Consistent Theoretical and Empirical Predictions of at‐a‐Station Hydraulic Geometry Exponents in Stream Reaches

Abstract

Reach-scale at-a-station hydraulic geometry (AHG) relationships are power laws that describe variations of reach-averaged water depth, wetted width, and current velocity in stream reaches when discharge varies. Modeling AHG exponents is important, because the variations of hydraulics with discharge in stream networks influence physical habitats of aquatic species, biodiversity, water temperature, nutrient fluxes, and sediment transport. Theoretical approaches indicated that AHG exponents should depend on topographic descriptors of cross sections and roughness elements. Empirical approaches suggested that AHG exponents partly depend on hydraulic characteristics measured at a single discharge. We used a unique data set of AHG observed in 812 stream reaches (obtained from measurements at several discharge rates or from hydrodynamic models) to (1) test the consistency of theoretical and empirical predictions of AHG exponents and (2) test the generality of AHG predictions across rivers of different countries with variable landscape settings. We found that observed AHG depended on topographic predictors (describing cross-section shape and substrate size) as expected from theory. However, AHG exponents were better predicted by empirical hydraulic characteristics of reaches: the ratio of wetted width to bankfull width and the reach Froude number. The effects of hydraulic variables were consistent with those of topographic predictors. In addition, relations between AHG and hydraulic predictors were significant and with similar direction in different data sets. Despite limited explanatory power, our results help identifying general drivers of AHG exponents. Their application still requires measurements at a single discharge rate but open perspectives of generalized AHG prediction by remote sensing.

River water temperatures are higher during lower flows after accounting for meteorological variability

“…Terms representing these antecedent conditions added explanatory power when the air temperature was applied as the meteorological variable but added very little explanatory power when solar radiation and earth temperature were applied. Lack of improvement in model fit with inclusion of lags was likely due to the relatively fast flowing water (see Morel, Booker, Gob, & Lamouroux, 2020b for details of hydraulic conditions in New Zealand conditions) and small catchments investigated. Soil has a greater capacity to maintain heat in comparison to air, and therefore earth temperature exhibits less day-to-day variability than air temperature.…”

“…Although between-site variability is present, river channel hydraulics dictate that reductions in flow result in reductions in water volume (and therefore thermal mass) at a greater rate than reductions in surface area (Dingman, 2007;Morel et al, 2020b). Thus, there is greater potential for water temperature change (typically water warming during daytime through sensible or latent heat transfer) during lower flows.…”

Watershed Controls and Tropical Cyclone-Induced Changes in River Hydraulic Geometry in Puerto Rico

“…Notwithstanding these constraints, the coefficients and exponents from Eqns. 1-4 can vary substantially from place to place (Morel et al, 2020b;Park, 1977), and researchers have yet to fully reveal the physical principles that underly AHG behavior (Jia et al, 2017;Morel et al, 2019; not for lack of trying, e.g. Dingman, 2007;Ferguson, 1986).…”