Quantifying Scale-Dependent Streamflow Responses to Precipitation, Temperature, and Humidity: A Wavelet-Based Multivariate Approach

Streamflow response to precipitation, temperature, and relative humidity is inherently nonlinear, non-stationary, and scale-dependent, challenging traditional statistical methods in the time–frequency domain. To address this, we applied wavelet techniques (CWT, DWT, XWT, and MWC with AWC and PASC indices) to monthly hydroclimatic time series (1981–2022) from the Khiav Chai watershed, Iran. Temperature and relative humidity exhibited persistent, significant 12-month cycles throughout the study period, whereas precipitation and streamflow displayed irregular clustering with short-term (4–8 months) and multiyear (32–64 months) periodicities. Bivariate coherence was strongest for temperature-streamflow (AWC = 0.488; PASC = 25.6%) and temperature-relative humidity (AWC = 0.446; PASC = 23.87%), while precipitation-temperature showed the weakest coherence (PASC = 9.16%). Multivariate MWC analysis revealed that the four-variable model (discharge, precipitation, temperature, and relative humidity) yielded the highest coherence (AWC = 0.736; PASC = 59.39%). Notably, including temperature alongside precipitation increased the PASC from 10.86% to 44.40%, a gain of 33.54 percentage points, highlighting the broader significant coherence captured by the combined climatic variables. The results confirm that streamflow is governed by a multivariate, multiscale hydroclimatic system. At seasonal scales, precipitation directly drives runoff, while at annual and longer scales, temperature becomes dominant through its control on evapotranspiration and atmospheric moisture content. Ignoring temperature and humidity alongside precipitation thus provides an incomplete picture of streamflow variability. These results show the necessity of incorporating diverse climatic variables in hydrological analyses and streamflow predictions under changing climate conditions.