Derive correlation coefficient between two dependent variables in terms of correlation coefficient of independent variables

Question

I have following two equations:

θ_t,s^obs = a_sX_t,s^obs + b_s ....................(1)

θ_t,s^sim = a_sX_t,s^sim + b_s ...................(2)

where t is time and s represent sites (I have data (time series) at 40 different sites). a and b vary only in space.

Here my question is that can we derive relationship correlation(θ_t,s^obs, θ_t,s^sim) in terms of correlation(a_s, s=1,2,....40), correlation(X_t,s^obs, X_t,s^sim), and correlation(b_s, s=1,2,....40)?