Journal of Marine Systems 27 Ž2000. 53–93 www.elsevier.nlrlocaterjmarsys

Northeast Water Polynya 1993: construction and modelling of a time series representative of the summer anticyclonic gyre pelagic ecosystem c Franck Touratier a,) , Louis Legendre b, Alain Vezina ´ a

Laboratoire d’oceanographie biologique, Station marine d’Arcachon, 2 rue du Professeur Jolyet, 33120 Arcachon, France ´ b Departement de biologie, UniÕersite´ LaÕal, Quebec, Quebec, Canada G1K 7P4 ´ c Bedford Institute of Oceanography, 1 Challenger DriÕe, Dartmouth, NoÕa Scotia, Canada B2Y 4A2 Received 30 March 1999; accepted 3 April 2000

Abstract A multidisciplinary international oceanographic expedition was conducted in the Northeast Water Polynya ŽNEW, northeast of Greenland. from May to August 1993, to understand the formation of the polynya and its influence on the pelagic ecosystem. The residual circulation in the polynya is characterized by an anticyclonic gyre, which follows a system of troughs. The numerous data acquired during the expedition and the resulting publications provide the background for an ecological modelling study. Since the sampling scheme during this expedition was not appropriate for implementing ecological models, the first objective of the present study was to build up a multivariate time series. Stations in the time series were selected by taking into account the residual circulation in the anticyclonic gyre. Model outputs were compared to data along the time series. From the time series alone, it was not possible to fully understand the development of a second phytoplankton bloom, so that we formulated three hypotheses on the functioning of the ecosystem during that period: ŽH1. horizontal supply of nitrate from waters located to the north; ŽH2. vertical diffusion of nitrate; ŽH3. local remineralization processes in the surface layer. H2 and H3 are evaluated using two ecological models, in which the same components are simulated, but the first considers only the nitrogen cycle and the second simulates both the carbon and nitrogen cycles. Comparing the chemical and biological variables simulated by the models to the observed time series data by reference to the three hypotheses lead to the conclusion that H2 is the most likely hypothesis. This also means that the summer pelagic ecosystem in the anticyclonic gyre was perhaps dominated by a short food chain that mostly comprised large phytoplankton, copepods and appendicularians. However, because the parameterization of vertical mixing used to test hypothesis H2 may be an oversimplification of field conditions, the hypothesis cannot be fully tested. q 2000 Elsevier Science B.V. All rights reserved. Keywords: polynya; Arctic Ocean; modelling; nitrogen; carbon

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Corresponding author. E-mail address: [email protected] ŽF. Touratier..

0924-7963r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 7 9 6 3 Ž 0 0 . 0 0 0 6 1 - 0

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F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

1. Introduction Polynyas are mesoscale areas of open water in ice-covered seas, which are found in the ice pack of the two hemispheres. Although their extent represents a small percentage only of the total area of the Arctic Ocean Ž- 5%; Parkingson and Cavalieri, 1989., polynyas there have recently been the subject of large scale studies because of their possibly high productivity ŽStirling, 1997. resulting from higher submarine photosynthetically active radiation ŽPAR. relative to the surrounding ice-covered areas. In these

‘oases’ of the Arctic ŽStruzik, 1989., it has been hypothesized that the planktonic food web plays a major role in transferring carbon from the atmosphere toward ocean depths ŽYager et al., 1995.. The Northeast Water Polynya ŽNEW. is located on the continental shelf off northeast Greenland ŽFig. 1.. It is presently the best known polynya in the Arctic because several multidisciplinary expeditions have been conducted there since 1991 as part of the International Arctic Polynya Programme ŽIAPP.. The biological productivity of polynyas is constrained by numerous factors that include the physical character-

Fig. 1. Northeast Water Polynya: bathymetry, and two main currents ŽNEGCC: Northeast Greenland Coastal Current; EGC: East Greenland Current.. The anticyclonic gyre is mainly caused by the NEGCC.

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istics of the system Že.g. extent and duration of the opening of the polynya, advection, PAR, water temperature., and its chemical Že.g. concentrations, distributions, and relative abundance of nutrients. and biological Že.g. composition and physiological characteristics of species. properties. In the NEW, the extent and duration of the polynya, combined with an increase of solar energy in the water column and a constant supply of new nutrients, mainly determined the high levels of productivity reached in the area. Consequently, the planktonic food web may develop. Ecological modelling can provide a quantitative and dynamic synthesis of the numerous components of the NEW’93 expedition. Considering the main physical characteristics of the system, the present study focus on ecological processes that govern the development of plankton. The overall objective of the present study is to develop a model of polynya pelagic ecosystems, test it using data from the NEW’93, and use it for exploring hypotheses on the functioning of the system. To achieve this, the study involves the objectives given below. Building up a time series from the NEW’93 data set, to which the results of model simulations could be compared ŽObjective 1.. Because several uncertainties remain after analyzing the NEW’93 data, several hypotheses can be formulated and evaluated using models. One of the uncertainties concerns the origin of nutrients Žnew or regenerated. to explain the occurrence of a second bloom in the polynya during the summer months. Kattner and Budeus ´ Ž1997. found that the growth of diatoms in the polynya continued during summer 1993 despite nitrate depletion, and they proposed that the source of nitrogen was in situ ammonium regeneration. It will be shown below that, in our time series Žcalled NEW Time Series, NTS., diatom growth effectively continued after nitrate depletion. In the present paper, three alternative hypotheses are examined to explain the growth of diatoms after nitrate depletion along the NTS: ŽH1. A horizontal supply of external nitrate allowed diatom growth after the depletion of local nitrate. The source could have been the nitrate-rich waters north of Ob Bank. ŽH2. A vertical supply of nitrate favored diatom growth after the exhaustion of nitrate in the surface layer. Since nitrate was abundant at depth, physical

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processes such as vertical diffusion generated by vertical shear, tides, wind stress, or internal waves may have replenished nitrate in the surface layer. ŽH3. After nitrate depletion, the growth of diatoms was only due to nitrogen remineralization by heterotrophic organisms such as zooplankton and bacteria that excrete mostly ammonium. Hypothesis H3 corresponds to the above opinion of Kattner and Budeus ´ Ž1997.. It must be mentioned that external horizontal supply or vertical replenishment of ammonium is unlikely because its concentrations were always very low in the whole NEW area ŽKattner and Budeus, ´ 1997.. Hypotheses H2 and H3 will be evaluated using one-dimensional models ŽNEWN and NEWCN , respectively. that make different assumptions about vertical mixing and remineralization by the food web. The second objective of the present study consists in building up these models. Hypothesis H1 cannot be evaluated using the type of model developed in the present study Ža 3D or at least a 2D horizontal model would be necessary., but the hypothesis will be discussed below. The third objective is to compare the observed and simulated results along the time series. The fourth objective, using Objective 3, is to evaluate hypotheses H2 and H3.

2. Study site and overview of the NEW’93 results The present study is based on the results of the 1993 3-month expedition ŽNEW’93. involving oceanographic ice breakers RV Polarstern Žleg 2: 22 May to 24 June; leg 3: 25 June to 3 August. and USCGC Polar Sea Žleg 4: 22 July to 17 August.. The western and eastern boundaries of the NEW are the Greenland coast and the slope of the East Greenland Shelf ŽEGS., respectively ŽFig. 1.. It is limited to the north and the south by the Ob Bank Ice Barrier ŽOBIB. and the Norske Øer Ice Barrier ŽNØIB., respectively ŽFig. 2.. The OBIB is located on the Ob Bank. The bathymetry of the NEW is characterized by a trough system around Belgica Bank Žfrom NØIB to OBIB, there are the Norske and the Westwind troughs; Fig. 1.. The EGS bathymetry strongly influences the residual circulation, which is

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Fig. 2. Positions of the stations sampled during NEW’93, and of the ice barriers ŽNBIB: Norske Ber Ice Barrier; OBIB: Ob Bank Ice Barrier.. Leg 2: 22 May–24 June; Leg 3: 25 June–3 August; Leg 4: 22 July–17 August 1993.

characterized by an anticyclonic gyre along the trough system Že.g. Bourke et al., 1987; Schneider and Budeus, ´ 1994; Bignami and Hopkins, 1997.. The gyre results from the Northeast Greenland Coastal Current ŽNEGCC. and the East Greenland Current ŽEGC. ŽFig. 1.. Its vertical structure can be schematized in two layers: the Polar Water ŽPW., in the upper 50 to 150 m, and the modified Atlantic Water ŽAW; Schneider and Budeus, 1995., below. The ´ summer maximum extent of the open waters during

NEW’93 Žca. 82 000 km2 . was intermediate between 1992 Ž59 000 km2 . and 1985 Ž120 000 km2 .; the polynya opened on the 178th day of 1993 Ž27 June. and lasted ca. 89 days ŽBohm ¨ et al., 1997.. Schneider and Budeus ´ Ž1995, 1997. and Minnett Ž . et al. 1997 described the complex mechanisms of the NEW opening. In summary, the two fast ice barriers play an important role in the opening because the sea–ice imported by the northward NEGCC and southward EGC is stopped by the NØIB and

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

OBIB, respectively. The opening of the polynya is explained by the emergence of PW from under the NØIB and its northward flow following the Norske and Westwind troughs, combined to the solar warming of the surface layer in spring and summer. In addition, the prevailing winds during the period contribute to the recurrent opening of the polynya ŽSchneider and Budeus, ´ 1997.. During NEW’93, a total of 457 stations were occupied in the whole NEW area, most of them being located in or around the Norske and Westwind troughs ŽFig. 2.. Kattner and Budeus ´ Ž1997. described the distributions of the major nutrients in the area: before the opening of the polynya, the concentrations of silicate and phosphate were uniform over the water column, i.e. 280 to 392 mg Si my3 and 34.1 mg P my3 , respectively, whereas nitrate vertically increased from 56 to 182 mg N my3 ; when the polynya opened, a tongue of nutrient-rich water was observed north of the NØIB, flowing northward in the Norske trough and then eastward in the Westwind trough; the growth of phytoplankton in that water mass, which was stimulated by the PAR, explain the depletion of nutrients which occurred over ca. 10 days. The taxonomic analysis of ice algae and phytoplankton was done by Hellum Ž1994, 1997., and the biomass and production of phytoplankton were described and discussed by several authors that include Gosselin et al. Ž1994., Legendre et al. Ž1995. and Smith et al. Ž1997a.. They found that large phytoplankton Žmostly diatoms. were dominant when the ice cover was - 50%; in these low ice-covered areas, which corresponds to the Ob Bank and the Norske and Westwind troughs, high biomass Ž1 to 89 mg Chl a my2 . and primary production Ž0.004 to 2.7 g C my2 dayy1 . were observed, with the highest values occurring in summer instead of spring. Based on the size structure of phytoplankton biomass and production, Legendre et al. Ž1995. and Pesant et al. Ž1996. identified three clusters of stations, each of them being associated with an area of the NEW that showed specific environmental conditions and biological processes. The biomass of mesozooplankton was dominated by calanoid copepods ŽDaly, 1997; Hirche and Kwasniewski, 1997. and appendicularians ŽAcuna ˜ et al., 1994; Deibel and Acuna, ˜ 1994.. The highest copepod biomasses occurred on the EGS continental slope and at the

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mouths of Belgica and Westwind troughs, whereas appendicularians dominated in the EGC and heavy ice-covered areas. Grazing was higher outside than inside the polynya in 1993 ŽPesant et al., 1998. and 1992 ŽAshjian et al., 1995., but its effect on phytoplankton was low ŽDaly, 1997.. Bacterial biomasses ranged from 0.1 to 52.9 mg C my3 ŽPong-Vong, 1996; Ritzrau and Thomsen, 1997., with maximum values in the surface layer and heavy or moderately ice-covered areas. These results are consistent with the hypotheses that Ž1. not only the amount but also the nature of primary production differ inside and outside the polynya, and Ž2. these differences lead to the development of different planktonic food webs in the two areas ŽFortier, 1995.. 3. NEW’93 data sets and construction of the NEW Time Series (NTS) 3.1. Data sets used in the present study Several data sets are required to run the models and to assess the quality of the simulated results. The methods used on board the RV Polarstern Žsecond and third legs. and the USCGC Polar Sea Žfourth leg. for sampling and estimation of variables were not always the same ŽTable 1.. The total biomass for nano- and microzooplankton Žcomputed as the sum of heterotrophic flagellates and ciliates., used for comparison with model results, is underestimated because neither the abundance or biomass of ciliates was determined along the NTS. 3.2. Construction of the time series Ideally, the model one-dimensional simulations should be compared to a time series of chemical and biological observations representative of dynamics within a single water mass. During NEW’93, a station located in the center of the polynya Ž80826X N; 13840X W; Time Series Station or TSS. was regularly sampled by the Polarstern and Polar Sea during the three legs. However, the TSS was located in the periphery of the anticyclonic gyre of the polynya, where the water masses were continually advected eastwards. The TSS is therefore inadequate for the present study because different seawater volumes were sampled there over the season.

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Table 1 Data sets used in the present study Legs 2 and 3 ŽRV Polarstern. Method or tool

Reference

Method or tool

Reference

Solar Radiation

POLDAT systema

Schneider Ž1994.

Eppley pyranometersb

Temperature and salinity

CTD measurements

CTD measurements

Nitrate, ammonium and silicate concentrations Chlorophyll a concentration Primary production Bacteria and heterotrophic flagellate abundances c Copepod and appendicularian abundancesd POC and PON Ice cover f-ratio h C:N uptake ratio for phytoplankton

Technicon Autoanalyser II system Whatman GFrF filter Žin vitro fluorescence. 14 C method Epifluorescence microscopy

Budeus ´ et al. Ž1994., Budeus ´ and Schneider Ž1994. Ahlers et al. Ž1994., Kattner et al. Ž1994. Legendre et al. Ž1994.

P. Minnett ŽRSMAS, University of Miami. Wallace et al. Ž1995.

Bongo sampler e

Perkin-Elmer CHN analyser SSMrI g 15 N tracer method 13 C and 15 N tracer methods

Leg 4 ŽUSCGC Polar Sea.

Bergeron et al. Ž1994. Juniper and Sime-Ngando Ž1994. Acuna ˜ et al. Ž1994. Fortier et al. Ž1994. Bergeron et al. Ž1994. Ramseier et al. Ž1994. Gosselin et al. Ž1995. Gosselin et al. Ž1995.

Technicon Autoanalyser II system Whatman GFrF filter Žin vitro fluorescence. 14 C method Epifluorescence microscopy MOCNESS sampler f

Wallace et al. Ž1995.

Pesant et al. Ž1998. Juniper and Sime-Ngando Ž1994. Lane et al. Ž1996.

Carlo–Erba model SSMrI g 15 N tracer method nd

Wallace et al. Ž1995. Ramseier et al. Ž1994. Smith et al. Ž1997a. nd

Wallace et al. Ž1995.

nd: no data. a Measurements every 5 s, but 5 min averages are used. b Measurements every 1 min, but 20 min averages are used. c The abundances of these organisms were converted into carbon biomasses by Pong-Vong Ž1996.. d The abundances of copepods were converted into carbon biomasses using only the copepodite and adult stages of the main species present during the sampling period Ži.e. Calanus glacialis, C. hyperboreus, C. finmarchicus, Metridia spp., and Pseudocalanus spp; Hirche and Kwasniewski, 1997. with the method described in Pesant et al. Ž1998.. The abundance of Metridia spp. was not used in Pesant et al. Ž1998., but the prosome length–weight relationship used by these authors for C. glacialis was applied to Metridia spp., from which the following individual dry weights were estimated: 2 ŽC1., 2 ŽC2., 5 ŽC3., 14 ŽC4., 49 ŽC5., 61 Žadult male., and 130 mg individualy1 Žadult female.. As a first estimate, the abundances of appendicularians were converted into carbon biomasses using the conversion factor of 21.3 mg C individualy1 calculated by Pesant et al. Ž1998. from Deibel and Acuna ˜ Ž1995.. This included the two most common species of the NEW area, Oikopleura Õanhoeffeni and O. labradoriensis. e The Bongo net provided integrated values from surface to 200 m or the bottom at shallow stations. f The MOCNESS ŽMultiple OpeningrClosing Net and Environmental System. provided vertically integrated abundances for eight layers in the water column. g The SSMrI ŽSpecial Sensor MicrowaverImager. has a resolution of 25=25 km2 . h During leg 4, the uptake of urea by phytoplankton was not estimated, so that the f-ratio was based on the uptake of nitrate and ammonium only.

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

Variable

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Therefore, we had to reconstruct a Lagrangian time series where we can follow a single water mass as it advected around the polynya. We used several hypotheses to build up the NEW Time Series ŽNTS.: Ž1. A water mass emerging from under the NØIB moves northwards in the Norske trough and eastwards in the Westwind trough Ždashed line in Fig. 3.. This hypothesis is justified by the available information on circulation Že.g. Bourke et al., 1987; Schneider and Budeus, ´ 1994; Bignami and Hopkins,

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1997.. Ž2. This water mass moves horizontally, at a mean speed of ca. 10 cm sy1 ŽSchneider and Budeus, ´ 1995; Budeus ´ and Schneider, 1995.. Ž3. The constituents in the water mass are homogeneously distributed. Ž4. The water mass is independent of the surrounding water; i.e. there is no import or export of materials Žmass conservation.. The distance covered by the water mass was discretized, spatially and temporally, by subdividing the trough system area in several boxes Žalong the

Fig. 3. Construction of the NEW Time Series ŽNTS.: the anticyclonic gyre is discretized in space and time as 13 boxes, whose sequential numbers and entry and exit dates ŽJulian days. are indicated below and above each box, respectively. The map also shows the position of the NTS stations for legs 3 and 4.

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Table 2 Stations included in the 13 boxes of the NEW Time Series ŽNTS. Box Number

Entry and exit dates ŽJulian days.

Station number

Leg

Sampling date ŽJulian day.

Latitude Ž8N.

Longitude Ž8W.

Water depth Žm.

1 2

181–184 184–187

3 4 5

187–190 190–193 193–196

6 7 8 9

196–199 199–202 202–205 205–208

10 11

208–211 211–214

12

214–217

13

217–220

nd 128 129 nd nd 166 167 nd 215 nd 301 302 303 304 319 350 351 357 358 359 378 379 380 381 386 387

nd 3 3 nd nd 3 3 nd 3 nd 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

nd 185.2 185.3 nd nd 193.8 193.9 nd 200.6 nd 207.3 207.3 207.4 207.5 208.6 212.3 212.4 213.4 213.5 213.5 216.0 216.0 216.1 216.2 217.0 217.0

nd 79.6 79.6 nd nd 80.3 80.2 nd 80.4 nd 80.3 80.3 80.4 80.4 80.3 80.1 80.1 80.1 80.2 80.2 80.1 80.0 80.0 80.0 79.9 79.8

nd 16.0 16.2 nd nd 14.7 14.3 nd 13.6 nd 11.0 11.0 11.0 11.0 10.1 8.1 8.5 9.2 8.9 8.9 7.7 7.8 7.6 7.6 6.7 7.4

nd 193 303 nd nd 367 291 nd 322 nd 285 288 310 293 328 324 328 292 303 301 307 335 283 283 286 230

nd: no data.

dashed line in Fig. 3.. The purpose was to use as many as possible of the 457 stations of NEW’93 to build the NTS, so that the length and width of boxes were critical parameters. The width of each box Žacross the dashed line. was 50 km, which is approximately the width of the trough system. The length of each box Žalong the dashed line. was 25.9 km, which corresponds to a residence time of 3 days for a current speed of 10 cm sy1 . Different box lengths Ži.e. different water residence times. were tested, showing that 3 days was the best compromise to maximize both the number of stations in the overall NTS and the homogeneity of the concentrations or biomasses in each box. This scheme discretizes the trough system into 13 boxes, each being characterized by entry and exit dates of the water mass ŽFig. 3.. All possible entry dates in the first box were tested in order to find the series with the largest

number of stations. The NTS thus selected has 21 stations ŽTable 2.. Its duration is 33 days because the first box is empty. Considering the middle date in each box Ži.e. the entry date plus 1.5 day., the NTS lasted from 3 July Žday 185.5. to 6 August Žday 218.5., so that there were, on average, 1.6 station boxy1 and 0.63 station dayy1 . The NTS stations are not uniformly distributed among boxes, most stations being in boxes 9, 11 and 12 ŽFig. 3 and Table 2.. All variables determined during NEW’93 are not available at all stations.

4. Evaluation of hypothesis H1: justification for a 1D-approach According to hypothesis H1, horizontal advection of nitrate-rich waters north of Ob Bank into the

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sampling area was responsible for the growth of diatoms after the depletion of local nitrate. Such hypothesis is realistic because, during summer 1992 ŽNEW’92., waters from the northern part of the

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NEW were advected into the 0 to 20 m layer of the Westwind trough ŽAshjian et al., 1997.. In 1993, such an event was only recorded during leg 2 when northerly winds prevailed ŽSchneider and Budeus, ´

Fig. 4. Nitrate versus silicate relationship, used to characterized the water masses of the time series. Four water masses were identified by Kattner and Budeus ´ Ž1997. from all nitrate and silicate concentrations during legs 2 and 3: ŽA. surface waters of the East Greenland Shelf ŽEGS. modified during the summer months; ŽB. deep water masses in the troughs; ŽC. water masses representative of the northernmost region and the area north of Ob Bank; ŽD. water masses influenced more by the Atlantic than the Polar Waters. For regression 4 in water mass A, see the text. Original units used by Kattner and Budeus ´ Ž1997. are also kept for comparison.

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1995., causing an increase of silicate concentrations on Ob Bank ŽBudeus ´ et al., 1997; Kattner and Budeus, ´ 1997.. On the Ob Bank, Ingram and Galbraith Ž1994. observed average southward currents of ca. 6 cm sy1 Žat a depth of 25.5 m., but such currents had little or no influence on the anticyclonic gyre circulation. For example, the direction and intensity of winds directly influenced currents on Ob Bank. Between days 200 and 220 Ži.e. the second bloom along the NTS., weak southerly winds were measured on Ob Bank in 1993, whereas weak northerly winds prevailed in 1992 during the same period ŽSchneider and Budeus, 1997.. This may ´ explain the differences between the 2 years, noted above. Schneider and Budeus ´ Ž1997., Budeus ´ et al. Ž1997., and Kattner and Budeus ´ Ž1997. think that currents on Ob Bank were insignificant, and that circulation there was isolated from the anticyclonic gyre during summer 1993. Kattner and Budeus ´ Ž1997. used the nutrient signature to classify the water masses in NEW’93, based on all nitrate and silicate data from legs 2 and 3 Žsee their Fig. 6.. Four main water bodies Žcalled A through D. were identified ŽFig. 4.. Fig. 4 follows the approach of Kattner and Budeus ´ Ž1997., but only the vertical profiles of silicate and nitrate in the NTS are used to identify the water masses. All nutrient concentrations along the NTS Žexcept 3 points. fall in boxes A and B Ži.e. water masses which are characteristic of surface waters of the EGS modified during the summer months, and of deep waters in the troughs, respectively; Fig. 4.. For nitrate concentrations ) 63 mg N my3 , it is concluded that the water masses of the Atlantic Žbox D. or the area north of Ob Bank Žbox C. do not influence the deep waters of the NTS. Concerning the nitrate concentrations between 7 and 63 mg N my3 in box A, Kattner and Budeus ´ Ž1997. evidenced three different groups of data points, each being represented by a specific regression line Ž1 to 3, Fig. 4.. The first regression line corresponds to water bodies north of Ob Bank, the second to the Ob Bank waters, and the third to waters from the central part of the NEW Ži.e. Belgica Bank, Norske Trough, and Westwind Trough.. In order to determine if the NTS surface waters during the second bloom were influenced by waters from Ob Bank, an additional regression line Ž4, Fig. 4. was computed on the leg 4 data of the NTS Žthey

correspond to days 205 to 220, see Table 2.. If there had been an effect from the north, the fourth regression line would occupy an intermediate position between regression lines 2 and 3. Given the location of regression line 4 ŽFig. 4., it is concluded that the Ob Bank waters did not influence the NTS surface waters between days 205 and 220. The conclusion would be the same for leg 3 Žopen squares, Fig. 4., because all the points are very close to regression line 3. It follows from the discussion of Fig. 4 that the deep and surface waters in the NTS were representative of waters from the central part of the NEW. From this and preceding arguments, it is concluded that the first hypothesis ŽH1. is unlikely. This also means that vertical 1D-models, representative of the anticyclonic gyre, can be used in the present study. 5. Construction of models Models NEWN and NEWCN are two-layered ŽFig. 5.. Layer A, with a constant thickness HA s 20 m, corresponds to the surface mixed layer as visually determined from the temperature and salinity profiles at the NTS stations ŽFig. 6.. Layer B, with a constant thickness H B s 180 m, will be used as a reservoir of nutrients Žsilicate and nitrate. to evaluate hypothesis H2. Depth Z2 s 200 m does not have any physical, chemical or biological meaning; it was imposed by the zooplankton data for legs 2 and 3 Ži.e. bongo net, which only provided vertically integrated abundance over the upper 200 m.. In the present study, the physical structure of models NEWN and NEWCN is kept as simple as possible because of a lack of field information on vertical mixing during the NTS. Models with constant mixing depth have often been used in the past Že.g. Steele, 1958; Ebenhoh, ¨ 1980; Parsons and Kessler, 1987.. The effects of using this simple structure on the conclusions of the study are discussed later. The forcing variables ŽPAR, temperature, and vertical diffusion coefficient. and the exchange processes between the two layers Ždiffusion and sinking. are described below. 5.1. Sedimentation and diffusion processes in the two models In Tables a1 and a2 Žthe letter ‘a’ stands for Appendix in the following sections., the terms ‘sink-

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Fig. 5. Schematic representation of the vertical structure of models NEWN and NEWCN . Depths Z0 , Z1 , and Z2 are used to compute the thicknesses HA and H B of layers A and B, respectively. The variables for solar radiation are E I : incident solar radiation; E0 : photosynthetic active radiation ŽPAR. at the air–sea or ice–sea interface; EA : averaged PAR in layer A; E1: PAR at the mixed layer depth. EB : averaged PAR in layer B. The temperature variables are TA : averaged temperature in layer A; TB : averaged temperature in layer B. The sinking and diffusion variables are Ž s x .A and Ž s x . B : sinking rate of a state variable X, from layer A to B, and from layer B to the underlying waters, respectively; Ž X .A and Ž X . B : concentration or biomass of a state variable X in layers A and B, respectively. j : mixing rate between layers A and B. Note that model NEWCN does not include the process of diffusion Žhypothesis H3..

ing’ and ‘diffusion’ appear in the differential equations of several state variables, for the two models. The equations for these terms differ in the two layers ŽFig. 5.. For sinking, the export of matter from layer A to B is Ž s x .A Žthe sinking rate of variable x in layer A. multiplied by Ž X .A Žthe concentration or biomass of state variable x in layer A.. Since Ž s x .A - 0, the matter lost from layer A is exported to layer B. Because H B ) HA , there is dilution of matter exported from layers A to B, so that the sinking term in layer B must be multiplied by the ratio HA : H B . Some matter is also lost from layer B to deeper waters, which is computed in the same way. The vertical distributions of all constituents, except mesozooplankton ŽZ2 and Z3, see below., are

influenced by vertical diffusion in model NEWN . Since mesozooplankton are large organisms with strong vertically migrating ability, we consider that the vertical component of turbulence does not influence their distributions. Because the large zooplankton ŽZ2 and Z3 in the models. resided permanently in the upper 30 m of the water column ŽFortier et al., 1994., vertical migrations were not included in the models. A simple formulation is applied to simulate vertical diffusion between the two layers ŽFig. 5.: the strength of diffusion is determined by the mixing rate Ž j . and the difference between the concentrations of a constituent in layers B and A ŽŽ X . B and Ž X .A , respectively., the direction of the net flux being determined by the sign of the difference. When

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Fig. 6. Vertical profiles of temperature and salinity for all NTS stations in each box. The dashed line in each box corresponds to the mixed layer depth in models NEWN and NEWCN , which is constant Ž20 m..

wŽ X . B y Ž X .A x ) 0, the matter exported from layer B is concentrated in layer A and, consequently, the diffusion term in layer A must be multiplied by ratio H B : HA ŽFig. 5.. When the difference is negative, the matter exported from layer A is diluted in layer B and, so that the diffusion term in layer B must be multiplied by ratio HA : H B . 5.2. Construction of model NEWN Model NEWN , which is used to evaluate hypothesis H2, simulates the main processes of the nitrogen cycle. Nitrogen is chosen as unit because nitrate and ammonium, more than phosphate, limited phytoplankton growth in the polynya ŽKattner and Budeus, ´

1997.. The model has 14 state variables ŽTable 3.. All interactions between the state variables are summarized in Table 4, where eight types of interactions are identified, i.e. uptake, grazing, mortality, feces production, exudation, excretion, decomposition, and hydrolysis. The processes of vertical exchanges between the two layers Ži.e. sinking and diffusion. are on the main diagonal of the Table. Small phytoplankton ŽP1n. take up NO 3 and NH 4 , whereas large phytoplankton ŽP2n, diatoms. take up NO 3 , NH 4 , and SI. The potential food items of nano- and microzooplankton ŽZ1n. are P1n, P2n, small and intermediate-sized detritus ŽD1n, D2n., and heterotrophic bacteria ŽBn.. Mesozooplankton Žcopepods and appendicularians, Z2n and Z3n. can also feed on Z1n and large detritus ŽD3n.. The mortality of small

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93 Table 3 State variables in model NEWN ŽN and Si stand for nitrogen and silicium, respectively. Symbol

Description

Units Žmg my3 .

NO 3 NH 4 SI P1n

Nitrate concentration Ammonium concentration Silicate concentration Small phytoplankton biomass Ž - 5 mm. Large phytoplankton biomass Ž ) 5 mm. Nano- and microzooplankton biomass Copepod biomass Appendicularian biomass Small detritus concentration Intermediate-sized detritus concentration Large detritus concentration Labile high molecular weight DOM concentration Labile low molecular weight DOM concentration Bacterial biomass

N N Si N

P2n Z1n Z2n Z3n D1n D2n D3n DOM1n DOM2n Bn

N N N N N N N N N N

organisms ŽP1n and Bn. supplies the D1n pool. The mortality or feces production of intermediate-sized organisms ŽP2n and Z1n. supply the D2n pool. The D3n pool contains all the products derived from the mortality and feces production of Z2n and Z3n. All detritus ŽD1n to D3n. are decomposed into labile high-molecular weight DOM ŽDOM1n.. Labile lowmolecular weight DOM ŽDOM2n. results from the hydrolysis of DOM1n and phytoplankton exudation. Bacteria assimilate DOM2n, and all excretion products from Bn, Z1n, Z2n, and Z3n return to the NH 4 pool. Parameterizations of the above processes are listed in Table a3 Žphytoplankton., Table a4 Žzooplankton., and Table a5 Ždetritus decomposition and bacterial growth.. The symbols, values and units of parameters in the model are listed in Table a6. Most processes in these tables are valid for both layers A and B, the exceptions being described later together with the forcing functions. Variables T and E, and parameters H refer to temperature, PAR and the thickness of a layer ŽA or B., respectively. The thickness H of

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each layer Ž HA and H B . is constant, whereas T ŽTA and T B . and E Ž EA and E B . vary with time. The nutrient uptake rates for NO 3 , NH 4 and SI are computed as the product of four terms, i.e. maximum growth rate, temperature, nutrient, and PAR limitation ŽEqs. Ž1. to Ž3., Table a3, respectively.. All process rates in model NEWN Žand in NEWCN . increase exponentially with temperature, as in other models Že.g. Andersen et al., 1987.. When two nutrients with different units ŽN and SI. are taken up by the phytoplankton ŽP2n., Liebig’s law of the minimum is applied Ži.e. the smallest of the two rates is used for the computation.. Nutrient limitation ŽEqs. Ž6. to Ž8. in Table a3. is computed with Michaelis–Menten functions, but the sum of nitrate plus ammonium limitation follows the parameterization proposed by Wroblewski Ž1977. where C is a constant that parameterizes the strength of ammonium inhibition of nitrate uptake. The resulting limitation must be F 1, a condition which is not always respected by Wroblewski’s equation so that, during the simulation, this condition must be checked and the equation adapted when necessary as proposed by Touratier Ž1996.. The limitation of growth by PAR ŽEq. Ž9., Table a3. is computed with the formula of Peeters and Eilers Ž1978., which has often been used in modelling studies Že.g. Andersen et al., 1987; Andersen and Rassoulzadegan, 1991. to take into account the effect of photoinhibition on phytoplankton growth. The growth rate of P1n ŽEq. Ž4., Table a3. is the sum of nitrate and ammonium uptake rates, whereas the growth rate of P2n depends on Liebig’s law ŽEq. Ž5., Table a3.. The release of dissolved organic matter by phytoplankton Žexudation., mortality, and sinking of living cells are processes that strongly depend on the physiological state of phytoplankton Že.g. Bienfang et al., 1982; Lancelot, 1983.. In the present model, the physiological state of phytoplankton is characterized by comparing the actual growth rate ŽmN x . to the maximum growth rate at the same temperature ŽmmN x umTx .. The comparison is made in Eq. Ž11. of Table a3. The resulting limitation ŽLm x . varies between 0 and 1; when mN x s 0, then Lm x s 1 and, when mN x s mmN x umTx , then Lm x s 0. Limitation Lm x is used to compute the exudation rate ŽEq. Ž10., Table a3., i.e. exudation is null for healthy phytoplankton, and it tends toward its maximum value

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Table 4 Conceptual table containing all interactions between the state variables in model NEWN . Boxes with border in bold contain the state variables. The flux is always from the row variable to the column variable. All boxes in nitrogen, except SI Žsilicium.. Vertical exchanges between the two layers are on the main diagonal. D: decomposition; E: exudation; G: grazing; H: hydrolysis; M: mortality; N: excretion; P: feces production; U: uptake; O: diffusion; S: sinking

with a deterioration of the physiological state. Constant ge x is used to control the shape of the Lm x curve. The same principle is used for the mortality rate ŽEq. Ž12., Table a3., with a minimum mortality rate Žm0 x .. The constant m0 x corresponds to the mortality of senescent cells. The physiological state also affects the sinking rate ŽEq. Ž13., Table a3., in the same way as mortality Žonly diatoms, P2n, can sink.. Since parameters v0 P2 and v1 P2 are sinking velocities Žsee Table a6., the calculation of sinking rates uses the thickness of each layer Ž H .. For a number of reasons, all particles cannot be ingested by zooplankton. Among the known reasons, the properties of particles Že.g. size, shape, speed, and taste. and those of zooplankton Že.g. size, capture apparatus. cannot be taken into account easily in

ecological models. In model NEWN , the capture efficiency of a food item y by zooplankton x Ž e x y . aims at representing all known properties cited above and the unknowns. The capture efficiency varies between 0 and 1, i.e. when e x y s 0, no food particle y is ingested by zooplankton x and, when e x y s 1, all food particles y can be ingested by x. Eq. Ž4. from Table a4 is used to compute the potential food biomass of zooplankton x ŽBn x . given the number of food items Ž i .. When Bn x is lower than the constant food concentration threshold ŽBn0 x ., the grazing rate for x ŽgN x . is null ŽEq. Ž1., Table a4.. When Bn x ) Bn0 x , the grazing rate is computed with Eq. Ž2. in Table a4. The rate is influenced by temperature and food concentration, the latter effect being parameterized with the expression developed

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

by Ivlev Ž1955. as modified by Parsons et al. Ž1967.. The grazing rate of x on a specific y is given by Eq. Ž3., Table a4. The rates of feces production and excretion are computed with Eqs. Ž5. and Ž6., respectively. All zooplankton parameterizations described here have been used in other models Že.g. Andersen et al., 1987; Andersen and Rassoulzadegan, 1991.. The decomposition rates of detritus ŽD1n, D2n, and D3n. are parameterized using Eq. Ž1., in Table a5. The decomposition fluxes are controlled by the biomass of bacteria, and a Michaelis–Menten function is used to account for the effect of detritus concentration on the flux. Since the sizes of detritus differ, their sinking rates also differ. The smallest detritus ŽD1n. do not sink, and D3n sink faster than D2n Žsinking speeds Õ D3 and Õ D2 , respectively, Table a6.. The sinking rates depend on the thickness of the layer ŽEq. Ž2., Table a5.. DOM1n Žalso called ‘bacterial indirect substrates’. must be hydrolyzed into DOM2n Žalso called ‘bacterial direct substrates’. before being assimilated by bacteria ŽBillen and Fontigny, 1987; Billen et al., 1990.. The hydrolysis is performed by bacterial exoenzymes, and the hydrolysis flux, which obeys a Michaelis–Menten kinetics ŽEq. Ž3., Table a5., also depends on bacterial biomass ŽBillen and Servais, 1989; Billen, 1990.. Bacterial growth is a function of DOM2n availability ŽEq. Ž4., Table a5.. The expressions for the bacterial and zooplankton excretion rates are identical ŽEq. Ž5. in Table a5 and Eq. Ž6. in Table a4.. The differential equations used for model NEWN are listed in Appendix A ŽTable a1.. 5.3. Construction of the model NEWC N One approach often used in the literature Že.g. Andersen et al., 1987; Andersen and Rassoulzadegan, 1991. is to model the fluxes of nitrogen only, and compute from them the carbon fluxes by applying a constant C:N ratio to all state and rate variables. This assumes a perfect parallelism between the C and N cycles, but it is known that numerous discrepancies exist between the two cycles Že.g. Lancelot and Billen, 1985; Touratier, 1996., e.g. the ratio of excretion Žnitrogen. to respiration Žcarbon. is not constant in several heterotrophs Že.g. Checkley, 1980; Lancelot and Billen, 1985; Kiørboe, 1989.. Although the excretion processes of bacteria and

67

zooplankton were considered in model NEWN , a better parameterization, detailed by Touratier et al. Ž1999a,b. is required in order to evaluate hypothesis H3, because excretion is not only influenced by temperature and biomass Žlike in NEWN ., but also by the quantity and quality of substrates assimilated by bacteria and food assimilated by zooplankton. There is no easy way to introduce the qualitative aspect of food in a model because it is difficult and complex to select the right criterion for quality Že.g. lipid, protein, or energy content.. In model NEWCN , which simulates the C and N biogeochemical cycles, the criterion used for food quality is its C:N ratio. Model NEWCN ŽTable 5. includes, as does model NEWN ŽTable 3., three nutrients ŽNO3, NH4, and SI., two phytoplankton ŽP1 and P2., three zooplankton ŽZ1, Z2, and Z3. and three detritus ŽD1, D2, and D3. size classes, two DOM molecular weight classes ŽDOM1 and DOM2., and bacteria ŽB.. There are 21 state variables in Table 5 vs. 14 in Table 3 because model NEWCN considers both C and N. The C:N ratios of phytoplankton, detritus and DOM are not constant, so that each component is represented by two state variables ŽXc and Xn, i.e. carbon and nitrogen biomass or concentration, respectively. where C:N ratios are defined by the ratio Xc:Xn. The C:N ratios for zooplankton ŽC:NZ1 , C:NZ2 , C:NZ3 . and bacteria ŽC:NB . are constant, so that only one state variable is used to model each group of organisms ŽZ1c, Z2c, Z3c, and Bc; the carbon unit was chosen arbitrarily.. Using a constant C:NB ratio is consistent with the study of Goldman et al. Ž1987., who showed this ratio to be stable for a wide range of growth conditions. Although the variability of zooplankton elemental ratios seems to be more interand intra-specific ŽUrabe, 1993; Sterner and Hessen, 1994., several species of marine copepods living at high latitudes may build up large reserves of lipids, which increases the proportion of C relative to N in their bodies. The processes responsible for this variability are poorly known, so that it would be premature to develop a model without the assumption of homeostasis. It follows that, in Table 6, variables Z1n, Z2n, Z3n, and Bn are not state variables. These variables and DIC Ždissolved inorganic carbon. are added to Table 6 to specify the origin and destination of each interaction. The eight types of interactions already in model NEWN Žsee above. are also present

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Table 5 State variables in model NEWCN ŽN, Si, and C stand for nitrogen, silicium and carbon, respectively. Symbol

Description

Units Žmg my3 .

NO 3 NH 4 SI P1c

Nitrate concentration Ammonium concentration Silicate concentration Small phytoplankton biomass Ž - 5 mm. Small phytoplankton biomass Ž - 5 mm. Large phytoplankton biomass Ž ) 5 mm. Large phytoplankton biomass Ž ) 5 mm. Nanoy and microzooplankton biomass Copepod biomass Appendicularian biomass Small detritus concentration Small detritus concentration Intermediate-sized detritus concentration Intermediate-sized detritus concentration Large detritus concentration Large detritus concentration Labile high molecular weight DOM concentration Labile high molecular weight DOM concentration Labile low molecular weight DOM concentration Labile low molecular weight DOM concentration Bacterial biomass

N N Si C

P1n P2c P2n Z1c Z2c Z3c D1c D1n D2c D2n D3c D3n DOM1c DOM1n DOM2c DOM2n Bc

N C N C C C C N C N C N C N C N C

in model NEWCN , plus the respiration of auto- and heterotrophs Ž R, Table 6.. All interactions have carbon or nitrogen units, except the uptake of silicate by P2. In model NEWCN , the uptake of ammonium by bacteria takes into account the possible competition between bacteria and phytoplankton for this nutrient. As a consequence of hypothesis H3 evaluated with the model, there is no vertical diffusion between layers. Parameterizations of the above processes are listed in Table a7 Žphytoplankton., Table a8 Žzooplankton., and Table a9 Ždetritus decomposition and bacterial growth.. The symbols, values and units of parameters used in model NEWCN are listed in Table a10.

The parameterization for the processes of nutrient uptake and phytoplankton growth Žnitrogen; Eqs. Ž6. to Ž13., Table a7. is very similar to that used for model NEWN ŽEqs. Ž1. to Ž8., Table a3.. Limitation by PAR ŽLi x , Eq. Ž9., Table a3. in model NEWN is changed here to a limitation by the phytoplankton C:N ratio ŽLcn2 x , Eqs. Ž14. and Ž15., Table a7.. Parameterization of the rates of gross and net primary production and of photoinhibition ŽEqs. Ž1. to Ž3., Table a7., without the effects of temperature Ž umTx . and the phytoplankton C:N ratio ŽLcn1 x ., is from Platt et al. Ž1980.. The effect of temperature Ž umTx . is the same for all phytoplankton growth processes ŽEqs. Ž1., Ž2., Ž9. and Ž10., Table a7.. Limitations Lcn1 x and Lcn2 x ŽEqs. Ž4., Ž5. and Ž14., Ž15., Table a7, respectively. allow to couple the C and N cycles for phytoplankton growth processes. In order to achieve this, three characteristic values of the phytoplankton C:N ratio are used. The first is the C:N ratio for healthy phytoplankton ŽC:Nm x ., which is considered to be equal to the Redfield ratio ŽTable a10.. The two other values define the range of variation of the phytoplankton C:N ratio ŽC:N x ., i.e. C:Ni x and C:Ns x are the minimum and maximum values of C:N x , respectively, for which the condition C:Ni x - C:Nm x - C:Ns x must be respected. It is assumed that phytoplankton try to keep C:N x near C:Nm x , which is modelled by comparing C:N x to values C:Ni x , C:Nm x , and C:Ns x , and by modifying the uptake rate of inorganic carbon or nitrogen. Three different cases can occur: Ž1. When C:Ni x F C:N x - C:Nm x , the nitrogen uptake rate is lowered Žthis is done with Lcn2 x , Eq. Ž14., Table a7. and the carbon uptake rate is increased Žthis is done with Lcn1 x , Eq. Ž4., Table a7. in order to increase C:N x . Ž2. When C:N x s C:Nm x , the phytoplankton is healthy so that the uptake of both the carbon and nitrogen is increased ŽLcn1 x s 1 and Lcn2 x s 1, Eqs. Ž4. and Ž14., respectively, Table a7.. Ž3. When C:Nm x - C:N x F C:Ns x , the carbon uptake rate is lowered Žthis is done with Lcn1 x , Eq. Ž5., Table a7. and the nitrogen uptake rate is increased Žthis is done with Lcn2 x , Eq. Ž15., Table a7., in order to decrease C:N x . Parameters gcn1 x and gcn2 x control the shape of the curves Lcn1 x and Lcn2 x , respectively. In model NEWCN , as in model NEWN , an indicator of the physiological state of phytoplankton is used to compute the exudation, mortality, and sink-

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Table 6 Conceptual table containing all interactions between the variables in model NEWCN . Boxes with border in bold contain only state variables. Other variables are in boxes without border. All boxes in carbon or nitrogen, except SI Žsilicium.. The flux is always from the row variable to the column variable. Vertical exchanges between the two layers are on the main diagonal. D: decomposition; E: exudation; G: grazing; H: hydrolysis; M: mortality; N: excretion; P: feces production; R: respiration; U: uptake; S: sinking

ing of cells. Since C:Nm x represents the C:N ratio for healthy phytoplankton, a lower or higher value of C:N x indicates a deteriorated physiological state, so that C:N x may be a good indicator of that state. Lancelot Ž1983. observed that the exudation rate increases with nitrogen limitation. Limitation Le x ŽEqs. Ž18. and Ž19., Table a7. is used to represent this effect: when C:Ni x F C:N x - C:Nm x , the exudation rate is null ŽEqs. Ž16. and Ž18., Table a7., but it increases with C:N x when C:Nm x - C:N x F C:Ns x

ŽEq. Ž19., Table a7.. The exudation rate for the nitrogen cycle is computed in order to keep the C:N ratio of released products ŽC:Ne . constant ŽEq. Ž17., Table a7.. The same mortality and sinking rates must be used in the C and N cycles ŽEqs. Ž20. and Ž23., Table a7, respectively.. These processes have the same expressions as in model NEWN , but the limitations differ since a different physiological state indicator is used. The mortality and sinking rates are both minimum when C:N x s C:Nm x , and they in-

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crease with a deterioration of the physiological state, i.e. for a low or high C:N x ŽEqs. Ž21. and Ž22. for mortality; and Eqs. Ž24. and Ž25. for sinking, Table a7.. The parameterization of zooplankton grazing rates in NEWCN ŽEqs. Ž1. to Ž3. and Eq. Ž6., Table a8. is similar to that in NEWN ŽEqs. Ž1. to Ž4., Table a4., but the units change since zooplankton biomasses are computed here in carbon. The grazing rate of each food item y by zooplankton x ŽgN x y , Eq. Ž4., Table a8. must be computed for the nitrogen cycle to estimate the C:N ratio of ingested food ŽC:Nf x , Eq. Ž5., Table a8.. Other processes in Table a8 Ži.e. the assimilation, quality of the assimilated food, feces production, respiration, and excretion by zooplankton. are examined in detail by Touratier et al. Ž1999b., so that the parameterization is only summarized here. All these processes depend directly or indirectly on the quantity and quality of the ingested food, and on temperature. In the digestive tract of zooplankton, a fraction only of the ingested food is assimilated, the remainder being egested as fecal pellets. For zooplankton, the nitrogen assimilation coefficient ŽAn x . is usually higher than its carbon equivalent ŽAc x . Že.g. Landry et al., 1984; Checkley and Entzeroth, 1985; Morales, 1987., which reflects the selection of nitrogen-rich compounds in the gut during the food assimilation process. Knowing these coefficients ŽAn x and Ac x , Table a10., the assimilation and feces production rates are estimated using Eqs. Ž7. and Ž8., and Ž10. and Ž11., respectively ŽTable a8.. The quantity and quality of assimilated food ŽEqs. Ž7. to Ž9., Table a8. largely determine the catabolic processes Ži.e. respiration and excretion.. According to the value of aC x and considering the respiration rate for maintenance Žrb x , Eq. Ž12., Table a8., two situations are modelled: Ž1. If 0 F aC x F rb x , the respiration and excretion rates ŽEqs. Ž13. and Ž14., Table a8. are independent of the carbon and nitrogen net growth efficiencies ŽK2c x and K2n x ,

respectively., because net production is null or negative in this case. Ž2. If rb x F aC x , the respiration and excretion rates are computed with the usual relationships Že.g. Billen et al., 1990; Weaver and Hicks, 1995; Eqs. Ž15. and Ž16., respectively, Table a8., that depend on K2c x and K2n x . K2n x varies linearly with the quality of the assimilated food, i.e. C:Na x ŽEqs. Ž17. and Ž18., Table a8. and K2c x are computed in such a way as to keep C:N x constant ŽEq. Ž19., Table a8.. In model NEWCN , the processes for detritus decomposition ŽEq. Ž1., Table a9. and sinking ŽEq. Ž3., Table a9., DOM2 hydrolysis ŽEq. Ž4., Table a9., and bacterial growth rates ŽEq. Ž6., Table a9. are very similar to those in model NEWN ŽEqs. Ž1. to Ž4., Table a5.. The only difference is, again, the use of carbon instead of nitrogen. The nitrogen rates for detritus decomposition, hydrolysis, and bacterial growth are calculated from the carbon rates with Eqs. Ž2., Ž5., and Ž7., respectively ŽTable a9.. The parameterization used in the present study for bacterial respiration and excretion processes ŽEqs. Ž8. to Ž19., Table a9. is detailed in Touratier et al. Ž1999a.. The parameterization of these processes is very similar to that used for zooplankton Žsee above., taking into account the facts that the assimilation process does not exist in bacteria, and that copepods cannot take up inorganic nitrogen from the medium when their food has low organic nitrogen content relative to carbon. The differential equations of the system used for model NEWCN are listed in Appendix A ŽTable a2.. 5.4. Models implementation In order to implement the models, the forcing variables Žincident solar radiation, ice cover, temperature, mixing rate, and several nutrient concentrations., the initial conditions for the state variables,

Fig. 7. Forcing variables of models NEWN and NEWCN . Ža. incident solar radiation Ž E I .; Žb. ice cover ŽIC.; Žc. photosynthetic active radiation ŽPAR. at the air–sea or ice–sea interface Ž E0 . computed with Eq. Ž1. Žsee the text.; Žd. average temperature in layers A and B ŽTA and TB , respectively.; Že. average salinity in layers A and B Ž SA and SB , respectively; salinity is not a forcing variable of the models.; Žf. rate of vertical mixing between layers A and B Ž j , only in model NEWN .; Žg. average nitrate concentration in layer B ŽNO 3 B .; Žh.: average silicate concentration in layer B ŽSI B ..

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

and the values of the parameters must be specified. The incident solar radiation measured on board the

71

RV Polarstern and USCGC Polar Sea was taken as representative of the total NEW area. Fig. 7a shows

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

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the incident solar radiation Ž EI . at the air–sea ice interface or air–seawater interface Žwhen the ice cover was absent. along the NTS. As already explained, each box represents a period of three days, during which EI is never null during the night ŽArctic summer.. The ice cover largely determines the penetration of solar radiation in the water column. The attenuation of solar radiation due to ice depends on numerous factors such as the percentage of ice cover, ice thickness and age, albedo, presence or absence of snow and modification of the spectral composition of solar radiation by organisms living in the sea ice Že.g. Legendre and Gosselin, 1991.. Only the percent ice cover ŽIC. was determined for the NTS stations, so that rough approximations must be made to estimate the PAR at the seawater–ice interface Ž E0 ; Fig. 5.. The present study used IC as determined by the SSMrI ŽSpecial Sensor MicrowaverImager. because the resolution Ž25 = 25 km2 . approximately corresponds to the length of a box in the NTS Ž25.9 km.. During the period of the NTS, IC ŽFig. 7b. first decreased, after which it increased to reach ca. 50% at the end of the NTS. The mean value of IC in each box was calculated, and used to compute E0 : E0 s

IC 100

ž

Tr q 1 y

IC 100

/

E I FPAR FE

Ž 1.

where Tr s 0.01 is an overall light transmission coefficient for snow and sea ice, which is a value slightly lower than the range Ž0.03–0.27. proposed by Gosselin et al. Ž1997. for the Arctic Ocean. FPAR s 0.43 ŽIvanoff, 1975. is the fraction of E I which is photosynthetically active ŽPAR., and FE s 4.15 mmol photons my2 sy1 ŽPrieur and Legendre, 1988. is the factor used to convert 1 W my2 into the PAR unit of the models. Fig. 7c shows the strong influence of IC on E0 . For the water column, the average PAR in each layer Ž EA and EB ; Fig. 5. is computed by using Beer’s law: E Ž z . s E0 e Ž ya1 zya2 HCHL a dz .

Ž 2.

The coefficient of PAR attenuation for pure water is a1 s 0.03 my1 ŽKirk, 1983.. Constant a2 s 0.01 m2 Žmg Chl a.y1 is the attenuation coefficient due

to chlorophyll a ŽCHL a.. The range proposed by Bannister Ž1974. is 0.013–0.02 m2 Žmg Chl a.y1 . CHL a is computed differently in NEWN and NEWCN : in NEWN ,

CHL a s P1n Ž C:NP1 . Ž Ch1:C P1 . q P2n Ž C:NP 2 . Ž Ch1:C P 2 .

Ž 3. in NEWCN ,

CHL a s P1c Ž Ch1:C P1 . q P2c Ž Ch1:C P 2 .

Ž 4.

The change in mean temperature ŽTA and TB ., which is used as forcing variable for all biological processes, is shown in Fig. 7d. The upper layer ŽA. progressively warms up from y28C to 28C, after which TA decreases until the end of the period, whereas T B remains constant over the whole NTS Žy18C.. The mean salinity in each layer is shown in Fig. 7e, but SA and SB are not forcing variables in the models. They will be used for discussing the stability of the water column. The mixing rate Ž j . is the sole forcing variable that differs between the two models, because hypothesis H2 Žmodel NEWN . assumes changing j ŽFig. 7f., whereas hypothesis H3 Žmodel NEWCN . considers that j Ž t . s 0. The change in mixing Ž j ; Fig. 7f. was chosen in such a way as to simulate a second bloom along the NTS Žsee Section 6.. The observed concentrations of nitrate and silicate in layer B are imposed in the two models ŽFig. 7g and h, respectively.. These are not simulated because the thickness of layer B Ž180 m., which was imposed by the zooplankton sampling method Žsee above., is too large to adequately simulate in that layer the growth of phytoplankton and, consequently, the uptake of nutrients. Even if there is no vertical mixing in model NEWCN , the same configuration as in model NEWN is used for nutrients in layer B. Since NO 3 and SI are imposed in layer B, the differential equations for these nutrients ŽTables a1 and a2 in Appendix A. are only used for layer A. Most data in the NTS are available from day 185.5 Žmean date in the second box., so that the simulations begin on this date, for which initial

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

conditions must be assigned to the state variables ŽTable a11.. There are three types of initial conditions: Ž1. Some initial values, i.e. nutrient concentrations, are directly taken from field observations. Ž2. Several initial values are derived from field data by using conversion factors, i.e. the concentrations of Chl a, zooplankton and bacteria were converted into carbon or nitrogen. Ž3. The other initial conditions could not be derived from observations because the variables were not determined at sea, i.e. detritus and dissolved organic matter Žthe values were thus chosen during the calibration step in order to obtain the best simulation.. The values of most parameters are within ranges found in the literature. Values chosen for models NEWN and NEWCN are those which provide the best fit to the data ŽTables a6 and a10, respectively., i.e. the differences between observed and simulated variables were visually appraised and the best simulation was selected after numerous runs of the models. Few of the parameters were determined during NEW’93 ŽTable 7.. The present modelling study does not focus on the actual values of the parameters because the results are primarily influenced by the two hypotheses and the respective structures of the two models. Since the hypothesis underlying each model differs, the context of the present study is not appropriate for comparing the structures of the models. Consequently, the aim here is neither to select the best values for the parameters nor to determine the best model structure, but to evaluate the hypotheses H2 and H3, as stated in Section 1.

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6. Results and discussion 6.1. Outputs of NTS and models Temporal changes of variables along the NTS and results simulated by the two models are compared in Fig. 8. In the case of complex models as NEWN and NEWCN , the number of observed variables used for the comparison must be high to obtain high-quality calibration. Although this number is the largest possible, it is smaller than that of simulated variables Žstate variables, fluxes., as is the case for most models. Only the results for layer A are discussed here because the most interesting events along the NTS occurred in this layer. The results for copepods, appendicularians, detritus, primary production, and grazing are shown for the 0–200 m water column Žlayers A and B., to allow comparison with the observed data. Fig. 8a shows that the two models simulate similar PAR in layer A Ž EA .. The observed and simulated results for nutrients Žnitrate, ammonium, and silicate. are shown in Fig. 8b–d. The results for nitrate ŽFig. 8b. and silicate ŽFig. 8d. from the two models correspond well to the observed values, but those for ammonium differ largely ŽFig. 8c.. The main phytoplankton characteristic along the NTS is the occurrence of two blooms in layer A ŽFig. 8e., with the same maximum values Žca. 1.5 mg Chl a my3 ; sum of the two phytoplankton size classes.. The simulated results from the two models

Table 7 Parameters determined during NEW’93 Parameter Carbon:Chlorophyll a ratio Phytoplankton growth rate Assimilation number for photosynthesislight relationship Initial slope for photosynthesislight relationship Ingestion rate for appendicularians Sinking speed for appendicularians fecal pellets and houses a

Value

Units

11–265 0.05–2.57 36–360

mg C Žmg Chl dayy1 mg C Žmg Chl

1.2–4.8

mg C Žmg Chl a.y1 dayy1 Žmmol photons my2 sy1 .y1 dayy1 m dayy1

1.3 a 100

Underestimated, because based on Chl a only.

Reference a.y1 a.y1 dayy1

Booth and Smith Ž1997. Booth and Smith Ž1997. Smith et al. Ž1994. Smith et al. Ž1994. Deibel and Acuna ˜ Ž1994. Acuna ˜ et al. Ž1994., Deibel and Acuna ˜ Ž1994., Bauerfeind et al. Ž1997.

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Fig. 8. Observed data and results of models NEWN and NEWCN along the NEW Time Series ŽNTS.. No observed data are available for comparison with EA Ža., the phytoplankton C:N ratio Žf., the detritus C:N ratio Žk., the concentration of dissolved organic carbon ŽDOC; l., the dissolved organic matter C:N ratio Žm., and cumulated grazing Žr. computed with the models.

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75

Fig. 8 Ž continued ..

are qualitatively similar, but they largely differ between days 199 and 208 ŽFig. 8e.. As explained

before, the phytoplankton C:N ratio is constant in NEWN ŽRedfield ratio, Table a6., but it varies in

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NEWCN ŽFig. 8f.. The ratio simulated by NEWCN first increases from the Redfield value to ca. 9 mg C Žmg N.y1 , after which it decreases to ca. 6 mg C Žmg N.y1 at the end of the first bloom. These changes are consistent with the field estimates of Smith et al. Ž1997b; their Fig. 4b. at the NEW time series during the same period. A similar change in the phytoplankton C:N ratio is simulated for the second bloom, but the maximum value of ca. 8 mg C Žmg N.y1 is lower than during the first bloom. These increases of the C:N ratio correspond to periods of nitrogen limitation ŽFig. 8b and c.. Fig. 8g–i compare the observed and simulated results for zooplankton. For the smallest component Žnano- and microzooplankton, Z1; Fig. 8g., the best results are from NEWN , but it is likely that the observed values are underestimates since the abundances of nanoflagellates only were available for the NTS stations; i.e. the abundances of ciliates, which are a major component in this size range, were not available, and copepod nauplii were not included because of their low contribution to the total biomass. For copepods ŽZ2; Fig. 8h. and appendicularians ŽZ3; Fig. 8i., the results of the two models reproduce the field data fairly well, with an increase at the end of the period. The concentrations of total field detritus, which were not determined during NEW’93, are estimated here from the carbon concentrations of POC, phytoplankton ŽP1 and P2., nanozooplankton ŽZ1., and bacteria ŽB. Žfield detrituss POC y ŽP1 q P2. y Z1 y 1r2B.. The computation assumes that large zooplankton ŽZ2 and Z3. were not present in the small water samples used for POC measurements, and that half the bacterial biomass went through the GFrF filters Žnominal pore size: 0.7 mm; the bacterial cell sizes ranged between 0.48 and 1.32 mm, assuming a spherical volume; Pong-Vong, 1996.. Concentrations of total detritus estimated in this way are compared to the sum of D1, D2, and D3 simulated by the two models ŽFig. 8j., showing that neither model is successful in reproducing the computed detritus concentrations. Fig. 8k–m shows the detritus C:N ratio, DOC concentration and DOM C:N ratio, to illustrate the decomposition processes. There are no corresponding field data, except the estimates of Ahlers et al. Ž1994. for total Žlabile q refractory. DON in the

surface Ž56 to 98 mg N my3 . and deep Ž28 to 56 mg N my3 . layers. By using a mean DOM C:N ratio of 6 mg C Žmg N.y1 ŽFig. 8m., these ranges were converted into carbon Ži.e. 336 to 588 and 168 to 336 mg C my3 , respectively.. The DOC concentrations ŽDOM1q DOM2. in layer A simulated by the models ŽFig. 8l. are - 200 mg C my3 but, because the models only consider the labile component of DOC, the relatively low simulated values may be realistic. The main difference between the two models is that DOC accumulates in NEWN , and is more constant in NEWCN ŽFig. 8l.. The bacterial biomasses simulated by the two models for layer A are often close to the observed values ŽFig. 8n.. The ranges and mean values for bacterial carbon given by Pong-Vong Ž1996., Ritzrau and Thomsen Ž1997. for year 1993, and those estimated by Ritzrau Ž1997. and Smith et al. Ž1995. for year 1992 are quite similar: range ca. 0.12 to 52.85 mg C my3 , and average ca. 7 mg C my3 . Since the maximum bacterial biomass simulated by NEWCN is ca. 140 mg C my3 , it is likely that this model overestimates the bacterial biomass. In the models, the POC concentrations are calculated as POC s P1 q P2 q Z1 q D1 q D2 q D3 q 1r2B. For layer A ŽFig. 8o. and during the first bloom, model NEWN best simulates the field POC but, during the second bloom, the results from the two models are similar. The field and simulated POM C:N ratios are shown in Fig. 8p. All components of POC have constant C:N ratios in model NEWN Žsee Table a6., but changes in their relative concentrations cause changes in the POM C:N ratio. The POM C:N ratio simulated by NEWCN is much more variable than in NEWN , because all components of POC Žexcept Z1 and B. have variable C:N ratios. The best results are those of model NEWCN , although it was not possible to reproduce the highest values observed during the second bloom ŽFig. 8p.. Primary production Ž14 C method. was estimated during NEW’93, the resulting cumulative values being compared with those of the two models in Fig. 8q. The field cumulative primary production ŽCPP. between days 185.5 and 215.5 is 19.16 g C my2 , and the mean daily primary production ŽMDPP. is 0.63 g C my2 dayy1. Over a slightly longer period Ždays 185.5 to 217.5., model NEWN underestimates the 14 C production ŽCPP s 17.94 g C my2 , and MDPP

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

s 0.56 g C my2 dayy1 ., and model NEWCN slightly overestimates it ŽCPP s 21.77 g C my2 and MDPP s 0.68 g C my2 dayy1 .. Two other approximate methods were used to estimate the cumulative primary production from the NEW’93 data sets, i.e. the ‘NO 3 method’ Žthe decreases in NO 3 concentrations are added up and converted into carbon by using the Redfield C:N ratio., and the ‘POC method’ Žthe increases in POC concentrations are added up.. In a closed system, when regenerated production is negligible, it is expected that the NO 3 method will overestimate and the POC method will underestimate the cumulative primary production. During the NTS, the NO 3 and POC methods yielded CPP s 21.7 and 7.74 g C my2 , and MDPPs 0.65 and 0.23 g C my2 dayy1 , respectively. The higher values for CPP and MDPP obtained with the NO 3 method are, however, only due to the last value in the NTS, because other cumulative values computed with this method were always lower than those from the 14 C method ŽFig. 8q.. There may be three explanations for this: the system is open, i.e. there is horizontal ŽH1. or vertical ŽH2. supply of nitrate, so that the NO 3 method underestimates the actual primary production; the system is closed and regenerated production is an important fraction of the total primary production; or the Redfield C:N ratio used for the computation is too low. Most simulated MDPP values are within the ranges estimated by several authors for the NEW area, e.g. 0.58 to 0.84 g C my2 dayy1 in the trough system in 1992 ŽWallace et al., 1995., and 0.004 to 2.7 g C my2 dayy1 for the Ob Bank and the Norske and Westwind troughs in 1993 ŽLegendre et al., 1995.. With model NEWN , the cumulative grazing ŽCG. for Z1, Z2, and Z3 represents 28.83% of CPP Ž5.17 g C my2 ; Fig. 8r., whereas the corresponding value with NEWCN is 56.46% Ž12.29 g C my2 .. The contributions of the three types of zooplankton to CG show a major difference in the functioning of the simulated ecosystem, i.e. in NEWN , most grazing is due to mesozooplankton ŽZ1:1.5%, Z2:51.3%, and Z3:47.2% of CG., whereas grazing in NEWCN is dominated by the smallest organisms ŽZ1:38.7%, Z2:34.4%, and Z3:26.9% of CG.. Model NEWN therefore tends toward a linear herbivorous food chain, whereas the microbial food web plays a central role in NEWCN .

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Concerning the phytoplankton C:N uptake ratio, two observed values only are available along the NTS Ž12.6 and 18.17 mg C Žmg N.y1 ; Fig. 8s., i.e. during the first phytoplankton bloom. These data can only be compared with the results of NEWCN for the same period Ždays 194.5 to 200.5., when the simulated ratio is between 8.41 and 15.68 mg C Žmg N.y1 . The values of model NEWCN are therefore lower than the field ratios, but the simulated increase corresponds to the limited field observations. Such a trend was also observed at the NEW time series station ŽTSS. by Smith et al. Ž1997b; their Fig. 4b., who observed an increase of the ratio to 18 mg C Žmg N.y1 , followed by a decrease to ca. 5 mg C Žmg N.y1 , from days 180 to 210. Hence, the simulated values in Fig. 8s are consistent with other observations. Changes in the f-ratio during the NTS may be very useful for assessing hypotheses H1, H2, and H3. A high f-ratio during the second bloom would favor hypotheses H1 or H2, whereas a low ratio would be consistent with hypothesis H3. The original data for the f-ratio during the NTS are plotted in Fig. 8t, but there is a major methodological difference between leg 3 Žbefore day 202. and leg 4 Žafter day 202.. During leg 3, the uptake of urea was determined and included in the estimates of f-ratios, whereas the uptake of only nitrate and ammonium was used to compute f-ratios during leg 4. According to Gosselin et al. Ž1995., urea was the main source of regenerated nitrogen used by phytoplankton during summer Žleg 3. in the polynya. During the same period, Smith et al. Ž1997a. found that urea uptake was highly variable and almost equal to ammonium uptake. The f-ratio data in leg 4 were therefore corrected by including an uptake of urea equal to that of the ammonium Žopen circles, Fig. 8t.. It was not possible to include a state variable for urea in the models because numerous uncertainties still exist concerning the potential producers and consumers of this nutrient in the planktonic food web. It follows that, in the models, the uptake of only nitrate and ammonium were used to estimate the f-ratio ŽFig. 8t., but it may be considered that regenerated ammonium in the models is representative of the total regenerated nitrogen irrespective of the form Žammonium or urea.. During leg 3, the simulated f-ratios are always much higher than the

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observed values, which is quite surprising because the low concentrations of ammonium ŽFig. 8c. and low biomasses of zooplankton ŽFig. 8g–i. and bacteria ŽFig. 8n., which are the main potential producers of regenerated nitrogen, should lead to high f-ratios during that period. The corrected f-ratios during leg 4 are intermediate between the values simulated by NEWN and NEWCN ŽFig. 8t.. During the whole period simulated by NEWN , 890 mg N–NH 4 my2 were locally produced in layer A, and 1480 mg N my2 Žmainly in the form of nitrate. were imported into layer A from layer B by upward diffusion. The low f-ratios, simulated by model NEWCN during leg 4 are due to ammonium regeneration in layer A. During the whole period simulated by NEWCN , 1380 mg N–NH 4 my2 were produced in layer A by zooplankton and bacteria. The high regeneration in layer A coincided with low export of P2, D2, and D3 from layer A to B, via sinking Žonly 23.9% of CPP were exported., which is half the amount of organic carbon exported from layer A in model NEWN Ž45.6% of CPP.. During leg 4, no sediment trap was deployed to estimate the export of biogenic carbon, but the average values computed with models NEWN and NEWCN Ž255.6 and 162.6 mg C my2 dayy1 , respectively. are in the range of values Ž43 to 327 mg C my2 dayy1 . provided by Pesant et al. Ž1996. for leg 3. The average value from NEWN seems, however, to be more realistic because the export of POC from the 0 to 50 m layer for the trough system was estimated by Cochran et al. Ž1995; 234 Th method. to be 396 mg C my2 dayy1 during leg 4. 6.2. EÕaluation of hypotheses H2 and H3 by comparing model results to the obserÕed NTS data The following discussion focuses on H2 Žvertical supply of nitrate from layer B to A, by vertical diffusion. and H3 Žlocal supply of regenerated nitrogen in layer A, performed by heterotrophic organisms that excrete mainly ammonium., in view of explaining the growth of diatoms after the exhaustion of nitrate in the surface layer. Several results from models NEWN and NEWCN ŽFig. 8. can be used to evaluate hypotheses H2 and H3. The main differences between the outputs of models occur for small zooplankton ŽZ1, Fig. 8g., detritus ŽFig. 8j., DOC ŽFig. 8l., bacteria ŽFig. 8n.,

cumulative grazing ŽFig. 8r., and the f-ratio ŽFig. 8t.. Although the NEW’93 data for Z1 ŽFig. 8g. are certainly underestimated, the very high biomasses simulated by NEWCN are not realistic because it means that the biomass of ciliates would have been much higher Žca. 15 = ; compare Fig. 8g and h. than that of copepods between days 211 and 214; hence, model NEWN gives the best results concerning Z1. Concerning detritus ŽFig. 8j., a huge quantity must be rapidly remineralized in layer A of model NEWCN to account for the development of the second phytoplankton bloom. Given the poor quality of the results simulated by models NEWN and NEWCN for detritus, it is not possible to assess hypotheses H2 and H3 on this basis. Concerning DOC, Ahlers et al. Ž1994. noted a slight inverse relationship between dissolved organic nitrogen ŽDON. and dissolved inorganic nitrogen ŽDIN., which was particularly marked at stations with high chlorophyll concentrations. Considering that the DOC and DON concentrations evolved in a similar way, this inverse relationship exists only for the results from NEWN Žsee the results for DOC and nitrate; Fig. 8l and b, respectively., which again favors model NEWN . Similarly, the bacterial biomasses simulated by NEWN are much more realistic than those computed with NEWCN ŽFig. 8n.. The original f-ratio data between days 200 and 220 and the corrected data ŽFig. 8t. show that the development of the second bloom could not have been solely caused by local remineralization, so that hypothesis H3 is unlikely. The f-ratio data for the second bloom ŽFig. 8t. suggest that both an external supply of nitrate and local remineralization were necessary to explain the growth of phytoplankton during this period. Model NEWN considers the two types of nitrogen supply, and the simulated f-ratios are generally closer to the original or corrected values, except between days 211 and 214 when the supply of nitrogen by local remineralization was high. The grazing results do not clearly favor model NEWN over model NEWCN , i.e. average grazing rates of large phytoplankton by copepods from models NEWN and NEWCN are 82.9 and 132 mg C my2 dayy1 , respectively, the two values being within the range Žfrom 0 to 250 mg C my2 dayy1 . given by Pesant et al. Ž1998. for the trough system during legs 2 to 4. Hence, the two models are equally plausible on the basis of zooplankton grazing. It follows from

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

the above that all differences between the two models, except those for detritus and cumulative grazing, favor hypothesis H2 Ži.e. model NEWN .. 6.3. Plausibility of hypothesis H2 and small-scale physical processes The above comparison between observations and simulations for chemical and biological variables ŽFig. 8. led to the conclusion that hypothesis H2 is more realistic than hypothesis H3. Concerning H2, four main reasons could explain the vertical diffusion of nitrate from layer B to A during the second bloom, i.e. wind stress, vertical shear, tides, andror internal waves. Kattner and Budeus ´ Ž1997. and Smith et al. Ž1997a. consider that the trough system was well stratified during summer. For legs 2 and 3, Gosselin et al. Ž1995. computed an index of stratification Žthe sigma-t difference between 50 and 0 m., whose values increase from south to north in the polynya, and from spring to summer. Booth and Smith Ž1997. computed another index of stability ŽBrunt ¨ Vaısala ¨ ¨ ¨ frequency averaged over the 0 to 40 m water column. at several leg 4 stations. These authors noted that their index of stability did not differ significantly among the different areas of the NEW, but the highest values occurred in the Norske and Westwind troughs. It is likely that the prevailing winds between days 200 and 220 had little influence on vertical mixing because of their low intensities ŽSchneider and Budeus, ´ 1997., and due to the presence of ice Žca. 50% cover; Fig. 7b. which can strongly inhibit the action of the wind. However, Klein and Coste Ž1984. and Lacroix and Nival Ž1998. have shown that a low wind intensity does not necessarily imply a negligible effect of wind stress on vertical mixing, so that the wind may have played some role on vertical turbulence. According to Budeus ´ and Schneider Ž1995., the vertical shear was concentrated at depths between 100 and 150 m, i.e. at the interface between Polar and Atlantic Water. The EGS tidal currents are poorly known, but it seems that they increase from NØIB to OBIB ŽPeter Galbraith, pers. com.. The passage of internal waves, which may enhance the flux of nutrients across the thermocline ŽCullen et al., 1983., is not mentioned in the NEW’93 literature. Nihoul and Djenidi Ž1990., however, consider that internal waves are particularly frequent on the continental slope and shelf.

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A general observation is that physical forcing Že.g. winds, tides, internal waves. at small time scales Ž- 3 days. may play a significant role in changing water column stratification Že.g. Pond and Pickard, 1983.. Such small-scale processes are beyond the temporal resolution of the NTS ŽG 3 days., so that they could not be included in the models. It follows that it is not possible to identify the exact causeŽs. of vertical mixing in model NEWN . It is normally expected that the mixing rate Ž j . decreases with increased stability of the water column, so that it is surprising that the mixing rate imposed in model NEWN Ži.e. chosen to obtain a second phytoplankton bloom, see above. does not follow this trend Ž j is high when differences TA y T B or SB y SA are maximum; Fig. 7f, d, e.. One plausible explanation is that short and strong mixing eventŽs. Žtime-scales - 3 days. occurred during the second bloom that could be not recorded given the resolution of the NTS. In other simulations Žnot shown here., j was made a decreasing function of water column stability but, during the first half of the NTS, the resulting simulated nitrate and silicate concentrations in layer A were always much higher than the observed values, so that it was not possible to correctly reproduce the observed nitrate depletion and, consequently, the development of the phytoplankton blooms. The rate of vertical mixing imposed between layers A and B to test hypothesis H2 with model NEWN ŽFig. 7f. may be an oversimplification of field conditions, although most simulated chemical and biological variables are in agreement with the corresponding observations ŽFig. 8.. Hence, because of the simple physical structure used in model NEWN Ži.e. constant mixed layer depth. it is not possible to fully test that hypothesis, contrary to H1 and H3 which are rejected. Other hypotheses than H1, H2 or H3 could perhaps be formulated to explain the development of the second bloom, e.g. a one-dimensional physical model which includes ice-melting process and mixed-layer physics, like that of Goosse and Hecq Ž1994., could be coupled to our biological model NEWN to further test hypothesis H2. 7. Conclusions In the present study, simple hypotheses concerning the spatio-temporal changes in the anticyclonic

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gyre Žsee Section 3.2. were used to build up a time series for modelling. The temporal changes in each variable and their intercomparison ŽFig. 8. show a coherent pattern along the NTS. In addition, models NEWN and NEWCN are both able to correctly reproduce the changes of the most important variables, i.e. nutrient concentrations Žnitrate and silicate; Fig. 8b and d., chlorophyll a concentration ŽFig. 8e., biomasses of copepods and appendicularians ŽFig. 8h and i., bacterial biomass ŽFig. 8n., and cumulative primary production ŽFig. 8q.. The biomass of Z1 is well reproduced in model NEWN only ŽFig. 8g.. Other simulated variables are of lower quality, but their ranges often correspond to those of observed data Ži.e. ammonium, detritus, POC, POM C:N ratio, and the uptake C:N ratio for phytoplankton; Fig. 8c, j, o, p, and s, respectively.. This met our first objective Žsee Section 1.. The analysis of the NTS shows that the main uncertainty on the functioning of the pelagic ecosystem in the anticyclonic gyre concerns the source of inorganic nitrogen that fuelled the second phytoplankton bloom. Three hypotheses ŽH1 to H3. concerning the functioning of the ecosystem were formulated, H2 and H3 being used to build up ecological models NEWN and NEWCN . This achieved the second objective of the study. Several studies Ži.e. Schneider and Budeus,1997; ´ Budeus 1997. ´ et al., 1997; Kattner and Budeus, ´ suggest that a horizontal supply of nitrate from the areas north of Ob Bank to the Norske and Westwind troughs Ži.e. hypothesis H1., during summer, is unlikely. Using the nitrate and silicate concentrations in the NTS, the water masses there were identified as corresponding to those in the central part of the NEW ŽFig. 4.. This agrees with the above studies, so that hypothesis H1 was rejected. Model NEWCN is characterized by a low export of detritus and phytoplankton from layer A to B, coupled with high bacterial activity and biomass. This leads to high and unrealistic decomposition of detritus, which is needed to produce enough ammonium to support the development of the second phytoplankton bloom. The consequences of this scenario are that the biomass and grazing of Z1 are high and the microbial food web plays a major role. The scenario in model NEWN differs in that there is moderate export of detritus and phytoplankton from

layer A, bacterial and Z1 biomasses and activities are low, and decomposition is moderate. In this case, the food chain is short Žfrom phytoplankton to copepods and appendicularians. and the microbial food web plays a secondary role. The conclusion concerning the third objective of the study is that the pelagic ecosystem within the anticyclonic gyre probably was a short food chain. Because our conclusions are based on the comparison between simulated and observed chemical and biological variables only, they suffer from the oversimplification used to force model NEWN . Consequently, the fourth objective stated in the Introduction Ževaluation of hypotheses H2 and H3. was only partly achieved, i.e. hypothesis H3 was rejected, but hypothesis H2 could not be fully tested. A full test of this hypothesis would require a more detailed description of the temporal variability of the physics of the water column.

Acknowledgements This paper is a contribution to the programs of the Groupe interuniversitaire de recherches oceanograph´ ŽGIROQ. and the Institut Mauriceiques du Quebec ´ Lamontagne ŽDepartment of Fisheries and Oceans, DFO.. The work was funded by grants from the Natural Sciences and Engineering Research Council of Canada and the Fonds FCAR du Quebec to L. ´ Ž . Legendre and A. Vezina, DFO A. Vezina and ´ ´ GIROQ thanks to the Fonds FCAR. The authors thank D. Wallace and P. Minnett who provided most data sets collected on board the USCGC Polar Sea and the radiation data during leg 4, respectively. We are grateful to K. Juniper and his student M. PongVong for providing their data on bacteria and flagellates. We are also grateful to S. Kovacs for the bathymetry of the NEW area. We also thank the two referees for their most useful comments and suggestions.

Appendix A The following are the Appendix tables mentioned in the preceeding sections ŽTables a1–11.

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93 Table a1 System of differential equations for model NEWN dNO 3rd t dNH 4rdt dSIrdt dP1nrdt dP2nrdt dZ1nrdt dZ2nrdt dZ3nrdt dD1nrdt dD2nrdt dD3nrdt dDOM1nrdt dDOM2nrdt dBnrdt

s ymNO 3 P1P1n y mNO 3 P2 P2n q diffusion s ymNH 4 P1P1n y mNH 4 P2 P2n q n Z1 Z1n q n Z2 Z2n q n Z3 Z3n q n B Bn q diffusion s ymNP2 P2nŽSI:NP2 . q diffusion s ŽmNP1 y m P1 y eNP1 .P1n y gNZ1P1 Z1n y gNZ2P1 Z2n y gNZ3P1 Z3n q diffusion s ŽmNP2 y m P2 y eNP2 .P2n y gNZ1P2 Z1n y gNZ2P2 Z2n y gNZ3P2 Z3n q diffusionq sinking s ŽgNZ1P1 q gNZ1P2 q gNZ1D1 q gNZ1D2 q gNZ1B y n Z1 y egNZ1 y m Z1 .Z1n y gNZ2Z1 Z2n y gNZ3Z1 Z3n q diffusion s ŽgNZ2P1 q gNZ2P2 q gNZ2D1 q gNZ2D2 q gNZ2D3 q gNZ2B q gNZ2Z1 y n Z2 y egNZ2 y m Z2 .Z2n s ŽgNZ3P1 q gNZ3P2 q gNZ3D1 q gNZ3D2 q gNZ3D3 q gNZ3B q gNZ3Z1 y n Z3 y egNZ3 y m Z3 .Z3n s m P1 P1n q Ž m B y dND1 .Bn y gNZ1D1 Z1n y gNZ2D1 Z2n y gNZ3D1 Z3n q diffusion s m P2 P2n y dND2 Bn q Ž m Z1 q egNZ1 y gNZ1D2 .Z1n y gNZ2D2 Z2n y gNZ3D2 Z3n q diffusionq sinking s Ž m Z2 q egNZ2 y gNZ2D3 .Z2n q Ž m Z3 q egNZ3 y gNZ3D3 .Z3n y dND3 Bn q diffusionq sinking s ŽdND1 q dND2 q dND3 y hN.Bn q diffusion s ŽhN y mNB .Bn q eNP1 P1n q eNP2 P2n q diffusion s ŽmNB y n B y m B .Bn y gNZ1B Z1n y gNZ2B Z2n y gNZ3B Z3n q diffusion

Table a2 System of differential equations for model NEWCN dNO 3rd t dNH 4rdt dSIrdt dP1crdt dP1nrdt dP2crdt dP2nrdt dZ1crdt dZ2crdt dZ3crdt dD1crdt dD1nrdt dD2crdt dD2nrdt dD3crdt dD3nrdt dDOM1crdt dDOM1nrdt dDOM2crdt dDOM2nrdt dBcrdt

s ymNO 3 P1P1n y mNO 3 P2 P2n s ymNH 4 P1P1n y mNH 4 P2 P2n q n Z1 Z1c q n Z2 Z2c q n Z3 Z3c q n B Bc s ymNP2 P2nŽSI:NP2 . s ŽmC2 P1 y m P1 y eC P1 .P1c y gC Z1P1 Z1c y gC Z2P1 Z2c y gC Z3P1 Z3c s ŽmNP1 y m P1 y eNP1 .P1n y gNZ1P1 Z1c y gNZ2P1 Z2c y gNZ3P1 Z3c s ŽmC2 P2 y m P2 y eC P2 .P2c y gC Z1P2 Z1c y gC Z2P2 Z2c y gC Z3P2 Z3c q sinking s ŽmNP2 y m P2 y eNP2 .P2n y gNZ1P2 Z1c y gNZ2P2 Z2c y gNZ3P2 Z3c q sinking s ŽgC Z1P1 q gC Z1P2 q gC Z1D1 q gC Z1D2 q gC Z1B y r Z1 y egC Z1 y m Z1 .Z1c y gC Z2Z1 Z2c y gC Z3Z1 Z3c s ŽgC Z2P1 q gC Z2P2 q gC Z2D1 q gC Z2D2 q gC Z2D3 q gC Z2B q gC Z2Z1 y r Z2 y egC Z2 y m Z2 .Z2c s ŽgC Z3P1 q gC Z3P2 q gC Z3D1 q gC Z3D2 q gC Z3D3 q gC Z3B q gC Z3Z1 y r Z3 y egC Z3 y m Z3 .Z3c s m P1 P1c q Ž m B y dC D1 .Bc y gC Z1D1 Z1c y gC Z2D1 Z2c y gC Z3D1 Z3c s m P1 P1n q Ž m B rŽC:NB . y dND1 .Bc y gNZ1D1 Z1c y gNZ2D1 Z2c y gNZ3D1 Z3c s m P2 P2c y dC D2 Bc q Ž m Z1 q egC Z1 y gC Z1D2 .Z1c y gC Z2D2 Z2c y gC Z3D2 Z3c q sinking s m P2 P2n y dND2 Bc q Ž m Z1 rŽC:NZ1 . q egNZ1 y gNZ1D2 .Z1c y gNZ2D2 Z2c y gNZ3D2 Z3c q sinking s Ž m Z2 q egC Z2 y gC Z2D3 .Z2c q Ž m Z3 q egC Z3 y gC Z3D3 .Z3c y dC D3 Bc q sinking s Ž m Z2 rŽC:NZ2 . q egNZ2 y gNZ2D3 .Z2c q Ž m Z3rŽC:NZ3 . q egNZ3 y gNZ3D3 .Z3c y dND3 Bc q sinking s ŽdC D1 q dC D2 q dC D3 y hC.Bc s ŽdND1 q dND2 q dND3 y hN.Bc s ŽhC y mC B .Bc q eC P1 P1c q eC P2 P2c s ŽhN y mNB .Bc q eNP1 P1n q eNP2 P2n s ŽmC B y r B y m B .Bc y gC Z1B Z1c y gC Z2B Z2c y gC Z3B Z3c

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Table a3 Phytoplankton processes in model NEWN , with x s P1 or P2 Nutrient uptake and phytoplankton growth Nitrate uptake rate Ammonium uptake rate Silicate uptake rate P1n growth rate Žnitrogen. P2n growth rate Žnitrogen. With: Nitrate limitation Ammonium limitation Silicate limitation PAR limitation

mNO 3 x s mmN x umTx Lno 3 xLi x mNH 4 x s mmN x umTx Lnh 4 xLi x mSI x s mmN x umTx minŽŽLno 3 x q Lnh 4 x .,Lsi x .Li x If x s P1 then mN x s mmN x umTx ŽLno 3 x q Lnh 4 x .Li x If x s P2 then mN x s mmN x umTx minŽŽLno 3 x q Lnh 4 x ., Lsi x .Li x

Ž1. Ž2. Ž3. Ž4. Ž5.

Lno 3 x s ŽNO 3rŽkno 3 x q NO 3 ..eŽy c NH 4 . Lnh 4 x s NH 4rŽknh 4 x q NH 4 . Lsi x s SIrŽksi x q SI. Li x s Ž1 q f x .ŽŽErIm x .rŽŽErIm x . 2 q 2 f x ŽErIm x . q 1..

Ž6. Ž7. Ž8. Ž9.

Exudation Exudation rate Žnitrogen. With: Limitation by the physiological state

eN x s emN x Lm gx e x

Ž10.

Lm x s ŽmmN x umTx y mN x .rŽmmN x umTx .

Ž11.

Mortality Mortality rate Žnitrogen.

m x s m0 x q m1 x Lm gx m x

Ž12.

Sinking (only P2) Sinking rate Žnitrogen.

s P2 s Žv0 P2 q v1 P2 Lm gP2s P2 .rH

Ž13.

Table a4 Zooplankton processes in model NEWN , with x s Z1, Z2 or Z3 and y s potential food items of x Grazing Grazing rate of x

If Bn x F Bn0 x then gN x s 0 If Bn x ) Bn0 x then gN x s gmN x ug Tx Ž1 y eŽy kn x ŽBn xyBn0 x .. . gN x y s ŽgN x e x y yn.rBn x .

Ž1. Ž2. Ž3.

Bn x s Ýiys1Ž e x y yn.

Ž4.

Feces production Fecal pellet production rate

egN x s gN x Ž1 y An x .

Ž5.

Excretion Excretion rate

n x s nm x unTx

Ž6.

Grazing rate of x on y With: Biomass of potential food items

All terms in nitrogen.

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Table a5 Detritus decomposition processes and bacterial growth in model NEWN Detritus decomposition, with x s D1, D2 or D3 Decomposition rate dN x s dmN x udTx Ž x nrŽkn x q x n..

Ž1.

Detritus sinking, with x s D2 or D3 Sinking rate

s x s vxrH

Ž2.

Hydrolysis of DOM1n into DOM2n Hydrolysis rate

hN s hmNuhT ŽDOM1nrŽ k DO M1n q DOM1n..

Ž3.

Bacterial growth Bacterial growth rate

mNB s mmNB umTB ŽDOM2nrŽ k DOM2n q DOM2n..

Ž4.

Bacterial excretion Ammonium excretion rate

n B s nm B unTB

Ž5.

All terms in nitrogen.

Table a6 Symbols, values, and units of parameters in model NEWN Parameters for phytoplankton, with x s P1 or P2 Parameter

Symbol

Chlorophyll a: carbon ratio Phytoplankton C:N ratio Maximum exudation rate Žnitrogen. Optimal PAR for growth Ammonium half-saturation constant Nitrate half-saturation constant Silicate half-saturation constant Minimum mortality rate Maximum mortality rate Uptake Si:N ratio Minimum sinking speed Maximum sinking speed Shape factor for exudation Shape factor for mortality Shape factor for sinking Maximum growth rate at 08C Žnitrogen. Nitrate uptake inhibition factor Shape factor Photoinhibition factor

Chl:C x C:N x emN x Im x knh 4 x kno 3 x ksi x m0 x m1 x SI:N x v0 x v1 x g ex g mx g sx mmN x c um x fx

Value

Units

P1

P2

0.01 5.674 0 59.5 8.4 9.8

0.01 5.674 0.2 170 11.2 14 28 0.1 0.15 2 0 y3 2 4 2 1.5 0.1042 1.1 y0.8

0.11 0.2

1 2 1.6 0.1042 1.1 y0.8

mg Chl a Žmg C.y1 mg C Žmg N.y1 dayy1 mmol photons my2 sy1 mg N my3 mg N my3 mg Si my3 dayy1 dayy1 mg Si Žmg N.y1 m dayy1 m dayy1 wd wd wd dayy1 m3 Žmg N.y1 wd wd (continued on next page)

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Table a6 Ž continued . Parameters for zooplankton, with x s Z1, Z2 or Z3 Parameter

Nitrogen assimilation coefficient Food concentration threshold for ingestion Zooplankton C:N ratio Capture efficiency of B by x Capture efficiency of D1 by x Capture efficiency of D2 by x Capture efficiency of D3 by x Capture efficiency of P1 by x Capture efficiency of P2 by x Capture efficiency of Z1 by x Maximum ingestion rate at 08C Žnitrogen. Ivlev coefficient for the ingestion curve Mortality rate Excretion rate at 08C Shape factor Shape factor

Symbol

An x Bn0 x C:N x exB e x D1 e x D2 e x D3 e x P1 e x P2 e x Z1 gmN x kn x mx nm x ug x un x

Value

Units

Z1

Z2

Z3

0.8 0 4.285 0.8 0.2 0.2

0.8 2.1 4.285 0.2 0.2 0.2 0.1 0.4 0.8 0.7 1.5 0.0021 0.03 0.11 1.1 1.1

0.8 2.1 4.285 0.8 0.85 0.6 0.05 0.9 0.6 0.7 1.5 0.0025 0.05 0.11 1.1 1.1

D1

D2

D3

5.674 0.5 2.8

5.674 0.5 2.8 y5 1.1

5.674 0.5 2.8 y100 1.1

0.8 0.3 1.7 0.0021 0.05 0.13 1.1 1.1

wd mg N my3 mg C Žmg N.y1 wd wd wd wd wd wd wd dayy1 m3 Žmg N.y1 dayy1 dayy1 wd wd

Parameters for detritus with x s D1, D2 or D3, and for bacteria ŽB. Parameter

Detritus C:N ratio Maximum decomposition rate at 08C Žnitrogen. Half-saturation constant for decomposition Sinking speed Shape factor

Symbol

C:N x dmN x kn x vx ud x

Values

1.1

Units mg C Žmg N.y1 dayy1 mg N my3 m dayy1 wd

B Bacteria C:N ratio DOM1 C:N ratio DOM2 C:N ratio Maximum hydrolysis rate at 08C Žnitrogen. Half-saturation constant for hydrolysis Half-saturation constant for substrate uptake Mortality rate Excretion rate at 08C Maximum uptake rate at 08C Žnitrogen. Shape factor Shape factor Shape factor wd: without dimension.

C:NB C:NDO M1 C:NDO M2 hmN k DO M1n k DO M2n mB nm B mmNB uh um B un B

4.66 5.674 5.674 1 187.46 14 0.02 0.2 2 1.1 1.1 1.1

mg C Žmg N.y1 mg C Žmg N.y1 mg C Žmg N.y1 dayy1 mg N my3 mg N my3 dayy1 dayy1 dayy1 wd wd wd

Table a7 Phytoplankton processes in model NEWCN , with x s P1 or P2 Phytoplankton growth (carbon) Gross primary production rate Net primary production rate With: Photoinhibition index C:N ratio limitation

mC1 x s Pm x Ž1yeŽy a x ErPm x . .eŽy b x ErPm x . ŽCh1:C x .Lcn1 x umTx mC2 x smC1 x yR x Pm x Ž a x rŽ a x q b x ..Ž b x rŽ a x q b x ..Ž b x r a x . ŽCh1:C x .Lcn1 x umTx

Ž1. Ž2.

b x s Pm x rIb x if ŽC:Ni x . F ŽC:N x . F ŽC:Nm x . then Lcn1 x s1 if ŽC:Nm x . - ŽC:N x . F ŽC:Ns x . then Lcn1 x s ŽŽŽC:Ns x .yŽC:N x ..rŽŽC:Ns x .yŽC:Nm x ...g cn1 x

Ž3. Ž4. Ž5.

Exudation Exudation rate Žcarbon. Exudation rate Žnitrogen. With: C:N ratio limitation

Mortality Mortality rate Žcarbon and nitrogen. With: C:N ratio limitation Sinking (only P2) Sinking rate Žcarbon and nitrogen. With: C:N ratio limitation

Ž6. Ž7. Ž8. Ž9. Ž10. Ž11. Ž12. Ž13. Ž14. Ž15.

eC x semC x Le x eN x seC x ŽŽC:N x .rŽC:Ne ..

Ž16. Ž17.

if ŽC:Ni x . F ŽC:N x . F ŽC:Nm x . then Le x s 0 if ŽC:Nm x . - ŽC:N x . F ŽC:Ns x . then Le x s1yŽŽŽC:Ns x .yŽC:N x ..rŽŽC:Ns x .yŽC:Nm x ...g e x

Ž18. Ž19.

m x s m0 x qm1 x Lm x

Ž20.

if ŽC:Ni x . F ŽC:N x . F ŽC:Nm x . then Lm x s ŽŽŽC:Nm x .yŽC:N x ..rŽŽC:Nm x .yŽC:Ni x ...g m1 x If ŽC:Nm x . - ŽC:N x . F ŽC:Ns x . then Lm x s ŽŽŽC:N x .yŽC:Nm x ..rŽŽC:Ns x .yŽC:Nm x ...g m2 x

Ž21. Ž22.

s x s Žv0 P2 qv1 P2 Ls P2 .rH

Ž23.

if ŽC:Ni P2 . F ŽC:NP2 . F ŽC:Nm P2 . then Ls P2 s ŽŽŽC:Nm P2 .yŽC:NP2 ..rŽŽC:Nm P2 .yŽC:Ni P2 ...g s1 P2 if ŽC:Nm P2 . - ŽC:NP2 . F ŽC:Ns P2 . then Ls P2 s ŽŽŽC:NP2 .yŽC:Nm P2 ..rŽŽC:Ns P2 .yŽC:Nm P2 ...g s2 P2

Ž24. Ž25.

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Nutrient uptake and phytoplankton growth (nitrogen) Nitrate uptake rate mNO 3 xsmmN x umTx Lno 3 xLcn2 x Ammonium uptake rate mNH 4 xsmmN x umTx Lnh 4 xLcn2 x Silicate uptake rate mSI x smmN x umTx minŽŽLno 3 xqLnh 4 x ., Lsi x .Lcn2 x P1n growth rate If x s P1 then mN x smmN x umTx ŽLno 3 xqLnh 4 x .Lcn2 x P2n growth rate If x s P2 then mN x smmN x umTx minŽŽLno 3 xqLnh 4 x ., Lsi x .Lcn2 x With: Nitrate limitation Lno 3 xs ŽNO 3 rŽkno 3 xqNO 3 ..eŽy c NH 4 . Ammonium limitation Lnh 4 xs NH 4 rŽknh 4 xqNH 4 . Silicate limitation Lsi x sSIrŽksi x qSI. C:N ratio limitation if ŽC:Ni x . F ŽC:N x . F ŽC:Nm x . then Lcn2 x s ŽŽŽC:N x .yŽC:Ni x ..rŽŽC:Nm x .yŽC:Ni x ...g cn2 x if ŽC:Nm x . - ŽC:N x . F ŽC:Ns x . then Lcn2 x s1

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Table a8 Zooplankton processes in model NEWCN , with x s Z1, Z2 or Z3, and y s potential food items of x Grazing and quality of the ingested food Grazing rate of x Žcarbon.

if Bc x F Bc0 x then gC x s 0 if Bc x ) Bc0 x then gC x s gmC x ug Tx Ž1 y eŽy kc x ŽBc xybc0 x .. . gC x y s ŽgC x e x y yc.rBc x gN x y s gC x yrŽC:N x . C:Nf x s gC xrŽÝiys1 gN x y .

Ž1. Ž2. Ž3. Ž4. Ž5.

Bc x s Ýiys1Ž e x y yc.

Ž6.

Assimilation and quality of the assimilated food Assimilation rate of x Žcarbon. Assimilation rate of x Žnitrogen. C:N ratio for the food assimilated by x

aC x s gC x Ac x aN x s ŽgC xrŽC:Nf x ..An x C:Na x s ŽC:Nf x .ŽAc xrAn x .

Ž7. Ž8. Ž9.

Feces production Fecal pellet poduction rate Žcarbon. Fecal pellet poduction rate Žnitrogen.

egC x s gC x Ž1 y Ac x . egN x s ŽgC xrŽC:Nf x ..Ž1 y An x .

Ž10. Ž11.

Respiration and excretion Respiration rate for the maintenance

rb x s gmC x ug Tx Ž1 y eŽy kc x ŽBc1 xyBc0 x .. .Ac x

Ž12.

r x s rb x n x s aN x q Žrb x y aC x .rŽC:N x .

Ž13. Ž14.

r x s aC x Ž1 y K2c x . n x s aN x Ž1 y K2n x . if S1 x - C:Na x F S2 x then K2n x s Ž1 y a x .ŽK2 xrŽC:N x ..ŽŽC:Na x . y ŽC:N x .. q K2 x if S2 x - C:Na x then K2n x s 1 K2c x s ŽK2n x ŽC:N x ..rŽC:Na x .

Ž15. Ž16. Ž17. Ž18. Ž19.

K2 x s K2m x ŽaC x y rb x .rŽ k K2 x q aC x y rb x . S1 x s Ž a x K2 x ŽC:N x ..rŽ1 q Ž a x y 1.K2 x . S2 x s Ž1 y a x K2 x .rŽŽ1 y a x .ŽK2 xrŽC:N x ...

Ž20. Ž21. Ž22.

Grazing rate of x on y Žcarbon. Grazing rate of x on y Žnitrogen. C:N ratio for the food ingested by x With: Biomass of potential food items Žcarbon.

If 0 F aC x F rbx Respiration rate Excretion rate If rbx - aC x Respiration rate Excretion rate Nitrogen net growth efficiency

Carbon net growth efficiency With: Net growth efficiency a Threshold S1 x Threshold S2 x a

K2 x is defined for ŽC:Na x . s ŽC:N x . because, in this case, K2c x s K2n x .

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Table a9 Detritus decomposition processes and bacterial growth in model NEWCN Detritus decomposition, with x s D1, D2 or D3 Decomposition rate Žcarbon. dC x s dmC x udTx Ž xcrŽkc x q xc.. Decomposition rate Žnitrogen. dN x s dC xrŽC:N x .

Ž1. Ž2.

Detritus sinking, with x s D2 or D3 Sinking rate Žcarbon and nitrogen.

s x s vxrH

Ž3.

Hydrolysis of DOM1 into DOM2 Hydrolysis rate Žcarbon. Hydrolysis rate Žnitrogen.

hC s hmCuhT ŽDOM1crŽ k DO M1c q DOM1c.. hN s hCrŽC:NDO M1 .

Ž4. Ž5.

Bacterial growth Bacterial growth rate Žcarbon. Bacterial growth rate Žnitrogen.

mC B s mmC B umTB ŽDOM2crŽ k DOM2c q DOM2c.. mNB s mC B rŽC:NDOM2 .

Ž6. Ž7.

Bacterial respiration and excretion Respiration rate for the maintenance

rb B s mmC B umTB ŽBcl B rŽ k DOM2c q Bcl B ..

Ž8.

r B s rb B n B s mNB q Žrb B y mC B .rŽC:NB .

Ž9. Ž10.

r B s mC B Ž1 y Yc B . n B s mNB Ž1 y Yn B . If S1 B - C:NDOM2 F S2 B then Yn B s Ž1 y a B .ŽYB rŽC:NB ..ŽŽC:NDOM2 . y ŽC:NB .. q YB if S2 B - C:NDOM2 then Yn B s Ž1 y a B .Ž YB rŽC:NB ..Lnh 4 BŽŽC:NDOM2 . y S2 B . q 1 Yc B s ŽYn B ŽC:NB ..rŽC:NDOM2 .

Ž11. Ž12. Ž13. Ž14. Ž15.

YB s Ym B ŽmC B y rb B .rŽ k YB q mC B y rb B . S1 B s Ž a B Y B ŽC:NB ..rŽ1 q Ž a B y 1.YB . S2 B s Ž1 y a B Y B .rŽŽ1 y a B .Ž YB rŽC:NB ... Lnh 4 s NH 4 rŽknh 4 q NH 4 .

Ž16. Ž17. Ž18. Ž19.

If 0 F m CB F rbB Respiration rate Excretion rate if rbB - m CB Respiration rate Excretion rate Nitrogen growth efficiency Carbon growth efficiency With: Growth efficiency a Threshold S1 x Threshold S2 x Ammonium limitation a

B

B

YB is defined for ŽC:NDOM2 . s ŽC:NB . because, in this case, Yc B s Yn B .

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Table a10 Symbols, values, and units of parameters in model NEWCN Parameters for phytoplankton, with x s P1 or P2 Parameters

Symbols

Values

Units

P1

P2

0.01 15 3 5.674 17 0.1 150 10 49

0.01 15 3 5.674 17 0.1 600 11.2 70 28 0.15 0.2 150 0.15 1.3 0 y2 2.4

Chlorophyll a :carbon ratio Exudation product C:N ratio Minimum C:N ratio for phytoplankton C:N ratio for healthy phytoplankton Maximum C:N ratio for phytoplankton Maximum exudation rate Žcarbon. PAR for photoinhibition Ammonium half-saturation constant Nitrate half-saturation constant Silicate half-saturation constant Minimum mortality rate Maximum mortality rate Assimilation number for PL curve Fraction for respiration Uptake Si:N ratio Minimum sinking speed Maximum sinking speed Initial slope for PL curve

Chl:C x C:Ne C:Ni x C:Nm x C:Ns x emC x Ib x knh 4 x kno 3 x ksi x m0 x m1 x Pm x Rx SI:N x v0 x v1 x ax

Shape factor for growth Shape factor for growth Shape factor for exudation Shape factor for mortality Shape factor for mortality Shape factor for sinking Shape factor for sinking Maximum growth rate at 08C Žnitrogen. Nitrate uptake inhibition factor Shape factor

g cn1 x g cn2 x g ex g m1 x g m2 x g s1 x g s2 x mmN x c um x

1.7 0.1042 1.1

Symbols

Values

0.15 0.2 300 0.25

3 3 3 1 0.2 0.2

3 3 1 0.2 0.2 2.5 2.5 1.6 0.1042 1.1

mg Chl a Žmg C.y1 mg C Žmg N.y1 mg C Žmg N.y1 mg C Žmg N.y1 mg C Žmg N.y1 dayy1 mmol photons my2 sy1 mg N my3 mg N my3 mg Si my3 dayy1 dayy1 mg C Žmg Chl a.y1 dayy1 wd mg Si Žmg N.y1 m dayy1 m dayy1 mg C Žmg Chl a.y1 dayy1 Žmmol photons my2 sy1 .y1 wd wd wd wd wd wd wd dayy1 m3 Žmg N.y1 wd

Parameters for zooplankton, with x s Z1, Z2 or Z3 Parameter

Carbon assimilation coefficient Nitrogen assimilation coefficient Food concentration threshold for ingestion Food concentration threshold for maintenance Zooplankton C:N ratio Capture efficiency of B by x Capture efficiency of D1 by x Capture efficiency of D2 by x Capture efficiency of D3 by x Capture efficiency of P1 by x Capture efficiency of P2 by x Capture efficiency of Z1 by x Maximum ingestion rate at 08C Žcarbon. Maximum net growth efficiency Ivlev coefficient for the ingestion curve

Ac x An x Bc0 x Bc1 x C:N x exB e x D1 e x D2 e x D3 e x P1 e x P2 e x Z1 gmC x K2m x kc x

Units

Z1

Z2

Z3

0.75 0.85 0 5 4.285 0.9 0.2 0.1

0.75 0.85 10 15 4.285 0.3 0.2 0.1 0.1 0.4 0.8 0.8 1.5 0.4 0.0045

0.75 0.85 10 15 4.285 0.8 0.8 0.6 0.05 0.8 0.6 0.8 1.6 0.4 0.0065

0.8 0.1 2.4 0.6 0.0075

wd wd mg C my3 mg C my3 mg C Žmg N.y1 wd wd wd wd wd wd wd dayy1 wd m3 Žmg C.y1

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Table a10 Ž continued . Parameters for zooplankton, with x s Z1, Z2 or Z3 Parameter

Net growth efficiency half-saturation constant Mortality rate Factor for the slope of the nitrogen net growth efficiency Shape factor

Symbols

k K2 x mx ax ug x

Values

Units

Z1

Z2

Z3

0.2 0.05 1 1.1

0.2 0.05 1 1.1

0.2 0.05 1 1.1

D1

D2

D3

1 15

1 15 y1 1.05

1 15 y100 1.05

dayy1 dayy1 wd wd

Parameters for detritus with x s D1, D2 or D3, and for bacteria ŽB. Parameters

Symbols

Maximum decomposition rate at 08C Žcarbon. Half-saturation constant for decomposition Sinking speed Shape factor

dmC x kc x vx ud x

Substrate concentration threshold for maintenance Bacteria C:N ratio Maximum hydrolysis rate at 08C Žcarbon. Half-saturation constant for hydrolysis Half-saturation constant for substrate uptake Half-saturation constant for ammonium uptake Growth efficiency half-saturation constant Mortality rate Maximum growth efficiency Factor for the slope of the nitrogen growth efficiency Maximum uptake rate at 08C Žcarbon. Shape factor Shape factor

Bc1 B C:NB hmC k DO M1c k DO M2c knh 4 B k YB mB Ym B aB mmC B uh um B

Values

1.05

Units dayy1 mg C my3 m dayy1 wd

B

wd: without dimension.

3 4.66 2.5 200 20 7 0.2 0.1 0.626 0 2.7 1.05 1.05

mg C my3 mg C Žmg N.y1 dayy1 mg C my3 mg C my3 mg N my3 dayy1 dayy1 wd wd dayy1 wd wd

F. Touratier et al.r Journal of Marine Systems 27 (2000) 53–93

90

Table a11 Initial conditions of the state variables in layers A and B, and for the two models State variable

Model NEWN Layer A

NO 3 NH 4 SI P1c P1n P2c P2n Z1c Z1n Z2c Z2n Z3c Z3n D1c D1n D2c D2n D3c D3n DOM1c DOM1n DOM2c DOM2n Bc Bn

a

55.65 1.577 a 284.45a nn 0.166 b nn 0.222 b nn 0.21b nn 3.72 b nn 0.1167 b nn 0.1762 c nn 19.38 c nn 0.1762 c nn 6.17 c nn 1.763 c nn 0.1639 b

Units Žmg my3 .

Model NEWCN Layer B a

107.67 1.862 a 304.53 a nn 0.0203 b nn 0.085 b nn 0.032 b nn 0.021b nn 0.00026 b nn 0.1762 c nn 7.049 c nn 0.1762 c nn 12.34 c nn 1.763 c nn 0.1639 b

Layer A a

55.65 1.577 a 284.45a 0.942 b 0.166 b 1.261b 0.222 b 0.9 b nn 15.95 b nn 0.5 b nn 1c 0.153 c 128c 19.69 c 1c 0.153 c 35c 6.17 c 10c 1.763 c 0.764 b nn

LayerB 107.67 a 1.862 a 304.53 a 0.115 b 0.0203 b 0.487 b 0.085 b 0.138 b nn 0.093 b nn 0.0011b nn 1c 0.105 c 62c 6.52 c 1c 0.105 c 70c 12.34 c 10c 1.763 c 0.764 b nn

N N Si C N C N C N C N C N C N C N C N C N C N C N

nn: not necessary a Field observation. b Value derived from field data. c Value chosen during the calibration Žsee the text for details..

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