# Seasonal Prediction of Sea Level Anomalies in the Western Pacific

## Seasonal sea level forecasts

Seasonal forecasts are the best available prediction of what the climate will be like in the upcoming months. They differ from a weather forecast in that instead of predicting individual events they show the average sea level anomalies over the next few months.

This page contains information about the generation and characteristics of seasonal sea level forecasts, details on the skill scores used to assess the forecasts, and published resources.

## POAMA and sea level output

POAMA is a global coupled ocean-atmosphere ensemble seasonal prediction system developed jointly by the Australian Bureau of Meteorology and the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Division of Marine and Atmospheric Research (CMAR). POAMA produces intra-seasonal-to-seasonal predictions of the global climate and has been running operationally at the Bureau of Meteorology since 2002.

POAMA calculates sea surface height (SSH) using a rigid-lid approximation that conserves volume. The SSH for each grid cell is determined by using the hydrostatic equations to calculate any changes to the height of the grid cell's surface generated by the perpendicular forcing from water being shifted into neighbouring grid columns due to horizontal temperature, salinity and wind gradients. This means that POAMA captures sea level contributions due to dynamic height, barotropic circulation, advection and dissipation processes.

It should be noted that the following contributions to sea level variations are not simulated within POAMA: changes in ocean mass from ice-sheet mass loss or other contributions, tectonic uplift, self-attraction and loading, glacial isostatic adjustment, land water storage, astronomical tides, surface waves, mesoscale eddies or atmospheric pressure effects.

## POAMA sea level anomaly forecast generation

POAMA seasonal sea level anomaly (SLA) forecasts are derived using an ensemble of 33 SSH forecasts by removing the corresponding model climatology, in order to correct for any model bias. The climatologies are computed relative to the start month and lead-time of each model configuration. The ensemble members are then averaged to create the multi-model ensemble mean and the distribution of the ensemble members is used to create the probabilistic forecasts.

## Lead-time

A seasonal SLA forecast is the average state of the SLA beginning from the start of the first month to the end of the final month i.e. a February-March-April forecast is the average of the daily conditions from 1 February up-to and including 30 April.

The lead-time is defined as the number of months that have elapsed between when the model is started (initialised) and the start of the forecast period. For example, if the model start date is the 1st January, the forecast for the season January-February-March, which happens to start on the same date, has a lead-time of 0 months. The forecast for March-April-May, from the same model run, would be lead-time 2 months, as two full months have elapsed between when the model was started (January) and the beginning of the forecast period (March).

## Initialisation date and lead-time

The model climatologies and skill scores to assess forecast performance are created using a comprehensive set of hind-casts that is created using exactly the same system as used for real-time forecasts. These hind-casts consist of a 33-member ensemble starting on the 1st, 11th and 21st of each month from 1981 to 2010.

Users should note that the real-time POAMA forecasts are generated at 00Z every Monday and Thursday at the Bureau of Meteorology. Because the initialisation day does not always correspond exactly with the hindcast day, the closest climatology is used. There are implications to the availability of the 0th lead-time:

- Forecasts initialised on the 1st of the month: The first forecast available has a lead-time of 0 months.
- Forecasts initialised between the 2nd to the end of the month: The partial month forecast is removed and the first available forecast starts on the 1st of the following month i.e. it has a lead-time 1 month.

For example, a forecast that is initialised on the 19th of January uses the 21st of January climatology, thus the first available forecast is February-March-April, at a lead-time of 1 month.

## Gridded outlook variables

A variety of seasonal SLA forecasts can be generated by POAMA.

### Deterministic forecasts

The seasonal SLA forecasts are created by comparing the model predictions of sea level in the coming months to the long-term averages using the recent 30-year average derived from the hind-cast set. Deterministic seasonal SLA forecasts show the predicted anomalous value of sea level over the season due to dynamic height, barotropic circulation, advection and dissipation processes.

### Probabilistic forecasts

The seasonal probabilistic forecasts indicate the most likely of three categories: above average (upper tercile), near average (middle tercile), and below average (lower tercile) for seasonal sea level anomalies.

The shaded areas on the maps show the probability (how likely as a %) that the upcoming SLA will be within the above normal, near average, or below normal limits. For each location and month, the lowest 10 years of SLA from the 30 years of 1981-2010 define the lower tercile, the highest 10 years define the above upper tercile, and the remaining 10 years define the middle tercile.

Without any forecast, the chance of the SLA being in each of the 3 categories is 33.3%. Using POAMA forecasts it is possible to identify areas where probability is greater than 33.3%. At any location on the map the probabilities for each of the 3 categories (upper tercile, middle tercile and lower tercile) will add up to 100%.

#### Upper tercile probability

These forecasts show for each grid point the percentage of ensemble members that predict a sea level anomaly equal to or above the upper tercile limit.

#### Lower tercile probability

These forecasts show for each grid point the percentage of ensemble members that predict a sea level anomaly equal to or less than the lower tercile limit.

#### Composite tercile map

These forecasts combine the upper, lower and middle tercile forecasts into one concise map. The colours represent the most likely tercile event to occur whilst the shading indicates the percentage of forecasts in agreement.

"Indeterminate" forecasts show grid points where all tercile states have a probability of less than 40% i.e. Upper tercile: 34%, Middle tercile: 36%, and Lower tercile: 30%.

"Ambiguous" forecasts show grid points where two terciles have the same probability of occurring i.e. Upper tercile: 45%, Middle tercile: 45%, and Lower tercile: 10%.

## EEZ outlook variables

Additional to the gridded forecasts the average SLA within each Exclusive Economic Zones (EEZ) is calculated for each ensemble member as well as the overall deterministic forecast. These results are then plotted as a "plume plot" where the average SLA value of the 33 ensemble members are shown along with the overall mean for all lead-times.

It should be noted that for some regions the SLA forecast could be high in some regions and low in others. When the average is taken, this has the effect of bringing the average value closer to zero. Thus it is important to consider the gridded forecasts in conjunction with the EEZ outlook.

## Skill Scores

Every forecast presented in this portal is accompanied by skill scores that correspond to the same forecast season and lead-time.

These scores are described below and are from Forecast Verification: Issues, Methods and FAQ. Another useful resources on verification and skill scores can be found at: Wilks, D.S., 2011: Statistical Methods in the Atmospheric Sciences. 3rd Edition. Elsevier.

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

## Verification dataset

PEODAS, POAMA’s data assimilation scheme, is used as a verification dataset to assess the performance of POAMA forecasts over the period of 1981-2010.

## Deterministic forecast skill scores

### Correlation

This score measures how well the forecast values corresponded to the observed values.

Correlation measures how close the points of a scatter plot are to a straight line if you were to plot forecasted values against observed values. This score does not take into account forecast bias i.e. it is possible for a forecast with large errors to still have a good correlation coefficient with the observations.

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

### Root Mean Square Error

Root Mean Square Error (RMSE) is the average magnitude of the forecast errors i.e. the lower the value the closer the forecast is to the observed.

It is calculated by subtracting the observed value from every forecast (error); squaring these values; determining the mean value; and finally, taking the square root.

Range: 0 to ∞, Perfect score: 0.

## Probabilistic forecast skill scores

### Accuracy

Accuracy is the percentage of probabilistic forecasts that were correct (in the correct tercile) when compared to observations.

Range: 0 to 100%, Perfect score: 100%.

### Relative operating characteristic score

The relative operating characteristic (ROC) is a measure of the forecast's ability to discriminate between events and non-events.

The ROC score is not sensitive to bias in the forecast. A biased forecast may still have good resolution and produce a good ROC curve, which means that it may be possible to improve the forecast through calibration. The ROC can thus be considered as a measure of potential usefulness.

Range: 0 to 1, No skill: < 0.5, Perfect score: 1.

## PASAP/PACCSAP Portal User Manuals

Documentation for navigating the PACCSAP Portal is contained within the “PASAP Portal User Manual”. This manual includes: (Part 1) A guide to using the PASAP Portal, featuring examples of how to select, display and download the various forms of seasonal forecasts; (Part 2) A description of the seasonal outlook products and their generation processes along with details regarding the skill score that are shown and the observational data used for comparison.

- Part 1: Website Guide [pdf]
- Part 2: Forecast Technical Information [pdf]
- Part 3: Website Technical Information [html]

## Publications

A number of publications that assess the skill of POAMA in predicting seasonal sea level anomalies have been compiled.

- E. Miles, C. Spillman, J. Church and P. McIntosh “Seasonal Prediction of Global Sea level Anomalies using an Ocean-Atmosphere Dynamical Model”, Submitted to Climate Dynamics.
- E. Miles, C. Spillman, P. McIntosh, J. Church, A. Charles and R. de Wit “Seasonal Sea level predictions for the Western Pacific”, Submitted to 20th International Congress on Modelling and Simulation, Adelaide, Australia.
- P. McIntosh, J. Church, E. Miles, K. Ridgway, C. Spillman “Seasonal Prediction of Western Pacific Sea level using a Coupled Ocean-Atmosphere Dynamical Model”, In prep.
- E. Miles, A. Griesser and A. Charles “An Overview of the PACCSAP Seasonal Prediction Web Portals CAWCR Technical Report”, In prep.

## Documentation

The About Sea Level Outlooks Page provides details on the PACCSAP Seasonal Seal Level Prediction Project.

Further information and outcomes will be published in scientific articles and online. For model information see the POAMA website.

## Related information

- Predictive Ocean-Atmosphere Model for Australia (POAMA)
- Sea level research at CSIRO
- CSIRO sea level satellite products
- PACCSAP Seasonal prediction of extreme ocean temperatures/coral bleaching
- ENSO Wrap-Up (BoM)
- POAMA climate model summary