The predictability horizon of convective boundary layers is investigated in this study. Large-eddy simulation (LES) and direct numerical simulation (DNS) techniques are employed to probe the evolution of perturbations in identical twin simulations of a growing dry convective boundary layer. Error growth typical of chaotic systems is observed, marked by two phases. The first comprises an exponential error growth as , with δ0 as the initial error, δ(t) as the error at time t, and Λ as the Lyapunov exponent. This phase is independent of the perturbation wavenumber, and the perturbation energy grows following a self-similar spectral shape dominated by higher wavenumbers. The nondimensional error growth rate in this phase shows a strong dependence on the Reynolds number (Re). The second phase involves saturation of the error. Here, the error growth follows Lorenz dynamics with a slower saturation of successively larger scales. An analysis of the spectral decorrelation times reveals two regimes: an Re-independent regime for scales larger than the boundary layer height and an Re-dependent regime for scales smaller than , which are found to decorrelate substantially faster for increasing Reynolds numbers