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and the trend adjustment for each year is:
ΔQ(t) = √R² × [Q̂(tref) − Q̂(t)]
The adjusted annual maximum is then:
Qadj(t) = Q(t) + √R² × [Q̂(tref) − Q̂(t)]
Since the fitted trend is linear, this can also be expressed as:
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Importantly, the adjustment does not replace individual annual maxima with values from the fitted regression. The original annual maxima remain the basis of the adjusted series, with only the √R²-weighted long-term trend difference added:
Qadj(t) = max[0, Q(t) + √R² × β₁(tref − t)]
Consequently, the interannual variability and individual extreme events contained in the original AMAX series are retained, while the estimated systematic long-term change is progressively corrected according to how strongly the fitted linear trend is supported by the AMAX series.
Following the annual maxima adjustment, the same stationary Gumbel extreme-value distribution is fitted to the adjusted annual maxima as used for previous GloFAS versions (see: GloFAS v4 and earlier versions). The Gumbel distribution parameters are estimated using the same sample L-moment method, and the return-period discharge thresholds are calculated from the resulting adjusted, stationary-equivalent AMAX sample.
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Example catchment in the Congo basin to demonstrate the behaviour and impact of the annual maxima adjustment on the related flood thresholds.
Impact on real-time GloFAS forecasts
The use of the adjusted flood thresholds in place of the original thresholds is expected to have a substantial positive impact on the reliability of the real-time GloFAS ensemble forecasts in areas affected by large trends in the reanalysis. In such locations, the original thresholds can be poorly representative of the more recent discharge regime and therefore inconsistent with the discharge levels of the real-time forecasts. The adjustment brings the flood thresholds into better alignment with the recent modelled discharge regime, while retaining the information provided by the complete 1979–2025 reanalysis period.
This impact can be particularly large in regions such as the Congo basin example shown above, where the original thresholds were substantially higher than those derived from the trend-adjusted annual maxima.
References
Zsótér, E., Cloke, H., Prudhomme, C., Harrigan, S., de Rosnay, P., Muñoz-Sabater, J. and Stephens, E. (2020): Trends in the GloFAS-ERA5 river discharge reanalysis. ECMWF Technical Memorandum No. 871.