Scientific reporting of time-varying covariates at different time frequencies

Say I have the following model:

$$y_{it} = \gamma_i + \delta {T}_{it} + \zeta Z_{i(k)} + \epsilon_{it}$$

where $$y$$ is some outcome for household $$i$$ in month $$t$$. $$\gamma_i$$ denotes household fixed effects. $$T_{it}$$ is treatment dummy. Say I have 240 months worth of data. The variable $$Z$$ represents a vector of time-varying covariates, but they vary across years.

Question:

I want to be very explicit about the variation, but I also don't want to confuse any readers. Is writing out $$Z_{i(k)}$$ appropriate, where $$k$$ is the subscript denoting the yearly variation? I figured this notation is a bit weird since I already stated that the time frequency was months, not years.

This question is about scientific reporting, so I believe it's apt for this community. I'm most concerned about the clarity of the model, in particular the subscripts.