Abstract
Glaciohydraulic tremor is the seismic energy generated by turbulent water flow through the subglacial environment, characterized by frequencies between 1.5 and 10 Hz. Tremor is known to serve as a reliable proxy for variations in glacier runoff, with theoretical power-law relationships relating tremor amplitude and subglacial discharge under distinct hydrological regimes. However, the quantitative relationship between tremor and discharge remains poorly constrained. Existing theory lacks rigorous testing across multiple glacial systems, and no existing model has the capacity to directly predict discharge quantities from seismic observations. This research integrates stream gauge records, passive seismic observations, meteorological data, and remote sensing imagery with hydrological modeling and statistical analysis to quantify this relationship across four alpine glaciers in Alaska and the French Alps. A degree-day melt model accounts for snow and ice melt, combined with precipitation contributions across surrounding watersheds, and is smoothed using exponential convolution and calibrated by least squares fitting to downstream gauge observations. I use the ratio between modeled discharges at the source and gauge to scale gauge observations and estimate the discharge at tremor source locations beneath the glacier. Comparison between source discharge and tremor amplitude corrected for attenuation across all sites yields a best-fit empirical relationship of Q=(5.50±1.20 )×10^8 V^(1.615±0.015), achieving R^2 of 0.739 with 95% of predictions falling within a factor of 2.89 of the corresponding estimated discharge. This result closely agrees with the theoretically derived relationship fitted with a fixed exponent giving V1.6 for conditions expected to govern fluctuations in discharge during peak melt season and exhibits identical statistical performance across this dataset. Model analysis reveals this relationship is highly sensitive to individual glacial environments. Cross-validation testing indicates that theoretical predictions with the fixed exponent of 1.6 perform best across diverse systems and broadly predict discharge within a factor of five. Unconstrained, best-fit relationships, where both the scaling factors and exponents are free parameters, vary considerably across testing iterations, likely reflecting differences in subglacial conditions and discharge magnitudes of the training dataset. The model demonstrates greatest reliability in well-developed, channelized drainage systems in smaller alpine environments. Ultimately, this work establishes the first multi-glacier empirical validation of the tremor-discharge power relationship, advancing seismic methods as a quantitative tool for hydrological monitoring of glacial systems where conventional gauging is impossible.