# Seasonal forecast calibration

Description of how seasonal forecast is calibrated and the category definitions used in the forecast.

Computer models of the ocean-atmosphere system, like their 'real-world' counterpart, have an 'average' behaviour or climatology. Since models are not perfect representations of the real world the model climatology does not correspond precisely with observed real climatology. For example, the model climatology may be warmer than observed climatology in some regions and cooler in other regions, and this can give rise to a systematic bias in the forecasts. To remove this bias, forecasts are expressed in terms of deviations from the model's own climatology - a process referred to as calibration. In any current prediction, the deviation of the model from its own climatology provides the forecast of how the real atmosphere is expected to deviate from real climatology.

For the GloSea system the model climatology is represented by retrospective forecasts (or 'hindcasts'), made with a seven-member ensemble at four start dates each month (the 1st, 9th, 17th and 25th), over the 24-year period 1993-2016. Thus, for each new forecast, there is a reference set of 672 (7 x 4 x 24) hindcasts. This reference set provides the basis for measuring the deviation of the current forecast away from 'average' model behaviour (or climatology) at each geographical location for the time of year. Deviations from climatology are usually expressed in terms of categories, for example a three category description - below, near or above the climate average - is often used. Details of how these categories are defined are given in the next section.

## Definitions of categories used in the forecasts

The calibration hindcasts referred to in the previous section are used to define the categories of temperature and precipitation used in the forecast.

*Three (tercile)-category forecasts: below-, near- and above-normal *

At each grid-point, three categories are defined by sorting the 672 individual hindcasts according to the magnitude of the predicted variable (temperature or rainfall) over the same three-month period as the current forecast. Two values of the variable may then be chosen which separate the 224 coolest/driest and the 224 warmest/wettest of the hindcasts from the 224 in the middle range. These two values define the boundaries of the three categories. Note that with this definition, each category has occurred equally frequently in the model climatology, and the baseline probability for any category is therefore 33.3%, with each category expected to occur, on average, once in three years.

The meaning of the three forecast categories may therefore be stated as:

- above normal: temperature/precipitation in the warmest/wettest one-third when compared to previous years;
- below normal: temperature/precipitation in the coolest/driest one-third when compared to previous years;
- near normal: temperature/precipitation in the middle one-third relative to previous years.

The category boundaries are then used to place the ensemble members from the current forecast into the three categories. For example if, of the 42 (3 x 14) GloSea members, five fall into the below-normal category, 17 in the near-normal category and 20 in the above-normal category then the (rounded) GloSea forecast probabilities for below-normal, near-normal and above-normal conditions are respectively 10%, 40% and 50%.

*Five (quintile)-category forecasts: well-below, below, near, above, well-above*

Only information on the probability of occurrence of the two outer-quintile categories, well-below and well-above, is provided on this website. The quintile categories are defined in an analogous way to the tercile categories such that each quintile category has occurred equally frequently in the model climatology, and the baseline probability for any category is therefore 20%, with each category expected to occur, on average, once in five years. The meaning of the outer-quintile categories may therefore be stated as:

- well-above normal: temperature/precipitation in the warmest/wettest one-fifth when compared to previous years;
- well-below normal: temperature/precipitation in the coolest/driest one-fifth when compared to previous years.

Thus forecasts of the probability for outer-quintile categories provide information on the likelihood of conditions more 'out-of-the-ordinary' than defined by outer tercile categories. The proportion of ensemble members falling into the lower or upper quintile category gives the forecast probability for that category.

*Two-category forecasts: below or above the climate normal*

The two-category format provides the most basic probability forecast information. The categories are delineated by the model climatological median calculated over all ensemble members and hindcast years (4 x 7 members x 24 years for GloSea). Thus if 31 out of 42 GloSea members indicate conditions warmer than the normal, the (rounded) forecast probability of that event from the GloSea system is 75% and the forecast probability for cooler than normal conditions is its complement (25%).