Download Temporal Relationships between daily Precipitation and NDVI Time

Temporal Relationships between daily Precipitation
and NDVI Time Series in Mexico
René R. Colditz1*, Violeta L. Arriola Villanueva2, Inder Tecuapetla-Gómez3, Leticia Gómez Mendoza2
1
National Commission for the Knowledge and Use of Biodiversity (CONABIO), Geomatics Unit, Mexico City, Mexico
2
National Autonomous University of Mexico (UNAM), Institute of Geography, Mexico City, Mexico
3
Council for Science and Technology (CONACYT) – CONABIO, Geomatics Unit, Mexico City, Mexico
*
Tel: +52-55-50045020, [email protected]
Abstract—Most of the vegetation growth in Mexico shows
clear responses to the availability and abundance of surface
water which can almost exclusively be linked to rainfall. This
study employs four years of time series with daily precipitation
and modeled surface reflectance at a spatial resolution of 0.05°
which were analyzed for lag-dependent linear serial correlation.
Positive lags of, on average, 1 to 1.5 months between
precipitation and NDVI as a surrogate for vegetation growth as
well as statistically significant correlation coefficients (p<0.05)
were found for vegetated surfaces. Vegetation types which are
physiologically more dependent on precipitation for seasonal
vegetation growth show a shorter response time and stronger
relationship to precipitation than evergreen forests and
shrublands. The relationship with respect to precipitation
variations among several years remains inconclusive.
Keywords—Climate-vegetation
interaction;
NDVI; Anomalies; MODIS; Mexico;
Precipitation;
I. INTRODUCTION
The causes and effects in the relationship between
vegetation growth and their respective drivers has been studied
and modeled since many years from regional to global scale [14]. At regional scales, drivers of vegetation growth may be
divided into categories: static and dynamic. Static refers to
parameters that do not follow seasonal cycles, such as
parameters related to the terrain (elevation, slope and aspect)
and soil such as composition, permeability and pH. Even
though they are often key parameters for local presence of a
particular vegetation type, they do not dynamically interact
with the seasonal cycle of vegetation growth.
Dynamic, climatic variables such as radiation, temperature
and precipitation strongly determine ecosystem structure [5].
Even though these variables are intrinsically related to each
other, at broad scales one can be identified as the limiting
factor for many regions of the world – or the cause that
determines seasonal vegetation growth [6,7]. While
temperature is the determining variable that triggers vegetation
growth in moist mid-latitudinal regions (Europe, eastern
United States, and coastal China), radiation is considered a
limiting factor in the inner tropics when clouds obscure the
direct transmission of light to the ground, and water limits
plant growth in arid and semi-arid areas [4].
For almost all regions of Mexico, water is considered the
limiting factor as temperature and radiation is abundant all year
long. Exceptions are areas of very high elevation in the Sierra
Madre Oriental and Occidental (temperature and precipitation)
and the southern portions of the country (radiation and
precipitation) due to persistent cloud cover during wet season.
In this study we will regard precipitation as the primary source
for water, which is reasonable as rainfall determines the entire
hydrological regime of the country, leaving out all
management and runoff regulation, natural water retention by
soil and vegetation as well as memory effects.
We study the serial correlation between time series of daily
images of precipitation and vegetation response measured by
the NDVI. We hypothesize that for vegetated areas: 1) there is
a positive lag time between precipitation and NDVI, 2) there is
a significant correlation between precipitation and NDVI for
the optimal lag time, 3) there is a shorter response time and
stronger correlation for vegetation types which are
physiologically dependent on water availability and abundance,
and 4) with respect to anomalies there is a more rapid response
and stronger relationship between precipitation and vegetation
for years with lower precipitation.
II. DATA PREPARATION AND STUDY AREA
The most recent version (collection 6) of the combined
daily MODIS Terra/Aqua nadir BRDF-adjusted reflectance
product with 0.05 degrees in climate modeling grid
(MCD43C4) [8] was obtained for the years 2009 to 2012 from
archives of the United States Geological Survey. This product
models surface reflectance for the ninth day of a 16-day
observation period as it would have been obtained by nadirlooking instruments at local solar noon. Following we
calculated the Normalized Difference Vegetation Index
(NDVI), the difference between the near infrared and red
reflectance divided by their sum, excluding pixels with no
valid observations.
Precipitation data were obtained from the University of
California, Santa Barbara using version 2.0 of the Climate
Hazards Group InfraRed Precipitation with Station data
(CHIRPS) product. This data set combines satellite images at
0.05° with in-situ station data for daily precipitation estimates
between 50° North and South since 1981 [9].
IV. RESULTS AND ANALYSIS
A. Precipitation
Table I. depicts the mean of annual precipitation totals for
each vegetation type. It shows the expected pattern of highest
precipitation in cloud forests, and both evergreen forest classes
depict higher rainfall than their corresponding deciduous
counterparts. Shrublands, the largest class, which dominates
the entire semi-arid region in northern and central Mexico and
the peninsula of Baja California, shows lowest precipitation.
Irrigated agriculture depicts a surprisingly low precipitation
value which is due to the azonal location of some areas in the
semi-arid interior. On average, years 2009 and 2011 show
rainfall clearly below the annual mean (considering the four
years in this analysis) while 2010 is well above.
TABLE I. MEAN OF ANNUAL TOTALS OF PRECIPITATION (MM) FOR EACH
VEGETATION TYPE.
Figure 1. Spatial distribution of vegetation types analyzed in this study. The
legend shows the area percentage of each class.
For regional stratification and extraction of summary
statistics we employed the most recent (version 5) vegetation
and land use map from the National Institute for Statistics and
Geography of Mexico [10]. This map was aggregated to 10
vegetation types and one class for non-vegetated surfaces
(Figure 1) and subsequently reprojected and resampled to
match with MODIS and precipitation data. All data sets were
clipped to the extent of Mexico.
III. METHODS
Linear temporal cross-correlation using Pearson’s
correlation coefficient [11] has been employed for studying the
time delay between precipitation and vegetation response.
=
∑
∑
−| |−1
=0
−
−1
=0
+
−
2
∑
−1
=0
− ̅
− ̅
2
(1)
Precipitation (P) was shifted in time against NDVI (I). For
computational purposes equation 1 calculates the estimator for
means and variances globally while the covariance of the series
was trimmed to the corresponding lag-dependent samples. The
maximum range of lag was set to ±90, which corresponds to a
maximum shift of one quarter of the time series length and
allowing for temporal lags of ±3 months, which is considered
sufficient for vegetation response to precipitation [2,6]. Of
interest in this study is the lag of the highest serial correlation
between precipitation and NDVI,
=
(2)
and the value of the highest correlation,
= max
(3)
which was tested for its statistical significance using Studentstest.
=
√ −2
1−
2
(4)
Vegetation types
Evergreen tropical forest
Deciduous tropical forest
Evergreen temperate forest
Deciduous temperate forest
Cloud forest
Mixed forest
Shrubland
Grassland
Dryland agriculture
Irrigation agriculture
mean
2009
1,372
749
799
662
1,568
837
263
806
823
480
836
2010
1,852
906
852
764
2,170
999
316
1,042
1,017
570
1,049
2011
1,616
823
686
638
1,801
824
197
823
827
449
868
2012
1,614
831
794
702
1,730
856
267
884
902
513
909
mean
1,613
827
783
692
1,817
879
261
889
892
503
916
B. Lag time between precipitation and NDVI
Figure 2 depicts lag times between precipitation and NDVI
as a surrogate for vegetation dynamics for four years. For the
vast majority of the country there is the expected positive lag
time, thus vegetation growth responds to precipitation with a
lag of 20 to 40 days. Exceptions are mainly non-vegetated
areas which were excluded from statistical analysis in Table II,
irrigated agriculture which follows specific management cycles
often independent from rainfall and coastal as well as inland
wetlands such as Cuatro Cienegas in northern-central Mexico
with a hydrology which makes them at least less responsive to
precipitation. Figure 2 also depicts spatial-temporal
differences, foremost in arid northern-central and northeastern
Mexico in dry years 2011 and 2012.
Vegetation types such as deciduous forests and grasslands
show, on average, shorter response times, often within less
than one month, than evergreen forests and shrublands (one to
1.5 months). Shortest responses are depicted for dryland
agriculture, however with high variability among all years.
TABLE II. MEAN OF LAG TIME (DAYS) BETWEEN PRECIPITATION AND NDVI
FOR EACH VEGETATION TYPE.
Vegetation types
Evergreen tropical forest
Deciduous tropical forest
Evergreen temperate forest
Deciduous temperate forest
Cloud forest
Mixed forest
Shrubland
Grassland
Dryland agriculture
Irrigation agriculture
mean
2009
49.4
25.0
34.3
26.2
34.5
32.9
30.8
29.0
28.2
24.1
31.4
2010
55.2
27.8
30.5
26.0
38.4
31.6
27.8
24.5
23.9
24.1
31.0
2011
45.6
27.5
42.0
32.5
43.8
38.8
32.4
28.7
12.6
29.0
33.3
2012
55.3
25.2
41.9
30.6
44.0
37.2
32.0
27.7
23.1
29.6
34.6
mean
51.4
26.4
37.2
28.8
40.1
35.1
30.7
27.5
22.0
26.7
32.6
Figure 2. Lag time (days) between precipitation and NDVI for four years.
C. Values of highest correlation coefficients
Figure 3 illustrates that highest correlation coefficients,
reaching values of 0.5, can be found in mountainous regions in
western and central Mexico. While the vast majority of the
country depicts significant correlations, area with insignificant
correlations (p<0.05) correspond to surfaces with no apparent
vegetation or irrigated agriculture, which often correspond
spatially to locations with negative lags in Figure 2.
Table III indicates that correlations are generally stronger
for vegetation types that physiologically depend on
precipitation. Similar to previous analysis of lag-times, both
deciduous forest classes and grasslands depict higher
correlations than their corresponding evergreen counterparts
and shrublands. Dryland agriculture was expected to also show
higher correlations, at least higher than irrigation agriculture,
but the contrary was found which will require further spatial
analysis.
TABLE III. MEAN OF HIGHEST CORRELATION COEFFICIENT BETWEEN
PRECIPITATION AND NDVI FOR EACH VEGETATION TYPE.
Vegetation types
Evergreen tropical forest
Deciduous tropical forest
Evergreen temperate forest
Deciduous temperate forest
Cloud forest
Mixed forest
Shrubland
Grassland
Dryland agriculture
Irrigation agriculture
mean
2009
0.22
0.35
0.34
0.34
0.27
0.35
0.20
0.28
0.23
0.31
0.29
2010
0.27
0.40
0.35
0.37
0.33
0.38
0.21
0.30
0.27
0.37
0.33
2011
0.26
0.39
0.35
0.38
0.32
0.37
0.19
0.29
0.27
0.34
0.32
2012
0.22
0.37
0.34
0.37
0.28
0.35
0.21
0.27
0.23
0.31
0.30
mean
0.24
0.38
0.34
0.36
0.30
0.36
0.20
0.29
0.25
0.34
0.31
V. DISCUSSION AND CONCLUSIONS
This study shows positive temporal lags between
precipitation and NDVI, which we attribute to a cause-effect
relationship, thus vegetation growth is a response to the onset
of rainfall at the end of the dry season. Besides spatially
consistent patterns for all four years this study also shows that
most correlation coefficients are statistically significant. Pixels
with negative lag times or insignificant correlation coefficients
correspond to non-vegetated areas and vegetation that are
physiologically decoupled from natural precipitation cycles.
Semi-arid areas in the northern-central portion of the country
may show insufficient responses in NDVI time series during
ephemeral rain in drought periods (2011, 2012), which caused
a decoupling between precipitation and vegetation growth.
We also found the hypothesized relationship of shorter time
lags and higher correlation coefficients between precipitation
and NDVI for vegetation types which physiologically depend
on rainfall. A long, pronounced dry season has caused
senescence and leaf fall, and once the rain season starts the
vegetation response is rapid and pronounced. A secondary
effect may be that classes such as deciduous forests and
grasslands also depict a higher dynamic range in NDVI
seasonal profiles, which may ease and stabilize linear serial
correlation using Pearson. The fourth hypothesis, a stronger
and faster reaction of vegetation for years with little
precipitation, is not conclusive. Results of the four years
suggest, in fact, the contrary but differences are yet too small
and further analysis of a longer time series, rainfall anomaly
analysis, and potentially other variables will be needed.
Figure 3. Best correlation coefficient as a measure of strength between precipitation and NDVI. Not significant for p<0.05.
We also note that, besides linking vegetation growth
exclusively to precipitation, the current study is based on
several methodological simplifications that require further
investigation. Precipitation data are gridded estimates from
satellite observations and in-situ measurements that may not
reflect the true precipitation for each grid cell. Precipitation
time series are not only notoriously noisy but also have a fixed
base value (0) which affects variance estimates, both
complicating linear serial correlation analysis with Pearson’s
correlation coefficient. Spatial analysis in tables I, II, III suffers
from using the full domain of Mexico for each vegetation type
which results in very high variances, and further studies should
use improved regionalization analyzing vegetation types for
each ecoregion.
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