Impacts of atmospheric variability on a coupled upper-ocean//ecosystem …web.uvic.ca/~monahana/monahan_denman.pdf · 2004-06-16 · ocean/ecosystem model. [5] Section 2 of this paper

Impacts of atmospheric variability on a coupled

upper-ocean//ecosystem model of the subarctic Northeast Pacific

Adam Hugh Monahan1

School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada

Kenneth L. Denman2

Canadian Centre for Climate Modeling and Analysis, University of Victoria, Victoria, British Columbia, Canada

Received 27 May 2003; revised 27 February 2004; accepted 22 March 2004; published 26 May 2004.

[1] The biologically-mediated flux of carbon from the upper ocean to below thepermanent thermocline (the biological pump) is estimated to be �10 PgC/yr[Houghton et al., 2001], and plays an important role in the global carbon cycle. Adetailed quantitative understanding of the dynamics of the biological pump is thereforeimportant, particularly in terms of its potential sensitivity to climate change and itsrole in this change via feedback processes. Previous studies of coupled upper-ocean/planktonic ecosystem dynamics have considered models forced by observedatmospheric variability or by smooth annual and diurnal cycles. The second approachhas the drawback that environmental variability is ubiquitous in the climate system,and may have a nontrivial impact on the (nonlinear) dynamics of the system, whilethe first approach is limited by the fact that observed time series are generally tooshort to obtain statistically robust characterizations of variability in the system. In thepresent study, an empirical stochastic model of high-frequency atmospheric variability(with a decorrelation timescale of less than a week) is estimated from long-termobservations at Ocean Station Papa in the northeast subarctic Pacific. This empiricalmodel, the second-order statistics of which resemble those of the observations to agood approximation, is used to produce very long (1000-year) realizations ofatmospheric variability which are used to drive a coupled upper-ocean/ecosystemmodel. It is found that fluctuations in atmospheric forcing do not have an essentialqualitative impact on most aspects of the dynamics of the ecosystem when primaryproduction is limited by the availability of iron, although pronounced interannualvariability in diatom abundance is simulated (even in the absence of episodic ironfertilization). In contrast, the impacts of atmospheric variability are considerably moresignificant when phytoplankton growth is limited in the summer by nitrogenavailability, as observed closer to the North American coast. Furthermore, thehigh-frequency variability in atmospheric forcing is associated with regions inparameter space in which the system alternates between iron and nitrogen limitationon interannual to interdecadal timescales. Both the mean and variability of exportproduction are found to be significantly larger in the nitrogen-limited regime than inthe iron-limited regime. INDEX TERMS: 1615 Global Change: Biogeochemical processes (4805);

3220 Mathematical Geophysics: Nonlinear dynamics; 4215 Oceanography: General: Climate and

interannual variability (3309); 4842 Oceanography: Biological and Chemical: Modeling; KEYWORDS:

atmospheric variability, ecosystem dynamics, HNLC regions

Citation: Monahan, A. H., and K. L. Denman (2004), Impacts of atmospheric variability on a coupled upper-ocean/ecosystem model

of the subarctic Northeast Pacific, Global Biogeochem. Cycles, 18, GB2010, doi:10.1029/2003GB002100.

1. Introduction

[2] The role of biological processes in the exchange ofcarbon between the ocean and the atmosphere is poorlyunderstood, and remains a major source of uncertainty inattempts to determine the climate system response toanthropogenic emissions of carbon dioxide and to under-

GLOBAL BIOGEOCHEMICAL CYCLES, VOL. 18, GB2010, doi:10.1029/2003GB002100, 2004

1Also at Earth Systems Evolution Program, Canadian Institute forAdvanced Research, Toronto, Ontario, Canada.

2Also at Institute of Ocean Sciences, Sidney, British Columbia, Canada.

Copyright 2004 by the American Geophysical Union.0886-6236/04/2003GB002100$12.00

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stand past climate variability [Houghton et al., 2001]. Inmost of the world ocean, summertime primary productionoccurs in sufficient quantities to induce macronutrientdepletion in the surface waters, with surface macronu-trients being recharged by subsequent winter mixing.However, in the surface waters of approximately 20%of the world ocean, primary production is not limited bythe abundance of surface macronutrients; these areas areusually referred to as high nutrient/low chlorophyll(HNLC) regions. Major HNLC regions are the equatorialPacific, the Southern Ocean, and the subarctic Pacific. Atpresent, the leading hypothesis is that primary productionin these oceanic provinces is limited by the abundance ofthe micronutrient iron [e.g., Coale et al., 1996; Boyd etal., 2000]. The dynamics of ecosystems in HNLC regionshave attracted considerable interest in recent years [e.g.,Archer et al., 1993; Denman and Pena, 1999, 2002;Signorini et al., 2001; Edwards et al., 2004; Denman,2003], motivated largely by the developing understandingthat changes in ocean-atmosphere carbon flux in theseregions may play a key role in global climate variabilityon centennial and longer timescales [e.g., Falkowski etal., 1998].[3] Of the three major HNLC regions of the world ocean,

the subarctic northeast Pacific is the best observed. From1956 to 1981, regular observations of meteorological andoceanographic variables were made by Canadian weather-ships at Ocean Station Papa (OSP; 145�W, 50�N). As well,regular observations were made along a line between OSPand the continental shelf off of Vancouver Island (denotedLine P; see Figure 1) by ships steaming to and from OSP.Since the cancellation of the weathership program in theearly 1980s, regular oceanographic cruises on an approxi-mately seasonal timescale have been made along Line P. Inconsequence, sampling along this line has been carried outfor a sufficiently long period, and with sufficient resolutionin time, that the variability of both physical and biogeo-chemical properties on seasonal to decadal timescales isbecoming relatively well understood [e.g., Whitney et al.,1998; Whitney and Freeland, 1999]. In particular, summer-time nitrogen limitation has not been observed at OSP,while it is generally observed to occur closer to shore iniron-replete waters.

[4] The coupled physical and biogeochemical system ofthe upper ocean at OSP is a natural candidate for modelingstudies, as by oceanographic standards it is well constrainedby data. Previous studies have either modeled the responseof the system to observed meteorological forcing [e.g.,Archer et al., 1993; Signorini et al., 2001] or to smoothlyvarying annual and diurnal cycles [e.g., Denman and Pena,1999, 2002; Denman, 2003]. The first of these approacheshas the drawback that only about 20 years of sufficientlyhigh-resolution observations of meteorological variables atOSP exist, so it is difficult to produce a robust statisticalcharacterization of variability at OSP using observationsalone. The second approach has the disadvantage that itneglects the considerable synoptic-scale variability ob-served at Station Papa [e.g., Fissel et al., 1976], whichmay play an important role in the dynamics of both theupper ocean and the ecosystem. In the present study,observations of meteorological variables from OSP are usedto construct an empirical stochastic model of the atmospherewhich reproduces the statistics of the observed variability toa good approximation. This empirical stochastic model isthen used to drive a coupled upper-ocean/ecosystem modeltuned to represent conditions at OSP. Because arbitrarilylong realizations of atmospheric forcing can be obtained, theupper-ocean/ecosystem model can be integrated to producesimulations sufficiently long to obtain robust characteriza-tions of variability on daily to interdecadal timescales.Alexander and Penland [1996] used meteorological obser-vations at OSP to build an empirical stochastic atmosphericmodel with which they forced an upper-ocean model, whileBailey and Doney [2001] investigated the effects of envi-ronmental fluctuations on a simple biogeochemical modelwithout a representation of upper-ocean dynamics. Thepresent study extends these previous studies by consideringthe effects of atmospheric variability on a coupled upper-ocean/ecosystem model.[5] Section 2 of this paper describes in detail the upper-

ocean and ecosystem models used in this study, alongwith a brief discussion of the atmospheric model.Section 3 details the results of the numerical experiments,and a discussion and conclusions follow in section 4.Detailed descriptions of the ecosystem model and theempirical stochastic model of the atmosphere are given inAppendices A and B, respectively.

2. Coupled Upper-Ocean Physics//EcosystemModel

[6] The model considered in this study is composed ofthree main components: a one-dimensional dynamicalmodel of the upper ocean, an idealized dynamical ecosys-tem model, and an empirical stochastic model of atmo-spheric variability. The upper-ocean and ecosystemcomponents are coupled, and both are driven by theatmospheric model. We proceed to discuss these compo-nents in detail.

2.1. Upper-Ocean Model

[7] The present study follows Denman and Pena [1999,2002] in using a Mellor-Yamada level 2.5 (MY2.5) model

Figure 1. Map of the subarctic northeast Pacific showingthe location of the original 13 stations along Line P (smallcircles). Stations P12, P16, and OSP are indicated byasterisks.

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[Mellor and Yamada, 1974, 1982] to represent the upperocean. The performance of the MY2.5 model in modelingthe turbulent upper ocean, relative to other mixed-layermodels, is discussed by Denman and Pena [1999]. Themodel domain is 250 m deep, consisting of 100 2.5-m-thicklayers. A constant background diffusivity of 1.5 �10�5 m2 s�1 was used, based on the value reported byMatear and Wong [1997]. Incoming solar radiation ispartitioned into longwave (60%) and shortwave (40%)fractions. The longwave fraction is entirely absorbed inthe uppermost layer, while the shortwave fraction, which isassumed to correspond to the photosynthetically activeradiation (PAR), is absorbed throughout the water column.At each model level a fraction exp(�1

2kt(z)dz) of the PAR is

absorbed by the water, where dz is the layer thickness andthe attenuation coefficient kt(z) depends on a constantbackground value for seawater and on the concentrationof phytoplankton (P1 + P2, defined in section 2.2) anddetritus (D) at the given layer,

kt zð Þ ¼ kw þ kc P1 zð Þ þ P2 zð Þ þ D zð Þð Þ: ð1Þ

The mixed layer depth (MLD) is diagnosed from the modelas the shallowest model layer at which the temperature is0.1�C less than the sea surface temperature.[8] In the work of Denman and Pena [1999, 2002], the

salinity was set at a constant 32.7 ppt throughout themodel domain. The domain of the present model is deeperthan that used by Denman and Pena [1999, 2002], and inparticular, extends below the depth of the permanenthalocline at OSP. A crude parameterization of the halo-cline was therefore prescribed in the present model byfixing the salinity to the profile shown in Figure 2a. Aswell, by relaxing the temperature below 150 m on atimescale of 6 months to the profile shown in Figure 2b, acrude representation of the permanent thermocline wasintroduced; model variability is qualitatively unchangedfor values of this relaxation timescale from 3 months to2 years. The profiles displayed in Figure 2 were designedto resemble those illustrated in Figure 3 of Gargett[1991].

2.2. Ecosystem Model

[9] The ecosystem model considered in this study is a six-component version of the model considered by Denman and

Pena [2002] and Denman [2003]. Small (<5 mm, P1) andlarge (>5 mm, P2) size classes of phytoplankton are repre-sented explicitly, as are microzooplankton (Z1) and detritus(D). To a first approximation, the large and small sizeclasses of phytoplankton along Line P may be consideredto represent, respectively, autotrophic flagellates and dia-toms [Boyd and Harrison, 1999]. Two species of nitrogen,NO3

� and NH4+, are modeled explicitly; the total nitrogen

concentration is denoted N = NO3 + NH4. Mesozooplankton(Z2), which graze on microphytoplankton (P2) and micro-zooplankton, are not modeled prognostically but are set to aconstant value throughout the year. All ecosystem modelparameters are expressed in terms of the equivalent con-centration of nitrogen.[10] The ecosystem variables are defined at each model

level and evolve according to the set of differentialequations outlined in Appendix A, as well as beingmixed between model levels as passive tracers by theupper-ocean turbulence model. The specific growth rateof the phytoplankton is limited by three factors: nitrogenabundance, light level, and iron availability, modeled by asimple threshold dependence of the phytoplankton spe-cific growth rate. Nitrogen uptake is represented bysimple Michaelis-Menten dynamics, while the light func-tion is as given by Webb et al. [1974]. In the absence ofa detailed representation of the cycling of iron in theupper ocean, iron limitation is simply represented by aconstant parameter LFe setting an upper limit on thespecific phytoplankton growth rate. There is no colimita-tion of growth in this model; at any time, only one oflight level, nitrogen abundance, or iron availability islimiting. Both P1 and P2 are modeled to take upammonium preferentially to nitrate. Furthermore, it isassumed that the large and small size classes of phyto-plankton are equally limited by iron availability. Apreliminary analysis of data from the SERIES iron-fertilization experiment at OSP suggests that both thesmall and large size classes of phytoplankton respond tofertilization with comparable specific growth rates, with aweak grazer-controlled bloom of the former occurringbefore the main diatom bloom, similar to results fromthe equatorial Pacific [Cavender-Bares et al., 1999] andthe Southern Ocean [Maldonado et al., 2001]. Sensitivityto differing values of LFe for large and small phytoplank-ton size classes has been explored with a similar modelby Pena [2003].[11] Microzooplankton are modeled to graze on the

small size fraction of phytoplankton and on detritus,with a relative preference that can be tuned. Similarly,the mesozooplankton graze (unpreferentially) on themicrophytoplankton, P2, and on the microzooplankton,Z1. Because of ‘‘sloppy feeding’’ and excretion offecal pellets by microzooplankton, only a fraction of thegrazed material is assimilated as microzooplankton bio-mass; the rest moves directly into the detritus pool. Aspecified fraction of mesozooplankton grazing is alsoinstantaneously excreted into ammonium. Losses of P1

and Z1 due to mortality and excretion enter the ammoniumpool, while those of P2 lead to both the ammonium anddetrital pools. Mechanisms for detritus removal other than

Figure 2. Plot of (a) salinity profile and (b) permanentthermocline profile to which the upper-ocean model isrelaxed.


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consumption by microzooplankton are remineralization toammonium by heterotrophic bacteria at the rate re, andsinking at speed ws. Finally, a depth-dependent nitrifica-tion of NH4 into NO3 by bacteria is represented in themodel as in the work of Denman [2003], as nitrificationis observed to be inhibited in the euphotic zone [Ward,2000; Denman, 2003]. Finally, all growth, grazing, andmortality rates are temperature dependent according toindividual Q10 parameters. A complete description of theparameterizations of the processes governing the ecosys-tem dynamics is presented in Appendix A.[12] Finally, a crude representation of the permanent

nutricline was used to close the nitrogen budget of themodel. Below 120 m, inorganic nitrogen concentrations arerelaxed to the deep-ocean value of 30 mmol-N m�3 on atimescale of 1 day. As with the relaxation timescale for thepermanent thermocline, it was found that variations in thenutricline relaxation timescale do not qualitatively affectthe model output.

2.3. Atmospheric Model

[13] The ecosystem and upper-ocean models are driven,respectively, by atmospheric radiative fluxes and bysurface mechanical and buoyancy fluxes. These fluxesare derived from a stochastic atmospheric model, de-scribed in detail in Appendix B, which producessynthetic time series of fractional cloud cover (c) and10 m air temperature (Ta), humidity (q), and windspeed (U). Model parameters were estimated from21 years of 3-hourly observations at OSP. For Ta, q,and U, the model was constructed to reproduce thefirst- and second-order moments (mean, standard devi-ation, lagged cross correlations) of the observed data;fractional cloud cover (measured in oktas) is modeledas a nine-state Markov chain with monthly varyingtransition probabilities.[14] Top of the atmosphere solar flux is calculated based

on latitude, date, and time of day using standard astronom-ical formulae. Surface insolation is then determined using atransmission coefficient depending on zenith angle andfractional cloud cover, following the formulation of Dobsonand Smith [1988] (which in fact was estimated using datafrom OSP).[15] The net outgoing longwave radiation (QL) from the

ocean surface depends on cloud cover, sea surface andatmospheric boundary layer temperatures, and boundarylayer humidity, calculated using the recent parameterizationof Josey et al. [2003],

QL ¼ �sSB Ts þ 273:15Kð Þ4� 1� aLð ÞsSB

� Ta þ 273:15K þ 10:77c2 þ 2:34c�

�18:44þ 0:84 Tdew � Ta þ 4:01Kð Þg4; ð2Þ

where � = 0.98 is the emissivity of the sea surface, aL =0.045 is the sea surface longwave reflectivity, sSB is theStefan-Boltzmann constant, and Tdew is the dew pointtemperature. Note that equation (3) assumes temperaturesTs, Ta, and Tdew in degrees Celsius.

[16] The wind stress t, sensible heat flux (QSH), and latentheat flux (QLH) are calculated from the standard bulkformulae,

t ¼ raCDU2; ð3Þ

QSH ¼ raCHcpU Ta � Tsð Þ; ð4Þ

QLH ¼ CELv q� qs Tað Þð Þ; ð5Þ

where ra is the surface atmospheric density, cp is the specificheat capacity of air, Lv is the latent heat of vaporization, andqs(Ta) is the saturation humidity at 10 m. The 10-m bulktransfer coefficients CD, CH, and CE are taken from theexpressions given by Large [1996], also based largely onobservations at OSP,

103CD ¼ 2:70

Uþ 0:142þ 0:764U ; ð6Þ

103CH ¼32:7C

1=2D ; QSH 0

18:0C1=2D ; QSH > 0

8<: ; ð7Þ

103CE ¼ 34:6C1=2D : ð8Þ

3. Results

[17] Three 1100-year integrations of the stochasticupper-ocean/ecosystem model were carried out for ironlimitation parameter values LFe of 0.26, 0.28, and 0.5,corresponding, respectively, to iron-limited, intermediate,and nitrogen-limited systems. In all three simulations, thelight limitation factor in equation (19), averaged over thelength of a day and the depth of the euphotic zone,varied between 0.05 and 0.4, with an average near0.2 and a standard deviation of 0.08. Therefore, ironlimitation is effectively removed with LFe above 0.4, andthe relative importance of light and iron limitation toecosystem dynamics can be expected to depend sensi-tively on the value of LFe between 0.1 and 0.3. Thevalue LFe = 0.26 was found to yield the best simulationsof ecosystem evolution at OSP, primarily in terms of therealized annual cycles of phytoplankton biomass anddissolved nitrate. A model year is denoted nitrogenlimited if at some point in the year N concentrationsdropped below the threshold for nitrogen abundance tobecome the limiting factor; from equation (19), assumingthe surface layers to be light-replete in the daytime, thisthreshold is

Nthresh ¼knLFe

1� LFe: ð9Þ

Otherwise, a year is said to be iron-limited. All threeintegrations were driven by the same realization of the


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stochastic atmospheric model. Output data were saved daily,and to remove the effects of initial transients, the first100 years of each integration were discarded beforeanalysis. Because of the externally imposed seasonal cycle,the statistics of model variables are cyclostationary ratherthan strictly stationary. That is, the joint distributions areinvariant under time translations of integer multiples of1 year, but not under arbitrary time translations.

3.1. Physical Parameters

[18] Figure 3 displays the model SST and daily maxi-mum MLD as a function of calendar day for all years ofthe 1000-year integration. The variability of these varia-bles resembles that observed at OSP, although comparisonwith Figure B1 in Appendix B indicates that the modelSST is somewhat warmer in the winter than is observed,and displays somewhat less variability. The annual cyclesof the mean and standard deviation of T for the upper125 m of the model are displayed in Figure 4. Theannual cycle of the mean illustrates the development anddeepening of the shallow seasonal thermocline over thesummer and its erosion in the late fall/early winter. Thegreatest variability in model MLD is in the spring,associated with variations in the timing of the develop-ment of the seasonal thermocline (Figure 3). The primesource of variability in subsurface temperature, on theother hand, is associated with the onset of mixing in theautumn, as is indicated by the localized maximum inthe standard deviation along the seasonal thermoclinefrom mid-summer to early winter. This variability isqualitatively in agreement with the results of Alexanderand Penland [1996, Figure 4].[19] The temporal structure of variability in MLD and

SST can be characterized by the lagged autocorrelation

functions (acf), presented in Figure 5. For variables x andy, the lagged cross-correlation function at lag t on year dayt0 is defined as

cxy t; t0ð Þ ¼y t0 þ tð Þ � my t0 þ tð Þ

� �x t0ð Þ � mx t0ð Þð Þ

D Esy t0 þ tð Þsx t0ð Þ ; ð10Þ

where mx(t) and sx(t) (my(t) and sy(t)) are, respectively, themean and standard deviation of x (of y) at time t, and theangle brackets h� � �i denote ensemble average overobservations at year day t0. By definition, positive tcorresponds to x leading y. For t < 0, cxy(t, t0) characterizesthe influence (in a linear sense) of past values of y on thepresent (t = t0) value of x; for t > 0, cxy(t, t0) characterizesthe influence of the present (t = t0) state of x on future valuesof y. The acf of x is obtained by taking y = x in equation (10).Note that because the correlation of x at day t0 with x somet days later equals the correlation of x at day t0 + t with xsome t days earlier, the acf is symmetric,

cxx t; t0ð Þ ¼ cxx �t; t0 þ tð Þ: ð11Þ

By definition, the acf takes the value 1 at t = 0 andasymptotes to zero as jtj increases. The rate at which thisdecay occurs is a measure of the memory of the system:The more rapid the decrease, the more readily therelevance of the present state to the future trajectory ofthe system (or the relevance of the past to the presentstate) decreases. The decay of the acf with increasing jtj isnot necessarily monotonic; if the process x containsdominant oscillatory components, these will be reflectedin oscillations of the acf.[20] As with the mean and standard deviation of these

variables, the lagged acfs of MLD and SST are not station-ary but contain prominent annual cycles. In general, SSTfluctuations have longer memories than do MLD fluctua-tions, and anomalies in both MLD and SST have longermemories in the fall and winter (when the mixed layer isdeep) than during the spring and summer (when there is ashallow seasonal thermocline). In particular, spring andsummer fluctuations in MLD decorrelate after just a fewdays. The relatively long-term memory in winter vanishessuddenly in the spring as the mixed layer shoals, anddevelops again as the mixed layer deepens in the fall.

Figure 3. Model output MLD and SST as a function ofcalendar day for the 1000-year simulation.

Figure 4. Annual cycles of (left) mean and (right) standarddeviation of model temperature (�C).

Figure 5. Annual cycles of lagged autocorrelation func-tion for MLD and SST.


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Inspection of the time series (not shown) indicate thepresence of intraseasonal fluctuations in MLD throughoutthe year, while substantial interannual variability appearsonly in wintertime; this leads to wintertime MLD decorre-lation times that are longer than those in the summer.Conversely, the simulated SST time series is characterizedby levels of subseasonal variability in the wintertime thatare markedly lower than those in the summer, and byinterannual variability in all seasons; together, these com-bine to yield SST autocorrelation times that are longer thanthose for MLD.[21] In fact, inspection of the 21-year observational record

(Appendix B) indicates that the mixed layer model under-estimates both interannual variability and wintertime sub-seasonal variability in SST. As the model is forced byfluctuations with decorrelation times on the order of days,and not with lower-frequency variability due to, for exam-ple, ENSO or the Pacific Decadal Oscillation, it is notsurprising that low-frequency variability in SST should beunderestimated. The simple representation of the permanentpycnocline by relaxation processes toward fixed profileswill also presumably contribute to the underestimation ofSST variability, especially in winter when the mixed layer isdeep. Cummins and Lagerloef [2002] note the presence ofconsiderable variability in the depth of the permanent

pycnocline on both intra-annual and interannual timescales;this variability is suggested to arise from, for example,fluctuations in Ekman pumping velocity, the passage ofmesoscale eddies, and baroclinic tides.

3.2. Iron-Limited Regime

[22] When the iron limitation parameter LFe is set to 0.26,never in the 1000-year simulation is the summer nitrogendrawdown sufficient to initiate nitrogen limitation. Figure 6displays the surface-layer values of P1, P2, Z1, D, NO3, andNH4 as a function of calendar day for each year of thissimulation. The small size class of phytoplankton displays aweak mean annual cycle, as is generally observed at OSP[e.g., Harrison et al., 1999]; a small mean springtimeincrease in P1 biomass is accompanied by a maximum invariability. The surface microzooplankton biomass reachesa maximum in the late spring, shortly after that of P1. Likethe small size class of phytoplankton, the variability of Z1 isgenerally small (compared to the mean value), and maximalin the spring. In contrast, the weak diatom bloom (P2, notescale change) that occurs in late summer is highly variable;we will return to this point later.[23] Figure 7 displays profiles of the annual cycles of the

means and standard deviations of ecosystem model varia-bles over the upper 125 m of the model domain. Annualvariability in the mean of P1 extends down through the

Figure 6. Model output surface layer values of P1, P2, Z1,NO3, NH4, and D as a function of calendar day for LFe =0.26 (iron limitation).

Figure 7. Profiles over the upper 125 m of the modeldomain of annual cycles in mean (left) and standarddeviation (right) of P1, P2, Z1, NO3, NH4, and D, for LFe =0.26. All panels are in mmol-N m�3.


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upper part of the water column. The early spring maximumin the standard deviation of P1 is coincident with themaximum in the mean, reflecting significant variability inthe springtime mixed layer depth (as this determines therelative importance of iron and light limitation). The annualcycle in the mean microzooplankton abundance lags that ofP1, while the corresponding annual cycles in the standarddeviations are approximately coincident. On average, am-monium concentrations decrease in the upper part of thewater column and increase at the base of the mixed layerover the summer, peaking just before the onset of wintermixing; variability is dominated by variations in the timingof winter mixing and in springtime shoaling of the mixedlayer. The mean profile of nitrate displays a late summerminimum throughout the mixed layer and a pronouncednutricline; variability is concentrated along the base of thewintertime mixed layer and reflects interannual variabilityin the depth of wintertime mixing. When plotted with thesame color scale as used in the nitrogen-limited regime(Figure 12 in section 3.3), the mean and standard deviationof P2 are too small to be evident in Figure 7.

[24] Plots of the lagged autocorrelation functions for sur-face P1, Z1, and N are given in Figure 8. The existence ofpredator/prey oscillations in the late spring and early summerbetween P1 and Z1 is confirmed by the presence of alternatingbands of positive and negative correlations on either side ofthe lag t = 0 line. The phasing of these oscillations israndomized by the environmental fluctuations, and so theydo not appear in the mean profiles. Predator/prey cycles arealso evident in Figure 9, which illustrates the lagged crosscorrelations between P1 and Z1 (such that positive t corre-sponds to P1 leading Z1). The period of the oscillationsappears to be minimum when the MLD is smallest (compareFigure 3). The long late-summer memory of Z1 indicates thatwhat little variance Z1 displays at this time is primarily oninterannual timescales. Finally, it is clear that the variance inN, for LFe = 0.26, is primarily on interannual timescales, asthe acf remains near 1 on subseasonal timescales. Because thesystem is iron limited, N is largely decoupled from thesubseasonal fluctuations in P1 and P2.[25] In general, the mean annual cycles of P1 and Z1 for

LFe= 0.26 are in qualitative agreementwith the simulations ofDenman and Pena [2002],Denman [2003], andPena [2003],in which the atmospheric forcing followed smooth diurnaland annual cycles. Furthermore, as variability inP1 and Z1 arerelativelyweak, themean annual cycles are representative of atypical annual cycle. In contrast, the size of the small latesummer diatom bloom displays substantial interannual vari-ability (Figure 10). Considerable interannual variability in thesummertime drawdown of silicate has been observed at OSP[Wong and Matear, 1999], with the observation of years inwhich an almost complete exhaustion of silicate occurs insurfacewaters. This interannual variability has been attributedto episodic aeolian delivery of iron to the ocean surface,enhancing diatom growth [e.g., Boyd et al., 1998; Bishop etal., 2002]. The present study suggests that considerableinterannual variability in peak diatom biomass (and thus insilicate drawdown) can result simply from fluctuations in thephysical forcing of the upper ocean, with no episodic ironfertilization. Such episodic inputs of iron may play a role inthe interannual variability in phytoplankton biomass in thenortheast subarctic Pacific, but the present study suggests thatconsiderable interannual variability occurs even in theirabsence. A quantitative assessment of the relative importanceof the two processes in producing interannual variabilityrequires the inclusion of silicate as a prognostic variable inthe model, and is beyond the scope of the present study.

3.3. Nitrogen-Limited Regime

[26] The surface P1, P2, Z1, NO3, NH4, and D concen-trations simulated by the model for LFe = 0.5 (no iron

Figure 8. Annual cycle of the autocorrelation function ofsurface P1, Z1, and N for LFe = 0.26 (iron limitation) andLFe = 0.5 (no iron limitation).

Figure 9. Annual cycle of lagged cross correlationbetween P1 and Z1 for LFe = 0.26 and LFe = 0.5. A positivelag time corresponds to P1 leading Z1.

Figure 10. Variability of P2 over a typical 50-year periodfor LFe = 0.26.


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limitation) are plotted as a function of calendar day inFigure 11. In contrast to the iron-limited case consideredabove, for LFe = 0.5, summer nitrate drawdown is suffi-ciently large to lead to nitrate limitation. The shift fromiron-limited to nitrogen-limited conditions is also evidentin the surface values of P1, P2, Z1, and D. While theannual cycle in the mean of P1 is generally similar to thatfor LFe = 0.26, the variability is considerably greater. Asummertime minimum in surface small phytoplanktonabundance follows a generally modest spring/early sum-mer bloom, and is followed by a secondary smallerautumn bloom, as is evident from Figure 11. The autumnbloom is due to nitrate entrained into the surface waters asthe mixed layer deepens (as is commonly found in modelsof nitrogen-limited regimes). In contrast to the small late-summer P2 blooms characteristic of the iron-limited re-gime, for LFe = 0.5, large P2 blooms occur in late spring/early summer, at which time the large size fractiontypically accounts for at least half of the phytoplanktonbiomass. Blooms in P2 typically follow the early summerblooms of P1, as is clear from inspection of the trajectoriesor the lagged cross-correlation function of P1 and P2 (notshown). The magnitude of the P1 bloom is limited bygrazing pressure from Z1, the biomass of which increasesin response to increasing prey abundance. In fact, through-out the annual cycle, the mean and standard deviation of

surface microzooplankton concentrations are significantlyhigher for LFe = 0.5 than for LFe = 0.26 [cf. Denman andPena, 2002]. A second small maximum in Z1 occurs inwinter following the autumn phytoplankton bloom.[27] Profiles of the annual cycles of the means and

standard deviations of P1, P2, Z1, NO3, NH4, and D overthe upper 125 m of the model appear in Figure 12. Thespring and autumn blooms are apparent in the mean annualcycle of P1, along with a third deep maximum in thesummer just below the seasonal thermocline where lightand nitrate are both sufficiently abundant to support signif-icant phytoplankton growth (similar to the subsurface chlo-rophyll maximum characteristic of low nitrate subtropicalgyres). The P2 bloom also extends to depth and persistsalong the base of the mixed layer after surface nutrientshave been depleted. Maxima of the annual cycle of standarddeviations of P1 and P2 are colocated with maxima of theannual cycle in the means and primarily reflect fluctuationsin the timing of the blooms. A maximum in Z1 occursshortly after the spring bloom in P1 as microzooplanktonstocks grow in response to abundant phytoplankton avail-ability. A maximum in the standard deviation of Z1 followssomewhat later, associated with variability in the timing ofthe collapse of the springtime Z1 populations. As was thecase for LFe = 0.26, the greatest values of the standarddeviation of NO3 occur in wintertime at the base of themixed layer; these are larger for LFe = 0.5 because ofthe enhanced vertical gradient of NO3 resulting from

Figure 11. As in Figure 6 for LFe = 0.5. Note that thescales of the y axes differ from those of Figure 6.

Figure 12. As in Figure 7 for LFe = 0.5. Note that thesame contour intervals are used both in this figure and inFigure 7.


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the summertime drawdown of nitrate in the euphotic zoneevident in the mean annual cycle. Ammonium concentra-tions peak in early summer at the base of the mixed layer,tracking subsurface maxima in P1, P2, and Z1. Variability inNH4 peaks at depth shortly after variability in phytoplank-ton and zooplankton abundance. Maxima of the mean andstandard deviation of D occur at depth shortly after those ofP2.[28] The annual cycles of the acfs of P1, Z1, and N for

LFe = 0.5 are illustrated in the right-hand panels of Figure 8.There is still evidence of predator/prey oscillations betweenP1 and Z1, but these are weaker than in the iron-limitedregime; this behavior is also apparent in the lagged cross-correlation function between P1 and Z1 (Figure 9). The mid-to late-summer memories of P1 and Z1 are longer for LFe =0.5 than for LFe = 0.26, with no predator-prey oscillationsafter the onset of nutrient limitation. This change reflects theimportance of interannual variability relative to subseasonalvariability for the period following the onset of nutrientlimitation. In contrast, the memory of surface N is muchshorter during this period in the nitrogen-limited regimethan in the iron-limited regime.[29] In general, the variability of each ecosystem model

variable around its annual mean is significantly greater inthe nitrogen-limited regime than in the iron-limited regime,so in the former regime a typical year will look less like anaverage year than in the latter. As well, the distributions ofboth P1 and Z1 display marked bimodality in late spring,reflecting variations in the timing of the drawdown ofsurface nutrients to limiting values. During this time period,the average annual cycle is a particularly poor representa-tion of overall variability. Furthermore, the distribution ofP2 is markedly asymmetric about its mean, so the mean ofP2 generally represents neither a typical nor a most likely

value. The effects of atmospheric fluctuations on the eco-system dynamics are both quantitative and qualitative.

3.4. Intermediate Regime

[30] Figure 13 shows surface N concentrations for anarbitrary 100-year period for values of the iron limitationparameter LFe of 0.26, 0.28, and 0.5. The first and third ofthese correspond to the iron-limited and nitrogen-limitedregimes discussed above; the second is intermediate. It isclear from Figure 13 that for this intermediate value of theiron limitation parameter, the model is not consistently iron-limited or nitrogen-limited, but alternates between theseregimes on interannual to interdecadal timescales. For thisvalue of LFe, phytoplankton growth rates are sufficiently highto draw down nitrogen abundance to the point thatN becomeslimiting in some years. In other years, iron abundance is at alltimes the limiting factor. The variability of N, P1, P2, Z1, andD for LFe = 0.28 is intermediate between that for LFe = 0.26and LFe = 0.5, and is thus not shown.[31] Whether the system is iron- or nutrient-limited in a

given summer is largely determined by the history of win-tertime mixing over the preceding winters. A linear regres-sion model for the summertime maximum N using thewintertime maximum MLD of the five previous winters aspredictors has a cross-validated hindcast correlation skill ofabove 0.7 (this skill is degraded if either more or fewerprevious winters are included). Most of the remaining vari-ability in summertime minimum N can be attributed to thevicissitudes of mixing and cloudiness during the previousspring.[32] From Figure 13 it is clear that iron-limited (or

nitrogen-limited) years may occur individually or for anumber of years in a row. Figure 14 displays a histogramof the duration of iron-limited and nitrogen-limited episodesfor the 1000-year integration with LFe = 0.28. The distri-bution of episode lengths falls off approximately exponen-tially for both iron- and nitrogen-limited regimes; these

Figure 13. Plot of the surface concentrations of N formodel years from 500 to 600, for values of the ironlimitation parameter LFe of 0.26, 0.28, and 0.5 (correspond-ing respectively to iron-limited, intermediate, and nitrogen-limited regimes). Note that all three integrations were drivenby the same realization of the empirical stochastic atmo-sphere model.

Figure 14. Histogram of the duration of nitrogen-limited(open bars) and iron-limited (solid bars) episodes with LFe =0.28.


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episodes do not occur with any dominant timescale. Note thatvariations between iron-limited and nitrogen-limitedregimes, occurring on interannual to decadal timescales, areexcited by stochastic variability in the atmospheric modelthat is characterized by a decorrelation timescale on the orderof days (Appendix B, Figure B2). Because the atmosphericmodel does not represent variability on seasonal scales andlonger (associated with both internal low-frequency extra-tropical dynamics and the midlatitude response to tropicalforcing), and because the lack of an explicit representation ofEkman pumping in the model precludes interannual andinterdecadal fluctuations in the depth of the permanentpycnocline [Cummins and Lagerloef, 2002], estimates ofinterannual to decadal variability produced by the model arelikely to underestimate those of the real system. The simpletreatment of iron limitation in the present study presumablyalso contributes to an underestimate of interannual variabil-ity, as the effects of episodic injections of iron into theeuphotic zone by mixing from below or aeolian depositionfrom above are not accounted for.

3.5. ‘‘Background-Bloom’’ Dynamics

[33] Over the last 15 years, it has been recognized that asthe total biomass of phytoplankton in a water sampleincreases, the relative proportion of small phytoplanktondecreases [e.g., Denman and Pena, 2002; Denman, 2003,and references therein]. That is, concentrations of smallphytoplankton tend not to vary much around a backgroundlevel, while blooms are dominated by the larger size class.This ‘‘background-bloom dynamics’’ was hard-wired intoearlier versions of the present ecosystem model by diag-nostically partitioning the single phytoplankton compart-ment into two classes, based on total phytoplanktonbiomass. While this parameterization produced reasonablesimulations for environmental conditions characteristic ofthe mean state at OSP, it proved to be problematic for thesimulation of blooms. In particular, at the peak of asimulated bloom, the grazing of microzooplankton on thesmall size fraction of phytoplankton reduced the total

plankton biomass, thereby changing the relative partitioningof large and small size classes and in essence relabelinglarge phytoplankton as small phytoplankton. By introducinga second prognostic phytoplankton variable, the presentmodel avoids this problem. Furthermore, the ‘‘back-ground-bloom’’ behavior in the present model can beinvestigated. Figure 15 displays a plot of the biomass ofthe small size fraction of the phytoplankton as a function ofthe total phytoplankton biomass for the iron-limited regime(LFe = 0.26). Two populations are evident. In one, lyingalong the 1:1 diagonal of the plot, diatoms are essentiallyabsent and the small size class of phytoplankton dominatesthe ecosystem. In the other, diatoms are present and therelative contribution of P1 decreases as the total biomassincreases. In fact, observations at OSP and in the NorthAtlantic also suggest the presence of two statistical popu-lations, respectively, with and without abundant diatoms, asis illustrated in Figure 3 of Denman and Pena [2002]. Theparameterization developed by Denman and Pena [2002]which diagnostically partitions the phytoplankton biomassinto large and small size classes falls between these twopopulations, thereby representing neither.

3.6. Export Fluxes

[34] A quantity of central importance in understanding therole of the oceanic biosphere in the global carbon cycle is therate atwhich particulate organicmatter sinks out of the surfacewaters, denoted the export flux. In the present model, theexport flux through 100 m consists of two primary compo-nents: (1) the net flux of D across the 100-m-depth level, and(2) the net flux to mesozooplankton (grazing on P2 and Z1minus excretion toNH4), which is assumed to be lost from thesurface waters via sinking fecal pellets, mortality, or meso-zooplankton sinking below the permanent pycnocline duringdiapause. Figure 16 displays histograms of annually averagedexport fluxes and export ratios (defined as export flux divided

Figure 15. Biomass of P1 plotted against the totalphytoplankton biomass P1 + P2 for LFe = 0.26.

Figure 16. Histograms of export fluxes and export ratiosfor 1000-year integrations in the iron-limited and nitrogen-limited regimes.


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by total new production) for iron-limited and nitrogen-limitedregimes. The mean export flux in the iron-limited regime,0.35 mol-Nm�2yr�1, is in good agreement with the observedvalue of 0.29 mol-Nm�2yr�1 at OSP, obtained from 1 year ofdrifting sediment trap data [Denman and Pena, 1999]. The35% increase in mean export flux in the nitrogen-limitedregime relative to the iron-limited regime is in good agree-ment with the results of Denman and Pena [2002]. Thisincrease in the annual mean export flux is consistent with theincrease in biomass of P2 for LFe = 0.5 relative to LFe = 0.26,as all diatom mortality is assumed to feed directly into thedetritus pool. Furthermore, because large diatom bloomsoccur in the nitrogen-limited regime and not in the iron-limited regime, the variability of export fluxes ismuch greaterin the former than in the latter, although the variability ofexport fluxes in the iron-limited regime is presumably under-estimated in this study due to the simple treatment of ironlimitation. In real HNLC regions, pronounced increases inexport flux may follow episodic inputs of iron into theeuphotic zone through entrainment from below or aeoliandeposition. In both iron-limited and nitrogen-limited regimes,the annual export flux time series have autocorrelation e-folding times of about one year. Not surprisingly, the distri-bution of export fluxes for L= 0.28 was intermediate betweenthe iron-limited and nitrogen-limited distributions. In gener-al, export ratios displayed less variability than export fluxes,both within and between integrations.[35] Estimates of the residence time of nitrate in the upper

part of the water column can be obtained by dividing thetotal stock of N in the upper 100 m by the export fluxthrough this depth. Values of about 3.3 and 1 years areobtained for the iron- and nitrogen-limited regimes, respec-tively. The fact that these values are on the order of a yearand greater is consistent with the presence of the significantinterannual variability in N evident in Figure 13.

4. Discussion and Conclusions

[36] In this study, we have extended the work of Denmanand Pena [1999, 2002] to consider the dynamics of acoupled upper-ocean/ecosystem model driven by an em-pirical stochastic model of the atmosphere, built to matchas closely as possible the joint distributions of the ob-served variability at Ocean Station Papa (up to second-order moments). Using a simple representation of ironlimitation of primary productivity, 1000-year integrationswere considered for parameter values corresponding toiron-limited, nitrogen-limited, and intermediate regimes.It was shown that the model is able to produce areasonable representation of the physical component ofthe upper ocean at OSP. The dynamics of the smallphytoplankton and zooplankton in the parameter regimecorresponding to iron limitation were not found to bequalitatively affected by atmospheric variability, althoughthe large phytoplankton size class (‘‘diatoms’’) displayedconsiderable interannual variability. This interannual vari-ability is consistent with interannual variability in surfacesilicate concentration observed at OSP, where instances oflarge summertime silicate drawdown have previously beenassociated with episodic iron fertilization by aeolian dust

[Boyd et al., 1998; Bishop et al., 2002]. In contrast,atmospheric variability had a qualitative effect on theecosystem dynamics in the nitrogen-limited regime. Theecosystem variables display considerable (and generallynon-Gaussian) variability around the mean annual cycle,so that average model years do not resemble either typicalor most likely years. Furthermore, a feature of the sto-chastically driven model not present in earlier studies isthe existence of an intermediate regime in which thesystem moves between nitrogen limitation and iron limi-tation on interannual to interdecadal timescales. In theselast two regimes, the average annual cycle of ecosystemvariables cannot be expected to agree with the ecosystemresponse to annually averaged forcing. Finally, the meanand variability of export fluxes are found to be signifi-cantly higher in the nitrogen-limited regime than in theiron-limited regime.[37] Summer nitrogen depletion has not been observed at

OSP. In contrast, surface nitrogen is observed to be drawndown to limiting concentrations in late summer along thefirst �500 km of Line P westward away from thecontinental shelf; station P12 (Figure 1) is characteristic.Furthermore, between �500 km and �1000 km alongLine P, there is considerable interannual variabilityin summertime surface nitrogen depletion, such that sur-face waters are nitrogen deplete in some summers andnitrogen replete in others [e.g., Whitney and Freeland,1999, Figure 6]; a characteristic station is P20. Theempirical stochastic atmosphere model was built usingdata from OSP, and the parameters of the upper oceanand ecosystem models were tuned so that the output forLFe = 0.26 resembled observed variability at OSP; there isno a priori reason to believe that these parameters shouldbe invariant across the subarctic northeast Pacific. How-ever, qualitatively, LFe can be imagined to be a proxy fordistance along Line P, decreasing westward from thecontinental shelf. The observed increase in wintertimemaximum surface nitrate concentrations westward alongLine P [Whitney and Freeland, 1999] is reproduced in themodel, from the nitrogen-limited regime off the NorthAmerican continental shelf, through the intermediate re-gime, and on to the iron-limited regime around OSP.[38] Previous studies of interannual to interdecadal var-

iability in the physical and biogeochemical properties ofthe upper waters of the northeast subarctic Pacific[e.g., Mantua et al., 1997; Whitney et al., 1998; Whitneyand Freeland, 1999; Haigh et al., 2001; Cummins andLagerloef, 2002] have highlighted the role of large-scale,low-frequency climate processes (e.g., ENSO or the Pa-cific Decadal Oscillation) in producing this variability.Similar arguments have been put forward for the role ofthe North Atlantic Oscillation in driving interannual var-iability in the physical and biogeochemical states of theNorth Atlantic Ocean [e.g., Gruber et al., 2002]. Thepresent study has demonstrated that high-frequency atmo-spheric variability decorrelating on synoptic timescales canproduce considerable variability on interannual to interde-cadal scales. This variability would not be expected to bespatially coherent on the basin scale, but could be asignificant component of the interannual variability at


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individual stations. Furthermore, this study suggests thatthe marked interannual variability in silicate drawdown(and thus diatom production) observed at OSP, typicallyascribed to episodic iron fertilization by aeolian dust, canbe produced by the response of the upper ocean to rapidlydecorrelating fluctuations in physical forcing from theatmosphere. Such episodic fertilization events may in factbe an important source of this interannual variability [e.g.,Bishop et al., 2002], but the present study suggeststhat other sources of variability may also contribute.Another potentially important contributor to interannualvariability is episodic entrainment of deep iron into theupper ocean, but the simple treatment of iron in this studyprecludes an estimate of the significance of this process.An interesting extension of this study would be theinvestigation of the effect on ecosystem dynamics of amore realistic representation of iron chemistry.[39] The analysis of model simulations in this study has

concentrated on first- and second-order statistics such asmeans, standard deviations, and lagged autocorrelationsand cross correlations; this was done because of therelative ease of interpretation of these statistics. Of course,the dynamics of the model contain significant nonlinear-ities, and second-order statistics are generally inadequatefor a complete characterization of a nonlinear system [e.g.,Ghil et al., 2002; Monahan et al., 2003]. Inspection ofFigures 6 and 11 indicates that although the forcingvariables have an approximately Gaussian distribution,nonlinearities in the upper-ocean/ecosystem model dynam-ics produce markedly non-Gaussian output. A more com-plete analysis of the coupled upper-ocean/ecosystemdynamics would involve the use of more sophisticatedstatistical tools (e.g., multichannel singular spectrum anal-ysis, suitably adapted to account for the cyclostationarityof the time series). Also, bifurcations in the dynamics ofthe system were only discussed briefly in the presentstudy, in the context of predator-prey oscillations. A morethorough exploration of parameter space, characterizingthe bifurcation structure of the model within the range ofphysically and ecologically plausible parameters, would bea useful extension of the present study (e.g., Denman[2003] for a slab model). Other natural extensions of thepresent study would be investigations of the response ofthe system to global warming (as in the work of Denmanand Pena [2002] and Pena [2003]), to iron fertilization (asin the work of Edwards et al. [2004]), or to atmosphericforcing with an explicit representation of interannual tointerdecadal variability (as in the work of Haigh et al.[2001]). Inclusion of silicate and iron as prognostic vari-ables would allow a quantitative diagnosis to be made ofthe relative importance of mixing variability and episodicaeolian dust fertilization in producing interannual variabil-ity in silicate drawdown.[40] The inclusion of stochastic atmospheric variability

increases the complexity of the model only modestly relativeto that studied by Denman and Pena [2002] or Denman[2003], but it results in a system displaying much richervariability. The price that must be paid is a substantialincrease in the complexity of the model output, along witha shift from the familiar deterministic conception of the

dynamics to a perhaps less familiar distributional one.Variability on a broad range of timescales is an ubiquitousfeature of both the physical and biogeochemical componentsof the climate system. Improving our understanding of thenature, origin, and implications of this variability is animportant challenge for the climate research community[Imkeller and Monahan, 2002].

Appendix A: Ecosystem Model Equations

[41] The set of differential equations governing the eco-system components at each model layer is

dP1

dt¼ nP1 � g1

P1

P1 þ pDDZ1 � mpaP1; ðA1Þ

dP2

dt¼ nP2 � g2

Z2

P2 þ Z1P2 � mpa þ mpd

P2; ðA2Þ

dZ1

dt¼ gag1Z1 � g2

Z2

P2 þ Z1Z1 � mzaZ1; ðA3Þ

dNO3

dt¼� n P1 þ P2ð ÞRNO3

NO3

NO3 þ NH4

þ hNH4 þ1

t zð Þ NO3 � NO3

; ðA4Þ

dNH4

dt¼� n P1 þ P2ð Þ 1� RNO3

NO3

NO3 þ NH4

� �þ reD

þ mpa P1 þ P2ð Þ þ mzaZ1 þ mcag2Z2 � hNH4; ðA5Þ

dD

dt¼ mpdP2 þ 1� gað Þg1Z1 � g1

pdD

P1 þ pdD� Z1 � reDþ ws

dD

dz:

ðA6Þ

The specific growth rates of both P1 and P2 are assumed forsimplicity to be equal and given by

n ¼ nm minN

kn þ N

� �;

1� exp � aI IPAR

nm

� �; LFe

�; ðA7Þ

where nm is the maximum specific growth rate, IPAR is theintensity of photosynthetically active radiation, and each ofthe arguments of the min function ranges between 0 and 1.The relative preference of the phytoplankton for the uptakeof ammonium relative to nitrate is described by a relativepreference function [Denman, 2003],

RNO3¼ a

aþ NH4

: ðA8Þ

The grazing rate of the microzooplankton is given by

g1 ¼ rmP1 þ pDDð Þ2

k2p þ P1 þ pDDð Þ2; ðA9Þ


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where kp is the grazing half-saturation constant and pD is thegrazing preference of D relative to P1; the grazing rate of themesozooplankton is

g2 ¼ rcP2 þ Z1ð Þ2

k2z þ P2 þ Z1ð Þ2: ðA10Þ

The fraction of the material grazed by microzooplanktonthat is assimilated as Z1 biomass is denoted by ga; the rest(fecal pellets and ‘‘sloppy feeding’’) moves directly into thedetritus pool. The specific loss rates of phytoplankton andzooplankton to the ammonium pool are denoted mpa andmza, respectively, while the specific loss rate of P2 todetritus is denoted mpd. A fraction mca of mesozooplanktongrazing is excreted instantaneously into ammonium; theremaining fraction is assumed to contribute to biomass ofmesozooplankton (and higher trophic levels).[42] The concentration of nitrate below the permanent

nutricline is denoted by NO3, and the nutricline relaxationtimescale t(z) is infinite above 120 m and 1 day below120 m. As nitrification of NH4 into NO3 is observed to beinhibited in the euphotic zone [Ward, 2000], the specificnitrification rate is represented as

h zð Þ ¼ noxzn

znox þ zn; ðA11Þ

where nox is the maximum specific nitrification rate, z is thedepth, zox is the depth at which the noontime irradiance dropsto 0.3Wm�2, and n=10 [Denman, 2003]. This representationallows a sharp transition from low specific nitrificationrateswithin the euphotic zone to relatively large values below.[43] Finally, the temperature dependence of the growth,

grazing, and mortality rates (nm, rm, rc, mpz, mpd, mza, and re)are given by individualQ10 parameters, defined as the factorsby which the rates increase due to a 10�C increase intemperature. For example, for the phytoplankton growth rate,

nm Tð Þ ¼ nm 10�Cð ÞQ T�10�Cð Þ= 10�Cð Þ10;n : ðA12Þ

The Q10 factors for phytoplankton are set to 2, while thosefor zooplankton and bacteria are set to 3 [Denman andPena, 2002].

[44] Table A1 lists the ecosystem model parameter valuesused in this study; these are essentially the same as thoseused in the study of Denman and Pena [1999, 2002], inwhich detailed justifications of the choices of parametervalues are given.

Appendix B: Stochastic Atmosphere Model

[45] As described in section 2.3, the atmospheric variablesrequired to calculate the mechanical and buoyancy fluxesacross the air/sea interface are fractional cloud cover (c, inoktas), and 10 m air temperature (Ta), absolute humidity (q),and wind speed (U). The Ocean Station P data set used inthis study consists of 21 years (1960–1981) of 3-hourlyobservations of these variables, along with sea surfacetemperature (SST, Ts) and wind direction. Because the windspeed U is highly non-Gaussian, it is convenient to workwith the zonal wind (u) and meridional wind (v) individu-ally. The observed variables (Ts, Ta, q, u, and v) are plottedas functions of calendar day in Figure B1.[46] Table B1 displays the correlations between the sur-

face ocean and meteorological variables at OSP. Not sur-prisingly, v is positively correlated with q and Ta, reflectingthe advection of warm and moist (cold and dry) air bysoutherly (northerly) winds. Furthermore, because of thestrong thermal coupling between the atmospheric boundarylayer and the ocean surface, Ta and q are significantly

Table A1. Ecosystem Model Parameter Values

Parameter Value Unit

kw 0.04 m�1

kc 0.06 m�1 (mmol-N m�3)�1

aI 0.08 d�1 (Wm�2)�1

nm 1.5 d�1

kn 0.1 mmol-N m�3

mpa 0 d�1

mpd 0.1 d�1

rm 1.0 d�1

kp 0.75 mmol-N m�3

ga 0.7 -mza 0.1 d�1

ws 7.5 m d�1

re 0.1 d�1

pD 0.5 -rc 6.5 d�1

kz 2 mmol-N m�3

mca 0.3 -nox 0.01 d�1

LFe variable -

Figure B1. Plots of Ts, Ta, q, u, and v as a function of yearday for observed data at Ocean Station Papa from 1960 to1981.


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correlated with Ts. It is convenient that the stochasticatmosphere model should represent variability intrinsic tothe atmosphere, and not include variability associated withthe model variable Ts. Thus the linear dependence of Ta andq on Ts was removed by subtracting least squares regressionfits to Ts from these variables; the resulting residual varia-bles are denoted T0a and q0. The variables T 0

a, q0, u, and v are

not stationary, but are characterized by pronounced annualcycles in their means and standard deviations. These annualcycles were estimated by fitting sine/cosine pairs withperiods of 1 year, 6 months, 3 months, and 1.5 months toraw estimates of the mean and variance at each of the3-hourly bins over the year. The variables (T0a, q

0, u, v) werestandardized by subtracting the smooth annual cycle in themean, and then dividing by the smooth annual cycle in thestandard deviation; the resulting residual variables aredenoted by carets ( ). The standardization procedure wasnot applied to c, as it is measured in octas and is thus not acontinuous variable. Table B2 displays the correlations ofthe standardized variables among themselves and with c.The standardized variables (T 0

a, q0, u, v) display significant

cross correlations and are thus not modeled as independentprocesses (as was done by Alexander and Penland [1996]).On the other hand, the correlations between c and thestandardized variables are generally small, and furthermore,c is a discrete Markov chain rather than a continuousprocess. Thus c will be modeled as independent of theother meteorological variables.[47] To model the four-dimensional process X = (T 0

a, q0, u,

v), we assume that the process is stationary, Markov, andmultivariate Gaussian. That is, it is assumed that X is amultivariate Ornstein-Uhlenbeck process described by thestochastic differential equation

_X ¼ AXþ B _W; ðB1Þ

where A and B are constant 4 � 4 matrices and _W is afour-dimensional white-noise process with independentcomponents,

_Wi t1ð Þ _Wj t2ð Þ� �

¼ dijd t1 � t2ð Þ: ðB2Þ

The matrices A and B can be estimated from data usingLinear Inverse Modeling [Penland, 1996]. The assumptionof stationarity implies that

A XXT� �

þ XXT� �

AT þ BBT ¼ 0; ðB3Þ

and that

X t þ tð ÞXT tð Þ� �

¼ exp Atð Þ XXT� �

: ðB4Þ

Covariance matrices at lags 0 and t can be estimateddirectly from the data; an estimate of the matrix A thenfollows from equation (B4). Knowing A, the matrix Bcan be estimated from equation (B3). Equation (B1) canthen be integrated numerically using the estimatedmatrices A and B to generate arbitrarily long realizationsof X which have the same second-order statistics as theobservations. Numerical integration of stochastic differ-ential equations is described in detail by Kloeden andPlaten [1992]. If X is actually a Markov process, thenthe estimates of A and B should not depend on the valueof t used in equation (B4); this can be used as a test ofthe appropriateness of the Markov assumption. In fact,for the standardized OSP data, these matrices do dependsomewhat on the value of t considered; however, thestatistics of the synthetic X process are essentiallyinsensitive to this dependence. Estimates of the auto-correlation functions for the individual components of X,from observations and from the simulated time series, areplotted in Figure B2. The autocorrelation functions of thesynthetic variables do not match exactly those ofobservations; in particular, the obvious diurnal cycle inT 0a is not captured in the synthetic model. As well, the

synthetic time series do not reproduce the weak long-term memory evident in the autocorrelation functions ofthe observations beyond about 4 days lag time, arisingpresumably from the movement of large-scale air masses[Fissel et al., 1976]. The assumption that the data aremultivariate Gaussian is also not satisfied exactly. Inparticular, the joint distribution of T 0

a and q0 cannot beGaussian because the Clausius-Clapeyron equation puts atemperature-dependent upper limit on the humidity.Overall, however, there is broad agreement between thegross features of the distributions of the observed andsimulated variables.[48] The simulated time series (Ta, q, u, v) are obtained

from (T 0a, q

0, u, v) by undoing the standardization processdescribed above. The estimated smooth annual cycles inthe standard deviations are multiplied with the syntheticresidual processes, and the product is added to theestimated annual cycles of the means. The SST-dependentvariables Ta and q are constructed using the regressioncoefficients calculated above and the observed annualcycle of Ts. If it happens that Td > Ta, q is reduced tothe saturation humidity. If the model-generated value ofTs rather than the observed annual average value is usedin calculating Ta and q, slight flux mismatches cause themodel to drift to an unrealistic equilibrium state. The useof the annually averaged Ts effectively acts as a fluxcorrection to eliminate this drift.

Table B1. Correlations Between Atmospheric and Surface Ocean

Variables Measured at Ocean Station Papa

Ts Ta q u v c

Ts 1 0.92 0.79 0.01 0.013 0.08Ta 1 0.90 �0.07 0.21 0.14q 1 �0.16 0.28 0.27u 1 �0.156 �0.18v 1 0.11c 1

Table B2. Correlations Between Atmospheric Variables Stan-

dardized as Described in Text

T 0a

q u v c

T 0a

1 0.70 �0.18 0.50 0.12

q 1 �0.26 0.46 0.28

u 1 �0.16 �0.15

v 1 0.11

c 1


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[49] The fractional cloud cover c is modeled as a nine-state Markov chain. A Markov chain is a random process xthat can take one of a finite number of discrete states {s1,. . ., sM} such that the probability of the system being in agiven state at time ti+1 is determined entirely by the state ofthe system at time ti,

p xtiþ1¼ sjjxti ¼ sk

¼ qjk ; ðB5Þ

where by definition

XMj¼1

qjk ¼ 1: ðB6Þ

The set of numbers qjk describing the transition probabilitiesare referred to as the transition matrix. The states of theprocess c are the cloud cover in oktas. The distribution of cdisplays a marked seasonal cycle, such that c has a lowermean and higher variability in the winter than in thesummer. This nonstationarity was reproduced by stratifyingthe data into 12 calendar months and estimating the onetime step (3-hour) transition matrices individually for eachof these months. These estimates were obtained by simplycalculating, for month and for each of the nine cloud coverstates ci, the relative frequency at which the cloud coverstate 3 hours later is cj. Arbitrarily long synthetic time seriesof c were then generated using these monthly varyingtransition matrices: at the end of each 3-hour period, apseudorandom number y was drawn from a uniformdistribution between 0 and 1. If the present cloud cover

state was ck, then the next cloud cover state was cj for (theunique) j satisfying

Xj�1

i¼1

qik y <Xj

i¼1

qik : ðB7Þ

[50] Acknowledgments. A. M. and K. D. are supported by theNatural Sciences and Engineering Research Council of Canada, and bythe Canadian Foundation for Climate and Atmospheric Sciences. A. M. isalso supported by Canadian Institute for Advanced Research, and K. D. issupported by the U.S. Office of Naval Research (PARADIGM project). Theauthors would like to thank Jim Christian, Rana El-Sabaawi, Debby Ianson,Angelica Pena, and an anonymous referee for their helpful comments andadvice.

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��K. L. Denman, Canadian Centre for Climate Modeling and Analysis,

University of Victoria, P.O. Box 1700, STN CSC, Victoria, BC, V8W 2Y2Canada. ([email protected])A. H. Monahan, School of Earth and Ocean Sciences, University of

Victoria, P.O. Box 3055 STN CSC, Victoria, BC, V8W 3P6 Canada.([email protected])


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Impacts of atmospheric variability on a coupled upper-ocean//ecosystem …web.uvic.ca/~monahana/monahan_denman.pdf · 2004-06-16 · ocean/ecosystem model. [5] Section 2 of this paper