Estuaries

4.4.1. Estuarine regions

An estuary is a water body that is connected at one end to a river and at the other end to the sea. An estuary velocity reverses with the tide, and an estuary can contain fresh or saline water, although it is generally less saline than that of the sea. For the purposes of this generic methodology a radioactive discharge is assumed to occur from one of the estuarine banks. The radionuclide concentration at the banks may be assessed using a methodology that is very similar to that for rivers, but with some adjustments to account for tidal effects. (See Annex VI for a detailed description of the estuarine methodology.)

4.4.2. Basic estuarine characteristics required for calculation

The following variables and parameters are required to calculate the radionuclide concentration in an estuary: estuarine width B (m); estuarine flow depth D (m); river width B–

(m) under a mean annual river flow rate upstream of the tidal flow area tidal period T_p(s); longitudinal distance from the release point to a potential receptor location x (m); and radionuclide decay constant l_i(s^–1).

The longitudinal distances at which complete vertical mixing is achieved is assumed to occur when the minimum concentration is at least half of the maximum concentration along the vertical direction. The longitudinal distance required to achieve this complete vertical mixing L_z(m) is

L_z= 7D

The radionuclide upstream travel distance L_u (m) is calculated by

L_u= 0.32ΩU_fΩT_p (15)

4.4.2.1. Estimating a default value for the river flow rate and tidal velocities From observation or a map the river width B–

(m) under normal river flow conditions upstream of the estuary, where there is no tidal effect on the river flow, may be estimated.

The mean river flow rate q–

r(m³/s) that corresponds to the river width B– may be obtained from Table III. For default purposes it may be assumed that the 30 year low annual river flow rate q–

r(m³/s) is 1/3 of the mean annual river flow rate q_r. The net freshwater velocity U (m/s) corresponding to the 30 year low annual river flow rate may be calculated by taking

If the maximum ebb (seaward) velocity U_e (m/s) and the flood (upstream) velocity U_f(m/s) is not available, it is possible to assume

U_e= 0.5 m/s U_f= 0.5 m/s

The mean tidal flow speed U_tand the tidal flow rate q_wmay then be estimated by taking

U_t = 0.32(ΩU_eΩ+ΩU_fΩ), q_w= DBU_t

4.4.3. Calculation of radionuclide concentrations

The procedure for calculating radionuclide concentrations in water at a location along the banks of an estuary is illustrated in the form of a flow chart in Fig. 13. Four situations are considered as described.

4.4.3.1. Water usage on the bank of the estuary opposite to the radionuclide discharge point

The maximum radionuclide concentration on the opposite bank is expected to be the cross-sectionally averaged concentration; thus the radionuclide concentration in this region is calculated by

C Q (16) q

x

U C

w i

w

i

te ,_tot = expÊ

-ËÁ ˆ

¯˜ = l U q

BD

= r

Select

If river condition is not known

Calculate

FIG. 13. Procedure for calculating radionuclide concentrations in water resulting from dis-charge into an estuary.

where

C_w,tot is the total radionuclide concentration in water (Bq/m³), Q_i is the average discharge rate for radionuclide i (Bq/s), U is the net freshwater velocity (m/s).

4.4.3.2. Water usage upstream or downstream prior to complete mixing

If water usage occurs at either upstream or downstream locations prior to complete vertical mixing (i.e. ΩxΩ £L_z= 7D), the radionuclide concentration in this case is assumed to be

C_{w, tot}= C₀

where C₀is the radionuclide concentration at the point of discharge (Eq. (11)) in Bq/m³.

4.4.3.3. Water usage upstream at a distance greater than L_u

In a case where water usage occurs upstream at a distance greater than L_u (i.e.

ΩxΩ> L_u= 0.32ΩU_fΩT_p), tidal flow cannot reach the water use location during the flood tide (when the estuarine flow moves landward). Thus

C_{w, tot}= 0

4.4.3.4. Water usage upstream at a distance less than L_uor downstream at a distance greater than L_z

If water usage occurs upstream but within the distance L_u(i.e. 7D <ΩxΩ£L_u= 0.32ΩU_fΩT_p) or if water usage occurs downstream beyond complete vertical mixing (i.e. x > 7D), the estimated radionuclide concentration should be modified to allow for partial mixing. In this case upstream and downstream dispersions are treated as the same. Annex VI describes the upstream concentration correction, which will enable a reader to improve the accuracy of the radionuclide concentration estimate in the upstream area.

The estuarine calculation procedure adopted here is similar to, although a little more complicated than, that described for rivers because tidal effects must be taken into account. The procedure is illustrated in Fig. 13. The parameters required are as follows.

As indicated in Ref. [50], the ratio M of the tidal period (T_p) to the timescale for cross-sectional mixing is

(17) where T_pis the tidal period in seconds (4.5 × 10⁴s for tides occurring twice per day or 9 × 10⁴s for a predominant tide occurring once per day).

The ratio of the longitudinal dispersion coefficient in the estuary to that in a river N corresponding to M may be obtained from Table V. The partial mixing index A is then

(18)

The mixing coefficient P_e corresponding to A may then be determined from Fig. 14. If P_eis less than unity it is recommended that P_e= 1 be assumed.

The radionuclide concentration at upstream or downstream distance x along the estuarine bank with the default longitudinal and lateral dispersion coefficients is obtained by

TABLE V. RATIO N OF THE LONGITUDINAL DISPERSION COEFFICIENT BETWEEN AN ESTUARY AND A RIVER^a

0.01

a Using linear interpolation between values.

M Ratio N M Ratio N M Ratio N

where C_teis obtained from Eq. (16).

As for the river, C_teis the completely mixed radionuclide concentration over an estuarine cross-section. The variable P_ecan be regarded as a correction factor for partial mixing and approaches unity as the downstream distance x increases. (Note that for x > 0.6B²/D, P_e ª 1 as discussed in Annex VI.)