Combining modelling and monitoring to determine fluxes of water

Continental ShelfResearch,

Vol. 16, No. 2, pp. 237-257, 1996 Elsevier Science Ltd Printed in Great Britain 0278-4343/96$9.50+ 0.00

0278-4343(95)-7

Combining modelling and monitoring to determine fluxes of water, dissolved and particulate metals through the Dover Strait D. PRANDLE,* G. BALLARD,* D. FLATT,* A. J. HARRISON,* S. E. JONES,? P. J. KNIGHT,* S. LOCH,* J. McMANUS,* R. PLAYER* and A. TAPPIN+ (Received 17 January 1994; in revised form 3 July 1994; accepted 5 January 1995)

Abstract-Contaminant fluxes in a shelf sea system are determined from a series of interrelated studies involving monitoring, modelling and theoretical development. Year-long measurements of currents through the Dover Strait were made in 1990-1991 using both shore-based high frequency (HF) radar and a bottom-mounted acoustic Doppler current profiler (ADCP). These measurements were combined to determine both the residual component of tidal flow and the wind-forced residual flow resulting in an estimate of the net long term flow into the North Sea of 94,000 m3 s-‘--a value in close agreement with the most recent high resolution modelling of Salomon etal. (1993). The temporal variability in these radar and ADCP observations are compared with synoptic wind, tide gauge and numerical model data. The fluxes of the dissolved metals Cd, Cu, Ni, Pb and Zn through the Straits are then calculated using concentrations in the Strait derived from a study by McManus and Prandle (1994). The latter involved multiple regression of model simulations of dispersion (with the model flow through the Dover Strait corresponding to the above monitored value) against data from four surveys in the southern North Sea carried out in 1988-1989 as part of the North Sea Project. The mean concentrations determined from this inverse modelling technique depend directly on the net water flux through the Strait. Thus, since it is shown here that the results for the more conservative metals Cd, Cu, Ni and Zn agree closely with direct measurements by Statham et al. (1993), this lends further confidence to this new estimate of net flow derived from monitoring. The flux of suspended sediments is calculated using time and cross-sectionally averaged suspended sediment concentrations obtained during a cruise in June 1990 (Jones et al., 1993). The particulate metal fluxes are calculated by combining these suspended sediment concentrations with the dissolved metal concentrations and published Kd (partitioning coefficient) values. These dissolved and particulate metal fluxes are also shown to be in reasonable agreement with the values derived by Statham et al. (1993). The net, particulate plus dissolved, flux of these metals through the Strait represents between one-sixth and one-third of the total from all other sources into the southern North Sea.

1. INTRODUCTION The net flux of dissolved contaminants

across a prescribed section of width W is

TWD

li00

I0

%Y

,t) * C(GY $1 dz dy dt

*Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, L43 7RA, U.K. tSchoo1 of Ocean Sciences, U.C.N.W., Menai Bridge, Gwynedd, LL59 5EY, U.K. $Oceanography Dept, University of Southampton, Southampton, SO9 5NH, U.K. 0 Crown copyright (1995). 237

(1)

238

D. Prandle et al.

where Uis the velocity normal to the section, C is the concentration, z is the height above the bed, y is the distance along the section, t is the time, D is the water depth and T is the duration of interest. The velocity U typically includes components associated with tides, storm surges, waves, localised wind-forcing, density gradients, gyres and eddies. The concentration C may include variability from all of these sources (via advection) together with temporal variability associated with the initial source release rate and any subsequent losses-especially to the particulate phase. The major difficulty in any direct monitoring programme is that U.C # o.i?, where the over-bars denote averaged values, except under carefully selected circumstances. Measuring currents and concentrations averaged over a time of 0(1 min.) filters most wave and eddy components. Likewise, adoption of a vertically well-mixed location reduces the need for extensive vertical profiling. It is generally considered that numerical model simulations now provide sufficient spatial and temporal resolution to adequately describe tidal and (low frequency) wind-driven flows and autonomous instrumentation (HF radar and ADCP described in Section 2) exists against which to verify these computations. Unfortunately, corresponding instrumentation to autonomously monitor concentrations is restricted to only a few parameters and thus other approaches are necessary. Statham ef al. (1993) measured dissolved and particulate metal concentrations at two depths for six positions across the Dover Strait over 15 consecutive months. While the auto-correlation of the measurements can be used to estimate the adequacy of the temporal and spatial resolution, questions remain about the relative contribution of short term episodic events especially where these coincide with extreme weather conditions that preclude sampling. Generally, the intensity of sampling required decreases with distance from the source, the following theoretical derivations offer some simplified guidelines. Complete vertical mixing requires a time d/K,, i.e. a source located at X > UoD2/Kz from the monitoring section for advective travel time X/U, (water depth D, vertical eddy diffusivity coefficient K,, residual velocity U,). With complete vertical mixing in open seas, lateral variability in concentration C(Y) at some distance X from a continuous source M is given by (Fischer et al., 1979) where

A2 = K,XIU,.

Thus, the concentration at some distance Y offset from the axial direction X, of the velocity U, differs by less than one-tenth of that at Y = 0, so long as Y < 0.63A. For a contaminant source with cyclical variability of amplitude B, and period 2rtlw discharging into a region with flushing time F, this cyclical amplitude will be reduced relative to a constant input B0 by B,I& = l/(1 + F2w2)“2 (Prandle et al., 1993b). The value of F associated with an advective velocity U, flowing through a prismatic channel of length Xis given by F = 0.37 X/U,. These criteria provide estimates of minimum travel times from the contaminant source to the monitoring section to ensure mixing vertically and horizontally across the section and to adequately filter variabilities in the rates of source discharges. Using values for the Dover Strait of K, = E (Section 2.3), Kx = 1000 R2 s-l [where R is the tidal current amplitude (Prandle, 1984)] and U, = 0.01 m s-l (English Channel), contaminants discharged greater than 100 km upstream (in a residual flow sense) should be reasonably sectionally mixed and, likewise, variability in discharges within periods of less than a few days should be adequately filtered.

Modelling and monitoring to determine water fluxes

239

Analysis of Statham’s (1993) dissolved metal data showed that the mean concentrations at the three central locations were almost all in the range OS-O.9 of the cross-sectional mean value with standard deviations (as a fraction of this cross-sectional mean) of Cu 0.23, Cd 0.30, Ni 0.23, Zn 0.40 and Pb 0.61. By contrast, the mean concentration at location 1 (U.K. coast) ranged from 1.10 to 1.37 times the mean cross-sectional value, with corresponding figures at location 6 (French coast) from 1.0 to 1.27. In addition, the standard deviations at these coastal sections were generally larger than at the central locations. These distributions suggest that while distant sources may be reasonably well mixed in the centre of the Strait, a degree of coastal trapping exists that both reduces lateral mixing of distant sources and retains localised coastal sources. The distributions of 125Sbreleased from Cap de la Hague and measured by Guegueniat et al. (1993) indicate the existence of a “coastal current” along the French coast. Similarly, the present analysis of the HF radar surface current measurements indicate that a discrete wind-driven residual flow can exist along the U.K. coast. In Section 2, the adequacy of numerical models in simulating tidal and wind-driven currents through the Dover Straits is assessed by comparison against year-long measurements using HF radar and a bottom-mounted ADCP. In Section 3, the fluxes of dissolved metals (Cd, Cu, Ni, Pb, Zn) through the Dover Strait are estimated using the above residual water flux measurements together with concentrations derived from the North Sea Project surveys (Howarth et al., 1993). These derivations involved the use of inverse modelling (McManus and Prandle, 1994) and yield an annual mean concentration in the Dover Strait from the “down-wind, far-field” dispersion patterns. In Section 4, estimates of particulate metal fluxes are made by simple multiplication of these dissolved fluxes by time and cross-sectionally averaged suspended sediment concentrations (using measurements by Jones et al., 1993) together with estimates for the partition coefficient Kd by Balls (1989). These fluxes are then compared with contemporaneous studies, involving direct concentration measurements (Statham et al., 1993) combined with flow estimates from the fine-scale numerical modelling studies by Salomon et al. (1993). Thus this final comparison of both dissolved and particulate metal fluxes involves estimates made entirely independently from radically different strategies. 2. THE FLUX OF SEA-WATER This section describes how the net tidal and wind-driven fluxes of sea water through the Dover Strait were determined by combining results from HF radar measurements of surface currents with ADCP measurements of vertical current profiles. These observational results are then compared with similar derivations from various numerical modelling simulations. The Dover Strait connects the southern North Sea with the English Channel (Fig. 1). These regions are characterised by strong tidal forcing and both are subject to occasional high storm activity. The narrowest section is about 34 km wide with depths of up to 60 m. The flow of water through the Dover Strait into the North Sea increases the flushing rate of coastal areas along the Continental coast but also transports contaminants originating from both the English Channel and the adjacent Atlantic. For some contaminants this

240

D. Prandle

et al.

51"O'N

50'50'N

I'O'E

Fig. 1.

1'20'E

(a) Strait of Dover, ?? radar sites. (b) Depth contours in metres below chart datum, ?? location of current meter observations (Position A).

source may be of the order of 50% of the observed concentrations in this coastal zone (Prandle et al., 1993b). Efforts to determine the long term rate of this flow and its variability with wind-forcing have been made for over 60 years with no definitive value established. The development of the HF radar system, OSCR (ocean surface current radar), by Marex U.K., promised for the first time continuous direct observations of surface currents throughout the Strait with sufficient accuracy over a long enough period to determine this flow. See Prandle (1991) for a review of the principles, performance and applications of the OSCR system. Simultaneous deployment of a bottom-mounted ADCP provided vertical resolution of the observed currents (at one location). 2.1. The residual component of tidaljlow The OSCR HF radar system was operated between June and December 1990 from Cap Gris Nez and Wimereux and between September 1990 and March 1991 from Dover and St Mary’s Bay (Fig. 1). The radar measured surface current vectors at 700 pre-selected locations every 20 min., i.e. a total of approximately 15 million current vectors. Prandle et al. (1993a) described the analysis of the tidal component of the HF radar measurement, while Prandle and Player (1993) analysed the wind-driven component from these measurements. Prandle (1993) extended this latter study to make intercomparisons with synoptic

Modelling and monitoring to determine water fluxes

241

measurements from an ADCP mooring and calculations from a shelf-wide numerical model. For tidal analysis purposes, the data were grouped into monthly sets; five months of data were obtained from both the French and English sites. Data from the 1 km observational grid were reduced to vector averages over rectangular regions 19’of latitude and 2’ of longitude (i.e. 2.5 km squares), i.e. typically an average of six values. Figures 2(a) and (b) show ellipses obtained for the two largest tidal constituents, M2 and SZ. Prandle et al. (1993a) show similar distributions for a further five constituents, together with detailed comparisons of these new observational results against values obtained from a numerical model. The M2 amplitudes vary from a maximum of 143 cm s-r immediately off Cap Gris Nez to less than 40 cm s-i at the western edge and show broad agreement with earlier current meter measurements. The surface tidal currents tend to align with the largescale topographic features through the Strait and do not adjust to the sharply varying local topography. The SZ amplitude of the OSCR ellipses range from 14 to 44 cm s-l, the latter value corresponding in location to the maximum M2 value of 143 cm s-l. The ratio of these S,: M2 maxima, 0.31, agrees closely with the ratio of the corresponding elevation amplitudes at Dover.

2.2. Mz residualflux The net residual flow, ST, over a tidal cycle associated with the M2 tidal current (8, 13) (confined to one direction) and elevation (t,g) in water depth D is P&os(~t-O)(D+~cos(wt-g))dt=~@cos(B-g).

(3)

0

Substituting (0,0) from the semi-major axis of the OSCR tidal ellipse data [Fig. 2(a)], a residual tidal streamline, r+!~,distribution was constructed corresponding to the pointvalues (Do,, OvO) with these net depth-integrated transport (per unit breadth) vectors calculated from equation (3). Figure 3 shows the resulting distributions together with the point values of (Da,, Dv,). These streamlines were drawn relative to an arbitrary zero reference point and using a smoothing function that satisfied the continuity equation. This component of net residual flow through the channel amounts to 40,000 m3 SK*with the greater proportion concentrated on the French side. This estimate of net flow assumes that the measured surface currents remain constant through depth. The vertical profile of tidal currents can be calculated easily using either analytical theory (Prandle, 1982) or from a numerical “point-model” (Prandle, 1993a). Introducing such vertical current structure reduces the estimate of net residual flow by approximately 10% (to 36,000 m3 s-r) and rotates the net vectors in Fig. 3 by typically 1” anticlockwise of the major axis of the tidal ellipse. This M2 tidal residual may be increased by contributions from the other tidal constituents. Calculations were made of the influence of M4 and M6 constituents of both 0 and 5 on the residual fluxes; in this application these were shown to contribute less than 1% to net fluxes. The expression (3). may be expanded to include the &constituent, this results in an additional residual 4 osz ts2 cos (0 - g)sZ. Assuming the same phase difference between elevation and current for S, as for M,, this term amounts to (0.31)2 = 0.1 of the M2

242

D. Prandle et al.

243

Modelling and monitoring to determine water fluxes

50“SO.N

1”O.E

Fig. 3.

1°20’E

Residual flows associated with M2 tidal propagation. Streamline units 1000 rr? s-’. 0 $I = 0 (arbitrarily designated).

residual. The amplitude ratio for the next largest constituent N,:M, is 0.19, producing a corresponding residual which = 0.04 of the M2 residual. Thus, a reasonable approximation of the full series expansion of residual tidal fluxes is estimated as 41,000 m3sm1. Model estimates of net residual flow in m3sw1 (associated with M2 tidal propagation) include: Pingree and Maddock (1977), 5 x 104, Pingree and Griffiths (1980), 3 x 104, Prandle (1984), 5 x 104, the Proudman Oceanographic Laboratory (POL) 35 km shelf model 4.6 x 10e4, the POL 9 km shelf model 3.8 x lo4 (J. E. Jones, personal communication), Salomon et al. (1993) 3.74 X lo4 (all tidal components). The 36,000 m3 s-t value from this radar study is close to both the POL 9 km shelf model and Salomon’s 3 km North Sea/Channel model. 2.3. Wind-driven residual Jlow A wind-driven component of the HF radar measurements was first derived by correlation, at each position, of the residual surface currents against locally observed winds. Wind data were supplied from the U.K. Meteorological Office at hourly intervals from Lydd (50” 56’N, 0” 54’E) and Langdon (51” 7’N, 1”20’E). Results showed a conventional Ekman theory response with surface currents aligned, on average, 20” clockwise of the wind. Consistent with this theory, the magnitude of the surface currents decreased in shallower water and indicated a near-surface value of vertical eddy viscosity E = 0,005 m2 s-l. These results are described in detail by Prandle and Player (1993).

244

D . Prandle et al.

.5105’?

51’5’N

51”0’1

51”O’N

50”55 ‘1

50”55’N

50”50’1

50”50’N

1

50”45’1

,

;

.

.

r

r

.

50’45’N

Fig. 4. Vectors from first modes of EOF analyses; (a) France, rotated 33” a-c from east; (b) England, rotated 10”a-c from east. Units: (i) vectors m s- ’when multiplied by a unit of the time series shown in Fig. S(a) and (b); “streamlines” indicate corresponding net flows in m3ss1.

Larger-scale organised motions were then examined using an Empirical Orthogonal Function (EOF) modal analysis (Prandle, 1987) with the time series pertaining to these modes subsequently correlated against wind data. (The horizontal circulations of the monthly averaged remaining (non-tidal, non-wind driven) residual currents indicate a persistent 20 km diameter gyre off Cap Gris Nez but a negligible through flow component.) For both sets of data, a predominant mode was identified accounting for 40% of the total variance in the French residual current data and 30% in the English data. Histograms of the orientation of the “eigenvalue” time series for the French data

Fig. 5.

Time-series of:

(a) (b) (c) (d) (e)

wind (speed squared) m* s-*; French radar mode 1; English radar mode 1; net flow in m3 s-l Numerical model calculation; 1 ADCP current vector in cm s-r; (f) ADCP surface gradient (X 10’); (g) tide-gauge surface gradient (X 10’). Time scale in days after 1st January, 1990. Vectors plotted with solid line principal axis, dotted line orthogonal. Principal and orthogonal axes are: (a) 50”, 140’; (d) 60”, 150”; (e) 160”, 250”; (f) 170°, 260” (measured E-W from 0”north).

245

Modelling and monitoring to determine water fluxes

2 x lmq, 1 x

I

ios-

(cl

0

fib.'

IOS-

-I x -2 x 105.

1, 200

250

300

350

400

200

250

300

350

400

2x10' Ix Cd)

1050

-I x IOS-2 x 1051

40 20 (e)

0 -20 -40

lOOI

-50 -100~

_I

w:---j ‘-,.

,,.,,,.,:.

:......

‘,.

200

250

300

i. 350

400

200

250

300

350

400

100 50 (g)

0 -50 -100'

Fig. 5.

246

D. Prandle et al.

showed that the orientations were between 22.5” and 45” (or 202.5”-225”) (measured anti-clockwise from the east) for 67% of the time (c.f. 12.5% for a random distribution) and this time accounted for 88% of the total amplitude. Likewise, for the English data, the orientation was between 0” and 22.5” (or MO”-202.5”) for 74% of the time, representing 87% of the total amplitude. Thus their vector time series were approximated by scalar components resolved along the principal axes 33” and 11” respectively; these modal patterns are translated into streamlines and shown in Fig. 4. The modal (scalar) time series Fand E, (Fig. 5) resolved along these principal axes, were then related to the east and north components of wind W(t), (W, and W,, respectively), by the expression,

(4) where At represents a time lag between the wind forcing and the resulting current. The two modes conveniently overlap in mid-channel and equation (5) shows the net flux Frassociated with both modes. The top line represents the French mode (r = 0.32 for 2348 data points) and the bottom line the English mode (I = 0.24 for 2458 points). The time lags (or advance in the French case) may be related to the time difference between the wind at the selected meteorological sites and the wind over the regions where these flows are generated. FT = (8.1 - 0.28E&VEj

- 2.27W,IW,I)

800 (At = -36 h)

+ (3.2 - 0.16WnjWnI + 0.65Wr,IW,I) 650 (At = 9 h) m3 s-l.

(5)

The above analyses assume the surface residual currents extend uniformly throughout the depth. A factor a = &R surface is introduced (relating depth-averaged to surface residual currents) to correct for this assumption. In the absence of wind, FT = 8560 a m3 s-i; for an easterly wind FT = -328 a W,lW,l and for a northerly wind FN = - 1394 a W,l W,l , the latter two may be combined to yield F, = 1432 a W2 cos (0 - 77”)

(6)

or for a = 0.75 (see next section): = 1074 W2cos (0 - 77”), where 8 is the direction towards which the wind blows and is here measured anti-clockwise from the east. Comparable values are as follows: Prandle (1978) Prandle (1984) Salomon et al. (1993) [assuming equation (lo)] Pingree and Griffiths (1980) Oerlermans (1978)

F, = 2400 W2 cos(B - 60”) F, = 1100 W* cos(B - 74”) F, = 1430 W* cos(8 - 84”) F, = 1600 W* cos(8 - 83”) F, = 1100 W* cos(B - 66”).

Intercomparison of these results is complicated by differing assumptions regarding: (i) the relationship between wind speed and surface stress; (ii) the selection of appropriate wind stations; and (iii) variable tidal interaction considered by Salomon. In the following section, it is shown that at position A (Fig. l), a = 0.75, hence the present result [equation (6)] is in very close agreement with Prandle (1984) and Oerlemans (1978). For the long term mean wind stress components r, = 0.04 N mm2 and rY = 0.05 N mW2estimated by

Modelling and monitoring to determine water fluxes

247

Prandle (1984)) equation (6) indicates a net wind-driven flow of 63 a lo3 m3 s-r or 47 000 m3 s-l for a = 0.75. 2.4. Vertical current profiles measured by ADCP Omitting time-varying, density gradient and non-linear terms, the horizontal momentum equation simplifies to:

where R is the velocity at height 2 above the bed, g is gravitational acceleration, c is the elevation of the sea surface, f the Coriolis parameter and E a vertical eddy viscosity parameter (constant). Adopting the solution R = A 1ebz + A 2 Eeb’ + C

b2=i$

requires

and

(8)

C=i&.

f

Values for E were calculated by least squares fitting of the vertical profile of observed M2 tidal current ellipses to the theoretical values of Prandle (1982). The ADCP current measurements at heights 3.9,5.3,6.7 and 8.1 m above the bed in a total height of 30 m were used in these calculations (Knight et al., 1992). A mean depth-averaged value of E = 0.02 m2 s-l was calculated, i.e. four times the “near-surface” value determined for localised wind-driven currents in Section 2.3, At the sea surface, 2 = D, the wind stress r, was taken as r, = 1.3 x lop3 W2 (N mp2)

(10)

where W is the observed wind speed in m s-r. From equation (6) zw=pE-=

C3R U,,D

pEb(A,ebD

- A,eCbD).

(11)

This equation can be used to relate A2 to AI, then equation (8) can be fitted to the observed vertical profile of residual currents to calculate both Al and C. The mean ratio of the depth-averaged value R to the residual current at the surface R,=, was found to be close to 0.75 for all ADCP deployments, R,,,is also rotated 5”a-c from R on average. From equation (9) the above calculations also provide time series of the sea surface gradients at the ADCP mooring position. A weakness in the above analysis of the ADCP measurements stems from the use of observations confined to the first third of the water column. This restriction was due to some uncertainty regarding the measurements higher in the water column (since rectified by instrument development). However, in the present circumstances this weakness is not appreciable since the residual flow primarily involves longer term components driven by sea-surface gradients (Prandle, 1993). Thus, on average the influence of localised windforcing introduced via equation (11) is small and, consequently, most of the current shear

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is confined to the lower one-third of the water column and hence derivation of A,, A2 and C based on these near-bed measurements is reasonably accurate. 2.5. Zntercomparison of: (i) HF radar measurements; (ii) A DCP measurements; (iii) tide gauge water level measurements; (iv) wind recordings and (v) numerical model simulations Complex correlation coefficients are calculated between: 6) the modal time series for both the French radar measurements, F, and the English radar measurements, E; (ii) the depth-averaged residual currents R and surface slopes Vc calculated for the ADCP measurements; (iii) gradients in sea-level recordings, S, from Dover (51” 07’N, 1”19’E), Boulogne (50 44’N, 1”35’E) and Newlyn (50” 06’N, 5” 33’W); (iv) the observed wind W (strictly WIWI with W measured in the direction towards which the wind blows); and the residual flow through the Strait, M, computed by the POL 35 km two(v) dimensional numerical model used for operational storm-surge forecasting (Flather et al., 1991). Hourly values were used in all cases, the extent of each data set is shown in Fig. 5. The locations from which sea-level recordings were available were less than ideal with Newlyn 600 km west of the Strait; however, data from other sites were too discontinuous. These sea-level recordings were tidally filtered and their separate long term means removed to calculate residual components of sea-surface gradient. Table 1 shows these correlations; amplitudes are followed by inclinations where these show the rotation (a-c) of the row parameter relative to the column parameter. Likewise the lags (or advance for a negative lag) represent the delay of the row parameter relative to the column parameter. The parameters determined from the ADCP measurements R and Vg‘are almost exactly correlated along orthogonal directions. The wind is significantly correlated with both R and Vg and is more closely aligned with V& The highest correlation with W is against the modelled flow M indicating a maximum new flow for winds aligned along a N-E to S-W axis of FrM= 870 W2 m3 s-l

(12)

in reasonable agreement with the result [see equation (6)] from the HF radar and ADCP measurements. Table 1 shows a correlation coefficient between the two radar components, E and F, of r = -0.27 with Fleading E by 18 h. This result emphasises the opposing components of flow between the French and English sections. The correlations between E and F with R indicate that residual currents observed at site A by the ADCP are more closely aligned with the French section (R lagging F by 24 h), whereas iii effectively opposes E in direction. The simultaneous existence of residual flows in opposing directions across the Strait was first recognised by Van Veen (1938). The numerical model calculations M are highly correlated with the ADCP results li and Vg. This correlation is a maximum when R is aligned 35” N of east, as anticipated from the channel geometry. The sea-level gradients Vc and S are significantly correlated with close alignment. The

249

Modelling and monitoring to determine water fluxes Table 1. Complex correlation coefjficients between: W-wind speed squared, Vg‘ and E residual surface gradient and depth-averaged current calculatedfrom the ADCP measurements, M, E and F net residual flows through the Dover Strait from a numerical model and English and French radar measurements S surface gradient calculated from tide gauge recordings at Dover, Boulogne and Newlyn Amplitudes V< R M E F S

0.50 0.43 0.58 0.25 0.25 0.50 W

0.95 0.70 0.47 0.31 0.50 K

0.80 0.45 0.35 0.54 R

0.28 0.37 0.52 M

0.27 0.19 E

0.34 F

Inclinations 11 -119 -116 83 - 124 -43

-106 -68 101 -74 8

34 -148 37 118

0 1 -3 -24 -1

-2 -24 -1

M 242 432

180 0 82

180 -96

81

-18 -2

-18 2

12

E 185 325

F 275 424

S 185 432

Lags (hours) 5 5 5 -12 -36

5 Measurement periods Day 1 = 1 January 1990 (hourly data) W V< and R Start 185 199 End 432 352 Standard deviations W V< 77 2.1 m2 sC2 x 10-6

1

R 15 ems -1

M 53.4 lo3 m3 s-l

E 76 lo3 m3 SC’

F S 115 3.9 lo3 m3 SK’ x 10-6

lower variance for 05 reflects the larger channel breadth at position A. The main slope is north-south as follows from the orientation of both Vc and S with the scalars M, E and F. For a minimum channel width of approximately 30 km between Dover and Boulogne, the mean variance for S corresponds to a cross-channel sea level difference of 11.7 cm. Prandle et al. (1993a) estimated an opposing gradient associated with tidal flow of 2-3 cm. Cartwright and Crease (1963) and Prandle (1978) estimated a mean cross-channel sea level difference of 8 cm. Thus, the net gradient calculated from the new observational results is close to earlier estimates. Several attempts to derive multiple correlation relationships between currents, winds and sea level gradients were made. The most successful were as follows: MODEL(t)

= 368 W2(t) cos (6’- No) + 1803 x lo7 V< (t + 12) cos (# + 43”) (R = 0.79)

RADAR(t)

= a[1078 W2(t) cos (0 - 93”) + 4166 x lo7 VlO W,D there is little vertical variation in sediment concentration and for K, > W, D the net transport closely approximates U, ED where c is the time- and depth-averaged suspended sediment concentration. Assuming that K, = E = 0.02 m2 s-i (Section 2.4) and that a typical water

(Statham

pug 1-l

A

el al., 1993, mean and standard

tonnes/year

deviation

leg I-’

0.6

2200

0.25

0.04

1100

0.2

0.02

tonnes/year

5670

380

2365

1890

190

B

Dissolved southerly flux 1989)

particulate/ dissolved concentration

104-10s

105-10’

10J-IO4 5

104-10s

103-s-10s

Kd (Balls, 32

tonnes/year

1310

3240

210

(’

1994)

490

(Jones,

Maximum particulate flux Dover Strait for SPM = 6 mg [-’

tonnes/year

170

74

190

19

1993)

D

Maximum particulate flux southerly for SPM = 1 mgl-’ (Howarth et al.,

tonnes/year

7500

1000

275

1300

50

E

Riverine sources (1987 QSR)

Dissolved and particulate metal fluxes into the southern North Sea

m brackets.)

Dissolved concentration 56 N (McManus, 1994)

55

820

(0.32,0.12) Ni 0.4

(0.38,O.ll) Pb 0.02 (0.05,0.04) Zn 0.8 (0.59.0.31)

55

0.02

Dissolved flux through Dover Strait

(0.02,0.007) cu 0.3

Cd

Dissolved concentration Dover Strait (McManus, 1994)

Table 2.

tonnes/year

11,000

7400

950

1600

240

QSR)

F

Atmospheric sources (1987

0.14

0.26

0.35

0.26

0.17

A+C B+D+E+F

I

2’

8

& 8 i 9 5’ fD $

0u

09

254

D. Prandle

et al.

I

Pb

I

000

Fig. 7. Net fluxes of dissolved Statham (1993), and present

and particulate metals through the Dover Strait calculated calculation. ?? Statham (1993); I- - - - - -1 present calculation.

by

depth D = 30 m, then K, > W, D for W, < 7 x lop4 m s- ‘. The settling velocity spectra obtained by Jones et al. (1993) shows that this holds for approximately 0.67 of the mass of suspended sediments. However, since the adsorptive capacity of the fine sediments is so much greater than for the coarser fraction, it can reasonably be assumed that the entire particulate flux of contaminants is transported in a manner equivalent to that of the dissolved phase. Exceptions to the above assumptions may occur in coastal boundary layers with distinct hydrodynamic and sedimentary regimes and also during storms when the tidal component of sediment transport may be less significant. Van Alphen (1990) measured suspended sediment concentrations along the BelgianDutch coast (extending to the Dover Strait) ranging from 1.1 mg 1-r to 22.8 mg E-’ with annual means of 10.6 mg 1-l in coastal water and 3.4 mg I-’ offshore. His estimate of net sediment flux through the Dover Strait of 8.5 x lo6 tonnes per year corresponds to a mean concentration of 3 mg I-’ for a flow of 94,000 m3 s-l. Thence, subject to the above assumptions and approximations, Table 2 shows the net flux of metals through the Dover Strait in both the dissolved and particulate phases. This table also shows the net (dissolved plus particulate) flux of metals through the Strait as a proportion of all other inputs to the southern North Sea. This factor is approximately onesixth for Cd and Zn, rising to one-quarter for Cu and Pb and is a maximum of one-third for Ni. These present estimates for dissolved and particulate metal fluxes, columns A and C in Table 2, are compared with independent estimates from Statham etal. (1993) in Fig. 7. The present values for particulate fluxes are shown as a range corresponding to the Kd values of Table 2. There is generally close agreement with both data sets indicating much larger fluxes in the dissolved phase except for lead where the particulate phase predominates. 5. SUMMARY By combining results from five monthly HF radar deployments on the French coast with five on the English coast, surface currents across the full width of the Dover Strait have

Modelling and monitoring to determine water fluxes

255

been measured. Simultaneous measurements of the vertical current profile at a single point in mid-channel were made using a bottom-mounted ADCP. These measurements have been combined to provide detailed descriptions of net tidal and residual flows through the Strait. Tidal current ellipse distributions have been drawn for seven major constituents. The predominant M2 constituent of tidal flow is shown to generate a tidal residual drift of 36,000 cm3 s-r (into the North Sea), the drift associated with the next major constituent, Sz, is estimated at one-tenth this value. The residual contributions from the phase-locked higher harmonics M4, M6 and MS4 is estimated as negligible. The net residual from all tidal constituents was estimated as 41,000 m3 s-r. A modal analysis of the time-varying residual currents identified predominant modes corresponding to axial flows through the Strait. Correlations of these corresponding modal time series with wind recordings provided a quantitative estimate of wind-forced fluxes through the channel consistent with earlier modelling studies. Analysis of the ADCP data involved the fitting of both tidal ellipse current profiles and residual current profiles to theoretical descriptions. This procedure showed that the winddriven surface currents were 1.33 times larger but closely aligned with the depth-averaged value. Using this ratio between surface and depth-averaged residuals, a net wind driven flow was estimated as 47 x lo3 m3 s-r. An additional long term Eulerian residual current through the Strait was estimated as 6 x lo3 m3 s-l , providing a net long term residual flux of 94 x ld m3 s-l. There was no clear evidence of any significant seasonal component (other than that directly associated with wind-forcing). The wind-driven residual transports computed from the radar measurements are in broad agreement with values from numerical model simulations. However the radar results reveal opposing responses between the English and French sections, indicating counter-flows across the Strait not generally resolved by the models. Thus while the residual currents from the ADCP measurements are significantly correlated with aligned flows both calculated by the model and measured from the French radar sites, these currents are negatively correlated with corresponding flows from the English radar sites. Results from a study by McManus and Prandle (1994) are used in conjunction with this estimate of residual flow to calculate the net flux of the dissolved metals Cd, Cu, Ni, Pb and Zn. This study involved multiple regression between separate model simulations of the spread of contaminants in the southern North Sea from seven sources against dissolved concentrations recorded during the 1983-1989 NSP surveys. The mean concentrations for the more conservative metals Cd, Cu, Ni and Zn, are shown to be in close agreement with direct measurements made by Statham et al. (1993). Similarly, results from a study by Jones et al. (1993) are used to estimate the time and sectionally averaged suspended sediment concentration. Thence, using published values for the partitioning coefficient Kd (relating particulate to dissolved concentrations) for each metal, the particulate metal fluxes are estimated. These new estimates of dissolved and particulate metal fluxes are shown to be in close agreement with values obtained by direct sampling by Statham et af. (1993). The total, dissolved plus particulate, flux of metals through the Dover Strait is shown to represent one-sixth of the net input into the southern North Sea for both Cd and Zn, one-quarter for Cu and Pb and one-third for Ni. AcknowZedgements-This

study was partially funded by the U.K. Department of the Environment (Contract No. PECD 7/8/217) as part of its co-ordinated programme of research on the North Sea. The results represent contributions to the Natural Environment Research Council’s North Sea Project.

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