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Investigating spatial variation in
the relationships between NDVI and
environmental factors at multi-scales:
a case study of Guizhou Karst Plateau,
China
Jiangbo Gao a , Shuangcheng Li a , Zhiqiang Zhao a & Yunlong Cai a
a College of Urban and Environmental Sciences, Peking
University , Beijing, 100871, China
Published online: 24 Oct 2011.
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International Journal of Remote Sensing Vol.33,No.7,10April 2012,2112–2129
Investigating spatial variation in the relationships between NDVI and environmental factors at multi-scales:a case study of Guizhou Karst
Plateau,China
JIANGBO GAO,SHUANGCHENG LI,ZHIQIANG ZHAO
and YUNLONG CAI*
College of Urban and Environmental Sciences,Peking University,Beijing 100871,China
(Received 15August 2010;in ?nal form 22February 2011)
Knowing the spatial relationships between the normalized difference vegetation index (NDVI)and environmental variables is of great importance for monitoring rocky deserti?cation.This article investigated the spatially non-stationary rela-tionships between NDVI and environmental factors using geographically weighted regression (GWR)at multi-scales.The spatial scale-dependency of the relationships between NDVI and environmental factors was identi?ed by scaling the bandwidth of the GWR model,and the appropriate bandwidth of the GWR model for each variable was determined.All GWR models represented signi?cant improvements of model performance over their corresponding ordinary least squares (OLS)models.GWR models also successfully reduced the spatial autocorrelations of residuals.The spatial relationships between NDVI and environmental factors sig-ni?cantly varied over space,and clear spatial patterns of slope parameters and local coef?cient of determination (R 2)were found from the results of the GWR models.The study revealed detailed site information on the different roles of related factors in different parts of the study area,and thus improved the model ability to explain the local situation of NDVI.
1.Introduction
The normalized difference vegetation index (NDVI)is one of the most extensively applied vegetation indices for its sensitivity to the presence,density and condition of vegetation (Herrmann et al .2005).NDVI is based on the principle that for a vegetated surface,red and near-infrared wavelengths are characterized by high and low absorp-tion,respectively (Chen et al .2003,Groeneveld and Baugh 2007).Several global and regional studies have found that NDVI is well related to environmental variables such as land surface temperature (Raynolds et al .2008),precipitation (Piao et al .2006,Onema and Taigbenu 2009),evapotranspiration (Dibella et al .2000)and topography (Li et al .2006).More recently,understanding how abiotic factors affect vegetation has taken on a more acute practical dimension,because of the conservation implications of anthropogenic environmental change.The critical link is that in order to assess the effects of anthropogenic or other changes,we need reliable measures of the association between vegetation features and environmental variables (Keitt et al .2002).
*Corresponding author.Email:caiyl@https://www.doczj.com/doc/c912685622.html,
International Journal of Remote Sensing
ISSN 0143-1161print/ISSN 1366-5901online ?2012Taylor &Francis
https://www.doczj.com/doc/c912685622.html,/journals
https://www.doczj.com/doc/c912685622.html,/10.1080/01431161.2011.605811
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Spatially non-stationary and scale-dependent relationships 2113
One issue that former studies often neglected is the fact that the relationships between NDVI and environmental factors are usually location dependent,which is known as instability in the ?eld of geography and non-stationarity in spatial data analysis (Fotheringham et al .1996,2002).Traditional statistical methods such as ordinary least squares (OLS)can only produce ‘average’and ‘global’parameter esti-mates (Foody 2003,Wang et al .2005b,Zheng et al .2009)and thus are unable to deal with spatial non-stationarity unless establishing separate models for each location.The establishment of separate models,however,implies a huge amount of data and in many cases is very expensive or extremely dif?cult.In addition,spatial autocorrelation in the source data violates the assumptions and requirements of conventional regres-sion techniques.From the point of view of statistic and spatial analysis,the violation may lead to problematic results,such as the overestimated coef?cient of determination and the underestimated standard error and mean square error (Clifford et al .1989,Tiefelsdorf 2000,Grif?th 2003).In recent years,a relatively simple,but effective new technique for exploring spatially varying relationships,called geographically weighted regression (GWR),has been developed (Brunsdon et al .1998,Fotheringham et al .2002).Studies such as by Foody (2003,2004),Zhang et al .(2004)and Propastin (2009)have detected the relationships between vegetation and environmental factors by using GWR.They concluded that spatially varying relationships,good performance and weak spatial autocorrelation were obtained from GWR models.However,most of them were single-scaled and just employed single independent variable.Additionally,few studies focused on the in?uences of environmental variables on vegetation in rocky desert areas.
The magnitude of local variance in NDVI and environmental factors should be sensitive to the spatial scale at which they are investigated,so their modelling rela-tionships are often scale dependent (Foody 2004,Propastin et al .2008).Developing a full understanding of how abiotic conditions impinge on vegetation cover therefore demands a multi-scale study.
The objective of this study,with a case study in Guizhou Karst Plateau,China,was to explore the application of GWR in modelling the relationships between NDVI and environmental factors.NDVI was employed as the dependent variable while cli-mate and topography were used as the independent variables.The issues of spatial non-stationarity and scale-dependency were addressed because they are important for estimating NDVI from in?uencing factors.A comparison of the local regression technique over the traditional methods was also presented.2.Study area
We used Guizhou Province (which lies in the core area of the southwestern Karst area in China at 24?37 –29?13 N and 103?36 –109?35 E)as our case study.It has a total terrestrial area of 176000km 2with a population of 37.93million in 2008.The average elevation is about 1100m above sea level.Its topography is relatively higher in the west and lower in the east,with elevation ranging from 156to 2885m (?gure 1).The primary landform type is mountainous plateau,which covers 87%of the province.Hilly and ?at areas account for only 10%and 3%,respectively.With a subtropical wet monsoon climate,the average annual precipitation is about 1000mm,and the mean annual temperature ranges from 12?C to 16?C.Carbonate rock is widespread and accounts for 62%of the total land area (Wang et al .2004).Under the conditions of widely distributing carbonatite and warm humid monsoon climate,
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Figure 1.Location of the study area.Guizhou Province is located in the southwest of China with gradual decrease in elevation from west to east.
about 73%of the total area belongs to the Karst bare region (Xiong et al .2002).Karst rocky deserti?cation has become the most serious problem in this region due to the fragile eco-environment and irrational land use in the past decades (Huang and Cai 2006).3.Methodology 3.1Dependent variable
As a very good proxy to represent the distribution and productivity of vegetation (Xiao and Moody 2004,Maselli and Chiesi 2006),NDVI was employed as the dependent variable of GWR and OLS models in this study.It is calculated as
NDVI =
N ?R
N +R
,(1)
where N refers to the spectral re?ectance in the near-infrared,where re?ectance from the plant canopy is dominant,and R is the re?ectance in the red portion of the spectrum,where chlorophyll absorbs maximally.
The temporal series (2000–2005),made up of 10-day maximum value composite (MVCs)(Holben 1986)of SPOT NDVI images with about 1km 2spatial resolution,are available free of charge at the Vlaamse Instelling voor Technologisch Onderzock (VITO)Image Processing Centre (Mol,Belgium)(http://www.vgt.vito.be).They were combined to produce one singular average NDVI map for Guizhou Karst Plateau,which was used as the data source for the dependent variable in this study.The VEGETATION instrument on board SPOT4(launched in March 1998)and the VEGETATION2on board SPOT5(since May 2002)provide measures of land surface re?ectance in the visible and in the infrared domains,and are regarded as improved measurements of surface vegetation condition and dynamics (Gao et al .2010).The data were subjected to atmospheric correlations on the basis of the simpli?ed method for atmospheric correlations (SMAC).The considered NDVI composition also allows
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Spatially non-stationary and scale-dependent relationships 2115
for reducing the contamination effects due to residual clouds,atmospheric perturba-tions,variable illumination and viewing geometry that are generally present in daily NDVI maps (Lasaponara 2006).3.2Independent variables
3.2.1Climatic factors.Mean annual precipitation,mean annual biotemperature and potential evapotranspiration rate (PETR)were employed as climatic predictors.PETR,expressed as the ratio of potential evapotranspiration (PET)to annual precipi-tation,represents the combined in?uence of temperature and precipitation (Post et al .1982).In most cases,PET is estimated from meteorological data and is taken to be 58.93times biotemperature.PETR was calculated by using the following expression (Holdridge 1947,Yang et al .2002):
PETR =
58.93T B
P
,(2)
where T B is the mean annual biotemperature,and P represents mean annual precipi-tation.Biotemperature refers to all temperatures above freezing,with all temperatures below freezing adjusted to 0?C.
All climatic data used in this study are raster maps on a 1km 2resolution grid,which were generated through the interpolation of average monthly climate data from weather stations (Hijmans et al .2005).
3.2.2Topographical factors.Topography could have important impacts on the spatial distribution of vegetation cover in the study area with severely dissected topog-raphy and fragmented landscape.Elevation,slope and the compound topographic index (CTI)were selected as topographical https://www.doczj.com/doc/c912685622.html,ually,temperature drops by 0.5–0.6?C and rainfall increases by 92mm for every altitude increase of 100m (Huang et al .2007).Slope could affect vegetation cover through its impacts on human activi-ties,local climate and soil erosion.CTI is a function of a speci?c catchment area (the area draining into a pixel)and slope,and is calculated as follows:
CTI =ln
A S
tan β
,
(3)
where A S is the speci?c catchment area (i.e.the drainage area per unit width orthogo-nal to a stream line)and βis the slope gradient.CTI was used to represent the spatial distribution of water ?ow and water stagnation across the study area (Irvin et al .1997).In areas of no slope,a CTI value is obtained by substituting a slope of 0.001.This value is smaller than the smallest slope obtainable from a 1000m data set with a 1m vertical resolution.
Topographical data are a subset of HYDRO1k,developed at the US Geological Survey’s (USGS)Earth Resources Observation Systems (EROS)Data Center (EDC).HYDRO1k is a geographic database providing comprehensive and consistent global coverage of topographically derived data sets.
Before simulating the relationships between NDVI and independent variables,the one-sample Kolmogorov–Smirnov tests (Massey 1951,Sheskin 2007)and Pearson correlation coef?cient (r )in SPSS 15.0(SPSS Inc.,Chicago,IL,USA)were employed
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to examine the normal distribution of variables and the correlations between NDVI and explanatory variables,respectively.3.3Geographically weighted regression
3.3.1Theoretical background of GWR.GWR,one of several spatial regression techniques,is an extension of traditional standard regression techniques such as OLS regression because it obtains local rather than global parameter estimates (Fotheringham et al .2002).These estimates,showing how relationships vary over space,can help to get the hidden possible causes of the spatial pattern of NDVI.The conventional global regression can be expressed as
?y
i =β0+
k
βk x ik +εi ,
(4)
where ?y
i is the estimated value of the dependent variable at location i ,β0represents the intercept,βk expresses the slope coef?cient for independent variable x k ,x ik is the value of the variable x k at location i and εi denotes the random error term for location i .This equation implies a spatially stationary relationship and gives a single summary statistic for the whole study area.
A separate GWR model is run for each observation point,using a spatial kernel that centres on the point,and weights observations subject to a distance decay function.The above model can be rewritten as
?y
i =β0(μi ,v i )+
k
βk (μi ,v i )x ik +εi ,
(5)
where (μi ,νi )denotes the coordinate location of the i th point,β0(μi ,νi )is the intercept
for location i and βk (μi ,νi )represents the local parameter estimate for independent variable x k at location i .The parameters are estimated from
?β
(μi ,v i )=(X T W (μi ,v i )X )?1X T W (μi ,v i )Y ,(6)
where ?β
(μi ,νi )represents the unbiased estimate of the regression coef?cient,W (μi ,νi )is the weighting matrix which acts to ensure that observations near to the speci?c point have a bigger weight value and X and Y are matrices for independent and dependent variables,respectively.
The weighting function,called the kernel function,can be stated using the exponen-tial distance decay form
w ij =exp
d 2ij
b 2
,
(7)
where w ij represents the weight of observation j for location i ,d ij expresses the Euclidean distance between points i and j ,and b is the kernel bandwidth.Parameter estimates in GWR are obtained by weighting all observations around a speci?c point i based on their spatial proximity to it.The observations closer to point i have higher impacts on the local parameter estimates for the location,and are weighted more than
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Spatially non-stationary and scale-dependent relationships 2117
data far away.If observation j coincides with i ,the weight value is one.If the distance is greater than the kernel bandwidth,the weight will be set to zero.
In ArcGIS 9.3(ESRI Inc.,Redlands,CA,USA),the GWR model was added into ArcToolbox.The input parameters include the input feature class (shape?le of ArcGIS in this study),dependent variable and explanatory variable(s).Other optional parame-ters cover kernel type,bandwidth method,distance,number of neighbours and weight.The bandwidth of GWR refers to the problem of choosing an appropriate scale to analyse the data.The multi-bandwidth simulation is important for determining the appropriate operating scale and can be easily conducted using GIS-based GWR.3.3.2Comparison of GWR and OLS.In this article,the corrected Akaike infor-mation criterion (AIC c )(Akaike 1973,Hurvich and Tsai 1989)and coef?cient of determination (R 2)values from GWR were compared with those from OLS to inves-tigate whether GWR models have better model performance than the corresponding OLS models.AIC c is a measurement of model performance and is useful for compar-ing different regression models.The model with the lower AIC c value means a better ?t to the observed data and better model https://www.doczj.com/doc/c912685622.html,ually,a decrease of AIC c values lower than three indicates that the model with the lower AIC c is held to be bet-ter.The performance of the two models was also compared using ANOV A and two F -tests based on Fotheringham et al .(2002)and Leung et al .(2000),respectively.Moreover,global and local Moran indexes (Moran’s I )of residuals from the OLS and GWR models were computed using the ArcToolbox in ArcGIS 9.3and the GS +7.0version (Gamma Design Software,LLC,Plainwell,MI,USA)to compare the ability to deal with spatial autocorrelation between OLS and GWR.Moran’s I is commonly used as an indicator of spatial autocorrelation,and its values range from ?1to 1.The larger the absolute value of Moran’s I ,the more signi?cant the spatial autocorrelation.A value of 0means perfect spatial randomness.
3.3.3Sampling data.All GIS layers for dependent and independent variables,which were raster data at 1km spatial resolution initially,were converted to vector formats to meet the requirement of ArcGIS-based GWR.The three steps of data con-version are as follows:(1)points in the study area were selected randomly;(2)values were extracted from raster data layers to points;and (3)points with property values were used to GWR model.
3.3.4Measuring non-stationarity.In this article,we calculated the stationary index using Matlab 7.4(The MathWorks Inc.,Natick,MA,USA).The stationary index was proposed by Brunsdon et al .(1998)and Osborne et al .(2007).It is designed to measure the spatial non-stationarity,and values smaller than 1indicate station-arity (Charlton et al .2003).The calculation included three steps:First,we computed the interquartile range of standard error for GWR coef?cients for each explanatory variable using Matlab function ‘iqr’;secondly,twice the standard error of the global regression coef?cient was obtained with Matlab function ‘glm?t’;thirdly,the ratio of these two factors was used as the stationary index.In addition,the Koenker (BP)statistic (Koenker’s studentized Bruesch-Pagan statistic)(Breusch and Pagan 1979,Koenker 1981)obtained from OLS models was also employed to test the heteroscedas-ticity and /or non-stationarity for NDVI–environmental factors relationships.
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Furthermore,the statistical signi?cance test of the spatial non-stationarity is neces-sary because the GWR model is equivalent to global regression model if the localized parameter estimates do not meet statistically signi?cant differences (Li et al .2010).In this article,the F 3-test (Leung et al .2000),based on the sample variance of the estimated model coef?cients,was calibrated for the GWR models.4.Results
All dependent and explanatory variables meet the condition of normal distribution,which means that they are suitable for regression analysis.Except CTI,all the envi-ronmental factors have signi?cant correlations with NDVI at p <0.01(table 1).Biotemperature,precipitation and slope exhibit signi?cant positive correlations with NDVI,while PETR and elevation show signi?cant negative relationships with NDVI.NDVI and CTI are not correlated (r =?0.018,p =0.199),that is,high NDVI values are not necessarily located in places with water ?ow.Although it is clear that NDVI is signi?cantly related to most environmental factors,the spatial heterogeneity and the scale dependency of their relationships usually remain unclear.4.1Scale-dependency of spatially non-stationary relationships
As shown in ?gure 2,the stationary index declines rapidly with the coarsening of the https://www.doczj.com/doc/c912685622.html,pared to the other two variables,the curve for elevation has not only a bigger decline gradient but also relatively larger stationary index values.
The declines of the stationary index for all predictors are larger within the spatial scale of 20km.It means that the dominant operating scales of each topographical variable on NDVI are located within 20km.The decline slopes of the curves become quite ?at above the spatial scale of 40km,and the relationships for NDVI and slope,and NDVI and CTI become stationary within the spatial scale range of 160km,whose stationary indexes are smaller than one at a spatial scale of approximately 10km.The Koenker (BP)statistic also indicated statistically signi?cant non-stationarity at the level of p <0.05for NDVI–elevation relationships.
The curves in ?gure 3display nearly opposite variation trends compared to ?gure 2,where all the rising slopes become quite plain at the spatial scale of above 120km.Elevation performs better goodness-of-?t than other two variables within the spatial scale range.
From these two ?gures it is found that the interrelations between NDVI and topo-graphical factors exhibit signi?cant spatial scale-dependence.Above the spatial scale of 40km,the curves in ?gure 2become quite plain while the curves in ?gure 3continue
Table 1.Pearson correlations between NDVI and environmental variables.Explanatory Variables N r p Elevation 4983?0.392<0.01Slope 49830.150<0.01CTI
4983?0.0180.199Biotemperature 49830.245<0.01Precipitation 49830.434<0.01PETR
4983
?0.058
<0.01
Note:N is the number of sampling points.
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Spatially non-stationary and scale-dependent relationships
2119
140012001000800600S t a t i o n a r y i n d e x S t a t i o n a r y i n d e x
S t a t i o n a r y i n d e x
40020005.04.54.03.53.02.52.01.51.00.503.5(a )(b )
(c )
3.02.52.01.51.00.50160
140
120
100
80
60
40
20
160
140120100806040200160
140
120
100Bandwidth (km)
80
6040
20
Figure 2.The stationary index at multi-scales for topographical variables.The stationary index is a ratio between the interquartile range of standard error for geographically weighted regression (GWR)coef?cients and twice the standard error of the global regression coef?cient.(a )Elevation;(b )slope;and (c )compound topographic index (CTI).
to rise.Therefore,the spatial scale of 40km is used as the bandwidth of the GWR models for topographical factors to obtain the optimal mishmash of bias and preci-sion and the clear spatial pattern of relationships.Likewise,40km is also employed as the bandwidth of the GWR models for biotemperature and PETR,and 120km is selected as the bandwidth of the GWR models for precipitation.Only the results for topographical variables are shown in this article.The analysis of scale-dependency and the choice of appropriate bandwidth for climatic factors are based on the same method.
4.2Comparison between GWR and OLS
4.2.1Model performance.The AIC c and R 2of GWR and OLS models are shown in table 2.In all cases,the GWR models outperform the OLS models,characterized by the higher R 2values and the lower AIC c values of the GWR models.As indicated by
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9 × 1058 × 1057 × 1056 × 105R e s i d u a l s q u a r e s
5 × 1054 × 1053 × 1052 × 1051 × 105
00
20
40
60
80Bandwidth (km)
100120140CTI
Slope Elevation 160
Figure 3.The sum of squared residuals (residual squares)of the geographically weighted regression (GWR)model at multi-scales for the normalized difference vegetation index (NDVI)and topographical variables.The smaller values mean the a closer ?t of GWR models to the observed data.
Note:CTI,compound topographic index.
Table https://www.doczj.com/doc/c912685622.html,parison of two diagnostics (AIC c and R 2)between OLS and GWR models.Explanatory variables AIC c R 2Elevation AIC O 41805R 2O 0.154
AIC G 37572R 2G 0.649Slope AIC O 42522R 2O 0.023AIC G 37919R 2G 0.624CTI
AIC O 42633R 2O 0.0003AIC G 38124R 2G 0.609Biotemperature AIC O 42328R 2O 0.060AIC G 26852R 2G 0.669Precipitation AIC O 41596R 2O 0.188AIC G 6857R 2G 0.643PETR
AIC O 42618R 2O 0.003AIC G
34803
R 2G
0.649
Notes:AIC c ,Akaike’s information criterion;CTI,compound topographic index;GWR,geographically weighted regression;OLS,ordinary least squares.AIC O and AIC G are the
AIC c for OLS and GWR models,respectively;R 2O and R 2G are the R 2
for OLS and GWR models,respectively.
the R 2from OLS models,single variable can only explain less than 20%of the variance in NDVI.The highest R 2(0.188)appears in the OLS model for NDVI and precipita-tion,and most values are lower than 0.1.While in GWR models,each explanatory variable can account for more than 60%of the variance in NDVI,and models for biotemperature and PETR perform best.The results of an ANOV A-test and two F -tests (not shown)indicate that the improvement of the GWR models over their corresponding OLS models is statistically signi?cant based on 500sampling data.The local models echo and amplify the relationships observed by the global models,so the performance of the local models represents a complex mix of the model’s overall
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performance and the relative degree of non-stationarity (Lafary et al .2008).Therefore,the relative performance of the global and local models illustrate that the parameters display non-stationarity,and that the relationships between NDVI and environmental factors are better understood when the statistical analyses are ‘scaled down’enabling case-wise examination of the parameter diagnostics.
4.2.2Spatial autocorrelation of residuals.The results of the global Moran I -test are shown in table 3.Signi?cant positive spatial autocorrelations are found for all the OLS models,characterized by Moran’s I values ranging from 0.71to 0.80at p <0.01,and all the GWR models,indicated by Moran’s I values ranging from 0.40to 0.58at p <0.01.The results show that the GWR models produced smaller global Moran’s I than OLS models with the same independent variable,meaning that GWR models improve the reliability of the relationships by reducing the spatial autocorrelations of residuals (Zhang et al .2005).The values for biotemperature and PETR are smaller than other variables,corresponding to the results of model performance.
The local Moran’s I for biotemperature was calculated at multi-scales.The results show that all the absolute values of local Moran’s I statistics on the residuals from GWR models within the spatial scale range are smaller than those from OLS models.Besides,no signi?cant spatial autocorrelation was found over 50km for the GWR models,while spatial autocorrelations of residuals from OLS models are relatively signi?cant.The results indicate that the GWR model represents an improvement over the OLS model by reducing spatial autocorrelation.4.3Spatial non-stationarity among relationships
The results of the F 3-test (not shown)con?rm that all explanatory variables exhibit signi?cant spatial non-stationarity at the 90%con?dential level.Maps of slope param-eters and local R 2obtained from GWR models provide a simple way to detect the spatial varying relationships between NDVI and related factors.Local R 2,ranging from 0to 1,indicates how well the local regression model ?ts the observations,and the local models with low values perform poorly.
The maps of slope parameters and local R 2from the GWR models for NDVI and topographical variables are shown in ?gure 4.From table 1,we know that a signi?-cant negative correlation exists between NDVI and elevation (r =?0.392,p <0.01).However,?gure 4(a )shows that both negative and positive correlations are distributed in the study area,and a clear spatial pattern is identi?ed.Negative correlations are
Table https://www.doczj.com/doc/c912685622.html,parison of Moran’s I of residuals between OLS and GWR.Explanatory variables I O p I G p Elevation 0.71<0.010.41<0.01Slope 0.79<0.010.42<0.01CTI
0.80<0.010.46<0.01Biotemperature 0.77<0.010.40<0.01Precipitation 0.75<0.010.58<0.01PETR
0.80
<0.01
0.39
<0.01
Notes:CTI,compound topographic index;PETR,potential evapotranspiration rate;GWR,geographically weighted regression;OLS,ordinary least squares.I O is Moran’s I for the OLS model;I G is Moran’s I for the GWR model.
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Coefficient
(a )
(c )
(d )
(f )
(b )
(e )
Coefficient
Coefficient
Local R 2
Local R 2
Local R 2
–0.031 to –0.010–0.448 to –0.238–0.237 to –0.107–0.106 – 0.0000.001 – 0.1610.000 – 0.0020.000 – 0.0250.205 – 0.299
0.140 – 0.2040.080 – 0.1390.032 – 0.0790.000 – 0.0310.026 – 0.0590.060 – 0.1040.169 – 0.251
0.105 – 0.1680.003 – 0.0060.007 – 0.0120.013 – 0.0210.022 – 0.043
0.162 – 0.625
–0.009 – 0.000–0.703 – 0.0000.001 – 0.7760.777 – 1.4171.418 – 2.3162.317 – 3.462
0.001 – 0.0150.016 – 0.0260.027 – 0.045
500km
250
125
N
Figure 4.Spatial variation of regression outputs from the geographically weighted regression (GWR)models for the normalized difference vegetation index (NDVI)and topographical vari-ables in the study area:(a )slope parameter for elevation;(b )local R 2for elevation;(c )slope parameter for slope;(d )local R 2for slope;(e )slope parameter for compound topographic index (CTI);and (f )local R 2for CTI.
mainly located in the northwest and south of the study area.Stronger positive corre-lations,which means that same amount of increase in the elevation may cause more increase in the NDVI,are found in the northeast and centre of the study area.The local R 2values for NDVI and elevation (?gure 4(b ))also exhibit a huge spatial vari-ability.The distribution of higher local R 2values,which can account for 14–20%of the variation in NDVI,coincides with the stronger positive correlations.
Likewise,as opposed to the signi?cant positive correlation between NDVI and slope found by the OLS model (r =0.150,p <0.01),both positive and negative correlations are obtained by the GWR models (?gure 4(c )).Stronger positive correlations lie in the middle and east of the study area.Negative correlations are located in the west,north-east and southeast of the study area.The local R 2also vary over space (?gure 4(d )),and slope can explain 10–25%of the spatial variation in NDVI in locations with stronger positive correlations.
CTI is the weakest predictor of NDVI in the OLS model.It has no signi?cant cor-relation with NDVI (r =?0.018,p =0.199;table 1).Similarly,the local correlations between NDVI and CTI are weak in the study area (?gure 4(e )).However,both pos-itive and negative correlations are observed for the study area,and a clear spatial non-stationarity is identi?ed from the results of GWR models.CTI has stronger pos-itive relationships with NDVI in the west,northeast and southeast of the study area and stronger negative correlations in the east.Most locations with stronger negative
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Spatially non-stationary and scale-dependent relationships
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Coefficient
Coefficient
Coefficient
(a )
(b )
–8.240 to –4.743–0.065 to –0.005–155.494 to –90.340–90.339 to –58.937–58.936 to –29.923–29.922 – 0.0000.000 – 0.0360.000 – 0.0330.000 – 0.0300.031 – 0.0730.074 – 0.1240.125 – 0.1850.186 – 0.290
0.034 – 0.0790.080 – 0.1320.133 – 0.1950.196 – 0.285
0.037 – 0.0910.092 – 0.1510.152 – 0.2260.227 – 0.384
0.001 – 60.834
–0.004 – 0.0000.001– 0.0690.070 – 0.114
0.115 – 0.179
–4.742 to –2.840–2.839 to –1.086–1.085 – 0.0000.001 – 4.290
500km
250
125
N
(c )
(d )
(f )
(e )
Local R 2
Local R 2
Local R 2
Figure 5.Spatial variation of regression outputs from the geographically weighted regression (GWR)models for the normalized difference vegetation index (NDVI)and climatic variables in the study area:(a )slope parameter for biotemperature;(b )local R 2for biotemperature;(c )slope parameter for precipitation;(d )local R 2for precipitation;(e )slope parameter for potential evapotranspiration rate (PETR);and (f )local R 2for PETR.
correlations usually have higher local R 2values (?gure 4(e )and (f )).The result indi-cates that CTI can also explain more variations in NDVI than the OLS model in most parts of the study area.
Figure 5shows the maps of slope parameters and local R 2from the GWR models for NDVI and climatic variables.Unlike the signi?cant correlations between NDVI and climatic factors (biotemperature:r =0.245,p <0.01;precipitation:r =0.434,p <0.01;PETR:r =?0.058,p <0.01)in table 1,both positive and negative corre-lations are obtained by the GWR models.Clear spatial patterns are also identi?ed in these maps.Positive correlations from GWR models for NDVI and biotemperature are mainly distributed in the west and south of the study area,and they are coupled with the lower local R 2values (?gure 5(a )and (b )).Stronger negative correlations and higher local R 2values are located in the east,north and middle of the study area.As shown in ?gure 5(c ),positive relationships between NDVI and precipitation are found in most locations,and negative correlations mainly lie in the southwest of the study area.The local R 2also vary over space,and higher values are located in the west and east of the study area,where precipitation can account for about 20%of the spatial variation in NDVI (?gure 5(d )).
The spatial distributions of slope parameters and local R 2from GWR models for NDVI and PETR (?gure 5(e )and (f ))are similar to ?gure 5(a )and (b ).It may be
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caused by the calculation method of PETR.Positive correlations and lower local R 2values mainly lie in the west and south of the study area,and stronger negative correlations and higher local R 2exist in the east,north and middle.5.Discussion
Vegetation cover is closely related to rocky deserti?cation,which has been one of the serious eco-environmental problems in the study area and has even become an obsta-cle to sustainable development.Knowing the spatially varying relationships between NDVI,a good proxy to the distribution and productivity of vegetation,and related factors,is of great importance for monitoring rocky deserti?cation.The hotspots or interesting regions for controlling Karst rocky deserti?cation can be identi?ed by analysing the spatial variation of simulated relationships.
Two properties of spatial data,spatial non-stationarity (Fotheringham et al .2002)and autocorrelation (Legendre 1993),violate the basic assumptions of global regres-sion models such as OLS,and could reduce the ef?ciency of the regression and mislead the interpretation of model results (Hamilton 1992).NDVI and environmental factors exhibit highly spatial heterogeneity and non-stationary correlations in the study area according to the GWR results.The possible reasons for the different relationships are listed here.Positive and negative correlations between NDVI and elevation may be caused by the impact of elevation on human activities and climate,respectively.In areas with lower altitude,the higher NDVI values are usually related to the higher ele-vation because of less human disturbance,while in higher altitude areas,the increase in elevation may cause the decrease of NDVI due to the more harsh natural environment.The reason for positive relationships between NDVI and slope may be that the higher slope is usually related to the less human activities and then the higher NDVI values.Negative relationships between NDVI and slope,and between NDVI and precipita-tion may be attributed to the combined effects of a large amount of precipitation and higher degree of slope on water and soil erosion.Some locations present positive cor-relations between NDVI and biotemperature,and between NDVI and PETR,because higher biotemperature is bene?cial to vegetation growth.One of the reasonable expla-nations for the negative correlations between NDVI and biotemperature may be that the increase of biotemperature in these locations is usually accompanied with the rise of elevation.The negative correlations between NDVI and PETR exist in most loca-tions because the higher PETR represents the higher degree of dryness and thus results in the lower NDVI values.
One sampling site may have more similar vegetation cover to a site nearby than to another site far away because the nearer sites may be affected by similar human activities (e.g.deforestation and urbanization)and environmental characters such as elevation,slope,temperature and precipitation.Statistically signi?cant clustering of high and /or low residuals indicates that at least one key explanatory variable,which could effectively capture the inherent spatial structure in the dependent variable,is missing from the model.The GWR model can improve the reliability of the rela-tionships by reducing the spatial autocorrelations of residuals.Furthermore,it was found that Moran’s I statistics on the residuals from GWR rise rapidly with a coars-ening of the bandwidth.It means that the reduction of spatial autocorrelations may be caused by the regional paradigm of the GWR model.However,the application of GWR requires a careful use of diagnostic parameters such as Moran’s I statistics.If an OLS model has a spatial autocorrelation problem,GWR can help in reducing it.
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On the other hand,if an OLS model does not have this problem,an application of GWR may increase spatial autocorrelation (Tu and Xia 2008).
The choice of an appropriate bandwidth is a very important issue in the GWR analysis (Gao and Li 2011).Small bandwidths produce estimates with a lower risk of bias.However,they will also provide estimates with large standard errors because each locally weighted regression will only be calibrated on a small number of samples.While using larger bandwidths,the variance of prediction is small but the bias is large (Propastin 2009).According to the calculation of the stationary index,it can quantify the non-stationarity of the spatial relationship,on the one hand,and the variance of prediction,on the other.The smaller the values of the stationary index,the closer the ?t of the GWR model to the observed data.Thus,calculating the stationary index and the sum of the squared residuals from GWR at multi-scales can not only help to analyse the scale-dependency of spatial relationships,but also provide a basis for determining a bandwidth for GWR with an optimal mishmash of bias and precision.The GWR model has irreplaceable superiority in presenting spatially varying rela-tionships,but there are still some limitations.It assumes spatial non-stationarity for all variables,while portions of regression coef?cients are constant in some cases,espe-cially in homogeneous regions.One effective approach is to extend GWR to mixed GWR (MGWR)(Mei et al .2006).As shown in table 3,the spatial autocorrelation of residuals from the GWR models is also statistically signi?cant;the possible solutions include extending the bandwidth to smaller scales,employing more explanatory fac-tors and coupling autoregression models to the GWR model.In this study,only one explanatory variable was used for OLS and GWR models to analyse its association with NDVI.In the future,multi-variables will be combined for models to improve model performance and to obtain more a reasonable explanation.In order to avoid the potential multi-collinearity among explanatory variables,principal component analysis or correlation analysis will also be employed.
More spectral vegetation indices will be coupled to the regression analysis.According to the research of Cohen et al .(2003),using a single index which is integrated from the multiple indices by canonical correlation analysis represents a signi?cant strategic improvement over regressions solely dependent on a single veg-etation index.Because global remote-sensing data archives are expanding with more and more spectral information besides the NDVI data set (Wang et al .2005a),this approach could be useful for estimating vegetation cover at regional and global scales.In the future,we will carry out multidimensional analysis to identify the dynamic causes of vegetation cover and integrate the drivers of vegetation cover at various spa-tial scales to obtain a good understanding of the spatial patterns and processes (Cai 2009).More environmental and socio-economic variables will be employed in regres-sion models to provide a more comprehensive basis for policymaking.In addition,scale matching between data sources also needs further study.6.Conclusions
In this study,we analysed the potential of a sound method,GWR,to accurately explore the relationships between NDVI and environmental factors.We have shown that GWR was successfully employed to reveal the spatial variation in the relation-ships between NDVI and environmental variables.GWR improved the model ability to explain the local situation of NDVI.The GWR model also represented improve-ment over the traditional regression models such as OLS in model performance and
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spatial autocorrelation.Thus,the relationships between NDVI and environmental factors were better understood when using the local regression method.
The spatially non-stationary relationships between NDVI and environmental variables were scale-dependent.The non-stationarity of spatial relationships at multi-scales and the appropriate bandwidth of the GWR models were identi?ed by scaling the bandwidth of GWR model.
Acknowledgements
The research is supported by the National Natural Science Foundation of China (40871047).The authors are grateful to the anonymous reviewers for offering valuable suggestions to improve the manuscript.
References
A KAIKE ,H.,1973,Information theory and an extension of the maximum likelihood princi-ple.In Second International Symposium on Inference Theory ,B.N.Petrov and F .Csaki (Eds.),pp.267–281(Budapest:Akademiai Kiado).
B REUSCH ,T.S.and P AGAN ,A.R.,1979,A simple test for heteroscedasticity and random
coef?cient variation.Econometrica ,47,pp.1287–1294.
B RUNSDON ,C.,F OTHERINGHAM ,A.S.and
C HARLTON ,M.,1998,Geographically weighted
regression –modeling spatial non-stationarity.The Statistician ,47,pp.431–443.
C AI ,Y .L.,2009,Spatial scales integration of land system change:a case study design on
Guizhou Karst Plateau.Advances in Earth Science ,24,pp.1301–1308.
C HARLTON ,M.,F OTHERINGHAM , A.S.and B RUNSDON , C.,2003,GWR 3:Software for
geographically weighted regression .Spatial Analysis Research Group,Department of Geography,University of Newcastle upon Tyne,Newcastle,England.
C HEN ,P .Y .,S RINIVASAN ,R.,F EDOSEJEVS ,G.and K INIRY ,J.R.,2003,Evaluating different
NDVI composite techniques using NOAA-14A VHRR data.International Journal of Remote Sensing ,24,pp.3403–3412.
C LIFFOR
D ,P .,R ICHARDSON ,S.and H EMON ,D.,1989,Assessing the signi?cance of the
correlation between two spatial processes.Biometrics ,45,pp.123–134.
C OHEN ,W .B.,M AIERSPERGER ,T.K.,G OWER ,S.T.and T URNER ,D.P .,2003,An improved strat-egy for regression of biophysical variable and Landsat ETM +data.Remote Sensing of Environment ,84,pp.561–571.
D IBELLA ,C.M.,R EBELLA ,C.M.and P ARUELO ,J.M.,2000,Evapotranspiration estimates using
NOAA-A VHRR imagery in the Pampa region of Argentina.International Journal of Remote Sensing ,21,pp.791–797.
F OODY ,G.M.,2003,Geographical weighting as a further re?nement to regression modeling:
an example focused on the NDVI-rainfall relationship.Remote Sensing of Environment ,88,pp.283–293.
F OODY ,G.M.,2004,Spatial nonstationary and scale-dependency in the relationship between
species richness and environmental determinants for the sub-Saharan endemic avifauna.Global Ecology &Biogeography ,13,pp.315–320.
F OTHERINGHAM ,A.S.,B RUNDSON ,C.and C HARLTON ,M.,2002,Geographically Weighted
Regression:The Analysis of Spatially Varying Relationships (Chichester:Wiley).
F OTHERINGHAM ,A.S.,C HARLTON ,M.and B RUNDSON ,C.,1996,The geography of parameter
space:an investigation of spatial non-stationarity.International Journal of Geographical Information Science ,10,pp.605–627.
G AO ,J.B.and L I ,S.C.,2011,Detecting spatially non-stationary and scale-dependent relation-ships between urban landscape fragmentation and related factors using geographically weighted regression.Applied Geography ,31,pp.292–302.
D o w n l o a d e d b y [I n s t i t u t e o f B o t a n y ] a t 19:15 28 J u l y 2014
Spatially non-stationary and scale-dependent relationships 2127
G AO ,J.B.,L I ,S.C.and Z HAO ,Z.Q.,2010,Validating the demarcation of eco-geographical
regions:a geostatistical application.Environmental Earth Sciences ,59,pp.1327–1336.
G RIFFITH ,D.A.,2003,Spatial Autocorrelation and Spatial Filtering (Berlin:Springer-Verlag).G ROENEVELD ,D.P .and B AUGH ,W .M.,2007,Correcting satellite data to detect vegetation signal
for eco-hydrologic analyses.Journal of Hydrology ,344,pp.135–145.
H AMILTON ,L.C.,1992,Regression with Graphics:A Second Course in Applied Statistics
(Belmont:Duxbury Press).
H ERRMANN ,S.,A NYAMBA ,A.and T UCKER ,C.,2005,Recent trends in vegetation dynamics in
the African Sahel and their relationship to climate.Global Environmental Change ,15,pp.394–404.
H IJMANS ,R.J.,C AMERON ,S.E.,P ARRA ,J.L.,J ONES ,P .G.and J ARVIS ,A.,2005,Very high
resolution interpolated climate surfaces for global land areas.International Journal of Climatology ,25,pp.1965–1978.
H OLBEN , B.N.,1986,Characteristics of maximum-value composite images for temporal
A VHRR data.International Journal of Remote Sensing ,7,pp.1435–1445.
H OLDRIDGE ,L.R.,1947,Determination of world plant formations from simple climate data.
Science ,105,pp.367–368.
H UANG ,Q.H.and C AI ,Y .L.,2006,Assessment of Karst rocky deserti?cation using the radial
basis function network model and GIS technique:a case study of Guizhou Province,China.Environmental Geology ,49,pp.1173–1179.
H UANG ,Q.H.,C AI ,Y .L.and P ENG ,J.,2007,Modeling the spatial pattern of farmland using
GIS and multiple logistic regression:a case study of Maotiao River Basin,Guizhou Province,China.Environmental Modeling &Assessment ,12,pp.55–61.
H URVICH ,C.M.and T SAI ,C.L.,1989,Regression and time series model selection in small
samples.Biometrika ,76,pp.297–307.
I RVIN ,B.J.,V ENTURA ,S.J.and S LATER ,B.K.,1997,Fuzzy and isodata classi?cation of land-form elements from digital terrain data in Pleasant Valley,Wisconsin.Geoderma ,77,pp.137–154.
K EITT ,T.H.,B J RNSTAD ,O.N.,D IXON ,P .M.and C ITRON P OUSTY ,S.,2002,Accounting
for spatial pattern when modeling organism-environment interactions.Ecography ,25,pp.616–625.
K OENKER ,R.,1981,A note on studentizing a test for heteroscedasticity.Journal of
Econometrics ,17,pp.107–112.
L AFARY , E.W .,G ATRELL ,J.D.and J ENSEN ,R.R.,2008,People,pixels and weights in
Vanderburgh County,Indiana:toward a new urban geography of human-environment interactions.Geocarto International ,23,pp.53–66.
L ASAPONARA ,R.,2006,On the use of principal component analysis (PCA)for evaluating
interannual vegetation anomalies from SPOT /VEGETATION NDVI temporal series.Ecological Modelling ,194,pp.429–434.
L EGENDRE ,P .,1993,Spatial autocorrelation:trouble or new paradigm?Ecology ,74,
pp.1659–1673.
L EUNG ,Y .,M EI ,C.L.and Z HANG ,W .X.,2000,Statistical tests for spatial nonstationarity based
on geographically weighted regression model.Environment and Planning A ,32,pp.9–32.
L I ,S.C.,G AO ,W .M.,Z HOU ,Q.F .and L IU ,F .Y .,2006,Multi-scale spatial analysis on
NDVI and topographical factors using wavelet transform.Acta Ecologica Sinica ,26,pp.4198–4203.
L I ,S.C.,Z HAO ,Z.Q.,X IE ,M.M.and W ANG ,Y .L.,2010,Investigating spatial non-stationary
and scale-dependent relationships between urban surface temperature and environ-mental factors using geographically weighted regression.Environmental Modelling &Software ,25,pp.1789–1800.
M ASELLI ,F .and C HIESI ,M.,2006,Integration of multi-source NDVI data for the estima-tion of Mediterranean forest productivity.International Journal of Remote Sensing ,27,pp.55–72.
D o w n l o a d e d b y [I n s t i t u t e o f B o t a n y ] a t 19:15 28 J u l y 2014
2128J.Gao et al .
M ASSEY J R .,F .J.,1951,The Kolmogorov-Smirnov test of goodness of ?t.Journal of the
American Statistical Association ,46,pp.68–78.
M EI ,C.L.,W ANG ,N.and Z HANG ,W .X.,2006,Testing the importance of the explanatory vari-ables in a mixed geographically weighted regression model.Environmental Planning A ,38,pp.587–598.
O NEMA ,J.K.and T AIGBENU ,A.,2009,NDVI-rainfall relationship in the Semliki watershed of
the equatorial Nile.Physics and Chemistry of the Earth ,34,pp.711–721.
O SBORNE ,P .E.,F OODY ,G.M.and S UáREZ -S EOANE ,S.,2007,Non-stationarity and local
approaches to modeling the distributions of wildlife.Diversity and Distributions ,13,pp.313–323.
P IAO ,S.L.,M OHAMMAT ,A.,F ANG ,J.Y .,C AI ,Q.and F ENG ,J.M.,2006,NDVI-based increase
in growth of temperate grasslands and its responses to climate change in China.Global Environmental Change ,16,pp.340–348.
P OST ,W .M.,E MANUEL ,W .R.,Z INKE ,P .J.and S TANGENBERGER ,A.G.,1982,Soil carbon pools
and world life zones.Nature ,298,pp.156–159.
P ROPASTIN ,P .,2009,Spatial non-stationarity and scale-dependency of prediction accuracy in
the remote estimation of LAI over a tropical rainforest in Sulawesi,Indonesia.Remote Sensing of Environment ,113,pp.2236–2242.
P ROPASTIN ,P .,K APPAS ,M.and E RASMI ,S.,2008,Application of geographically weighted
regression to investigate the impact of scale on prediction uncertainty by modeling relationships between vegetation and climate.International Journal of Spatial Data Infrastructure ,3,pp.73–94.
R AYNOLDS ,M.K.,C OMISO ,J.C.,W ALKER ,D.A.and V ERBYLA ,D.,2008,Relationship between
satellite-derived land surface temperatures,arctic vegetation types,and NDVI.Remote Sensing of Environment ,112,pp.1884–1894.
S HESKIN ,D.J.,2007,Handbook of Parametric and Nonparametric Statistical Procedures:Fourth
Edition (Boca Raton,FL:Chapman &Hall /CRC).
T IEFELSDORF ,M.,2000,Modelling Spatial Processes:The Identi?cation and Analysis of Spatial
Relationships in Regression Residuals by Means of Moran’s I (Berlin:Springer-Verlag).
T U ,J.and X IA ,Z.G.,2008,Examining spatially varying relationships between land use and
water quality using geographically weighted regression I:model design and evaluation.Science of the Total Environment ,407,pp.358–378.
W ANG ,S.J.,L I ,R.L.,S UN ,C.X.,Z HANG ,D.F .,L I ,F .Q.,Z HOU ,D.Q.,X IONG ,K.N.and Z HOU ,
Z.F .,2004,How types of carbonate rock assemblages constrain the distribution of Karst rocky deserti?ed land in Guizhou Province,PR China:phenomena and https://www.doczj.com/doc/c912685622.html,nd Degradation &Development ,15,pp.123–131.
W ANG ,Q.,N I ,J.and T ENHUNEN ,J.,2005b,Application of a geographically weighted regression
analysis to estimate net primary production of Chinese forest ecosystem.Global Ecology and Biogeography ,14,pp.379–393.
W ANG ,Q.,A DIKU ,S.,T ENHUNEN ,J.and G RANIER ,A.,2005a,On the relationship of NDVI
with leaf area index in a deciduous forest site.Remote Sensing of Environment ,94,pp.244–255.
X IAO ,J.F .and M OODY ,A.,2004,Trends in vegetation activity and their climatic correlates:
China 1982to 1998.International Journal of Remote Sensing ,25,pp.5669–5689.
X IONG ,K.N.,L I ,P .and Z HOU ,Z.F .,2002,Typical Study on Karst Rock-Deserti?cation Using
Remote Sensing and GIS—Taking Guizhou Province for Example (Beijing:Geological Publishing House).
Y ANG ,X.,W ANG ,M.X.,H UANG ,Y .and W ANG ,Y .S.,2002,A one-compartment model to study
soil carbon decomposition rate at equilibrium situation.Ecological Modelling ,151,pp.63–73.
Z HANG ,L.J.,B I ,H.Q.,C HENG ,P .F .and D AVIS ,C.J.,2004,Modeling spatial variation in the
tree diameter-height relationships.Forest Ecology and Management ,189,pp.317–329.
D o w n l o a d e d b y [I n s t i t u t e o f B o t a n y ] a t 19:15 28 J u l y 2014
Spatially non-stationary and scale-dependent relationships 2129
Z HANG ,L.J.,G OVE ,J.H.and H EATH ,L.S.,2005,Spatial residual analysis of six modeling
techniques.Ecological Modelling ,186,pp.154–177.
Z HENG ,Y .F .,N IU ,L.Y .,W U ,R.J.,W U ,Z.P .,L UO ,X.J.and C AI ,Z.Y .,2009,Vegetation cover
change in Guizhou of Southwest China in 1982–2003in response to climate change.Chinese Journal of Ecology ,28,pp.177–1778.
D o w n l o a d e d b y [I n s t i t u t e o f B o t a n y ] a t 19:15 28 J u l y 2014