Adjustment of annual maximum discharge series for long-term trends
Flood return-period thresholds in GloFAS are derived from annual maximum discharge (AMAX) series extracted from the long-term river discharge reanalysis. The standard approach 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. 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.
To address this, an adjustment is applied to the annual maxima before fitting the extreme-value distribution. The objective is to remove the estimated long-term change in the magnitude of the annual maxima while retaining the complete historical sample and its interannual variability.
For each location, a trend function is fitted to the annual maximum discharge series. The fitted trend represents the gradual change in the expected magnitude of annual maxima through time. Each historical annual maximum is then shifted according to the difference between the fitted value for its year and the fitted value at a common reference time:
[
Q^{adj}y = Q_y + \left[f(t{ref})-f(t_y)\right],
]
where (Q_y) is the original annual maximum in year (y), (f(t_y)) is the fitted trend value for that year, (f(t_{ref})) is the fitted value at the selected reference time, and (Q^{adj}_y) is the adjusted annual maximum.
The adjustment therefore changes the location of individual annual maxima according to the estimated long-term trend but does not replace the observations with fitted values. Year-to-year deviations from the fitted trend are retained. In other words, the method aims to preserve the interannual variability and the individual extreme events contained in the original reanalysis while removing the systematic temporal change represented by the fitted trend.
The reference time is chosen to represent the recent discharge regime. Consequently, earlier annual maxima are shifted towards the level expected under the recent-period conditions. For an increasing trend, earlier maxima are generally adjusted upwards; for a decreasing trend, they are adjusted downwards. Annual maxima close to the reference period receive little or no adjustment.
A key advantage of this approach is that the complete historical AMAX sample remains available for the extreme-value analysis. No years are discarded and the effective sample size is therefore unchanged. This is particularly important for flood-frequency estimation, where the available record is relatively short and the largest events contain substantial information about the upper tail of the distribution.
Following the adjustment, the flood-frequency analysis is performed on the adjusted annual maxima. The resulting return-period thresholds can therefore be interpreted as thresholds based on the historical range of interannual and extreme-event variability, but referenced to the more recent discharge regime rather than to the average conditions over the entire reanalysis period.
The adjustment is intended primarily to correct gradual, systematic temporal changes in the AMAX series. It does not imply that the underlying climate or hydrological system is strictly stationary, nor does it attempt to predict future changes. Instead, it provides a pragmatic way of producing a stationary-equivalent historical sample representative of a selected reference period while retaining as much information as possible from the available reanalysis.g