Nutrient spiraling

The processes of advection, dispersion, and transient storage included in the above models describe only the influences of hydrology and the channel upon the downstream transport of a solute. However, reactive solutes experience additional processes that retard their downstream passage. By comparing the passage of reactive and conservative solutes, the magnitude of these additional processes can be quantified. Some reactive solutes may have their dynamics governed solely by physical-chemical processes such as sorption-desorption, whereas nutrients are strongly influenced by biological processes, although physical-chemical processes also can be important. To accommodate these processes of uptake and mineralization or release of a reactive solute, the hydrologic models of the previous section must be modified to include an uptake rate and a release or mineralization rate. By adding these additional terms to Equation 11.1, changes in the concentration of a solute as it passes a point over time is modeled as:

OC OC d2C 1

at ax ox2 z

Additional terms include depth (z), the dynamic uptake rate (Ac), the mineralization rate (Ab), and the mass per unit of area of immobilized nutrient in the streambed (Cb) (Webster and Valett 2006).

The complete cycle of a nutrient atom as it is transported downstream includes its transformation from inorganic to organic form by biological uptake and its subsequent release and mineralization (Newbold et al. 1981). Therefore, spiraling length (S, in meters) is the sum of the distance traveled in dissolved inorganic form in the water column, called the uptake length (SW), and the distance traveled within the biota before being mineralized and returned to the water column, called the turnover length (SB) (Figure 1.6).

Uptake length is a measure of nutrient limitation and efficiency of nutrient use in streams, with short travel distances indicating high demand relative to supply and greater retentiveness by the stream ecosystem, whereas long travel distances indicate the opposite. Turnover length is a measure of distance traveled by the atom within the biota until its eventual release back into the water column, thus completing one spiral passage downstream. The biological compartment generally is associated with the streambed, as attached microorganisms, periphyton, and benthic invertebrates. Typically an atom will travel the greatest distance in the water column, and so one expects SW to be much greater than SB. In fact, field studies have shown that SW represents the greatest fraction of total spiraling distance, so most studies focus on uptake length and related metrics including uptake velocity and areal uptake rate. In addition, the uptake of dissolved available nutrient from the water column is easier to quantify than its subsequent release.

Uptake length is estimated using plateau values of the concentration of a reactive solute at successive points downstream from its release (Figure 11.5). Certain conditions must be met and are evidenced by the simultaneous arrival of a definite plateau of both conservative and reactive solute. Plateau concentrations of the reactive solute, corrected for dilution by dividing through by the conservative tracer, will form a straight line plot against distance on a logarithmic scale. The slope (kw) is 1 /SW. The term kw, also known as the longitudinal uptake rate, is the dynamic uptake rate (Ac) of Equation 11.4 divided by velocity (v):

Uptake length depends strongly on discharge and velocity and thus varies with stream size, and so it is desirable to standardize SW by converting it to a measure of the uptake velocity (vf) of the solute. Also referred to as the mass transfer coefficient, vf quantifies the velocity at which a molecule moves from the water column to the stream bottom as a result of biotic or abiotic processes. It is calculated as:

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