Modelling Primary Production Dynamics in the Arctic Under Changing Sea Ice Conditions

Modelling primary production dynamics in the Arctic under changing sea ice conditions

Alice Stuart-Lee

University of Utrecht

Supervisors : Jack Middelburg - University of Utrecht Karline Soetaert - Royal Netherlands Institute for Sea Research © 2017, A. E. Stuart-Lee Department of Earth Sciences Faculty of Geosciences Utrecht University Abstract

A dramatic decline in sea ice is underway in the Arctic and we have reason to anticipate complete summer melting within this half of the century. With our current understanding of the ecological effects of this change limited, and Earth system models not yet accounting for sympagic (sea ice ecosystem) primary production, this study has been motivated to contribute towards efforts to effectively model this system. With the aim of investigating the role of sea ice in the primary production dynamics in the Arctic, an existing nutrient-phytoplankton-zooplankton-detritus (NPZD) biogeochemical model has been extended to include a parameterised ice module and sympagic primary production via an ice algae variable. This model revealed a picture of how the modelled ice algae, phytoplankton and zooplankton entities fared under varying levels of ice cover, providing a potential progression of the basic bloom dynamics in pelagic-sympagic ecosystems in which total productivity increases with reduced ice cover. Sensitivity analysis has been conducted, with considerations offered for further tests, means of model refinements and potential future developments.

Acknowledgements

Many thanks to my marvellous supervisors Jack Middelburg and Karline Soetaert. I am very grateful for your time and insight.

i Contents

List of Figures iv

List of Tables iv

1 Introduction 1

2 Biological Background 3 2.1 Sea ice habitat ...... 3 2.2 Ice algae ...... 5 2.3 Phytoplankton ...... 7 2.4 Bloom dynamics ...... 8 2.5 Benthos ...... 9

3 Physical Processes 11 3.1 Light ...... 11 3.2 Temperature ...... 12 3.3 Salinity ...... 12 3.4 Mixing ...... 13

4 Sympagic-Pelagic Ecosystem Models 14 4.1 Example 1: Production on the Canadian Beaufort Sea shelf ...... 14 4.2 Example 2: Production in the Hudson Bay ...... 15 4.3 Example 3: Production on the west coast of Greenland ...... 15

5 Model Design 16 5.1 Physical setup ...... 16 5.2 Biological activity ...... 18 5.3 Forcing data ...... 19

6 Results 21 6.1 Simulation descriptions ...... 21 6.2 Parameter sensitivity ...... 27

7 Discussion 29 7.1 Scenario analysis ...... 29 7.2 Model validation ...... 30 7.3 Further model considerations ...... 31

ii 8 Conclusions 33

Bibliography 34

Appendices 41 A Annotated model code ...... 41 B Model scenario output plots ...... 49 C Total primary production with time ...... 55 D Annual state variable ﬂows ...... 56 E Model scenario ice parameterisations ...... 57

iii List of Figures

2.1 An observed sympagic-pelagic-benthic ecosystem ...... 4 2.2 The strand-forming diatom Melosira arctica ...... 6 2.3 Phytoplankton bloom in the Barents Sea ...... 9 5.1 Conceptual model diagram ...... 18 6.1 Summary of scenario 2: seasonal ice ...... 22 6.2 Summary of scenario 3: multiyear ice ...... 24 6.3 Scenario 1: model currency flows in a year ...... 25 6.4 Scenario 2: model currency flows in a year ...... 26 6.5 Scenario 3: model currency flows in a year ...... 26 6.6 Total column integrated biomass for one year ...... 27 B.1 Scenario 1: Icethickness, Light, SedimentOrgN, Mixingcoefficient, NH4br, NO3br . . 49 B.2 Scenario 1: NH4, NO3, Phyto, Zoo, Detritus, IceAlgae ...... 50 B.3 Scenario 2: Icethickness, Light, SedimentOrgN, Mixingcoefficient, NH4br, NO3br . . 51 B.4 Scenario 2: NH4, NO3, Phyto, Zoo, Detritus, IceAlgae ...... 52 B.5 Scenario 3: Icethickness, Light, SedimentOrgN, Mixingcoefficient, NH4br, NO3br . . 53 B.6 Scenario 3: NH4, NO3, Phyto, Zoo, Detritus, IceAlgae ...... 54 C.1 Column integrated biomass with time ...... 55

List of Tables

5.1 Model parameters ...... 17 5.2 Mass balance equations ...... 19 5.3 Rate expressions ...... 20 6.1 Parameters ranked by sensitivity value ...... 27 D.1 Total model currency ﬂows between state variables ...... 56 E.1 Ice parameterisation for scenario 1: ice free ...... 57 E.2 Ice parameterisation for scenario 2: seasonal ice ...... 57 E.3 Ice parameterisation for scenario 3: multiyear ice ...... 57

iv Chapter 1

Introduction

Winter satellite coverage of the Arctic between 1979 and 2011 records strongly declining sea ice with respect to both extent (deﬁned as ocean with a minimum ice concentration of 15%) and area. The most rapid rates of decline have been recorded for the thick multiyear component of the ice (-15.6% in extent and -17.5% in area per decade), which has increasingly been replaced by ﬁrst year ice and thinner ice cover (Comiso, 2011). Further satellite observations from the National Snow and Ice Data Center (NSIDC) show that a new record low was reached in September 2012 for both minimum sea ice extent and sea ice area. These major changes to the Arctic are expected to continue over the coming decades. Complete summer melting is predicted for this half of the century, with projections varying from 2020 with trend extrapolation, to 2040, with alternative methods (Overland and Wang, 2013).

These changes to the sea ice have numerous physical feedbacks that are resulting in Arctic amplification, a regional temperature increase greater than the Earth’s average. Serreze et al. (2011) outline the most prominent causes of Arctic amplification, which include the ice albedo positive feedback, changing ocean-atmosphere heat fluxes, changing cloud and water vapour cover affecting the longwave radiation flux, and additional soot and other dark aerosols increasing heat absorption. The implication is that not only will the Arctic experience rapid change, but that the rate of change will also continue to rise, with far reaching consequences (Serreze et al., 2011).

For ecosystems, these include the loss of habitats for a wide range of life, from the microalgae in the ice to the ringed seals and polar bears using the environment to hunt, forage and reproduce. At the former end of the scale, both past and future changes related to ice algal and pelagic phytoplankton primary productivity are not fully understood. This is in part due to difficulty in quantifying productivity, with a lack of physical research trips due to inhospitable conditions as well as inadequacies with remote sensing techniques. Furthermore, Tedesco et al. (2012) note that regions with changing light conditions over short time periods are not suited to the use of constant Chl:C ratios for the calculation of biomass, and thus that existing estimates for the Arctic region may be biased. One quantification of changing marine primary productivity was made by Arrigo et al. (2008), using an Arctic-specific algorithm with satellite measurements of sea ice, sea surface temperature (SST) and chlorophyll. The result was that annual Arctic primary production increased by a yearly average of 27.5 Tg C yr-1 between 2003 and 2006, and then by 35 Tg C yr-1

1 between 2006 and 2007, mostly as a result of increased open water area and extended phytoplankton growth seasons.

Looking to the future, Tedesco et al. (2012) predict that in the areas that maintain seasonal ice, algae may thrive, but that as ice melts earlier, phytoplankton blooms may coincide with lower light conditions and become less productive, and that overall production in these areas may start decreasing at the end of this century. Although it is not clear exactly how Arctic marine production will change over the coming decades, ecosystem disruption appears inevitable. Changes have already been seen to cause mismatches in bloom timings that were previously strongly coupled for eﬃciency between the ice algae, under-ice phytoplankton and grazing zooplankton, with consequences for the rest of the food web, such as Arctic cod, sea birds, seals and polar bears (Søreide et al., 2010).

Motivated by the need for a better understanding of what to expect from primary production dynamics, this project starts with an examination of the biology of the Arctic sea ice and ocean in chapter 2. Existing knowledge of sea ice as a habitat for microorganisms is reviewed, and ice algal life is addressed with a particular emphasis on their adaptation to the particularities of their Arctic environment and the controls on their growth. Their bloom dynamics are explored alongside those of phytoplankton and of zooplankton. Examination of the tight coupling of this ecosystem proceeds by looking into how the surface production aﬀects the benthos. Key processes that control light availability, temperature, salinity and mixing are reviewed in chapter 3 and the primary factors for ecological modelling are investigated. Chapter 4 provides concise and comparative summaries of the biological structure of three existing biogeochemical sympagic-pelagic ecosystem models of varying complexity, where sympagic refers to the ice-based ecosystem. These serve as key examples for the adaption of a biogeochemical model to incorporate ice dynamics and ice algal production, described in chapter 5. Chapters 6 and 7 detail and discuss the output of the model, and conclusions are presented in chapter 8.

2 Chapter 2

Biological Background

Although known for its extremes of temperature, salinity and light availability, Arctic ice lends itself to a plethora of life. Not only does the ice provide a habitat for microorganisms and their grazers, the seasonal melting releases this organic matter into the water column below, fuelling further productivity and life in the water and benthos. These sea ice communities and their nearby pelagic and benthic counterparts are reviewed here, with an overview of the factors aﬀecting their growth, bloom and export dynamics.

2.1 Sea ice habitat

As ice forms, a large proportion of its salt content is rejected at the ice-water interface, and a vertical convective process arises from this brine rejection whereby the dense water migrates towards the primary drainage channels, with less dense water taking its place (Lake and Lewis, 1970). Following the ice formation, brine continues to drain from the interior of the ice through brine channels whose diameters vary on a scale of several micrometers to several centimeters (Weissenberger et al., 1992), and thousands of small brine tubes develop in each square meter of the bottom ice surface (Lake and Lewis, 1970). During this formation process, inorganic nutrients required for microorganisms are trapped in the ice along with small pockets of seawater. Although these early stocks can be depleted as life multiplies, various mechanisms exist for their resupply. Considering new supplies (rather than regeneration by the biological community), the primary source is the underlying water column, with nutrients absorbed from the flow of seawater through the brine channels at a rate that varies with the hydrodynamics and with the rate of ice growth (Cota et al., 1991). When the ice is sufficiently permeable, nutrients may also be sourced from the surface through atmospheric precipitation flushing nutrients downward through the ice (Granskog et al., 2003). The result is a solid matrix of ice with a non-uniform distribution of liquid brine networks and nutrient supplies.

In addition to the sea ice microalgae, the focus of this study, this ice matrix plays host to many other microorganisms including abundant bacteria, less common archaea, viruses, and a variety of heterotrophic protists that graze on the aforementioned groups (Junge et al., 2004; Sherr et al., 1997; Wells and Deming, 2006). Although a strong spatial bias exists for the most habitable locations, life has been observed throughout the ice. The upper surface of Arctic ice is often limited by low nutrient concentrations, but when exchange with the underlying water is suﬃcient, surface

3 melt ponds and the layers immediately beneath can be thriving with microbial activity (Mundy et al., 2011). Similarly, the ice interior has potential for life when the conditions are appropriate. High salinity values are usually the strongest barrier to growth here (Arrigo and Sullivan, 1992), but when values decline enough, microorganisms have been observed inside brine channel networks, especially those near edges or fractures where seawater exchange is greatest (e.g. Buck et al., 1998; Mundy et al., 2011). It has been suggested, though, that due to imperfect observations these algal cells may not necessarily be actively growing, but rather that their presence reﬂects a build up due to physical processes (Ackley et al., 1979).

Figure 2.1: An observed sympagic-pelagic-benthic ecosystem (courtesy of A. Thurber, Oregon State University, US NSF Award No. 1642570.)

Most popular with microorganisms is the bottom of the ice (ﬁgure 2.1), where the key properties of temperature, salinity and available space render this layer closer in habitability to seawater, and allow nutrients to be more easily sourced from the underlying water. Some specialised environmental adaptation is often required, especially in managing the low light conditions (refer to section 2.2.1). Nonetheless, this area remains the most biologically productive part of the sea ice, with most of

4 the algal biomass concentrated in the bottom few centimeters where convective nutrient exchange with seawater is greatest (Mundy et al., 2007). A preference has been observed for areas with denser brine networks (Mundy et al., 2007), although most of the cells in this layer are not clumped together in the major channels (as for the deeper interior), but are instead more spread out over the smaller brine tubes and boundary irregularities, and thus in direct contact with the sea water (Cota et al., 1991).

2.2 Ice algae

A high level of diversity exists for the microalgae in sea ice. The most abundant and widely studied are the ice diatom algae (IDA), with close to 600 taxa of both pennate and centric forms identified in the Arctic (Il’iash and Zhitina, 2009). In measurements of algal biomass made throughout a transect from the Chukchi Sea to the Nansen Basin, Gosselin et al. (1997) identified the dominance of particular communities in different parts of the ice. Pennate diatoms were seen to dominate the bottom surface of the ice, centric diatoms the ice-water interface, and flagellates the under-ice water column (Gosselin et al., 1997). Key species include the colonial pennate diatoms Nitzschia frigida, Fragilariopsis cylindrus and F. oceanica, and the colonial centric diatom Melosira arctica, all of which have been found widely distributed in Arctic sea ice and often as the majority species (Horner et al., 1992; Poulin et al., 2011; Rózanska et al., 2009). The strand-forming Melosira arctica (figure 2.2) are a particularly productive member of the bottom ice community. Although their shells are only tens of microns in diameter, they can grow strands that are meters in length, and have been observed to cover up to 90% of the underside surface of sea ice (Ambrose et al., 2005). Their impressive productivity under such hostile conditions and our lack of knowledge of how they may respond to the changing Arctic have led to their being awarded ‘Alga of the Year’ in 2016 (Phycology Section, German Society for Plant Sciences).

2.2.1 Environmental adaptation Specialised environmental adaptation is key for these ice algae in managing extremes of temperature, salinity, light and nutrient availability. For large variations in temperature, an important adaptation is the flexibility in the rate of metabolism. This is quantified using the temperature coefficient, Q10, which measures how the growth rate changes with an increase in temperature of 10 degrees Celsius. For ice algae this has been reported as ranging from 1.0 to 6.0, which indicates that they have the potential to adapt to a wide range of temperatures (Arrigo and Sullivan, 1992). Other strategies for coping with extreme temperatures include the production of cryoprotectants for avoiding the formation of ice crystals in the organisms, modification of membrane lipids to increase the unsaturated fatty acid content for enhanced fluidity, and the production of cold-shock proteins (Lizotte, 2003; Varin et al., 2012). One prominent cryoprotectant and antifreeze, dimethylsulfonio- propionate (DMSP), may also serve as an osmolyte as a means of managing the large variations in salinity, and is produced in significant quantities by ice algae diatoms (Dickson and Kirst, 1986; Levasseur et al., 1994).

For the light environment, ice algal photo-adaptation is commonplace in the Arctic, where the low

5 Figure 2.2: The strand-forming diatom Melosira arctica (courtesy of ©J. Gutt, Alfred Wegener Institute) light availability at the bottom of ice can be one of the most limiting factors to growth (refer to section 2.2.2). One observed strategy for algae is to increase photosynthetic eﬃciency, with higher photosynthetic eﬃciencies found for populations of ice algae under the deepest snow cover (Cota, 1985). On the other end of the light scale is the danger of high irradiance at the surface, which brings the risk of damage by UV radiation to existing organisms. Leu et al. (2010) studied the response of sea ice algae in the high Arctic to high light levels and found that as they were exposed to higher irradiances, their nutritional quality (in terms of fatty acid content) decreased and more photoprotective pigments were produced.

In addition to the key nutrients nitrogen and phosphorus, usually available as nitrate and phosphate, ice algal diatoms also require silicon, usually as silicic acid, for the construction of their frustules (Lizotte, 2003). Those on the underside of the ice benefit from the resupply of these nutrients by seawater exchange, with the fluxes varying laterally. Krembs et al. (2001) show how the irregular undersides of ice floes affect nutrient exchange, with much higher vertical fluid fluxes around bulges in the ice. The supply also decreases rapidly away from the boundary, implying that algae are increasingly likely to be nutrient limited with distance above the ice-water interface (McMinn et al., 1999). As far as the most limiting nutrient is concerned, nitrogen, phosphorus and silicon have

6 each been recorded to limit algal growth in Arctic sea ice (e.g. Carmack et al., 2004; Gosselin et al., 1990; Gosselin et al., 1997). Although this appears to be partly location-dependent (refer to section 4 for examples), the most common limiting nutrient is often cited as silicon because of differences in the regenerative fluxes. While nitrogen and phosphorus are remineralised in sea ice, the dissolution recycling mechanism of silicon is not as efficient (Lizotte, 2003).

2.2.2 Growth limitation Some of the most important environmental conditions that aﬀect algal growth and loss have been brieﬂy explored - light, temperature, salinity and nutrients. Also important on the seasonal scale are loss factors related to the growth and melting of ice. It has been hypothesised that fast ice growth may cause death by trapping cells in the ice matrix or through upward advection towards less favourable conditions (Lavoie et al., 2005). With the subsequent melting comes not only the loss of cells from the melted areas as they are displaced into the water column, but also the loss at the ice-water interface due to the accumulation of low salinity melt water, the osmotic shock of which can cause cells to lyse (Lizotte, 2003). Grazing from metazoans and heterotrophic protists is another danger, especially at this interface where algae have less protection from the larger grazing species than when in the refuge of the ice matrix and its narrow channels (Krembs et al., 2000). Of these terms, observational and modelling evidence strongly supports light availability as the most limiting factor before the growth season begins in Spring, with nutrient limitation becoming more likely during the later phases of blooms as algal biomass increases (Gosselin et al., 1990; Lavoie et al., 2005; Leu et al., 2015). For more on algal bloom dynamics refer to section 2.4.

2.3 Phytoplankton

One key aspect of pelagic phytoplankton growth dynamics that contrasts with ice algal growth relates to the exposure to the vertical mixing of the water. While ice algae are almost motionless in the ice matrix, and thus experience a relatively steady light climate, phytoplankton can be subject to large variations as they make vertical journeys with the convection of the water (Cota et al., 1991). A traditional view of phytoplankton growth places these physical processes that control light and nutrient availability as the primary control on rates of cell division, and therefore on the timing of blooms. This is the case for the critical depth and critical turbulence hypotheses (Sverdrup, 1953; Huisman et al., 1999). The theory surrounding phytoplankton bloom dynamics is, however, far from conclusive. Behrenfeld and Boss (2014) provide examples of observations that do not support the aforementioned hypotheses. Based on results from a modelling investigation of the annual subarctic Atlantic phytoplankton blooms, they argue instead for governance by predator- prey and other ecosystem imbalances (which themselves may be prompted by physical processes).

Under-ice phytoplankton blooms are even less well understood, although in recent years observations have allowed an insight into the potential scale of these occurrences. Arrigo et al. (2012) observed a massive under-ice bloom on the Chukchi Sea continental shelf extending for over 100 km into the ice pack. Although many questions remain open, a modelling study of Horvat et al. (2017) suggests that the thinning sea ice cover may be responsible for an increase in occurrences and extent in recent years, owing to the increased availability of photosynthetically active radiation (PAR) to

7 the upper water column. There may also be close ties to the ice algal bloom dynamics, as explored in the following section.

2.4 Bloom dynamics

Algal species diversity is maintained over the course of the Arctic winter, but biomass is greatly reduced. Evidence points to the most signiﬁcant growth limitations during this period as low light availability at the bottom of the ice, and cold temperatures and high salinity in the upper parts (Gosselin et al., 1990; Werner et al., 2007). Various adaptive strategies have been explored for how algae survive these harsh winter conditions, such as the transition from photoautotrophy to heterotrophy (Palmisano and Sullivan, 1985) and those detailed in section 2.2.1. The exact survival dynamics, however, are not yet well determined, due in part to the current lack of observational data from the winter months. As conditions soften in Spring, the onset and rate of algal growth responds strongly to the increased light availability (Watanabe et al., 2015). Growth continues to increase, with large algal blooms generally occurring at the end of spring or the start of summer. The highest biomass concentrations develop near the ice-water interface and the blooms last from around 6 weeks at subarctic sites to around 3 months at high latitudes (Cota et al., 1991). These blooms are generally not composed of a large diversity of algae. Small diatoms are often the most common constituent, which may be due to the special adaption required for extreme conditions (Lizotte, 2003).

As the season progresses, algal growth rates start to reduce and eventually biomass declines (Cota and Smith, 1991). Various modelling studies have identified the ice melt as the primary factor in this algal decline and eventual bloom termination on large scales (e.g. Deal et al., 2011, Lavoie et al., 2005). With increased melt, more algal biomass is expelled (“flushed”) from the bottom of the ice, and the fresh meltwater lenses that form beneath the ice can further restrict nutrient availability and prompt temperature and salinity stress (Arrigo and Sullivan, 1992; Lavoie et al., 2005). Other factors that negatively affect the growth rate of algae, which may also affect the termination of a bloom, include the self-shading and accumulation of toxic waste products that result from accumulation, and increased grazing pressure (Elliott et al., 2012; Lizotte, 2003).

These seasonal algal cycles are, in turn, one of the controls on the phytoplankton bloom timing. At high biomass stages of the algal bloom, phytoplankton growth may be restricted in the underlying water because of the algal absorption of available light, delaying the onset of the phytoplankton bloom (Arrigo et al., 1991). As the ice retreats and this effect is diminished, the increased irradiance can result in large phytoplankton blooms (e.g. Arrigo et al., 2012). There may also be a seeding effect from the release of algal biomass into the water, with the timing and magnitude driven by the viability of the released algae and by their degree of aggregation, as shown by the modelling study of Tedesco et al. (2012). Expelled material that sinks may be grazed on further down the water column, resulting in a coupling of the algal and phytoplankton blooms with those of zooplankton. Michel et al. (1993) showed, for example, that the Arctic zooplankton species Calanus glacialis (C. glacialis) depends critically on algal production. Their life cycles were described in further detail by Søreide et al. (2010), who observed that the maturation and reproduction of C. glacialis was synchronised with and fuelled by the ice algal bloom, and that the offspring then benefitted a few

8 months later from the ample food supply of the pelagic bloom.

Figure 2.3: Cropped Envisat image of a phytoplankton bloom in the Northeast Passage of the Barents Sea (ESA/NASA)

2.5 Benthos

As the Arctic ice melts following the growth season, the large build up of algal organic matter that gets released into the water benefits not only the pelagic community, but also life under the water column. Excess organic matter that does not get consumed in the food web of the water column is exported to the sediment alongside the sinking detritus that results from pelagic activity, providing an important source of sustenance for benthic fauna. The exported material has been shown in some Arctic cases to be closely coupled to benthic productivity. In an observational investigation of the Northeast Water Polynya, for example, Ambrose and Renaud (1995) found a close link between export and benthic biomass and density under varying levels of ice cover. (Where a link was not found it was explained by a high level of grazing, which significantly reduced the quantity of material reaching the benthos.) As such, changes in Arctic primary productivity in the ice and water directly affect benthic activity. Because the reactions taking place in the sediment are highly important for the recycling of settled nutrients and carbon back into the water column (Soetaert

9 et al., 2000), changes thus also play into the nutrient and carbon dynamics of the entire Arctic system.

Recent studies have attempted to understand how the export to the benthos has changed in the short term history of the Arctic. In the summer of 2012 Boetius et al. (2013) measured algal biomass export to the deep-sea floor of the central Arctic basin (between 82 to 89N and 30 and 130E). This study focused on the widespread strand-forming diatom Melosira arctica (M. arctica), which grows attached to the underside of the ice, absorbing nutrients directly from the water column, and sinking rapidly once released from the ice. Higher oxygen fluxes were observed for the sediments that were covered in algal biomass compared to those of the adjacent sea floor areas, presumed to be a result of microbial respiration of the algal carbon. Accordingly, the oxygen penetration depth was drastically reduced in the biomass covered sediment, from tens of cms to a few mm. They concluded that, if the high algal exports now observed had been commonplace before the year of study, then they would have observed smaller oxygen penetration depths and, as such, these large exports were rare before 2012, supporting the hypothesis that the changes in the Arctic sea ice are contributing to higher ice-algae export (Boetius et al., 2013).

10 Chapter 3

Physical Processes

This chapter provides an introduction to some of the key physical processes in the Arctic that control the light, temperature, salinity and mixed layer depth of the ice covered waters. In this way, these processes largely determine the degree of success in primary production for ice algae and under-ice phytoplankton.

3.1 Light

Scattering and absorption properties of ice and snow restrict the amount of harmful UV radiation that reaches life in and below the ice, while also restricting the supply of photosynthetically active radiation (PAR) required for primary production. In an investigation of light transmission, Perovich (1990) found that even small variations in the thickness of sea ice and snow cover can cause drastic differences in the light that reaches the under layers. Snow is estimated to attenuate light by approximately an order of magnitude more than ice (e.g. Mundy et al., 2005; Perovich, 1990), although the exact properties depend on the characteristics of the material concerned. The wetness of the snow, for example, can significantly reduce the amount of light scattered (Perovich, 1990). Similarly, the internal structure of ice affects the way it distributes radiance (Trodahl et al., 1989). As such, the albedo value of ice changes according to its internal structure and ability to support snow cover. Perovich and Polashenski (2012) showed that, on the scale of 0 to 1 that represents the fraction of returned radiation, thinner seasonal ice cover has an albedo approximately 0.1 lower than that of the thicker multiyear ice. Contributing structural factors listed included the number of bubbles in the upper layers and style of pond formation at the surface. This is also supported by the findings of Palmer et al. (2014) who demonstrated a link between thin ice with a high coverage of melt ponds and light conditions conducive to massive under ice phytoplankton blooms.

In addition to the ice and snow thickness and characteristics, the distribution of particles in the ice and pigment-containing ice algae also play an important role in determining light availability (SooHoo et al., 1987). While the light attenuation by snow is dominated by scattering (Mundy et al., 2007b), for algae and particles it is through absorption (SooHoo et al., 1987).

11 3.2 Temperature

Large seasonal variations characterise Arctic air temperatures, with typical annual ranges at the ice surface between 40-50°C (Werner et al., 2007). Annual ranges at the bottom of the ice are much smaller. In an observational study of pack ice and under-ice physical and biological properties, Schnemann and Werner (2005) measured large differences in winter-summer temperature at the ice surface, compared to minimal fluctuations at the ice bottom, with strong vertical gradients through the ice layer. These big swings in atmospheric temperature result in changing ice conditions, which then play back into the heat budget of the Arctic through environmental feedbacks. One such feedback is the ice albedo effect. As ice has a higher albedo than open ocean, ice loss results in a lower overall albedo, resulting in further warming and, in turn, further ice loss (Curry et al., 1995). The albedo also changes with different ice types. As Perovich and Polashenski (2012) observed, the albedo properties for multiyear and seasonal ice are the same with ample snow-cover, but from the point of melting, seasonal ice albedo is consistently lower than that of multiyear ice, by a difference of approximately 0.1. This difference in heat absorption by the upper ocean of the Arctic has been analysed by Perovich et al. (2007), who found an increase in the amount of solar energy absorbed in 89% of the Arctic ocean for the period studied (1979 to 2005) associated with an increase in bottom ice melt.

Changes in ice and snow cover also translate to diﬀerent levels of insulation provided to the upper water column, and thus the amount of solar radiation absorbed. Mundy et al. (2005) investigated thermal (among other) properties of ice and snow in the Arctic and described the importance of the snow cover from the perspective of algal growth conditions. Observational results suggested that too thin a cover would not provide suﬃcient insulation from a warming atmosphere, and the resulting warming and desalination would reduce algal biomass through sloughing. Thick snow cover would increase the period of light limitation, but the thermal insulation would also provide conditions that would allow the algae to extend their growth season.

3.3 Salinity

As is the case for temperature, brine salinity proﬁles also reveal strong vertical gradients in the ice. The highest values are found near the cold surface, and the lowest at the ice-water interface, where salinity and temperature values are closer to those of the upper water column and do not diﬀer substantially between summer and winter (Schnemann and Werner, 2005). Temperature provides a key control on the salinity, as this determines the amount of salt that freezes within the ice (Weeks and Ackley, 1982).

The brine rejection process is introduced in section 2.1. For the Arctic Ocean open water, factors other than ice formation and melt that affect the salinity budget include the freshwater input from rivers and from net precipitation, and exchanges of water with the Pacific and North Atlantic oceans (Carmack et al., 2016). These processes together result in an ocean with strong salinity gradients. This halocline is important in effectively restricting vertical convection that brings heat up from the deep ocean, which would otherwise limit the formation of sea ice (Carmack et al., 2015).

12 3.4 Mixing

Arctic Ocean mixed layer depths remain relatively shallow throughout the year, with minimum values found during the summer. Measurements by Boetius et al. (2013) show that the summer mixed layer depth in the central Arctic basin in 2012 remained between 10-30 m, not an atypical measurement. This shallow mixed layer represents the notable stratiﬁcation of the water column, for which the temperature and salinity processes mentioned in the previous sections play a role in determining through their control on vertical convection (Aagaard and Carmack, 1989). Another important factor is the atmospheric forcing, with wind transferring kinetic energy to the ocean, driving vertical mixing in the upper water column. The presence of sea ice signiﬁcantly constrains the wind-induced mixing and other existing motions in the water, depending on its mechanical properties (including its thickness and how consolidated it is), which has given the Arctic Ocean this characterisation of being generally poorly mixed in the upper layers (Bluhm et al., 2015; Rainville and Woodgate, 2011). When the sea ice cover is reduced, however, the wind is able to induce much stronger mixing in the upper water through its generation of inertial motions and internal waves that are not dampened by ice, meaning an increased importance of these processes for the Arctic Ocean of the future (Rainville and Woodgate, 2011).

In addition to changes in the ice cover in terms of the algal habitat, an important biological consequence of the mixing of the water involves the nutrient supply, with mixing increasing the supply of nutrients to surface waters. This renders the level of water column stratiﬁcation as very important for primary production in the Arctic (Bluhm et al., 2015). In experiments run on the coupled sea ice-pelagic biogeochemical model of Tedesco et al. (2012), a deepening of the mixed layer (with other conditions kept constant) resulted in a delayed, but larger scale diatom bloom.

13 Chapter 4

Sympagic-Pelagic Ecosystem Models

This section reviews some key biological aspects of three sympagic-pelagic ecosystem models, including the choice of nutrients and functional groups, how organic matter and nutrients are transferred between the ice and the ocean, and the factors aﬀecting primary production. These examples have been chosen for their relevance to the objectives of this project and in order to illustrate diﬀerent approaches and levels of complexity.

4.1 Example 1: Production on the Canadian Beaufort Sea shelf

Lavoie et al. (2005) developed a 1D coupled snow-ice - ice algae model based on that of Arrigo et al. (1993), in which the ice algal response is a function of temperature, spectral irradiance, nutrient (silicic acid) concentration and salinity. Temperature, silicic acid and salinity in the ice layer are controlled via diﬀusion between the ice and a mixed ocean layer, whose values are based on supply from the underlying water and loss to the ice. In addition to grazing (taken as a fraction of algal growth), this model contains an algal loss term based on the rate of ice growth, hypothesising that too high a growth rate results in algal loss from entrapment in the ice, and too negative a rate results in expulsion to the water with melt. This level of detail in the algal growth function allowed the model to distinguish the limiting factors at diﬀerent points in the seasonal cycles, the conclusions of which are outlined in section 2.4.

This model was later coupled to a pelagic model in an investigation of primary productivity on the Canadian Beaufort Sea shelf (Lavoie et al., 2009)1. This provided phytoplankton and zooplankton dynamics in the water column, additional nutrients (nitrogen and phosphate), and detritus. De- tritus was split across three state variables of algal, slow-sinking or fast-sinking detritus, with a variety of production, remineralisation, sinking and consumption dynamics. This model was able

1Other modelling studies that have incorporated the snow-ice - ice-algae module of Lavoie et al. (2005) include those of Dupont (2012) and Pogson et al. (2011).

14 to distinguish between primary and export production, and to simulate seasonal production cycles and changes due to variations in ice cover.

4.2 Example 2: Production in the Hudson Bay

The model of Sibert et al. (2011) builds on an earlier sea ice ecosystem model of Sibert et al. (2010) and the pelagic biogeochemical model of Le Quéréet al. (2005). The model currency is nitrogen, and the modelled nutrients are nitrate and ammonium. As for the Lavoie et al. (2005) model, nutrients for algal growth in the static ice layer are also taken from the upper water column. In contrast to the diffusion mechanism, though, nutrients are removed as required for growth and scaled by the amount of ice cover for each grid cell. Regenerated nutrients are returned in the same way and algal organic matter is released from the ice with melt. Algal biomass increases with incorporation into growing ice and primary productivity, and decreases with grazing from ice fauna, mortality and the release into the water from ice melt. Phytoplankton are modelled as flagellates and diatoms, both grazed on by mesozooplankton, with flagellates also serving as prey to microzooplankton. Dead cells, detritus and excretion products from the algae, phytoplankton and zooplankton activities result in release of particulate organic nitrogen (PON) and dissolved organic nitrogen (DON) to the water column. Some of this is regenerated to ammonium (and then nitrified to nitrate in the water column or taken up directly by the diatoms or flagellates), and some sinks to a benthic trap for the recording of exported material. The model was able to distinguish and describe the production features of 4 different areas of the Hudson Bay system in terms of timing, quantity, algal contribution and related physical characteristics.

4.3 Example 3: Production on the west coast of Greenland

Tedesco et al. (2012) describe the most complex of the reviewed models. This coupled sympagic- pelagic biogeochemical model comprises 2 algal groups (adapted diatoms and survivors), 2 phytoplankton counterparts in the upper water (diatoms and flagellates), 3 groups of zooplankton (omnivorous, microzooplankton and heterotrophic nanoflagellates), and the addition of bacterio- plankton. Separate ice and ocean pools exist for the 4 nutrients (phosphate, nitrate, ammonium and silicate) as well as dissolved gases (oxygen and carbon dioxide) and organic matter (labile DOM and particulate detritus). Algal growth is the gross primary production with loss terms for respiration, exudation, lysis and the boundary flux to the water column, which is based on the growth rate of the ice. A unique aspect of this ice model is its inclusion of a Biologically-Active Layer (BAL), which dynamically defines the fraction of sea ice connected to the ocean via brine channels, and thus allows a more accurate representation of the algal distribution (Tedesco et al., 2010). The model was built to investigate various modelling questions related to sea ice algae and phytoplankton coupling, including the photoacclimation strategies, the seeding effect, and changes in productivity under different climate conditions (Tedesco et al., 2012).

15 Chapter 5

Model Design

The model employed in this study has been adapted and extended from the nutrient-phytoplankton- zooplankton-detritus (NPZD) pelagic biogeochemical model of Meire et al. (2013). This model employs functions from the ReacTran package (Soetaert and Meysman, 2010) for dealing with reactive transport equations, from the deSolve package (Soetaert et al., 2010) for solving diﬀerential equations, and from the FME package (Soetaert and Petzoldt, 2010) that includes algorithms for sensitivity analysis. Core model activity and the prescribed forcing data are described in the following sections, with a focus on the sea ice and ice algae elements. The full annotated code is available in the appendices (section A).

5.1 Physical setup

Ice cover, ocean water and the upper boundary of the benthos are represented in a 1D column of 100 equally spaced cells of 0.5 m thickness. When ice is present, it grows from the topmost cell downwards into the column, replacing water cells. Ice attenuates the availability of photosynthetically active radiation (PAR) for the life below in two ways. Firstly, the albedo eﬀect reduces the surface solar radiation by between 55 and 65% according to the thickness of the ice (albedo values from Perovich and Polashenski, 2012). Secondly, an extinction coeﬃcient for ice, higher than those for water and phytoplankton biomass, is applied for ice cells and contributes to the calculation of PAR availability at each depth and time step. The full list of model parameters together with their approximated values can be found in table 5.1.

Ice presence and its growth rate at any one time step also effect the level of turbulence of the underlying water. In this context, 3 phases are considered. The first concerns a complete lack of ice cover, whereby the water would be most exposed to the wind stress and subsequent vertical mixing. The second is that of positive ice growth, during which brine rejection would induce vertical convection as the rejected brine sinks. A constant mixing coefficient (kzhigh) is applied when the ice cover meets one of these conditions. In the third phase, that of steady or declining ice cover, the water would have protection from wind, brine rejection would be lower, and any freshwater melt would reduce turbulence through water column stratification. As such, a lower mixing coefficient (kzlow) is applied to the water in this case.

16 Table 5.1: Model parameters

Symbol Value Description Unit TotalN 6 Total Nitrogen concentration mmolN m-3 Q10 2 Q10 coefficient - MaxUptake 1.5 Uptake at 20°C d-1 KsDIN 0.5 Half-saturation concentration of DIN uptake mmolN m-3 MaxGrazing 0.75 Maximum grazing rate of zooplankton d-1 KsGrazing 2 Half-saturation concentration of grazing zooplankton mmolN m-3 Pfaeces 0.3 Fraction of faeces production - ExcrRate 0.08 Excretion rate zooplankton d-1 MortRatePh 0.03 Mortality rate phytoplankton d-1 MortRateSlough 0.03 Mortality rate sloughed ice algae d-1 MortRateZoo 0.01 Mortality rate zooplankton m3 d-1 mmolN -1 MortRateTrap 0.95 Mortality rate trapped zooplankton m3 d-1 mmolN -1 SinkDet 1 Sinking speed detritus m d-1 SinkAlg 0.3 Sinking speed ice algae m d-1 MinRate 0.04 Mineralisation rate d-1 MinRate2 0.02 Mineralisation rate anoxic d-1 RNit 0.05 Nitrification rate d-1 alpha 0.03 Photosynthesis coefficient µEinst m-2 s-1 kW 0.198 Extinction coefficient: water m-1 kI 1.2 Extinction coefficient: ice m-1 kP 0.029 Extinction coefficient: phytoplankton m-1 (mmolN m-3)-1 kzLow 1e-5 Water mixing coefficient for steady and declining ice m2 s-1 kzHigh 1e-4 Water mixing coefficient for no ice and growing ice m2 s-1 kzWithinIce 1e-7 Nutrient diffusion coefficient within ice cells m2 s-1 brinevolmax 0.3 Maximum brine volume (lowermost ice cell) - brinevolmin 0.01 Minimum brine volume (topmost ice cell) - brinek 0.5 Curve of brine volume profile -

The ice is modelled as a porous medium made up of solid ice and liquid brine. It is assumed that during ice formation the contents of the cell are encapsulated in the ice and no initial rejection occurs. Accordingly, the concentration of algae and nutrients in a newly formed ice cell remains the same, but its distribution shifts from the bulk (combined solid and liquid) to the liquid phase. The molecular diﬀusion of nutrients in ice cells takes place only in the liquid phase. Brine volume is imposed using the parameters for minimum and maximum porosity from Mikkelsen et al. (2008), as listed in table 5.1. Water cells have a brine volume value of 1, and an exponential proﬁle is calculated for the ice cells based on the provided parameters. The value is calculated at each cell interface as per equation 5.1, and then at the cell mid points. Φmax and Φmin are the maximum

17 and minimum brine volume parameters, z is depth, and k determines the steepness of the proﬁle curve (brinek in table 5.1).

Φz = (Φmax − (Φmax − Φmin))exp(−kz) (5.1)

5.2 Biological activity

Nitrogen is the growth limiting nutrient and model currency. The total amount of nitrogen to be distributed in the column is based on the integrated total dissolved nitrogen concentration of 6 mmolN m−3 in the surface waters at 85 deg N latitude (Wheeler et al., 1997). The state variables are NH4, NO3, Phyto, Zoo, Detritus, Sediment and IceAlgae.

Figure 5.1: Conceptual model diagram

Free ﬂoating ice algae and detritus are encapsulated in the liquid fraction of ice as it forms. Once contained in an ice cell, ice algae are not exposed to mixing processes and can draw on the nutrients available in the liquid fraction for photosynthesis. When the ice melts, the ice algae sink through the water column and a higher mortality rate is applied to account for eﬀects related to the change of environment such as salinity shock. Phytoplankton in the water draw on nutrients available in their respective water cell for photosynthesis, and are susceptible to mortality and to grazing by zooplankton. Zooplankton mortality is modelled as a quadratic function of biomass, and a high rate (MortRateTrap) is applied to ice cells.

Mortality of ice algae, phytoplankton and zooplankton, and fecal pellet production of the latter all lead to the formation of detritus. Detritus sinks through the water with the rate SinkDet.

18 A proportion is remineralised to ammonium, and a proportion of this is subject to nitriﬁcation. Detritus that arrives at the lowermost boundary, which represents the benthos, contributes to the sediment pool. In reality, the sediment would return some of this as ammonium, which would then be promptly oxidised to nitrate. This is simpliﬁed in the model to a return of nitrate. The full list of mass balance equations can be found in table 5.2.

Table 5.2: Mass balance equations

dNH4 = T ranNH4 + Excretion + Mineralisation − Nitrification dt − (fNH4 ∗ (P hotosynthesisP hyto + P hotosynthesisIA))

dNO3 = T ranNO3 + Nitrification dt − ((1 − fNH4) ∗ (P hotosynthesisP hyto + P hotosynthesisIA))

dP hyto = T ranP hyto + P hotosynthesisP hyto − Ingestion − MortalityP hyto dt

dZoo = T ranZoo + (Ingestion ∗ (1 − P faeces)) − MortalityZoo − Excretion dt

dDetritus = T ranDetritus + MortalityZoo + MortalityP hyto + MortalityIA dt + (Ingestion ∗ P faeces) − Mineralisation

dSediment = DownwardF luxP hyto + DownwardF luxDetritus dt + DownwardF luxIA − SedimentMineralisation

dIceAlgae = T ranIA + dIA − MortalityIA + P hytosynthesisIA dt

N.B. DownwardFluxX is the flux for variable X across the lowermost boundary. IA stands for ice algae, and dIA is the difference in ice algal flux at each layer (calculated manually to allow for differences between entities in water and ice cells).

5.3 Forcing data

Initial sea ice thickness data was acquired from a ﬁxed mooring station in Cambridge Bay. A year of measurements from the ice proﬁler showed steady build up from November 2015 through to June 2016, followed by fast summer melt and very thin to no ice between August and October 2016 (Ocean Networks Canada Data Archive). This pattern formed the basis of the ice thickness parameterisation for both the the seasonal and the multi-year sea ice representations (provided in appendix E). In addition, Arctic sea ice thickness data from Hendricks (2012) provided an indication

19 of sea ice thickness at latitudes between 75 and 90°N. Solar radiation follows the formulation of the original model (as per Meire et al., 2013), with the latitude updated to 80°N.

Table 5.3: Rate expressions

PhotosynthesisPhyto = MaxUptake ∗ T empF un ∗ Limitation ∗ P hyto PhotosynthesisIA = MaxUptake ∗ T empF un ∗ Limitation ∗ IceAlgae Ingestion = MaxGrazing ∗ T empF un ∗ (P hyto/(P hyto + KsGrazing)) ∗ Zoo Excretion = ExcrRate ∗ T empF un ∗ Zoo SedMin = MinRate2 ∗ T empF un ∗ Sediment[N] Mineralisation = MinRate ∗ T empF un ∗ Detritus Nitriﬁcation = RNit ∗ T empF un ∗ NH4 MortalityPhyto = T empF un ∗ MortRateP h ∗ P hyto MortalityZoo = T empF un ∗ MortRateZoo ∗ Zoo2 MortalityZoo[ice cells] = T empF un ∗ MortRateT rap ∗ Zoo[ice cells]2 MortalityIA = T empF un ∗ MortRateP h ∗ IceAlgae MortalityIA[water cells] = T empF un ∗ MortRateSlough ∗ IceAlgae[water cells]

N.B. Limitation is the minimum of the calculated light and nutrient limitations. TempFun is the temperature function that adapts the reaction rate via the Q10 temperature coeﬃcient.

20 Chapter 6

Results

Plots and descriptions in the ﬁrst part of this chapter summarise changes in the distribution of the model currency, nitrogen, between state variables across the model runs. The full selection of scenario plots can be found in appendix B. Section 6.2 provides a parameter sensitivity analysis.

6.1 Simulation descriptions

Scenario 1, as a control simulation, covers a year long period without any ice cover and the corre- sponding high mixing levels. Plots of the model activity under these conditions, which can be found in appendix B (figures B.1 and B.2) show ice algae levels almost depleted, with no cell reaching a concentration of 0.01 mmolN m-3. Phytoplankton and zooplankton accumulate only in the upper half of the water column, with little variation over time. Minor growth pulses can be recognised and these occur in coordination with each other (phytoplankton growth preceding that of zooplankton). Nitrate and ammonium concentration profiles are fairly consistent, with the highest values in the lower half of the water column and declining upwards to depletion in the top 15 m. The detritus pattern displays similar uniformity with time, with the highest concentration of 0.6 mmolN m-3 in the lower half of the water column and very low levels in the surface waters. Nitrogen in the sediment is consistently very high in comparison to the other state variables, fluctuating between values of 111 - 117 mmolN m-2. The highest level occurs a short delay of ˜50 days after the highest levels of light availability, and vice versa.

The seasonal ice variation of scenario 2 (summary plots available in ﬁgure 6.1) shows phytoplankton dominating the water column to start, with highest concentrations at a depth of ˜15 m. A strong decline is experienced as the ice builds up, and very low concentrations are maintained throughout the rest of the period of ice cover. Ice algae accumulate steadily in the lowermost ice cells during ice growth before a rapid decline to very low levels with the melt. Following a short delay, concurrent with the low mixing period of ice melt, the ice algae resurge in the upper 20 m of the once-again turbulent column. From this point, phytoplankton concentrations start building up again, most eﬀectively at a depth of ˜15 m. Zooplankton patterns mimic those of phytoplankton with a delay and at lower concentrations - the highest reached being ˜0.6 mmolN m-3 in the top 20 m of the water column during the early ice growth phase.

Figure 6.1: Scenario 2 (seasonal ice) summary: brine ammonium, brine nitrate, phytoplankton, zooplankton, detritus and ice algae (concentrations in mmolN m-3, times are simulation days) The detritus pattern consists of a single dense vertical pulse following on from the ice algal water column bloom and lasting for ˜60 days. The maximum concentration reached in any cell is 2 mmolN m-3 between depths of 20 - 40 m. Water nitrate concentrations increase steadily throughout ice growth and melt, and are highest (at ˜5 mmolN m-3) in the lower half of the water column following the melt, while mixing levels are low. Ammonium also builds up during ice growth, but with a stronger bias towards the deeper cells, with highest levels of ˜2.5 mmolN m-3 reached in the bottom 5 m during ice growth. A second pulse during the low mixing period of ice melt is also distinct, though less so than for nitrate. In contrast to the pattern for nitrate, ammonium concentrations are lowest immediately following the end of the low mixing period, when ice cover is absent. Sediment nitrogen levels display greater variation than for the ice free scenario, steadily declining from an early maximum of ˜140 mmolN m-2 as ice thickness increases, throughout its melt to the minimum of ˜60 mmolN m-2. Following ice melt, values increase again quickly.

Finally, the multiyear ice scenario, as summarised by the plots in ﬁgure 6.2, shows a similar, though less pronounced, pattern of ice algal activity and detritus patterns to that of scenario 2. Phyto- plankton are, however, less successful under the low light conditions, only reaching concentrations higher than 2 mmolN m-3 following the ice melt and release of ice algae into the water column. Nitrate concentrations in the water column are generally high in comparison to scenarios 1 and 2, with highest levels of up to 6 mmolN m-3 found in the lowermost 15 - 20 m of the water column. Ammonium is less abundant, only reaching concentrations above 2 mmolN m-3 in the lowermost 5m at the very start of the simulation, and in the period of steady ice cover during which mixing levels are very low. Levels of organic nitrogen in the sediment are the lowest across all three scenarios, steadily declining from ˜75 to 40 mmolN m-2 until day 240, before starting to build back up again.

Flows of nitrogen between state variables were summed over the 7th simulation year (allowing the model to reach steady state) for each scenario. These totals are presented in ﬁgures 6.3, 6.4 and 6.5. It is clear that across all three scenarios very little of the ice algae reaches the sediment. The majority is instead transferred to the detritus pool via the mortality process. For phytoplankton, the majority is also transferred to the detritus pool via both mortality and ‘sloppy grazing’ by zooplankton, although a higher proportion reaches the sediment than that of ice algae. The majority of zooplankton biomass, however, is transferred to the pools of dissolved inorganic nitrogen via excretion, with a smaller proportion contributing to detritus. The proportion of phytoplankton biomass that is transferred to zooplankton via grazing decreases signiﬁcantly with increasing ice cover, from 63% for scenario 1, to 35% for scenario 2, and 12% for scenario 3. The most phytoplankton biomass sinks to the bottom of the water column during scenario 2, resulting in the highest delivery of nitrogen to the sediment, and the highest sediment mineralisation rate across the three scenarios.

Figure 6.2: Scenario 3 (multiyear ice) summary: brine ammonium, brine nitrate, phytoplankton, zooplankton, detritus and ice algae (concentrations in mmolN m-3, times are simulation days) A comparison of total production between the three scenarios is provided in ﬁgure 6.6. This total is the sum of all transfers of nitrogen from the pools of dissolved nutrients to the variables for ice algae and phytoplankton, i.e. their combined production, for the duration of the 7th year of each simulation. This ﬁgure shows that the total production decreases with increasing ice cover, from a value of 607 mmolN m-2 for scenario 1, to 180 mmolN m-2 for scenario 3. The jump from S1 to S2 is a loss of 45%, and the jump from S2 to S3 is a further loss of 46%. For the most productive case, the ice-free scenario 1, this total production is almost entirely from phytoplankton photosynthesis, while for scenarios 2 and 3, ice algal photosynthesis contributes 39% and 28% of the total, respectively.

Figure 6.3: Total model currency ﬂows between state variables from one year of the scenario 1 (ice free) simulation. Values are rounded to the nearest whole number. All ﬂows are expressed in mmolN m-3.

25 Figure 6.4: Total model currency ﬂows between state variables from one year of the scenario 2 (seasonal ice) simulation. Values are rounded to the nearest whole number. All ﬂows are expressed in mmolN m-3.

Figure 6.5: Total model currency ﬂows between state variables from one year of the scenario 3 (multiyear ice) simulation. Values are rounded to the nearest whole number. All ﬂows are expressed in mmolN m-3.

26 Figure 6.6: Total column integrated phytoplankton and ice algae biomass over one year for each of the scenarios, S1 to S3. Left: absolute values (mmolN m-2 year-1). Right: Phytoplankton and ice algae biomass as a percentage of the total (%).

6.2 Parameter sensitivity

Local sensitivity analysis quantifies differences in the model output produced by making very small changes to the parameters under investigation (Soetaert and Herman, 2008). The sensFun function from the FME package does so through the calculation of a matrix of sensitivity functions, whose summary values provide an estimation of the importance of the parameters investigated (Soetaert and Petzoldt, 2010). This function was applied to the model using the seasonal ice parameterisation of scenario 2 and a two year simulation period. For this period, the total combined primary production of phytoplankton and ice algae was specified as the argument against which to measure the sensitivity of the model to the parameters investigated.

Table 6.1: Investigated parameters listed in increasing order of the value L1.

Symbol Description Value Scale L1 kzWithinIce Nutrient diffusion coefficient within ice cells 1.0e-07 1.0e-07 0.00 kzLow Water mixing coefficient for steady and declining ice 1.0e-05 1.0e-05 0.01 kzHigh Water mixing coefficient for no ice and growing ice 1.0e-04 1.0e-04 0.22 brinevolmin Minimum brine volume (topmost ice cell) 1.0e-02 1.0e-02 0.73 brinevolmax Maximum brine volume (lowermost ice cell) 3.0e-01 3.0e-01 24.73 MortRateSlough Mortality rate sloughed ice algae 4.0e-01 4.0e-01 26.01 MortRateTrap Mortality rate trapped zooplankton 9.5e-01 9.5e-01 31.13 SinkAlg Sinking speed ice algae 3.0e-01 3.0e-01 42.02 brinek Curve of brine volume profile 5.0e-01 5.0e-01 68.54 kI Extinction coefficient: ice 1.2e+00 1.2e+00 75.72

27 Results are summarised in table 6.1, with the parameters listed in the order of increasing values of L1. L1 is a representation of the sensitivity functions calculated for that parameter, in which:

• Si,j is the sensitivity of parameter i for variable j

• L1 = sum(abs(Si,j))/n

This value therefore allows a ranking of parameters based on their impact on the total production, as provided in table 6.1. It can be seen that kI, the light extinction coefficient of ice has the highest sensitivity value of all the parameters tested, while kzWithinIce, which determines the diffusion of nutrients in ice cells, has almost no effect on total production. Of the top five parameters, the effects on production are mostly negative. Higher levels of light extinction, steeper brine profiles, faster sinking and higher ice algal mortality all lead to decreased production, while higher mortality rates for zooplankton trapped in ice cells leads to increased production.

28 Chapter 7

Discussion

This chapter starts with a reﬂection on the causes of the patterns observed in the model output, primarily in terms of light and nutrient limitation. Results of the sensitivity analysis are then discussed in section 7.2 with proposals for further tests and ways in which to determine model validity. In section 7.3 future extensions are considered, including an improved representation of vertical mixing in the water column, and the incorporation of temperature and snow thickness data.

7.1 Scenario analysis 7.1.1 Phase 1: ice growth As described in section 3.4, an important consequence of the level of mixing is the nutrient supply to the surface waters. In the model employed here, a higher mixing value during periods of ice growth reﬂects the process of expelled brine water sinking and causing turbulence. This allows the advection of water upwards from lower depths, which may provide new nutrients with which to fuel primary production. This nutrient resupply pattern can be recognised in the nitrate and ammonium plots of both the seasonal and multiyear ice scenarios as ice (and its inhabitants) are growing. The converse is also noticeable for both when the ice is melting and the nutrients are promptly depleted from the upper water cells. Regardless of the abundant nutrient supply under the growing ice, however, phytoplankton levels do not start to recover until the end of both scenarios 2 and 3, under ice-free or thin-ice conditions, indicating that light limitation was restricting their growth for the majority of the ice growth period.

7.1.2 Phase 2: ice melt This is the low turbulence period of this scenario, representing the stratiﬁcation induced by the freshwater lens ﬂoating on more saline seawater below. As a result, nutrient concentrations at the top of the water column decline, accumulating instead at the base. Little life persists in this phase. Phytoplankton and zooplankton do not yet recover, and the majority of ice algae have disappeared by this point, having been subject to the higher mortality rates of the water cells that represent the salinity shock experienced upon exposure to the water column. The low mixing conditions,

29 however, ensure that some of the few remaining algae maintain their position in the surface waters, allowing for a potential future bloom.

7.1.3 Phase 3: ice break As the ice cover has disappeared, turbulence increases once again, due to the increased impact of wind stress, with the potential for nutrient replenishment. Additionally, light is no longer limiting growth, with the highest availability in the water column throughout the course of the simulation. The results for life can be seen in the plots, as this turbulent water plays host to a resurgence of ice algae, whose success is fast and dense, but short-lived, presumably most hampered by the higher mortality rate of the water cells. This is followed in turn by a phytoplankton bloom in the upper water column. This timing sequence, and the way in which the phytoplankton spatially stem from the ice algae, may indicate that the ice algal death contributes to the phytoplankton bloom, as the resulting detritus is remineralised to dissolved inorganic nitrogen in the water. During the same period a single, dense plume of detritus is prominent from the surface waters down through the water column to the sediment, resulting from the success of life in the surface waters, and then declining along with the phytoplankton and zooplankton in the water as light levels become restrictive again.

7.1.4 Total production Considering the production totals calculated over one simulation year (ﬁgure 6.6), it is clear that ice algae are at their most proﬁcient, with the highest proportion of total production, under the seasonal ice conditions of scenario 2. An increase in ice cover, as tested with scenario 3, resulted in a notably reduced share of the total. As there is a higher availability of light for ice algae than for the underlying phytoplankton, this reduction can be attributed to the nutrient supply, which is poor in the upper waters during the low mixing conditions associated with constant ice cover. In this case, phytoplankton have the advantage of movement in the water column. In both scenarios, the production peaks occurred at the same times in the year, most prominently after the main period of ice melt. This can be seen most clearly from plots of column integrated biomass over the year, which are available in the appendices (C.1).

The overall pattern of reduced ice cover leading to increased productivity, and its attribution to the higher availability of light in the upper water column, is in agreement with a recent modelling study that used the improved light conditions to explain a hypothesised increase in sub-ice phytoplankton bloom occurrences and extent in recent years (Horvat et al., 2017). If, however, the ice melt for the seasonal ice scenario had been set to occur earlier in the year than for the multiyear ice scenario, the main blooms may have coincided with lower light conditions and not proved so successful. This emphases the limitations of the ice parameterisations used in this study.

7.2 Model validation

In table 6.1, new model parameters are listed in order of their sensitivity summary value L1, from least to most influential. This identifies those that have the largest effect on the model output, and thus those with the potential to introduce the most error when inaccurately defined. In this model, for the seasonal ice parameterisation, these are kI and brinek, which should therefore be prioritised

30 in deﬁning as closely to reality as possible. This could be by applying measured real-world values, or by using other primary production data that would allow parameter calibration methods to be applied.

Additional tests could be performed to build on this initial understanding of the parameter space. The FME package contains a suite of further tools including collinearity tests, for estimating parameter identifiability, and Markov chain Monte Carlo (MCMC) analysis, for estimating parameter uncertainties (Soetaert and Petzoldt, 2010). With greater computational power it may be beneficial to investigate all of the model parameters, rather than just those listed, as the model function has changed significantly from its original design intention. The runs could also be performed using the ice parameterisations for scenarios 1 (ice-free) and 3 (multiyear ice) in order to allow for a greater range of background conditions. A similar line of reasoning could be applied to the forcing data used in the model runs - ideally, observational data would instead be imposed for the ice thickness and solar radiation values. If primary production measurements were also available from the same site, a comparison between model output and real data would be possible, as well as inverse modelling for further refinement.

Alongside improving the parameterisations and forcing data, another major element affecting the quality of model output is its design - how well reality is reflected. A first port of call is the existing assumptions and simplifications. These include decisions such as employing the same limiting nutrient across each form of life in the model, although silicon rather than nitrogen is often regarded as the most limiting in sea ice ecosystems (as discussed in section 2.2.1). Secondly is whether or not the most salient processes to the focus of research are incorporated. For both, this will involve further trials and evaluations to assess the impact of specific updates. In deciding whether or not they should be included, the trade-off between model simplicity and completeness must be considered. Simplicity provides ease of understanding, of interpretation, fewer sources of error and a faster running time, whereas the addition of new processes may offer new and more insightful results. With this balance in mind, the next section describes some potential contenders for future model updates.

7.3 Further model considerations

As water turbulence has been seen to be central to the dynamics of the simulations described in chapter 6, its accurate representation is of high importance. As such, it may be worthwhile to improve the existing abstraction in which any phase of positive ice growth in the model results in the same constant value for the mixing rate, regardless of how quickly the ice is forming. One possibility would be to break the mixing values down to a ﬁner gradient dependent on the rate of ice formation, allowing very slow and very fast growth levels to produce diﬀerent levels of turbulence accordingly. This calculated growth rate may have further relevant applications, such as a closer representation of the nutrient concentrations in the ice, on which the ice algae are reliant. These concentrations are partially dependent on the rate of ice formation, as demonstrated in the brine and nutrient modelling study of Vancoppenolle et al. (2010).

Another fundamental factor in primary production dynamics is temperature. For a more realistic projection, observed air and water temperature data could be imposed, with a proﬁle calculated

31 by interpolating the values. This would not be computationally demanding, and would allow for a number of further possibilities. One is the modelling of salinity, which would be redistributed to the liquid fraction of the bulk with brine rejection, and could act as a useful tracer in further simulations. In turn, this could lead to brine volume calculated as a dynamic function of salinity and temperature (in place of the existing parameters). Temperature values may also provide useful limits for other parameters, or additional controls. In the model of Lavoie et al. (2005), an overview of which is available in chapter 4, a rapid decline in ice algae during summer ice melt was attributed to the increase in ice temperature. The hypothesised mechanism was the enlargement of brine channels leading to increased flushing, which would result in additional cells lost to the underlying water. As this flushing process is highly relevant to the model focus of primary production, it may be beneficial to include. Lavoie et al. (2005) did so with a loss term proportional to ice warming at temperatures above -4C, possible with the inclusion of temperature calculation.

A final update considered here is the distinction between ice and snow. As for the previous potential developments, this is chosen for reflection for its pertinence to primary production dynamics, relative simplicity in modelling terms, and potential for the inclusion of observational data (as snow quantities are often taken alongside ice thickness measurements). As discussed in chapter 3, snow attenuates light much more efficiently than ice, and the albedo effect is notably different. Thus a distinction would allow a more accurate representation of the light availability, which as a growth-limiting factor is important to represent accurately.

32 Chapter 8

Conclusions

Running the developed N2PZD model under varying levels of ice cover, from ice-free to multiyear scenarios, conveyed the core elements of potential diﬀerent futures for the modelled ice algae, phytoplankton and zooplankton entities. Explanations in terms of nutrient and light limitation have been proposed for the patterns revealed, oﬀering a hypothesis for the potential progression of the basic primary production dynamics in sympagic-pelagic ecosystems. The incorporation of a benthic component with measurements of nitrogen build-up allowed a comparison of the implications of varying ice-coverage on the benthos. The seasonal ice scenario was shown to result in the highest delivery of nitrogen to the sediment (through higher levels of sinking phytoplankton) and in turn the highest sediment mineralisation rate. Reduced ice cover was seen to increase overall productivity across the simulations examined, with the seasonal ice projection totalling 55% of that of the ice free scenario, and the multiyear projection totalling just 30%. These results, however, are questioned with respect to how well the forcing data and model parameters represent true Arctic conditions, and whether or not the model captures the most integral components of the system.

An investigation of the model parameter space revealed which of the new parameters had the largest calculated effect on model output, and thus would be most suited to further refinement and as candidates for inverse modelling, should appropriate data become available. As well as direct comparisons with real data, a more in-depth testing of the model could be achieved through inter-model comparisons using an identical set of forcing data, and an improved understanding of the parameter space, for example, by applying collinearity tests and MCMC analysis. Following on from means of validation, specific model extensions have been proposed as high priority candidates for further development, including an improvement to the mixing representation, the incorporation of temperature and salinity data, and the differentiation between ice and snow levels with respect to light attenuation and the albedo effect.

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40 Appendices

A Annotated model code

Introduction

The model employed in this study has been adapted from the extended NPZD pelagic biogeochemical model of Meire et al. (2013). Some elements have been removed, most notably the state variable for oxygen and its related reactions.

Setup, Parameters

# ======# N2PZD 1D Sea Ice Model # ======rm(list = ls(all = TRUE)) # Remove everything require(ReacTran) # ReacTran: reactive transport modelling require(FME) # FME: flexible modelling environment

# Nitrogen TotalN <-6 # Total Nitrogen in the system (mmolN m-3)

# Light alpha <- 0.03 # Photosynthesis coeff (m2 W-1) kW <- 0.198 # Extinction coeff water (m-1) kI <- 1.2 # Extinction coeff ice (m-1) kP <- 0.029 # Extinction coeff phytop m-1 (mmolN m-3)-1

# Biology Q10 <-2 # Q10 coefficient

MaxUptake <- 1.5 # Uptake at 20 degrees C (d-1) KsDIN <- 0.5 # Ks (half sat constant) DIN (mmolN m-3)

MaxGrazing <- 0.75 # Maximum grazing rate (d-1) KsGrazing <-2 # Ks Grazing (mmolN m-3) Pfaeces <- 0.30 # Fraction faeces (-) ExcrRate <- 0.08 # Excretion Rate (d-1) SinkDet <-1 # Sinking speed Detritus (m d-1) SinkAlg <- 0.3 # Sinking speed Algae (m d-1) MinRate <- 0.04 # Mineralisation Rate (d-1) MinRate2 <- 0.02 # Anoxic, sediment Mineral. (d-1)

RNit <- 0.05 # Nitrification Rate (d-1)

MortRatePh <- 0.03 # Mortality Phytoplankton (d-1) MortRateSlough <- 0.4 # Mortality Sloughed algae (d-1) MortRateZoo <- 0.01 # Mortality Zooplankton (d-1 (mmolN m-3)-1) MortRateTrap <- 0.95 # Mortality Trapped zoo (d-1 (mmolN m-3)-1)

Mixing parameters The low mixing rate, kzLow, is employed with steady ice cover and during ice decline. High mixing, kzHigh, is employed when there is no ice cover and during ice growth. kzWithinIce represents diﬀusion within the ice and is used solely for the nutrient transport. # Mixing parameters kzLow <- 1e-5 # water mixing with steady or declining ice (m2 s-1) kzHigh <- 1e-4 # water mixing with no ice or growing ice (m2 s-1) kzWithinIce <- 1e-7 # mixing within ice (m2 s-1)

Model Grid

100 equally spaced layers over a 50m water column. # Define grid N <- 100 # Number of cells in system (-) L <- 50 # Depth of system (m) b <- L/N # size of one cell (m) grid <- setup.grid.1D(x.up =0,L=L,N=N) # Build grid

Physical Conditions

DepthMean <- grid$x.mid # Mid points DepthInt <- grid$x.int # Border points

Biogeochemical reaction rates are automatically set at 20 degrees C. Q10 is the temp coeﬃcient that adapts this via TempFun. TempFun <- function (T) Q10^((T-20)/10)

# SCENARIO 1: NO ICE COVER # Icethickness <- data.frame(time = c(0, 800), thick = c(0, 0))

# SCENARIO 2: SEASONAL ICE Icethickness <- data.frame(time = c(0, 95, 260, 290, 365, 460, 625, 655, 730, 800), thick = c(0,1, 3.5,0,0,1, 3.5,0,0,1))

# SCENARIO 3: MULTIYEAR ICE # Icethickness <- data.frame(time = c(0, 260, 290, 365, 625, 655, 800), # thick = c(1, 4, 1, 1, 4, 1, 1)) icefun <- approxfun(x = Icethickness$time,y= Icethickness$thick)

# Brine volume brinevolmax <- 0.3 # Maximum brine volume (lowermost ice cell) brinevolmin <- 0.01 # Minimum brine volume (topmost ice cell) brinek <- 0.5 # Steepness of brine volume ice profile

Derivative function

Documentation for ReacTran can be found at: https://www.rdocumentation.org/packages/ReacTran/ versions/1.4.2/topics/setup.grid.1D. (dx are the distances between grid cell interfaces, and dx.aux are an auxiliary set of distances between grid cell mid-points). Note for the transport that although the measurement of nutrients is by bulk, the transport only takes place in the liquid phase. NPZDice <- function(t, y, parms) { with (as.list(parms), { kzLow <- kzLow # water mixing with steady or declining ice (m2 s-1) kzHigh <- kzHigh # water mixing with no ice or growing ice (m2 s-1) kzWithinIce <- kzWithinIce # mixing within ice (for nutrients) (m2 s-1) brinevolmax <- brinevolmax # Maximum brine volume (lowermost ice cell) brinevolmin <- brinevolmin # Minimum brine volume (topmost ice cell) brinek <- brinek # Steepness of exponential brine volume ice profile MortRateSlough <- MortRateSlough # Mortality Sloughed algae (d-1) MortRateTrap <- MortRateTrap # Mortality Trapped zoo (d-1 (mmolN m-3)-1) SinkAlg <- SinkAlg # Sinking speed Algae (m d-1) kI <- kI # Extinction coeff ice (m-1)

# State variables NH4 <- as.vector(y[1:N]) NO3 <- as.vector(y[(N+1):(2*N)]) Phyto <- as.vector(y[(2*N+1):(3*N)]) Zoo <- as.vector(y[(3*N+1):(4*N)]) Detritus <- as.vector(y[(4*N+1):(5*N)]) Sediment <- as.vector(y[(5*N+1):(6*N)]) IceAlgae <- as.vector(y[(6*N+1):(7*N)])

# Current light (at 80N) and ice thickness I <- 0.5*(800+440*sin(2*pi*(t-179)/365)) icethick <- icefun(t)

# Brine volume at cell interfaces and mid points BrineVolint <- rep(1,N+1) # water BrineVolint[DepthInt <= icethick] <- (brinevolmax - # ice (brinevolmax - brinevolmin)*(exp(-brinek*DepthInt[DepthInt <= icethick]))) BrineVolmid <- 0.5*(BrineVolint[-1] + BrineVolint [-(N+1)])

# Albedo, insulation if (icethick > 0.1){ # ice is present (>10cm) TT <-1 # temperature (ocean is warmer with ice insulation) if (icethick >1){ I <- 0.35*I # thick ice (>1m) albedo of 0.65 } else { I <- 0.45*I # thin ice (<1m) albedo of 0.55 } } else { # no ice coverage TT <--1 # temperature } icechange <-( icefun(t+1)-icefun(t)) # ice thickness change from previous day (m d-1)

# Mixing rate MixIce <- rep((kzLow*3600*24), (N+1)) # low mixing default MixIce[which(grid$x.int < icethick)] <- (kzWithinIce*3600*24) # kzWithinIce for ice cells if ((icechange >0) | (icethick ==0)) { # high mixing (growth/no ice) MixIce[which (grid$x.int > icethick)] <- (kzHigh*3600*24) # water cells only } MixIce[1] <-0 # top boundary: no diffusion D <- MixIce

# Light extinction kIce <- rep(0, N) kIce[which (grid$x.int < icethick)] <- kI # light extinction by ice for each cell kExt <- kW + kP*Phyto + kIce # total light extinction (water, phyto and ice) ID <- rep(I, N)

# Total extinction for each grid cell for(i in1:(N-1)){ ID[i+1] <- ID[i]*exp(-kExt[i]*grid$dx.aux[i]) }

PAR <- ID[-(N+1)]*exp(-kExt*grid$dx/2) Lightlim <- tanh(alpha*PAR)

# Ice algae transport SinkRate <- rep(0, N) SinkRate[which (grid$x.mid > icethick)] <- SinkAlg # water cells: algae sinking rate

IAFluxOut <- SinkRate * IceAlgae # ice algae flux out of each layer dIA <-(- diff(c(0, IAFluxOut))) / grid$dx # difference for each layer

# Transport (using tran.1D fn, part of the ReacTran pkg) # C: concentration; D: diffusion coeff; v: advective velocity; dx: cell thickness transport <- function (C,v=0, flux.down = NULL){ TranC <- tran.1D(C = (C/BrineVolmid), D=D, v= v, flux.up =0 # liquid phase , flux.down = flux.down, VF = BrineVolint, dx = grid) TranC$dC <- TranC$dC*BrineVolmid # convert back to bulk return (TranC) }

TranNO3 <- transport(NO3) TranPhyto <- transport(Phyto,v= SinkAlg) TranIce <- transport(IceAlgae,v=0) # sinking already calc'd TranZoo <- transport(Zoo) TranDetritus <- transport(Detritus,v= SinkDet) fluxdown <- TranDetritus$flux.down + TranPhyto$flux.down + IAFluxOut[N] TempFun <- TempFun(TT) SedMin <- MinRate2*TempFun*Sediment[N] TranNH4 <- transport(NH4, flux.down =- SedMin)

# Reactions in the brine NO3brine <- NO3/BrineVolmid NH4brine <- NH4/BrineVolmid Nlim <- (NH4brine+NO3brine)/(NH4brine+NO3brine + KsDIN) Limitation <- pmin(Lightlim, Nlim)

# Photosynthesis PhotosynthesisPhyto <- MaxUptake*TempFun*Limitation*Phyto PhotosynthesisIA <- MaxUptake*TempFun*Limitation*IceAlgae

# Zoo grazing and excretion Ingestion <- MaxGrazing*TempFun*(Phyto/(Phyto + KsGrazing))*Zoo Excretion <- ExcrRate*TempFun*Zoo

# Mortality MortalityPhyto <- TempFun*MortRatePh*Phyto MortalityZoo <- TempFun*MortRateZoo*Zoo^2 MortalityIA <- TempFun*MortRatePh*IceAlgae

# Increase mortality rate for IA in water cells (sloughed algae) MortalityIA[which(grid$x.mid > icethick)] <- (TempFun * MortRateSlough * IceAlgae[which(grid$x.mid > icethick)])

# Increase mortality rate for Zoo in ice cells (trapped zoo) MortalityZoo[which (grid$x.mid < icethick)] <- (TempFun * MortRateTrap * Zoo[which(grid$x.mid < icethick)]^2)

Mineralisation <- MinRate*TempFun*Detritus Nitrification <- RNit*TempFun*NH4 fNH4 <- NH4/(NO3+NH4) # NH4 fraction of total DIN

# Mass balance equations dNH4 <- TranNH4$dC + Excretion + Mineralisation - Nitrification - (fNH4*(PhotosynthesisPhyto + PhotosynthesisIA)) dNO3 <- TranNO3$dC + Nitrification - ((1-fNH4)*(PhotosynthesisPhyto + PhotosynthesisIA)) dPhyto <- TranPhyto$dC + PhotosynthesisPhyto - Ingestion - MortalityPhyto dZoo <- TranZoo$dC + Ingestion*(1-Pfaeces) - MortalityZoo - Excretion dDetritus <- TranDetritus$dC + MortalityZoo + MortalityPhyto + Ingestion*Pfaeces - Mineralisation + MortalityIA dSediment <- c(rep(0,N-1), + fluxdown - SedMin) dIceAlgae <- TranIce$dC + dIA - MortalityIA + PhotosynthesisIA list(c( dNH4, dNO3, dPhyto, dZoo, dDetritus, dSediment, dIceAlgae), SedimentOrgN = as.double(Sediment[N]), Icethickness = icethick, Mixingcoefficient =D, Temperature =T, Light =I, Foto = PhotosynthesisPhyto, NL = Nlim, PL = Lightlim, Lim = Limitation, Min = Mineralisation, flux = fluxdown, Ing = Ingestion, Mor = MortalityZoo, Ex = Excretion, MorP = MortalityPhyto, TNH4 = TranNH4$dC, TNO3 = TranNO3$dC, TPhyto = TranPhyto$dC, TZoo = TranZoo$dC, TDet = TranDetritus$dC, Temp = TempFun, Nitr = Nitrification, fN = fNH4, TotalN = sum((NH4 + NO3 + Phyto + Zoo + Detritus + IceAlgae)*grid$dx + Sediment), NO3br = NO3brine, NH4br = NH4brine, BrineVoli = BrineVolint, BrineVolm = BrineVolmid, SEDtoDIN = SedMin, DINtoIA = sum(PhotosynthesisIA*grid$dx), DINtoPHYTO = sum(PhotosynthesisPhyto*grid$dx), DETtoDIN = sum(Mineralisation*grid$dx), ZOOtoDET = sum(MortalityZoo*grid$dx), ZOOtoDIN = sum(Excretion*grid$dx), PHYTOtoZOO = sum((Ingestion*(1-Pfaeces))*grid$dx), IAtoDET = sum(MortalityIA*grid$dx), PHYTOtoDET = sum((MortalityPhyto + (Ingestion*Pfaeces))*grid$dx), DETtoSED = TranDetritus$flux.down, PHYTOtoSED = TranPhyto$flux.down, IAtoSED = IAFluxOut[N], TotalIAPhyto = sum((PhotosynthesisIA + PhotosynthesisPhyto)*grid$dx), TotalIAPhytoZooDet = sum((PhotosynthesisIA + PhotosynthesisPhyto + Ingestion + MortalityIA + MortalityZoo + MortalityPhyto)*grid$dx), TotalIAPhytoZooDetDinSed = sum((PhotosynthesisIA + PhotosynthesisPhyto + Ingestion + MortalityIA + MortalityZoo + MortalityPhyto + Excretion + Mineralisation)*grid$dx) + SedMin + fluxdown ) }) } Solution

To start, 20% of (totalN - 1) mmolN m-3 is assigned to each of the variables ammonium, nitrate, phytoplankton, ice algae and detritus, with the remainder assigned to zooplankton. The sediment does not contain any to start. Nsys <- (TotalN-1)/5

NH4ini <- rep(Nsys , len =N) NO3ini <- rep(Nsys , len =N) Phytoini <- rep(Nsys , len =N) Zooini <- rep(1, len =N) Detritusini <- rep(Nsys , len =N) Sedimentini <- rep(0, len =N) IceAlgaeini <- rep(Nsys , len =N) yini <- c(NH4ini,NO3ini, Phytoini, Zooini, Detritusini, Sedimentini, IceAlgaeini)

Model runs: The model run is split into two. The vector of initial conditions, yini, is supplied to the first run (as ‘y’). The final condition of the first run provides the input to the second, which is then plotted. The output is a matrix with columns for time and for each of the state variables, and rows for depth. Time is in days. # Dynamic run - two steps niter <-1 for (i in1: niter){ outdyn <- ode.1D(y = yini, times =0:730, func = NPZDice, parms = NULL, nspec =7, method = "lsodes", lrw = 46000, names = c("NH4","NO3","Phyto","Zoo","Detritus","Sediment","IceAlgae")) yini <- outdyn[nrow(outdyn),2:(N*7+1)] } outdyn <- ode.1D(y = outdyn[nrow(outdyn),2:(N*7+1)], times =0:365, func = NPZDice, parms = NULL, nspec =7, method = "lsodes", lrw = 46000, names = c("NH4","NO3","Phyto","Zoo","Detritus","Sediment","IceAlgae"))

# Annual model currency flows between state variables annualflows <- outdyn[,c("DINtoIA", "DINtoPHYTO", "SEDtoDIN", "DETtoDIN", "ZOOtoDET", "PHYTOtoZOO", "IAtoDET", "PHYTOtoDET", "DETtoSED", "ZOOtoDIN", "PHYTOtoSED", "IAtoSED")] round(colSums(annualflows), digits =0)

Sensitivity analysis: For running the following tests, the code at the start of the NPZDice function that allows parameter values to be fed in must be uncommented, and the parameter values themselves left undeﬁned in the setup. # List of parameters for which to test local sensitivity parms <- list(kzLow = 1e-5, kzHigh = 1e-4, kzWithinIce = 1e-7, brinevolmax = 0.3, brinevolmin = 0.01, brinek = 0.5, kI = 1.2, SinkAlg = 0.3, MortRateSlough = 0.4, MortRateTrap = 0.95)

# Wrapper function NPZDwrap<-function(parms){ out <- ode.1D(y = yini, times =0:730, func = NPZDice, parms = parms, nspec =7, method = "lsodes", lrw = 46000, names = c("NH4","NO3","Phyto","Zoo","Detritus","Sediment","IceAlgae")) sumTotalIAPhyto <- sum(out[,"TotalIAPhyto"]) return(c(sumTotalIAPhyto = sumTotalIAPhyto)) }

NPZDsens <- sensFun(func = NPZDwrap, parms = parms, sensvar = "sumTotalIAPhyto") summary(NPZDsens) sum<-summary(NPZDsens)

B Model scenario output plots

Figure B.1: Scenario 1 (no ice cover): ice thickness (m), light at the surface (W), sediment organic nitrogen (mmolN m-2), mixing coeﬃcient (m2 s-1), brine ammonium (mmolN m-3) and brine nitrate (mmolN m-3)

Figure B.2: Scenario 1 (no ice cover): ammonium, nitrate, phytoplankton, zooplankton, detritus and ice algae (all in mmolN m-3)

Figure B.3: Scenario 2 (seasonal ice cover): ice thickness (m), light at the surface (W), sediment organic nitrogen (mmolN m-2), mixing coeﬃcient (m2 s-1), brine ammonium (mmolN m-3) and brine nitrate (mmolN m-3)

Figure B.4: Scenario 2 (seasonal ice cover): ammonium, nitrate, phytoplankton, zooplankton, detritus and ice algae (all in mmolN m-3)

Figure B.5: Scenario 3 (multiyear ice cover): ice thickness (m), light at the surface (W), sediment organic nitrogen (mmolN m-2), mixing coeﬃcient (m2 s-1), brine ammonium (mmolN m-3) and brine nitrate (mmolN m-3)

Figure B.6: Scenario 3 (multiyear ice cover): ammonium, nitrate, phytoplankton, zooplankton, detritus and ice algae (all in mmolN m-3) C Total primary production with time

Figure C.1: Column integrated biomass (y-axis, in mmolN m-2) with time (x-axis, in simulation days) for ice algae (left), phytoplankton (middle) and their combined value (right). Top: scenario 2 (seasonal ice). Bottom: scenario 3 (multiyear ice).

55 D Annual state variable ﬂows

Table D.1: Total model currency ﬂows between state variables from the 7th year of simulation. Values are rounded to the nearest whole number. All ﬂows are expressed in mmolN m-3.

Scenario 1: ice free Scenario 2: seasonal ice Scenario 3: multiyear ice DIN to IceAlgae 0 129 51 DIN to Phyto 607 204 129 Sediment to DIN 195 201 120 Zoo to DIN 333 64 14 Detritus to DIN 74 67 39 Detritus to Sediment 183 163 85 Phyto to Sediment 11 37 32 IceAlgae to Sediment 0 1 0 IceAlgae to Detritus 0 128 51 Phyto to Detritus 213 97 71 Zoo to Detritus 44 5 1 Phyto to Zoo 382 70 15

56 E Model scenario ice parameterisations

Ice thickness values in the model runs are interpolated between the day-thickness pairs provided in the following tables. Two years’ values are provided, running from October onwards to mark the start of the growth season.

Table E.1: Ice parameterisation for scenario 1: ice free

Time (day) Ice thickness (m) 0 0 800 0

Table E.2: Ice parameterisation for scenario 2: seasonal ice

Time (day) Ice thickness (m) 0 0 95 1 260 3.5 290 0 365 0 460 1 625 3.5 655 0 730 0 800 1

Table E.3: Ice parameterisation for scenario 3: multiyear ice

Time (day) Ice thickness (m) 0 1 260 4 290 1 365 1 625 4 655 1 800 1