Physical transport

Solute dynamics are closely coupled with the physical movement of water, and the net flux is downstream. The modeling of a conservative solute in transport involves only physical processes and so is less complex than models for reactive solutes. If a conservative solute is released at some point, and measurements are made at another location downstream, the concentration will be observed to rise, reach a plateau, and then decline as the pulse passes the point of monitoring (Figure 11.5). A first approximation to this curve can be achieved with a basic equation describing advection and dispersion, taking into account stream dimensions and water velocity. The solute is transported from its point of release due to the unidirectional force of current (advection), and disperses due to molecular diffusion and primarily by turbulent mixing. Under certain simple conditions, which include a uniform channel,

FIGURE 11.5 Concentrations of 32P in streamwater at 15 (*), 47 (■), and 120 m (A) locations downstream of a 30 min release of radioactive phosphorus in a small woodland stream. (Reproduced from Newbold et al. 1983.)

FIGURE 11.5 Concentrations of 32P in streamwater at 15 (*), 47 (■), and 120 m (A) locations downstream of a 30 min release of radioactive phosphorus in a small woodland stream. (Reproduced from Newbold et al. 1983.)

constant discharge, and no subsurface flow, the change in solute concentration (C) over time is described as follows:

dt Ox dx2

The first term describes downstream advection and is proportional to water velocity, . The second term describes mixing of the solute randomly throughout the water mass according to a dispersion coefficient, D.

More complicated models are needed to account for additional variables such as groundwa-ter and tributary inputs, channel storage, and subsurface flow (Stream Solute Workshop 1990). Solute dynamics are less complex in large rivers compared to small streams because large rivers generally have low slopes, are deeper than the roughest bed feature, and have relatively uniform and perhaps regulated flows. Small streams tend toward the opposite characteristics and often have substantial exchange of surface water with interstitial water, back eddies behind obstructions, and areas of slow-moving water (Bencala and Walters 1983). The net effect is that water and solutes move downstream more slowly than would be expected based on the main flow of current. This can be demonstrated by releasing a conservative solute such as a dye and recording its passage at successive distances downstream. Tracer quantities decline due to mixing and dilution. In addition, the time between tracer release and its downstream arrival is longer than would be predicted from water velocity in the main channel, and the peak broadens as one proceeds downstream.

One can model the complex effects of surface-subsurface exchange and back eddies by assuming that solutes are temporarily retained in a "transient storage zone'' of slowly moving or even stationary water. Solute diffuses into the storage zone during the initial passage of the pulse, and is released back into the stream as the pulse passes and stream concentrations decline. The equations to describe the temporal and spatial changes in the concentration of a conservative solute, including transient storage are:

OC 0 C d2C

at As where A (m2) is the main channel cross-sectional area and AS is the cross-sectional area of the modeled storage zone. The rate of dispersion of solute in or out of this zone is proportional to the difference between solute concentration in the storage zone (CS) and in the water column (C ), and the transient storage exchange coefficient (a). These equations can become more complex when other terms like groundwater inputs are included (Webster and Valett 2006). Adding a term for transient storage permits the model to account for significant features of the observed passage of a solute pulse that Equation 11.1 is unable to mimic. Specifically, measured passage of a tracer pulse usually shows the rising shoulder of the actual pulse to be more gradual and the descending tail to be prolonged relative to the symmetrical curve generated by the first equation.

It should be recognized that these models are empirically useful descriptions of observed dynamics in which transient storage clearly takes place. However, the storage zone component of the model is an abstraction. In contrast to the cross-sectional area of the stream channel, which can be measured directly, AS is determined by fitting the model to observed solute dynamics. Nonetheless, storage zones exist and are numerous. Bencala and Walters (1983) recognized five in their study of solute transport in a small mountain stream, including turbulent eddies generated by large-scale bottom irregularities, large but slowly moving recirculating zones along the sides of pools, small but rapidly recirculating zones behind flow obstructions, side pockets, and flow in and out of beds of coarse substrate.

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