Impacts of Atmospheric Variability on a Coupled
Upper-Ocean/Ecosystem Model of the Subarctic
Northeast Pacific
Adam Hugh Monahan ([email protected])
School of Earth and Ocean Sciences
University of Victoria
P.O. Box 3055 STN CSC
Victoria, BC, Canada, V8P 5C2
and
Canadian Institute for Advanced Research
Earth Systems Evolution Program
and
Kenneth L. Denman ([email protected])
Canadian Centre for Climate Modelling and Analysis
University of Victoria
P.O. Box 1700, STN CSC
Vitoria, BC, Canada, V8W 2Y2
and
Institute of Ocean Sciences
Sidney, BC, Canada
Submitted to Global Biogeochemical Cycles
May 27, 2003
1
Abstract
The biologically-mediated flux of carbon from the upper ocean to below the permanent 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. A detailed quantitative understanding of the dynamics of the biological pump is therefore important,
particularly in terms of its potential sensitivity to climate changes and its role in these
changes via feedback processes. Previous studies of coupled upper-ocean/planktonic
ecosystem dynamics have considered models forced by observed atmospheric variability or by smooth annual and diurnal cycles. The second approach has the drawback
that environmental variability is ubiquitous in the climate system, and may have a
nontrivial impact on the (nonlinear) dynamics of the system, while the first approach
is limited by the fact that observed time series are generally too short to obtain statistically robust characterisations of variability in the system. In the present study, an
empirical stochastic model of high-frequency atmospheric variability (with a decorrelation timescale of less than a week) is estimated from long term observations at Ocean
Station Papa in the northeast subarctic Pacific. This empirical model, the second-order
statistics of which resemble those of the observations to a good approximation, is used
to produce very long (1000-year) realisations of atmospheric variability which are used
to drive a coupled upper-ocean/ecosystem model. It is found that fluctuations in atmospheric forcing do not have an essential qualitative impact on most aspects of the dynamics of the ecosystem when primary production is limited by the availability of iron,
although pronounced interannual variability in diatom abundance is simulated (even
in the absence of episodic iron fertilisation). In contrast, the impacts of atmospheric
variability are considerably more significant when phytoplankton growth is limited in
the summer by nitrogen availability, as observed closer to the North American coast.
Furthermore, the high-frequency variability in atmospheric forcing is associated with
regions in parameter space in which the system alternates between iron and nitrogen
limitation on interannual to interdecadal timescales. Both the mean and variability of
export production are found to be significantly larger in the nitrogen-limited regime
1
than in the iron-limited regime.
1
Introduction
The role of biological processes in the exchange of carbon between the ocean and the atmosphere is poorly understood, and remains a major source of uncertainty in attempts to
determine the climate system response to anthropogenic emissions of carbon dioxide and to
understand past climate variability (Houghton et al., 2001). In most of the World Ocean,
summertime primary production occurs in sufficient quantities to induce macronutrient depletion in the surface waters, with surface macronutrients being recharged by subsequent
winter mixing. However, in the surface waters of approximately 20% of the World Ocean,
primary production is not limited by the abundance of surface macronutrients; these areas
are usually referred to as High Nutrient/Low Chlorophyll (HNLC) regions. Major HNLC
regions are the equatorial Pacific, the Southern Ocean, and the subarctic Pacific. At present,
the leading hypothesis is that primary production in these oceanic provinces is limited by
the abundance of the micronutrient iron (e.g. Coale et al. (1996); Boyd et al. (2000)).
The dynamics of ecosystems in HNLC regions have attracted considerable interest in recent
years (e.g. Archer et al. (1993); Denman and Peña (1999, 2002); Signorini et al. (2001);
Edwards et al. (2003); Denman (2003)), motivated largely by the developing understanding
that changes in ocean-atmosphere carbon flux in these regions may play a key role in global
climate variability on centennial and longer timescales (e.g. Falkowski et al. (1998)).
Of the three major HNLC regions of the World Ocean, the subarctic northeast Pacific is the best observed. From 1956 to 1981, regular observations of meteorological and
oceanographic variables were made by Canadian weatherships at Ocean Station Papa (OSP;
145◦ W,50◦ N). As well, regular observations were made along a line between OSP and the
continental shelf off of Vancouver Island (denoted Line P; see Figure 1) by ships steaming to
and from OSP. Since the cancellation of the weathership program in the early 1980s, regular
2
oceanographic cruises on an approximately seasonal timescale have been made along Line P.
In consequence, sampling along this line has been carried out for a sufficiently long period,
and with sufficient resolution in time, that the variability of both physical and biogeochemical properties on seasonal to decadal timescales is becoming relatively well understood (e.g.
Whitney et al. (1998); Whitney and Freeland (1999)). In particular, summertime nitrogen
limitation has not been observed at OSP, while it is generally observed to occur closer to
shore in iron-replete waters.
The coupled physical and biogeochemical system of the upper ocean at OSP is a natural
candidate for modelling studies, as by oceanographic standards it is well constrained by data.
Previous studies have either modelled the response of the system to observed meteorological
forcing (e.g. Archer et al. (1993); Signorini et al. (2001)) or to smoothly-varying annual and
diurnal cycles (e.g. Denman and Peña (1999, 2002); Denman (2003)). The first of these
approaches has the drawback that only about 20 years of sufficiently high-resolution observations of meteorological variables at OSP exist, so is difficult to produce a robust statistical
characterisation of variability at OSP using observations alone. The second approach has the
disadvantage that it neglects the considerable synoptic-scale variability observed at Station
Papa (e.g. Fissel et al. (1976)), which may play an important role in the dynamics of both
the upper ocean and the ecosystem. In the present study, observations of meteorological variables from OSP are used to construct an empirical stochastic model of the atmosphere which
reproduces the statistics of the observed variability to a good approximation. This empirical
stochastic model is then used to drive a coupled upper-ocean/ecosystem model tuned to
represent conditions at OSP. Because arbitrarily-long realisations of atmospheric forcing can
be obtained, the upper-ocean/ecosystem model can be integrated to produce simulations
sufficiently long to obtain robust characterisations of variability on daily to interdecadal
timescales. Alexander and Penland (1996) used meteorological observations at OSP to build
an empirical stochastic atmospheric model with which they forced an upper-ocean model,
while Bailey and Doney (2001) investigated the effects of environmental fluctuations on a
3
simple biogeochemical model without a representation of upper-ocean dynamics. The present
study extends these previous studies by considering the effects of atmospheric variability on
a coupled upper-ocean/ecosystem model.
Section 2 of this paper describes in detail the upper-ocean and ecosystem models used
in this study, along with 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 the empirical stochastic model of the
atmosphere are given in Appendices A and B, respectively.
2
Coupled Upper-Ocean Physics/Ecosystem Model
The model considered in this study is composed of three main components: a one-dimensional
dynamical model of the upper ocean, an idealised dynamical ecosystem model, and an empirical stochastic model of atmospheric variability. The upper-ocean and ecosystem components
are coupled, and both are driven by the atmospheric model. We proceed to discuss these
components in detail.
2.1
Upper-Ocean Model
The present study follows Denman and Peña (1999, 2002) in using a Mellor-Yamada level
2.5 (MY2.5) model (Mellor and Yamada (1974, 1982)) to represent the upper ocean. The
performance of the MY2.5 model in modelling the turbulent upper ocean, relative to other
mixed-layer models, is discussed in Denman and Peña (1999). The model domain is 250 m
deep, consisting of 100 2.5-m thick layers. A constant background diffusivity of 1.5 ×10 −5
m2 s−1 was used, based on the value reported by Matear and Wong (1997). Incoming solar
radiation is partitioned into longwave (60%) and shortwave (40%) fractions. The longwave
fraction is entirely absorbed in the uppermost layer, while the shortwave fraction - which
is assumed to correspond to the photosynthetically active radiation (PAR) - is absorbed
4
throughout the water column. At each model level a fraction exp(− 12 kt (z)δz ) of the PAR
is absorbed by the water, where δz is the layer thickness and the attenuation coefficient
kt (z) depends on a constant background value for seawater and on the concentration of
phytoplankton (P1 + P2 , defined in Section 2.2) and detritus (D) at the given layer:
kt (z) = kw + kc (P1 (z) + P2 (z) + D(z)).
(1)
The mixed layer depth (MLD) is diagnosed from the model as the shallowest model layer at
which the temperature is 0.1◦ C less than the sea surface temperature.
In Denman and Peña (1999, 2002), the salinity was set at a constant 32.7 ppt throughout
the model domain. The domain of the present model is deeper than that used in Denman
and Peña (1999, 2002), and in particular extends below the depth of the permanent halocline
at OSP. A crude parameterisation of the halocline was therefore prescribed in the present
model by fixing the salinity to the profile shown in Figure 2(a). As well, by relaxing the
temperature below 150 m on a timescale of 6 months to the profile shown in Figure 2(b),
a crude representation of the permanent thermocline was introduced; model variability is
qualitatively unchanged for values of this relaxation timescale from 3 months to two years.
The profiles displayed in Figure 2 were designed to resemble those illustrated in Fig. 3 of
Gargett (1991).
2.2
Ecosystem Model
The ecosystem model considered in this study is a six-component version of the model considered in Denman and Peña (2002) and in Denman (2003). Small (< 5µm, P 1 ) and large
(> 5µm, P2 ) size classes of phytoplankton are represented explicitly, as are microzooplankton (Z1 ) and detritus (D). To a first approximation, the large and small size classes of
phytoplankton along Line P may be considered to represent respectively autotrophic flagel+
lates and diatoms (Boyd and Harrison, 1999). Two species of nitrogen, NO −
3 and NH4 , are
modelled explicitly; the total nitrogen concentration is denoted N = NO 3 + NH4 . Mesozooplankton (Z2 ), which graze on microphytoplankton and microzooplankton, are not modelled
5
prognostically but are set to a constant value throughout the year. All ecosystem model
parameters are expressed in terms of the equivalent concentration of nitrogen.
The ecosystem variables are defined at each model level and evolve according to the set of
differential equations outlined in Appendix A, as well as being mixed between model levels
as passive tracers by the upper-ocean turbulence model. The specific growth rate of the phytoplankton is limited by three factors: nitrogen abundance, light level, and iron availability,
modelled by a simple threshold dependence of the phytoplankton specific growth rate. Nitrogen uptake is represented by simple Michaelis-Menten dynamics, while the light function
is as in Webb et al. (1974). In the absence of a detailed representation of the cycling of iron
in the upper ocean, iron limitation is simply represented by a constant parameter L F e setting
an upper limit on the specific phytoplankton growth rate. There is no co-limitation of growth
in this model; at any time, only one of light level, nitrogen abundance, or iron availability
is limiting. Both P1 and P2 are modelled to take up ammonium preferentially to nitrate.
Furthermore, it is assumed that the large and small size classes of phytoplankton are equally
limited by iron availability. A preliminary analysis of data from the SERIES iron-fertilisation
experiment at OSP suggests that both the small and large size classes of phytoplankton respond to fertilisation, with a weak grazer-controlled bloom of the former occurring before
the main diatom bloom, similar to results from the equatorial Pacific (Cavender-Bares et al.,
1999) and the Southern Ocean (Maldonado et al., 2001).
Microzooplankton are modelled 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 the microphytoplankton, P 2 , and on the microzooplankton,
Z1 . Because of “sloppy feeding” and excretion of fecal pellets by microzooplankton, only a
fraction of the grazed material is assimilated as microzooplankton biomass; the rest moves
directly into the detritus pool. A specified fraction of mesozooplankton grazing is also instantaneously excreted into ammonium. Losses of P1 and Z1 due to mortality and excretion
enter the ammonium pool, while those of P2 lead to both the ammonium and detrital pools.
6
Mechanisms for detritus removal other than consumption by microzooplankton are remineralisation to ammonium by heterotrophic bacteria at the rate r e , and sinking at speed
ws . Finally, a depth-dependent nitrification of NH4 into NO3 by bacteria is represented in
the model as in Denman (2003), as nitrification is observed to be inhibited in the euphotic
zone (Ward, 2000; Denman, 2003). Finally, all growth, grazing, and mortality rates are
temperature dependent according to individual Q10 parameters.
A complete description of the parameterisations of the processes governing the ecosystem
dynamics is presented in Appendix A.
Finally, a crude representation of the permanent nutricline was used to close the nitrogen
budget of the model. Below 120 m, inorganic nitrogen concentrations are relaxed to the deepocean value of 30 mmol-N m−3 on a timescale of 1 day. As with the relaxation timescale for
the permanent thermocline, it was found that variations in the nutricline relaxation timescale
do not qualitatively affect the model output.
2.3
Atmospheric Model
The ecosystem and upper-ocean models are driven respectively by atmospheric radiative
fluxes and by surface mechanical and buoyancy fluxes. These fluxes are derived from a
stochastic atmospheric model, described in detail in Appendix B, which produces synthetic
time series of fractional cloud cover (c) and 10 m air temperature (T a ), humidity (q), and wind
speed (U ). Model parameters were estimated from 21 years of 3-hourly observations at OSP.
For Ta , q, and U , the model was constructed to reproduce the first- and second-order moments (mean, standard deviation, lagged cross-correlations) of the observed data; fractional
cloud cover (measured in oktas) is modelled as a 9-state Markov chain with monthly-varying
transition probabilities.
Top of the atmosphere solar flux is calculated based on latitude, date, and time of day
using standard astronomical formulae. Surface insolation is then determined using a transmission coefficient depending on zenith angle and fractional cloud cover, following the for7
mulation of Dobson and Smith (1988) (which in fact was estimated using data from OSP).
The net outgoing longwave radiation (QL ) from the ocean surface depends on cloud cover,
sea surface and atmospheric boundary layer temperatures, and boundary layer humidity,
calculated using the recent parameterisation of Josey et al. (2003):
QL = σSB (Ts + 273.15K)4
(2)
n
−(1 − αL )σSB Ta + 273.15K + 10.77c2 + 2.34c − 18.44 + 0.84(Tdew − Ta + 4.01K)
o4
where = 0.98 is the emissivity of the sea surface, αL = 0.045 is the sea surface longwave
reflectivity, σSB is the Stefan-Boltzmann constant, and Tdew is the dew point temperature.
Note that equation (3) assumes temperatures Ts , Ta , and Td in degrees Celsius.
The wind stress τ , sensible heat flux (QSH ), and latent heat flux (QLH ) are calculated
from the standard bulk formulae :
τ = ρa CD U 2
(3)
QSH = ρa CH cp U (Ta − Ts )
(4)
QLH = CE Lv (q − qs (Ta ))
(5)
where ρa is the surface atmospheric density, cp is the specific heat capacity of air, Lv is the
latent heat of vaporisation, and qs (Ta ) is the saturation humidity at 10 m. The 10-m bulk
transfer coefficients CD , CH , and CE taken from the expressions given in Large (1996), also
based largely on observations at OSP.
103 CD =
3
10 CH =
2.70
+ 0.142 + 0.764U
U







(6)
1/2
32.7CD , QSH ≤ 0
1/2
(7)
18.0CD , QSH > 0
1/2
103 CE = 34.6CD
8
(8)
3
Results
Three 1100-year integrations of the stochastic upper-ocean/ecosystem model were carried out
for iron limitation parameter values LF e of 0.26, 0.28, and 0.5, corresponding respectively to
iron-limited, intermediate, and nitrogen-limited systems. A model year is denoted nitrogen
limited if at some point in the year N concentrations dropped below the threshold for nitrogen
abundance to become the limiting factor; from equation (19), assuming the surface layers to
be light-replete in the daytime, this threshold is
Nthresh =
k n LF e
.
1 − LF e
(9)
Otherwise, a year is said to be iron-limited. All three integrations were driven by the same
realisation of the stochastic atmospheric model. Output data were saved daily, and to
remove the effects of initial transients, the first 100 years of each integration were discarded
before analysis. Because of the externally-imposed seasonal cycle, the statistics of model
variables are cyclostationary rather than strictly stationary. That is, the joint distributions
are invariant under time translations of integer multiples of one year, but not under arbitrary
translations.
3.1
Physical Parameters
Figure 3 displays the model SST and daily maximum MLD as a function of calendar day
for all years of the 1000-year integration. The variability of these variables resembles that
observed at OSP, although comparison with Figure 17 indicates that the model SST is
somewhat warmer in the winter than is observed, and displays somewhat less variability.
The annual cycles of the mean and standard deviation of T for the upper 125 m of the
model are displayed in Figure 4. The annual cycle of the mean illustrates the development
and deepening of the shallow seasonal thermocline over the summer and its erosion in the
late fall/early winter. The greatest variability in model MLD is in the spring, associated
with variations in the timing of the development of the seasonal thermocline (Figure 3). The
9
prime source of variability in subsurface temperature, on the other hand, is associated with
the onset of mixing in the autumn, as is indicated by the localised maximum in the standard
deviation along the seasonal thermocline from mid-summer to early winter. This variability
is qualitatively in agreement with the results of Alexander and Penland (1996) (see their
Fig. 4).
The temporal structure of variability in MLD and SST can be characterised by the
lagged autocorrelation functions (acf), presented in Figure 5. For variables x and y, the
lagged cross-correlation function at lag τ on year day t0 is defined as
cxy (τ ; t0 ) =
< (y(t0 + τ ) − µy (t0 + τ ))(x(t0 ) − µx (t0 )) >
σy (t0 + τ )σx (t0 )
(10)
where µx (t) and σx (t) (µy (t) and σy (t)) are respectively the mean and standard deviation of
x (of y) at time t, and the angle brackets < · > denote ensemble average over observations
at year day t0 . By definition, positive τ corresponds to x leading y. The acf of x is obtained
by taking y = x in equation (10). Note that because the correlation of x at day t 0 with x
some τ days later equals the correlation of x at day t0 + τ with x some τ days earlier, the
acf is symmetric:
cxx (τ, t0 ) = cxx (−τ, t0 + τ )
(11)
By definition, the acf takes the value 1 at τ = 0 and asymptotes to zero as τ increases. The
rate at which this decay occurs is a measure of the memory of the system: the more rapid
the decrease, the more readily the relevance of the present state to the future trajectory of
the system decreases. The decay of the acf is not necessarily monotonic; if the process x
contains dominant oscillatory components, these will be reflected in oscillations of the acf.
As with the mean and standard deviation of these variables, the lagged acfs of MLD and
SST are not stationary but contain a prominent annual cycles. In general, SST fluctuations
have longer memories than do MLD fluctuations, and anomalies in both MLD and SST
have longer memories in the fall and winter (when the mixed layer is deep) than during the
spring and summer (when there is a shallow seasonal thermocline). In particular, spring
10
and summer fluctuations in MLD decorrelate after just a few days. The relatively longterm memory in winter vanishes suddenly in the spring as the mixed layer shoals, and
develops again as the mixed layer deepens in the fall. Inspection of the time series (not
shown) indicate the presence of intraseasonal fluctuations in MLD throughout the year, while
substantial interannual variability appears only in wintertime; this leads to wintertime MLD
decorrelation times that are longer than those in the summer. Conversely, the simulated
SST time series is characterised by levels of subseasonal variability in the wintertime that
are markedly lower than those in the summer, and by interannual variability in all seasons;
together these combine to yield summertime SST autocorrelation times longer than those
for MLD.
In fact, inspection of the 21-year observational record (Appendix B) indicates that the
model underestimates both interannual variability and wintertime subseasonal variability.
As the model is forced by fluctuations with decorrelation times on the order of days, and not
with lower-frequency variability due to, e.g., ENSO or the Pacific Decadal Oscillation, it is
not surprising that low-frequency variability in SST should be underestimated. The simple
representation of the permanent pycnocline by relaxation processes toward fixed profiles will
also presumably contribute to the underestimation of SST variability, especially in winter
when the mixed layer is deep. Cummins and Lagerloef (2002) note the presence of considerable variability in the depth of the permanent pycnocline on both intra- and interannual
timescales; this variability is suggested to arise from, e.g., fluctuations in Ekman pumping
velocity, the passage of mesoscale eddies, and baroclinic tides.
3.2
Iron Limited Regime
When the iron limitation parameter LF e is set to 0.26, never in the 1000-year simulation is
the summer nitrogen drawdown sufficient to initiate nitrogen limitation. Figure 6 displays
the surface-layer values of P1 , P2 , Z1 , D, NO3 , and NH4 as a function of calendar day for
each year of this simulation. The small size class of phytoplankton displays a weak mean
11
annual cycle, as is generally observed at OSP (e.g. Harrison et al. (1999)); a small mean
springtime increase in P1 biomass is accompanied by a maximum in variability. The surface
microzooplankton biomass reaches a maximum in the late spring, shortly after that of P 1 .
Like the small size class of phytoplankton, the variability of Z 1 is generally small (compared
to the mean value), and maximal in the spring. In contrast, the weak diatom bloom (P2,
note scale change) that occurs in late summer is highly variable; we will return to this point
later.
Figure 7 displays profiles of the annual cycles of the means and standard deviations of
ecosystem model variables over the upper 125 m of the model domain. Annual variability in
the mean of P1 extends down through the upper part of the water column. The early-spring
maximum in the standard deviation of P1 is coincident with the maximum in the mean,
reflecting significant variability in the springtime mixed layer depth. The annual cycle in the
mean microzooplankton abundance lags that of P1 , while the corresponding annual cycles
in the standard deviations are coincident. On average, ammonium concentrations decrease
in the upper part of the water column and increase at the base of the mixed layer over
the summer, peaking just before the onset of winter mixing; variability is dominated by
variations in the timing of winter mixing and in springtime shoaling of the mixed layer. The
mean profile of nitrate displays a late summer minimum throughout the mixed layer and
a pronounced nutricline; variability is concentrated along the base of the wintertime mixed
layer and reflects interannual variability in the depth of wintertime mixing.
Plots of the lagged autocorrelation functions for surface P 1 , Z1 , and N are given in Figure
8. The existence of predator/prey oscillations in the late spring and early summer between P
and Z1 is confirmed by the presence of alternating bands of positive and negative correlations
on either side of the lag τ = 0 line. The phasing of these oscillations is randomised by the
environmental fluctuations, and so they do not appear in the mean profiles. Predator/prey
cycles are also evident in Figure 9, which illustrates the lagged cross-correlations between P 1
and Z1 (such that positive τ corresponds to P1 leading Z1 ). The long late-summer memory
12
of Z1 indicates that what little variance Z1 displays at this time is primarily on interannual
timescales. Finally, it is clear that the variance in N , for L F e = 0.26, is primarily on
interannual timescales, as the acf remains near one on subseasonal timescales. Because the
system is iron-limited, N is largely decoupled from the subseasonal fluctuations in P 1 and
P2 .
In general, the mean annual cycles of P1 and Z1 for LF e = 0.26 are in qualitative agreement with the simulations of Denman and Peña (2002) and Denman (2003), in which the
atmospheric forcing followed smooth diurnal and annual cycles. Furthermore, as variability
in P1 and Z1 are relatively weak, the mean annual cycles are representative of a typical annual cycle. In contrast, the size of the small late summer diatom bloom displays substantial
interannual variability (Figure 10). Considerable interannual variability in the summertime
drawdown of silicate has been observed at OSP (Wong and Matear, 1999), with the observation of years in which an almost complete exhaustion of silicate occurs in surface waters.
This interannual variability has been attributed to episodic aeolian delivery of iron to the
ocean surface, enhancing diatom growth (e.g. Boyd et al. (1998); Bishop et al. (2002)). The
present study suggests that considerable interannual variability in peak diatom biomass (and
thus in silicate drawdown) can result simply from fluctuations in the physical forcing of the
upper ocean, with no episodic iron fertilisation. Such episodic inputs of iron may play a role
in the interannual variability in phytoplankton biomass in the NE subarctic Pacific, but the
present study suggests that considerable interannual variability occurs even in their absence.
A quantitative assessment of the relative importance of the two processes in producing interannual variability requires the the inclusion of silicate as a prognostic variable in the model,
and is beyond the scope of the present study.
3.3
Nitrogen-Limited Regime
The surface P1 , P2 , Z1 , NO3 , NH4 , and D concentrations simulated by the model for
LF e = 0.5 (no iron limitation) are plotted as a function of calendar day in Figure 11. In
13
contrast to the iron-limited case considered above, for LF e = 0.5, summer nitrate drawdown
is sufficiently large to lead to nitrate limitation. The shift from iron-limited to nitrogenlimited conditions is also evident in the surface values of P 1 , P2 , Z1 , and D. While the
annual cycle in the mean of P1 is generally similar to that for LF e = 0.26, the variability
is considerably greater. Following a summertime minimum in surface small phytoplankton
abundance, a secondary smaller autumn bloom is also evident from Figure 11, due to nitrate
entrained into the surface waters as the mixed layer deepens (as is commonly found in models
of nitrogen-limited regimes). In contrast to the small late-summer P 2 blooms characteristic
of the iron-limited regime, for LF e = 0.5 large P2 blooms occur in late spring/early summer,
at which time the large size fraction typically accounts for at least half of the phytoplankton biomass. Blooms in P2 typically follow modest early-summer blooms of P1 , as is clear
from inspection of the trajectories or the lagged cross-correlation function of P 1 and P2 (not
shown). The magnitude of the P1 bloom is limited by grazing pressure from Z1 , the biomass
of which increases in response to increasing prey abundance. In fact, throughout the annual
cycle, the mean and standard deviation of surface microzooplankton concentrations are significantly higher for LF e = 0.5 than for LF e = 0.26 (cf. Denman and Peña (2002)). A second
small maximum in Z1 occurs in winter following the autumn phytoplankton bloom.
Profiles of the annual cycles of the means and standard deviations of P 1 , P2 , Z1 , NO3 ,
NH4 , and D over the upper 125 m of the model appear in Figure 12. The spring and autumn
blooms are apparent in the mean annual cycle of P1 , along with a third deep maximum in the
summer just below the mixed layer where light and nitrate are both sufficiently abundant to
support significant phytoplankton growth. The P2 bloom also extends to depth and persists
along the base of the mixed layer after surface nutrients have been depleted. Maxima of the
annual cycle of standard deviations of P1 and P2 are colocated with maxima of the annual
cycle in the means and primarily reflect fluctuations in the timing of the blooms. A maximum
in Z1 occurs shortly after the spring bloom in P1 as zooplankton stocks grow in response to
abundant phytoplankton availability. A maximum in the standard deviation of Z 1 follows
14
somewhat later, associated with variability in the timing of the collapse of the springtime Z 1
populations. As was the case for LF e = 0.26, the greatest values of the standard deviation
of NO3 occur in wintertime at the base of the mixed layer; these are larger for L F e = 0.5
because of the enhanced vertical gradient of NO3 resulting from the summertime drawdown
of nitrate in the euphotic zone evident in the mean annual cycle. Ammonium concentrations
peak in early summer at the base of the mixed layer, tracking subsurface maxima in P 1 , P2 ,
and Z1 . Variability in NH4 peaks at depth shortly after variability in phytoplankton and
zooplankton abundance. Maxima of the mean and standard deviation of D occur at depth
shortly after those of P2 .
The annual cycles of the acfs of P1 , Z1 , and N for LF e = 0.5 are illustrated in Figure 8.
There is still evidence of predator/prey oscillations between P 1 and Z1 , but these are weaker
than in the iron-limited regime; this fact 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 LF e = 0.5 than for LF e = 0.26, with no predator-prey oscillations after the
onset of nutrient limitation. This change reflects the importance of interannual variability
relative to subseasonal variability for the period following the onset of nutrient limitation. In
contrast, the memory of surface N is much shorter during this period in the nitrogen-limited
regime than in the iron-limited regime.
In general, the variability of each ecosystem model variable around its annual mean is
significantly greater in the nitrogen-limited regime than in the iron-limited regime, so in
the former regime a typical year will look less like an average year than in the latter. As
well, the distributions of both P1 and Z1 display marked bimodality in late spring, reflecting
variations in the timing of the drawdown of surface nutrients to limiting values. During
this time period, the average annual cycle is a particularly poor representation of overall
variability. Furthermore, the distribution of P2 is markedly asymmetric about its mean.
The effects of atmospheric fluctuations on the ecosystem dynamics are both quantitative
and qualitative.
15
3.4
Intermediate Regime
Figure 13 plots surface N concentrations for an arbitrary 100-year period for values of the
iron limitation parameter LF e of 0.26, 0.28, and 0.5. The first and third of these correspond
to the iron-limited and nitrogen-limited regimes discussed above; the second is intermediate.
It is clear from Figure 13 that for this intermediate value of the iron limitation parameter,
the model is not consistently iron-limited or nitrogen-limited, but alternates between these
regimes on interannual to interdecadal timescales. For this value of L F e , phytoplankton
growth rates are sufficiently high to draw down nitrogen abundance to the point that N
becomes limiting in some years. In other years, iron abundance is at all times the limiting
factor. The variability of N , P1 , P2 , Z1 , and D for LF e = 0.28 is intermediate between that
for LF e = 0.26 and LF e = 0.5, and is thus not shown.
From Figure 13 it is clear that iron-limited (or nitrogen-limited) years may occur individually or for a number of years in a row. Figure 14 displays a histogram of the duration
of iron-limited and nitrogen-limited episodes for the 1000-year integration. The distribution of episode lengths falls off approximately exponentially for both iron- and nitrogenlimited regimes; these episodes do not occur with any dominant timescale. Note that variations between iron-limited and nitrogen-limited regimes, occurring on interannual to decadal
timescales, are excited by stochastic variability in the atmospheric model that is characterised by a decorrelation timescale on the order of days. Because the atmospheric model
does not represent variability on seasonal scales and longer (associated with both internal
low-frequency extratropical dynamics and the midlatitude response to tropical forcing), and
because the lack of an explicit representation of Ekman pumping in the model precludes interannual and interdecadal fluctuations in the depth of the permanent pycnocline (Cummins
and Lagerloef, 2002), estimates of interannual to decadal variability produced by the model
are likely to underestimate those of the real system.
16
3.5
“Background-Bloom” Dynamics
Over the last 15 years, it has been recognised that as the total biomass of phytoplankton
in a water sample increases, the relative proportion of small phytoplankton decreases (e.g.
Denman and Peña (2002); Denman (2003) and references therein). That is, concentrations
of small phytoplankton tend not to vary much around a background level, while blooms
are dominated by the larger size class. This “background-bloom dynamics” was hard-wired
into earlier versions of the present ecosystem model by diagnostically partitioning the single phytoplankton compartment into two classes, based on total phytoplankton biomass.
While this parameterisation produced reasonable simulations for environmental conditions
characteristic of the mean state at OSP, it proved to be problematic for the simulation of
blooms. In particular, at the peak of a simulated bloom, the grazing of microzooplankton on
the small size fraction of phytoplankton reduced the total plankton biomass, thereby changing the relative partitioning of large and small size classes and in essence relabelling large
phytoplankton as small phytoplankton. By introducing a second prognostic phytoplankton
variable, the present model avoids this problem. Furthermore, the “background-bloom” behaviour in the present model can be investigated. Figure 15 displays a plot of the biomass
of the small size fraction of the phytoplankton as a function of the total phytoplankton
biomass for the iron-limited regime (LF e = 0.26). Two populations are evident. In one,
lying along the 1:1 diagonal of the plot, diatoms are essentially absent and the small size
class of phytoplankton dominates the ecosystem. In the other, diatoms are present and the
relative contribution of P1 decreases as the total biomass increases. In fact, observations
at OSP and in the North Atlantic also suggest the presence of two statistical populations,
respectively with and without abundant diatoms, as is illustrated in Figure 3 of Denman and
Peña (2002). The parameterisation developed in Denman and Peña (2002) to diagnostically
partition the phytoplankton biomass into large and small size classes falls between these two
populations, thereby representing neither.
17
3.6
Export Fluxes
A quantity of central importance in understanding the role of the oceanic biosphere in the
global carbon cycle is the rate at which particulate organic matter sinks out of the surface
waters, denoted the export flux. In the present model, the export flux through 100 m consists
of two primary components: (1) the net flux of D across the 100 m depth level, and (2) the net
flux to mesozooplankton (grazing on P2 and Z1 minus excretion to NH4 ), which is assumed
to be lost from the surface waters via sinking fecal pellets, mortality, or mesozooplankton
sinking below the permanent pycnocline during diapause. Figure 16 displays histograms of
annually-averaged export fluxes and export ratios (defined as export flux divided by total
new production) for iron-limited and nitrogen-limited regimes. Note that the mean export
flux is smaller in the iron-limited regime than in the nitrogen-limited regime, as would be
expected because of the smaller diatom abundances in the former regime than in the latter.
The mean export flux in the iron-limited regime, 0.35 mol-Nm −2 yr−1 , is in good agreement
with the observed value of 0.29 mol-Nm−2 yr−1 at OSP, obtained from sediment trap data
(Denman and Peña, 1999). The 35% increase in mean export flux in the nitrogen-limited
regime relative to the iron-limited regime is in good agreement with the results of Denman
and Peña (2002). Furthermore, because large diatom blooms occur in the nitrogen-limited
regime and not in the iron-limited regime, the variability of export fluxes is much greater
in the former than in the latter. 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 distribution of export fluxes for L = 0.28 was intermediate between the ironlimited and nitrogen-limited distributions. In general, export ratios displayed less variability
than export fluxes, both within and between integrations.
Estimates of the residence time of nitrate in the upper part of the water column can be
obtained by dividing the total stock of N in the upper 100 m by the export flux through
this depth. Values of about 3.3 and 1 years are obtained for the iron- and nitrogen-limited
regimes, respectively. The fact that these values are on the order of a year and greater is
18
consistent with the presence of the significant interannual variability in N evident in Figure
13.
4
Discussion and Conclusions
In this study, we have extended the work of Denman and Peña (1999, 2002) to consider
the dynamics of a coupled upper-ocean/ecosystem model driven by an empirical stochastic
model of the atmosphere, built to match as closely as possible the joint distributions of the
observed variability at Ocean Station Papa (up to second-order moments). Using a simple
representation of iron limitation of primary productivity, 1000-year integrations were considered for parameter values corresponding to iron-limited, nitrogen-limited, and intermediate
regimes. It was shown that the model is able to produce a reasonable representation of the
physical component of the upper ocean at OSP. The dynamics of the small phytoplankton
and zooplankton in the parameter regime corresponding to iron limitation were not found to
be qualitatively affected by atmospheric variability, although the large phytoplankton size
class (“diatoms”) displayed considerable interannual variability. This interannual variability
is consistent with interannual variability in surface silicate concentration observed at OSP,
where instances of large summertime silicate drawdown have previously been associated with
episodic iron fertilisation by aeolian dust (Boyd et al., 1998; Bishop et al., 2002). In contrast,
atmospheric variability had a qualitative effect on the ecosystem dynamics in the nitrogenlimited regime. The ecosystem variables display considerable (and generally non-Gaussian)
variability around the mean annual cycle, so that typical model years do not resemble average years. Furthermore, a feature of the stochastically driven model not present in earlier
studies is the existence of an intermediate regime in which the system moves between nitrogen limitation and iron limitation on interannual to interdecadal timescales. In these two
regimes, the average annual cycle of ecosystem variables cannot be expected to agree with
the ecosystem response to annually averaged forcing. Finally, the mean and variability of
19
export fluxes are found to be significantly higher in the nitrogen-limited regime than in the
iron-limited regime.
Summer nitrogen depletion has not been observed at OSP. In contrast, surface nitrogen
is observed to be drawn down to limiting concentrations in late summer along the first ∼
500 km of Line P; station P12 (Figure 1) is characteristic. Furthermore, between ∼ 500km
and ∼ 1000km along Line P, there is considerable interannual variability in summertime surface nitrogen depletion, such that surface waters are nitrogen deplete in some summers and
nitrogen replete in others (e.g. Figure 6 of Whitney and Freeland (1999)); a characteristic
station is P20. The empirical stochastic atmosphere model was built using data from OSP,
and the parameters of the upper ocean and ecosystem models were tuned so that the output
for LF e = 0.26 resembled observed variability at OSP; there is no a priori reason to believe
that these parameters should be invariant across the subarctic northeast Pacific. However,
qualitatively, LF e can be imagined to be a proxy for distance along Line P, increasing eastward from Station Papa. The observed decrease in wintertime maximum surface nitrate
concentrations eastward along Line P (Whitney and Freeland, 1999) is reproduced in the
model, moving from the iron-limited regime to the intermediate regime, and then on to the
nitrogen-limited regime.
Previous studies of interannual to interdecadal variability in the physical and biogeochemical properties of the upper waters of the northeast subarctic Pacific (e.g. Mantua
et al. (1997); Whitney et al. (1998); Whitney and Freeland (1999); Haigh et al. (2001)) have
highlighted the role of large-scale, low-frequency climate processes (e.g. ENSO or the Pacific
Decadal Oscillation) in producing this variability. Similar arguments have been put forward
for the role of the North Atlantic Oscillation in driving interannual variability in the physical and biogeochemical states of the North Atlantic ocean (e.g. Gruber et al. (2002)). The
present study has demonstrated that high-frequency atmospheric variability decorrelating
on synoptic timescales can produce considerable variability on interannual to interdecadal
scales. This variability would not be expected to be spatially-coherent on the basin scale,
20
but could be a significant component of the interannual variability at individual stations.
Furthermore, this study suggests that the marked interannual variability in silicate drawdown (and thus diatom production) observed at OSP - typically ascribed to episodic iron
fertilisation by aeolian dust- can be produced by the response of the upper ocean to rapidly
decorrelating fluctuations in physical forcing from the atmosphere. Such episodic fertilisation
events may in fact be an important source of this interannual variability (e.g. Bishop et al.
(2002)), but the present study suggests that other sources of variability may also contribute.
Another potentially important contributor to interannual variability is episodic entrainment
of deep iron into the upper ocean, but the simple treatment of iron in this study precludes
an estimate of the significance of this process.
The analysis of model simulations in this study has concentrated on first- and secondorder statistics such as means, standard deviations, and lagged auto- and cross-correlations;
this was done because of the relative ease of interpretation of these statistics. Of course,
the dynamics of the model contain significant nonlinearities, and second-order statistics are
generally inadequate for a complete characterisation of a nonlinear system (e.g. Ghil et al.
(2002); Monahan et al. (2003)). Inspection of Figures 6 and 11 indicate that although the
forcing variables have an approximately Gaussian distribution, nonlinearities in the upperocean/ecosystem model dynamics produce markedly non-Gaussian output. A more complete
analysis of the coupled upper-ocean/ecosystem dynamics would involve the use of more sophisticated statistical tools (e.g. multichannel singular spectrum analysis, suitably adapted
to account for the cyclostationarity of the time series). As well, bifurcations in the dynamics
of the system were only discussed briefly in the present study, in the context of predator-prey
oscillations. A more thorough exploration of parameter space, characterising the bifurcation
structure of the model within the range of physically and ecologically “realistic” parameters,
would be a useful extension of the present study (e.g. Denman (2003) for a slab model).
Other natural extensions of the present study would be investigations of the response of the
system to global warming (as in Denman and Peña (2002)), to iron fertilisation (as in Ed-
21
wards et al. (2003)), or to atmospheric forcing with an explicit representation of interannual
to interdecadal variability (as in Haigh et al. (2001)). Inclusion of silicate as a prognostic
variable would allow a quantitative diagnosis to be made of the relative importance of mixing variability and episodic aeolian dust fertilisation in producing interannual variability in
silicate drawdown.
The inclusion of stochastic atmospheric variability increases the complexity of the model
only modestly relative to that studied in Denman and Peña (2002) or Denman (2003),
but it results in a system displaying much richer variability. The price that must be paid
is a substantial increase in the complexity of the model output, along with a shift from
the familiar deterministic conception to a perhaps less familiar distributional conception
of the dynamics. Variability on a broad range of time scales is an ubiquitous feature of
both the physical and biogeochemical components of the climate system. Improving our
understanding of the nature and origin of this variability is an important challenge for the
climate research community (Imkeller and Monahan, 2002).
Appendix A: Ecosystem Model Equations
The set of differential equations governing the ecosystem components at each model layer is
dP1
dt
dP2
dt
dZ1
dt
dNO3
dt
dNH4
dt
P1
Z1 − mpa P1
P1 + p D D
Z2
νP2 − γ2
P2 − (mpa + mpd )P2
P 2 + Z1
Z2
g a γ 1 Z1 − γ 2
Z1 − mza Z1
P 2 + Z1
NO3
1
−ν(P1 + P2 )RN O3
+ ηNH4 +
(NO3 − NO3 )
NO3 + NH4
τ (z)
NO3
+ re D +
−ν(P1 + P2 ) 1 − RN O3
NO3 + NH4
= νP1 − γ1
(12)
=
(13)
=
=
=
mpa (P1 + P2 ) + mza Z1 + mca γ2 Z2 − ηNH4
dD
pd D
dD
= mpd P2 + (1 − ga )γ1 Z1 − γ1
Z1 − r e D + w s
dt
P1 + p d D
dz
22
(14)
(15)
(16)
(17)
(18)
The specific growth rates of both P1 and P2 are assumed for simplicity to be equal and given
by
ν = νm min
aI IP AR
N
, 1 − exp −
, LF e ,
kn + N
νm
(19)
where νm is the maximum specific growth rate, IP AR is the intensity of photosynthetically
active radiation, and each of the arguments of the min function range between 0 and 1. The
relative preference of the phytoplankton for the uptake of ammonium relative to nitrate is
described by the relative preference index (Denman, 2003)
RN O 3 =
α
.
α + N O3
(20)
The grazing rate of the microzooplankton is given by
γ 1 = rm
(P1 + pD D)2
kp2 + (P1 + pD D)2
(21)
where kp is the grazing half-saturation constant and pD is the grazing preference of D relative
to P1 ; the grazing rate of the mesozooplankton is
γ 2 = rc
(P2 + Z1 )2
kz2 + (P2 + Z1 )2
(22)
The fraction of the material grazed by microzooplankton is assimilated as Z 1 biomass is
denoted by ga ; the rest (fecal pellets and “sloppy feeding”) moves directly into the detritus
pool. The specific loss rates of phytoplankton and zooplankton to the ammonium pool are
denoted mpa and mza , respectively, while the specific loss rate of P2 to detritus is denoted
mpd . A fraction mca of mesozooplankton grazing is excreted instantaneously into ammonium;
the remaining fraction is assumed to contribute to biomass of mesozooplankton (and higher
trophic levels).
The concentration of nitrate below the permanent nutricline is denoted by NO 3 , and
the nutricline relaxation timescale is infinite above 120 m, and 1 day below 120 m. As
nitrification of NH4 into NO3 is observed to be inhibited in the euphotic zone (Ward, 2000),
the specific nitrification rate is represented as
η(z) = νox
zn
n + zn
zox
23
(23)
where νox is the maximum specific nitrification rate, z is the depth, z ox is the depth at which
the noontime irradiance drops to 4 Wm−2 , and n = 10 (Denman, 2003). This representation
allows a sharp transition from low specific nitrification rates within the euphotic zone to
relatively large values below.
Finally, the temperature dependence of the growth, grazing, and mortality rates
(νm , rm , rc , mpz , mpd , mza , and re ) are given by individual Q10 parameters, defined as the
factors by which the rates increase due to a 10◦ C increase in temperature. For example, for
the phytoplankton growth rate:
(T −10◦ C)/(10◦ C)
νm (T ) = νm (10◦ C)Q10,ν
(24)
The Q10 factors for phytoplankton are set to 2, while those for zooplankton and bacteria are
set to 3 (Denman and Peña, 2002).
Table 1 lists the ecosystem model parameter values used in this study; these are essentially
the same as those used in the study of Denman and Peña (1999, 2002), in which detailed
justifications of the choices of parameter values are given.
Appendix B: Stochastic Atmosphere Model
As described in Section 2.3, the atmospheric variables required to calculate the mechanical
and buoyancy fluxes across the air/sea interface are fractional cloud cover (c, in oktas), and
10 m air temperature (Ta ), absolute humidity (q), and wind speed (U ). The Ocean Station P
dataset used in this study consists of 21 years (1960-1981) of 3-hourly observations of these
variables, along with sea surface temperature (SST, Ts ) and wind direction. Because the
wind speed U is highly non-Gaussian, it is convenient to work with the zonal wind (u) and
meridional wind (v) individually. The observed variables (T s , Ta , q, u, and v) are plotted as
functions of calendar day in Figure 17.
Table 2 displays the correlations between the surface ocean and meteorological variables
at OSP. Not surprisingly, v is positively correlated with q and T a , reflecting the advection of
24
warm and moist (cold and dry) air by southerly (northerly) winds. Furthermore, because of
the strong thermal coupling between the atmospheric boundary layer and the ocean surface,
Ta and q are significantly correlated with Ts . It is convenient that the stochastic atmosphere
model should represent variability intrinsic to the atmosphere, and not include variability
associated with the model variable Ts . Thus, the linear dependence of Ta and q on Ts was
removed by subtracting least-squares regression fits to T s from these variables; the resulting
residual variables are denoted Ta0 and q 0 . The variables Ta0 , q 0 , u, and v are not stationary, but
are characterised by pronounced annual cycles in their means and standard deviations. These
annual cycles were estimated by fitting sine/cosine pairs with periods of one year, 6 months,
3 months, and 1.5 months to raw estimates of the mean and variance at each of the 3-hourly
bins over the year. The variables (Ta0 , q 0 , u, v) were standardised by subtracting the smooth
annual cycle in the mean, and then dividing by the smooth annual cycle in the standard
deviation; the resulting residual variables are denoted by carets ( ˆ ). The standardisation
procedure was not applied to c, as it is measured in octas and is thus not a continuous
variable. Table 3 displays the correlations of the standardised variables among themselves
and with c. The standardised variables (T̂a0 , q̂ 0 , û, v̂) display significant cross-correlations and
are thus not modelled as independent processes (as was done in Alexander and Penland
(1996)). On the other hand, the correlations between c and the standardised variables are
generally small, and furthermore, c is a discrete Markov chain rather than a continuous
process. Thus, c will be modelled as independent of the other meteorological variables.
To model the four-dimensional process X = (T̂a0 , q̂ 0 , û, v̂), we assume that the process is
stationary, Markov and multivariate Gaussian. That is, it is assumed that X is a multivariate
Ornstein-Uhlenbeck process described by the stochastic differential equation
Ẋ = AX + B Ẇ
(25)
where A and B are constant 4×4 matrices and Ẇ is a 4-dimensional white-noise process
25
with independent components:
< Wi (t1 )Wj (t2 ) >= δij δ(t1 − t2 ).
(26)
The matrices A and B can be estimated from data using Linear Inverse Modelling (Penland,
1996). The assumption of stationarity implies that
A < XXT > + < XXT > AT + BB T = 0
(27)
< X(t + τ )XT (t) >= exp(Aτ ) < XXT >
(28)
and that
Covariance matrices at lags 0 and τ can be estimated directly from the data; an estimate of
the matrix A then follows from equation (28). Knowing A, the matrix B can be estimated
from equation (27). Equation (25) can then be integrated numerically using the estimated
matrices A and B to generate arbitrarily long realisations of X which have the same secondorder statistics as the observations. Numerical integration of stochastic differential equations
is described in detail in Kloeden and Platen (1992). If X is actually a Markov process, then
the estimates of A and B should not depend on the value of τ used in equation (28); this
can be used as a test of the appropriateness of the Markov assumption. In fact, for the
standardised OSP data, these matrices do depend on the value of τ considered; however, the
statistics of the synthetic X process are essentially insensitive to this dependence. Estimates
of the autocorrelation functions for the individual components of X, from observations and
from the simulated time series, are plotted in Figure 18. The autocorrelation functions of
the synthetic variables do not match exactly those of observations; in particular, the obvious
diurnal cycle in T̂a0 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 of
the observations beyond about 4 days lag time, arising presumably from the movement of
large-scale air masses (Fissel et al., 1976). The assumption that the data are multivariate
Gaussian is also not satisfied exactly. In particular, the joint distribution of T̂a0 and q̂ 0 cannot
be Gaussian because the Clausius-Clapeyron equation puts a temperature-dependent upper
26
limit on the humidity. Overall, however, there is broad agreement between the gross features
of the distributions of the observed and simulated variables.
The simulated time series ( Ta , q, u, v) are obtained from (T̂a0 , q̂ 0 , û, v̂) by undoing the
standardisation process described above. The estimated smooth annual cycles in the means
are added to the synthetic residual processes, and the sum is multiplied by the estimated annal cycles of the standard deviations. The SST-dependent variables T a and q are constructed
using the regression coefficients calculated above and the observed annual cycle of T s . If it
happens that Td > Ta , q is reduced to the saturation humidity. If the model-generated value
of Ts rather than the observed annual average value is used in calculating T a and q, slight
flux mismatches cause the model to drift to an unrealistic equilibrium state. The use of the
annually-averaged Ts effectively acts a flux correction to eliminate this drift.
The fractional cloud cover c is modelled as a 9-state Markov chain. A Markov chain is
a random process x that can take one of a finite number of discrete states {s 1 , ..., sM } such
that the probability of the system being in a given state at time t i+1 is determined entirely
by the state of the system at time ti :
p(xti+1 = sj |xti = sk ) = qjk
(29)
where by definition
M
X
qjk = 1
(30)
j=1
The set of numbers qjk describing the transition probabilities are referred to as the transition
matrix. The states of the process c are the cloud cover in oktas. The distribution of c displays
a marked seasonal cycle, such that c has a lower mean and higher variability in the winter
than in the summer. This nonstationarity was reproduced by stratifying the data into twelve
calendar months and estimating the one time-step (3-hour) transition matrices individually
for each of these months. These estimates were obtained by simply calculating, for month
and for each of the nine cloud cover states ci , the relative frequency at which the cloud cover
state 3 hours later is cj . Arbitrarily long synthetic time series of c were then generated using
27
these monthly-varying transition matrices: at the end of each 3-hour period, a pseudorandom
number y was drawn from a uniform distribution between 0 and 1. If the present cloud cover
state was ck , then the next cloud cover state was cj for (the unique) j satisfying:
j−1
X
i=1
qik ≤ y <
j
X
qik .
(31)
i=1
Acknowledgements
AM and KD are supported by the Natural Sciences and Engineering Research Council of
Canada, and by the Canadian Foundation for Climate and Atmospheric Sciences. AM is also
supported by Canadian Institute for Advanced Research, and KD is supported by the US
Office of Naval Research. The authors would like to thank Jim Christian, Rana El-Sabaawi,
Debby Ianson, and Angelica Peña for their helpful advice.
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32
Table Captions
Table 1: Ecosystem model parameter values.
Table 2: Correlations between atmospheric and surface ocean variables measured at
Ocean Station Papa.
Table 3: Correlations between atmospheric variables standardised as described in text.
Figure Captions
Figure 1: Map of the subarctic northeast Pacific showing the location of the original 13
stations along Line P (small circles). Stations P12, P16, and OSP are indicated by
asterisks.
Figure 2: Plot of (a) salinity profile and (b) permanent thermocline profile to which the
upper-ocean model is relaxed.
Figure 3: Model output MLD and SST as a function of calendar day for the 1000-year
simulation.
Figure 4: Annual cycles of (a) mean and (b) standard deviation of model temperature
(◦ C).
Figure 5: Annual cycles of lagged autocorrelation function for MLD and SST.
Figure 6: Model output surface layer values of P1 , P2 , Z1 , NO3 , NH4 , and D as a function
of calendar day for LF e = 0.26 (iron limitation).
Figure 7: Profiles over the upper 125 m of the model domain of annual cycles in mean
(left panels) and standard deviation (right panels) of P 1 , P2 , Z1 ,NO3 , NH4 , and D, for
LF e = 0.26. All panels are in mmol-N m−3 .
Figure 8: Annual cycle of the autocorrelation function of surface P 1 , Z1 , and N for
LF e = 0.26 and LF e = 0.5.
Figure 9: Annual cycle of lagged cross-correlation between P 1 and Z1 for LF e = 0.26 and
LF e = 0.5. A positive lag time corresponds to P1 leading Z1 .
33
Figure 10: Variability of P2 over a typical 50-year period for LF e = 0.26.
Figure 11: As in Figure 6 for LF e = 0.5. Note that the scales of the y-axes differ from
those of Figure 6.
Figure 12: As in Figure 7 for LF e = 0.5. Note that the same contour intervals are used
both in this Figure and in Figure 7.
Figure 13: Plot of the surface concentrations of N for model years from 500 to 600, for
values of the iron limitation parameter LF e of 0.26, 0.28, and 0.5 (corresponding
respectively to iron-limited, intermediate, and nitrogen-limited regimes). Note that all
three integrations were driven by the same realisation of the empirical stochastic
atmosphere model.
Figure 14: Histogram of the duration of nitrogen-limited (open bars) and iron-limited
(solid bars) episodes.
Figure 15: Biomass of P1 plotted against the total phytoplankton biomass P1 + P2 for
LF e = 0.26.
Figure 16: Histograms of export fluxes and export ratios for 1000-year integrations in the
iron-limited and nitrogen-limited regimes.
Figure 17: Plots of Ts , Ta , Td , q, u, and v as a function of year day for observed data at
Ocean Station Papa from 1960 to 1981.
Figure 18: Lagged autocorrelation functions for observed (thin line) and simulated (thick
line) (a) T̂a0 (b) q̂ 0 (c) û (d) v̂.
34
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
νm
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
mca
0.3
-
νox
0.01
d−1
LF e
mmol-N m−3
variable -
Table 1: Ecosystem model parameter values.
35
Ts
Ts
Ta
q
u
v
c
1
0.92
0.79
0.01
0.013
0.08
1
0.90
-0.07
0.21
0.14
1
-0.16
0.28
0.27
1
-0.156
-0.18
1
0.11
Ta
q
u
v
c
1
Table 2: Correlations between atmospheric and surface ocean variables measured at Ocean
Station Papa.
T̂a0
q̂
û
T̂a0
q̂
û
v̂
c
1
0.70
-0.18
0.50
0.12
1
-0.26
0.46
0.28
1
-0.16
-0.15
1
0.11
v̂
c
1
Table 3: Correlations between atmospheric variables standardised as described in text.
36
o
54 N
52oN
o
50 N
OSP
P20
P12
o
48 N
o
46 N
145oW
140oW
135oW
130oW
125oW
120oW
Figure 1: Map of the subarctic northeast Pacific showing the location of the original 13
stations along Line P (small circles). Stations P12, P16, and OSP are indicated by asterisks.
(b)
0
−50
−50
−100
−100
z (m)
z (m)
(a)
0
−150
−200
−250
32.5
−150
−200
33
33.5
−250
2.5
34
S (ppt)
3
3.5
o
4
4.5
T ( C)
Figure 2: Plot of (a) salinity profile and (b) permanent thermocline profile to which the
upper-ocean model is relaxed.
37
Figure 3: Model output MLD and SST as a function of calendar day for the 1000-year
simulation.
Mean
Standard Deviation
0
15
−50
z (m)
z (m)
0
10
−100
1
−50
0.5
−100
60 120 180 240 300 360
day
5
60 120 180 240 300 360
day
0
Figure 4: Annual cycles of (a) mean and (b) standard deviation of model temperature ( ◦ C)
MLD
SST
1
350
300
300
0.5
250
200
year day
year day
1
350
0
150
100
−0.5
50
0.5
250
200
0
150
100
−0.5
50
−100 −50
0
50
100
−1
−100 −50
lag (days)
0
50
100
−1
lag (days)
Figure 5: Annual cycles of lagged autocorrelation function for MLD and SST
38
Figure 6: Model output surface layer values of P1 , P2 , Z1 , NO3 , NH4 , and D as a function
of calendar day for LF e = 0.26 (iron limitation).
39
Mean
Standard Deviation
P1
0
0.4
−50
0.2
z (m)
z (m)
0
−100
0.1
−50
0.05
−100
60
120 180 240 300 360
0
60
0
120 180 240 300 360
0
0.3
−50
0.2
z (m)
z (m)
0.4
P
−100
2
0
−50
0.2
0.1
−100
60
120 180 240 300 360
0
60
0
120 180 240 300 360
0
0
0.2
0.2
−100
1
60
120 180 240 300 360
z (m)
0
NH4
−50
60
z (m)
60
10
−50
0.2
−100
120 180 240 300 360
0
−100
0
4
−50
2
−100
60
120 180 240 300 360
0
0
60
−50
0.1
−100
120 180 240 300 360
0
0.2
z (m)
z (m)
0
0.4
60
20
120 180 240 300 360
0
30
−50
0.1
−100
120 180 240 300 360
0
D
−50
0
1.2
1
0.8
0.6
0.4
0.2
−100
NO3
z (m)
0.4
z (m)
Z
−50
z (m)
z (m)
0.6
0.08
0.06
−50
0.04
0.02
−100
60
120 180 240 300 360
0
day
0
60
120 180 240 300 360
0
day
Figure 7: Profiles over the upper 125 m of the model domain of annual cycles in mean (left
panels) and standard deviation (right panels) of P1 , P2 , Z1 ,NO3 , NH4 , and D, for LF e = 0.26.
All panels are in mmol-N m−3 .
40
1
year day
−100 −50
Z
360
300
240
180
120
60
year day
−100 −50
N
360
300
240
180
120
60
−100 −50
0.5
0
−0.5
0
50
lag (days)
100
−1
0
−0.5
100
−1
0.5
0
−0.5
0
50
lag (days)
100
360
300
240
180
120
60
−100 −50
1
−1
1
360
300
240
180
120
60
−100 −50
1
0.5
0
50
lag (days)
year day
1
360
300
240
180
120
60
year day
1
LFe = 0.5
year day
P
year day
LFe = 0.26
360
300
240
180
120
60
−100 −50
0.5
0
−0.5
0
50
lag (days)
100
−1
1
0.5
0
−0.5
0
50
lag (days)
100
−1
1
0.5
0
−0.5
0
50
lag (days)
100
−1
Figure 8: Annual cycle of the autocorrelation function of surface P 1 , Z1 , and N for LF e = 0.26
(iron limitation) and LF e = 0.5 (no iron limitation).
41
LFe = 0.26
LFe = 0.5
1
360
1
360
300
300
0.5
240
year day
year day
0.5
0
180
120
240
0
180
120
−0.5
−0.5
60
60
−100 −50
0
50
lag (days)
100
−1
−100 −50
0
50
lag (days)
100
−1
Figure 9: Annual cycle of lagged cross-correlation between P1 and Z1 for LF e = 0.26 and
2
−3
P (mmol−N m )
LF e = 0.5. A positive lag time corresponds to P1 leading Z1 .
0.1
0.05
0
300
305
310
315
320
325
330
335
340
345
year
Figure 10: Variability of P2 over a typical 50-year period for LF e = 0.26.
42
350
Figure 11: As in Figure 6 for LF e = 0.5. Note that the scales of the y-axes differ from those
of Figure 6.
43
Mean
Standard Deviation
P1
0
0.4
−50
0.2
z (m)
z (m)
0
−100
0.1
−50
0.05
−100
60
120 180 240 300 360
0
60
0
120 180 240 300 360
0
0.3
−50
0.2
z (m)
z (m)
0.4
P
−100
2
0
−50
0.2
0.1
−100
60
120 180 240 300 360
0
60
0
120 180 240 300 360
0
0
0.2
60
120 180 240 300 360
z (m)
0
NH
4
−50
−100
z (m)
60
10
−50
0.2
−100
120 180 240 300 360
0
−100
0
4
−50
2
−100
60
120 180 240 300 360
0
0
60
−50
0.1
−100
120 180 240 300 360
0
0.2
z (m)
z (m)
0
0.4
60
20
120 180 240 300 360
0
30
−50
0.1
−100
120 180 240 300 360
0
D
−50
0
1.2
1
0.8
0.6
0.4
0.2
60
NO3
z (m)
0.2
−100
z (m)
Z1
0.4
z (m)
z (m)
0.6
−50
0.08
0.06
−50
0.04
0.02
−100
60
120 180 240 300 360
0
day
0
60
120 180 240 300 360
0
day
Figure 12: As in Figure 7 for LF e = 0.5. Note that the same contour intervals are used both
in this Figure and in Figure 7.
44
L
Fe
= 0.26
mmol−N m−3
15
10
5
L
Fe
= 0.28
mmol−N m−3
0
500
15
mmol−N m−3
540
560
580
600
520
540
560
580
600
520
540
560
580
600
10
5
0
500
15
LFe = 0.5
520
10
5
0
500
year
Figure 13: Plot of the surface concentrations of N for model years from 500 to 600, for values
of the iron limitation parameter LF e of 0.26, 0.28, and 0.5 (corresponding respectively to
iron-limited, intermediate, and nitrogen-limited regimes). Note that all three integrations
were driven by the same realisation of the empirical stochastic atmosphere model.
45
110
100
90
80
number
70
60
50
40
30
20
10
0
0
5
10
15
20
duration (years)
Figure 14: Histogram of the duration of nitrogen-limited (open bars) and iron-limited (solid
bars) episodes.
Figure 15: Biomass of P1 plotted against the total phytoplankton biomass P1 + P2 for
LF e = 0.26.
46
LFe = 0.5
80
80
60
60
Number
Number
LFe = 0.26
40
20
40
20
0
0.2
0.4
0.6
0
0.2
0.8
−1
80
80
60
60
40
20
0
0.2
0.4
0.6
0.8
Export Flux (mol−N m −2 yr−1)
Number
Number
Export Flux (mol−N m −2 yr )
40
20
0.3
0.4
0
0.2
0.5
Export Ratio
0.3
0.4
0.5
Export Ratio
Figure 16: Histograms of export fluxes and export ratios for 1000-year integrations in the
iron-limited and nitrogen-limited regimes.
47
Ts(°C)
15
10
5
0
100
200
300
0
100
200
300
0
100
200
300
0
100
200
300
0
100
200
300
0
100
200
t (days)
300
Ta(°C)
15
10
5
0
−5
q (g/m3)
Td (°C)
5
0
−5
−10
15
10
5
v (m/s)
u (m/s)
0
20
0
−20
20
0
−20
Figure 17: Plots of Ts , Ta , Td , q, u, and v as a function of year day for observed data at
Ocean Station Papa from 1960 to 1981.
48
(b)
1
0.8
0.8
0.6
0.6
correlation
correlation
(a)
1
0.4
0.2
0
−0.2
−15
0.4
0.2
0
−10
−5
0
5
lag (days)
10
−0.2
−15
15
−10
−5
1
0.8
0.8
0.6
0.6
0.4
0.2
0
−0.2
−15
10
15
10
15
(d)
1
correlation
correlation
(c)
0
5
lag (days)
0.4
0.2
0
−10
−5
0
5
lag (days)
10
−0.2
−15
15
−10
−5
0
5
lag (days)
Figure 18: Lagged autocorrelation functions for observed (thin line) and simulated (thick
line) (a) T̂a0 (b) q̂ 0 (c) û (d) v̂.
49