Surface storage dynamics in large rivers: Comparing three‐dimensional particle transport, one‐dimensional fractional derivative, and multirate transient storage models

Abstract

[1] Large rivers are major conduits for sediment and nutrient transport and play an important role in global biogeochemical cycles. While smaller rivers received attention in recent decades for hyporheic exchange and nutrient uptake, fewer studies have focused on the dynamics of surface storage zones in large rivers. We investigate transport dynamics in the St. Clair River, an international river straddling the U.S.-Canadian border, using a combination of modeling and dye tracer studies. We describe a calibrated three-dimensional hydrodynamic model to generate (synthetic) breakthrough data to evaluate several classes of 1-D solute transport models for their ability to describe surface storage dynamics. Breakthrough data from the 3-D particle transport model exhibited multimodal behavior and complex dynamics that could not be described using a single first-order exchange coefficient-an approach often used to describe surface storage in transient storage models for small rivers. The 1-D models examined include multirate transient storage (MRTS) models in which storage zones were arranged either in series or parallel as well as 1-D models based on fractional derivatives. Results indicate that for 1-D models to describe data adequately, the timing of solute pulses that correspond to various in-channel features such as sandbars, islands or meander bends should be taken into account. As a result, the MRTS model with storage zones arranged in series (i.e., exchange rates triggered sequentially) provided the best description of the data. In contrast, fractional derivative models that assume storage zones were arranged in parallel failed to capture the multimodal nature of the breakthrough curves.Citation: Anderson, E. J., and M. S. Phanikumar (2011), Surface storage dynamics in large rivers: Comparing three-dimensional particle transport, one-dimensional fractional derivative, and multirate transient storage models, Water Resour. Res., 47, W09511,

Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

“…Mathematical models have long proved useful for analyzing or predicting the fate and transport of contaminants in streams and rivers (Bencala, 1983;Fischer et al, 1979;Runkel, 1998;Thomann, 1973), including contaminant exchange with fluvial sediments and the surrounding stream bed (Thackston and Schnelle, 1970;Bencala and Walters, 1983;Wörman, 1998;Anderson and Phanikumar, 2011), often referred to as the hyporheic zone (Wörman, 1998;Runkel et al, 2003;Bencala, 2005;Gerecht et al, 2011). Such models may be used also for subsurface streams and karst systems (Field, 1997).…”

“…Constituents in surface waters may involve a range of specific natural and anthropogenic chemicals, including toxic trace elements, radionuclides, industrial solvents, pesticides, nutrients, pathogenic microorganisms, pharmaceuticals, and a variety of water quality variables such as total salinity or dissolved oxygen. Because of the many complex and often nonlinear physical, chemical and biological processes affecting contaminant transport in streams and rivers, numerical models are now increasingly used for prediction purposes (e.g., Anderson and Phanikumar, 2011;O'Connor et al, 2009;Runkel, 1998;Runkel and Chapra, 1993). Still, analytical and quasi-analytical approaches are useful for simplified analyses of a variety of contaminant transport scenarios, especially for relatively long spatial and time scales, when insufficient data are available to warrant the use of a comprehensive numerical model, and for testing numerical models.…”

A fluid-mechanics based classification scheme for surface transient storage in riverine environments: quantitatively separating surface from hyporheic transient storage

“…(2009a,b) solved the groundwater flow equation to estimate HTS, and Anderson and Phanikumar (2011) used a 3-D hydrodynamic and particle transport model to generate synthetic STS breakthrough curves (BTCs). O'Connor et al (2010) estimated STS from predictive equations based on the geometry of emergent lateral cavities at channel sides.…”

“…5a), the upstream detachment distance (from the obstacle), x FFS , and reattachment distance (from the streambank), y FFS , are weakly dependent on Reynolds number, Re W , (based on obstacle width) for 4000 < Re W < 26 300 (Awasthi, 2012). The upstream detachment distance ranges from about 0.8 to 1.2 W and the reattachment distance ranges from about 0.5 to 0.6W (Addad et al, 2003;Fiorentini et al, 2007;Camussi et al, 2008;Leclercq et al, 2009). The second separation region at the obstacle head results in a more complex flow field than the upper boundary layer separation region.…”

“…Exact relationships between flow and geometry parameters and downstream attachment distance are poorly understood due to the unsteady nature of the mixing layer at the obstacle head and the amplification of mixing layer instabilities from the upstream recirculating flow and mixing layer (Pearson et al, 2001;Awasthi, 2012). A generalized result for reattachment distance is that W/δ = 1.43 yields reattachment distances ranging between 4.7 and 5.0 W for 17 000 < Re W < 50 000 (Moss and Baker, 1980;Addad et al, 2003;Gasset et al, 2005), and decreases to 3.2 W at higher Re W (= 170 000) (Leclercq et al, 2009). At lower W/δ (∼ 0.2), reattachment distances range between 1.5 and 2.1 W for 8000 < Re W < 26 300 (Camussi et al, 2008), and decrease to 1.4 W at higher Re W (= 50 000) (Castro and Dianat, 1983).…”