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In a sub-seasonal forecast, especially at the the longer ranges, the day-to-day variability of the river flow, with prediction of the actual expected flood severities, can not be predicted expected due to the very high uncertainties. What is possible, is to rather give an indication of the river discharge anomalies and confidence in those predicted anomalies. As the forecast range increases, the uncertainty will also generally increase and with it the sharpness of the forecast will gradually decrease and more and more often the forecast just going to show the climatologically expected conditions.
The determination of the sub-seasonal forecast signal is reflective of this and was designed to deliver a simple to understand categorical information on the anomalies and uncertainties present in the forecast, relative to the underlying climatology.
Climatological bins and anomaly categories
From the 660 reforecast values in the climate sample, 99 climate percentiles are determined (y-axis), which represent equally likely (1% chance) segments of the river discharge value range that occurred in the 20-year climatological sample. Figure 1 shows an example climate distribution, with only the deciles (every 10%), the two quartiles (25%, 50% and 75%), of which the middle (50%) is also called median, and few of the extreme percentiles are plotted near the minimum and maximum of the climatological range indicated by black crosses. Each of these percentiles have an equivalent river discharge value on the x-axis. From one percentile to the next, the river discharge value range is divided into 100 equally likely bins, some of which is indicated in Figure 1, 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.
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Based on the percentiles and the related 100 bins, there are seven anomaly categories defined. These are indicated in Figure 1 by shading. The two most extreme categories are the bottom and top 10% of the climatological distribution (<10% as red and 90%< as blue). Then the moderately low and high river discharge categories from 10-25% (orange) and 75-90% (middle-dark blue). The smallest negative and positive anomalies are defined by 25-40% and 60-75% and displayed by yellow and light blue colours in Figure 1. Finally, the normal condition category is defined from 40-60%, so the middle 1/5th of the distribution, coloured grey in Figure 1.
Forecast extremity rank computation
The forecast has 51 ensemble members, which all check where they fall in the 100 bins of the climate. This will be the anomaly or extremity value (called hereafter rank) of the ensemble members as one of the values from 1 to 100. For example, 1 will mean the forecast value is below the 1st climate percentile (i.e. extremely anomalously low), then 2 will mean the value is between the 1st and 2nd climate percentiles (i.e. slightly less extremely low), etc., and finally 100 will mean the forecast value is above the 99th climate percentile (i.e. extremely high as higher than 99% of all the considered reforecasts representing the model climate conditions for this time of year, location and lead time).
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Then the population and probabilities of each of the 7 anomaly categories are determined by counting the ensemble members in each category. In the example of Figure 2, there is no member in the 3 low flow anomaly categories, while the normal category has 2, the bit high category 13, the high category 17 and finally the extreme high category 18 ensemble members. These numbers then are converted to probabilities by dividing them with 51. The inset table in Figure 2 also shows the size (in probabilities) of the 7 categories. This highlights that the nomral category got, for example, 2 members, which results in 3.9% probability, but the expected climatological probability of this category is 20%.
Treatment of 0 values
The extremity rank can be computed for any value above 0 m3/s. However, the rank computation becomes undefined when the values drop to 0. This is actually a major problem, as large parts of the world has dry enough areas combined with small enough catchments to have near zero or totally 0 river discharge values. For this singularity case, a special treatment was defined. Here, all river discharge values below 0.1 m3/s are treated as 0, and will get the special rank computation. All the 0 ensemble member values get a randomly assigned rank from any of the percentiles that have 0 (i.e. below 0.1 m3/s) values in the model climatology. This effectively means, the 'rank-undefined' section of the ensemble forecast is going to be spread across the 'rank-undefined' section of the climatology during the rank computation.
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