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This page describes the way the anomaly signal and uncertainty of the ensemble forecasts in the sub-seasonal and seasonal products are determined using the climatology as reference. This includes also how the expected forecast anomaly category (amongst 5 or 7 pre-defined categories) and the uncertainty category (divided in 3 categories low/medium/high) of the ensemble forecasts are determined. This is a generic procedure, which is the same for both EFAS and GloFAS, as it is executed the same way for each river pixel, regardless of the resolution, and also the same for the sub-seasonal and seasonal products, as it works in the exact same way regardless of whether it is weekly mean values, as in the sub-seasonal, or monthly mean values, as in the seasonal.

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From the climate sample, 99 climate percentiles are determined, which represent the range of equally likely (1% chance) segments of the river discharge magnitude that occurred in the 20-year climatological sample (both sub-seasonal and seasonal is currently based on 20 years). Figure 1 shows an example generic climate distribution, either based on weekly means or monthly means, with  with the percentiles represented along the y-axis. Only the deciles (every 10%), the quartiles (25%, 50% and 75%), of which the middle (50%) is also called median, and few of the extreme percentiles are indicated near the minimum and maximum of the climatological range shown by black crosses. Each of these percentiles have an equivalent river discharge value magnitude along the x-axis. From one percentile to the next, the river discharge value magnitude range is divided into 100 equally likely bins (separated by the percentiles), some of which is indicated in Figure 1percentiles), such as bin1 of values below the 1st percentile, bin2 of values between the 1st and 2nd percentiles or bin 100 of river discharge values above the 99th percentiles, etc. In Figure 1, only the deciles (every 10%), the quartiles (25%, 50% and 75%), of which the middle (50%) is also called median, and few of the extreme percentiles are indicated near the minimum and maximum of the climatological range shown by black crosses. 

Figure 1. Schematic of the forecast anomaly categories, defined by the climatological distribution.

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Table 1: Definition and description of the 7-anomaly categories. The possible value ranges in the 'Rank column' are inclusive at the start and exclusive at the end, so for example for the category of 'Extreme low' the possible ranks are 1, 2, 3, ... and 10. For the graphical products (maps and hydrographs), the middle three categories ('Bit low', 'Normal' and 'Bit high') are combined into one extended 'Near normal' category. The categories are colour-coded as they appear on the web products.

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The sub-seasonal or seasonal forecasts have 51 ensemble members each. The members are all checked for climatological extremity and placed in one of the 100 climate bins (modelled climate conditions for this time of year, location and lead time); the corresponding allocated bin corresponds to the the anomaly or extremity level of the ensemble member, called hereafter rank (from 1 to 100). For example, rank 1 means the forecast value is below the 1st climate percentile (i.e. extremely anomalously low, less than the value that happened in the climatological period only 1% of the time), rank 2 means the value is between the 1st and 2nd climate percentiles (i.e. slightly less extremely low), etc., and finally rank 100 means the forecast value is above the 99th climate percentile (i.e. extremely high as higher than 99% of all the considered reforecastsclimatological distribution).

Figure 2 shows the process of determining the ranks for rank of each ensemble member. In this example, the lowest member gets the rank of 54 (red r54 on the graph in Figure 2) by moving vertically until crossing the climatological distribution and then moving horizontally to the y-axis to determine the two bounding percentiles and thus the right percentile bin. In this case, the lowest ensemble member value is between the 53rd and 54th percentile, which results in bin-54. Then all ensemble members, similarly, get a bin number, the 2nd lowest values with bin-60 and so on until the largest ensemble member value getting bin-97, as the river discharge value is between the 96th and 97th percentiles. 

Figure 2. Schematic of the forecast extremity ranking of the 51 ensemble members and the 7-anomaly categories in the context of the climatological distribution.

The probability of the forecast to be within one of the 7-anomaly category is calculated by counting of the ensemble members in each category and then dividing by 51, the total number of members. In the example of Figure 2, there is no member in the 3 low anomaly categories, while the 'Normal' category has 2 members, resulting in a 3.9% probability, the 'Bit high' category has 13 members, with a probability of 27.5%, the 'High' category has 17 members, with a probability of 33.3%, and finally the 'Extreme high' category has 18 ensemble members, with a 35.3% probability. The inset table in Figure 2 shows the number the number of ensemble members with the corresponding probabilities in the 7 categories, but also shows the climatological 'size' in terms of probabilities of the 7 categories. For ease of interpretation, the 7 categories are displayed here with different colours. This highlights, e.g., that the normal flow category's 3.9% probability is much lower than the climatologically expected probability of 20%, however, the three high flow categories have each much higher probabilities than the climatological reference probability, especially the extreme high category, where the forecast probability (35.3%) is more than double the corresponding climatological probability (15%). In addition, the extended 'Near normal' category would have 15 members with 31.4% probability, which is lower than the climatological probability of 50%.  

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