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Flood return-period thresholds in GloFAS are derived from annual maximum discharge (AMAX) series extracted from the long-term river discharge reanalysis. The same procedure is applied for every GloFAS river pixel. The generation of the GloFAS flood thresholds follows the below workflow:

  • Extract the annual maxima time series in the long reanalysis period
  • Fit a Gumbel extreme value distribution using the first two L-moments (λ1, λ2)
  • The Gumbel parameters are:

and 

  • For return period T, the related flood threshold X is calculated as:

The plot below demonstrate the process for an example station on the Ganges river (Harding Bridge). It displays the empirical distribution of the extracted annual maxima and the flood threshold curve (out to return period 100 years) based on the Gumbel distribution. In this example for GloFAS v4, the considered reanalysis period was 1979-2022.

Adjusting for non-stationarity

The standard approach described above assumes that the annual maxima are stationary over the reanalysis period. However, long-term changes in the meteorological forcing or other components of the modelling system can introduce systematic trends in the simulated annual maxima. Large trends in GloFAS river discharge have previously been documented, for example by Zsótér et al. (2020), particularly in the Congo basin and the southwestern USA. If such trends are sufficiently large, fitting a stationary extreme-value distribution directly to the complete historical sample may result in flood thresholds that are not representative of the more recent discharge regime and, consequently, of the real-time forecasts.

Up to GloFAS version 4, including the v1, v2 and v3 model families, flood thresholds were generated directly from the unadjusted annual maxima. With the introduction of GloFAS v5 in 2026, an annual maxima adjustment methodology was introduced to address the impact of non-stationarity, particularly large long-term trends in river discharge that are present in some regions of the GloFAS reanalysis. The annual maxima adjustment is applied globally on all river pixels, with the adjustment's impact only noticeable over areas with pronounced river discharge trends.

The adjustment methodology, used from GloFAS version 5 onwards, is described here: Handling of non-stationarity in the flood thresholds.

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