Temporal scaling in hydrological variables: Methods, patterns, and comparative insights

• This review synthesizes advances in the temporal scaling of key hydrological signals and clarifies the methods commonly used to quantify it. • Variations in temporal scaling behaviors among hydrological variables are emphasized via spectral slope comparisons and transfer function analyses, reflecting watershed filtering processes. • Temporal scaling in hydrological variables support sustainable water management by detecting climate/land-use–driven regime shifts and guiding targeted monitoring and adaptive water-quality/quantity strategies. Temporal scaling of hydrological signals has been recognized since the mid-20th century, with early studies on surface water and more recent work extending to subsurface flow, where signals display distinct scaling behaviors. Despite this progress, studies remain fragmented across variables and methods, and a systematic review is needed to consolidate current understanding. This review synthesizes recent advances in understanding the temporal scaling behavior of precipitation, stream discharge, groundwater levels, baseflow, soil moisture, and solute concentrations, drawing on both observations and modeling. Commonly applied approaches such as rescaled range analysis, detrended fluctuation analysis, and spectral analysis are compared, with attention to their strengths in quantifying scaling behavior. Differences in scaling characteristics across signals are summarized, reflecting hydrological signal filtering and watershed regulation processes. Particular emphasis is given to spectral slope ( β ) evaluations and transfer function (TF) analyses, which reveal how watersheds convert high-frequency climatic inputs into smoother and more persistent outputs such as baseflow. By integrating variable-specific and cross-scale perspectives, this review establishes a coherent framework linking temporal scaling mechanisms to watershed functioning. Future research should advance multi-source datasets, nonstationary and multivariate modeling, and physics-informed machine learning to better reveal causal drivers and support sustainable water resources management under changing climate and human influences.