Forecasting terminology
Meat & Livestock Australia October 24, 2023
Interpretation of forecasting information can become confused if the terminology is not well understood. Meaningful interpretation of the information presented enables better decision making.
Medians
The median of a dataset represents the middle value when the data is arranged from lowest to highest value. It is often used as a measure to capture the most central values, especially when a dataset contains outliers (unusual or extreme values). As such, it can provide an understanding of the typical or more representative value of a dataset.
The median is different from the average, or mean, because it is less affected by outlier data. An average considers all values, including outliers, by summing all values and dividing that by the number of data points. the average is a mathematically calculated value and may not actually appear in the dataset. The average is a useful value of summarising data into a single, central value, though the value can be skewed by outliers and misrepresent the central value or ‘typical’ value of a dataset.
After the median of a dataset is determined, other values can be compared to it, and either be higher or lower than the central value: this is referred to as the dataset being binomial. In the FWFA’s tools, the median is used to describe the typical or more representative value of historical weather events at a certain time of year. An example is shown in Figure 1. The forecasts use the median to explain if we can expect a typical weather event more like the average historical value for that time of year, or if we can expect an unusual weather event, which is much lower or higher than the median historical value for that time of year.
Deciles and quartiles
While comparing values to the median, we deal with a binomial distribution of the dataset where the values can either be higher or lower than the median. Further detail from a dataset can elaborate on where the ‘value of interest’ is positioned on the data scale from high to low. For example, if it’s not equal to the median, is it much higher, lower, or not that much different?
Figure 1. The binomial distribution of August-October rainfall for 146 years (1875-2021) in Dubbo, NSW. Rainfall is either above or below the median rainfall (124mm). Reproduced from Agriculture Victoria’s eLearning course ‘Using seasonal climate prediction tools’.
Figure 2. Decile bar graph showing August-October rainfall for 146 years (1875-2021) in Dubbo, NSW. Rainfall is divided in equal groups of data (deciles) each with a lower upper value defining the decile. Reproduced from Agriculture Victoria’s eLearning course ‘Using seasonal climate prediction tools’.
Instead of dividing the dataset into two groups and creating a binomial distribution (higher and lower), the dataset can be divided into 10 equal groups, referred to as deciles. Each decile contains a group of data that explains 10% of the dataset, with a lower and an upper value defining the decile, as shown in Figure 2.
As such, we can understand the context of and refer to the value as being (for example) in decile 9 (significantly higher than the median but not quite the most extreme value measured) or in decile 5 (not that far off the median, but a little lower).
Figures 3a and 3b. Decile bar graphs showing August-October rainfall for 146 years (3a at top) and December-February maximum temperatures for 101 years (3b) in Dubbo, NSW. Reproduced from Agriculture Victoria’s eLearning course ‘Using seasonal climate prediction tools’.
In the FWFA tools, this concept is used to describe rainfall (Figure 3a) or temperature (Figure 3b) as summarised in Table 1. These tools visually combine two deciles (referred to as a quintile) which describes 20% of a dataset, or one of five equal groups of data. Another common term used to group data is quartile, where a dataset is divided into four equal groups and each quartile explains 25% of the dataset.
A short video about understanding percentiles in climate data can be viewed at Understanding percentiles in climate data
Table 1. Decile descriptors for rainfall and temperature used in the Bureau of Meteorology climate outlook and forecasting tools.
Rainfall
Temperature
Decile 1 & 2
Unusually dry
Unusually cool
Decile 3 & 4
Drier
Cooler
Decile 5 & 6
Average
Average
Decile 7 & 8
Wetter
Warmer
Decile 9 & 10
Unusually wet
Unusually warm
Probabilities
A probability is a measure of the likelihood (or chance) of an event occurring. It is calculated by determining the number of times an event has happened, divided by the total number of events and expressing the outcome as a value between 0 and 1, or 0% and 100%. Probability is often used to explain the likelihood of future events based on historic information.
When referring to deciles, there is a 20% chance of a historic rainfall or temperature value falling in any of the decile groupings. For the purpose of climate forecasts, we are focused on the chance of a decile 1 & 2, or a decile 9 & 10 event. The FWFA tools present this chance for us.
Box and whisker plots
A box and whisker plot graphically summarises the distribution of a dataset, as shown in Figure 4. It displays the data distribution including the median, quartiles and outliers. It consists of a box and two ‘whiskers’ extending from above and below the box. The box represents the middle 50% of the data, with the bottom of the box delineating the first quartile (Q1) and the top of the box delineating the third quartile (Q3). The median, or second quartile (Q2), is typically represented by a line within the box.
The whiskers represent the minimum and maximum values of the data which are not considered outliers (outliers are sometimes represented as individual points or circles beyond the whiskers). The length of the box and whiskers are dependent on the distribution of the dataset. If the data is evenly distributed, the box will be longer and the whiskers shorter. If the data is skewed, the box and whiskers will be shorter on one side and longer on the other.
The neutral forecast
As previously explained, a forecast places probabilities of certain forecast model runs occurring in the deciles that describe the hindcast weather data for a particular point in time. If a particular extreme weather event occurs, then the data input from climate drivers and weather patterns might influence the forecast model outcomes, implying a high chance of an extreme event. If the majority of forecast model runs suggest a high chance of a particular extreme event occurring, the chance of the event not occurring remains, because not all model runs would have generated the same outcome.
Figure 4. A box and whisker plot explained. Reproduced from Agriculture Victoria’s eLearning course ‘Using seasonal climate prediction tools’.
Table 2. Summary of FWFA tools.
FWFA tool
Format
Parameters
Time frame/s
Limitations
Best use
Chance of extremes
Australia-wide map
Rainfall and temperature
1 week, 2 weeks, 1 month, 3 months
- Not location specific, so need to zoom in on the map.
- No information about heatwave or extended cold period.
- Simple, quick overview, for all timeframes, to highlight if can expect something unusual or average. May provide a prompt to dig deeper with the other tools.
Chance of 3-day totals
Australia-wide map
Rainfall only
1-2 weeks
- Not location specific (which might be expected), so need to zoom in on the map.
- Most useful for northern Australia.
- Northern Australia – monsoon and heavy rain forecast. Start of wet season prediction
- Southern Australia – autumn break indication.
Decile bar chart
Australia-wide map
Rainfall and temperature
1 week, 2 weeks, 1 month, 3 months
- Next level up from chance of above median map – provides some more detailed information. Often helps with understanding of above median maps and chance of extremes map.
Timeline graph
Australia-wide map
Rainfall and temperature
4 weeks, 5 months
- Categorised rating for accuracy.
- Box and whisker plots shape and size is visual and provides information about the confidence in the model runs.
- Provides recent history as well.
Probability of exceedance
Australia-wide map
Rainfall only
1 week, 2 weeks, 1 month, 3 months
- More complex to understand
- In-depth understanding (essentially all of the information in other tools in one); most suitable for deliverers.
So, in essence, the more forecast model runs that align, the higher the chance of the forecasted outcome. In some instances, the distribution of forecast model outcomes can be so spread there is no skew to the outcomes and any outcome is just as likely to occur as another. This is referred to as a neutral forecast. Examples are a 20% chance of all quintiles occurring, or a 50% chance of exceeding the median. In such situations, any outcome can be expected because all outcomes are equally possible.