Modelling Patch Dynamics During Ocean Fertilisation

Modelling Patch Dynamics During Ocean Fertilisation

Andrew Crawford Submitted in partial fulfilment of the requirements for the Bachelor of Engineering (Environmental) degree with Honours at the University of Western Australia School of Water Research University of Western Australia November 2003

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Abstract In light of global warming, the efficiency of the biological pump has become an increasingly

interesting process in the sequestration of carbon from the atmosphere. Iron enrichment of

high nitrate, low chlorophyll oceanic regions have been shown capable of stimulating growth

and increasing the efficiency of the biological pump in these regions. This study uses a model

incorporating nutrient-limited phytoplankton growth, lateral diffusion and export by sinking

of aggregates to investigate the factors which enable maximum export of carbon from the

mixed layer. Export per unit area and total export increases with increasing maximum growth

rate, fertilising concentration and the length scale of the patch. Growth rate was found to be a

major determinant of the time scales involved in export, including the time at which nutrients

become depleted, and the time to first export. Increasing growth and fertilising concentration

increase maximum export flux, and multiple export peaks may occur when either growth or

fertilising concentration are sufficiently large to allow the critical concentration for export to

be reached before diffusion can dissipate concentrations. Successively fertilising the same

patch demonstrates that export increases as the inter-fertilising period increases. The time

series of export is complex and does not suggest a stable pattern of export in runs conducted

for 18 days. The scale of randomness in the initial phytoplankton distribution has little effect

on the export per unit area generated, however, introducing small scale subpatches within the

fertilising patch significantly increases export by allowing diffusion into areas vacated by

export. Knowing these characteristics in which export is maximized, and the parameters

which characterise the export behaviour, allows for the more efficient implementation and

management of iron enrichment to mitigate global climate change.

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Acknowledgements I’d like to thank my supervisors, Anya Waite, Greg Ivey and David Johnson for all their

guidance and support throughout the year.

Anya has aided me all the way through this project, not only in an academic sense but also by

giving me just enough space to go at my own pace, but keeping me on track when I asked for

it. Most importantly though, she has given me the encouragement needed to move forward

whenever my confidence was fading.

David has provided invaluable help in understanding the model and has been great for

bouncing some ideas off. His enthusiasm for the project was fantastic.

Greg has given fluid mechanics know-how and constructive criticism when presented with

‘rough and ready’ material.

Also a host of family and friends for helping me through the year. Mum, Dad, Lisa and Bec;

The Quaternity – Abi, Chris and Emma; All who have ever played soccer with me on Sunday;

and the final year engineering crew who have all suffered together with me.

Also others; some over-enthusiastic third years; Michelle Carey for running a club for which I

was meant to be president; and Luke Brown for quick and cheerful computer support.

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Table of Contents

Table of Contents v List of Figures vi List of Tables viii Chapter 1 Introduction 1

1.1 Background 1 1.2 Direction of this study 2

Chapter 2 Literature Review 3 2.1 Climate change and the role of the oceans 3 2.2 In-situ iron fertilisation experiments 6

2.2.1 IronEx I 7 2.2.2 IronEx II 9 2.2.3 SOIREE 11

2.3 Modelling an iron-stimulated biological pump 13 2.3.1 Models of phytoplankton dynamics 13 2.3.2 Models of carbon export 14

Chapter 3 Methodology 21 3.1 Model Theory 21 3.2 Application of model theory 22 3.3 Investigation of parameters 23

3.3.1 Basic parameter set 24 3.3.2 Variation of growth and fertilising concentration 24 3.3.3 Variation of spatial distribution 25 3.3.4 Multiple fertilisation events 26

Chapter 4 Results 28 4.1 Variations of growth and fertilising concentration parameters 28

4.1.1 Time scales of export 29 4.1.2 Maximum growth rate 30 4.1.3 Fertilising concentration 31 4.1.4 Variation of the initial phytoplankton distribution length scale of randomness 33 4.1.5 Variation of the fertilising concentration length scale 36 4.1.6 Multiple fertilisation events 40 4.1.7 Multiple fertilisation export time series 41

Chapter 5 Discussion 48 5.1 Interpretation of results 48

5.1.1 Variations of maximum growth rate and fertilising concentration 48 5.1.2 Time scales of export 50 5.1.3 Spatial distributions 51 5.1.4 Multiple fertilisation events 52 5.1.5 Summary of interpretations 54

5.2 Practical implications 55 5.3 Issues concerning iron fertilisation for the mitigation of climate change 59 5.4 Recommendations 60

Chapter 6 Conclusions 63 References 65 Appendix 1 70 Appendix 2 74

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List of Figures

Figure 2.1 – Atmospheric and oceanic carbon interactions. (from Chisholm, 2000) 4

Figure 2.2 – Time series of mean export of a nutrient-limited growth-diffusion export model (from Waite and Johnson, 2003) 19

Figure 2.3 – Export simulated from a growth-diffusion-export model and its relationship with patch size and the non-dimensional parameter, Q (from Waite and Johnson, 2003) 19

Figure 3.1 – Example of initial phytoplankton distributions at the four different random length scales input. 26

Figure 3.2 – Nutrient distributions of the three fertilising patch variations used. 26

Figure 4.1 – The effect of variations of maximum growth rate, µmax and fertilising concentration for the three different patch lengths shown. The plots represent export per unit area in the left column, time to nutrient depletion, tN in the central column and tN x µmax in the right column. Derived from 10-run ensemble. 28

Figure 4.2 – Export per unit area per unit concentration of nutrient applied, generated by variations of maximum growth rate and fertilising concentration for three different patch lengths – 10k, 25 km and 50km. 29

Figure 4.3 –Time series of export showing variations with maximum growth rate. 30

Figure 4.4 – The variation of parameters characterising export time series behaviour with maximum growth rate. 31

Figure 4.5 – Time series of export showing variations with fertilising concentration. 32

Figure 4.6 - The variation of parameters characterising export time series behaviour with fertilising concentration. 33.

Figure 4.7 – Export time series for four length scales of randomness in initial phytoplankton distribution. Patch length 25km. 34

Figure 4.8 – Export time series for four length scales of randomness in initial phytoplankton distribution. Patch length 40km. 34

Figure 4.9 - Export time series for four length scales of randomness in initial phytoplankton distribution. Patch length 70km. 34

Figure 4.10 - Export time series for four length scales of randomness in initial phytoplankton distribution. Patch length 85km. 34

Figure 4.11 – Export per unit area generated over 10 days from a single fertilisation for different length scales of randomness of the initial phytoplankton distribution. 35

Figure 4.12 - Export time series for three length scales of fertilising subpatch distribution. Patch length 25km. 36

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Figure 4.16 – Export per unit area generated over 10 days from a single fertilisation for different length scales of fertilising subpatch. 37

Figure 4.17 - Maximum export flux occurring in different spatial scales of initial phytoplankton distribution and fertilising subpatch scale and how these vary with the length scale, L. 38

Figure 4.18 - Mean time of export weighted by export flux occurring in different spatial scales of initial phytoplankton distribution and fertilising subpatch scale and how these vary with the length scale, L. 38

Figure 4.19 - Timing of the first export occurring in different spatial scales of initial phytoplankton distribution and fertilising subpatch scale and how these vary with the length scale, L. 39

Figure 4.20 - Timing of the first export occurring in different spatial scales of initial phytoplankton distribution and fertilising subpatch scale and how these vary with the length scale, L. 39

Figure 4.21 – Export per unit area generated by three fertilising distributions – at length scales of L/10 and L/5 – and uniform. Q varied by patch length, L. 41

Figure 4.22 – Export per unit area generated by the uniform fertilising distribution. Q varied by µmax. Note that the range of Q, especially where the downturn occurs, is not shown in Figure 4.21. 41

Figure 4.23 - Ten-run ensemble of export time series for multiple fertilisations at different patch length scales corresponding to Q = 0.0431, 0.0271, 0.0207, 0.0171, 0.0147, 0.0130, 0.0118, 0.0108 respectively. Growth rate is 0.4 /day. The period between fertilisations is 1 day (upper left), 3 days (above) and 9 days (left) and is indicated by the dotted line. 42

Figure 4.24 - Ten-run ensemble of export time series for multiple fertilisations at different patch maximum growth rates corresponding to Q = 0.0936, 0.0624, 0.0468, 0.0374, 0.0312, 0.0267, 0.0234, 0.0208, 0.0187, 0.0170 and 0.0156 respectively. Patch length is 25km. The period between fertilisations is 1 day (upper left), 3 days (above) and 9 days (left) and is indicated by the dotted line. 43

Figure 4.25 - Power spectrum density of export time series of 180 day pass. Analysis of final 160 days. The 6 fertilising periods are shown. 44

Figure 4.26 - Power spectrum density of export time series of 180 day pass. Analysis of final 160 days. 8 patch lengths for a fertilising period of 6 days. 45

Figure 4.27 - Power spectrum density of export time series of 18 day pass of different spatial distributions. 44

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List of Tables

Table 3.1 - Inputs into MATLAB code, “diffgrow2.m” 31

Table 3.2 - Outputs from MATLAB model, “diffgrow2.m” 31

Table 4.1 – Number of export peaks in 10-run ensemble. 35

Table 4.2 - Distinguishable periods of export from spectral analysis of export time series. 45

Modelling Ocean Fertilisation Patch Dynamics Introduction

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Chapter 1 Introduction

1.1 Background The biological pump is the process by which atmospheric carbon, in the form of carbon

dioxide (CO2), is fixed by phytoplankton during photosynthesis and then conveyed to the

deep ocean when they die and sink. In as much as 25% of the world’s oceans the efficiency of

the biological pump is greatly reduced and these areas are known as high nutrient, low

chlorophyll (HNLC) regions (de Baar et al., 1999).

In the past decade several mesoscale in-situ iron enrichment experiments have demonstrated

that the HNLC condition and consequently the inefficiency of the biological pump is due to

the limitation of iron in these areas (Boyd, 2002; Coale et al., 1996; Coale et al., 1998). By

applying iron it is possible to create a phytoplankton bloom and, in at least one of the

experiments it has been shown that this leads to a significant increase in the carbon that is

moved from the atmosphere and ‘exported’ from the mixed layer to the deep ocean. These

experiments have been conducted over scales of 8 to 12 km2 and numerical models have

shown that scales of at least 10km are necessary to generate this carbon export (Waite and

Johnson, 2003).

Iron fertilisation of HNLC iron-depleted regions is gaining interest both for its scientific value

and its potential for mitigating climate change. Atmospheric carbon is believed to be

responsible for the majority of the climate change observed over the previous 1000 years

(Crowley, 2000) and because ocean fertilisation promises to increase the rate that atmospheric

carbon is moved and sequestered in the deep ocean, it is thought that it can be used in the

mitigation of climate.

Whether for scientific research or for mitigating climate change, in-situ iron enrichment

experiments, by necessity, require very large areas, and expensive and time consuming

methodologies. Numerical modelling of the characteristics of phytoplankton dynamics, and in

particular export of carbon to deep waters exist as an attractive option in determining how

Modelling Ocean Fertilisation Patch Dynamics Introduction

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most efficiently to apply iron in specific natural conditions, and how the resulting patch might

be suspected to behave.

1.2 Direction of this study Waite and Johnson (2003) have developed a simple model that considers three important

processes in phytoplankton dynamics under a nutrient-limited regime – nutrient-limited

growth, lateral diffusion and export by aggregation. They have also highlighted the spatial

and temporal complexity that exists in phytoplankton dynamics, even when simplifying

assumptions are used, and how this complexity leads to carbon export behaviour that is non-

trivial.

This study aims to investigate the parameters that characterise the carbon export behaviour of

the Waite and Johnson (2003) growth-diffusion-export model. In particular, it seeks to

determine the conditions and methodology for applying the fertilising nutrient that most

efficiently generates carbon export from the mixed layer.

Modelling Ocean Fertilisation Patch Dynamics Literature Review

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Chapter 2 Literature Review

2.1 Climate change and the role of the oceans Since the industrial revolution, anthropogenic activity has unbalanced the process known as

the global carbon cycle, by which carbon is moved and partitioned over the earth. Changing

land use and the mining and consumption of fossil fuels have converted terrestrial carbon into

atmospheric carbon, in the form of the greenhouse gas, carbon dioxide (CO2), at a rate that

has not been seen in the previous 1000 years (Crowley, 2000). The CO2 present in the

atmosphere has increased by more than 25% since 1957 (Wigley and Schimel, 2000) and it

has been determined that CO2 contributes most significantly to the changing global climate

(Crowley, 2000). The effect of this increasing pool of carbon in the atmosphere is an increase

in global temperatures as famously reported from the Mauna Loa research station in 1985

(Bacastow et al., 1985).

Although the atmospheric carbon pool is increasing, it is by no means the largest carbon pool

in the global carbon cycle. The intermediate and deeper layers of the world’s oceans contain

98% (38,100 Gt) of the earth’s carbon (Wigley and Schimel, 2000). Consequently, it is the

oceans that offer the greatest capacity for buffering the atmospheric carbon change and global

temperature increase.

The atmospheric and oceanic carbon pools interact via several pathways, including chemical

gradient processes, biological processes and physical processes such as subduction (Chisholm

1995). Sarmiento and Bender (1994) estimate, however, that 75% of the difference in

dissolved inorganic carbon concentrations between the surface and deep ocean is due to the

biologically-mediated pathway known as the ‘biological pump’. The biological pump is the

process by which CO2 fixed in photosynthesis is transferred to the deeper layers of the ocean,

resulting in temporary or permanent sequestration (storage) of carbon (Figure 2.1).

Atmospheric CO2 is initially fixed by autotrophs, such as phytoplankton, which then either

become senescent and sink out as aggregates or are consumed by herbivores that produce

sinking faecal pellets (Chisholm, 1995). Removing the biological pump, and allowing carbon


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to be cycled in the ocean only by physical and chemical processes, would more than double

the CO2 concentration in the atmosphere through carbon release as the ocean equilibrated

(Chisholm, 1995).

The efficiency of the biological pump for carbon sequestration is not uniform across the

world’s oceans. High nitrate, low chlorophyll (HNLC) regions, namely the sub-arctic north-

east Pacific, the equatorial Pacific and the Southern Ocean (Chisholm et al., 2001), have long

provided a puzzling phenomenon for oceanographers because despite the favourable nutrient

conditions for production in these regions, productivity is extremely low (Gran, 1931). In

these regions productivity is not coupled to macronutrient concentrations, and even where

upwelling occurs, the resulting nutrients are not utilised (Martin, 1990). Considering that

these regions make up 25% of the world’s oceans (de Baar et al., 1999) they have attracted

considerable research interest into how they are sustained. This scientific interest has been

further accentuated in the last 30 years by the notion that one might use oceanic carbon

sequestration to mitigate the effects of global climate (Chisholm et al., 2001).

Figure 2.1 – Atmospheric and oceanic carbon interactions. The biological pump, with the fixation and removal of carbon to deep waters and recycling through grazing is shown on the left. Physical processes, subduction downwards and upwelling upwards, are represented on the right. (from Chisholm, 2000)


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Several theories have been put forward to address the HNLC phenomenon since its discovery.

It seemed apparent given the adequate light availability in these regions that nutrient

limitation was occurring, but the nutrient of limitation was debated. As early as the mid

1930s, iron was invoked as the limiting nutrient responsible (Hart, 1934), however only

recently has the pervasive contamination that distorted early trace element measurements been

reduced so that such propositions could be accurately tested (Morel et al., 1991). One of the

reasons for the limitation of iron has been that it is poorly recycled in the oceans and must

therefore come from wind-transported dust from terrestrial sources. This process is known as

Aeolian deposition (Duce and Tindale, 2001). The HNLC regions have poor rates of Aeolian

deposition because they are many hundreds of kilometres from a terrestrial arid source (Duce

and Tindale, 2001). Some offshore upwelling regions, with high macronutrient

concentrations, do not exhibit HNLC conditions and these regions coincide with areas of

relatively high Aeolian deposition via long-range transport (Martin, 1990).

It is generally considered (Boyd, 2002, Chisholm et al., 2001., Coale et al., 1998, Cullen,

1995) that what is now termed Martin’s Iron Hypothesis (Martin, 1990) was a major

development in the case for iron limitation in HNLC areas. Martin’s hypothesis states that

oceanic productivity during glacial periods may have been higher due to increased upwelling

of nutrients and greater Aeolian deposition of iron from atmospheric dust loads 10-20 times

greater than at present. Martin (1990) hypothesised that these conditions maximised the

efficiency of the biological pump, transporting much more atmospheric carbon to the

intermediate and deeper oceans than currently occurs and resulting in the lower CO2 levels

observed in the paleogeological ice core record. The low atmospheric CO2 in turn had already

been suggested as a mechanism for preventing radiative heating and ultimately leading to the

freezing of the planet over the short time scales observed. Martin’s Iron Hypothesis framed

iron limitation in oceanic regions within the context of geological CO2 levels, thereby

providing circumstantial evidence and a testable theory for the role of iron in large-scale

oceanic processes.

Several elaborations of Martin’s hypothesis have emerged since it was first proposed as

successive bottle and in-situ iron enrichment experiments refined the knowledge of iron

limitation in the open ocean (Cullen, 1995). Cullen (1995) notes that much of the early focus

of Martin’s ideas was considered in the context of HNLC regions. The outcome from a formal

workshop on the topic in 1990 formulated what Cullen calls “the HNLC-iron hypothesis: “An

increase in the rate of supply of iron to the surface layer of the ocean will reduce to depletion


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the unused macronutrients, nitrate and phosphate.” ” (Cullen, 1995, p1336). It was intended

that this hypothesis would provide a testable theory of iron limitation. When the rate of supply

of iron to the surface layer of the ocean was increased in the first in-situ iron enrichment

experiment, IronEx I, but the concentrations of nitrates and phosphates varied very little, there

was good evidence to reject the HNLC-iron hypothesis. Cullen (1995) suggests however, that

neither the test nor the hypothesis were perfect since the increase in the rate of supply of the

iron is not defined by the hypothesis and that the iron infusion applied in IronEx I was too

ephemeral to be considered an appropriate test of the hypothesis.

When later discussions progressed, those inclined towards the ecological implications of

Martin’s hypothesis, independently arrived at what is called the “ecumenical iron hypothesis”

(Cullen, 1995). The ecumenical iron hypothesis states that when iron is scarce, smaller cells,

with greater surface:volume ratios can grow more rapidly than larger cells. Therefore the

population of small cells is not limited by iron, but by microzooplankton grazers whose rapid

growth rates can keep phytoplankton under control. By contrast, large cells are not able to

achieve high growth rates when iron is scarce. Under enrichment, however, they can

assimilate macronutrients at a rate that is too great for mesozooplankton to respond, and their

size prevents them from being consumed by microzooplankton. Although this hypothesis

views the HNLC condition by the vague notion of a grazer controlled iron-limited system,

ultimately it predicts that during the enrichment of HNLC areas, we would expect larger

phytoplankton to dominate (Cullen, 1995).

The testing of these hypotheses formed the impetus behind more than 4 in-situ iron

fertilisation experiments including IronEx I, IronEx II, SOIREE and EisenEx, conducted so

far.

2.2 In-situ iron fertilisation experiments

Martin and his colleagues realised that in vitro bottle experiments that had been executed to

date were inadequate in testing the ecosystem and carbon export consequences of their iron-

limitation hypotheses, in particular the ecumenical iron hypothesis (Coale et al., 1996).

Martin therefore proposed “perform[ing] realistic large-scale Fe enrichment experiments in

which phytoplankton species composition, elemental ratios of C:N:P and Si, δ13C ratios, etc

… can be determined, as well as [investigating] the effects of grazing and associated fecal

pellet production, sinking rate and oxygen consumption processes” (Martin, 1990, p10).


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The greatest hindrances to such an experiment lay in the lateral and vertical exchanges

between enriched and ambient waters due to advection and turbulent diffusion (Frost, 1996).

The logistics of the number and accuracy of measurements were also significant, however

more than four in-situ experiments have now been carried out, demonstrating that the

technology and the methodology for successful testing does exist.

2.2.1 IronEx I

Conducted in 1993 in the Equatorial Pacific, this is considered the first in-situ testing of

Martin’s hypothesis. Coale et al. (1998) implicitly refer to the hypothesis tested during this

experiment as “determin[ing] whether iron enrichment in the presence of the entire

community results in an increase in the net new production” (p921). The site near the

Galapagos Islands was chosen as the most favourable location for an initial iron experiment

for a number of reasons (Martin and Chisholm, 1992). Primarily these were its high light

intensities and warm temperatures (~25ºC) which would enable high phytoplankton growth

rates, and the vast oceanographic and biological data already available for the area. In

particular, National Oceanic and Atmospheric Administration (NOAA) drifters suggested that

surface flow paths with eddies were rarely observed. This was important since the physical

coherence of the patch was deemed to be of particular concern for the experiment (Stanton et

al., 1998). The NOAA data suggested that the problem of spreading and streaking of the patch

by turbulent diffusive processes at eddy or frontal boundaries (Garret, 1983) could be avoided

at this site.

Pre-fertilisation testing demonstrated that the site was typical of the equatorial Pacific HNLC

area (Coale et al., 1998). Concentrations of nitrate and Chlorophyll a were 10.8 µM and 0.24

µgL-1 respectively and there was a strong pycnocline, well mixed surface layer to 30m and

low horizontal gradients. Initial concentrations of dissolved and particulate iron were

measured at depleted levels of 0.07 and 0.22 nM respectively (Gordon et al., 1998).

443kg of iron as pharmaceutical grade Fe(II) sulphate was deployed once to a large square

patch approximately 8km × 8km. The choice of spatial distribution was due to sampling

considerations which ruled out other methods such as ‘point source’ (Martin and Chisholm,

1992) or ‘streak’ (Watson et al., 1991) applications.


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The quantity of iron released was intended to achieve an ocean concentration of 4nM. This

was double the concentration necessary to achieve maximal phytoplankton growth in

laboratory bottle experiments but was considered necessary to account for possible iron

removal processes in the experiment. It was assumed that the concentration of iron when

released would be mixed through to the depth of the mixed layer within 24 h (Martin and

Chisholm, 1992). The root mean square distance for horizontal diffusion (square root of 2kxt)

in this period was calculated to be ~415m assuming a horizontal eddy diffusion coefficient of

kx ~ 10 km2d-1 (Coale et al., 1998). Therefore fertilisation tracks were separated by 450m.

These factors combined were intended to achieve the 4nM concentrations throughout the

patch after 1 day.

Iron behaviour was as expected. One day after iron release, maximum values in the patch

were 3.6 nM due to horizontal eddy diffusion and convective overturn (Coale et al., 1998).

The concentration of dissolved iron (DFe) decreased rapidly in the core of the patch over the

first four days of the experiment to 0.25nM Fe.

The biological response to fertilisation was dramatic. Productivity increased 3 to 4-fold in all

size fractions. Primary production increased monotonically from 10-15 mg C L-1 d-1 to 48 mg

C L-1 d-1 over three days and chlorophyll increased nearly 3-fold to 0.65 mg L-1. The chemical

response, however, was not correlated to this biological response. Although the biological

changes were sizeable, the magnitude of macronutrient drawdown was less than expected. In

contrast to bottle enrichment experiments in which there is complete drawdown (Coale et al.,

1998), nitrate drawdown was undetectable (<0.2 µM) and carbon dioxide fugacity was only

reduced by 10 µatm (Coale et al., 1996).

Approximately five days after the infusion of iron to the system, the core of the patch was

subducted to a depth of 30-35m beneath a low salinity front. At this depth it was confined to a

5-10m layer just above the thermocline. Although the patch could no longer be sampled by

the ship’s flow through system, the presence of the patch was still detectable from the SF6

signal, its distinct salinity and low light transmission (Coale et al., 1998). Since the SF6 signal

remained constant it is likely that the unfertilised waters did not penetrate and dilute the

subducted patch core (Coale et al., 1998).

Several theories were put forward to explain the subdued geochemical response observed in

IronEx I. These were that (1) iron was lost form the patch, (2) the subduction of the patch to


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lower light levels minimised the photodissolution of iron colloids and decreased rates of

bioavailable iron production, (3) zooplankton quickly cropped the increase in phytoplankton

biomass, and (4) another nutrient, such as zinc or silicate, became limiting thus preventing

further growth (Coale et al., 1996)

Although the experimental results were confounded by a subduction event, the results were

heartening. This initial experiment heralded the start of a new wave of oceanographic research

by demonstrating that that oceanographers were no longer restricted to observation but that

the problems associated with large scale in-situ experiments could be overcome.

2.2.2 IronEx II

The second iron fertilisation experiment which occurred in 1995 near 3.5°S, 104°W in the

Pacific, followed very closely the methodologies of IronEx I but tried to address the

hypotheses put forward for the unexpectedly low geochemical response to iron enrichment. It

was important that this experiment recreated the biological responses of IronEx I without the

confounding subduction event (Coale et al., 1996).

Prior to fertilisation, the concentrations of nitrate were typical of the HNLC region (~ 10µM)

and initial iron concentrations were expectedly low, recorded at 0.05 nM (Cavender-Bares et

al., 1999).

At day 0 (29th May), iron, in the form of FeSO4 and a SF6 tracer were applied over a 72km2

rectangular deployment area. This was done by creating streaks 400m apart, which were noted

to merge within 1 day. Mixed layer depth measured over the infusion period was averaged at

25m (Coale et al., 1996). Consequently, the day 1 concentration of iron was 2nM. Subsequent

infusions in days 3 and 7 maintained the iron concentration in the infused patch at

approximately 1nM (Landry et al., 2000).

The mixed layer of the patch increased to 50m by day 11 due to small mixing events. Periodic

increases in nitrate concentrations suggested these mixing events introduced nutrient-rich

waters from below into the patch. The patch also expanded horizontally with time from the

initial 72 km2 to 120 km2, however it retained cohesion throughout the experiment (Coale et

al., 1996).


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Chlorophyll a concentrations demonstrated a rapid and monotonic increase from 0.15-0.2

µgL-1 initially to almost 4 µgL-1 on day 9, two days after the last infusion of iron. Following

this peak, concentrations decreased to 0.30 µgL-1 on day 17 (Coale et al., 1996).

The biogeochemical response was significantly more developed than that observed in IronEx

I. Nitrate drawdown was approximately 5 µM, however this may be conservative considering

that some nitrate was probably mixed through from below during mixing events on days 11

and 14. After two days, nitrate drawdown tracked silicate drawdown suggesting that diatom

growth was responsible for most of the nitrate uptake (Coale et al., 1996).

Carbon dioxide drawdown also paralleled nitrate drawdown. Maximum depletion occurred on

day 9 in conjunction with the maxima of most of the other biological and chemical indicators

of growth. The south equatorial Pacific near the site is recognised as a strong source of CO2 to

the atmosphere (fco2 in seawater, 526 ppm; fco2 in the atmosphere, 360ppm), however, iron

enhanced growth enabled a drawdown of about 90 µatm, which significantly reduced

outgassing of CO2 from these waters. However, it is not believed that drawdown was so

severe as to limit carbon (Coale et al., 1996).

Iron was rapidly taken up or removed following each of the infusions (initial and day 3 and 7

‘top ups’). It was noted that as the biomass increased in the patch due to iron addition, the rate

of iron removal also increased (Coale et al., 1996).

The community response to the iron enrichment was a shift towards larger organisms,

particularly diatoms. Diatom biomass increased over 85 times to dominate over the naturally-

abundant small (<5µm) phytoplankton which only doubled in size. Total phytoplankton

abundance increased dramatically since they were able to grow faster than predators could

consume them. This led to an imbalance in the early phase of the iron-induced bloom. The

modest picoplankton biomass increase demonstrates that these were most controlled by

zooplankton grazing. However, diatoms increased because they were too large to be

consumed by the fast-growing microzooplankton and too fast-growing to be controlled by the

slower-growing mesozooplankton (Landry et al., 2000).

Estimates of carbon new production suggest that between 5 and 12 µM C was exported from

the surface layer (Coale et al., 1996). Since community analysis showed a lack of larger

mesozooplankton grazers, which are commonly responsible for producing rapidly sinking


11

fecal pellets that transport carbon below the mixed layer, Coale et al. (1996) suggests that

grazing export did not remove the surface carbon. More likely is that export occurred by

vertical mixing and sinking of diatom aggregates. This is supported by the removal of the SF6

tracer to erosion at the base of the mixed layer by exchange with waters moving relative to the

advection of the patch and thus spread horizontally within the mixed layer (Coale et al.,

1996).

2.2.3 SOIREE

After the success of the iron enrichment experiments in the HNLC areas of the Pacific, the

next step was to trial the meso-scale perturbation experiment in the Southern Ocean. The

conditions of the Southern Ocean are significantly different to those of the equatorial Pacific,

in its physics, its geochemistry and its ecology/biology (Boyd, 2002). More importantly, an

experiment in the Southern Ocean is the ultimate test of the Iron Hypothesis because the

Southern Ocean has the greatest potential for carbon drawdown. This potential is due to the

size of the Southern Ocean, its vast quantities of unused nutrients, except for iron, and the

intermediate and deep water formation delivering surface waters (Chisholm, 2000). It is also

where the coherence between paleoclimate iron flux and carbon export has been observed

most strongly (Coale et al., 1996). Regardless of the iron hypothesis implications, its potential

for carbon drawdown also makes the Southern Ocean the most important place to implement

large-scale iron enrichment to further the understanding of the Southern Ocean’s ability to

mitigate climate change (Chisholm et al., 2001).

The Southern Ocean study site was chosen to be representative of a broad region of

circumpolar HNLC waters but have small current shear stresses in order to maximise the

timescales for tracking the fertilised patch. It was also necessary to try and balance a

regionally representative depth of the mixed layer, whilst making sure that the mixed layer

depth was not too deep so that phytoplankton would become dually iron and light co-limited,

and also so that the iron/sulphur hexaflouride (SF6) would be overly diluted (Boyd and Law,

2001). Whether a true balance was made between a regionally representative site, in the

horizontal and vertical sense, and one which fitted the criteria for successful experimental

design is difficult to say. The up- and down-welling behaviour of the Southern Ocean as well

as other physical behaviours are highly seasonal and also spatially variable (Trull et al.,

2001). Trull et al. (2001), also members of the SOIREE science team, contend that “less than

half of the Southern Ocean is likely to exhibit a response similar to that which occurred

during SOIREE (because only waters well south of the Polar Front are silica-rich throughout


12

the year), and that carbon export by bloom subduction is unlikely” (p2440). This is unless

there are significant changes in the community structure or algal physiology (Trull et al.,

2001). Given this, the site chosen is relatively representative of the summer period in which

the experiment was conducted, but will not represent any response seen in the winter at the

same site (Trull et al., 2001). The average mixed layer depth for the chosen site was 65m.

Pre-fertilisation testing showed that at the site, mixed layer nitrate and phosphate, at ~25 ±

1µM and ~1.5 ± 0.2µM respectively, were relatively high. Dissolved iron levels were low at

~0.08 ± 0.03 nM for polar waters and chlorophyll a concentration was 0.25 mg m-3 (Boyd et

al., 2000). These concentrations are indicative of the Southern Ocean.

The methods for conducting a mesoscale iron enrichment experiment were quite well

established at SOIREE, following both IronEx I and II. As in the case of both the earlier iron

enrichment experiments, SF6 was used as a tracer for iron added as acidified FeSO4.7H2O.

Testing was conducted in a Lagrangian framework. The study site was infused with iron to

3.8nM in a patch ~50km2 at day 0 (9th February 1999). Subsequent infusions occurred on day

3, 5 and 7 to ~2.6nM over areas of 32, 33.8 and 38.5 km2 respectively (Boyd and Law, 2001).

The initial patch had mixed through within two days to 100 km2 and within 13 days to ~200

km2. No physical structural changes were observed within the first four days of the

experiment, however, calm days caused the generation of transient and temporary thermal

strata on days 5/6, 8/9 and 13. (Boyd et al., 2000)

Dissolved iron was measured as a criterion for subsequent iron infusions. After the first

infusion, levels were initially increased similar to those in Iron Ex I and II and iron rich areas

of the Atlantic polar front (Boyd et al., 2000). By day 2, however, levels of iron had

decreased rapidly, presumably due to the effects of the patch spreading and conversion to

particulate iron. Total (unfiltered) iron remained at ~2nM. Later infusions followed when

dissolved iron concentrations approached background levels. After the fourth and final

infusion iron levels decreased, but thereafter remained relatively stable at ~1nM until the end

of the study site occupation (Boyd et al., 2000).

The geochemical response was expectedly large. Nitrate drawdown was 3µM and pCO2

drawdown was 35µatm, which, although less than the equatorial pacific equivalents, are still

sizeable (Boyd, 2002). The biological and physiological changes that were observed in both

IronEx I and II were also observed in SOIREE. Ratios of carbon to chlorophyll a halved by


13

day 13 to ~45 within the patch compared to just prior to the first infusion. The community

structure also changed. There was a floristic shift over the period of the experiment with

initial chlorophyll a increases attributed to pico-eukaryotes, to autotrophic flagellates between

days 2 and 8, and finally to large diatoms (particularly Fragilariopsis kerguelensis) from day

6. These large diatoms, of between 30-50 µm cell length and growing at 4.4 x 104 cells L-1 by

day 12, also increased the number of cells in their diatom chains twofold to 14 by day 12. It is

believed that this floristic shift is responsible for mediating changes in the concentration of

climate-reactive gases in surface waters (Boyd et al., 2000). The dominance by F.

kerguelensis is also believed to be responsible for the low rates of diatom herbivory as it is

morphologically adapted, with a highly silicified skeleton, to minimise grazing. Diatoms

accounted for 75% of production (Boyd et al., 2000)

Although the SOIREE study supported the first tenant of Martin’s iron hypothesis by

demonstrating a significant biological response to iron addition, it did not support the second

tenant in that there was no evidence of increased particle export (Boyd et al., 2000). It is

likely that the lateral diffusion, which amounted to 25% of the algal growth rate, prevented a

single large export event (Waite and Nodder, 2001). Furthermore, sediment traps suggest that

sinking rates and aggregation characteristics did change over the course of the experiment.

This is consistent with Muggli et al. (1996) who have shown that sinking rates are higher

under iron stress. The phenomenon of aggregate formation was increased during iron

enrichment (Waite and Nodder, 2001).

2.3 Modelling an iron-stimulated biological pump

Modelling the biological pump is important in understanding the role that the oceans play in

the global carbon cycle. Accurate modelling requires consideration of aspects of

phytoplankton growth and distribution, and how the carbon fixed by phytoplankton is

conveyed to the intermediate and deep ocean.

2.3.1 Models of phytoplankton dynamics

The early work of Kierstead and Slobodkin (1953) developed a classical model for oceanic

phytoplankton dynamics by balancing horizontal diffusion with growth of phytoplankton in

the mixed layer. They considered a body of water that was favourable to growth bounded by,

and mixing at the edges with, water that is unsuitable. The unsuitable water could be


14

characterised by any of several parameters including salinity, temperature or nutrients. In the

case of iron enrichment the suitable waters are no longer limited by iron whereas unsuitable

water is still iron-constrained and therefore has relatively small growth rates. By assuming

that diffusive losses were large, or that the water was otherwise unsuitable for concentrations

of phytoplankton outside a particular area of patch, the Kierstead and Slobodkin model

delivers a critical minimum patch size able to be sustained. Subsequent elaborations of this

model incorporated the effect of grazing by zooplankton (Wroblewski et al., 1975; Platt,

1975), the scale dependence of the diffusion coefficient (Platt and Denman, 1975), nutrient

limitation and light periodicity (Wroblewski and O’Brien, 1976).

In its simplest form, considering only horizontal diffusion with spatially constant diffusion

coefficients and by neglecting advection, phytoplankton dynamics within the patch can be

represented by:

QCSCdx

CdKdtdC

h −+= max2

2

µ

where C is the concentration of phytoplankton

Kh is the horizontal diffusion coefficient

µmax is the maximum growth rate

S is the function that details the growth formulation

and; Q is the rate of collective removal of phytoplankton from predation by herbivores,

extracellular release, and sedimentation.

(Wroblewski and O’Brien, 1976)

2.3.2 Models of carbon export

Below the surface or mixed layer it can be assumed that oceanic waters are quiet and that

there is little return of particles to the surface (O’Brien et al., 2003). In modelling the

biological pump one therefore needs only to consider carbon export from this mixed layer.

Sedimentation of particulate organic carbon (POC) is the primary biologically-mediated

method of carbon export from the mixed layer in marine systems. Due to Stokes’ Law larger

particles sink faster than smaller particles or cells and therefore have a significant effect on

the fate of organic matter (Jackson and Lochmann, 1992). They contribute disproportionately

to the carbon flux into deeper waters. Consequently, carbon export models have focussed on

these larger particles and the processes which form them.


15

Large particles may exist as large phytoplankton, especially diatoms, or as accumulations of

smaller particles, especially smaller phytoplankton (nanoplankton or picoplankton).

Furthermore, these accumulations may be aggregates formed from the collisions between

particles, or as non-aggregate particles formed through mechanisms including algal division

and diatom chain formation.

Aggregates of organic matter (also known as flocs or “marine snow”) are a highly visible

phenomena observed in the wake of an algal bloom (Jackson, 1990). The collision processes

by which they form have been artificially replicated in the laboratory with naturally occurring

organic matter (Waite et al., 1997). Kinetic coagulation theories developed in understanding

particle dynamics of lakes, conclude that the rates of algal losses to aggregation (coagulation)

can be comparable to losses caused by zooplankton grazing. This is supported by algal losses

in in-situ iron enrichment experiments in oceanic systems (Boyd et al., 2002; Coale et al.,

1996) and the ecumenical iron hypothesis (Cullen, 1995) which both demonstrate that when

iron is abundant sedimentation losses are at least as important as herbivory losses.

In coagulation theory, an aggregate is a particle formed by collision of two smaller particles,

the largest aggregates being the product of repetitive collisions and coalescence of smaller

ones. Up until Jackson (1990) the concepts of coagulation theory had been applied primarily

to freshwater environments to explain mass fluxes. Jackson applied these principles to a

marine system and expanded the focus of the theory to explain the effect of coagulation and

carbon export on phytoplankton dynamics. In the Jackson model a number of different size

classes were considered. Particles were removed from a particular size class either into a

larger size class following a collision and coagulation, or as they were exported below the

mixed layer. The likelihood of incorporation into larger and larger sized particles, the

collision rate, was given by a function of sizes of colliding particles, their concentrations and

environmental and physiological parameters. Three collision mechanisms were used to

describe particle collisions – Brownian motion, shear (either laminar or turbulent) and

differential sedimentation (in which a larger particle falling faster than a smaller one ‘runs

into the back’ of the smaller one).

The Jackson model used the criteria that the fundamental size class was a solitary cell and the

size of each particle is given by the number of cells it contains. The source of particulate


16

matter for the model was cell growth, increasing the size of aggregates and increasing the

number of separate solitary cells. The ultimate source is removal by sinking.

An important conclusion of Jackson’s model is that algal systems have a two-state nature,

either coagulation is not important or it is dominant. The distinction between these two states

occurs at some critical cell concentration (Ccr) (Jackson and Lochmann, 1992). This provides

a parameter to compare the likelihood of continued growth (<Ccr) or rapid loss of particles to

coagulation and decrease in particle concentration (>Ccr). The value of this Ccr therefore

becomes important when we are considering the aggregation response of a system and the

relationship between growth as a source and export as a sink. Jackson and Lochmann (1992)

further developed this model by incorporating light and nutrient limitations, which

constrained the growth dynamics of the phytoplankton.

Since coagulating particles can occur when growth occurs even at reasonably constant rates,

there is likely to be a cap placed on phytoplankton concentrations in natural systems because

export from the mixed layer is ongoing (Jackson and Lochmann, 1992). The importance of

coagulation in controlling biomass is not likely to be great in areas where shear is low or

grazing is high. In natural systems, this value of Ccr will roughly correlate with the maximum

phytoplankton concentrations that exist (Jackson and Lochmann, 1992).

Results from SOIREE suggest that one of the primary algal losses from the iron-enriched

bloom was due to diffusive losses at the edges of the patch. The entrainment of surrounding

HNLC waters and subsequent dilution of phytoplankton stocks in the labelled patch was

given as a reason for its longevity. Abraham et al. (2000) report losses due to lateral diffusion

to be 0.1d-1, 75% of net growth rate. Boyd et al. (2001) call this a “physical artefact” in as far

as it obscures the biological processes underlying Martin’s hypothesis. Boyd et al. (2002)

investigate these “physical artefacts” in an aggregation model (Jackson and Lochmann, 1992)

modified by imposing a constant specific algal growth rate representative of both the SOIREE

and IronEx II mesoscale experiments. Two cases were modelled – a standard run,

incorporating best guesses of parameters from the respective enrichment experiments; and a

run with a higher net growth rate. The purpose of the higher net growth rate was in order to

mimic a larger scale enrichment experiment (~100km) where it was assumed that dilution of

bloom stocks via horizontal diffusion is negligible. An algal monoculture was assumed

because of its simplicity and the dominance of a single species in both the IronEx II and

SOIREE studies.


17

By using a higher net growth rate to represent lower diffusive losses the consideration of

diffusive losses by Boyd et al. (2002) is a simple one. Although the model is based upon a

thorough aggregation model (Jackson and Lochmann, 1992) it fails to consider classical

diffusion-growth theory (Kierstead and Slobodkin, 1953). Boyd et al. (2002) and Boyd et al.

(2001) mistakenly refer to lateral losses of phytoplankton bloom stocks as “lateral advective

losses” (eg – Boyd et al., 2002. pp 36-4) and the authors refer to Abraham et al. (2000) to

provide an estimate of this lateral loss. What these authors term “lateral advective losses” are,

however, more accurately referred to as “horizontal diffusive losses”. Indeed, this is the actual

context of Abraham et al. (2000) estimates quoted in Boyd et al. (2002) and Boyd et al.

(2001). In contrast to some of the assertions of Boyd et al. (2001), the concept of diffusive

losses is not uncommon in phytoplankton patch modelling (see Kierstead and Slobodkin,

1953). This paper will refer accordingly to lateral losses as horizontal diffusive losses, in the

more accurate context used by Abraham et al. (2000) and followed by Waite and Johnson

(2003).

The results of Boyd et al. (2002) do accurately reflect the timing of downward particle flux

measurements of both IronEx II and SOIREE. They do not, however, simulate the magnitude

of the changes in particle concentrations and downward flux from observations.

In modelling the role of diffusive losses in mesoscale enrichment experiments, applying a loss

term that is dependent upon length scale provides a more realistic consideration of the process

than merely using a higher net growth rate. This is the approach taken by Waite and Johnson

(2003). A simple horizontal diffusion-growth model is employed for phytoplankton dynamics

(Kierstead and Slobodkin, 1953; Wroblewski and O’Brien, 1976). Horizontal diffusion is

made to be length-scale dependent (Okubo, 1971) and spatially uniform.

A 2-dimensional model is justified by considering only phytoplankton which are uniformly

distributed vertically in the mixed layer. This is justified since sinking rates of unaggregated

phytoplankton are low (O’Brien et al., 2002). Vertical diffusion out of the mixed layer is

assumed to be small also. Vertical export from the mixed layer occurs only through

aggregation and sinking which is modelled as a two-state function (Jackson, 1990)

E= -1Ccr C≥Ccr

0 C<Ccr


18

This means that once concentration reaches a certain critical threshold there is an

instantaneous export of this amount out of the mixed layer. The rate of sinking of single cells

is considered to be negligible and it is assumed that the timescale of export by aggregation

and sinking is shorter than the timescale of growth (Jackson and Lochmann, 1992). Thus the

phytoplankton dynamics can be modelled according to the following relationship:

ECCKdtdC

h −+∇= µ2

Waite and Johnson (2003) investigate both the non-limited and nutrient-limited cases of

phytoplankton growth by developing the non-dimensional parameter, Q. Q represents the

ratio between diffusion growth and patch length scale.

2LKQµ

=

In both cases total mean export is dependent upon Q. The non-limited case demonstrates

characteristics chaotic patterns in surface patch structure as holes form from sinking in

concentrated areas.

In the nutrient-limited case the growth term, µ, is made to be dependent upon nutrient

concentration via the Monod equation (McCarthy, 1981). Nutrients are modelled in a similar

diffusion model to phytoplankton, diffusing horizontally but not vertically. Nutrient removal

is via uptake by phytoplankton. As phytoplankton sink out it was assumed that they take the

associated nutrients with them so there is no assumed recycling by grazing. Coagulation

theory also suggests that rapid removal of particles moves organic matter to the deep ocean

faster and makes it more likely they will fall rather than be eaten (Jackson and Lochmann,

1992).

In contrast to the non-limited case, nutrient limitation makes µ and therefore Q, time

dependent. Therefore Q is considered to be dependant upon µmax rather than µ in the nutrient-

limited case. Due to the time dependence, export occurs in events (Figure 2.2) with a primary

sedimentation event followed by smaller secondary events as nutrients are removed and

become increasingly limited (Waite and Johnson, 2003).


19

Figure 2.3 – Export simulated from a growth-diffusion-export model and its relationship with patch size and the non-dimensional parameter, Q. Note that export only occurs after Q ~ 0.7 (from Waite and Johnson, 2003).

Figure 2.2 – Time series of mean export of a nutrient-limited growth-diffusion-export model over 10 passes. At 10 km there is no export generated as the patch is too small. Duration and intensity increases as patch size increases. (from Waite and Johnson, 2003).


20

The total export increases with decreasing Q and therefore with increasing patch size (for

constant µmax) (Figure 2.3). The critical Q at which export begins to occur is 0.07 however the

maximum export occurs far beyond the assumptions of this model. At low values of Q (large

patch size) vertical diffusion out of the patch becomes comparable to the horizontal diffusion

and cannot be neglected.

The Waite and Johnson model highlights the spatial and temporal complexity of export and

phytoplankton concentration in fertilised patches, and therefore the inadequacies in field

sampling, especially in the in-situ enrichment experiments conducted so far. Furthermore, it

demonstrates that such experiments are not likely to be testing the second tenet of Martin’s

iron hypothesis, that is, export to intermediate and deep waters, because patch size is too

small to initiate export.

The temporal and spatial complexities in phytoplankton dynamics implied by the Waite and

Johnson model are inherently interesting, but especially so in the context of how these

complexities may affect the way that future in-situ experiments and non-scientific projects are

conducted. To date, the use of numerical models to simulate carbon export behaviour of a

phytoplankton system has been progressive but needs to be continued. Diffusion-growth-

export models address the key processes identified by in-situ experiments as determining

phytoplankton dynamics. The next step is too fully interrogate such models as to how these

processes create the phytoplankton and export behaviour observed.

Modelling Ocean Fertilisation Patch Dynamics Methodology

21

Chapter 3 Methodology

3.1 Model Theory A diffusion-growth-export model (Waite and Johnson, 2003) was used to simulate carbon

export from the phytoplankton system. This model is based upon a simple nutrient-limited

diffusion-growth equation with export from the mixed layer governed by a two-state function.

The model solves the diffusion-growth equation given below;

ECCKdtdC

h −+∇= µ2

where Kh is a spatially uniform horizontal diffusion coefficient, µ is growth rate and E is an

export function. This model considers only export by aggregation and sinking because the

time scales of sinking by aggregation are considered to be much smaller than those for

sinking of individual cells, or of other mechanisms of carbon removal, such as grazing

(Jackson and Lochmann, 1992).

The export function represents a simple two-state process. Either export is important when the

concentration is over some critical concentration, Ccr, and phytoplankton aggregate and sink,

or it is not significant (Jackson and Lochmann, 1992).

E= -1Ccr C≥Ccr

0 C<Ccr

The model considers only the domain given by the mixed layer. Vertical diffusion is

dominant over the low sinking rates of unaggregated phytoplankton within the mixed layer.

Therefore, the distribution of phytoplankton is considered to be vertically uniform (O’Brien et

al., 2002). However, vertical diffusion is small in comparison to the fast sinking rates of

aggregated phytoplankton exported from the mixed layer. Therefore vertical diffusion in and


22

out of the mixed layer is considered negligible. There is no resuspension of particles after they

have been exported.

Diffusion in the horizontal is assumed to be important (Boyd et al., 2002). A spatially

constant length scale dependent diffusion coefficient is applied given by Kh= α L4/3 (Okubo,

1971).

Growth is nutrient-limited according to the Monod equation:

+=

SNN

maxµµ

where N is the total available nutrient, µmax is the maximum growth rate and S is the half-

saturation constant. Nutrients are assumed to be distributed by similar processes to

phytoplankton, diffusing horizontally and removed due to uptake by growing phytoplankton

according to an uptake ratio C:nutrients (eg C:Fe). Vertical diffusion of nutrients outside the

mixed layer is neglected but within the mixed layer the concentration is assumed to be

vertically uniform.

In both IronEx II and SOIREE, a single species has been shown to be dominant following

iron fertilisation (Jackson and Lochmann, 1992). Consequently, this model takes a single

species approach. This also maintains simplicity in the model by necessitating that only one

growth rate aggregation threshold is chosen.

3.2 Application of model theory The model is coded in MATLAB as diffgrow2 (see Appendix 1) and model inputs shown in

Table 3.1. Some of these inputs have been added to the model developed by Waite and

Johnson (2003), however, these affect peripheral behaviour of the model only and neither the

phytoplankton nor export dynamics.

The model outputs are shown in Table 3.2. Some of these outputs are additional to those of

the basic Waite and Johnson model. These have been incorporated into the model to identify

aspects of the nutrient dynamics (for example, tNdeplete, the time to nutrient depletion)

whereas others show phytoplankton dynamics by simply outputting what is already

determined in the model itself. This was necessary to understand how the phytoplankton

growth over time corresponds to export changes.


23

Table 3.1 – Inputs into MATLAB code, “diffgrow2.m” Model inputs Description

C Initial phytoplankton concentration (in terms of carbon)

Nf Fertilising nutrient distribution

Nb Background nutrient

K Horizontal diffusion coefficient

G 3 element growth vector G(1) – growth rate, µ

G(2) – half-saturation constant, S

G(3) – nutrient uptake rate (percent nutrient usage per unit growth).

T Threshold for export. Equivalent to Ccr

C=0 if C>T

dx Grid size (square matrix)

dt Time step size

steps Number of time steps

bound Defines the boundary condition 0=open

1=closed

2=periodic

movname Name of animation, if generated

p Defines plotting and animation condition

0=no plotting or animation

1=plotting and animation

Table 3.2 – Outputs from MATLAB model, “diffgrow2.m”

Model outputs Description

Cout Final surface phytoplankton distribution

Nout Final surface nutrient distribution

Eout Spatial export distribution

Et Export time series

tNdeplete Time to nutrient depletion

Cc Biomass time series

Cpua Concentration per unit area time series

3.3 Investigation of parameters Investigation of parameters was conducted by varying the values of a number of inputs and

observing the time series of export and total export generated. A basic parameter set was


24

determined and the values of parameters not intentionally varied were maintained at this

setting.

The parameters varied were maximum growth rate, µmax, the concentration of the nutrients

applied, f, the initial distribution of phytoplankton and the concentration distribution of

applied nutrients. Batch codes were created that took the mean of 10 passes of the model and

sampled the variation due to the random initial phytoplankton distribution.

3.3.1 Basic parameter set

The basic input parameters adopted were those used by Waite and Johnson (2003). The half

saturation constant in the Monod equation (G(2) input into the model) is set at S=0.2

µmol.Fe.m-3 and the maximum growth rate is 0.4 day-1. The uptake ratio for C:Fe is given as

0.002 by Waite and Johnson (2003), however, this is in error, and should be set at 0.2

(Johnson, pers. comm.). An uptake ratio of 0.2 is considered throughout all model runs,

however such a value is ad hoc in nature because other nutrients are likely to become limiting

when iron is in excess (Hutchins and Bruland, 1998). The threshold, or Ccr, value used

throughout all model runs was 14 mmol C m-3. This is used by Waite and Johnson (2003) but

is also supported by field samples from the subarctic Pacific and the Ross Sea, Antarctica

(Jackson and Lochmann, 1992).

The initial phytoplankton concentration, C, was given by a random concentration distribution

over the 5L by 5L domain of the model. A square patch of nutrients was seeded on the centre

of this background over an area of L by L. An L=10 cells resolution was used to represent

these length scales in the model (i.e. dx =L/10).

The timestep dt was made to be dependent upon the grid size, dx, by taking the minimum

value of either 0.2 or 0.5(dx)2. This methodology is used by Waite and Johnson (2003). The

horizontal diffusion coefficient, Kh is also length scale dependent according to the fertilizing

patch length scale, L as Kh= α L4/3 with α= 0.08 km2/3day-1 (Okubo, 1971)

3.3.2 Variation of growth and fertilising concentration

Values of maximum growth rate, µmax, were varied over the range encountered in natural

oceanic waters. Fertilising concentration, f, was more broadly varied near the range used in

the in-situ experiments conducted to date.


25

3.3.3 Variation of spatial distribution

As the spatial variation was deemed to be an important factor leading to high concentrations

and therefore carbon export, several patterns of initial phytoplankton distribution and

fertilised patch were trialled. These variations are demonstrated in Figure 3.1 and 3.2. All

spatial variations retain the same fertilising length scale, L, (area of enrichment is L by L) and

the same initial phytoplankton background domain of 5L by 5L.

Initial phytoplankton distribution has four cases, length scales of randomness - of L/10, L/5

and L/2 - and a deterministic case in which the concentration is uniformly applied (Figure

3.1). In random distributions, cell values are randomly generated in MATLAB with a

maximum of 6.0 mmol C m-3 and a mean of 3.0 mmol C m-3. The deterministic case applies

concentrations of 3.0 mmol C m-3. These initial phytoplankton variants will be referred to as

the randomness length scales of L/10, L/5, L/2 and the deterministic case.

Three fertilising concentration distributions were applied (Figure 3.2). Each of these had a

fertilising patch length of L but two had subpatches of lengths L/10 and L/5 (Figure 3.2 (b)

and (c)). The variants of fertilising patch distribution will be referred to as uniform, subpatch

length L/10 and subpatch length L/5 ordered as shown in Figure 3.2. In order to allow

comparison of total export between different patch variants, the overall nutrient concentration

applied over the domain was kept constant. This meant that the concentration per unit area in

some cells was increased. Applied nutrient concentration was 2.44 times higher in nutrient

cells for the L/10 case and 6.25 times higher for the L/5 case.


26

3.3.4 Multiple fertilisation events

Temporal variations in the way nutrients were applied were investigated, in particular, the

total export and export time series, by applying nutrients to the domain more than once.

Multiple applications of iron were a feature of both IronEx II and SOIREE.

A further function which encompassed the diffgrow model in a user-specified repeat

procedure was created (coding in Appendix 2). The domain was repeatedly fertilised with the

same fertilising patch variant over an 18 day period, followed by a period of 15 days ‘cooling

down’ without fertilisation. The period between nutrient applications was varied from 1 day

Figure 3.1 – Example initial phytoplankton distributions at the different random length scales input - a) L/10, b) L/5, c) L/2 and deterministic distribution d) uniform. The basic passes of the model use the distribution shown in a).

a

dc

b

Figure 3.2 – Nutrient distribution of fertilising patch variations – length scales a) uniform, b) L/10, c) L/5. Green indicates the presence of nutrients and blue the absence. The basic passes of the model use the distribution shown in a).

L a cb


27

to 2 days, 3 days, 6 days, 9 days and once in the 18 day period. It was necessary to choose

integer factors of the 18 day fertilisation period so that each fertilisation period could fit

wholly into the 18 day period. In order to allow comparison of total export the same amount

of nutrients needed to be applied overt the 18 day fertilisation period. Therefore, the total

nutrients applied at each fertilisation event was made to be a factor of the fertilisation

frequency. When fertilising once every day the factor was times1, and when fertilising once

over the 18 days the factor was times 18.

Spectral density estimates (using MATLAB’s in-built PSD function) were carried out on the

export time series output of the 10-pass ensemble of these multiple seeding runs to identify

the dominant frequencies present. Spectra were also calculated for an ensemble of 10 passes

of a longer 180 day run from which periodicity was expected to be more evident. To identify

only the dominant periods only spectral powers greater than 1x104 were considered.

Modelling Ocean Fertilisation Patch Dynamics Results

28

Chapter 4 Results

4.1 Variations of growth and fertilising concentration parameters Export per unit area increases both with increasing fertilising concentration and increasing

maximum growth rate (Figure 4.1). Export increases linearly with applied nutrient

concentration, but is non-linearly affected by maximum growth rate. This means that the

effect of increasing growth rate is greatest when growth rate is small and tapers off when

growth rate is larger.

Figure 4.1 – The effect of variations of maximum growth rate, µmax, (on axis from 0 to 1) and fertilising concentration (on axis from 0 to 10) for the three different patch lengths shown. The plots represent, on the z axis, export per unit area (mmol C m-2) in the left column, time to nutrient depletion, tN (days) in the central column and tN x µmax in the right column. Derived from 10-run ensemble.

Export /area (mmol C m–2) tN (days) tN x µ

10km

25km

50km

Fertilising conc. µM/m3

µmax (/day) µmax (/day)

Fertilising conc. µM/m3

µmax (/day)


29

Increasing the patch size is also important for the amount of export generated. The frontier for

export to occur moves towards lower concentrations and lower growth rates as patch size

increases. That is, export occurs for a greater range of growth and fertilising concentration

parameters at larger length scales than it does at smaller lengths scales.

By normalising the export by the fertilising concentration, export still increases with

fertilising concentration, however the curvature of the export slope with fertilising

concentration is no longer linear. Instead it shows concentration increase to be more important

when concentration is low than when it is high.

4.1.1 Time scales of export

Figures 4.5 and 4.1 demonstrate that time to first dump and time to nutrient depletion are

unaffected by changes in fertilised concentration. These parameters are significantly affected

by growth rate and appear to be bound by an inverse relationship (Figures 4.1 and 4.4). This

means that the inverse of growth rate can be considered an important timescale in export. This

proposal is partly supported by Figure 4.1 which demonstrates a somewhat constant

relationship between the maximum growth rate, µmax multiplied by time to nutrient depletion,

tN, and maximum growth rate. An inverse relationship between µmax and tN would lead to a

constant relationship between µmaxtN and µmax, however, Figure 4.1 does not show an entirely

constant relationship. Deviations from this pattern occur when growth rate is large and where

fertilising concentration is large and these are propagated to lower maximum growth rates and

lower fertilising concentrations with increasing patch length scale.

Figure 4.2 – Export per unit area per unit concentration of nutrient applied, generated by variations of maximum growth rate, µmax (on axis from 0 to 1) and fertilising concentration (on the axis from 0 to 10). Patch length is a) 10 km, b) 25 km and c) 50km.

Exp

ort

(mm

olC

m-2

µm

olFe

-1 m

3 )

a b c


30

4.1.2 Maximum growth rate

As maximum growth rate increases the time until the first export event reduces. There is a

significant reduction from approximately 10 days, when export begins to occur, to close to 2

days at maximum growth rates of 0.7 /day. The weighted average of export flux moves

closely with the time to first export since the duration of the export event is short and

reasonably constant.

At higher growth rates there is evidence of two export peaks. The maximum export flux

increases with growth rate but there is also a secondary event with a smaller export flux. This

secondary event usually occurs after the maximum export event, however it may also occur

before (Figure 4.3e)).

a c b

d e f

Figure 4.3 – Ten-run ensemble of time series of export showing variations with maximum growth rate. Maximum growth rates a) – f) are 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7 /day respectively. The fertilising concentration is 4.0 µmol m-3. Patch length, L = 25 km.

Expo

rt (m

mol

C m

-2 day

-1)

Time since nutrient fertilisation (days)


31

Figure 4.4 demonstrates the behaviour of the export time series with changing maximum

growth rate by considering some descriptive parameters. The time of the first export is related

to maximum growth rate in an apparently inverse relationship. The mean time of export,

weighted by export flux closely resembles this pattern, because as shown, export occurs

reasonably instantaneously and only increases slightly with µmax. This increase is due to the

multiple peaking demonstrated in the complete time series (Figure 4.3).

4.1.3 Fertilising concentration

Increasing fertilising concentration has little impact on the time scales involved in the export

time series (Fig 4.5). For the maximum growth rate of 0.4 day--1 used, the timing of the first

export event falls consistently about 4.2 days. The fertilising time scale does, however, appear

to have a more significant impact on the distinction of export ‘events’ that occur. Two events

are clearly distinguished for concentrations of 6.0 and 7.0 µM m-3 that are far more distinct

than the multi-peaking seen in Figure 4.3 for high growth rates. Less distinct multi-peaking of

the kind seen in Figure 4.3 are, however, evident in both the 4.0 and 5.0 µM m-3 and also

within the first and second distinguishable peaks. The multi-peaking at high fertilising

Figure 4.4 – Three parameters of export time series behaviour and how they change with increasing maximum growth rate. Weighted average is the mean time of export weighted by export flux.

0123456789

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Maximum growth rate (/day)

Tim

e (d

ays)

Weighted average Time of first export Export duration


32

concentrations is distinguishable due to the long duration of both peaks. This means that

although the initial export timing is unaffected by changes in fertilising concentration the

weighted average of export occurs more than 1 day later for the 7 µM m-3 than it does for the

3 µM –3 case. In contrast to the multi-peaking of short duration (Figure 4.5 c) and d)), the

distinguishable peaks are of relatively even export, indicating two major export events in their

own right. The characteristics of the second export event are of an increasing export flux

leading to the second peak. Animations created by the model show phytoplankton export

occurs at peripheral concentrated nodes, before the central area removed by the first export

event has recovered sufficiently from growth and diffusion from other areas to be at the

critical export concentration again, thus leading to the second export flux peak. The maximum

export flux of the time series is not substantial and if anything reduces as fertilising

concentration increases. Since export is sustained for a greater duration, however, the total

exported increases linearly as demonstrated in Figure 4.1.

a c b

d e f

Figure 4.5– Ten-run ensemble of time series of export showing variations with fertilising concentration. Fertilising concentrations a) – f) are 2.0, 3.0, 4.0, 5.0, 6.0, and 7.0 µmol m-3 respectively. The maximum growth rate is 0.4 /day. Patch length, L = 25 km.

Exp

ort (

mm

ol C

m-2 d

ay-1

)



33

Figure 4.6 demonstrates that after fertilising concentration is significantly large enough to

generate export, at 2 µmol m-3, it has little effect on the timing of the first export. There is,

however, a significant jump in the export duration at 6 µmol m-3 when the distinguishable

peaks in export begin to occur. This causes the weighted average to increase.

4.1.4 Variation of the initial phytoplankton distribution length scale of randomness

The random length scale of initial phytoplankton distribution does not cause any obvious

patterns of difference for export time series at smaller length scales, however as length scales

increase more export events occur (Figures 4.7 - 4.10). At 25km, single peaks occur for all

length scales.

Figure 4.6 - Three parameters of export time series behaviour and how they change with increasing fertilising concentration Weighted average is the mean time of export weighted by export flux.

0

1

2

3

4

5

6

0 2 4 6 8

Fertilising concentration (umol m^-3)

Tim

e (d

ays)

Weighted average Time to first export Export duration


34

Figure 4.7 – Patch length 25 km, 10-run ensemble of export time series for four length scales of randomness in initial phytoplankton distribution. Random length scale is (a) L/10, (b) L/5, (c) L/2 and (d) uniform.

a

c

b

d


Exp

ort (

mm

ol C

m-2

day

-1)

Figure 4.8 – Patch length 40 km, 10-run ensemble of export time series for four length scales of randomness in initial phytoplankton distribution. Random length scale is (a) L/10, (b) L/5, (c) L/2 and (d) uniform.

a

c

b

d


Expo

rt (m

mol

C m

-2 d

ay-1

)

Figure 4.9 – Patch length 70 km, 10-run ensemble of export time series for four length scales of randomness in initial phytoplankton distribution. Randomlength scale is (a) L/10, (b) L/5, (c) L/2 and (d) uniform.

a

c

b

d


Exp

ort (

mm

ol C

m-2

day

-1)

Figure 4.10 – Patch length 85 km, 10-run ensemble of export time series for four length scales of randomness ininitial phytoplankton distribution. Random length scale is (a) L/10, (b) L/5, (c) L/2 and (d) uniform.

a

c

b

d


Exp

ort (

mm

ol C

m-2

day

-1)


35

The number of export peaks occurring in each of the fertilising length scales is summarised in

Table 4.1. It shows that the number of peaks increases as the patch length scale increases but

this then decreases at the largest length, 85km.

Table 4.1 – Number of export peaks in 10-run time series ensemble.

Growth rate is 0.4 /day.

L/10 L/5 L/2 Uniform

25 km 1 1 1 1

40 km 2 2 3 1

70 km 3 3 4 2

85 km 1 2 3 1

The timing of the end of export is constant for each of the background phytoplankton

distributions, however, the duration of export is greater when the randomness length scale is

L/2 than in other cases. Consequently the time of the first export is earlier in the case of the

L/2 randomness length scales distribution.

Figure 4.9 demonstrates that there is very little difference between the amounts of export per

unit area generated by any of the different randomness length scales. The export per unit area

increases with patch length at the same rate for each of the random phytoplankton distribution

length scales, however there is a great deal of variation about this trend.

Figure 4.11 – Export per unit area generated over 10 days from a single fertilisation for different length scales of randomness of the initial phytoplankton distribution.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 20 40 60 80 100

Patch length (km)

Expo

rt (m

mol

C m

^-2)

length L/10

length L/5

length L/2

uniform


36

4.1.5 Variation of the fertilising concentration length scale

Figures 4.12-4.15 show that the uniform application of nutrients mainly generates single

peaks. By contrast, the smaller subpatch length scales are associated with multiple peaks at all

patch length scales. The maximum export flux of the different distributions is greatest at the

smallest (L/10) length scale. The L/5 length scale generally has a smaller maximum export

flux than either of the other distributions but has a greater duration of export than the uniform

nutrient application and equal or greater duration than the L/10 length. Note that the scales of

the ‘export’ axis vary between Figures 4.12 to 4.15 (but not within a figure).

The length scale of the fertilising subpatches has a significant effect on the export per unit

area (Figure 4.16). There is greatest divergence between the exports generated for different

fertilising distributions when the fertilising length scale is large.

Figure 4.12 – Patch length 25 km, 10-run ensemble of export time series for three length scales of fertilising subpatch application. Length scale is (a)uniform, (b) L/5 and (c) L/10.

a

c

b


Expo

rt (m

mol

C m

-2 d

ay-1

)

Figure 4.13 – Patch length 40 km, 10-run ensemble of export time series for three length scales of fertilising subpatch application. Length scale is (a) uniform, (b) L/5 and (c) L/10.

a

c

b


Expo

rt (m

mol

C m

-2 d

ay-1

)


37


a

c

b


Exp

ort (

mm

ol C

m-2

day

-1)


a

c

b


Exp

ort (

mm

ol C

m-2

day

-1)

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100

Patch length (km)

Expo

rt (m

mol

C m

^-2)

uniform

length L/5

length L/10

Figure 4.16 – Export per unit area generated over 10 days from a single fertilisation for different length scales of fertilising nutrient subpatch. Note significant divergence between length scales.


38

0

50

100

150

200

250

300

350

400

450

0 50 100

Patch length, L (km)

Max

imum

exp

ort f

lux

(mm

ol C

m^-

2 da

y^-1

)

BasicRandomness L/5Randomness L/2DeterministicSubpatch L/5Subpatch L/10

0

1

2

3

4

5

6

7

0 20 40 60 80 100


Mea

n ex

port

tim

e w

eigh

ted

by e

xpor

t flu

x (d

ays)


Figure 4.17 – Maximum export flux occurring in different spatial scales of initial phytoplankton distribution and fertilising subpatch scale and how these vary with the length scale, L.

Figure 4.18 – Mean time of export weighted by export flux occurring in different spatial scales of initial phytoplankton distribution and fertilising subpatch scale and how these vary with the length scale, L.


39

0

1

2

3

4

5

6

0 20 40 60 80 100


Tim

e to

the

first

exp

ort (

days

)


0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100


Expo

rt d

urat

ion

(day

s)


The greatest export flux at most L occurs at the smallest, L/10 subpatch length scale (Figure

4.17). This is in addition to generating the greatest export per unit area (Figure 4.16) The

deterministic, uniform initial phytoplankton distribution also demonstrates large export flux

associated with simultaneous sinking of the entire patch which occurs, as Figure 4.20 shows,

over small durations relative to the rest of the spatial distributions. The duration of export

does not increase greatly even as the length scale increases for the deterministic case,

however, in most other spatial variants there is an increases with the length scale, and in the

case of the L/5 scale subpatch, a significant jump in the export duration that coincides with

Figure 4.19 – Timing of the first export occurring in different spatial scales of initial phytoplankton distribution and fertilising subpatch scale and how these vary with the length scale, L.

Figure 4.20 – Timing of the first export occurring in different spatial scales of initial phytoplankton distribution and fertilising subpatch scale and how these vary with the length scale, L.


40

temporally distant multiple export events (Figures 4.12-4.15). The export duration is

considerably affected by the spatial variations. By contrast, the spatial variations do not have

a significant impact on the timing of the first export (Figure 4.19). These remain constant with

the length scale L also, suggesting that the length scale does not affect this timescale. The

exception to this is in the largest random length scale, L/2 which is variable, but does not

exhibit any discernible relationship with L. Figures 4.17 to 4.20 demonstrate that export does

not occur for L=10km and the fertilising concentration of 3 µmol m-3 and maximum growth

rate of 0.4 day-1 used throughout. This is with the exception of the smallest, L/10 subpatch

length scale of fertilising concentration distribution, which does export, demonstrating that

this variant is capable of supporting export at a wider range of parameters.


During multiple fertilisations, the amount exported from the mixed layer increases as

fertilisations become less frequent (Figure 4.21). It is likely that the effect of the amount of

nutrients applied at each fertilisation which is coupled to how often fertilisations occur also

has a significant impact on the greater amount exported. Q has little effect on the amount

exported by comparison to the effect of the inter-fertilising period.

Figure 4.21 demonstrates that the same relationship between fertilising period and Q exists for

each of the fertilising patch distributions. Export is, however, greater as fertilising patch

length scales decrease. This effect is most pronounced for large fertilising periods.

Although Q appears to have very little effect on export for values between 0.01 and 0.05, at

larger values of Q export decreases rapidly. There is an especially large downturn at large

fertilising periods (Figure 4.17). This demonstrates that when Q is small, maximum export is

greatly favoured by large fertilising periods, however, when Q is large, maximum export is

only marginally increased by applying greater fertilising periods and the associated increase

in fertilising concentration.


41

4.1.7 Multiple fertilisation export time series

The export time series produced by multiple fertilisation events are complex and appear

highly random (Figure 4.23 and 4.24). There is not clear evidence of regular periods of

export, for any of the fertilising frequencies, in the 18 day pass, however, regularity of export

is most obvious when the patch length is small (e.g. – 10km). At small length scales, export

Figure 4.22 – Export per unit area generated by the uniform fertilising distribution. Q varied by µmax. Note that the range of Q, especially where the downturn occurs, is not shown in Figure 4.21.

Figure 4.21 – Export per unit area generated by three fertilising distributions – at length scales of L/10 and L/5 – and uniform. Q varied by patch length, L. µmax = 0.4 /d.

L/10 L/5

Uniform


42

flux variation is large in comparison to larger patch lengths (80km) where the export flux is

smaller but more consistent. At inter-fertilisation periods of 9 days it is possible to see the

distinctive patterns of individual fertilisation events as export ceases and then resumes

following fertilisation. Export flux is often greatest when nutrients are reapplied following a

period of no export.

Figure 4.23 – Ten-run ensemble of export time series for multiple fertilisations at different patch length scales corresponding to Q = 0.0431, 0.0271, 0.0207, 0.0171, 0.0147, 0.0130, 0.0118, 0.0108 respectively. Growth rate is 0.4 /day. The period between fertilisations is 1 day (upper left), 3 days (above) and 9 days (left) and is indicated by the dotted line.

10km

20km

30km

40km

50km

60km

70km

80km

10km

20km

30km

40km

50km

60km

70km

80km

10km

20km

30km

40km

50km

60km

70km

80km


43

Variations of µmax clearly alter the time scales in the export time series, most obviously the

time to the first export event (Figure 4.24). Large export flux spikes are observed in low Q

values when µmax is varied, in contrast to the same being observed in high Q when length

scale is varied. At high Q (low µmax) export is still variable but the amplitude of export flux is

smaller. Export peaks are evident following re-fertilisation after a period of no export.

Figure 4.24 – Ten-run ensemble of export time series for multiple fertilisations at different patch maximum growth rates corresponding to Q = 0.0936, 0.0624, 0.0468, 0.0374, 0.0312, 0.0267, 0.0234, 0.0208, 0.0187, 0.0170 and 0.0156 respectively. Patch length is 25km. The period between fertilisations is 1 day (upper left), 3 days (above) and 9 days (left) and is indicated by the dotted line.

0.15 /d

0.1 /d

0.2 /d

0.25 /d

0.3 /d

0.35 /d

0.4 /d

0.45 /d

0.55 /d

0.6 /d

0.5 /d

0.15 /d

0.1 /d

0.2 /d

0.25 /d

0.3 /d

0.35 /d

0.4 /d

0.45 /d

0.55 /d

0.6 /d

0.5 /d

0.15 /d

0.1 /d

0.2 /d

0.25 /d

0.3 /d

0.35 /d

0.4 /d

0.45 /d

0.55 /d

0.6 /d

0.5 /d


44

Power spectral analysis of a 180 day re-fertilisation length reveals dominant periods of export

at a variety of values. These can be seen in Figure 4.25, and are summarised from closer

investigation, in Table 4.2. The dominant period coincides with the fertilising period,

however, other periods are also important. Multiples of the forcing period are evident. Export

periodicity of approximately 2 days is evident in Figure 4.25 at all fertilising periods.

Powerful periods are densely distributed at lower values. The dominant export periods that are

evident for each of the different fertilising periods are summarised in Table 4.2.

When the fertilising period is 1 day the dominant export periods are approximately 1.5 days

and 0.5 days. Figure 4.25 demonstrates how the fertilising periodicity represents a period of

low power, not high, at fertilizing periods of 1.

Figure 4.26 demonstrates the effect of the patch length on the dominance of certain periods,

for the 6 day inter-fertilising period. The 6 day fertilising period is important but generally of

equalled in dominance by the 2 day period at all patch sizes. Important periods between 0.2

days and 2 days that are evident at the 10km patch length are not important as the length scale

1 day

3 days

6 days

9 days

18 days

2 days

Figure 4.25 – Power spectrum density of export time series of 180 day pass. Analysis of final 160 days. The 6 fertilising periods are shown. Power is on a logarithmic scale.


45

increases. For small length scales, a greater variety of small periods are dominant in the time

series, in comparison to the larger patch lengths. The lower extent of these periods exists at

approximately 0.2 days, corresponding to the timestep, dt.

Table 4.2 – Distinguishable periods of export from spectral analysis of export time series.

Fertilising period (days) Important export periods (days) 1 1.5 2 2 3 1.5, 3 6 1, 1.5, 2, 3, 6 9 1, 1.125, 1.25, 1.5, 1.7, 2.25, 3, 4.5, 9 18 Several small periods, 1.5, 1.6, 1.75, 2, 2.25, 2.6, 3, 3.6, 4.5, 6, 9, ~18

The spectral density plots of each of the spatial distributions of fertiliser application (Figure

4.27) do not show consistent periods of export between them. Phytoplankton initially applied

uniformly at a specified concentration has the most numerous and powerful period peaks.

Periods of 0.5 and 2 days appear dominant in many cases.

10 km

40 km

50 km

60 km

70 km

80 km

30 km

20 km

Figure 4.26 - Power spectrum density of export time series of 180 day pass. Analysis of final 160 days. 8 patch lengths for a fertilising period of 6 days. Power is on a logarithmic scale.


46

Basic

Phyt.

Fert. L/5

Phyt.

Phyt.

Fert.

b

Basic

Phyt.

Phyt.

Phyt.

Fert. L/5

Fert.

c

Phyt.

Phyt.

Fert.

Basic

Phyt.

Fert. L/5

d

Basic

Phyt.

Phyt.

a

Phyt.

Fert. L/5

Fert

Figure 4.27 - Power spectrum density of export time series of 18 day pass of different spatial distributions. Power is on a logarithmic scale with lower cut-off at 10,000. ‘Basic’ represents phytoplankton randomness at a length scale of L/10 and uniform fertilising distribution. ‘Phyt. L/5’ represents initial phytoplankton randomness at a length scale of L/5 and uniform fertilising distribution. ‘Phyto. L/2’ represents initial phytoplankton randomness at a length scale of L/2 and uniform fertilising distribution. ‘Phyt. deterministic’ represents uniform initial phytoplankton distribution and uniform fertilising distribution. ‘Fert. L/5’ represents initial phytoplankton randomness at a length scale of L/10 and fertilising distribution at sub-patch length scale of L/5. ‘Fert. L/10’ represents initial phytoplankton randomness at a length scale of L/10 and fertilising distribution at sub-patch length scale of L/10. a) – f) are for fertilising periods of 1, 2, 3, 6, 9 and 18 respectively. Patch length, L = 40km, µmax=0.4 /d.


47

Basic

Phyt.

Phyt.

Phyt.

Fert. L/5

Fert.

e

Basic

Phyt.

Phyt.

Phyt.

Fert. L/5

Fert.

f

Figure 4.27 (continued) -

Modelling Ocean Fertilisation Patch Dynamics Discussion

48

Chapter 5 Discussion

5.1 Interpretation of results

5.1.1 Variations of maximum growth rate and fertilising concentration

The optimal conditions for export of carbon below the mixed layer are shown to occur in this

model at high fertilising concentrations and high maximum growth rates. However, neither of

these parameters can be considered to directly affect export in any particular cell. At each cell

the amount exported in any one event must be Ccr, the critical threshold at which aggregation

is specified to occur, regardless of how fast the given µmax enables Ccr to be reached.

Likewise, the fertilising concentration, f, will not directly affect how much is exported at any

particular cell in one event, because the ratio of nutrient uptake remains constant and thus the

concentration Ccr corresponds to a constant amount of nutrients, Ncr.

The method by which these parameters have the impact on export shown, is therefore not by

how much export is generated at one spot at one time, but rather how many of these areas can

be made to reach this critical export threshold, Ccr and also how areas that have already

exported once in the run, can do so again. Increasing µmax and f enables this to occur by

sustaining a high nutrient-limited growth rate, µ(t) at many cells for a large amount of time,

where µ(t) is the Monod growth rate given in Chapter 3. Consequently, growth increases and

diffusive inputs are larger than diffusive losses at as many cells as possible throughout the

length of the run. This means that Ccr can be reached in as many times in as many places as

possible, resulting in the most efficient export for the amount of nutrients supplied.

There is a constant increase in export with both µmax and fertilising concentration, f, because

this enables growth increases to dominate over diffusive losses in more of the patch and

generate greater total export fluxes.

One of the other ways that the efficient use of nutrients is manifested is in the pattern of

‘multiple peaking’. Multiple export peaks are shown to occur in the export time series at the

same large values of µmax and f at which the maximum export occurs. It can be speculated that


49

the processes by which multiple peaks occur as µmax increases will be in sustaining large µ(t)

in space, whereas multiple peaks as f increases can be attributed to sustaining large µ(t) over

time. These spatial and temporal processes will, of course, work in concert. That is, as both

µmax and f increase, µ(t) will be sufficient to promote growth increases over diffusive losses in

space as well as over time.

This idea can be illustrated by considering an export time series that occurs when either µmax

or f is large. Firstly consider µmax.

When µmax is large, phytoplankton in the centre of the patch will grow rapidly and quickly

attain the concentration threshold for export. This results in the first export event. The timing

of this first export event is dependent primarily upon µmax. This is because the realised growth

rate is not initially nutrient-limited, nor are the diffusive losses substantial because the

concentration gradients in the centre of the patch are small. By contrast, at the edges of the

patch there are significant nutrient and phytoplankton concentration gradients between the

nutrient enriched patch and the surrounding waters. This results in significant losses of both

nutrients and phytoplankton to the surrounding waters. Therefore growth rates are highly

nutrient-limited and a large proportion of the phytoplankton that does grow is lost across the

diffusive gradients. When µmax is large, however, these losses are less than the overall

increases in phytoplankton concentration from growth. The concentrations of phytoplankton

therefore reach threshold concentrations for aggregation and export, resulting in a second

export event. The timing of this second event is delayed because unlike in the centre of the

patch, diffusive losses of both nutrients and phytoplankton reduce the net growth rates.

In the case that f is large, phytoplankton concentrations again increase in the centre of the

patch faster than they do at the edges. However, the speed at which they grow in the centre is

in this case not dependent upon f. When f is even reasonably large, the nutrients available will

not be greatly limiting and therefore µmax, and not f, remains the best predictor of the timing of

the first export event. At the edges of the patch, the large concentration gradients again result

in losses from the patch to the surrounding waters. For intermediate values of µmax, these

losses dominate over the growth. Nutrients are lost at a rate greater than they can be taken up.

Consequently, no export occurs at the edges of the patch. In the centre of the patch, however,

this first export event has vacated areas of the patch for which the phytoplankton

concentration has returned to zero. Since f is large, however, there remains a significant

nutrient base in the vacated centre of the patch. The realised growth rate, µ(t) therefore


50

remains large and the diffusive gradient setup initially between the rim and the empty centre

of the patch favours input rather than loss of phytoplankton. Consequently, growth increases

of phytoplankton dominate in the centre of the patch and this area once again reaches the

export threshold. This second export event now occurs some time after the first and is

characterised by an increasing export flux prior to the peak, probably as areas closer and

closer to the centre reach Ccr. It can be seen that as f is increased the duration of the entire

export series increases.

If µmax and f are both large enough there will be evidence of these processes operating

together and delivering several peaks corresponding to export at different distances from the

centre of the patch, as Figure 4.5 f. shows.

Diffusion has been mentioned as an important part of the spatial phytoplankton dynamics. It

can be assumed that concentration gradients of the same order will exist in any 10-run

ensemble of a specified combination of µmax and f. Therefore by increasing L we are

increasing Kh and the effective contribution that diffusive processes make to the spatial

dynamics of the phytoplankton patch. At the edges of the patch this will increase losses,

however in the rest of the patch, this aids in how rapidly phytoplankton concentrations return

to threshold levels. Overall, this study shows that increasing the length scale, L, increases the

export per unit area.

5.1.2 Time scales of export

Maximum growth rate is one of only two time based parameters input to the model. Since

many of the timescales are greatly dependent upon the maximum growth rate, the inverse of

growth rate µmax-1 can be considered an important time scale. In particular, the inverse of

growth rate is correlated with the timing of the first export event and of nutrient depletion.

The time to the first export does not change greatly with the patch length, which, since Kh is

length scale dependent, suggests that Kh does not affect this timescale.

The time to nutrient depletion, tN, is not wholly dependent upon µmax. At high maximum

growth rates and fertilising concentrations, there is not a linear relationship between tN and

µmax-1. High values of µmax and f coincides both with the greatest export and the occurrence of

multiple export peaks in the export time series. Multiple export peaks continue to remove

phytoplankton from the domain not once but several times. Therefore nutrients are able to

diffuse into areas where there are no nutrients more often and hence reside for longer before


51

the domain is finally depleted. Due to the role that diffusion plays in this scenario, L2/Kh may

be an important timescale at high growth maximum growth rates and high fertilising

concentrations.

5.1.3 Spatial distributions

The length scale of the randomness of the initial phytoplankton distribution is used as a crude

attempt to quantify the correlation of different patch scales that exist in the open ocean. It was

suspected that due to the non-linear nature of the phytoplankton dynamics, changes in the

randomness applied may be propagated through to the export generated. Areas randomly

assigned high concentrations close together would be expected to grow quickly together,

diffusive losses would be small across small concentration gradients, and export would be

high. By comparison, smaller length scales may not necessarily have a high concentration of

phytoplankton nearby and high concentration gradients will be formed which deplete

phytoplankton stocks via diffusive losses. This makes it less likely that the critical

concentration will be reached in such areas. However, this effect is not shown to be important.

It is likely that the concentrations of the background phytoplankton are too low in comparison

to the nutrient-rich patch to have a significant effect on the patch dynamics.

There is no obvious pattern in the time series of export within or between the different

random length scales. It is likely, however, that the export behaviour becomes more variable

as we increase the length scale of randomness since the random concentrations generated, be

they high or low, occur over a larger area and thus have a greater effect on export flux than

would more localised high or low concentrations.

The distribution of the applied nutrient, by contrast, has a significant effect on the amount of

export generated. In order to generate the greatest export, it is desirable to maintain as large

an area as possible at the critical concentration for aggregation. Areas where export has

occurred reduce their concentration from Ccr to 0 within one time step, and they are of little

use for export until they return back to the Ccr range. Restoring concentrations is done firstly

by diffusion from neighbouring phytoplankton areas and secondly by growth of

phytoplankton diffused into the vacated area. Hence in order to return the exported area most

quickly back to Ccr adequate diffusion must occur. This means that ideally every exported

area will have an adjacent area of relatively high phytoplankton such that the concentration

gradients are large. Hence we desire the exported areas to be small.


52

In order to achieve this growth-export pattern it is necessary to promote growth in certain

areas, through the addition of fertilising nutrients, whilst leaving other areas to grow at a

different rate. This reasoning was tested by the variations in the spatial distributions of the

fertilising patch. This study shows that by decreasing the length scale of the subpatches from

a uniform application to an L/5 subpatch size, to a L/10 subpatch size increases the amount of

export generated.

No particular patterns are evident in the export time series between or within different

fertilising length scales when fertilising once. Since only one fertilising event was modelled

here, it is likely that the effect of random seeding and the non-linearity of the model cause

significant variations in the exact fluxes or the exact duration of multiple flux peaks. It is

expected that any regularity in export time series behaviour will only be observed when the

fertilising patch regime is applied repeatedly through multiple fertilising events.


Fertilising more than once enables concentrations of phytoplankton to be maintained at or

close to the critical aggregation threshold. This study shows that longer periods between

fertilisation generate the greatest carbon export. However, in order to compare fertilising

frequencies the same amount of nutrients need to be applied for each frequency over the entire

fertilising period. This means that longer periods are also those associated with the greatest

instantaneous inputs of nutrients.

Given the importance of fertilising concentration in generating the greatest total export,

mentioned above, it is not clear whether it is the fertilising concentration or the length of time

that is responsible for export being greater at greater inter-fertilising periods. In a practical

sense, the reasons are inconsequential because the more general result, that a certain amount

of iron is best applied at higher concentrations rarely rather than at lower concentrations more

often, is valid regardless of the process.

In comparison to the effect that the inter-fertilising period plays in the export generated, the

Waite and Johnson non-dimensional parameter, Q, plays only a minor role. In considering the

most effective inter-fertilising period, it is important to note, though, that at low Q the effect

on total export of having long periods between fertilising is much greater than if the same

decision were to be made at higher values of Q.


53

The export time series generated during multiple fertilisations is highly complex, reflecting

the non-linearity of the model. Periodicity is evident in the 18 day passes of the model only at

the later days. Power spectral density analysis of the 180 day base case reveals distinct

periods in the time series. These periods are dominated by the forcing period of the fertiliser

application and integer multiples of these periods (e.g. – T, T/2, T/3, T/4,…,T/n). This

pattern, and the relative power at each of the periods, is evidence of a saw-tooth pattern of the

time series, for which the period is that of the fertiliser application. That is, there is an initial

abrupt export flux peak and that export flux following this decreases approximately linearly

until the next fertilising event.

The power associated with the 2 day period is greater than one would expect for an exact

sawtooth formation. It is usually of equivalent power to the forcing (fertilising) period itself.

This suggests that 2-daily export is an important period of export, at all patch lengths. The 2

day period is also the most consistently observed period in the power spectral density analysis

of the spatial distribution variations. The results of the power spectral density analysis of the

spatial distribution analysis should be considered very tentatively, however, as they were

computed from only 18 day passes and are therefore insufficient to reliably apply power

spectral analysis.

It is evident that for small length, L, the behaviour of the export time series is quite ‘peaked’.

Export fluxes are higher and then fall again regularly. As L is increased the time series is

characterised by more constant export flux. Although, as mentioned above, this does not

contribute to a substantially greater amount of total export in comparison to the effect of the

period between fertilising events, it again illustrates the importance of the role of diffusion,

mediated by the length scale, L, on the phytoplankton dynamics. A particular behaviour that

is observed for longer inter-fertilisation periods, where L is small, is an especially large export

flux immediately following the reapplication of fertiliser. This behaviour is not observed

when L becomes larger as it is an effect of the size of Kh. As L is small, Kh is small and the

nutrients become low or depleted before the next fertilising event takes place. Growth is very

nutrient-limited during this period and diffusion is important in spreading the patch more

uniformly over the domain. Therefore, when fertiliser is reapplied, a large peak in export flux

is observed as a large amount of phytoplankton simultaneously grow and sink out.


54

5.1.5 Summary of interpretations

Although there are a number of aspects of the results of this study analysed, the major

conclusions are easily summarised. Almost all the behaviour observed in every aspect of the

study can be considered a balance between the parameters affecting growth increases and

those affecting diffusion.

In order for the maximum export to be generated the growth rate increases need to be greater

than the losses for as much of the patch as possible for as much of the time. This can be

achieved by increasing the maximum growth rate, µmax or increasing the nutrients that are

available, by increasing f. Large µmax has an effect on export by making sure that growth

increases are greater than diffusive losses even quite close to the edges where concentration

gradients are high. This can result in multiple peaks close together as the centre and then parts

of the outer rim reach the aggregation threshold soon after one another. Large f has an effect

on export by making sure that nutrients are always readily available, thus maintaining

sufficient growth increases even when some has been removed over concentration gradients at

the edges of the patch or allowing more than one export event to occur at the centre of the

patch.

Promoting this constantly high growth increases across the domain is critical in overcoming

diffusive losses. In both time and space, this study shows it is a more efficient use of

fertilising nutrient to apply more at small time or space scales than less over larger domains.

Therefore spatial distributions of nutrients are shown to be most effective when nutrients are

applied to localised areas rather than at lower concentrations over broader areas. In the spatial

case diffusive effects can also be advantageous in reseeding areas that have been vacated by

an export event, therefore smaller sub-patch scales effectively allow diffusion to have a

greater effect as every point on the surface is close to a diffusing source of phytoplankton and

the concentration gradients set up are large.

In the time domain, it is again shown that applying nutrients at high concentrations

infrequently generates greater export than does applying nutrients frequently at low

concentrations. This is analogous to the spatial case as this regime firstly promotes rapid

growth, but secondly gives a long enough time for diffusion to act to reseed all areas that have

been vacated by export, and thus efficiently access the nutrients as they are reapplied.


55

Due to these simple balances, only a small number of parameters are important: µmax and the

fertilising concentration, and L. These not only affect the export generated but also the timing

of many of the export events. µmax-1 is the dominant timescale affecting the timing of the first

export, and the time until the nutrients become depleted for small fertilising concentrations

and small µmax. At larger values of these, L affects the diffusive timescale L2/Kh which is

important. The duration of the export event is correlated with how much nutrients were

available initially, i.e. – the fertilising concentration, f. That most of the time and export

behaviour of this model can be represented by simple balances between µmax, fertilising

concentration and L is an important result in easily applying the results.

Although the exact spatial dynamics of phytoplankton distribution are never the same in any

model run, if we at least assume that the internal scales of the export generated ‘holes’ are

similar for the same µmax and f then the concentration gradient is not likely to be significantly

different. This means that the diffusive processes can be considered to increase as L. Where

this reasoning does not apply is in explaining where comparisons are made for different

spatial distributions of the fertilising patch. In this case the internal length scales will be

different between different variants and quantifying these differences merely by L is not

sufficient. This also affects the consideration of a single number designed to characterise the

complete behaviour of the exporting system. Although Waite and Johnson (2003) have aptly

applied the non-dimensional parameter, Q, to a uniform fertilising patch when considering

merely the total export generated, the spatial scales on which it works make it alone,

unsuitable for representing the effect of smaller internal scales generated by more complex

fertilising patch distributions.

5.2 Practical implications

Scientific interest in the role that iron plays in the phytoplankton physiology and bloom

development needs to be set aside if iron fertilisation were to be used for reducing the impact

of global carbon emissions. The ultimate goal in using iron fertilisation for climate change

regulation must be in line with the second tenet of Martin’s iron hypothesis, to increase the

carbon export to the deep and intermediate oceans (Martin, 1990). In the deep ocean carbon

can be removed from the atmospheric carbon pool for a substantial amount of time (Wigley

and Schimel, 2000).


56

Waite and Johnson (2003) have shown that large patch lengths (> 10km) are necessary to

generate export for growth rates of 0.4d-1. In particular, the Southern Ocean, which offers the

greatest HNLC region in which to apply iron fertilisations, requires especially large length

scales due to the temperature-limited growth rates. Considering that such large scales of

application are necessary it is important that the efficient use of resources be considered. The

amount of iron used, the time required to carry out the fertilisation and the number of times it

is necessary to reapply iron are all factors that need to be optimised.

Many factors affect the maximum amount of export that can be generated. This study has

identified growth rate, fertilising concentration and the spatial distribution of the fertilising

patch in particular, but others have been identified in the literature, especially wind shear

which affects aggregation behaviour (Jackson and Lochmann, 1992), and zooplankton grazing

(Boyd, 2002). Only a proportion of these will, however, be able to be manipulated in order to

achieve maximum carbon export from a natural system, while others are properties of the

natural system to which the fertilising patch is applied. The most obvious is fertilising

concentration and the timing and distribution of the nutrient applied.

This study has attempted to make different variations in spatial distribution and timing of

fertilising by ensuring that over the entire length of multiple fertilisations, or over the entire

spatial domain, the total applied nutrients is constant. Consequently, this has resulted in high

concentrations needing to be applied per unit area or per unit time to balance other cases

where low concentrations are applied over a larger domain or more regularly. This presents

the following problems – 1) That the increased export observed is due to the high growth rates

created and not directly from the spatial or temporal variation, 2) That growth will actually be

limited by another nutrient as a result of high growth; and 3) That there is a practical limit to

how specific the actual time or space that nutrients are applied at is.

As mentioned previously, the first problem is a problem only for differentiating the processes

responsible. The result, that nutrients applied locally, in space or in time, generate the greatest

export remains valid regardless of which process is responsible. Unfortunately the outcome of

this first problem leads directly to the second. If the very high growth rate is responsible for

the export amounts seen, then such estimates are not practically possible.

One of the assumptions made by the model is that only one nutrient limits growth, and this is

taken to be iron when considering iron enrichment experiments. When very large growth rates


57

are generated in the model, this is because iron is not limiting anymore. In reality, however,

other nutrients will then become limiting. Silicate limitation has been put forward to explain

the phytoplankton dynamics, especially of the dominant diatoms, in the IronEx I experiment

(Coale et al., 1998) and carbon limitation due to carbon drawdown was also of concern in

IronEx II (Coale et al., 1996). This means that although the model predicts that large amounts

of export can be generated as the fertilising concentration is increased (up to 18µM m-3 for the

18 day inter-fertilising period) the growth with which this export is associated is not realistic.

It is more likely that, in reality, a total export peak will be observed at which the most export

is generated for increasing fertilising concentrations. After this peak, increasing the amount of

iron will do little to increase export.

This study has demonstrated that, per unit fertiliser, the greatest increase in total export occurs

when fertilising concentration is increased from small to medium values, rather than from

medium to high values. This implies that the best return for an application of iron occurs

when the first amounts are applied. At this end, iron is still limiting and therefore the models

predictions hold. Therefore the benefits of even small additions of iron should be considered.

The third problem mentioned above is one of the application of this concentrated iron

solution. Theoretically, this model predicts that decreasing the length scale of the subpatches

will lead to greater carbon export from the mixed layer. There will be a limit, however, to

what is a practicable area to fertilise.

The time at which events within the export time series occur is important for efficient

monitoring of the iron fertilisation process. Using µmax-1 needs to be investigated further, but

is an important timescale in defining these events. A parameter like L2/Kh becomes important

if the iron fertilising concentration increases also. Quantifying how these timescales affect

timing of export needs to be considered in increasing the ability to predict the behaviour of

the phytoplankton patch.

Developing a small number of parameters that combine the values µmax, fertilising

concentration, and L would be valuable in defining regimes under which certain export

behaviours would be expected to occur. The Waite and Johnson parameter, Q, was developed

to characterise the conditions for which export would occur. However, Q can best be

considered a parameter which defines bulk parameters of export rather than fine scale

variations. Other non-dimensional parameters may also need to be considered.


58

Clearly, in a nutrient-limited model using the Monod equation or similar, the ‘realised’

growth rate µ(t) in Q will be variable with time, and therefore cannot be used as a quantitative

measure to characterise the conditions needed for the onset of export. Choosing µmax seems to

be the logical approach to overcoming this, however, it is also clear that fertilising

concentration has considerable impact on the nutrients that are available at any point in time,

governing the realised growth, µ(t). Thus, the initial fertilising concentration needs to be taken

into consideration when formulating a bulk characterising parameter, as Q was intended to do.

This is especially true if such a parameter were to be considered when developing a fertilising

methodology to mitigate climate change. Fertilising concentration, unlike µmax is easily

manipulated, and, in addition to the timing of multiple fertilisations and the spatial

distribution of the fertilising patch, is likely to be a major factor to consider in generating the

greatest, and most efficient carbon export.

Q also incorporates the length scale, L and therefore is sensitive to changes in L. However,

the time to the first export event, which is an important timescale in managing export

behaviour, is mostly dependent upon µmax alone.

The non-dimensional parameter Q also fails to accurately consider the different length scales

at work when subpatches of fertilising concentration are applied. Q is applicable for the

uniform application of a fertilising patch, however, when subpatches exist, the scale at which

the important concentration gradients are formed are at scales significantly smaller than L.

Nevertheless, Q remains a robust parameter for the description of the bulk export in the patch.

What is needed is the development of other parameters that can be used in conjunction with Q

to better describe the spatial and temporal complexities of phytoplankton dynamics in these

optimised schemes. Examples of such parameters may be Tfertilsing vs L2/Kh for quantifying

temporal variation from multiple fertilisations (Tfertilsing is the period of these fertilisations), or

l vs L for quantifying spatial variation where l is the length of the subpatches of the fertilising

patch and L is the length of the patch as used in Q.


59

5.3 Issues concerning iron fertilisation for the mitigation of climate change

The imminence of global climate change is becoming politically accepted as its likely effect

on the world’s economy and environment. Despite this, there is still little suggestion that

political forces will engage the issue of fossil fuel consumption that lies at the heart of the

problem and it is therefore more and more likely that quick-fix, band-aid solutions will be

trialled. Already, entrepreneurial peoples have harnessed the desire of concerned individuals

and companies wishing to prove there environmental commitment, by developing tree

plantations throughout the world such as Future Forests which holds the registered trademark

for the term Carbon Neutral® (Future Forests Ltd., 2003). Such plantations are intended to

supply ‘carbon credits’ whereby the amount of carbon emitted is considered to be balanced by

the amount sequestered in the trees. There is still scientific uncertainty over whether this

provides a real and long-term sequestration option, and it also clear that the amount of tree

planting being carried out is more of a token effort than the actual amount of reforestation

required to combat the problem (Schimel et al., 2001).

The same approach is likely to happen with iron fertilisation. To date, there are several

patents already taken out by private individuals and companies on specific techniques for the

application of iron to the ocean, many of which are not much more complicated than spraying

acidified FeSO4.7H2O from a boat (Chisholm, 2000). One example is an enterprise known as

GreenSea Venture, Inc. which has recruited leading oceanographers and proposed an 8000

km2 demonstration experiment (Chisholm, 2000). Such proposals are attractive because they

harness the ‘carbon credit’ system of the post-Kyoto environmentalism (Jepma and van der

Gaast, 1998). It is intended that these private firms would charge the U.S government up to

$10 per tonne of carbon removed from the atmosphere via carbon drawdown through iron

fertilisation (McKie, 2003).

The scientific credentials of these proposals quote the results of the successful in-situ

experiments conducted so far. There has been little discussion, however of the effects that this

proposal will have on the ecological community composition of the areas where iron is

repeatedly supplied, and over the areas proposed. All the in-situ experiments have noted a

significant floristic shift towards a monoculture comprised of large phytoplankton species as a

result of iron fertilisation (Boyd et al., 2000, Coale et al. 1996, Coale et al., 1998). Such


60

changes are likely to have flow on effects to higher trophic levels, both those that have

already been documented, for examples changes in herbivory patterns, (Boyd et al., 2000,

Coale et al., 1996) and those that cannot foreseen.

Despite the associated uncertainties, iron fertilisation for mitigating global climate change is

still likely to go ahead at some stage. The results of the current study should not be viewed

only as the most economical way to facilitate the application of these fertilising projects, but

rather the best way to minimise the damage caused by the projects. If the same amount of

carbon can be sequestered by applying less iron over a shorter length of time and over a

smaller area, the ecological destabilising effects can be reduced. This is perhaps, a naïve view

considering from an economic perspective it is still more beneficial to apply more nutrients in

a more efficient manner. However, it does provide avenues for best practice and appropriate

regulation if commercial ocean fertilisation were to be accepted.

5.4 Recommendations

The approach taken in characterising the dynamics of export in the growth-diffusion-export

model in the current study has been primarily a qualitative one. The results presented are all

means of ten passes of the model under the same input parameters. Although some

quantitative analysis has been attempted by presenting the means of these ten passes, there is

often little evidence of patterns when parameters are varied. Considering the nature of the

export, modelled essentially by a stepped decrease in phytoplankton concentration, the export

flux often appears as instantaneous, where the duration of export is the smallest possible,

merely the time step assigned. Since the random seeding of the initial phytoplankton can

cause export events to vary, at least by a single time step, averaging over 10 passes may be

unrepresentative of the export flux and the duration of flux. Large peaks, for example of 100

mmol C m-2 day-1 that occur at the 4th time step in 1 pass and in the 5th time step in another

will be averaged to occur at a flux of 50 mmol C m-2 day-1 over both the 4th and 5th time step.

Thus the flux is reduced but the duration is increased. This effect will not be considerable but

may account for the unpredictable behaviour often seen in export time series.

Combining the passes of the runs could be done by other techniques, for example moving

averages, however, a more appropriate technique, given the random nature of the initial

phytoplankton distribution would be to identify important parameters and consider each of

these statistically, quantifying the mean, and variance. This approach would enable better


61

application of the results for those who wish to predict the behaviour of a phytoplankton patch

that has had iron applied to it.

It has been noted that the size of the subpatches of the fertilising patch are important in

governing the amount of export occurring. The approach taken here is by quantifying this

subpatch size by its length scale relative to the length of the entire patch. Since the export

generated is due to the relative areas occupied by fast growing phytoplankton (areas fertilised)

and limited growing phytoplankton (not fertilised) an area ratio approach may be another

approach which may better correlate the quantified fertilising regime with the amount of

export generated, and thus provide a more predictive method on what results might follow the

application of certain fertilising patches.

Although this study has been developed considering iron-depleted waters, the fertilising

nutrient applied during passes of the model could equally be any other limiting nutrient in a

different system with the same result. In reality only oceanic waters could be represented by

the length scales used here, or the use of length scale dependent diffusion, however nutrient

limitation is common in many inland waters, notably rivers and lakes. Modifications of this

model would enable it to be applied to such cases. The most obvious modification is that the

assumption of negligible vertical diffusion in and out of the mixed layer must be removed.

Adding the necessary third dimension would be greatly aided by incorporating the work of

O’Brien et al. (2003). Removing the assumption of the negligible vertical diffusion in and out

of the mixed layer, this model could be applied not only to inland waters where phytoplankton

dynamics are important, but also to larger length scales in the open ocean where vertical

diffusion becomes comparable to horizontal diffusion (Waite and Johnson, 2003).

Predicting the temporal behaviour is important in judging the most effective time to reapply

iron to the system. Power spectral density analysis is a powerful tool for identifying the

periods that are dominant in the time series behaviour of export, however, only one pass has

been conducted, using the basic parameters, that is sufficiently long to allow reliable analysis.

Future work would benefit from identifying the dominant periods that exist in the variations

of the fertilising concentration distributions.

As this study has been primarily a qualitative, considering the relative export capabilities of a

number of variations, there has been only limited discussion of real world comparisons. In

order to move beyond the qualitative approach it is necessary to calibrate the model to a


62

variety of conditions. The most significant parameter sets to investigate would be IronEx II

and SOIREE, to identify if the export generated by the model is of the same order as that

demonstrated in the in-situ experiments. Initial calibrations would then enable the

investigation of the reasons why the export was reduced so significantly in SOIREE in

comparison to IronEx II. Maximum growth rate and lateral diffusion are two parameters that

have been proposed thus far, for this discrepancy (Boyd, 2002). Calibration could also be

made to simulate the Aeolian deposition of iron to the HNLC areas, potentially investigating

the viability of Martin’s hypothesis using a growth-diffusion-export model.

Finally, it is recommended that other limiting factors be incorporated into the model to enable

a more realistic analysis of the phytoplankton and export dynamics at higher fertilising

concentrations.

Modelling Ocean Fertilisation Patch Dynamics References

63

Chapter 6 Conclusion

If ocean fertilisation is to be successfully applied to mitigate climate change, the objective of

sequestering large amounts of carbon in the deep ocean will need to be done in a way that

makes the most efficient use of the nutrients applied. This study has used a growth-diffusion

and export model to interrogate a number of parameters which regulate the amount of export

that is generated from applying a nutrient patch; and how the export flux behaves over the

time of fertilising.

As maximum growth rate increases so does the amount exported. It is proposed that it does so

by allowing not only the centre of the patch, but areas towards the edge of the patch, to be in a

state where increases in concentration due to growth are greater than the losses due to

diffusion. However, in practice µmax cannot be manipulated to achieve greater export, it is a

property of the natural system to which it is applied. Understanding µmax does however enable

reasonable predictions of the timing of export events that are important to managing the state

of the enriched patch. The value of µmax is related to the timing of the first export event and is

also related to the timing of the complete depletion of nutrients if µmax and the fertilising

concentration are sufficiently small.

The parameter that can be most easily be manipulated to achieve the greatest export is the

fertilising concentration and how it is applied. Large concentrations of the fertilising nutrient

generate the greatest amount of export because it means that even with diffusive losses at the

edges of the patch, and multiple export events in the centre of the patch, sufficient nutrients

remain to encourage growth. If fertilising concentrations are sufficiently high, multiple export

peaks are induced and this means that the timing of some events such as the time to nutrient

depletion are no longer represented merely by µmax.

If ocean fertilisation was conducted, this study suggests that the most efficient use of iron

applied in generating carbon exported from the mixed layer will occur if the iron is applied at

high concentrations in localised areas rarely, rather than smaller concentrations spread over a

larger domain and applied more often. There will be a maximum concentration that it is


64

feasible to apply, however, since other nutrients may become limiting. Characterising how

export will occur over time will depend both on µmax, the fertilising concentration, the period

between fertilising events and the length of the fertilising patch. The non-dimensional

parameter, Q needs to be used in addition to other parameters to properly describe the time

series behaviour of export so that adequate predictions can be used in management of ocean

fertilisation operations.


65

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Modelling Ocean Fertilisation Patch Dynamics Appendices

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Appendix 1 “diffgrow2.m” script for growth-diffusion-export model

function [Cout,Eout,Nout,Et,tNdeplete,Cc,Cpua]=diffgrow2(C,Nf,Nb,K,G,T,dx,dt,steps,bound,movname,p) %diffgrow2 - diffgrow with nutrient limitation %usage: = %[Cout,Eout,Nout,Et]=diffgrow2(C,Nf,Nb,K,G[3],T,dx,dt,steps,bound,) % %solves the diffusion-growth-threshold equation: %dC/dt = K*del^2(C) + m*C - F(T,C) %over an arbitrary rectangular domain of the same size as input concentration matrix [C] with %grid size of [dx] (same for x and y) for [steps] timesteps of size [dt] % %[K] is the diffusion coefficient, and m is the growth rate - this is determined by the Monod equation: %m=G(1)*(N/G(2)+N); %where N is the total nutrient N=Nf+Nb , [G(1)] is the maximum growth rate %and [G(2)] is the half-saturation constant. %[G] contains the growth parameters and must be a three component vector % %Nutrients are put in as a background quantity [Nb] which remains constant %and a fertilized amount[Nf] which is used up as plankton grow and obeys: %d(Nf)/dt = K*del^2(Nf+Nb) - G(3)*m*C %where [G(3)] percentage nutrient usage per unit growth. % %[T] is the threshold criteria %so that: C=0 if C>=T % %[bound] defines the boundary condition (0=open 1=closed 2=periodic) %[movname] required for labelling movie %[p] for plotting and movie p=1. no plotting or movie p=0 % %[Cout] returns final concentration %[Eout] returns total removal due to threshold in a matrix same size as [Cout]; %[Nout] returns total remaining fertilizer %[Et] returns the timeseries of total export %[tNdeplete] returns time at which nutrient becomes depleted %[Cc] returns the timeseries of concentration over the entire test area %[Cpua] returns the time series of the mean concentration over the domain % %By default the plankton color range is set to [0 max(max(C),T)] and the nutrient color to max(max(Nf)); % %To view demo, type diffgrow('demo'); tNdeplete=0; %plotting switch: 1 for plotting, 0 for no plotting plotting=p; if nargin==1 if strcmp(C,'demo'); demo=1; else


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demo=strcmp('Yes',questdlg('Run demo?','Demo')); end if (demo) C=rand(61);Nf=zeros(61);Nf(20:40,20:40)=0.9;Nb=0.01;K=0.1;G=[0.2 0.2 0.2];T=3.0;dx=1;dt=0.5;steps=100;bound=2; UIWAIT(msgbox({'Demo:';... 'Fertilization of a random plankton concentration with a square blob of fertilizer of concentration 0.9';' ';... 'Running demo simulation on a 61x61 grid with periodic boundaries';'using normalised parameters of:';... 'Diffusion coefficient K=0.1';'Growth parameters G = [0.2 0.2 0.2]';'Threshold parameter T=3.0;';... 'Input plankton concentration random values between 0 and 1'},'Diffgrow2 Demo','modal')); else return end elseif(nargin~=12) %fix up for different parameter numbers error('Diffgrow: Incorrect number of input parameters'); end [nx,ny]=size(C); nn=nx*ny; Cmax=max(max(max(C)),T); Nmax=max(max(Nf))+Nb; if plotting==1 Ff1=figure;set(Ff1,'NumberTitle','off','Name','Diffgrow2','Position',[50 120 780 500]); end %generate general coefficient matrix: K=K*dt/(dx*dx); m=G(1)*dt; AC=coeffmat(K,0,bound,nx,ny); AN=coeffmat(K,0,bound,nx,ny); %make plotting grid if plotting==1 [yy,xx]=meshgrid(1:dx:dx*ny,1:dx:dx*nx); end Nb=max(Nb,0.000001); Ct=reshape(C,nn,1); Nbmat=Nb*ones(nn,1); Nt=reshape(Nf,nn,1)+Nbmat; E=zeros(size(Ct)); if plotting==1 set(gcf,'DoubleBuffer','on') mov=avifile([ movname '.avi'], 'compression','indeo5', 'fps', 7); end for t=1:steps %calculate growth and m=G(1)*(Nt./(G(2)+Nt)); P=G(3).*Ct.*m; AC=spdiags(1+4*K-0.5*m*dt,0,AC);


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DC=(1+0.5*dt*m).*Ct; DN=Nt-dt*P; %solve with Matlab Preconditioned Conjugate Gradient method [Ct,flag1] = pcg(AC,DC); [Nt,flag2] = pcg(AN,DN); if (flag1>0)|(flag2>0) warndlg('Solution failed - input parameters may be bad'); return end %----------- Cc(t)=sum(sum(Ct)); %threshold criteria - remove appropriate and store exported values fallout=(Ct>=T); E(fallout)=E(fallout)+Ct(fallout); Et(t)=sum(sum(Ct(fallout))); Ct(fallout)=0; %---------- Cpua(t)=mean(mean(Ct)); %maintain background level of nutrient Nt=max(Nt,Nbmat); if Nt<=Nbmat & tNdeplete==0 tNdeplete=t; end %plot results if plotting==1 figure(Ff1); set(gcf,'MenuBar', 'none') subplot('position',[0.05 0.3 0.4 0.6]) s=pcolor(xx,yy,reshape(Ct,nx,ny)); set(s,'FaceColor','Interp','LineStyle','none', 'Erasemode', 'normal'); axis equal; axis([1 dx*nx 1 dx*ny]);caxis([0 Cmax]);colormap(winter);%colorbar('vert'); title('Plankton concentration'); xlabel('Arbitrary units'); drawnow; subplot('position',[0.55 0.3 0.4 0.6]) s=pcolor(xx,yy,reshape(Nt,nx,ny)); set(s,'FaceColor','Interp','LineStyle','none','Erasemode', 'normal'); axis equal; axis([1 dx*nx 1 dx*ny]);caxis([0 Nmax]);colormap(winter);%colorbar('horiz'); title('Nutrient concentration'); xlabel('Arbitrary units'); subplot('position',[0.05 0.05 0.9 0.15]); plot([1:t],Et,'k-', 'Erasemode','none'); axis([1 steps 0 200]); %set(gca,'Color','none') title('Total export'); xlabel('Time (arbitrary units'); drawnow; F=getframe(gcf); mov=addframe(mov, F); end


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end if plotting==1 mov=close(mov); end Eout=reshape(E,nx,ny); Cout=reshape(Ct,nx,ny); Nout=reshape(Nt,nx,ny); function A=coeffmat(K,m,bound,nx,ny) %function to construct the coefficient matrix nn=nx*ny; C1=(4*K-0.5*m+1); C2=-K; D=1+0.5*m; D1=C1*ones(nn,1); D2u=C2*ones(nn,1); D2l=D2u; D2l(nx:nx:nn)=0; D2u(1:nx:nn)=0; D3l=C2*ones(nn,1); D3u=D3l; %open boundaries if(bound==0) A=spdiags([D3l D2l D1 D2u D3u],[-nx -1 0 1 nx],nn,nn); %closed boundaries elseif(bound==1) D1([2:nx-1 nx+1:nx:nn-nx+1 nn-nx+2:nn-1])=C1-K; D1(nx+nx:nx:nn)=C1-K; D1([1 nx nn-nx+1 nn])=C1-2*K; A=spdiags([D3l D2l D1 D2u D3u],[-nx -1 0 1 nx],nn,nn); %periodic boundaries elseif(bound==2) D4u=zeros(nn,1); D4l=D4u; D4l(1:nx:nn)=C2; D4u(nx:nx:nn)=C2; D5l=C2*ones(nn,1); D5u=D5l; A=spdiags([D5l D3l D4l D2l D1 D2u D4u D3u D5u],[-nn+nx-1 -nx -nx+1 -1 0 1 nx-1 nx nn-nx+1],nn,nn); end


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Appendix 2 “difffert.m” script for multiple fertilisation events

function [Earea,Etlong,Cclong,Cpualong,Nzero,dt,sumsteps]=difffert(fert,L,alph,g,Nn,C,p) % difffert - runs diffgrow specified number of times % usage: = % [Earea,Etlong,Cclong,Cpualong,Nzero,dt,sumsteps]=difffert(fert,L,alph,g,Nn,C,p) % % Applies nutrients in the concentration pattern given by [Nn], a 10 x 10 matrix over an initial % phytoplankton background given by [C] (50 x 50 matrix). Nutrient fertilisation is done initially % and then at intervals after this denoted by the elements of [fert]. The maximum growth rate is % given by [g] and the [alph] denotes the coefficient in the definition of length scale dependent % horizontal diffusion (see diffgrow2.m). p switches the plotting and movie creation to on (p=1) % or off (p=0). % % [Earea] gives the spatial distribution of total export % [Etlong] returns the time series of total export % [Cclong] returns the time series of total concentration % [Cpualong] returns the time series of concentration per unit area % [Nzero] returns a vector of the times at which nutrients became depleted to zero % [dt] returns the timestep used % [sumsteps] returns the total number of timesteps evaluated movname='pres_movie'; sumsteps=0; %defining length scale dependence K=alph*L^(4/3); dx=L/10; dt=min(0.5*dx*dx/K,0.2); %growth terms G(1)=g; %maximum growth rate G(2)=0.2; %1/2 saturation 3* Nb G(3)=0.2; %uptake ratio iron % fertilizer iron in uM/m3 Nnb=0.0; %concentration of fertilisation in non-targeted cells Nb=0; %background concentration in environment Nf=Nnb*ones(50); Nf(21:30,21:30)=Nn; %fertilised cells %plankton conc in mM C m-3 T=14; %threshold Etlong=[]; Cclong=[]; Cpualong=[]; Earea=zeros(50);


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for i=1:length(fert) steps=floor(fert(i)/dt); sumsteps=sumsteps+steps; %for plotting later [Cout,Eout,Nout,Et,tNdeplete,Cc,Cpua]=diffgrow2(C,Nf,Nb,K,G,T,dx,dt,steps,2,movname,p); Earea=Earea+Eout; Etlong(end+1:end+length(Et))=Et; Cclong(end+1:end+length(Cc))=Cc; Cpualong(end+1:end+length(Cpua))=Cpua; Nzero(i)=tNdeplete*dt; %refertilisation C=Cout; reNn=Nn; reNf=Nnb*ones(50); reNf(21:30,21:30)=reNn; Nf=Nout+reNf; end

Modelling Patch Dynamics During Ocean Fertilisation

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