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.