The SOI expresses the isotopic signature of soil and xylem water
(δx ) relative to the seasonal cycle of
precipitation, using amount-weighted annual precipitation
(δ annP), summer precipitation
(δ summerP, defined as the peak of a fitted sine
curve representing seasonal cycles of precipitation), and winter
precipitation (δ winterP, defined as the trough of
the same fitted sine curve). An SOI close to -1.0 indicates that the
water mostly originates from winter precipitation, whereas a SOI close
to 1.0 indicates that the water mostly originates from summer
precipitation.
To analyze how much of xylem water is composed of recent precipitation
(from the time between two xylem sampling dates) we calculated the
fraction of new water (Fnew ) as suggested in
Kirchner (2019):
\begin{equation}
F_{\text{new}}=\frac{\text{δxyl}_{i}-\ \text{δxyl}_{i-1}\ }{\delta P-\ \text{δxyl}_{i-1}}\nonumber \\
\end{equation}Whereas δxyli is the xylem water signature of the
most recent sampling date, δxyli-1 is the xylem
water signature of the previous sampling date, and δP is the
volume-weighted average of precipitation between the two sampling dates
(typically three-week intervals).
To assess the fractions of xylem water for each sampling date
(Xyl(t=2) ) consisting of bulk soil waters and
recent precipitation, we used a simple mixing model that calculates the
relative contribution of two different sources (f1 andf2 ):