Ecosystem level temporal stability
Temporal stability is a measure of the productivity change (increase or
decrease) during a climatic anomaly. We calculated resistance [Eq 1]
and resilience [Eq 2] following Isbell et al. (2015), for
each plot at each anomalous climatic event. We log-transformed the
values to smooth outliers with no clear ecological meaning, which also
avoided the denominator in the equations approaching zero.
The first step was to use normal SPEI events to calculate the average
productivity of each plot for each month in the time series (2000 to
2018). This average for normal periods was adopted as the productivity
baseline, \(\overset{\overline{}}{Y_{n}}\).
Resistance describes the change of NDVI related to its baseline:
\(\Omega=log\left(\frac{\overset{\overline{}}{Y_{n}}}{\left|Y_{e}\ -\ \overset{\overline{}}{Y_{n}}\right|}\right)\)[Eq 1]
Resilience describes the return ratio to baseline value:
\(=log\left(\left|\frac{Y_{e}\ -\ \overset{\overline{}}{Y_{n}}}{Y_{e+1}-\ \overset{\overline{}}{Y_{n+1}}}\right|\right)\)[Eq 2]
In these equations, \(Y_{e}\) e \(Y_{e+1}\) are, respectively, the
ecosystem productivity during a climatic anomaly, and after a climatic
anomaly. We calculated resilience only when an anomalous event with
productivity \(Y_{e}\) at a given month was followed by at least two
normal months. Note that the identified anomalous events may not be
synchronous across plots at the regional scale, but they were
synchronous at the spatial resolution of our 5 x 5 km grids.