Bogden et al. 1996 definition of skill takes into account the climatology as a first guess to produce a more robust skill. It is interpreted as model error variance normalized by the data variance. The idea is to evaluate if a model provides new information. In other words: evaluate if a model is better than a "initial state." Of course this only makes sense for deviations from the climatology that are unknown before the model run. The effectiveness of this idea goes away when the data we are using to compare was assimilated into the model.
s = 1 - \frac{\sum_{i=1}^N(d_i - L[m_i])^2}{\sum_{i=1}^N(d_i - c_i)^2}
Bogden et al. 1996 definition of skill takes into account the climatology as a first guess to produce a more robust skill. It is interpreted as model error variance normalized by the data variance. The idea is to evaluate if a model provides new information. In other words: evaluate if a model is better than a "initial state." Of course this only makes sense for deviations from the climatology that are unknown before the model run. The effectiveness of this idea goes away when the data we are using to compare was assimilated into the model.