Load estimation discharge consents and compliance

As noted within the introduction to this chapter, the calculation of the mass flux or load of a substance within rivers rather than just its concentration is important for hydrological research and in the assessment of water quality by regulatory agencies. Load, L, is defined over a time period of length, T, as:

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Fig. 8.7 A time series of total phosphorus (total P or TP) measured with a bank-side spectrophotometer. These data are shown with rainfall, river discharge and specific conductance data for a tributary of the Loch Neagh basin, Northern Ireland, UK. (Reproduced from Jordan et al., 2007 with permission of Phil Jordan.)

where C is the measured concentration and Q is the river discharge (or discharge of an effluent) being considered. When continuous samples of discharge and concentration are not available, then this can be expressed in the discrete increment form:

where i is a time step index in a period of N time increments. Ideally, monitoring of river discharge (via sub-hourly monitoring of river stage; Section 7.3) and monitoring of concentration (Section 8.5) or sampling of concentration (Section 8.6) is at a very high intensity (i.e. sub-hourly). Loads calculated from such intensive sampling (e.g. Fig. 8.7) have a high degree of accuracy (Littlewood, 1995). It is, however, more common for UK regulatory authorities to collect river stage and hence discharge at such a high intensity, but for the water quality to be sampled only once a week or once every 3 weeks. To obtain the concentration data on the same time step as the discharge data (for subsequent load estimation), a relationship between the observed concentration values and discharge values at the same time is established. This rating curve approach does, however, introduce a substantial error into the load calculations. These errors arise because the C—Q relationship is different on the rising and falling stages of storm hydrographs (a phenomenon called hysteresis), and because different hydrographs in a time series have different C—Q relationships (see e.g. Sivakumar, 2006; Jordan et al., 2007)

Such load estimates are particularly important in setting licences for discharge consents for point sources of effluents, e.g. an industrial effluent discharge or discharge from a waste water treatment works. Consents are issued as a way of controlling effluent discharges into designated rivers to ensure that the water-quality standards for that river reach can be maintained. This is achieved by taking account of how upstream river and effluent discharges might affect downstream water quality. For a simple conservative substance, this involves simple mixing calculations (see Section 7.5 on dilution gauging and Section 11.3 on mixing models) given information about the upstream load in a river (QCu) and the load from the effluent (qCe). Thus, under steady discharge conditions and after downstream mixing has taken place, the downstream concentration (Cd) is calculated:

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