We first performed spectrum decompositions of the forecast difference (error) of all prognostic variables between the control forecast and a slightly perturbed simulation. The ratio of error and total energy spectrum was then defined as an index of predictability. A value equal to 200% for a certain variable at a given scale (or a range of scales) indicates that this variables lost complete predictability at that time. Consistent with previous studies, it is found that errors grow much faster at the smaller scales than their larger-scale features. It is also found that different forecast variables may have different predictable limits and the predictability of a given quantity is closely related to its reference power spectrum distribution. For example, since the vertical motions and precipitation have more energy in smaller scales, they are generally less predictable than horizontal winds, temperature and pressure which have more large-scale components. Moreover, even at the same scales, some variables are more predictable than the others with hydrometers of clouds and precipitation being the least predictable.

We also examined spectral distribution of different variables simulated with different horizontal resolutions. It is found that, except for precipitation and clouds, the spectra computed from different model resolutions match well at larger scale while they differ at the small scales. The resolvable modes are closely related to the grid spacing used in simulation. The effective resolution of a model is defined as where the model's spectrum begins to decay relative to a spectrum from a higher resolution simulation (Skamarock 2004). Consistent with the WRF model result of Skamarock, it is also revealed that the model effective resolution of MM5 model with 30, 10 and 3.3-km grid spacing is approximately 7 times of the grid increments. In terms of error growth estimated from different resolutions, the difference total energy in the higher-resolution simulations grows more rapidly and spread to larger scales more quickly, especially at the earlier times of the simulations.