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 ):