David did not define $T_i(t)$ before saying:

> Define the time-delayed cross-covariance function by:

> $$ C_{i,j}^{t}(-\tau) = \langle T_i(t) T_j(t - \tau) \rangle - \langle T_i(t) \rangle \langle T_j(t - \tau) \rangle $$

**I'm guessing $T_i(t)$ is the temperature at time $t$ at site $i$.** Of course, I could look at the paper and remind myself, but maybe David or I should add the definition to his first post.

Why my confusion?

In our earlier discussion of [Yamasaki et al's paper](http://forum.azimuthproject.org/discussion/1357/paper-yamasaki-et-al-climate-networks-around-the-globe-are-significantly-effected-by-el-nino/?Focus=10682#Comment_10682), we used a notation resembling $T_i(t)$ to denote the temperature at time $t$ at site $i$ _minus the average temperature at that site on that day of the year_, where we take an average over all years.

It seems both concepts can be useful.

> Define the time-delayed cross-covariance function by:

> $$ C_{i,j}^{t}(-\tau) = \langle T_i(t) T_j(t - \tau) \rangle - \langle T_i(t) \rangle \langle T_j(t - \tau) \rangle $$

**I'm guessing $T_i(t)$ is the temperature at time $t$ at site $i$.** Of course, I could look at the paper and remind myself, but maybe David or I should add the definition to his first post.

Why my confusion?

In our earlier discussion of [Yamasaki et al's paper](http://forum.azimuthproject.org/discussion/1357/paper-yamasaki-et-al-climate-networks-around-the-globe-are-significantly-effected-by-el-nino/?Focus=10682#Comment_10682), we used a notation resembling $T_i(t)$ to denote the temperature at time $t$ at site $i$ _minus the average temperature at that site on that day of the year_, where we take an average over all years.

It seems both concepts can be useful.