The regression-based relationships can be established using seasonal mean quantities, to create a downscaling system for forecasting seasonal mean quantities. However, the approach can also be applied to daily fields.

Two concerns with perfect prognosis are as follows:

i) Space. The GCM's response to SST forcing (e.g. associated with El Niño ) is sometimes shifted by a few hundred kms, relative to observations. In such a situation, the first step in the perfect prognosis downscaling scheme is not affected, and will likely establish a good relation between observed large-scale features and observed station rainfall. However, applying these relationships to daily fields from a GCM seasonal forecast, uses information that is sub-optimal - the geographically shifted prediction information in the GCM does not enter into the downscaling statistical prediction model, because the geographical location and spatial structure of the predictors were established based on observed relationships.

ii) Time. The GCM needs to capture the correct daily variability of the predictor fields, for the daily downscaled sequences to have realistic statistical properties of, for example, dry spells. In mid-latitudes, GCMs often have good representation of daily variability, as they represent well the synoptic weather disturbances like mid latitude cyclones. However, in the tropics, current GCMs have more difficulty with synoptic weather disturbances, such that their daily sequences can be distorted, leading to distortion in the statistics of daily weather diagnosed through perfect prognosis.

Systematic spatial differences between observed and GCM fields can be accounted for in seasonal predictions by using the methods described in the previous section e.g. Eq. 2 (i.e. the space problem of perfect prognosis can be reduced). Whether this impacts utility for seasonal prediction downscaling is not yet tested, though the improvements that are emerging through statistical spatial transformation of seasonal predictions, suggest perfect prognosis approaches may currently fail to incorporate significant prediction information for some regions. However, there may be ways to include such information on systematic spatial anomaly shifts in these regression based perfect prognosis methods.

A further approach to generating daily sequences is through weather typing. Various methods exist to identify a small set of discrete weather types typical of a region, and to assign each day to one of those weather types. For downscaling to individual sites, the simplest strategy is to establish the relationship between each observed daily weather type over a region, and the weather at the individual site. For example, for a given weather type, to determine the probability that the day will be rainy or dry. Each GCM day is then categorized to a weather type, and associated weather statistics are generated. This approach again relies on the perfect prognosis concept.

A more sophisticated example of the weather typing approach that is being tested employs the Hidden Markov Model statistical technique. This classifies each day to a particular synoptic type based on the observed rainfall characteristics, assuming daily rainfall evolves according to a Hidden Markov Model. For example, Fig. 4.13 shows daily typing sequences for a set of March-May seasons for the state of Ceara in Northeast Brazil. The downscaling prediction problem becomes one of forecasting the statistical character of the sequences of the daily weather types, from which rainfall and other climate variables for each station can be generated. The probability of transition from one weather type to another is conditioned on the prevailing synoptic situation. The different probabilities of transition are established using observed daily fields and observed weather state transitions. The GCM predicted daily fields are then used to drive the stochastic model of weather state transition. An element of perfect prognosis is still present in this approach, since it is assumed that the GCM large scale fields have realistic spatial and daily sequence characteristics, to drive realistic day-to-day changes in the probability of weather state transitions. However, there are ways in which the perfect prognosis problem could be overcome, if aspects of the GCMs seasonal prediction fields are used to modify the transition probabilities, rather than the individual daily fields of the GCM.