With reasonable confidence derived from the correlation skill scores, the models can now be used to make actual forecasts. Two types of forecasts can be made with CPT. One is the actual or absolute value rainfall rate forecasts for each grid being forecasted for, while the other type is the corresponding probabilistic forecasts of the grids.
Absolute Value Forecasts
Generating absolute value forecast for each grid is a relatively straightforward process. Once the models are generated for each grid, all that needs to be done is for the future predictor values, say the value of SSTs at grid 1, 2, 3, ... , n (x1, x2, x3, ..., xn) for next year to be supplied to the regression model below and the forecasted rainfall rate for a particular grid (y1) is subsequently churned out.
y1 = a1x1 + a2x2 + a3x3 + ... + anxn + b
Once the rainfall rates for all the grids have been calculated, we get a map of absolute value forecasts such as the one shown below. The values are read in x100 mm/day. So, for example, the rainfall rate over Singapore for this particular seasonal forecast can be read as 0.065 x 100 mm/day, or simply 6.5mm/day.
Probabilistic Forecasts
But the absolute value forecasts generated above are not without uncertainties, i.e. there are inaccuracies inherited from the developed models' error variances, which in CPT's case is by default calculated from the variance of the errors in the cross-validated predictions, and also the current values of the predictors themselves. So, for each forecasted grid, you could have a forecast spread, or probability density function, which is centred around the forecasted value of 6.5 and following a Student's t-distribution curve, that looks like the figure below (red line):
The 2 black vertical lines marking the boundaries of the below normal, normal and above normal categories can be calculated by considering the highest and the lowest thirds of the historical, observed rainfall rate dataset. So to illustrate from the example above, it can be said that, there are 10 years where the rainfall measured 10.3 mm/day or above, 10 years where the rainfall measured 3.0 mm/day or below, and the remaining 10 years measured rainfall in between 3.0 and 10.3 mm/day.
The forecast probabilities can then be derived from the area underneath the probability density function corresponding to the categories marked out as in the example above. So in this particular case, it is 17% probable that the forecast is below normal rainfall rate, 70% probable that it is expected to be normal rainfall, and only 13% probable for it to be above normal. Hence, normal values of rainfall rate can be expected for this particular grid in the coming season.
And when we have all the grids calculated for their above normal, normal and below normal probabilities, the outcome can be presented in 3 separate maps - Below Normal, Normal and Above Normal. And from the example probabilistic forecasts shown below, we can conclude that much of the ASEAN region, especially for places near the equator, is going to get above normal rainfall rate in the coming season.
