The atmosphere, hydrosphere and cryosphere form a fully coupled climate system. This system exhibits a number of large-scale phenomena, such as the El Nino Southern Oscillation (ENSO), the Asian Monsoon, the North Atlantic Oscillation (NAO), and the Madden-Julian Oscillation (MJO). While these modes of variability are not exactly periodic, they are oscillatory in character, and their state is monitored using so-called climate indices. Each of these scalar indices is a combination of several climate variables. Here, we use a comprehensive set of 25 climate indices for time intervals that range between 1948 and 2011, and estimate an optimal set of lags between these indices to maximize their correlation. We show that most of the index pairs drawn from this set present a significant correlation on interannual time scales. It is also shown that, on average, about two-thirds of the total variability in each index can be described by using only the four leading principal components of the entire set of lagged indices. Our index set's leading orthogonal modes exhibit several interannual frequencies and capture separately variability associated with the North Atlantic and the North Pacific. These modes are associated, in turn, with large-scale variations of sea surface temperatures.