Multifractal detrended fluctuation analysis of hydroclimatic series across Uganda in East Africa

Abstract

ABSTRACT This study applied Multifractal Detrended Fluctuation Analysis (MFDFA) to investigate the scaling behaviour of streamflow, precipitation, and potential evapotranspiration (PET) in nine Ugandan catchments during 1990–2013. We estimated, among others, the Hurst exponent ( H ), mass exponent τ ( q ) , multifractal spectra f ( h ) , and multifractal width ( Δ h ). All hydroclimatic variables exhibited H values greater than 0.5 and were significantly ( p < 0.05 ) different from white noise, confirming long-range dependence (LRD). Across catchments, precipitation persistence was lower than that of streamflow but higher that of PET. Strong multifractality was observed in streamflow (1.04 ≤ Δ h ≤ 4.81) and precipitation (1.4 ≤ Δ h ≤ 3.9), whereas PET exhibited weak multifractality (0.12 ≤ Δ h ≤ 0.32). The f ( h ) were predominantly right-skewed, suggesting a stronger contribution from small fluctuations. The τ ( q ) further confirmed multifractality driven by both small- and large-magnitude variations. The results indicate that streamflow is the most persistent hydroclimatic variable, while precipitation behaves as a climate-synchronized but weakly integrated process, with PET playing an intermediate role largely associated with short-term moisture modulation. Streamflow, through precipitation runoff generation, partially inherits its scaling behaviour more from precipitation than PET. These results underscore the multiscale complexity of hydrological processes across Uganda and emphasize the significance of incorporating multifractality and LRD in hydrological modelling and water resources planning.