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Two-dimensional nitrogen and carbon flux model in a coastal upwelling region Ianson, Debby; Allen, Susan E. 2002

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A two-dimensional nitrogen and carbon flux model in a coastalupwelling regionDebby Ianson1and Susan E. AllenEarth and Ocean Sciences Department, University of British Columbia, Vancouver, British Columbia, CanadaReceived 9 May 2001; revised 2 November 2001; accepted 2 November 2001; published 23 February 2002.[1] Coastal upwelling regions are associated with high primary production and disproportionatelylarge fluxes of organic matter relative to the global ocean. However, coastal regions are usuallyhomogenized in global ocean carbon models. We have developed a carbon and nitrogen flux modelincluding all major processes both within and below the euphotic zone over seasonal to decadaltimescales for coastal upwelling regions. These fluxes control surface pCO2. The model is appliedto the west coast of Vancouver Island, Canada (C2449C176N, 126C176W). Net annual air-sea CO2exchangeand export flux of inorganic and organic carbon and nitrogen from the system to the rest of theocean are estimated for different model scenarios. Model sensitivities are discussed. Results showstrong biological drawdown of pCO2during summer and atmospheric CO2invasion. However, thisinvasion is nearly balanced by gas evasion during winter. Therefore the region is a much smallersink of atmospheric CO2(6 g C mC02yrC01, or equivalently 200 kg C yrC01per m coastline) than thesummer season predicts. More significantly, there is a large flux of inorganic carbon (3 C2 104kg CyrC01per m coastline) from intermediate depth ocean water to the surface ocean via the coastalsystem compared to a small export of organic carbon (all dissolved) (2 C2 103kg C yrC01per mcoastline) back into the lower layer of the open ocean. Thus we suggest that the dominant effect ofcoastal upwelling on the global ocean is providing a conduit for inorganic carbon to the surfaceocean. INDEX TERMS: 4219 Oceanography: General: Continental shelf processes; 4516Oceanography: Physical: Eastern boundary currents; 4806 Oceanography: Biological andChemical: Carbon cycling; 4845 Oceanography: Biological and Chemical: Nutrients and nutrientcycling; KEYWORDS: upwelling, downwelling, carbon, coastal, nutrients, export-flux1. Introduction[2] It is becoming an accepted fact that the large anthropogenicincrease in atmospheric CO2is influencing our climate [Crowley,2000], and so great importance is being placed on understandingthe global carbon system. The ocean holds the largest activecarbon reservoir on Earth [Siegenthaler and Sarmiento, 1993] andultimately sets the atmospheric CO2concentration [Broecker andPeng, 1982]. Accurate and well-tested oceanic carbon models arerequired to interpolate sparse data and to predict future CO2levels.[3] Simple ocean box models have demonstrated the importanceof biology in setting the carbon capacity of the ocean by drawingdown the surface partial pressure of CO2(pCO2) and transportingorganic carbon into the deep ocean via sedimenting organicdetritus, where remineralization occurs [Sarmiento, 1992]. Thisprocess has been termed the biological pump [Volk and Hoffert,1985]. A disproportionate amount of carbon is fixed and verticallyexported in coastal waters, particularly in upwelling regions[Eppley and Peterson, 1979; Harrison et al., 1987]. Therefore itis expected that coastal upwelling regions form an important part ofthe biological pump.[4] Despite the global importance of coastal regions, they areseldom included in current global numerical ocean models becauseresolution is not high enough to deal with the smaller spatial scalesand inherent nonhomogeneity. It is one of the major weaknesses ofthese models [Doney, 1999]. Bulk ocean models and budgets havebeen used to consider coastal processes in a global context. Forexample, Christensen [1994] suggested, using a box model, thatover large timescales (thousands of years), coastal denitrificationhas an important effect on atmospheric pCO2and that organiccarbon export to the deep sea does not. Another modeling studyindicated that net heterotrophy over continental margins hasinfluenced the global carbon budget over the last hundreds ofyears [Mackenzie et al., 1998]. Also, it has been shown that theeffect of terrestrial inputs (particularly anthropogenic) on coastaleutrophication can impact the annual global carbon budget [Smithand Hollibaugh, 1993]. Tsunogai et al. [1999] suggest that con-tinental shelf areas absorb atmospheric CO2and transport it intothe subsurface layers of the open ocean based on carbon data fromthe East China Sea.[5] Coastal upwelling brings intermediate-depth (100–200 m),nutrient-rich waters to the surface, fueling high primary production[Smith, 1994]. These waters also have higher inorganic carbonconcentrations and so could be a source of CO2to the atmosphere[Christensen, 1994]. However, the few inorganic carbon datawhich have been reported from coastal upwelling regions showstrong biological drawdown of pCO2and suggest that suchregions may be net sinks for atmospheric CO2[Friederich et al.,1994; Simpson, 1986; Simpson and Zirino, 1980]. These studiesdid not investigate the winter season.[6] There are detailed physical models of coastal upwelling[e.g., Allen et al., 1995; Federiuk and Allen, 1995] and fordownwelling [Allen and Newberger, 1996]; however, they applyto short timescales. Current computer speed does not allow suchGLOBAL BIOGEOCHEMICAL CYCLES, VOL. 16, NO. 1, 1011, 10.1029/2001GB001451, 20021Now at Texas A&M University, College Station, Texas, USA.Copyright 2002 by the American Geophysical Union.0886-6236/02/2001GB001451$12.0011 - 1detailed models to be run for full-year simulations. Two-dimen-sional physical models of an upwelling event have been coupledwith nitrogen-based biological models [Wroblewski, 1977;Edwards et al., 2000]. Again, biological cycles were not modeledover the winter season and over longer timescales. A primitiveequation model [Haidvogeletal., 1991] has been used tosimulate circulation in the California Current System. This modelhas been coupled with an ecological model [Moisan et al., 1996]to investigate offshore transport of phytoplankton by filamentsgenerated in the physical model. There are no previous modelsspecific to coastal upwelling regions which include a carboncycle.[7] Furthermore, the current oceanic ecosystem models thatwe are aware of use fixed C:N (or C:P) ratios to extrapolatecarbon fluxes [e.g., Bacastow and Maier-Reimer, 1991; Sar-miento et al., 1993], and many carbon models are not pre-dictive but rely on observations (i.e., the relaxation technique[e.g., Najjar et al., 1992]).[8] We have developed a simple model of a coastal upwell-ing region which incorporates a biological and a carbon cycleover all seasons for the entire water column. Carbon andnitrogen are not always coupled by a fixed ratio. The systemthat we are modeling is complex and nonhomogeneous. Fur-thermore, few measurements exist of many relevant quantities.Thus our primary objective was to develop a model whichproduced sensible results and then to identify the parametersthat strongly influence the system and need to be measured.We provide estimates of net annual primary production (PP),CO2gas exchange, and carbon and nitrogen mass exchangebetween the model system and the open ocean.2. Model[9] Our goal is to model the system as simply as possibleand obtain reasonable seasonal cycles compared with availabledata. We only include those processes occurring on timescalesof days (weeks) to years that are necessary to determine netcarbon fluxes. Horizontally, the model distinguishes betweenthe shelf, slope, and offshore regions, and there are two levelsin the vertical (Figure 1a). (The inner shelf is considered onlyin the upper layer.) The upper layer is the mixed layer whereprimary production occurs, while in the lower layer, onlyremineralization occurs. The system has 42 ordinary differentialequations, which are solved by a standard Runge-Kutta method[Press et al., 1992] using an adaptive stepper with a time stepof 0.1 days or less.[10] We first define the modeled quantities (state variables) andcurrencies. Model structure is separated into physical and bio-logical components, and the chemical portion (gas flux calculation)is described last.2.1. Currencies[11] Carbon and nitrogen are the two currencies that are used inthe model. Carbon is the currency of particular interest, andnitrogen is modeled as the biologically limiting nutrient [Hutchingset al., 1994]. While it is possible that other macronutrients might belimiting at times (e.g., silicic acid [Dugdale et al., 1995]), theyoccur in such similar ratios (with nitrogen) to the biologicaldemands that choosing one will not greatly affect our model.Micronutrients such as iron are rarely limiting close to the coast(although iron limitation has been observed in coastal California[Hutchins and Bruland, 1998]). Each currency has its own set ofparameters. Carbon is exchanged at the air-sea interface, whereasnitrogen is not. The dissolved inorganic nitrogen (DIN) pool doesnot include N2or processes involving N2, such as nitrogen fixationand denitrification.2.2. State Variables[12] Three state variables are modeled for each currency(Table 1): dissolved organic (DO), particulate organic (PO)and dissolved inorganic (DI). What is important in the modelis whether organic matter sinks or not. Thus the modeldefinition of the DO pool is organic matter which is nonlivingand nonsinking, while the nonliving PO pool sinks and so isfound only in the lower layer. The living PO pool can controlits buoyancy and does not sink, so it stays in the upper layer.Because of the timescales of interest, only the semilabileportion of the total DO (which includes about 30% of theoperationally defined DO [Carlson and Ducklow, 1995; Carlsonet al., 1994]) is modeled. This pool has remineralizationtimescales of months to years. Labile pools are difficult toestimate and measure and can have faster remineralization ratesthan the model timescales [Carlson and Ducklow, 1995; Carl-son et al., 1994]. Fluxes associated with the refractory pool arenegligible despite its large size (C2470% of the measurable DOmatter) because of its long lifetime (order of 1000 years). Thedifference between PO and DO matter is traditionally definedby standard filter size (0.45 mM), which will make our DOpool larger than the reported semilabile fraction, while our totalorganic (TO) pools should be comparable after the refractoryportion is subtracted. The DI pools include all forms ofinorganic materials which are biologically accessible. TheDIN pool is made up of nitrate, ammonium and nitrite, andthe dissolved inorganic carbon (DIC) pool of bicarbonate,carbonate, and carbon dioxide.[13] Salinity is modeled as a state variable to tune the physicalmodel and also to determine several quantities (including alkalin-ity) in the carbonate system necessary to calculate pCO2. (Nitratedata were also used to tune the physical model [Ianson, 2001].)2.3. Physical Circulation[14] All state variables are subject to the circulation (Figure 1a)with the exception of PO matter, which is advected (both verticallyand horizontally) and mixed horizontally but is not verticallymixed or entrained because of partitioning between viable (non-sinking, upper layer) and nonviable (sinking, lower layer) frac-tions. Physical parameters and geometry are presented in Table 2.2.3.1. Advection. [15] Coastal upwelling (flux Up, verticalvelocity A, Figure 1a) occurs inside the shelf break [Lentz, 1992].In the model, intermediate-depth water advects from the outerFigure 1. (opposite) (a) Vertical cross section through a coastal upwelling system showing the geometry of the model. Illustrated are thephysical processes: physical advection between shelf, slope, and open ocean with Up representing upwelling flux (Up = Awsh) and Downrepresenting downwelling flux (Down = Dwsh), where wshis the width of the shelf box. Input from the inner shelf is shown by B. Thevertical mixing fluxes are MVsh= MVwshand MVsl= MVwsl, where wslis the width of the slope box. The changes in mixed layer depthbetween horizontal regions approximate sloping isopycnals. The horizontal mixing fluxes are MH, sh C0 sl= MHhsh, uand MH, slC0oc= MHhsl, uin the upper layer and MH, shC0sl= MH(htC0 h C0 u)shand MH, slC0oc= MH(htC0 h C0 u)slin the lower layer, where MHis the horizontal mixingcoefficient. (b) The vertical structure of model concentrations using salinity Sas an example. The linear gradient between the upper layerand the permanent pycnocline allows for more realistic vertical entrainment and mixing between layers. (c) The biological model withfluxes shown for the two-layer system using carbon as a currency.11 - 2 IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODELCoastash slVshVslsl, tsl, usea surfaceupperlayerlowerlayerocean floorOceanSlopewMhhMwOpenMH, sh-slH, sh-slH, sl-oH, sl-oMShelfMMUpDownDownUpUpDown Down UpDownUptlbhShppzSmixing depth of dmhupermanentpycnoclinelower layeruSupper layerIANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODEL 11 - 3ocean through the lower layers of the slope and shelf and then intothe surface layer over the shelf. Our shelf box does not include thatpart of the inner shelf which is landward of the upwelling center.When there are important inputs from the inner shelf, these aremodeled as a mixing process (see section 3.3). The modelequivalent of the upwelling front is the offshore edge of theslope box. The extent of advection between the coast and openocean through the front is unknown [Smith, 1994; Mackas andYelland, 1999]. In our model the full upwelled volume is advectedthrough the front, recognizing that a portion of it may be advectedin the alongshore current. Although downwelling is actually adepression of the pycnocline at the coast, salinities are reproducedreasonably well when representing it by advection (the reverse ofupwelling). Alongshore flow is strong in coastal upwelling systems[Smith, 1994] but not necessarily the gradients. We assume thatthese gradients are small (with the exception of the inner shelfbuoyancy current, discussed in section 3.3); thus alongshoreadvection is not modelled. Thisl assumption may be incorrect attimes; however, it provides us with a starting point for thismodeling exercise.2.3.2. Entrainment and mixing. [16] The upper layer depth(hu) is the mixed layer depth which varies seasonally. When huchanges with time t, entrainment e occurs into the layer, whichbecomes thicker. It is unrealistic to entrain or mix averaged lowerlayer concentrations into the upper layer because density profilesdo not conform to a perfect two-layer structure, particularly in latesummer and early fall. Instead, there is some gradient structurebetween the bottom of the mixed layer and the nearlyhomogeneous lower layer. We approximated this structure bymodeling a permanent pycnocline (hpp) (different for eachhorizontal region and fixed in time) with a linear densitygradient from it to the bottom of the upper box (Figure 1b),ensuring that hu< hpp(equation (A5)). The upper box and theregion below the pycnocline have uniform concentrations.2.4. Biological Model[17] The biological model is a two-layer system. State variablesare related to one another by biological fluxes (Figure 1c, (A1), andparameters in Table 3). In addition, dissolved state variables (DI,DO, and S) are exchanged between levels by mixing and entrain-ment (Figure 1c) as well as by advection (Figure 1a). PO mattercan only sink into the lower layer (or be advected between levels).This system was embedded into each of the horizontal shelf andslope regions in the physical circulation model described above.Biological source-sink processes were not modeled in the openocean system. Open ocean state variable concentrations werespecified using data (described in section 3.5).[18] We model the living PO pool as temperate diatoms, whichdominate primary production in coastal upwelling systems wherethere are large fluxes of nutrients into the euphotic zone [Hutchingset al., 1994]. Diatoms have high growth rates, and their popula-tions often crash suddenly when nutrients become limiting. Sinkingrates of single cells can be high (up to 10 m dC01in rare cases) andan order of magnitude higher when cells coagulate and becomemarine snow [Smetacek, 1985; Alldredge and Silver, 1988]. Valuesof the f ratio [Dugdale and Goering, 1967] are high [Harrison etal., 1987].[19] Inorganic nutrients are taken up by the surface (living) POpool, which is the modeled primary production (PP) via MichaelisMenton kinetics [e.g., Wroblewski, 1977]. This uptake is limited bylight and the nutrient nitrogen such that only one factor is limitingat any one time. Light-limited photosynthetic rates are determinedfrom an exponential saturation curve (g) [e.g., Denman and Pen˜a,1999], which is vertically integrated over the upper layer. (There isTable 1. State Variables for Each CurrencyaState Variable DescriptionDIC dissolved inorganic carbonDIN dissolved inorganic nitrogenDOC dissolved organic carbonDON dissolved organic nitrogenPOC particulate organic carbonPON particulate organic nitrogenaUnits are mM.ctuppremineralizationexcretion, mortality etc.uptakeremineralizationremineralizationoceanfloorsurfaceoceansinkingverticalgasfluxfluxPOCPOCDICDOCDICDOCuluullhhhFigure 1. (continued)11 - 4 IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODELno primary production below the upper layer.) Light is absorbedexponentially with depth by both water and phytoplankton (i.e.,self-shading) [e.g., Fasham, 1995].[20] During winter, modeled PP was higher than expected eventhough integrated light levels were realistic. Since many diatomsgo into nonsinking resting stages when growth conditions are notfavorable [Garrison, 1984], we chose to make part of the surfacePO pool dormant during the winter months (equation (A2)).2.4.1. Excess carbon uptake. [21] In the model, additionaluptake of DIC (PC) can occur when DIN is limiting but lightis not:PC ¼ chlrvmp0gC0 PPðÞ; ð1Þwhere chlris a factor to account for the reduction of cellularchlorophyll (chl) relative to carbon, vmis the maximum nutrientuptake, and g is the light limitation function averaged over theupper layer. Variable uptake ratios of DIC:DIN that are greater thanthe Redfield ratio [Redfield et al., 1963] have been observed in theocean [Sambrotto et al., 1993]. In an attempt to model this excessuptake we assume that phytoplankton still respond to light andprocess carbon regardless of nutrient limitation but with anincreased C:chl ratio. In the absence of DIN, however, carbon isnot incorporated into the cell. Live phytoplankton maintain aC:N ratio in a narrow range close to the Redfield ratio, whileC:chl (likewise N:chl) ratios vary widely and are highest whennutrients are limiting but light is not [Sakshaug et al., 1989;Taylor et al., 1997]. Measured DOC:DON ratios are usually wellabove (7 < DOC:DON > 20) POC:PON (Redfield) ratios [Hilland Wheeler, 2002; C. S. Wong, unpublished data, 1997]. Thuswe model the excess carbon uptake as passing directly into theDOC pool ((A1a) and (A1c)).[22] Loss from the living (upper) PO pool is first-order decay(equation (A1b)). The decay rate sis scaled by a dimensionlessloss function dependent on either nutrient or light limitation(equation (A3)). The numerical coefficients (in (A3)) werechosen so that model equivalent sinking rates (sbphu) are inthe range of diatom single-cell sinking rates under nutrient andTable 3. Biological Parameters and Values Used for Model RunsaParameter Description Value UnitsI0daily averaged IPARat the surface 47–301 W mC02IPARphotosynthetically available radiation W mC02ISAtlight intensity at which vmis reached 50 W mC02Knhalf saturation constant for nitrogen uptake 0.1 mMKslhalf saturation constant for PO decay due to light limitation 0.06 ...Ksnhalf saturation constant for PO decay due to N limitation 0.1 mMa slope of vmversus IPARcurve at IPAR= 0 (0.028–0.04) dC0(W mC02)chlrchlorophyl reduction factor 0.2 ...kpIPARattenuation coefficient for PON 0.06 mC01(mMN)kwIPARattenuation coefficient for seawater 0.04 mC01p fraction of particulate flux leaving POupool 0.6 ...p0active surface PO concentration (C or N) mMpc excess carbon uptake mM Cdpp primary production (C or N) mM dC01rddissolved organic matter decay rate: C, N 0.005, 0.0065 dC01rpparticulate organic matter decay rate 0.2 dC01s decay rate of surface PO pool 0.0385 dC01vmmaximum growth rate for phytoplankton (1.4–2.0) dC01vm0maximum growth rate for phytoplankton at 0 K 5.696C210C09dC01g 1C0exp(C0aIPAR(z/vm)01...aSee Appendix D. Values in parenthesis are results of model conclusions. Ranges show seasonal variation.Table 2. Physical Parameters and Geometry With Values Used in the Model RunsaParameter Description Value UnitsA average upwelling velocity 0.785 m dC01tuupwelling season length 145 dC flux per length along coast from VICC (0.009–0.082) m dC01D average downwelling velocity: typical, ENSO 0.7, 2.8 m dC01tddownwelling season length 65 dMHhorizontal mixing 20 m dC01MVvertical mixing 0.2 m dC01P precipitation (0.002–0.013) m dC01R flux per length along coast from terrigenous runoff (0.003–0.024) m dC01dmdepth of mixing below hu2melentertainment to the lower layer (C00.007–0) dC01euentertainment to the upper layer (0C00.555) dC01hpppermanent pycnocline: shelf, slope 73, 43 mHttotal depth: shelf, slope 120, 400 mhudepth of upper layer: shelf (10C040) mdepth of upper layer: slope (15C070) mwshshelf width 20 kmwslslope width 10 kmaValues in parenthesis were calculated from time dependent functions within the model. Ranges show seasonal variation.IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODEL 11 - 5light limitation, respectively [Bienfang et al., 1982, 1983]. Thetotal decay flux is partitioned between the lower PO and upperDO pools ((A1e)) and (A1c)), so that the fraction p goes intothe lower PO pool. In a one-dimensional system in steady state,p is a first-order approximation of the f ratio, as all particulateflux sinks immediately to the lower box while the dissolvedportion stays in the surface. Transfers between trophic levels arenot modeled. Nonliving organic matter (DO and lower POpools) remineralizes ((A1c), (A1f), and (A1e)) to DI pools((A1a) and (A1d)) via first-order exponential decay at theirrespective decay rates (rd, rp), which are different for eachcurrency.2.5. Gas Flux[23] The surface partial pressure of CO2(pCO2w) was calcu-lated from modeled DIC and alkalinity (ALK) using the relation-ships of Skirrow [1975], prescribed sea surface temperatures T,and modeled S. The sea surface salinities are fresher than theaveraged box value, so they were extrapolated by subtracting DSfrom Su. Model DIC was diluted by the same amount to-- 25 75 175 275 375-- 6.5-- 3035.5Downwelling (m d-  1) Upwellingyear dayaDJFM AMJ J ASONDtypicalsmoothedbIslandVancouverterrigenousVICCVICCsurfaceShelfsurfaceSloperunoffP wslP wslshR wshC wP wsh(C+R+P)wshFigure 2. (a) A typical year of realistic external forcing. Positive values are A during the upwelling season andnegative values are D during the downwelling season. The dashed curve shows smoothed forcing for the sameintegrated flux as the typical year. (b) A schematic of the upper layer shelf and slope boxes showing buoyancy fluxes.Buoyancy fluxes (volume per length coastline) from precipitation are Pwshand Pwsl. Buoyancy fluxes (volume perlength coastline) from the inner shelf are from terrigenous runoff (Rwsh) and from the VICC (Cwsh).11 - 6 IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODELdetermine surface DIC. The model assumes that dilution exertsthe major control over ALK (based on summer measurements inthe study area [Ianson, 2001]); thus calcium carbonate (CaCO3)formation is not modeled. We use a linear relation between themeasured ALK and salinity (ALK = 52.85 S + 472 meq kgC01;r2= 0.80) [Ianson, 2001] to estimate model ALK. The singlenegative charge associated with modeled DIN (assuming that thebulk of the DIN is nitrate) was then subtracted to estimatecarbonate ALK. Annual variability of atmospheric pCO2awasprescribed [Manning, 1993]. Gas flux Gwas determined from thesolubility of CO2, piston velocity k, and the pCO2of water andair using the standard equation [e.g., Watson, 1993]. Solubility-- 25 75 175 275 37501020DIN (µM)year day01234PP (gC m-- 2 d-- 1)aDJFM AMJ J ASONDupperlower-- 25 75 175 275 3750102030DIN (µM)year day01234PP (gC m-- 2 d-- 1)bDJFM AMJ J ASONDupperlowerFigure 3. (a) Integrated shelf and (b) slope primary production (top panel) and upper and lower layer shelf DIN(bottom panel) for a typical year. Advective forcing is shown in Figure 2a. The modulating wave in DIN is caused byentrainment in response to storm forcing. Time is in year days, where year day 0 is 1 January.IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODEL 11 - 7was estimated from S and T using the relationship of Weiss[1974]. The relationship of Wanninkhof [1992] for k based onlong-term averaged wind was used.3. Physical Forcing[24] The external physical forcing makes the model specific to aparticular coastal upwelling region. We present results for the westcoast of Vancouver Island, Canada. Upwelling and downwellingcirculation, light, mixed layer depth, and buoyancy fluxes are allforced by external functions based on local data and are describedbelow.3.1. Upwelling and Downwelling[25] The upwelling index of Thomson and Ware [1996] wasused to specify the average timing of the seasons as well as thefrequency and relative strength of upwelling and downwellingevents. The average of the absolute upwelling and downwellingstrength was based on field estimates [Freeland and Denman,1982; Freeland and McIntosh, 1989]. A smoothed version of thisforcing function with the same averaged velocities and seasonaltiming was also used to compare the effects of smooth versusrealistic forcing (Figure 2a). Forcing during El Nin˜o-SouthernOscillation (ENSO) years was based on Hsieh et al. [1995], whoshowed that during a typical ENSO year in our study area,downwelling strength is enhanced while upwelling strengthremains constant.3.2. Light, Wind, Temperature, and Salinity[26] Sea surface measurements of IPAR(D. Crawford, personalcommunication, 1997; S. Harris, unpublished data, 1998) set theannual light cycle. The Pacific Northwest experiences thick cloudcover during a large part of the year, so light availability is oftenlow. Wind data [Faucher et al., 1999] were averaged over theseasons to calculate the piston velocity. A typical seasonal cycle intemperature was prescribed (http://www.ios.bc.ca/ios/osap/data/lighthouse/bcsop.htm; R. Brown, unpublished data, 1998). Theamount of surface freshening, DS, relative to the average box valuefor shelf and slope was 0.2 and 0.03, respectively (R. Brown,unpublished data, 1998).3.3. Buoyancy Flux[27] Coastal freshwater additions are important to our model asthey dilute both DIC and alkalinity and so have a major impact onpCO2. The west coast of Vancouver Island experiences C243myrC01of rain (British Columbia Department of Agriculture (Victoria,British Columbia, Canada), Climatic normals 1941–1970), mostof which falls in the late fall and early winter. Buoyancy flux isadded to the model via rainfall P over both the shelf and slope andalso as terrigenous runoff R into the shelf box (Figure 2b andAppendix B).[28] A buoyancy current, the Vancouver Island Coastal Current(VICC), flows northward year-round over the inner shelf [Freelandet al., 1984] and provides a large flux of DIN [Pawlowicz, 2001],although gradients of other state variables are assumed small[Ianson, 2001; C. S. Wong, unpublished data, 1997]. The VICCis modeled like runoff as a scaled flux into the surface shelf box(Appendix B). The additional volume added to the shelf and slopesurface boxes exits the system in the alongshore current (Figure 2b).3.4. Mixed Layer Depth[29] The depth of the upper box huis the mixed layer depth. Theannual cycle in mixed layer depth was prescribed using the resultsof Thomson and Fine (personal communication, 1999) with addi-tional variability at storm frequencies added (Appendix C).3.5. Open Ocean[30] Seasonal variations in all surface ocean state variableconcentrations were forced, while deep ocean concentrations wereheld constant [Ianson, 2001] based on the data of Whitney et al.[1998], Wong et al. [1997], Bishop et al. [1999], Whitney andFreeland [1999], C. S. Wong (unpublished data, 1997), and R.Brown (unpublished data, 1998).4. Results4.1. Primary Production[31] The response to the typical upwelling and downwellingforcing (Figure 2a) by DIN and primary production presented overthe shelf and over the slope (Figure 3, run 1) shows a gradualincrease in PP in response to increased light availibility (in the senseof Sverdrup[1953]) followed by an abrupt crash when DIN in theupper layer becomes depleted (occurring later over the slope).Storm mixing and entrainment provide DIN for small bursts ofprimary production until the upwelling season begins (year day145). Upwelled fluxes into the upper layer are large so that upperlayer DIN builds up faster than the biota can draw it down, so sharppeaks in DIN and PP over the shelf occur (Figure 3a). Much of theTable 4. Comparison of Annual Gas Flux GC0C1, Annual PP PPC0C1, and Nitrogen Inventory NiC0C1for Different Model RunsaRun Description Winter ShelfpCO2; ppmSummer ShelfpCO2; ppmTotal G,gCmC02yrC01Total DPP;%Total DNi;%1 typical 505 230 6 0 02 a increased 35% 470 230 19 10 23 smooth forcing 530 230 3 20 64 Atu:Dtd¼ 3:2 530 230 1 2–3 65 p = 0.3 470 230 14 C010bC06b6 rdis doubled 540 230 C015<b7 A ¼ D ¼ 0 450 270 14 C050 C0258 ENSOc435 230 22 C020cC012c9 PC = 0 505 310 0.6 0 0aPositive G is invasion. Shelf pCO2were averaged over January to represent maximum winter values and over June and July to represent minimumsummer values. G, DPP and DNiwere calculated by weighting annual flux over the shelf by two relative to the slope to account for its larger area. DPP andDNiwere determined relative to run 1.bThese differences are relative to a run with p = 0.7 rather than p = 0.6 (run 1). (All other parameters are from run 1.)cNote that the ENSO year follows a typically forced year, while forcing is the same each year in other runs. When ENSO years repeat, differences (withrespect to run 1) increase.11 - 8 IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODELupwelled DIN is taken up over the shelf before it can be advectedoffshore into the upper slope box. Thus, over the slope these peaksare much smaller and only occur for large upwelling events (Figure3b). In the fall, DIN increases in the surface mainly due to entrain-ment and reduced demand because of decreasing light availability.In the lower shelf layer (Figure 3a, bottom panel), DIN decreases asthe nutricline becomes depressed during the short winter downwel-ling season (year days 349–45), but DIN increases throughout theupwelling season (year days 145–285) due both to advection fromthe open ocean and remineralization. DIN in the lower slope box(Figure 3b, bottom panel) behaves similarly but with less variationthroughout the year. Net annual primary production for the typicallyforced case is 410 and 330 g C mC02yrC01for the shelf and slope,respectively. Model PP is higher than previously expected (around250 g C mC02yrC01from local observations (P. Harrison, personalcommunication, 1997)) but is in agreement with recent measure-ments [Ianson, 2001; S. Harris, unpublished data, 1998].[32] In the surface shelf box, DIN supplied by upwelling isresponsible for 50% of PP, while mixing and entrainment provides35% and the VICC provides 15%. Over the inner shelf, which wedo not model, the VICC is likely the major nutrient source. Overthe slope, upwelled DIN fuels 30–35% of the PP, mixing fuels65–70%, and the VICC fuels <5%.[33] Primary production is mainly controlled by light availabilityin our study area when physical forcing is realistic, i.e., notsmoothed in time (Figure 2a). The maximum possible daily PPwhen nutrients are not limiting is controlled by IPARthrough thebiological uptake parameters, a (uptake rate per light intensity atlow light levels), and to a lesser degree, vm(maximum uptake rate).When the model PP drops during the summer, it is nutrient limitedor briefly light limited through PO matter self-shading. BecauseIPARis usually below ISATthroughout the upper layer, the model isnot sensitive to changes in vm. To understand the sensitivity of themodel to these and other parameters, additional runs were pre-formed (Table 4). Increasing vm0by 35% (but maintaining athrough a comparable increase in ISAT) has no effect on modelPP. At low light levels, a is important. Increasing a by 35% (withvm0constant; run 2) causes PP to increase by 10% as the maximumpossible daily PP is higher. However, changing the way thatnutrients are delivered to the euphotic zone has a major effect on PP.[34] When forcing is smoothed (peak width of each eventincreased by a factor of 4) (Figure 2a) but integrated upwellingand downwelling flux is the same (run 3), primary productionincreases significantly (by 24%) over the shelf (510 g C mC02yrC01)but decreases (by 15%) over the slope (280 g C mC02yrC01). There ishigher primary production in the system because the peak upwelledDIN fluxes are small enough that the biota can respond before theDIN is horizontally advected into the open ocean. In the moresporadic (typical; run 1) case some DIN is advected out of thesystem during strong events before it can be utilized by the biota.The effect of this higher production (20%) under smooth forcing isto maintain a larger nutrient inventory in the system (C246% innitrogen) despite the same net advected nitrogen flux into thesystem. Much of the additional primary production is remineral-ized over the shelf, and so more nutrients are retained.[35] Nutrient inventory is clearly influenced by primaryproduction as in the example above. Of the physical parame-ters, the most important to nutrient inventory are the averageupwelling and downwelling velocities (A and D), in particularthe ratio of total annual fluxes (Atu:Dtd), where tuand tdarethe lengths of the upwelling and downwelling seasons, respec-tively. Horizontal mixing is less important. The higher Atu:Dtd;the higher the nutrient inventory over the shelf. Some of theincreased nutrient supply is used in PP. Increasing this ratio to3.2 (A ¼ 0:865 and D ¼ 0:6 with unchanged season durations, tuand td; run 4) from 2.5 (typical value; run 1) causes a 2–3%increase in PP and an increase in total nitrogen inventory by 6%.Also, the nutrient concentration in the lower layer of theneighboring open ocean (the depth of upwelling) is important, asthis water is advected onshore each summer.-- 70 180 430 680 93010152025lower DIN (µM)year day05101520upper DIN (µM)Jan 1 Jan 1 Jan 1ENSOtypicalENSOtypicalFigure 4. Shelf DIN in upper layer (top panel) and shelf DIN in lower layer (bottom panel) for 3 years. ENSOresponse (solid curve) to ENSO forcing during the first year (followed by typical forcing in the second and third year)is compared to 3 years of typical forcing (dashed curve).IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODEL 11 - 9[36] Increasing the fraction p of the decay flux from thesurface PO pool which sinks and becomes PO in the lowerlayer also increases nutrient inventory (6% with a change in pfrom 0.3 (run 5) to 0.7) and therefore primary production (10%for the same change). With the higher p, more remineralizationoccurs over the shelf as the particulate rate rpis an order ofmagnitude higher than the dissolved rate rd. In addition, itoccurs in the lower layer, where it is more likely to be retainedin the system as most PP occurs during the upwelling season.In the case where p is low, there is higher horizontal export ofDO matter out of the system in the surface layer. Doubling theratesofPOremineralizationrphas little effect on eithernutrient inventory or PP, as the original rate was high enoughthat close to complete remineralization already occurred withinthe system. Doubling the remineralization rates of DO matter rd(run 6) increases the nutrient inventory only slightly (<1%) butincreases total PP by 5% as the excess remineralization occursmostly in the surface and so is quickly taken up by the biota.[37] When upwelling and downwelling circulation is shut offcompletely (run 7), the model behaves more like an oligotrophicocean. Primary production decreases to half and is nutrient limitedduring the entire summer. DIN concentrations are lower every-where in the system. Surface DIN is 30% less in the winter over theshelf and is zero throughout the summer. The total nitrogeninventory decreases by 25%.4.1.1. ENSO. [38] Simulations of ENSO (run 8) showeffects of interannual variability in forcing and that winterforcing can affect the summer season. During ENSO years,modeled downwelling is enhanced, while upwelling remains thesame. Despite the same upwelled flux during the summer, primaryproduction is lower (C2420% from increasing D from 0.7 to 2.8).The nutrient inventory in the system is decreased because thenutricline is so strongly depressed during the winter that thesummer upwelled water has lower DIN (Figure 4). This effectcan clearly be seen in the DIN concentration of the lower shelf box(Figure 4, bottom panel) which drops to 11 mM during the ENSOwinter. If the nutricline in the open ocean were also depressed or ifsummer upwelling were decreased, the effects of ENSO would beenhanced. After one winter of increased downwelling, the systemtakes C244 years to reach its previous steady state nutrient inventory(Figure 4), though in the second year after ENSO, primaryproduction is within 5% of its initial value (but less nutrients areadvected out of the system). ENSO events occurring at frequencieshigher than every 4 years decrease the nutrient inventory andproduction in the system over the long term.4.1.2. Residence Time. [39] The residence time for waterover the shelf in the model is of the order of weeks in the surfacelayer (C2410 days in the summer and C2450 days in the winter) and C244months in the lower layer. These times seem reasonable relative tothe natural system; however, the strong alongshore circulation isnot modeled and could shorten them substantially depending onthe alongshore extent of the model (larger spatial scale, less effecton residence time). In the case of the ENSO example above thespatial extent of the physical forcing is large (order of 1000 km),and so our model results would not be greatly affected by theaddition of the alongshore circulation. In addition, residence time-- 25 75 175 275 375100250400550pCO2 (ppm)year day-- 0.4-- 0.200.20.4Gas flux (gC m-- 2 d-- 1)DJFM AMJ J ASONDshelfslopeINVASIONEVASIONFigure 5. Model gas flux (top panel) and pCO2(bottom panel) for shelf (solid curve) and slope (dashed curve).Positive gas flux is from the atmosphere (invasion). Measured pCO2in the study area from ship of opportunity cruises(C. S. Wong, unpublished data, 1997) collected September 1995 (during an upwelling event), May 1995 and 1996,and February 1996 over the shelf (pluses) and slope (open circles) and an ellipse of measured pCO2[Ianson, 2001]collected in July 1998 are shown for comparison with the model. The July 1998 data were collected following anupwelling event and during a relaxation period (i.e., between events) and so cover a range in pCO2as shown by theellipse. (The ellipse is centered on the average of the data (in time and pCO2) over both shelf and slope.) Note that themodel forcing is that of a ‘‘typical’’ year, and so the timing of upwelling events is not the same as in the data.11 - 10 IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODELfor nutrients is longer because nutrients are incorporated into thePO matter, some of which sinks into the lower layer, retainingnutrients in the system.4.2. Gas Flux[40] For all model configurations, there is air-sea CO2evasion during the winter and invasion during the summer,when PP draws down surface DIC (Figure 5, top panel).However, net annual CO2flux is much smaller than theseseasonal fluxes. For the typically forced case (run 1; Figure 5),there is net annual invasion (6 g C mC02yrC01, which is 2 C2105gCyrC01per m coastline) (Table 4). Over the shelf, surfacepCO2varies over a larger range (200–550 ppm) than over theslope (200–450 ppm), similar to sparse field measurements(Figure 5, bottom panel). The highest model pCO2occurs overthe shelf in response to strong upwelling events (year days 159and 251). While these values seem high, surface measurementsof 525 ppm have been recorded during an upwelling event inthe area (day 240, Figure 5). Between upwelling events, pCO2is around 200–250 ppm, which compares with measurements(year days 195–205, Figure 5, discussed by Ianson [2001]). Inthe winter model, pCO2is high due to low alkalinity (fromhigh rainfall) and increased DIC (from vertical mixing) inagreement with data (day 45, Figure 5). The pCO2is highestover the shelf, where the surface waters are freshest. Primaryproduction draws pCO2down earlier in the spring over theshelf than over the slope (Figure 5, days 100–125 in themodel, day 130 in the data), but otherwise, the model output issimilar for both.[41] Sensitivity studies show that variations in model param-eters do affect pCO2; however, summer pCO2is remarkablyinsensitive as long as upwelling and downwelling circulation arenot set to zero. Only large changes in assumed deep ocean DICconcentration or setting excess carbon uptake (PC) to zero (run9) cause summer pCO2to vary from the typically forced case.Most variations appear during the winter season even fordiffering PP.[42] Increasing carbon inventories (by either using smoothedforcing (run 3) with the same Atu:Dtdratio or by increasingAtu:Dtdto 3.2 (run 4) with realistic forcing) causes winter andfall pCO2to increase by 20–30 ppm, while summer values areunchanged. There is still net annual CO2invasion, but it issignificantly decreased (Table 4). There is higher invasion in thesmoothed case because there are no high pCO2peaks in summerfrom upwelling. Doubling the remineralization rate of DOC (rd)(run 6) does not change summer pCO2but increases fall and winterpCO2by C2450 ppm. Decreasing nutrient inventory by lowering pto0.3 (run 5) makes for lower winter pCO2(by 40 ppm), increasingthe net gas invasion (Table 4).[43] Winter pCO2is lowered in the case of ENSO forcing(enhanced downwelling; run 8). The depression of the pycno-cline and the concentration decrease of DIC is strong, and sowinter pCO2decreases by C2470–80 ppm, while summer valuesremain the same (Table 4). Winter and spring pCO2are lowered(40–50 ppm) when PP is increased (10%) by increasing thebiological parameter a (35%; run 2) while summer valuesremain unchanged despite higher daily PP. In both the aboveexamples, there is larger net annual CO2invasion (C2420 g CmC02yrC01).[44] When there is no excess DIC uptake by the surface PO pool(run 9), pCO2is significantly higher, as much as 80–90 ppm,during the summer (Table 4). The carbon inventory does notchange though, so winter pCO2is not affected. Net annual gasinvasion decreases relative to the typical case to near zero. In thisscenario, however, model DIC between upwelling events is higherthan measured [Ianson, 2001] (Figure 5).[45] Shutting off the upwelling and downwelling circulationentirely (run 7) causes a 40 ppm increase in summer pCO2asPP is reduced by about half. Net annual CO2invasion stillincreases (by a factor of 2) because of decreases in winter andfall pCO2. With no upwelling circulation, nutrient inventoriesare significantly less (because primary production is lower andalso because DIC is not advected into the system duringsummer), causing fall and winter DIC concentrations to belower. A much larger portion of the summer DIC drawdown inthis scenario, however, is due to PC. If it were not for thisexcess uptake of carbon, there would be close to zero netannual CO2flux.4.3. Net Annual Exchange Fluxes Between the Model and theOpen Ocean[46] For both carbon and nitrogen the dominant annualexchange flux is the import flux of DI nutrients into the lowerslope box from the open ocean (Figure 6). This nitrogen inputis balanced mainly by export of PON from the upper layer tothe surface open ocean (50%). Lower layer exports of PON aresmall, two orders of magnitude less than surface exports. Afurther 20% of the DIN import is exported to the open oceanas DON, mainly in the upper layer (Figure 6), while 10%leaves as DIN in the upper layer. The remaining 20% leavesthe system in the alongshore surface current as a result of thebuoyancy fluxes. While there is a net import of DIN from theVICC, a much larger alongshore export occurs as DON andPON.[47] In the case of carbon, most (75%) of the lower layer DICimport flux returns to the open ocean as DIC in the upper layer(Figure 6) because the fraction of biological DIC drawdown is somuch smaller than that of DIN. Only 10% of the carbon importleaves as organic carbon in the surface layer in equal fractions ofDOC and POC. Fifteen percent of the imported DIC is exported inthe alongshore surface current due to buoyancy fluxes, mostly asDIC over the shelf. Although gas flux provides an additional netimport of carbon, it is two orders of magnitude less than the lowerlayer import of DIC.[48] The C:N ratio of the PO export is 6.7 (set in the model),while the C:N ratio of the model DO export is in the range of10–20. The ratio of total TOC:TON export is C2410, which agreesOpen oceanUpwelling system(slope)200gas carbonDICDICPOCPONDONDOCnitrogen 120)DIN(alongshore lossof carbon 6000,2000200030 00040 000DIN 60060100300DON 20200POC 203PONDOCFigure 6. Net annual exchange between the model system andthe ocean are shown for each form of carbon and nitrogen. Inaddition, net alongshore fluxes occur from upper shelf and slopeboxes. All units are per length of coastline (in m) (kg yrC01mC01).IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODEL 11 - 11well with depth-integrated measurements in the upwelling regionalong the Oregon coast (44.65C176N, 124.18C176W) [Hill and Wheeler,2002].[49] Sensitivity studies show that when upwelling strength isincreased relative to downwelling strength (Atu:Dtd¼ 3:2 run 4),both lower layer DI imports increase by 20%. Almost all of theexcess DIC import is exported into the surface ocean as DIC.About half of the excess DIN leaves in the surface as DIN, whilethe other half is converted to organic nitrogen, which is thenexported into the surface ocean. When PP is increased throughsmooth forcing (run 3), DIC exchanges are unchanged, but there isno longer any DIN export in the upper layer. There is a shift (factorof 2) in organic matter export in the surface from POC to DOC.Likewise, increasing PP (10%) by raising a (run 2) does not affectDIC exchange while DIN export to the surface ocean is muchlower (60%). Organic matter exports increase in both layers by10–20%.[50] If upwelling and downwelling circulation is shut off (run 7),exchange fluxes with the open ocean decrease by an order ofmagnitude. Import of DIC still occurs in the lower layer, but it isbalanced mainly by the export of DOC rather than DIC in theupper layer.5. Discussion[51] Results show that the winter season is very important indetermining model fluxes, despite the fact that the majorbiological fluxes occur during the summer. Downwellingstrength has a major impact on lower layer nutrient concen-trations over the shelf and in turn PP the following summer.Interannual variability (such as ENSO events) affects thesystem over timescales of 3–5 years. Furthermore, it is differ-ences in winter (not summer) surface pCO2that cause differ-ences in modeled net annual CO2flux. During the winter thelower layer is thoroughly mixed and entrained into the surfacelayer over the shelf. Because of this winter mixing, nutrientinventories in the system have a strong influence on both PPand pCO2. The primary influences on nutrient inventory are theratio of upwelling and downwelling strengths, PP, and p(mainly because more organic matter is remineralized at ahigher rate when p is increased). In addition, the nature ofadvective forcing is important. Realistic and more sporadicforcing versus smoothed forcing (Figure 2a) yields significantlylower PP (20%) and nutrient inventory (6%). Freshwater inputsduring winter also exert strong control over pCO2by loweringALK.[52] To develop this model, we made several additions whichare nonstandard relative to the biological models reviewed byFasham [1993]. These additions were necessary to producereasonable results. Physically, a permanent pycnocline wasadded to create more realistic vertical variability in statevariables (Figure 1b). Without this variability, entrained andmixed fluxes were too large, particularly during late summerand fall. Entraining-averaged lower layer DIN at these timesmade fall surface DIN unrealistically high and produced a largefall phytoplankton bloom (comparable to upwelling blooms).Biologically, winter PP was too high (>0.3 g C mC02dC01)despite realistic light levels. High PP during the winter meantthat surface nutrients did not attain measured spring values, andthe resultant spring bloom was much smaller than expected. Tosolve this problem, we made a portion of the living PO pooldormant during the winter months (equation (A2)) representingthe formation of nonsinking resting stages by diatoms. We alsomodeled excess uptake of DIC during times of nutrientlimitation (1) so that summer surface DIC values reflectedmeasured values. This excess flux was added to the DOCpool, thereby increasing the model TOC:TON ratio from theRedfield ratio to a more realistic value of C2410. Raising theDON remineralization rate relative to that of DOC also raisesthe TOC:TON ratio. In addition, our characterization of non-living organic matter as sinking (PO) or nonsinking (DO) isunique. Because the living PO pool maintained quite largeconcentrations even when nitrogen and light became limiting,we made the decay rate of this pool increase at these times.We based increased losses on changes in phytoplankton single-cell sinking rates. This representation produced better resultsthan a mathematical representation of zooplankton grazing[Ianson, 2001].[53] The model parameters which are most important to predictthe system are the offshore lower layer inorganic nutrient concen-trations, a (particularly at middle to high latitudes), p, and rd. Theformer is generally known, while the three latter parameters are notas well known. The most poorly known are p and rd, whichdetermine the character of the nonliving organic matter, whethersinking or nonsinking, and the remineralization rates.[54] The model is limited to decadal timescales becauseimportant processes (over longer timescales) such as denitrifica-tion and sedimentation are not modeled. In locations whereCaCO3formation occurs, it would be necessary to incorporatethis cycle to model pCO2(due to the reduction of surface ALK[Broecker and Peng, 1982]). In addition, if N2fixation occurs inthe study area, it could have a major impact on the ecosystemdynamics; however, there is currently no evidence for it in ourstudy area.[55] Our model was developed to be general and could easilybe extended to other upwelling regions. What makes the modelarea specific is the physical forcing. Most important are quanti-fication of the advective circulation and exchange with thecomplex inner shelf (buoyancy fluxes). In addition, the openocean concentrations of inorganic state variables are crucial tothe model, and reliable seasonal data are needed for two statevariables (in our case, S and DIN) to tune the physical model.In other upwelling regions, riverine input of DO matter andstronger upwelling circulation would be interesting to investigateand would provide different outcomes. However, many upwell-ing regions do not experience the downwelling season as in ourstudy area, and so our results of large net flux of DIC into thesurface ocean would be enhanced, as would the importance ofwinter mixing and gas evasion.[56] It is difficult to calculate CO2gas flux accurately, sowe do not pretend that the results of our simple model yieldfirm numbers. Our model does indicate the chief influences ongas flux and shows that within the system, winter evasion isof the same order as summer invasion (so the net flux isrelatively small) in all model runs. This net flux is usuallyinto the ocean even when the parameters are stretched to theirlimits (the exception is the doubling of rd, which causes smallevasion).6. Conclusions[57] The model suggests that the largest influence on the globalcarbon budget from coastal upwelling regions is ventilatingintermediate depth oceanic DIC through large imports of DICinto the lower layer of the system, most of which exits back tothe open ocean in the surface layer. Furthermore, this advectedsurface flux is relatively deplete in DIN. High PP over the shelfdoes not make for strong biological pumping; rather, it createshigh nutrient inventories that are mixed into the surface (whereDIC is ventilated) during winter. Organic matter is also horizon-tally exported into the open ocean but mostly in the upper layer.There is little export of organic matter in the lower layer (over an11 - 12 IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODELorder of magnitude less). The surface organic carbon export issplit roughly equally into DO and PO, so that some of it maysink in the open ocean but most of it is likely to be remineralizedin the surface. Thus, while coastal upwelling regions havedisproportionately high PP and pCO2drawdown, they areunlikely to absorb atmospheric carbon via the biological pump.The dynamic physical processes in winter ventilate the DIC,which accumulates in the lower layer during the summer, and theadvective circulation transports large quantities of intermediatedepth ocean water, rich in DIC, to the surface.Appendix A. Model EquationsA1. Biological Model[58] Using carbon as a currency, the general ordinary differentialequations for the upper layer aredDICudt¼C0PP C0 PC þ rdDOCuþGhuþ V þ X þ H ðA1aÞdPOCudt¼ PP C0 s POCubðÞþX þ H ðA1bÞdDOCudt¼ 1 C0 pðÞsPOCub½C138þPC C0 rdDOCuþ V þ X þ H;ðA1cÞwhere PP is primary production, rdis the DOC remineralizationrate, G is the gas flux, and PC is excess carbon uptake(described in text). Physical terms are represented by V (verticalmixing and entrainment), X (advection), and H (horizontalmixing) and are defined below. In (A1b) the second term on theleft-hand side is the decay of the upper (living) POC pool,where s is the decay rate and b is a dimensionless functiondependent on growth conditions (equation (A3)). The fraction ofthis decay flux that sinks into the lower layer as particulate fluxis p. In the lower layer,d DICldt¼ rdDOClþ rpPOClþ V þ X þ H ðA1dÞdPOCldt¼sphubhtC0 huPOCuC0 rpPOClþ X þ H ðA1eÞdDOCldt¼C0rdDOClþ V þ X þ H ; ðA1fÞwhere rpis the POC remineralization rate. The fraction of the ofthe POC (po) which is active (i.e., takes up nutrients in PP) isp0¼ PO 1 C0 exp C00:1WC01m2C2I0noonðÞðC8C043 WmC02C1C3C9; ðA2Þwhere I0(noon) is IPARat midday. The loss function isb ¼ MAX 9C0 8DINDIN þ K2snC18C19; 6 C0 5g2g2þ K2slC18C19C18C19; ðA3Þwhere Ksnis the half saturation constant for PO decay due tonitrogen limitation and Kslis that for light limitation. Values ofbiological parameters are shown in Table 3. Fluxes are describedin the text and illustrated in Figure 1c. The equations areidentical for nitrogen, except that there is no gas flux or excessuptake (PC), while for salinity, there are only physical terms.A2. Physical Terms[59] The physical terms in the model equations V(q), H(q), andX(q) represent vertical mixing, horizontal mixing, and advection,respectively, for the state variable q. The indices i and j representhorizontal (sh, sl,ando) and vertical (u and l) dimensions,respectively. Note that (i C0 1) is the horizontal region immediatelyinshore of i and similarly (i + 1) is the horizontal region immedi-ately offshore of i.Vi; jqðÞ¼Mvdmhi; jhi; ppC0 hi; uC0C1iþ ei; j !qi; kC0 qi; jC0C1; ðA4Þwhere k = ‘ if j = u and vice versa. The entrainment rates (ei, j)areei;u¼ MAXdhi;udthi; ppþ hi;uC0C1C01; 0C18C19ðA5aÞei;l¼ MINdhi;udt2hi;tC0 hi; ppC0 hi;uC0C1C01; 0C18C19; ðA5bÞwhere j = pp and j = t represent the permanent pycnocline anddepth of the total water column, respectively. These terms arisefrom the vertical structure described in section 2.3.2. Note thatthe vertical mixing coefficient (MV) is multiplied by dm(hi, ppC0hi, u)C01for (hi, uC20 (hi, ppC0 dm)) so that mixing occurs betweenthe upper layer and the fluid centered at a depth of dmbelow theinterface.Hi; jqðÞ¼MHwihiC01; jhi; jqiC01; jC0 qi; jC0C1di; s‘þMHwiqiþ1;jC0 qi;jC0C1;ðA6Þwhere di, s‘= 1 for i = sl and 0 otherwise following the standardconvention.[60] The advective terms from each physical box do not general-ize and are expressed in full:Xsh;u¼Ahsh;uqsh;lC0 qsh;uC0C1þDhsh;uqsl;uC0 qsh;uC0C1þ BshðA7aÞXsh;l¼Ahsh;lqsl;lC0 qsh;lC0C1þDhsh;lqsh;uC0 qsh;lC0C1ðA7bÞXsl;u¼Ahsl;uqsh;uC0 qsl;uC0C1þDhsl;uqo;uC0 qsl;uC0C1þ BslðA7cÞXsl;l¼Ahsl;lqo;lC0 qsl;lC0C1þDhsl;lqsh;lC0 qsl;lC0C1; ðA7dÞwhere B represents the buoyancy flux terms (defined in AppendixB). Definitions and values of physical parameters are presented inTable 2. The open ocean is considered an infinite source and sinkwith respect to the shelf and slope system.Appendix B. Buoyancy Fluxes[61] The shelf box buoyancy fluxes B for state variable q areBsh¼Phsh;uqpC0 qsh;uC0C1þRhsh;uqrC0 qsh;uC0C1þChsh;uqcC0 qsh;uC0C1ðB1aÞand in the surface slope boxBsl¼Phsl;uqpC0 qsl;uC0C1; ðB1bÞwhere P, R, and Care flux per length of coastline for rainfall,terrigenous runoff, and the Vancouver Island Coastal Current(VICC), respectively, with corresponding subscripts in lower case.IANSON AND ALLEN: COASTAL NITROGEN AND CARBON FLUX MODEL 11 - 13Subscripts u, sh, and sl are upper, shelf, and slope, respectively.The coefficients vary in time for precipitationP ¼ 0:029 exp C00:5C203:5 C0 2 cos2ptC18t þ 20 daysðÞC19C21C27mdC01;C26ðB2Þterrigenous runoffR ¼ 0:05 exp C00:53:5 C0 2cos2ptC18C20t þ 20 daysðÞC19C21C27mdC01;C26ðB3Þand the VICCC ¼ 0:05exp C00:65C0 2 cos2ptC18C20t þ 150 daysðÞC19C21C27mdC01;C26ðB4Þwhere t is 365 days and phases are relative to 1 January. We choseexponential functions to make short, steep peaks relative to abroader baseline (corresponding to data). The annual cycle ofrunoff volume was scaled from Thomson et al. [1989] to accountfor mixing in the inner shelf [Ianson, 2001]. The runoff has a lowconcentration of DIC (based on regressions from data in the studyarea [Ianson, 2001]), and since the area is relatively pristine, verylow concentrations of organic matter are assumed. Mixing fluxfrom the VICC (C) is based on peak values [Pawlowicz andFarmer, 1998] and a seasonal cycle from Thomson et al. [1989].Appendix C. Mixed Layer Depth[62] Annual variability in mixed layer depth was prescribed(Figure C1). Variations were added in response to prescribed stormforcing (periods of 5 and 10 days) with modulated amplitudes sothat forcing was weaker during summer months:storm ¼ 4cos2p10dtC18C19þ cos2p5dt C0 3 daysðÞC20C21C26C27C1 1:2 þ 0:3cos2ptt C0 50 daysðÞC20C21C26C27m : ðC1ÞAppendix D. Parameter Choice[63] Biological parameters are challenging to choose. Singlenumbers are used to represent many processes and may also bespecies dependent. Often, the processes are poorly understood andnonlinear. Field measurements are difficult to make and usuallyscarce. We used data from many sources combined with steadystate solutions of the biological model to constrain parameters.Maximum growth rates (vm) are temperature dependent followingthe standard Q10rule,vm¼ vm0exp 0:069 KC01TC0C1; ðD1Þwhere vm0would be the maximum growth rate at 0 K and T is theaverage temperature in the upper layer. Field data [Harrison andPlatt, 1986] were used to set growth rates. In this data compilationthe saturation light intensity Isatvaried less than a throughout theyear for similar sea surface temperatures and light intensities as inour study area, so it was kept constant in the model and a (uptakeper IPARat low light intensity) was calculated froma ¼vmTðÞIsatC1ðD2ÞTo make vmand a independent of chl, we assumed that activephytoplankton had a C:chl ratio of 35.[64] The particle remineralization rate (rp) for lower layer POmatter was set using measured remineralization depth scales fromsediment traps [Martin et al., 1987; Timothy and Pond, 1997]. Thedepth scales were combined with the sinking rate associated withthe particle flux that sediment traps measure (100 m dC01[Fowlerand Knauer, 1986]).[65] To deal with the most poorly known parameters (e.g., thedecay of the living PO pool (s) which represents many processes),quasi-steady state solutions were found for a simplified two-boxversion of the biological model (Figure 1c and (2)) [Ianson, 2001].Known values (or ranges of values) of parameters and statevariables were used to constrain the equations and to provide asolution for s and to narrow the range for the remineralization rateof DO matter (rd).[66] Acknowledgments. We thank K. Denman, K. Orians, C. S.Wong, and P. J. Harrison for many helpful discussions during the develop-ment of this model. We are also grateful to K. Denman, S. Calvert, N.Jeffery, and an anonymous reviewer for their constructive commentsconcerning preparation of this manuscript. 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