (LULC), NDVI, elevation, slope, average temperature, and cumulative precipitation. In this study, the quantitative relationship between surface albedo changes and their driving factors in Beijing were studied by using geographical detector. The contributions of different driving factors to surface albedo change were compared, and the correlations of driving factors in influencing surface albedo change were studied. The results provide not only a new method for studying the driving factors of surface albedo variability but also a reference for improving regional-scale climate and land-surface process simulations.

2 Materials and methods

2.1 Study area

Beijing, the capital of China, is the national centre of politics, culture, and scientific and technological innovation, is located in the north of China and the north of the North China Plain, at 39°54'20"N and 116°25'29"E (Fig. 1). The total area of Beijing is 16412 km2, with a built-up area of 1485 km2. The terrain of the city is high in the northwest and low in the southeast with the mountainous areas accounting for 62% of the total area and the remaining 38% consisting of flatter plains. The average elevation is 43.5 m, while the elevation of the plain is 20-60 m, and the elevation of the mountain is generally 1000-1500 m. Beijing’s climate is a typical north temperate semi-humid continental monsoon climate, with a high temperature and rainy in summer, cold and dry in winter, and a short spring and autumn. The average annual sunshine hours in Beijing are between 2000 and 2800 hours and the annual average solar radiation is 112-136 kcal cm‒2. Therefore, Beijing is taken as the research area for the exploration of spatial heterogeneity and driving factors of surface albedo in this study.
Fig. 1 Study area: Beijing, China.

2.2 Datasets

2.2.1 Surface albedo
Surface albedo data were obtained in the form of the Global Land Surface Satellite (GLASS) products from the National Earth System Science Data Sharing Infrastructure, National Science & Technology Infrastructure of China (http://www.geodata.cn) (Liu et al., 2013a; Liu et al., 2013b; Qu et al., 2014). These data have a 1-km spatial resolution and an eight-day temporal resolution. Compared to the Moderate Resolution Imaging Spectroradiometer (MODIS) MCD43 product, GLASS albedo products overcome the missing values resulting from snow-covered areas (Schaaf et al., 2002). By including black-sky albedo and white-sky albedo data, the GLASS albedo product has been widely favoured, and its level of precision can meet the needs of most surface albedo spatio-temporal analyses.
Data for 46 periods in 2015 were obtained as a total of 92 HDF files. The black-sky and white-sky albedo data were first extracted from each file and converted to an appropriate file format. A mosaic was then created for Beijing from two images acquired during the same period. Average black-sky and white-sky albedo values were then determined to quantitatively represent the surface albedo across the city. Finally, the average surface albedo during each period was determined along with the annual average (2015).
2.2.2 Explanatory factors
Land-use data for 2015 were acquired from the current Chinese Land-Use/Cover Datasets of Resource and Environment Data Cloud Platform (http://www.resdc.cn/) (Liu et al., 2014). The spatial resolution of land use data used in this study is 1 km, and the primary land-use classifications include cropland, forestland, grassland, water bodies, built-up land, and unused land. Figure 2a shows the distribution of land-use types and land covers in Beijing in 2015, which yields the following ranked order: forestland > cropland > built-up land > grassland > water body > unused land. Cropland and built-up land are mainly distributed in the southeast of the city, while forestland and grassland are mainly distributed in the northwest.
The Normalized Difference Vegetation Index (NDVI) products were the Terra Moderate Resolution Imaging Spectroradiometer (MODIS) Vegetation Indices (MOD13A3) obtained from the National Aeronautics and Space Administration (NASA). The data are provided monthly at 1km spatial resolution. In this study, the MODIS NDVI data for Beijing in 2015 were used to calculate its average to represent the characteristics of NDVI in Beijing. As shown in Fig. 2b, the NDVI of Beijing in 2015 is between 0.08-0.74, and the spatial distribution of NDVI in Beijing is quite similar to the spatial distribution of LULC. The NDVI of built-up land in the south-central part is the lowest, while the NDVI of grassland and forest land in the northwest is higher, and the NDVI of cropland is moderate.
A digital elevation model (DEM) of Beijing is available from the Geospatial Data Cloud Site, Computer Network Information Center, Chinese Academy of Sciences (http://www.gscloud.cn). These datasets were processed using the Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM V1), which is a digital elevation data product with a global spatial resolution of 30 m. The elevation map of Beijing is shown in Fig. 2c and spans an altitudinal range of between -129 m and 2270 m. Slope data for Beijing were generated from the DEM, which refers to the angle between the tangent plane passing through one point on the ground surface and the horizontal ground surface. A lower slope value indicates flatter terrain while a higher slope value indicates steeper terrain. The obtained slope values were categorised into five levels as shown in Fig. 2d.
Fig. 2 Explanatory factor classification maps for (a) land use and land cover (LULC); (b) NDVI; (c) elevation; (d) slope; (e) annual mean temperature; and (f) annual cumulative precipitation.
Average temperature and cumulative precipitation data were acquired from the Resource and Environment Data Cloud Platform (http://www.resdc.cn/Default.aspx). The spatial interpolation database of annual temperature and precipitation data provided for China by the website is based on the daily observation data of more than 2400 meteorological stations in China, which is generated through sorting, calculation and spatial interpolation. The data for Beijing in 2015 were clipped using ArcGIS. The annual mean temperature of Beijing in 2015 ranged from 2.5 ℃ to 13.5 ℃, and annual total cumulative precipitation ranged from 534 mm to 630 mm. The spatial distribution of precipitation and rainfall are shown in Fig. 2e and Fig. 2f, respectively.
When exploring the relationships between independent variables and dependent variables, the geographical detector requires that the independent variables should be discrete data. If the independent variables are continuous data, they need to be discretized. Data discretization is the process of dividing continuous data into several intervals, where each interval corresponds to a qualitative symbol. The discretization can be based on expert knowledge or classified using algorithms such as k-means. User-defined discretization can also be used for geographical detector models (Wang et al., 2010; Hu et al., 2011; Cao et al., 2013). The explanatory factors in this study are all continuous data except for the LULC, therefore, the remaining five variables needed to be discretized. As shown in Table 1, the NDVI is discretized into six intervals: N1(0.08-0.30), N2(0.30-0.37), N3(0.37- 0.44), N4(0.44-0.50), N5(0.50-0.56), N6(0.56-0.74); The elevation is discretized into six intervals: E1(-129-158 m), E2(158-389 m), E3(389-617 m), E4(617-854 m), E5 (854-1187 m), E6 (1187-2270 m); The slope is discretized into five intervals: I (<2°), II (2°‒6°), III (6°‒15°), IV (15°‒ 25°), V(>25°); The temperature is discretized into five intervals: T1(2.5‒7.5 ℃), T2(7.5‒9.5 ℃), T3(9.5‒10.5 ℃), T4(10.5‒12 ℃), T5(12‒13.5 ℃); And the precipitation is discretized into five intervals: C1 (534-565 mm), C2 (565-575 mm), C3 (575-585 mm), C4 (585-595 mm), C5 (595-630 mm). The slope is discretized based on expert knowledge, while NDVI, elevation, temperature and precipitation are discretized according to the actual values of each factor in Beijing.
Table 1 Discretization results of explanatory factors
Factors NDVI Elevation Slope Temperature Precipitation
Values Types Values (m) Types Values (°) Types Values (℃) Types Values (mm) Types
1 0.08-0.30 N1 ‒129‒158 E1 <2 I 2.5‒7.5 T1 534‒565 C1
2 0.30-0.37 N2 158‒389 E2 2‒6 II 7.5‒9.5 T2 565‒575 C2
3 0.37-0.44 N3 389‒617 E3 6‒15 III 9.5‒10.5 T3 575‒585 C3
4 0.44-0.50 N4 617‒854 E4 15‒25 IV 10.5‒12.0 T4 585‒595 C4
5 0.50-0.56 N5 854‒1187 E5 >25 V 12.0‒13.5 T5 595‒630 C5
6 0.56-0.74 N6 1187‒2270 E6 ‒ ‒ ‒ ‒ ‒ ‒

Note: “‒” means that the data is only divided into five categories.

2.3 Methods

Geographical detector is a novel tool for the measurement and attribution of SSH. It includes four detectors: factor detector, risk detector, ecological detector and interaction detector. In this study, geographical detectors were used to determine the influence of the explanatory factors outlined in Section 2.2.2 (LULC, NDVI, elevation, slope, average temperature, and cumulative precipitation) on the spatial pattern of surface albedo in Beijing. The factor detector, ecological detector, and interaction detector were applied as follows.
2.3.1 Factor detector
The factor detector mainly measures the SSH of variable Y, or the influencing power of an explanatory variable X on Y. Therefore, the power of the determinant of the explanatory factors of albedo can be measured by the q-statistic of factor detector by the following method (Wang et al., 2010):
$q=1-\tfrac{\sum\limits_{k=1}^{n}{{{N}_{k}}\sigma _{k}^{2}}}{N{{\sigma }^{2}}}$
where N and $\sigma^{2}$ stand for the number of units and the variance of surface albedo in a study area, respectively; the population surface albedo is composed of n strata (k = 1, 2, …, n) divided by the explanatory factors, Nk and $\sigma^{2}_{k}$ stand for the number of units and the variance of surface albedo in stratum k, respectively. The value of q is within [0, 1], and q = 0 indicates that there is no coupling between surface albedo and the explanatory factors, while q = 1 indicates that the surface albedo is completely determined by the explanatory factors.
2.3.2 Ecological detector
The ecological detector identifies the difference in the impacts of two explanatory variables and is measured by the F statistic (Wang et al., 2010):
$F=\frac{{{N}_{{{x}_{1}}}}\left( {{N}_{{{x}_{2}}}}-1 \right)\sigma _{{{x}_{1}}}^{2}}{{{N}_{{{x}_{2}}}}\left( {{N}_{{{x}_{1}}}}-1 \right)\sigma _{{{x}_{2}}}^{2}}$
where $N_{{{x}_{1}}}^{{}}$ and ${{N}_{{{x}_{2}}}}$ are the numbers of units of the two explanatory factors, and $\sigma _{{{x}_{1}}}^{2}$ and $\sigma _{{{x}_{2}}}^{2}$ are the population dispersion variances of the two factors, respectively, where the null hypothesis is ${{\text{H}}_{0}}:\ \sigma _{{{x}_{1}}}^{2}=\sigma _{{{x}_{2}}}^{2}$ . If the null hypothesis is rejected at the significance level, then two factors are considered to have significantly different effects on the spatial distribution of surface albedo.
2.3.3 Interaction detector
The interaction detector can be used to identify the interactions between different explanatory factors on the spatial distribution of the dependent variable. This detector compares the interaction between two factors A and B on the surface albedo, and determines whether the two determinants when taken together weaken or enhance each another, or are independent in affecting the surface albedo. This relationship evaluation method involves comparing q(A), q(B), and q(A∩B) and includes weakening, independent, and enhanced relationships, with the five relationships shown in Table 2 (Wang et al., 2012). Therefore, the interaction results not only indicate the contributions of the two factors to surface albedo, but also reveal whether there is co-linearity between the two factors.
Table 2 Types of interactions between two covariates
Description Interaction
1 $q(A\cap B)\text{}\ \text{min}\ \text{(}q(A),\ q(B)\text{)}$ Weaken, nonlinear
2 $min\ (q(A),\ q(B))< q(A\cap B)< \max \ (q(A),\ q(B))$ Weaken, univariate
3 $q(A\cap B)>\max \text{(}q(A),q(B)\text{)}$ Enhance, bivariate
4 $q\left( A\cap B \right)=q\left( A \right)+q\left( B \right)$ Independent
5 $q\left( A\cap B \right)>q\left( A \right)+q\left( B \right)$ Enhance, nonlinear

3 Results

3.1 Spatio-temporal variation of surface albedo in Beijing, 2015

Annual average surface albedo can be used to characterise the overall albedo of a region. The average surface albedo of 46 periods was calculated to represent the surface albedo of Beijing. Based on Fig. 3, the annual average surface albedo in Beijing varied between 0.050 and 0.196 in 2015 and showed marked spatial variation; values were relatively high in the southeast of the city (0.14-0.18) and relatively low in the northwest (0.05-0.14). The surface albedo of most regions was between 0.10 and 0.18, and the maximum (0.18-0.20) or minimum (0.05-0.10) surface albedo only occupied a small part of the region. As shown in Fig. 3, the spatial distribution of surface albedo is roughly similar to that of LULC, but there are differences. That is, the surface albedo of given land use type is not exactly the same and may show significant variations even within the same land-use category. For example, the surface albedo of an area of built-up land in the south-central region of the city was notably lower than the surrounding land of the same cover type. This indicates that the surface albedo is not only determined by the type of land use, but is also affected by many other factors. For example, such as, in the case of built-up land, the likely results from the differences in the types of buildings or other factors.
Fig. 3 Spatial pattern of annually averaged surface albedo in Beijing, 2015.
The average surface albedo across the whole region was determined as a representative value for the entire city. The average daily surface albedo of Beijing (as a whole) in 2015 varied between 0.114 and 0.227, with a mean of 0.131. As shown in Table 3, the seasonal averages of surface albedo of Beijing in 2015 are ranked in the following order: autumn (0.122) < spring (0.127) < summer (0.134) < winter (0.142), indicating that the surface albedo is the lowest in autumn and the highest in winter. Combining these results with Fig. 4, the smallest variability occurred in spring, remaining at approximately 0.127 (day 30-120), but rising slightly towards the beginning of summer to reach 0.136. A slight decrease in variability occurred during the middle and late summer (day 145-210) and a more marked decline occurred during the autumn (day 210-300) reaching a minimum of 0.114. Variation was greatest during the winter (day 300-30 of the next year), reaching a significant peak of 0.227 on day 329.
Fig. 4 Intra-annual variations in the surface albedo of Beijing, 2015.
Table 3 Seasonal averages of surface albedo in Beijing, 2015.
Seasons Spring
(day 30-120)		 Summer
(day 120-210)		 Autumn
(day 210-300)		 Winter
(day 300-30 of next year)
Mean 0.127 0.134 0.122 0.142
Standard deviation 0.001 0.002 0.006 0.030

3.2 Factors influencing albedo

3.2.1 Driving factor detection
Factor detector is a method to measure the relative importance of various factors for surface albedo. The greater the q-statistic of the factor detector, the greater is the influence of the respective explanatory factor on albedo. Moreover, the factor with the largest q-statistic is defined as the dominant factor. In this analysis, the response variable was taken as the annual average of the surface albedo of Beijing in 2015. According to the results of factor detection analysis (second row in Table 5), the degrees of influence of the six considered explanatory factors are ranked in the following order: NDVI (0.625) > LULC (0.537) > slope (0.531) > temperature (0.515) > elevation (0.512) > precipitation (0.190). All explanatory factors of surface albedo distribution passed the significance test (P < 0.05).
These explanatory factors all had significant individual effects on the spatial distribution of surface albedo values (Table 4). Among these different explanatory factors, the NDVI q-statistic is the largest, at is 0.625, indicating that this driving factor had the greatest influence overall. Therefore, NDVI is the dominant factor affecting surface albedo distribution in Beijing. LULC is the second-largest influence (q-statistic = 0.537); the influence of slope was less than that of LULC, which a q-statistic of 0.531; the average temperature and elevation had a similar level of influence (q-statistic = 0.515 and 0.512, respectively). These five factors all accounted for more than 50% of the surface albedo distribution. However, the q-statistic of cumulative precipitation is only 0.190, which is the smallest among all explanatory factors. That suggests the cumulative precipitation has only a minimal influence on the albedo distribution.
3.2.2 Ecological detection of explanatory factors
The ecological detector results are shown in Table 4. Y indicates that the influence of each explanatory factor on the spatial distribution of surface albedo is significantly different at the 95% confidence level, while N indicates that there is no significant difference.
The results show that there are no significant differences between the slope and the three other factors on surface albedo except for the NDVI and precipitation; and the influence of temperature and elevation were not significantly different. This shows that these factors have similar effects on the spatial distribution of surface albedo. The NDVI and cumulative precipitation each have a significantly different influence than all other factors on the pattern of surface albedo; and other than for slope, LULC had significantly different influence compared to NDVI, elevation, temperature and precipitation. This shows that these factors play their respective roles in influencing the spatial distribution of surface albedo.
Table 4 Influence power index of the explanatory factors on the pattern of surface albedo in Beijing, 2015, and the significant differences between them.
Variables LULC NDVI Elevation Slope Temperature Precipitation
q-statistic 0.537 0.625 0.512 0.531 0.515 0.190
P value 0.000 0.000 0.000 0.000 0.000 0.000
LULC - - - - - -
NDVI Y - - - - -
Elevation Y Y - - - -
Slope N Y N - - -
Temperature Y Y N N - -
Precipitation Y Y Y Y Y -

Notes: Y indicates a significant difference between explanatory factors at the 95% confidence level; N indicates no significant difference.

3.2.3 Interactive detection of explanatory factors
The spatial heterogeneity of surface albedo values results from multiple factors and there is often no single factor that can fully account for this variability. Interaction detector was used to assess whether the explanatory factors had an interactive influence on surface albedo. Based on the interaction detector results (Table 5), all of the considered explanatory factors were found to have a synergistic effect. This indicates that the combined influence of any two factors was greater than their individual effects. The q-statistic of the interactive influence between factors on surface albedo are ranked in the following order: NDVI∩LULC (0.710) > elevation∩NDVI (0.691) > slope∩NDVI (0.690) > temperature∩NDVI (0.689) > precipitation∩NDVI (0.648) > elevation∩LULC (0.645) > slope∩LULC (0.644) > temperature∩LULC (0.641) > temperature∩slope (0.630) > slope∩elevation (0.629) > precipitation∩LULC (0.573) > precipitation∩slope (0.567) > temperature∩elevation (0.553) > precipitation∩elevation (0.535) > precipitation∩temperature (0.531).
Table 5 Interactions between explanatory factors in their influences of the spatial pattern of surface albedo in Beijing, 2015
Variables LULC NDVI Elevation Slope Temperature Precipitation
LULC 0.537
NDVI 0.710* 0.625
Elevation 0.645* 0.691* 0.512
Slope 0.644* 0.690* 0.629* 0.531
Temperature 0.641* 0.689* 0.553* 0.630* 0.515
Precipitation 0.573* 0.648* 0.535* 0.567* 0.531* 0.190

Notes: * indicates that the interaction results in bivariate enhancement.

According to the results of the interaction detection, the q-statistic of the interaction between any two factors on the surface albedo is greater than the q-statistic for either of the two factors individual influences, but less than the sum of their q values, showing the bivariate enhancement results. Among them, NDVI and LULC had the largest interactive effect (0.710) while the combined effect of temperature and precipitation was lowest (0.531). The q-statistics of the four 2-factor combinations of NDVI∩LULC, elevation∩NDVI, slope∩NDVI and temperature∩NDVI are all greater than 0.680, indicating that these factors working together can explain more than 68% of the spatial distribution of surface albedo. The interaction of NDVI∩elevation is larger than that of NDVI∩slope or NDVI∩temperature, while the individual influence of elevation is smaller than that of slope or temperature. Similarly, the degree of interaction of elevation∩LULC was greater than between temperature∩LULC while the individual influence of elevation was lower than that of temperature. This indicates that NDVI has a greater enhancement of elevation than slope or temperature, and LULC enhanced the influence of elevation on surface albedo more than the temperature. It also indicates that a given factor may have different enhancement effects on the influence of different factors on surface albedo. In addition, while the influence of cumulative precipitation on the other factors was small, this factor cannot be ignored when its interactive effects are considered.

4 Discussion

4.1 Spatio-temporal heterogeneity of surface albedo

The spatio-temporal distribution of surface albedo in Beijing in 2015 was distinctly heterogeneous. The spatial variation of the average surface albedo in Beijing in 2015 was between 0.050 and 0.196. Higher albedo values were mainly distributed in the southeast of the city, which is densely populated, has a relatively flat topography, and is dominated by cropland and built-up land. In the northwest of the city, the terrain is higher and the main land-use types are grassland and forestland resulting in lower surface albedo values. Previous studies obtained the albedo of different surface features through remote sensing inversion, and the results were as follows: cropland > built-up land > grassland > forestland > unused land > water body (Bao et al., 2007). Bounoua et al. (2002) found that the surface albedo of forestland was significantly lower than that of cropland, because the color of the forestland canopy was generally darker than that of cropland, and the roughness of forestland was greater than that of cropland (Betts et al., 2007). The finding of these previous studies are consistent with the results of this study. In fact, even within the same type of land use, there are differences in surface albedo. This is because the surface albedo, as a quantitative index reflecting the reflective ability of the surface of earth to solar radiation, is not only related to the type of LULC, but it is also affected by other factors such as solar elevation angle, surface roughness, soil moisture and meteorological conditions (Chen, 1999; Liu et al., 2008; Guan et al., 2009). The factor detectors have also shown that LULC is only the dominant factor determining the change of surface albedo, not the only determinant. Therefore, when a given land use type is located in different regions, its climatic conditions, soil types and solar radiation received are very different, resulting in differences in surface albedo.
In 2015, the temporal variation of the overall mean surface albedo across the entire city was between 0.114 and 0.227, with a mean of 0.131. This variation reflected significant seasonal patterns, with higher and more fluctuating values occurring in the winter, relatively stable values occurring in the summer and spring, and a slight decline in values in the autumn. Snow and ice have a high albedo to solar radiation, only a small part of the incoming solar radiation energy is absorbed by the snow-and ice-covered areas. The melting of snow will expose the surface that will significantly reduce the surface albedo (Nolin et al., 1997; Robinson, 1997). So the large variation of surface albedo during the winter is probably due to the snow. These annual changes of albedo are consistent with existing research results (Yang et al., 2006). The spatio-temporal results of this study help to understand the temporal and spatial variability of Beijing’s surface albedo and provided a powerful reference for the simulation of environmental climate change.

4.2 Relative influences of factors on surface albedo

According to the analysis results of the factor detector, all each of the factors considered in this study show a significant relationship with the spatial heterogeneity of surface albedo. Among these, NDVI had the highest q-statistic value of 0.625, indicating it had the greatest level of influence. Previous studies have also shown that NDVI has a strong negative correlation with the surface albedo (Xue et al., 2019). This is because NDVI reflects the type of land cover, and the change of land cover type directly leads to the difference of land cover albedo (Li et al., 2012). However, in the summer with high NDVI, the surface albedo of Beijing is even higher than in spring and autumn when NDVI is low, which also indicates that NDVI is only the dominant factor determining the spatial distribution of surface albedo, not the only determinant. The fact that surface albedo increases in summer in Beijing indicates that the decrease of the surface albedo caused by NDVI is less than the increase of the surface albedo caused by other factors. LULC is second only to NDVI in influencing the spatial distribution of surface albedo, with a q-statistic of 0.537. This is consistent with the results of previous studies which have also shown that surface albedo is strongly correlated with land use and land-cover type (Zhou et al., 2003; Liu et al., 2015). That correlation is mainly due to the different surface properties of ground objects, which have distinct reflective characteristics with respect to solar radiation (Zhang, 2008). In addition, the q-statistics of slope, elevation, and average temperature were all above 0.500 indicating that they also had large influences on surface albedo. In comparison, the effect of cumulative precipitation was low with a q-statistic of 0.190, indicating it does not play a dominant role in surface albedo. Some studies based on classical statistics can only show a good correlation between surface albedo and precipitation but cannot indicate how much influence it has (Wang et al., 2011). The geographical detector approach has no linear hypothesis, so the relationship between dependent variables and independent variables is, as such, more reliable than that obtained by classical statistics. It judges the influence of independent variables on the spatial differentiation of dependent variables using the q-statistic, whereby independent variable X explains the dependent variable Y as q, which is also an advantage of the geographical detector over classical statistical methods. Comparing the spatial distribution maps of the six factors considered with surface albedo, the greatest degree of similarity can be seen between surface albedo and LULC, NDVI, slope, elevation, and temperature. This conforms to the core premise of the geographical detectors approach, that the spatial distribution of a dependent variable should be similar to an independent variable if they are significantly associated with each other (Wang et al., 2010; Wang et al., 2016).
The ecological detector results show that some factors are significantly different from other variables in terms of their effects on the spatial distribution of surface albedo. For example, there are significant differences between cumulative precipitation and other factors in influencing the spatial distribution of albedo. These differences also show that some factors play their respective roles in influencing the distribution of the albedo. The results of the interactive detector show that there is interaction between all variables, indicating that the spatial heterogeneity of surface albedo is the result of multiple factors. The results also show that the interaction of any two factors will enhance the driving force for albedo spatial differentiation. However, the driving force of the two variables acting together is not simply the sum of the driving forces of the two variables acting independently. Different variables have different enhancement effects when interacting with each other and any given variable has different enhancement effects on other variables. The interaction detector can not only judge whether there is variable interaction or not, but it can also judge the strength, direction, linearity or nonlinearity of the interaction (Wang et al., 2010). Therefore, it is useful for studying the interactions between variables.
Admittedly, only some of the factors influencing surface albedo were quantitatively analysed in this study. In addition to the factors considered here, previous studies have shown that solar height angle, atmospheric composition, surface roughness, and snow cover also have important influences on surface albedo (Davidson and Wang, 2005; Wang, 2005). In addition, this study only used the average surface albedo of Beijing in 2015 to quantitatively analyse the driving forces of various factors on the spatial heterogeneity of the surface albedo, which lacked the consideration of the time changes of the driving forces. In the follow-up work, we analysed the change of the q-statistic between the explanatory variable and surface albedo with the changes of time and space. Studies have shown that the main factors affecting the albedo of temperate grassland surfaces are different in different periods (Wang and Davidson, 2007). Therefore, the influence of other possible factors on the spatial distribution of surface albedo and their variability over time in urban areas such as Beijing require further research.

5 Conclusions

This study used GLASS surface albedo data to study the spatial and temporal distribution of surface albedo in Beijing in 2015. Combined with LULC, NDVI, elevation, slope, average temperature, and cumulative precipitation data, the degree of influence of these factors on albedo was studied by using the geographical detector approach. The results show that:
(1) The annual average albedo in Beijing ranged between 0.050 and 0.196, and there were significant spatial differences with higher values in the southeast and lower values in the northwest of the city. Across the year, the spatially averaged albedo varied between 0.114 and 0.227, with an annual mean of 0.131. Albedo was relatively stable during the spring, peaked at 0.227 during the winter, and reached its lowest value of 0.114 in the autumn.
(2) The factor detector analysis showed that each of the considered factors had a significant influence on the spatial heterogeneity of surface albedo, with their effects being ranked based on their q-statistics in the following descending order: NDVI (0.625) > LULC (0.537) > slope (0.531) > temperature (0.515) > elevation (0.512) > precipitation (0.190). As such, NDVI had the greatest influence on the spatial heterogeneity of surface albedo in 2015 and precipitation had the smallest influence.
(3) The relative influences of the explanatory factors on the spatial distribution of surface albedo varied significantly. For example, both NDVI and precipitation are significantly different from all the other factors. Except for slope, LULC also had a significantly different effect than the other factors. However, interactions occurred among all of the factors, with the combination of any two explanatory factors having an enhanced effect on surface albedo; the effects of these interactions were additive. LULC and NDVI had the strongest interactive effect, with a combined q-statistic of 0.710, while the interactive effect between temperature and precipitation was weakest, with a combined q-statistic of 0.531. Overall, these findings demonstrate that the observed spatial and temporal patterns of albedo were the result of multiple, interacting factors.

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