Estimating Non-Stationary Extreme-Value Probability Distribution Shifts and Their Parameters Under Climate Change Using L-Moments and L-Moment Ratio Diagrams: A Case Study of Hydrologic Drought in the Goat River Near Creston, British Columbia

Here, we investigate the use of rolling-windowed L-moments (RWLMs) and L-moment ratio diagrams (LMRDs) combined with a Multiple Linear Regression (MLR) machine learning algorithm to model non-stationary low-flow hydrological extremes with the potential to simultaneously understand time-variant shape, scale, location, and probability distribution (PD) shifts under climate change. By employing LMRDs, we analyse changes in PDs and their parameters over time, identifying key environmental predictors such as lagged precipitation for September 5-day low-flows. Our findings indicate a significant relationship between total August precipitation L-moment ratios (LMRs) and September 5-day low-flow LMRs (τ2-Precipitation and τ2-Discharge: R2 = 0.675, p-values < 0.001; τ3-Precipitation and τ3-Discharge: R2 = 0.925, p-value for slope < 0.001, intercept not significant with p = 0.451, assuming α = 0.05 and a 31-year RWLM), which we later refine and use for prediction within our MLR algorithm. The methodology, applied to the Goat River near Creston, British Columbia, aids in understanding the implications of climate change on water resources, particularly for the yaqan nuʔkiy First Nation. We find that future low-flows under climate change will be outside the Natural Range of Variability (NROV) simulated from historical records (assuming a constant PD). This study provides insights that may help in adaptive water management strategies necessary to help preserve Indigenous cultural rights and practices and to help sustain fish and fish habitat into the future.