The Seasonal Cycles of Temperature, Salinity, Nutrients and Suspended Sediment in the Southern North Sea in 1988 and 1989

Estuarine, Coastal and Shelf Science (1997) 45, 669–680

The Seasonal Cycles of Temperature, Salinity, Nutrients and Suspended Sediment in the Southern North Sea in 1988 and 1989 D. Prandlea, D. J. Hydesb, J. Jarvis and J. McManusa a b

Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside L43 7RA, U.K. Southampton Oceanography Centre, Empress Dock, European Way, Southampton SO14 3ZH, U.K.

Received 4 January 1996 and accepted in revised form 9 December 1996 Simple statistical analyses are used to summarize the large data set available from the 15 consecutive monthly surveys of the U.K. North Sea Project (NSP). The seasonal cycles of temperature, salinity, phosphate, nitrate, nitrite, silicate, ammonium and suspended particulate matter (SPM) are approximated by a mean value plus a year-long cosine wave. The mean concentrations, with standard deviationc given in parentheses, for each of these water quality parameters covering the whole area throughout the 15-month period are: salinity 34·26 (&0·74), ammonia 1·3 (&1·0) µM, nitrate 4·9 (&6·0) µM, nitrite 0·4 (&0·5) µM, phosphate 0·5 (0·3) µM, silicate 2·5 (&2·5) µM and suspended sediment 2·6 (&3·5) mg l "1. This approximate seasonal cycle accounts for most of the variance in temperature and nutrients. The spatially-averaged seasonal amplitudes for both nitrate and silicate are approximately equal to their mean values—this is consistent with these being limiting nutrients. Salinity shows little seasonality. Spatial distributions are shown of the mean values, the seasonal amplitudes and the percentage variances accounted for by a combination of these mean values and seasonal amplitudes. Correlations between the determinands are calculated; these confirm the similarity in the spatial distributions for the nutrients, especially between nitrate, phosphate and silicate. Maximum concentrations are confined to the coastal regions, except for ammonium and nitrite for which they occur offshore. Spatial distributions of the anomalous (non-seasonal) components can be interpreted to indicate the effect of specific riverine and oceanic exchanges. Correlations between nitrate, nitrite and ammonium correspond to the interconversion of these compounds. The oceanic/riverine inflow rates of phosphate, nitrate and silicate are shown to be insufficient to support their seasonal variability, suggesting that internal recycling is required to maintain the seasonal cycle. ? 1997 Academic Press Limited Keywords: seasonal cycles; nutrients; temperature; salinity; North Sea

Introduction The NERC’s North Sea Project (NSP) monitored the annual variability of a number of parameters to form the basis for developing water quality models. Observations were made at over 100 locations along a 3000 km track (Figure 1) surveyed on each of 15 consecutive months, between August 1988 and October 1989. The area covered ranges from the Dover Strait to an E–W section along 56)N. The general features of the annual cycle of nutrient and plankton levels in the North Sea have been established for some time (Cushing, 1973; Johnston, 1973; Brockman et al., 1988; Gerlach, 1988; Nelissen & Stefels, 1988). However, data sets lacked sufficient coherence and breadth of synoptic coverage over an c Standard deviations (or seasonal amplitudes in Equation 2) in excess of mean values indicate asymmetric distributions since parameters values (excluding temperature) cannot be negative.

0272–7714/97/050669+12 $25.00/0/ec960227

appropriate range of determinands to develop models linking physical and chemical processes to biological production (Huthnance et al., 1993; Radach et al., 1993; Hydes et al., 1995). Within the southern North Sea, the NSP provided the first data set with sufficient information to allow changes in nutrient concentrations and plankton biomass to be investigated quantitatively (Howarth et al., 1994). Ironically, the sheer size of such data sets presents new problems. The aim of this work was to see how successfully the annual cycle of nutrients in the southern North Sea could be summarized by a ‘ first-cut ’ approach, and whether this would reveal new insights into the relationships of changing water masses, nutrients and sediment loads. This paper does not include any detailed consideration of how emergent findings relate to prior knowledge in this region—ground comprehensively covered by Charnock et al. (1994). The emphasis is on ? 1997 Academic Press Limited

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F 1. Bathymetry and route of the research vessel Challenger during data collection for the North Sea Project. The model grid shown has a resolution of 35 km. Isobaths show depth in metres.

developing constituent methodology for multiparameter analyses and thence, on illustrating how salient characteristics emerge without a priori assumptions. Whilst it is hoped that such emergent characteristics will stimulate examination elsewhere, the present scope is deliberately circumscribed.

by least squares fitting. In most cases, two or three observations through depth were made at each location; here, only depth-averaged values are considered. For each monthly survey of each parameter, the value at any grid point, fi,j,t was calculated by fitting a separate plane to all observed data: fi,j,t =ai,j,t Wx+bi,j,t Wy+ci,j,t

(1)

Analytical methods The data were interpolated to provide values on a 35 km rectangular grid (30* longitude#20* latitude). These gridded values are then analysed to determine: (i) the annual means; (ii) the seasonal amplitudes and phases; and (iii) the percentage of the observed variance accounted for by (i) and (ii). Finally, crosscorrelations of all these values are calculated for the parameters; temperature, salinity, phosphate, nitrate, nitrite, silicate, ammonium and total suspended particulate matter (SPM). These parameters were selected on the basis of there being, on average, at least 90 data locations per survey on at least 12 of the monthly surveys. Gridding The interpolation procedure used for gridding the original observations involved approximating a plane

where the weighting factors W were made inversely proportional to the distance of the observation at (x,y) from the grid position (i,j). The parameters ai,j,t, bi,j,t and ci,j,t were then determined by least squares fitting. Seasonal cycle calculation In the above gridding procedure, no account was taken of the time variations of the observations over the 12 days of each survey. Likewise, in the following determination of the annual cycle from these gridded data, the monthly data are assumed to be synoptic. For each grid point (i,j), the 15 monthly values (fi,j,t=1,15) were approximated by: Ft =A0 +A1cos(ùt"è)

(2)

(where ù corresponds to the annual cycle) with A0, A1 and è again determined by least squares fitting.

Seasonal cycles in the Southern North Sea 671 T 1. Spatial means and standard deviations of A0, A1 (Equation 2), spatial and temporal means of observed values f, percentage variance accounted for by the seasonal cycle (Equation 3), and spatial correlations of A0 and A1 with depth d and with 1/d Parameter fi,j,t ó of f A0 ó of A0 A1 ó of A1 P% Correlation of A0 with (i) depth (ii) 1/depth Correlation of A1 with (i) depth (ii) 1/depth Maximum value

Temp.

Salin.

PO4

NO3

NO2

SiOn

NH4

Sed.

10·905 3·723 10·176 1·269 4·221 1·475 89·2

34·262 0·737 34·279 0·630 0·155 0·102 37·3

0·478 0·326 0·518 0·127 0·375 0·110 95·2

4·483 5·976 5·329 3·316 5·471 3·790 91·5

0·384 0·488 0·418 0·177 0·408 0·297 78·7

2·501 2·484 2·705 1·196 2·284 1·551 92·7

1·340 0·963 1·072 0·421 0·448 0·325 84·6

2·613 3·478 2·773 2·726 1·612 1·577 77·3

"0·737 0·412

0·562 "0·633

"0·463 0·566

"0·631 0·675

"0·351 0·259

"0·416 0·544

"0·468 0·515

"0·407 0·275

"0·824 0·537 3 Sep

"0·329 0·273 5 Feb

"0·703 0·627 11 Jan

"0·658 0·677 29 Jan

"0·341 0·179 28 Dec

"0·521 0·623 29 Dec

"0·428 0·542 18 Nov

"0·436 0·327 13 Jan

Temp., temperature ()C); Salin., salinity; PO4, phosphate (µM) (1 µM=95 µg l "1); NO3, nitrate (µM) (1 µM=62 µg l "1); NO2, nitrite (µM) (1 µM=46 µg l "1); SiOn, silicate (µM) (1 µM=76 µg l "1); NH4, ammonium (µM) (1 µM=96 µg l "1); Sed., total sediment (mg l "1).

The percentage of the total variance, P, accounted for by Equation 2 is then calculated from:

where Ei,j,t =fi,j,t "Fi,j,t is the non-seasonal anomaly and Ó indicates summation over all i,j. In the case of temperature and salinity, the observed variabilities relative to the scale origins (0)K and fresh water) are so small that the denominator in Equation 3 is replaced by Ó(fi,j,t "fi,j,t)2 where fi,j,t is the mean of all fi,j,t values.

Cross-correlations Correlations between pairs, R and S, of the above parameter distributions were carried out as follows: for A0 and A1 correlate Ri,j:Si,j

(4)

for the gridded values fi,j,t and the anomalies fi,j,t "Fi,j,t: correlate Ri,j,t:Si,j,t

(5)

Calculations of statistical significance are complicated by the degree of independence of the gridded values. For 194 ‘ independent ’ gridded data, a correlation coefficient r§0·2 indicates 99% significance,

while for 194#15 ‘ independent ’ data points r§0·1 indicates 99% significance.

The seasonal cycle of temperature, salinity, phosphate, nitrate, nitrite, silicate, ammonium and suspended particulate matter Figures 2–9 show: (a) the mean A0, (b) the seasonal amplitude A1 and (c) the percentage of the total variance accounted for by the seasonal cycle. Table 1 lists the corresponding spatial mean values together with the spatial mean values of the phase è. A summary of salient characteristics follows. Temperature, Figure 2(a–c) Spatial mean A0 =10·2), A1 =4·2 )C, è=3 September, P=89% The seasonal cycle approximation (Equation 2) accounts for 89% of the total distribution, the mean (A0) values range from 7 )C at the NW limit to 12–13 )C along the continental coast. The cooler northern waters reflect the effect of lower near-bed temperatures in deeper areas. The seasonal amplitude varies in a similar fashion from 2 )C in the NW to 6 )C in the German Bight. The non-seasonal anomalies are greatest in the deeper waters along the Northern Boundary where horizontal advection influences add to the localized atmospheric exchanges that predominate further south.

672 D. Prandle et al. 56°

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F 2. Temperature: (a) mean ()C), (b) seasonal amplitude ()C) and (c) percentage of total variance associated with the seasonal cycle.

F 3. Salinity: (a) mean, (b) seasonal amplitude and (c) percentage of total variance associated with the seasonal cycle.

Salinity, Figure 3(a–c) Spatial mean A0 =34·3, A1 =0·15, è=5 February, P=37%

any imbalance between precipitation and evaporation are enhanced. The seasonal amplitude is less than 0·5 everywhere, with the maximum associated with Rhine outflow.

The seasonal cycle for salinity accounts for only 37% of the total distribution, i.e. Equation 2 does not adequately describe the annual variation. The mean values show freshest water of salinity 32·4 in the German Bight with saltiest water (34·8) at the NW limit. Salinities are generally lower along the coasts where river inflows and the depth-integrated effects of

Phosphate, Figure 4(a–c) Spatial mean A0 =0·52 ìM, 11 January, P=95%

A1 =0·37 ìM,

è=

The seasonal cycle accounts for 95% of the phosphate distribution. Mean values range from 0·3 to 0·75 µM

Seasonal cycles in the Southern North Sea 673 56° (a)

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F 4. Phosphate: (a) mean (µmol), (b) seasonal amplitude (µmol) and (c) percentage of total variance associated with the seasonal cycle.

F 5. Nitrate: (a) mean (µmol), (b) seasonal amplitude (µmol) and (c) percentage of total variance associated with the seasonal cycle.

with largest values occurring closest to the coast. The seasonal amplitude shows a similar distribution with values ranging from 0·2 to 0·6 µM.

in the central parts of the northern boundary. The seasonal amplitudes correspond almost exactly with the mean values, indicating a seasonal cycle ranging everywhere from near zero in July to a maximum in January of up to 22 µM.

Nitrate, Figure 5(a–c) Spatial mean A0 =5·3 ìM, A1 =5·5 ìM, è=29 January, P=90% The seasonal cycle accounts for 90% of the nitrate distribution. Mean values range from 1 to 11 µM with largest values occurring along the coasts, and smallest

Nitrite, Figure 6(a–c) Spatial mean A0 =0·42 ìM, 28 December, P=79%

A1 =0·41 ìM,

è=

While, overall, the seasonal cycle accounts for 79% of the nitrite distribution, significant anomalies occur

674 D. Prandle et al.

Silicate, Figure 7(a–c) Spatial mean A0 =2·71 ìM, 29 December, P=93%

A1 =1·55 ìM,

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both in the German Bight and in the central region close to the northern boundary. Mean values range from 0·2 to 0·8 µM with minimum values in the west, and maximum offshore of the Danish coast. The seasonal amplitudes show a similar distribution with amplitudes ranging from 0·1 to 1·0 µM with the maximum occurring offshore in the eastern section.

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The seasonal cycle accounts for over 93% of the silicate distribution. Mean values range from 1 to over 5 µM with largest values along the U.K. and Danish coasts. Seasonal amplitudes show a similar distribution with values ranging from 1 to 6 µM.

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Ammonium, Figure 8(a–c) Spatial mean A0 =1·07 ìM, 18 November, P=85%

è= 0.30

The seasonal cycle accounts for 85% of the ammonium distribution with the largest anomaly found off the Danish coast. The mean values range from 0·6 to 1·4 µM, with the largest values located along the continental coast, particularly in the German Bight. The seasonal amplitudes range from 0·2 to 1·2 µM with a similar distribution to the mean values.

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SPM, Figure 9(a–c) Spatial mean A0 =2·77 mg l "1, A1 =1·61 mg l "1, è=13 January, P=77% The seasonal cycle accounts for approximately 77% of the SPM with the largest anomaly close to the NW limit. Mean values range from 0·5 to nearly 6 µg l "1 and seasonal amplitude from 0·5 to 5 µg l "1. Reduced SPM concentrations occur along the western section of the Northern boundary and in the Rhine outflow region off the Dutch Coast. Correlations The highest correlations (Table 2) of approximately 0·7–0·8 are calculated between all three parameters, phosphate, nitrate and silicate. This indicates that not only are their geographical distributions similar but, also, that their rates of variation in concentration are reasonably similar throughout time and space. The next most correlated parameters, all approximately 0·5, are phosphate with both nitrite and SPM, together with nitrate and temperature (negatively correlated).

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F 6. Nitrite: (a) mean (µmol), (b) seasonal amplitude (µmol) and (c) percentage of total variance associated with the seasonal cycle.

Parameters with correlations of less than approximately 0·1 are SPM with temperature, salinity and ammonium, and temperature with ammonium and nitrite with salinity. Seasonal mean A0 (Table 3) Maximum correlations (all >0·75) are again found between phosphate, silicate and nitrate. Salinity and ammonium show high (negative for salinity) correlations (§0·6) with all parameters except

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F 7. Silicate: (a) mean (µmol), (b) seasonal amplitude (µmol) and (c) percentage of total variance associated with the seasonal cycle.

temperature and SPM. Remaining correlations >0·5 are between phosphate and SPM, 0·61; silicate and nitrite, 0·56; and temperature and nitrate 0·60).

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F 8. Ammonium: (a) mean (µmol), (b) seasonal amplitude (µmol) and (c) percentage of total variance associated with the seasonal cycle.

three nutrients. Likewise, correlations in excess of 0·7 are found for salinity with nitrate and temperature with phosphate. Anomalies, gridded observations Ei,j,t (Table 5)

Seasonal amplitude A1 (Table 4) The nutrients phosphate, silicate and nitrate all show correlations in excess of 0·9 indicating that their seasonal cycles are integrally related. Correlations in excess of 0·7 are calculated for ammonium and these

Again, the maximum correlations (approximately 0·6– 0·7) are found between nitrate, silicate and phosphate. In addition, there is a highly negative correlation with salinity of each of these three highly seasonallydependent parameters (phosphate, nitrate and

676 D. Prandle et al.

January. Fitting of the seasonal cycle assumes that the removal and regeneration processes which give rise to the cycle are symmetrical. The authors cannot say from this analysis whether the earlier occurrence of the silicate maximum in December is due to more rapid regeneration than the other nutrients, or due to its more complete and earlier removal by the diatoms which are the dominant plankton at the start of the spring bloom. Nitrate and silicate have seasonal amplitude values (A1) approximately equal to the mean values (A0) indicating near-zero values in June– July and thereby suggesting their limiting role in microbiological processes. Maximum values are generally found along coasts and minima in the deeper northern waters. The sources influencing these distributions are:

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The influence of sources (i) and (ii) should be evident from the geographical distributions in Figures 2–9; these are discussed below. Any spatially constant exchange at the sea surface (iv) or sea bed (iii) should shown an inverse correlation between concentration and depth.

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F 9. Suspended sediment: (a) mean (mg l ), (b) seasonal amplitude (mg l "1) and (c) percentage of total variance associated with the seasonal cycle.

silicate). This suggests that the non-seasonal processes which affect salinity concentration (variability in oceanic and river flow conditions) may also contribute to the non-seasonal phosphate, nitrate and silicate variation. The ‘ anomaly ’ patterns shown in Figures 4(c), 5(c) and 7(c) appear to support this view. Discussion and conclusions Phosphate, nitrate, nitrite and silicate exhibit strong seasonal cycles with maximum values in December–

Depth-averaged temperature is not greatly affected by riverine inputs. Colder water is present on the northern boundary in deeper areas, whilst warmer water associated with the English Channel region extends up the continental coastline into the German Bight. Salinity is slightly lower in regions of major river outflow, particularly in the German Bight. Elevated phosphate levels occur at the mouths of the Thames, the Wash and Humber, the Rhine, the Wadden Sea, the Ems, the Weser and the Elbe [Figure 4(a)]. The non-seasonal effects in the region of the Humber [Figure 4(c)] may indicate that the discharge of phosphate loads from the Humber is more out of phase with the production-regeneration cycle than for other rivers, or that the tendency for this phase difference it is most easily observed off the Humber. Nitrate concentrations are elevated at the mouth of the Wash and Humber, the Thames, the Rhine, the

Seasonal cycles in the Southern North Sea 677 T 2. Correlation of fi,j,t for each parameter for all i,j and t (approximately 2910 paired values for each coefficient) Parameter

Temp.

Salin.

PO4

NO3

NO2

SiOn

NH4

SPM NH4 SiOn NO2 NO3 PO3 Salin.

"0·106 "0·013 "0·347 "0·272 "0·491 "0·404 "0·234

"0·072 "0·474 "0·396 "0·101 "0·367 "0·232

0·493 0·334 0·794 0·521 0·799

0·446 0·304 0·703 0·392

0·214 0·379 0·470

0·377 0·458

0·107

See Table 1 for definitions.

T 3. Correlation of means, A0 for all i, and j (194 paired values for each coefficient) Parameter SPM NH4 SiOn NO2 NO3 PO3 Salin.

Temp. 0·462 0·316 0·238 0·278 0·596 0·482 "0·385

Salin.

PO4

NO3

NO2

SiOn

NH4

"0·115 "0·903 "0·907 "0·590 "0·889 "0·694

0·611 0·592 0·753 0·239 0·908

0·468 0·767 0·861 0·413

"0·060 0·667 0·564

0·235 0·853

0·004

See Table 1 for definitions.

T 4. Correlation of season amplitudes, A11i,j for all i, and j (194 paired values for each coefficient) Parameter

Temp.

Salin.

PO4

NO3

NO2

SiOn

NH4

SPM NH4 SiOn NO2 NO3 PO3 Salin.

0·473 0·582 0·610 0·517 0·077 0·782 0·463

0·015 0·610 0·395 0·705 0·464 0·489

0·386 0·748 0·907 0·496 0·937

0·406 0·810 0·929 0·393

"0·023 0·468 0·391

0·228 0·773

0·106

See Table 1 for definitions.

Wadden Sea, and in the German Bight from the mouth of the Elbe northwards. The Northern Boundary Region has the lowest nitrate concentrations. The area with the least variance accounted for by the seasonal cycle is the mouth of the Ems. Concentrations of phosphate dissolved in river waters tend to increase as river flow decreases, so concentrations will tend to be highest in summer when flows are lowest. Conversely, concentrations of dissolved nitrate tend to increase with flow so that the seasonal variation in nitrate inputs is better matched to the

seasonal cycle of concentrations in the North Sea than is the case for phosphate (Balls, 1992, 1994). The nitrite maximum in the main area of the southern North Sea occurs in December, but at the river mouths and the Northern Boundary the peak occurs much earlier in August, September and October (data not shown). Mean nitrite levels are high at the mouth of the Weser and in the northeastern area of the grid. Concentrations in the north-west are low with some increase at the mouths of the Tyne and the Wash. The amplitude distribution

678 D. Prandle et al. T 5. Correlation of anomalies, Ei,j,t for all i,j and t (approximately 2910 paired values for each coefficient) Parameter

Temp.

Salin.

PO4

NO3

NO2

SiOn

NH4

SPM NH4 SiOn NO2 NO3 PO3 Salin.

"0·243 "0·322 "0·063 "0·210 0·003 0·072 0·019

"0·190 "0·122 "0·660 "0·032 "0·607 "0·554

0·278 0·140 0·562 0·047 0·681

0·270 0·122 0·691 0·028

0·190 0·183 0·023

0·327 0·215

0·145

See Table 1 for definitions.

for nitrite again is high near the Weser and in the north-east, but a patchy effect is more evident. This may be an indication of biological turnover of nitrite. The highest mean silicate levels are associated with the German Bight region followed by the Wash [Figure 7(a)]. Most noticeable is the steady fall away from the coast and towards the Northern Boundary of mean silicate concentrations. The amplitudes have a very similar distribution. The exceptions to this are regions in the German Bight, at the Northern Boundary and at the mouths of the Rhine and Humber. Ammonium has high seasonal mean values in the German Bight and at the mouth of the Channel [Figure 8(a)]. All the British river outflows appear to be sources of ammonium, particularly the Tyne. The patchiness observed with ammonium amplitudes (which differs from nitrite amplitude patches) may be due to biological activity. This patchiness observed with nitrite and ammonium data is not seen for the other parameters. The SPM distribution has well-defined maximum values on the coast of south-east England [Figure 9(a)]. The amplitudes appear largest in the same area, but with an arm extending north-eastwards to an area north of the Wadden Sea. This area was associated with patchiness of amplitudes for both nitrite and ammonium. Nitrogen balance—N:P ratio Nitrogen was present in seawater in a number of different forms (Ward, 1992). The three principal inorganic forms—ammonium, nitrate and nitrite— were determined during the NSP surveys. The distributions of the three compounds are determined both by their source terms and their involvement in microbiological processes, which, depending on the particular environment, can either reduce nitrate to

ammonia or oxidize ammonia to nitrate. In either case, nitrite is produced as an intermediate compound. In certain conditions, nitrite is reduced (denitrified) to di-nitrogen which is lost from solution as nitrogen gas. The relative importance of denitrification in the North Sea is not yet well constrained by direct measurements (Law & Owens, 1990), but comparison of the ratio of nitrogen to phosphorus in the different inputs to that observed in the North Sea suggests it must be significant. This analysis gives an N:P ratio of 13·2 (based on the mean values of A0 in Table 1) which is lower than the value in ocean waters coming into the North Sea, which is close to the Redfield ratio of 16 (Redfield, 1934; Spencer, 1975), and substantially lower than in rivers inputs (Brockman et al., 1988; Hupkes, 1990, 1991). The inter-relationship between the different nitrogen-containing compounds is partly demonstrated by the degree of statistical correlation between them. Correlations between nitrate and nitrite; nitrate and ammonium; and nitrite and ammonium are all higher through space (Table 3) alone than through both time and space [0·413, 0·767 and 0·667 vs. 0·392, 0·304 and 0·379 (Table 2), respectively]. There is little positive correlation through time alone for nitrate with ammonium or for nitrite with ammonium (not tabulated). In some areas, there is negative correlation, which indicates that net reduction of one parameter is accompanied by net production of another. As the nitrogen-containing compounds show fairly high correlation through space, this net reduction/production through time is unlikely to be merely due to advection. The reduction of nitrate under anoxic conditions may explain the negative correlation ("0·308) of nitrite with dissolved oxygen which occurs during summer months. The latter correlation was calculated for interpolated, paired data; the correlation value over the full 15 months of interpolated data is positive, 0·228.

Seasonal cycles in the Southern North Sea 679 T 6. Consumption rate á and continuous inflow I derived from Equation 8

Nitrate (1 mole=62 g) Phosphate (1 mole=95 g) Silica (1 mole=60 g)

A0

A1

á

I

Advection

Winter concentration

330

340

6·0

24·8

3·2

(8 µM)

50

35

0·6

2·65

0·4

(0·6 µM)

160 µg l "1

90 µg l "1

1·6 µg ld

7·4 106t a "1

1·5 106t a "1

Annual nutrient budgets Some simplified calculations of the rates of supply and consumption of nutrients within the southern North Sea are now made. It is assumed that there is: (i) A continuous (external) supply at a fixed rate I; (ii) A continuous loss to adjacent seas of "C/F where C is the mean concentration and F the southern North Sea flushing time (2240 days, Prandle et al., 1994); and (iii) An internal consumption rate with a seasonal variation á(1"cosùt), i.e. zero at ùt=0 and a maximum of 2á at ùt=ð. The resulting balance is:

where the volume V=8780 km3, with the solution:

or substituting for F and ù (annual cycle):

(4 µM)

á=A1/56·6 day "1

(9)

and the continuous external supply:

Taking the advective inflow across the Northern Boundary as 20 000 m3 s "1 (Prandle, 1984) and the representative (winter) concentrations, the mean rate of supply by advection, from Atlantic waters is shown in Table 6. These advective sources are smaller than the calculated required values I by factors of: nitrate, 8; phosphate, 7; and silicate, 5. These sources may be supplemented by flows through the Dover Strait, benthic, atmospheric and riverine sources. However, these are unlikely to increase these estimates of advection by more than a factor of 2. Thus, the supply of nutrients to maintain the annual cycle, I, most likely depends on internal cycling as indicated by Howarth et al. (1994)).

Acknowledgements This study forms part of the POL contribution to the EEC MAST project NOWESP, No. MAS2-CT930067.

with á and I in daily units. Equation 8 indicates that maximum concentrations will occur 76) (or days) after minimum consumption. Thus, the observed maximum concentrations in mid-January correspond to maximum consumption in early May. Table 6 shows the values of the annual amplitudes A1 and means A0 for nitrate, phosphate and silicate (in µg l "1 corresponding to the values shown in Table 1). Then, from the correspondence between Equations 2 and 8, the amplitude of the seasonally varying daily consumption rate is given by:

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Appendix A i,j=Grid notation to indicate location t=Time, from August 1988 fi,j,t =Observed value at time t at location i,j fi,j =Mean observed value at location i,j Fi,j,t =Predicted value at time t at location i,j Ei,j,t =Anomaly at time t at location i,j A0 =Seasonal mean value circulated from Fi,j,t A1 =seasonal amplitude calculated from Fi,j,t ù=The seasonal frequency (2ð/365 days è=Phase P=Percentage of total variance attributable to seasonal variance Fi,j,t =A0 +A1·cos (ùt"è) Ei,j,t =Fi,j,t "fi,j,t

except for temperature and salinity where: