Often, there is a need to interpret the consequences of the seasonal forecast in terms of features that are closer to the problems faced by society, such as crop production and stream flow. Models in other academic disciplines have been developed to predict such features, conditional on climate. However, to estimate the consequences of a climate scenario, these models often require daily weather information. For example, most crop models require a range of daily weather features. To meet this need, a number of techniques have been used to generate daily weather features that are consistent with a given seasonal prediction. When daily weather sequences are generated, the prediction is not interpreted as the exact sequence of daily weather (i.e. whether it will rain or not on any given day), but rather, the forecast is interpreted in terms of the statistics of the daily weather, like the number of storms in the season and the number of dry spells. For driving impact models, it is therefore usually best to create a range of the possible weather sequence scenarios that are consistent with the seasonal prediction, and use these to drive the impact model. In this way, a sample of possible outcomes are generated, tfrom which can be constructed the mean expected outcome along with the range of possible outcomes, which could be expressed in the form of a probability distribution.

Two widely used methods for generating daily weather sequences from seasonal forecasts are weather generators and analogue methods:

(i) Weather Generator. A weather generator uses information about the observed weather statistics at the site of interest to parametrize a stochastic model that can generate sequences of daily weather, all consistent with the statistics of the target site. A typical daily rainfall generator is often rooted in a Markov Chain model. The Markov Chain is a widely-used statistical technique to describe a time-series of discrete states. For a rainfall generator, we define two states: either the day is classified as dry (no rain) or rainy. The Markov Chain model considers that the likelihood of a particular state on any given day is determined by the states taken in the previous day or sequence of days. Therefore, the likelihood of any given day being rainy is conditioned only by whether the previous day or sequence of days were rainy. Knowing these probabilities of transition, and using random number generators, the stochastic model can generate series of rain and no rain days through the season. For the rainy days, the amount of rain must also be generated. Usually, a distribution (e.g. Gamma) is fitted to the observed rainfall amounts for the target site. For the rainy days in the stochastic simulation, rainfall amount values are sampled from the fitted distribution. Thus, the parameters of this simple rainfall weather generator would be the Markov Chain transition probabilities and the parameters of the distribution fitted to the rainfall amounts (mean, standard deviation etc). These weather generator parameters can be modified conditional on the seasonal forecast (e.g. changing the probability of rain and the mean rain on rainy days) to generate predictions of weather sequences that are consistent with the seasonal forecast. Alternatively, simpler approaches can be taken, such as running the weather generator many times, and only selecting those runs that produce rainfall totals consistent with the seasonal forecast. This whole process of generating daily sequences based on the seasonl prediction is often referred to as stochastic disaggregation.. While rainfall is often the key variable of interest, often other variables are also needed to drive impact models (such as solar radiation). These may be sampled from climatological distributions, or distributions conditioned on whether the day is rainy or dry.

ii) Analogue Method. Past years can be sought that are similar to the seasonal forecast. Various metrics can be used to measure similarity. The forecast seasonal rainfall from the GCM (after correction) is one choice. Say, the ten years closest to the seasonal prediction for this year are selected, and the daily sequences observed in those 10 years provide a range of daily sequences to drive impact models, like crop models, to provide a range of possible consequences for the coming season. The leading one or two PCs from a relevant GCM field (cf Equation 2) could also be used. One could also use direct indices of SST if these are well established for the target region. Indices of El Niño have been widely used in this way. Analogue years can either be weighted equally, or given unequal probability weights based on how similar they are to the target. The k-nearest neighbour analogue method performs such a weighting and was applied in the creation of the probability forecasts in Fig. 4.1.

Downscaling of global change scenarios (see e.g. Wilby and Wigley, 1997) has often been tackled using an approach known as perfect prognosis. The schemes are said to employ perfect prognosis, because they assumes that the GCM predicted fields can be inserted into relationships established using actual observed data from the historical record. In the approach, statistical prediction models are established using observed large-scale circulation features to predict the downscaled information needed (e.g. station rainfall). The fields predicted by the GCMs are then fed into the statistical relationships, and predictions of the downscaled information are generated. One class of methods used is regression-based, ranging from simple regression to non-linear regressions and coupled-pattern regressions like canoninical correlation analysis. Being regression-based, a particular problem is to ensure the variance (i.e. variability) of the daily sequences is realistic, since regression- based methods usually create predictions with variance that is systematic less than the observed. Either this is addressed through variance correction (as was introduced for Equations 4.1 and 4.2) or through addition of stochastic noise to the downscaled values.