Box 8 Stream Tracer Breakthrough Models
Cardenas (2015) and Boana and others (2014) offer a comprehensive review of conceptual models and methods to evaluate stream tracer test results. Boana and others (2014) present governing equations representing four models to assess tracer breakthrough data: advection-dispersion and fractional advection-dispersion equation, the space-time fractional advection-dispersion equation, fractional spatial-derivative advection-dispersion equation, and the fractional temporal-derivative advection-dispersion equation. Most approaches attempt to fit model parameters to reproduce the behavior of observed tracer breakthrough. These results are used to describe the magnitude of exchange between the stream and groundwater.
Often modeling is simplified to represent tracer transport in a one-dimensional setting with a storage mechanism (e.g., Hays, 1966; Thackston and Schnelle, 1970; Valentine and Wood, 1979; Bencala and Walters, 1983; Jackman et al., 1984; Kim et al., 1992; Wörman, 1998; Bencala et al., 2011). The basic One-Dimensional Transport with Inflow and Storage (OTIS) code developed by the United States Geological Survey is widely used and usually applied before more sophisticated modeling is attempted (e.g., Runkel and Chapra, 1993; Runkel et al., 1998). A limitation is that OTIS allows the adjustment of only a few parameters, whereas the transport process is generally more complicated (e.g., Choi et al. 2000; Runkel, 2002; Bencala et al., 2011). Improvements to this code incorporate additional field characterization to include other components in the exchange analyses (e.g., Haggerty et al., 2000; O’Connor et al., 2010; Worman et al., 2002; Boano et al., 2007). The STAMMTL model adds multi-rate mass transfer to transport models (Haggerty and Reeves, 2002). The Solute Transport in Rivers Model includes the designation of separate storage locations and the timing of hyporheic exchanges (Marion et al., 2008). Refer to Boano and others (2014) for a more complete discussion of tracer modeling methods.
As analysis techniques have advanced, new models account for varying exchange time scales (Haggerty et al., 2002; Gooseff et al., 2003ab) and multiple storage mechanisms (Harey and Fuller, 1998; Haggerty et al., 2009). Some researchers (e.g., Haggerty et al., 2009; Liao and Cipka, 2011; Liao et al., 2013) have developed methods to look at geochemical changes in water cycled in the hyporheic zone. Transient changes of stream channel depths and vegetation have been noted to change stream retention conditions and studies may need to account for changes in physical conditions of the stream (e.g., Harvey et al., 2003).