\begin{equation}
X_{l} = \frac{X_{l} \, (\tau - {\Delta}t) + X_{s} \, {\Delta}t}{\tau}
\end{equation}

\noindent where X$_{l}$ is the long-term variable (e.g. monthly temperature/moisture availability), X$_{s}$ is the short-term variable (e.g. daily temperature/moisture availability), $\Delta$t is the time step, and $\tau$ is the time constant (in days) which varies according to the length of time represented by the long-term variable (equation (3) in Krinner et al., 2005). Values for tau set are based on calibration against observations CHECK.
