Ubiquitous fractal scaling and filtering behavior of hydrologic fluxes and storages from a mountain headwater catchment

Authors: DWIVEDI, R. - University Of Vermont; Knowles, John; EASTOE, C. - University Of Arizona; MINOR, R. - University Of Arizona; ABRAMSON, N. - University Of Arizona; MITRA, B. - University Of Arizona; WRIGHT, W.E. - University Of Arizona; MCINTOSH, J. - University Of Arizona; MEIXNER, T. - University Of Arizona; FERRE, P.A. - University Of Arizona; CASTRO, C. - University Of Arizona; NIE, G-Y - University Of Arizona; BARRON-GAFFORD, G.A. - University Of Arizona; CHOROVER, J. - University Of Arizona

Submitted to: Water
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/20/2020
Publication Date: 2/24/2020
Citation: Dwivedi, R., Knowles, J.F., Eastoe, C., Minor, R., Abramson, N., Mitra, B., Wright, W., Mcintosh, J., Meixner, T., Ferre, P., Castro, C., Nie, G., Barron-Gafford, G., Chorover, J. 2020. Ubiquitous fractal scaling and filtering behavior of hydrologic fluxes and storages from a mountain headwater catchment. Water. 12. https://doi.org/10.3390/w12020613.
DOI: https://doi.org/10.3390/w12020613

Interpretive Summary: Mountain headwater catchments are critically important water sources and storage reservoirs for agricultural, industrial, and residential consumers. Hydrological measurements in the mountains, however, are complicated by difficulties associated with remote access, harsh conditions, and rugged terrain. Long-term and/or high frequency mountain hydrological data sets are therefore scarce and often contain large data gaps. As a result, this study used spectral analysis to constrain the expected variability of mountain streamflow, precipitation, evaporation, and subsurface storage on time scales from hours to years in Arizona, USA. This type of analysis represents an effective way to evaluate the presence of behaviors that persist across multiple scales in time series data, termed fractal behavior. When this type of behavior is identified, it can provide information about the expected movement of water in areas that are not measured or when measurements are not possible. In this way, we found evidence of fractal scaling over periods of days (precipitation and soil water storage) to months (streamflow and evaporation) that corresponded to wet and dry periods between storms and seasons, respectively. In general, the catchment transformed random precipitation inputs into predictable streamflow outputs by means of structural properties that determined water storage and flow dynamics. This research contributes to an improved understanding of water movement through mountain catchments that are disproportionately important to water resources globally.

Technical Abstract: We used the weighted wavelet method to perform spectral analysis of precipitation, streamflow, actual evapotranspiration, and soil water storage at a sub-humid mountain catchment near Tucson, Arizona, USA. Fractal scaling in precipitation and the daily change in soil water storage occurred up to a period of 14 days, and corresponded to the typical duration of relatively wet and dry intervals. In contrast, fractal scaling could be observed up to a period of 0.5 years in streamflow and actual evapotranspiration. Phase relationships between water balance components changed with component period and were not perfectly in- or out-of-phase at all periods. Self-averaging behavior was apparent, but the temporal scales over which this behavior was applicable differed among the various water balance components. Conservative tracer analysis showed that this catchment acted as a fractal filter by transforming white-noise in the precipitation input signal to a 1/f flicker in the streamflow output signal by means of both spatial and temporal subsurface advection and dispersion processes and soil wetting properties. This study provides an improved understanding of hydrological filtering behavior in mountain critical zones that are critical sources of water and ecosystem services throughout the world.