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# Users Guide of the Probabilistic Long-Range Forecasts

The probabilistic forecasts provide users with additional information that is not contained in the deterministic forecasts. This product gives estimates of the probability that the seasonal mean will be above, near or below normal. For each category, the probability is obtained by first computing the anomalies or departures from normal for each ensemble member and then applying a calibration procedure, similar to that described in Kharin and Zwiers (2003), to these values. (Forecast probabilities prior to June 2013 were uncalibrated, and obtained by counting the ensemble members in each of the three categories and then dividing by the ensemble size.)

## What do the probabilistic forecast maps represent?

The forecast maps are composed of 5 panels. The first displays at each location the probability for the most likely of the three tercile categories (above normal, near normal and below normal), with white over Canada representing "equal chance" where no category exceeds 40%. The next 3 maps show the probabilities for each of the individual categories. On the maps for temperature, the colors range from yellow to red for above normal; grey to purple for near normal and light to dark blue for below normal. On the maps for precipitation, the colors range from green to blue for above normal; grey to purple for near normal and yellow to dark brown for below normal. The months for which the forecast is valid is indicated at the bottom of each panel. The date of issuance is shown on the top right corner. The color scale on the right side of the maps indicates forecast probability, in 10% intervals, that predict this specific category. Note that the top map combining the 3 categories chooses for each region the category with the highest probability of at least 40%, whereas white over Canada areas on the map indicates that no category has reached the threshold of 40% and therefore the most probable category in those regions is considered uncertain. Finally, the reliability diagram, also known as attributes diagram, shows, for all locations, the frequency with which each category occurs (vertical axis) versus the probability with which it was forecast (horizontal axis). Ideally, the observed frequencies should equal the forecast probabilities, in which case the dots in the reliability diagrams would lie along the diagonal dashed line.

## How are the deterministic and probabilistic forecasts related?

The deterministic and probabilistic forecasts are two different ways of presenting the forecast information. The deterministic forecasts show the predicted forecast category (above, near or below normal), resulting from the average of the 20 model runs. The historical percent correct maps attached to the deterministic maps give an indication of the skill of the prediction system based on verification of the forecasts over a number of years (typically 30 years). This is useful but unfortunately, the skill maps do not provide information on the confidence that might be attributed to the specific current forecast.

This is where the probabilistic forecasts can add important information to the deterministic forecasts by giving an indication of the specificity of the forecast. For example, a deterministic forecast of above normal conditions that is accompanied by probabilities of 45%, 30% and 25% for the above normal, normal and below normal categories would be less clear than a forecast with probabilities of 60%, 25% and 15% respectively. In the latter case, the forecast is that there are better than even odds of above average conditions, and that this is accompanied by relatively small odds of below average conditions. Similarly, a forecast of near normal conditions might be accompanied by probabilities of 30%, 40% and 30%, in which case the forecast is not very specific, or probabilities of 15%, 70% and 15%, in which case the forecast of near-normal conditions is much more specific.

It must be noted that while the deterministic forecasts skill maps are based on the verification of the 3 categories, many studies done on various seasonal forecast systems developed around the world show that the near normal category is always less well predicted than the above and below categories (van den Dool and Toth, 1991; Gagnon et al. 2000; Gagnon and Verret, 2000, 2001; Kharin and Zwiers, 2003). The main reason for this is that the above and below categories are open ended. In other words, they are only constrained on one side (i.e. by the near normal category). Thus, a forecast of above normal will be correct whether the observed conditions are slightly or much above normal. The same applies to the below normal category. On the other hand, the near normal category is constrained on both sides. Hence only a comparatively smaller range of values in observed conditions allow it to be correct. Therefore, less confidence should be placed on the near normal forecasts, irrespective of what the probabilistic forecasts show compared to above or below normal forecasts.

The calibration procedure for the probabilistic forecasts is described in the calibration section.

## How are the probabilistic forecasts produced?

The current seasonal forecast results from an ensemble of 20 coupled climate model runs, with 10 runs of each of the Environment and Climate Change models: GEM-NEMO (developed at Numerical Research Division, Dorval) and CanCM4 (developed at Canadian Centre for Climate Modelling and Analysis, Victoria).

Previous to June 2013, forecast probabilities were calculated by counting the number of individual members in each of the three categories at every location and then dividing by the ensemble size. For example, if at one location 13 members predicted above normal, 6 members near normal and 1 member below normal, the forecast probabilities were respectively 65% for above normal, 30% for near normal and 5% for below normal.

Beginning in June 2013, the probabilities were calculated by means of the following procedure, based on Kharin and Zwiers (2003).

First, from the historical forecasts (hindcasts) for 1981-2010 the following statistics are computed for each initialization month, lead time and averaging period:
- Climatological means for each model
- Estimate of the standard deviation of interannual variability for both models combined, which is used to derive the 3 tercile categories of the normal distribution: below normal, near normal and above normal
- A calibration coefficient (CAL) that optimally rescales the two-model ensemble mean anomaly and ensemble spread to maximize the continuous ranked probability skill score for the set of hindcasts

Probabilities for each forecast are then obtained by
- Computing anomalies A1 and A2 for each model by subtracting the corresponding model climatologies from the raw predicted values
- Compute the 2-model unweighted ensemble mean anomaly as AU=(A1+A2)/2
- Rescaling this anomaly by the optimal calibration factor derived from the hindcasts: AC=CAL*AU
- Deriving probabilities for the 3 tercile categories using analytical expressions for a normal distribution using formulae 4 in Kharin and Zwiers (2003)

For precipitation forecasts one additional processing step is undertaken. Since the interannual variability distribution of precipitation forecasts on monthly to seasonal time scales deviates substantially from a normal distribution, the precipitation forecasts are transformed to be more normal-like as follows. It is assumed that the distribution of the raw precipitation forecasts can be approximated by a Gamma distribution (2 parameters, scale and shape). These parameters are estimated from the 30-yr hindcasts and are used to transform forecasts to a nearly-normally distributed variable. Then all the above steps are performed for such a transformed variable.

On the seasonal forecast maps,these calibrated probabilities are grouped in 10% bin intervals. Therefore a 5% probability is indicated as being in the 0-9% interval while a 65% probability is indicated as being in the 60-69% interval.

The influence of calibration methods such as the one described above on the forecast probabilities is described here.

## Definition of the categories

The probabilistic forecasts are categorized as below normal, near normal and above normal. The definition of these 3 categories is the same as for the deterministic forecasts.

## How to use the maps?

1. Look at the deterministic forecast and skill map for the temperature and precipitation anomalies to determine the forecast category (above, near or below normal). This is what you would use if you had to quantify the forecast with one word.
2. Look at the probabilistic forecast maps for each of the 3 categories in the area of interest.
3. Compare the color on the probabilistic maps with the scale on the right side. The number that you obtain is an estimate of the probability of occurrence for each category. As a rough estimate, one can say that a higher probability equals a higher confidence in the forecast (see examples below).

It has to be noted that the surface air temperature forecast is a prediction of the anomaly of the mean daily temperature at 2 meters (i.e. at standard observation Stevenson screen height). It is not a forecast of the maximum or of the minimum daily temperature. For more information on what is predicted by Environment Canada seasonal forecasts please read this frequently asked questions page.

## Examples

The following table shows 3 cases of deterministic and probabilistic forecasts for temperature for a given location. For each case, the forecasts context is presented, followed by the conclusions on the forecasts and the degree of confidence to give to those forecasts.
Context Conclusions
• deterministic forecast
• above normal
• probabilistic forecast (%)
• above : 80-89%
• near   : 10-19%
• under : 0-9%
• High probability that temperatures will be above normal.
• High confidence in the forecast.
• Low probability that temperatures will be below normal.
• deterministic forecast
• above normal
• probabilistic forecast
• above : 50-59%
• near   : 20-29%
• below : 20-29%
• Probability that temperatures will be above normal.
• Low confidence since the probability to be above normal is only slightly over 50%.
• deterministe forecast
• near normal
• probabilistic forecast
• above : 20-29%
• near   : 40-49%
• below : 40-49%
• Average probability that temperatures will be near or below normal.
• Low confidence since no probability is over 50%.
• Low probability that temperatures will be above normal.

## References

• Gagnon, N. and R. Verret, 2001: Probabilistic Approach to Seasonal Forecasting, Proceedings of the Long-Range Weather and Crop Forecasting Work Group Meeting IV, Regina, Saskatchewan, March 5-6, 2001, 13-18.
• Gagnon, N. and R. Verret, 2000: Probabilistic Approach to Seasonal Forecasting at the Canadian Meteorological Centre. Proceedings of the Twenty-Fifth Annual Climate Diagnostics and Prediction Workshop, Palisades, New York, October 23-27 2000, 169-172
• Gagnon, N., R. Verret, A. Plante, L. Lefaivre and G. Richard, 2000: Long-Range Forecasts Verification, Preprints, 15th Conference Probability and Statistics in Atmospheric Sciences, AMS, Asheville, North Carolina, May 2000, 65-68.
• Kharin, V. V., and F. W. Zwiers, 2003: Improved seasonal probability forecasts. Journal of Climate, 16, 1684-1701.
• van den Dool, Huug M., Toth, Zoltan. 1991: Why Do Forecasts for "Near Normal" Often Fail? Weather and Forecasting: Vol. 6, No. 1, 76-85.

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