# Seasonal Prediction of Extreme Ocean Temperatures/Coral Bleaching

## Introduction

This page provides further technical detail about the forecast products.

## Model Terminology

#### Lead Time

Lead-time is defined as the time elapsed between when the model was run (the model start date) and the forecast date. E.g. if the model was run on 1 January (the model start date), the forecast for January is 'lead zero', as there is no elapsed time between when the model was run and the start of the forecast period. The forecast for February would be 'lead one', as there is one month between when the model was run and the start of February. Likewise, for the March and April forecasts, the lead times are 2 and 3 months, respectively.

Generally, forecast accuracy is highest for lead-time 0 months and decays as forecasts predict further into the future (i.e. increasing lead-time).

#### Ensemble Member

POAMA is an ensemble forecast system. This means that to produce each forecast, the model is run numerous times (33 times in the case of POAMA version m2.4). The *collection* of these simulations is the *ensemble*, and individual simulations are called *ensemble members*.

#### Ensemble Mean

The average value of the forecast *ensemble* (which comprises 33 ensemble members) is the *ensemble mean* forecast.

#### Chance of Exceeding

The 25th, 50th, and 75th percentile forecast values are calculated from the forecast ensemble. These values provide the 75%, 50%, and 25% chance-of-exceeding forecasts, respectively.

For example, in the case of the 75% chance-of-exceeding SST forecast, POAMA is indicating that the temperature shown on the map is likely (75%) to be exceeded: 25 of 33 ensemble members (75%) are *above* the forecast value which is shown on the map.

## Climatologies

Climatologies are long-term averages, calculated separately for each month and lead time. Climatologies used and shown in the Extreme Ocean Temperatures/Coral Bleaching werb portal are calculated over the period 1982 to 2010 inclusive.

#### Observed

The observed monthly climatology is based on the NOAA Optimum Interpolation (OI) Sea Surface Temperature (SST) V2 re-analysis.

#### Maximum Monthly Mean

The maximum monthly mean climatology is the maximum value of the observed monthly climatology.

## Gridded Outlook Variables

#### Sea Surface Temperature

The temperature of the water in the top few metres of the ocean (the uppermost layer of the ocean model: this layer is 15m in depth, in POAMA version m2.4).

#### Sea Surface Temperature Anomaly

The predicted water temperature minus the climatological water temperature for this month.

#### HotSpots

HotSpots show the areas where the SSTA is greater than the maximum monthly mean climatology.

HotSpot = SSTA - MMM climatology

#### Degree Heating Months

Degree heating months is the accumulation (integration) of HotSpots over a four month period.

#### Most-likely tercile

Indicates the SST tercile predicted by the majority of ensemble members. A value of 'indeterminate' (green shading) indicates that there is no single most-likely tercile (e.g. ensemble members are evenly distributed among terciles). Ambiguous values (pink shading) indicate that two of three terciles are equally likely.

Tercile bounds are calculated based on the climatology.

#### Probability of lower tercile

The likelihood of SST values falling in the lower tercile, i.e. cooler than normal conditions.

Tercile bounds are calculated based on the climatology.

#### Probability of upper tercile

The likelihood of SST values falling in the upper tercile, i.e. warmer than normal conditions.

Tercile bounds are calculated based on the climatology.

## Skill Scores

Skill scores shown on the web portal are described below. Other useful resources on verification and skill scores can be found at:

- Forecast Verification: Issues, Methods and FAQ
- Wilks, D.S., 2011:
*Statistical Methods in the Atmospheric Sciences*. 3rd Edition. Elsevier

#### Verification dataset

The NOAA Optimum Interpolation (OI) Sea Surface Temperature (SST) V2 re-analysis is used as a verification dataset, over the period 1982 to 2010 inclusive. "Observed" HotSpot and Degree Heating Month values are calculated based on this reanalysis. Reynolds, R. W., N. A. Rayner, T. M. Smith, D. C. Stokes, and W. Wang, 2002: An Improved In Situ and Satellite SST Analysis for Climate. *Journal of Climate*, **15**, pp1609-1625.

The Hit Rate and the Peirce Skill Score are only calculated for HotSpot or Degree Heating Month forecasts in areas in which HotSpots or Degree Heating Months (respectively) have occurred during the verification period. E.g. these skill score values are not shown for the Great Barrier Reef during August because, being a cool month in this southern-hemisphere location, no HotSpots or Degree Heating Months have occurred and the scores are therefore undefined.

In some locations there will be very few occurrences of an event during the hindcast period. A skill score calculated based on very few events can be unrealistic or misleading. This happens because the few recorded events can potentially be an unrepresentative of long-term behaviour (i.e. under-sampled). For example, we might roll a dice five times and get values below four on all five occasions, but that does not mean that we would never roll a six. Extending this reasoning to HotSpot forecasts, there are areas where the Hit Rate is zero over the hindcast period, but that does not necessarily mean that we will never forecast a HotSpot event.

Degree Heating Month values are accumulated HotSpots over the *previous* three months. For the first forecast month, the previous three months' HotSpot values are known as they have already been observed, and the Degree Heating Month value can therefore be calculated without involving forecast quantities; the Peirce Skill Score for Degree Heating Months is therefore 1 everywhere for the first month.

#### Correlation Coefficient

Range: -1 to 1, No Skill: 0, Perfect score: 1.

The correlation coefficient is a measure of the strength of the linear relationship between two quantities. No relationship exists between two quantities if the correlation is 0; correlation values of 1 and -1 indicate a perfect positive and negative relationship, respectively.

This score does not take forecast bias into account i.e. it is possible for a forecast with large errors to still have a good correlation coefficient with the observations.

#### Normalised Root Mean Square Error

Range: 0 to ∞, Perfect score: 0, Forecast error = range of natural variability: 1.

Normalised Root Mean Square Error (NRMSE) is the average magnitude of the forecast errors, scaled by the standard deviation of observations at that point.The *lower* the value, the closer the forecasts were to the observed values over the verification period.

The standard deviation of observations is a measure of the interannual variability: scaling by this amount shows more clearly where the forecast error is larger or smaller than natural variability. NRMSE is calculated by subtracting the observed value from every forecast (error); squaring these values; determining the mean value; taking the square root ; and finally dividing by the standard deviation of observations at that point.

#### Hit Rate

Hits / (Hits + Misses)

Range: 0 to 1, Perfect score: 1.

The number of correct forecast events (when the event was forecast, and it happened) divided by the total number of forecast events, including false alarms (when the event was forecast but didn't happen).

#### False Alarm Rate

False Alarms / (False Alarms + Correct Negatives)

Range: 0 to 1, Perfect score: 0.

The number of false positives divided by the total number of occasions when the event did not happen.

#### Proportion Correct

(Hits + Correct Negatives) / (Total number of forecasts)

Range: 0 to 1, Perfect score: 1.

The number of correct (positive and negative) forecasts divided by the total number of forecasts made.

#### Frequency Bias

(Hits + False Alarms) / (Hits + Misses)

Range: 0 to inf, Perfect score: 1.

Ratio of the number of forecast events to the number of observed events.

#### Peirce Skill Score

Range: -1 to 1, Perfect score: 1.

Hit Rate - False Alarm Rate

An equitable skill score which is not influenced by the frequency of events.