Dec., 2010
Journal of Resources and Ecology
J. Resour. Ecol. 2010 1(4) 361-367
Vol.1 No.4
Article
DOI:10.3969/j.issn.1674-764x.2010.04.009
www.jorae.cn
Scale-dependent Spatial Relationships between NDVI
and Abiotic Factors
LI Shuangcheng*, YANG Zhuoxiang and GAO Yang
College of Urban and Environmental Sciences, Peking University; The Key Laboratory for Earth Surface Processes, Ministry of Education, Beijing 100871,
China
Abstract: Wavelet transform demonstrates that abiotic factors’ impact change with spatial scale, confirming
a scale-dependent relationship between NDVI and factors that influence it. To elaborate these scale
effects, NDVI transect data and abiotic variables—climatic and topographic—at the 32.5 degree north
latitude on the Qinghai-Tibet Plateau in China, were analyzed at different spatial scales by using wavelet
transform. The results show that climatic variables such as precipitation and temperature are not dominant
factors of NDVI patterns at the less than 80 km scale, while significant wavelet coherency is observed at
the more than 80 km scale in some ecoregions. As a differentiating factor, elevation affects NDVI patterns
only at the local level in longitudinal range-gorge region at certain specific scales. Wavelet transform is an
alternative approach to examining multiscale relationships between NDVI and abiotic factors.
Key words: NDVI; abiotic factors; scale-dependence; wavelet transform; Qinghai-Tibet Plateau
1 Introduction
Terrestrial ecosystems exhibit spatial variability at scales
ranging from centimeters to kilometers. Spatial complexity
results from both underlying patterns of the physical
environment and complex biotic interactions (Logan et al.
1998; Nelsona et al. 2007; Crawford 2008). Ecological
patterns and processes are dependent on the spatial scale at
which they are investigated, and a process at any particular
scale may be influenced by factors at other scales (Allen
and Starr 1982; Menge and Olson 1990; Levin 1992;
Bunnell and Huggard 1999; Bugmann et al. 2000; Elkie
and Rempel 2000; Thompson et al. 2000; Whittaker et al.
2001; Schneider 2001; Blackburn and Gaston 2002; Chase
and Leibold 2002; Urban 2005; Tylianakis et al. 2006;
Field et al. 2008; Parviainen et al. 2010). Developing a
full understanding of the spatial scales at which abiotic
conditions impinge on ecological patterns and processes
therefore demands a multiscale approach (Wiens 1989).
Concerns about the detection of scale-dependent
phenomena and modeling ecological processes across
scales have increased significantly in recent years.
Bian and Walsh et al. (1993) examined the effects of
spatial scale on the relationships between vegetation
biomass and three topographic variables with regression,
semivariance and fractal analyses, and then identified
a characteristic length of variables interaction. Moody
et al. (1995) investigated the scale-dependence of the
relationship between NDVI variability and variability in
land cover for a complex mountainous landscape. Walsh
et al. (1997) further conducted an elaborate research to
develop the hypotheses that the relationships between
NDVI, cover types, and elevation are scale-dependent.
Foody (2004) used geographical weighted regression to
study the relationship between species richness and a set
of perceived environmental determinants, comprising
temperature, precipitation, and normalized difference
vegetation index (NDVI), and confirmed the existence
of scale-dependent relationships between species
richness and abiotic factors. By introducing waveletcoefficient regression, Keitt and Urban (2005) formalized
scale-specific relationships between vegetation and
environmental factors. Saunders et al. (2005) examined the
utility of three techniques (lacunarity, spectral, and wavelet
analyses) for detecting scales of pattern of ecological data
and concluded that the appropriate technique for assessing
scales of pattern depends on the type of data available, the
question being asked, and the detail of information desired.
Received: 2010-10-05 Accepted: 2010-11-12
Foundation: National Key Research Development Plan No. 2010CB951704 and National Natural Science Foundation of China No. 40771001
* Corresponding author: LI Shuangcheng. Email: [email protected].
362
The main goal of this research is to further examine the
large-scale spatial dependence of statistical relationships
between a group of selected abiotic factors and the spatial
structure of NDVI at multiple spatial scales by using
wavelet transform. We seek to address: (i) the effective
range of spatial scales within which NDVI and abiotic
variables were spatially dependent; (ii) optimum spatial
scales for representing the relationships between abiotic
factors and NDVI; and (iii) regional differentiation of
spatial dependence of these relationships in different
ecoregions of the study area.
This paper is organized as follows: the methodology
and data, especially the theoretical background and
algorithm of wavelet transform technique as applied to
multiscale analysis are explained in section 2, including
the introduction of Morlet wavelet and wavelet coherence.
In section 3, the geographical features of the study area
are briefly described. In section 4, we present results of the
investigation of spatial dependent relationships between
NDVI and abiotic factors. Section 5 is conclusions and
discussions.
2 Methods and Data
2.1 Wavelet transform
Wavelet transform (WT) is a merited technique for
analyzing localized variations of power within a time
series. Compared with Fourier analysis, the main
advantage of wavelet transform is the use of varying
window size, being wide for low frequencies and narrow
for high frequencies, leading to an optimal time-frequency
resolution in all the frequency ranges. Continuous
wavelet transform (CWT) can decompose a signal into
a set of finite basis functions, so it can uncover transient
characteristics in the signal. Wavelet coefficients Wx (a,τ )
are produced through the convolution of a mother wavelet
function ψ (t ) with the analyzed signal x (t ), as a function
of both time t and frequency (scale) a, it is:
where a and b denote the dilation (scale factor) and
translation (time shift parameter) respectively. ψ is
called a mother wavelet, a smooth and quickly vanishing
oscillating function. W are wavelet coefficients, which are
a function of scale and position. The symbol * indicates
the complex conjugate. By adjusting the scale a, a series
of different frequency components in the signal can be
obtained.
The Morlet wavelet is a symmetric and periodic
wavelet that results from the superposition of a sine and a
Gaussian. In complex notation this can be written as:
Journal of Resources and Ecology Vol.1 No.4, 2010
where π-1/4 is a normalization term, η is the dimensionless
time parameter, ω 0 is the dimensionless frequency
parameter (taken as ω0=6 for this work), and ω is the
frequency parameter. Because of its smoothness and
periodicity, Morlet wavelet is a good choice for data that
is varying continuously in time and is periodic or quasiperiodic. Another advantage of Morlet wavelet transform
(MWT) is that the phase information of signal can be
obtained; therefore this tool can also be used to study the
phase synchronization between two signals. A graph of this
function is presented in Fig.1, in the left, the real part, and
on the right, the imaginary part.
2.2 Wavelet coherency
Wavelet coherency analysis is a powerful tool to measure
intensity of the covariance of two series in time-frequency
space that provides a perfect view of linear and nonlinear
correlation between the two time series. Wavelet coherence
is defined as correlation coefficient between the wavelet
transform coefficients representing two time series in timefrequency domain (Popinski and Kosek 1994). Wavelet
coherency is computed using the wavelet power spectrum
of the two time series. To measure wavelet coherency,
following Torrence and Webster (1998) we define it as
“ < > “ indicates smoothing in both time and frequency,
W x(a, b) is the wavelet transform of series x(t), Wy(a,
b) is the wavelet transform of y(t), and Wxy(a, b) is the
cross-wavelet transform. The smoothing is performed,
as in Fourier spectral approaches, by a convolution
with a constant-length window function both in the
time and frequency directions. Detailed information on
the smoothing procedure can be found in Torrence and
Webster (1999).
Wavelet coherence ranges from 0 to 1, with a value of 1
indicating maximum coherency. It gives a measure of the
dependency and synchrony between the two time series
as a function of both scale (or period) and time. Wavelet
phase measures the phase difference between the complex
Fig. 1 Real (left) and imaginary (right) part of the Morlet
wavelet with ω0=6.
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LI Shuangcheng, et al.: Scale-dependent Spatial Relationships between NDVI and Abiotic Factors
wavelet transforms and indicates whether two time series
tend to oscillate simultaneously, rising and falling together
with the same period.
Wavelet coherence and significance levels for wavelet
power spectra were computed following the methods of
Grinsted et al. (2004). CWT has edge artifacts because a
wavelet is not completely localized in time. It is therefore
useful to introduce a Cone of Influence (COI), where
edge effects may become important because of the finite
duration of the time series. Here we take COI as the area in
which the wavelet power caused by a discontinuity at the
edge has dropped to e−2 of the value at the edge (Grinsted
et al. 2004).
We conducted all wavelet transforms using Matlab (Fig.
2).
2.3 Data and transect sampling
2.3.1 Data
For this study, we used 18 years (1982–2000, 1994
not used because of the sensor failure) NDVI monthly
data produced by the Global Inventory Monitoring and
Modeling Studies (GIMMS) group from measurements of
the advanced very high resolution radiometer (AVHRR)
onboard the NOAA 7, NOAA 9, NOAA 11, and NOAA
14 satellites. After data preprocessing for improving
navigation, sensor calibration, and atmospheric corrections,
we extracted spatial pattern of mean annual NDVI value
during 1982–2000 by using Calculator in ArcGIS (ESRI
Inc. 1999–2009).
For the period 1982–2000, we obtained monthly
meteorological data of 104 stations in the study area,
including air temperature, precipitation, maximum
temperature, minimum temperature, surface temperature,
and hours of sunshine, from the China Meteorological
Administration (CMA). Unlike the NDVI data that are
raster images, meteorological variables are point data.
After they were aggregated into mean annual values, all
meteorological factors were interpolated to create raster
data layers using Kriging method in ArcGIS, whose grid
size equals to that of NDVI.
Basic topographic data files of the study area are digital
elevation model (DEM) data, which were produced by the
National Geomatics Center of China at a scale of 1:250000.
The terrain attribute chosen to perform the analysis is
elevation, which is directly calculated using built-in
functions in ArcGIS.
To elaborate the spatial scale-dependent relationship
between NDVI and environmental variables, we
subsampled the NDVI and abiotic factors spaced at 5000m
intervals along the north 32.5 degree latitude by running
the Zonal Statistics function in Spatial Analyst of ArcGIS.
3 Study area
The Qinghai-Tibet Plateau, the largest geomorphologic
unit on the earth with an area of 2.5 million km 2 and
average 4500 m elevation above sea level, is an important
part of the global terrestrial ecosystem. From southeast to
northwest, four types of ecosystems can be identified on
the Plateau, namely, montane forest, alpine shrub/meadow,
alpine steppe, and alpine desert.
The transect along the 32.5 degree latitude runs across 4
ecoregions from the east to the west, i.e. western Sichuaneastern Tibet montane coniferous forest zone, GologNagqu high-cold shrub-meadow zone, Qiangtang highcold steppe zone, and Ngari montane desert-steppe and
desert zone (Zheng 1996). The mean values of NDVI and
abiotic factors of each ecoregion are listed in table 1.
4 Results
4.1 NDVI and precipitation
Visual inspection of wavelet coherency between NDVI
and precipitation reveals three scales of variation across
the transect: 0 to 40 km, 40 to 80 km, and >80 km (Fig.
2). For the less than 40 km scale, the wavelet coherency
is relatively small, especially in the 0–800 km part of the
transect, which crosses the western Sichuan-eastern Tibet
montane coniferous forest zone. The phase relationship
between NDVI and precipitation changes significantly at
the 1250 km location of the transect. In-phase relationship
appear at 0 to 1250 km of the transect, which corresponds
to the ecoregions of montane coniferous forest and highcold shrub-meadow, while anti-phase relationships are
observed at greater than1250 km locations in the transect,
where ecoregions are montane desert-steppe and desert.
For the 40 to 80 km scale, there are two high wavelet
coherency regions with the centre of 1250 km and 1500
Table 1 NDVI and abiotic factors of different ecoregion on the Qinghai-Tibet Plateau.
Eco-region*
I
II
III
IV
NDVI Annual temperature (℃) Annual precipitation (mm)
Mean
Min
Max
Mean
Min
Max
174
161
140
137
125
137
121
126
204
189
161
154
6.8
–0.1
–0.2
1.6
–1.0
–6.9
–7.3
0.2
15.2
5.6
8.4
4.2
Elevation (m)
Mean
Min
Max
Mean
Min
Max
252
331
32
33
676
555
234
73
1651
826
623
187
4112
4506
5023
4933
1219
3136
1890
3054
7213
6166
6836
7410
* I. western Sichuan-eastern Tibet montane coniferous forest zone, II. Golog-Nagqu high-cold shrub-meadow zone, III. Qiangtang high-cold steppe
zone, IV. Ngari montane desert-steppe and desert zone.
364
km respectively, and the former has in-phase relationship
while the latter has anti-phase relationship between NDVI
and precipitation. For the more than 80 km scale, regions
of high wavelet coherency are centered along the transect
at 200–500 km and 1700–1900 km locations with in-phase
relationships, which are located in the montane coniferous
forest region and shrub-meadow region, and characterized
by high elevation and rugged landform.
4.2 NDVI and temperature
Figure 4 shows the patterns of wavelet coherency between
the NDVI and the temperature series. For the less than
40 km scale, six wavelet coherency regions are observed
with the centers at 175 km, 780 km, 1175 km, 1280 km,
1750 km and 2000 km along the transect. The phase
relationship between NDVI and temperature also changes
around 1250 km, and shows in-phase relationship at the
less than 1250 km part and in anti-phase at the greater
than 1250 km part. For the 40–80 km scale, only two
dispersed regions with centers at 1300 km and 2100 km
have relatively high wavelet coherency values. For the
more than 80 scale, three significant wavelet coherency
regions are found along the transect. In the montane
coniferous forest ecoregion, a high coherency region spans
100 km and centered at 250 km of the transect, which
corresponds to the spatial scale of 100–200 km. The outof-phase relationship appears from 1000–1500 km in the
high-cold shrub-meadow ecoregion, which corresponds to
Fig. 2 Matlab toolbox window of Morlet wavelet transform. Journal of Resources and Ecology Vol.1 No.4, 2010
the spatial scale of 250–300 km. For the more than 400 km
scale, there is a significant coherency region, with in-phase
relationship that range from 600 km to 1350 km along the
transect.
4.3 NDVI and elevation
From Figure 5 we can see that the patterns of wavelet
coherency between NDVI and elevation are much simpler
than that between NDVI and climatic factors. For the less
than 40 km scale, only small scattered wavelet coherency
regions with centers at 450 km, 1200 km, and 1700 km
are shown. For the 40 to 80 km scale, there is a significant
wavelet coherency region with anti-phase relationship
between NDVI and elevation from 0 to 900 km along the
transect, which corresponds to the montane coniferous
forest ecoregion. There is another very significant
coherency region with in-phase relationship ranging from
1800 km to 1900 km along the transect, which is located in
the ecotone between Qiangtang high-cold steppe and Ngari
montane desert-steppe and desert zone, indicating that
elevation dominates the pattern of NDVI. For the more
than 80 km scale, a significant wavelet coherency region
with spans of 750 km from 0 to 750 km along the transect
is observed in the western Sichuan-eastern Tibet montane
coniferous forest ecoregion and transitional region between
montane coniferous forest and Plateau high-cold scrub
meadow, which are dominated by anti-phase relationship.
LI Shuangcheng, et al.: Scale-dependent Spatial Relationships between NDVI and Abiotic Factors
365
Fig. 3 Morlet squared wavelet coherence
between NDVI and precipitation along
the 32.5 degree north transect (the
values are coherency coefficient that
ranges from 0 to 1). The 5% significance
level against red noise is shown as a
thick contour, and the cone of influence
(COI) where edge effects might distort
the picture is shown with lighter shade.
The relative phase relationship is shown
as arrows. The direction of the arrows
in the coherence spectrum indicates the
phase between the two series involved:
horizontal right is 0° and corresponds to
an in-phase situation, horizontal left is
180° and corresponds to an anti-phase
situation, and both vertical up (90°) and
vertical down (270°) correspond to an
out-of-phase situation.
5. Conclusions and discussions
5.1 Conclusions
From the results of wavelet coherency analysis between
precipitation and NDVI, we can conclude that precipitation
is not the dominant factor of NDVI at the less than 40 km
scale, but it controls the spatial pattern of NDVI at the
more than 80 km scale, especially at the scale of 200 km.
The phase relationships between NDVI and precipitation
varies in different eco-geographic regions at the less than
80 km scale, and it shows an in-phase relationship in the
forest and scrub regions and anti-phase relationship in the
high-cold steppe, desert and semi-desert regions. For the
more than 80 km scale, phase relationship shows as inphase.
Consistent with the coherency between NDVI and
precipitation, temperature affects the patterns of NDVI
insignificantly at the less than 80 km scale but significantly
at the more than 80 km scale, and this is observed along
almost the entire transect. Again, phase conversion also
occurs around the 1250 km location of the transect at
the less than 80 km scale, and in-phase dominates the
relationship between NDVI and temperature at this scale.
The topographic factor, elevation, is not a global
variable that dominates NDVI pattern along the whole
2300 km sample transect. The significant NDVI-elevation
wavelet coherency regions cannot be found at the less
than 25 km scale, indicating that elevation-related NDVI
pattern does not exist below this scale. Elevation affects
NDVI pattern at the 25 km to 600 km scale in this study,
and significant elevation-NDVI coherency is only localized
in regions with high variations of relief, especially in
Fig. 4 Morlet squared wavelet
coherence between NDVI and
temperature along the transect (all
other parameters are the same as
described in the caption of Fig. 3).
366
Journal of Resources and Ecology Vol.1 No.4, 2010
Fig. 5 Morlet Squared wavelet
coherence between NDVI and elevation
along the transect (all other parameters
are the same as described in the
caption of Fig. 3).
longitudinal range-gorge region, i.e., along the 0–1000 km
part of the transect.
In conclusion, climatic variables such as precipitation
and temperature are not dominant factors of NDVI patterns
at the less than 80 km scale. Moreover, phase relationships
often reverse around the 1250 km location along the
transect. At the more than 80 km scale, the significant
wavelet coherency regions appear in some ecoregions
along the transect, indicating that macro-patterns of NDVI
are correlated with climatic factors. Unlike the climatic
variables, the topographic factor, elevation, only affects
NDVI pattern in some ecoregions and at a specific range
of scales. Elevation has the most prominent effect on the
variation of NDVI in longitudinal range-gorge zone with
high variations of relief and surface fragmentation.
5.2 Discussions
By multiscale analysis on the transect data using wavelet
transform, the research confirms that there is a spatial
scale-dependent relationship between NDVI and climatic
factors, which changes with different eco-geographical
regions. The scale-dependent phenomena suggest that
we should be more prudent when predicting or scaling
up / scaling down only using single-scale regression
relationship.
Besides, multiscale examination of the interaction of
NDVI and climatic factors is helpful for ascertaining
the effective scale of environmental factor’s impacts on
ecosystem, which is useful for prediction and ecological
regionalization.
Acknowledgements
This research was funded by a grant from the National Key Research
Development Plan (grant no. 2010CB951704) and the National
Natural Science Foundation of China (NSFC 40771001). The
authors thank anonymous reviewers for their helpful comments.
References
Allen T F H and T B Starr. 1982. Hierarchy: perspectives for ecological
complexity. Chicago: The University of Chicago Press, 310.
Bian L and S J Walsh. 1993. Scale dependencies of vegetation and topography
in a mountainous environment of Montana. The Professional Geographer.
45:1–1.
Blackburn T M and K J Gaston. 2002. Scale in macroecology. Global Ecol.
Biogeog. 11:185–189.
Bugmann H, M Lindner, P Lasch, M Flechsig, B Ebert and W Cramer. 2000.
Scaling issues in forest succession modelling. Climatic Change, 44:265–
289.
Bunnell F L and D J Huggard. 1999. Biodiversity across spatial and temporal
scales: problems and opportunities. Forest Ecology and Management,
115:113–126.
Chase J M and M A Leibold. 2002. Spatial scale dictates the productivitybiodiversity relationship. Nature, 416:427–430.
Crawford J. 2008. Multi-scale investigations of alpine vascular plant species
in the San Juan Mountains of Colorado, USA GLORIA target region.
Scientifica Acta, 2(2):65– 69.
Elkie P C and R S Rempel. 2000. Detecting scales of pattern in boreal forest
landscapes. Forest Ecology and Management, 147:253–261.
Field R, et al. 2008. Spatial species-richness gradients across scales: A metaanalysis. Journal of Biogeography. doi:10.1111/j.1365-2699.2008.01963.x
Foody G M. 2004. Spatial nonstationarity and scale-dependency in the
relationship between species richness and environmental determinants for
the sub-Saharan endemic avifauna. Global Ecology and Biogeography, 13:
315–320.
Grinsted A, J C Moore and S Jevrejeva. 2004. Application of cross wavelet
transform and wavelet coherence to geophysical time series. Nonlinear
Processes in Geophysics, 11: 561–566.
Keitt T H and D L Urban. 2005. Scale-specific inferences using wavelets.
Ecology, 86:2497–2504.
Levin S A. 1992. The problem of pattern and scale in ecology. Ecology,
73:1943–1967.
Logan J A, P White, B J Bentz and J A Powell. 1998. Model analysis of spatial
patterns in mountain pine beetle outbreaks. Theoretical Population Biology,
53: 236–255.
Menge B A and A MOlson. 1990. Role of scale and environmental factors in
regulation of community structure. Trends Ecol. Evol., 5:52–57.
Moody A, S J Walsh, T R Allen and D G Brwon. 1995. Scaling properties of
NDVI and their relationship to land-cover spatial variability. Proc. 15th Int.
Geosci. and Remote Sens. Symp., Firenze, Italy, 10–14 July 1995, vol. 3,
pp. 1962–1964.
Nelsona A, T Oberthrb, S Cookb. 2007. Multi-scale correlations between
topography and vegetation in a hillside catchment of Honduras.
International Journal of Geographical Information Science, 21(2): 145–
LI Shuangcheng, et al.: Scale-dependent Spatial Relationships between NDVI and Abiotic Factors
174.
Parviainen M, M Luoto, R K Heikkinen. 2010. NDVI-based productivity and
heterogeneity as indicators of plant-species richness in boreal landscape.
Boreal Environmental Research, 15:301–318.
Popinski W and W Kosek . 1994. Wavelet transform and its application
for short period earth rotation a analysis. Artificial Satellites, Planetary
Geodesy, 29(2):75–86.
Saunders S C, Chen J, T D Drummer, E J Gustafson and K D Brosofske. 2005.
Identifying scales of pattern in ecological data: A comparison of lacunarity,
spectral and wavelet analysis. Ecological Complexity, 2:87–105
Schneider D C. 2001.The rise of the concept of scale in ecology. Bioscience,
51:545–553.
Thompson F R, S K Robinson, T M Donovan, J R Faaborg, D R Whitehead
and D R Larsen. 2000. Biogeographic, landscape, and local factors affecting
cowbird abundance and host parasitism levels. In: J. N. M. Smith J N M,
T L Cook, S I Rothstein, S K Robinson and S G Sealy (eds.). Ecology and
Management of Cowbirds and Their Hosts. Austin, TX: University of Texas
Press, 271–279.
Torrence C and P J Webster. 1999. Interdecadal changes in the ENSOMonsoon system. J. Climate, 12: 2679–2690.
367
Torrence C and P J Webster. 1998. A practical guide to wavelet analysis.
Bulletin of the American Meteorological Society, 79(1): 61–78
Tylianakis J M, A-M Klein, T Lozada and T Tscharntke. 2006. Spatial scale
of observation affects α, β and γ diversity of cavity-nesting bees and wasps
across a tropical land-use gradient. Journal of Biogeography, 33:p1295–
1304.
Urban D L. 2005. Modeling ecological processes across scales. Ecology,
86:1996–2006.
Walsh S J, A Moody, T R Allen and D G Brown. 1997. Scale dependence of
NDVI and its relationship to mountainous terrain. In: Quattrochi D A and M
F Goodchild (eds.). Scale in Remote Sensing and GIS, Lewis Publishers,
27–55.
Whittaker R J, K J Willis and R Field. 2001. Scale and species richness:
towards a general, hierarchical theory of species diversity. Journal of
Biogeography, 28: 453–470.
Wiens J A. 1989. Spatial scaling in ecology. Functional Ecology, 3:385-397.
Zheng D. 1996. The system of physio-geographical regions of the QinghaiXizang (Tibet) Plateau. Science in China (Series D), 39:410–417.
基于小波分析的NDVI与环境因子空间尺度依存关系研究
李双成，杨卓翔，高 阳
北京大学城市与环境学院 地表过程分析与模拟教育部重点实验室，北京 100871
摘要：本文通过多尺度分解途径分析了NDVI与环境因子如地形与气候之间的空间尺度依存关系。为了揭示两者关系的尺度
效应，选取青藏高原北纬32.5度作为研究样带，应用小波变换分析了不同空间尺度下的小波一致性和相位关系。研究结果表明：
在青藏高原小于80km空间尺度上，气候变量如降水和气温不是控制NDVI的主导因素；而大于这个尺度，在一些生态区可以发现
NDVI和气候因子具有显著的小波一致性。作为一个分异因子，海拔高度在青藏高原东南缘的纵向岭谷区对NDVI有着显著影响。
通过这一研究发现，小波变换是研究NDVI与影响因素之间多尺度关系的一个有力途径。
关键词：NDVI；环境因子；尺度依存；小波变换；青藏高原