Hydrological drought and flood extreme events were quantitatively defined to occur when daily water levels in Manaus fall below 15.8 m or rise above 29.0 m, respectively. These thresholds are used by the CPRM to monitor severe droughts and floods in this gauge and correspond to the long-term mean of minimum and maximum annual values ±1 SD. Furthermore, when water levels at Manaus reach 29 m, the municipality declares emergency status as the lower parts of the city start to be flooded. The duration and intensity of a drought (flood) event were determined as the number of days with water levels below (above) 15.8 m (29.0 m) and the minimum (maximum) daily water level reached during the event, respectively.

Temporal changes in the occurrence rates of drought and flood events were estimated using a nonparametric Gaussian kernel technique (36, 37). Here, the estimated time-dependent occurrence rate, λ(t), corresponds to the probability of an extreme event per time interval, and thus its inverse gives the time-dependent return period. Kernel smoothing over a window of 15 years was used to explore decadal and longer-term changes in λ(t) together with their 90% confidence intervals from 2000 bootstrap simulations by resampling the list of yearly events with replacement. This technique is especially suited for modeling nonstationary processes such as our peak-over-threshold chronologies of extreme events (37). The Cox-Lewis statistic (36) was used to test the null hypothesis of constant occurrence rate over the observation interval (1903–2015) against the alternative hypothesis of a monotonic trend in the occurrence rate. The bivariate return periods of drought and flood events based on their observed duration and intensity were estimated using a two-dimensional Gumbel copula analysis (38).

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