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8-day
irregular
8-day
8-da
- data used.
of STARFM
sentation for
interpolated
als.
acted for the
centage cover
provides a
tation cover,
s (Armston, et
' cover in the
n a per pixel
r the common
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1 significance
regressed are
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lated residual
he assumption
error in the
coefficients is
ted lag model
bstituted by a
ation. To this
ponents were
nomalies were
distributed lag
anomalies as
r estimation:
NDI =a+bRE+J,RE +... +b RF_„+&
where t is the time, a is the, b; are the regression coefficients at
lag i.
In a second step an autoregressive moving average (ARMA)
model is fitted to the error term & to assess the temporal
autocorrelation structure of the series. The next step is to filter
the original time-series (NDVI and rainfall anomalies) using the
identified ARMA-model. The last step is to repeat the OLS-
regression of the anomalies. This results in a distributed lag
model in which the residuals are "white noise" and to an
unbiased assessment of the significance of the regression
coefficients (Udelhoven et al., 2009).
A Durbin-Watson test was applied to detect the presence of a
remaining autocorrelation in the time series.
3. RESULTS
A time series plot of rainfall and NDVI in a forested area (open
woodland) displays the seasonality within the NDVI data.
Figure 3: Time series of rainfall (blue line) and NDVI (black
line) for a location in an open woodland.
3.1 Simple lagged correlation
A smoothing filer with a window length of 5 was applied to
both time series. The maximum correlation at the respective lag
Was reported on a per pixel basis (Figure 4).
Correlation Lag “(orange=0, yellow=1,
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B8, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
red=2, white =4, black=neg.)
Figure 4: Lagged correlation between rainfall and NDVI.
The response times lag times appear to have very little spatial
pattern with generally quick vegetation response with a lag of 0.
In the forested areas appear a lag of 1 and a lag of 2 along the
riparian areas.
3.2 Distributed lag model
Raster layers of the 5% significance level demonstrate the
difference in the response times in the different land types. In
this 14 day aggregation it appears that no significant response
of the NDVI exists after a lag period of 4 (56 days). In the
grasslands or open woodlands with low tree cover appears a
significant response at lag times of 0 to 3. The distinct pattern
visible in Figure 3 between forest and grasslands are less
pronounced, but visible in Figure 5 (TO to T3).
eo : Á
i not sig.
eese
E sig. (5%, neg. irends)
Figure 5: NDVI vs Rainfall anomalies significance (t-test) at the
5% significance level of the regression coefficients at times TO
to T5.
3.3 Test for autocorrelation
A simple test for temporal autocorrelation in the residual is the
Durbin-Watson (DW) statistics. The outcome of this test is
shown in Figure 6. A series without serial no autocorrelation
results in a DW-value of 2.0. Smaller values (0 in the
minimum) indicate positive autocorrelation whereas higher
values (4.0 in the maximum) indicate negative autocorrelation.
Figure 6 demonstrates that the residuals of the distributed lag
model are indeed white noise using GLS-parameter estimation,
except for singular, scattered pixels.