A Numerical Study of the Circulation, Ecology and Biogeochemistry on the Southern New England Shelf

This Ph.D. dissertation presents a process-oriented study with two primary objectives: 1) to obtain a physical understanding of the impacts of local and remote forcing, including basin-scale natural climate variability, on the interannual variability of along-shelf transport and water properties of the Middle Atlantic Bight (Chapter 1); 2) to explore the impacts of physical processes on the seasonal variation of phytoplankton biomass in Rhode Island coastal waters (Chapter 2). To achieve the two objectives, we apply a numerical modeling approach employed by the Regional Ocean Modeling System (ROMS) together with substantive analyses of both in-situ and remote observations. Chapter 1 focuses on the interannual-to-decadal variability of along-shelf transport and water properties of the Middle Atlantic Bight (MAB). A suite of process oriented numerical experiments is designed for separating local and remote forcing in order to explore their contributions to the interannual-to-decadal variability of along-shelf transport. Results show that the low-frequency variability is dominated by remote forcing from the open boundaries of the region. The penetration of the Labrador Current into the region contributes to a significant increase of along-shelf transport in the winters of 2009 and 2010. By contrast, the anticyclonic mesoscale eddies associated with the Gulf Stream have a negative impact on the along-shelf jet, and in certain cases even reverse the alongshelf transport. The along-shelf transport is also found to possess a decadal transition, i.e. weaker during 2004-2008 but stronger during 2009-2013. Chapter 2 focuses on the mechanisms controlling the seasonal variation and spatial distribution of phytoplankton biomass in Rhode Island (RI) coastal waters. We first apply an Empirical Orthogonal Function (EOF) analysis to a nine-year monthly chlorophyll-a dataset in order to determine the spatial/temporal structure of the signal. The first EOF mode shows that the spatial variations of chlorophyll-a are in phase from the RI coast to the outer shelf, and the temporal variations are dominated by the strong seasonal cycle characterized by a broad peak during the fall-winter months (October to March). The spatial distribution of chlorophyll-a indicates that the phytoplankton biomass decreases with distance offshore as the water depth increases. To understand the mechanisms controlling the abovementioned features, we first set idealized onedimensional (1-D) numerical experiments, using a physical-biological model (ROMSNPZD), to isolate advective processes. Results show that the fall-winter bloom is initiated by enhanced vertical turbulent mixing, which results from the combined effects of the increased surface momentum forcing and surface cooling, bringing nutrients up into the euphotic zone. The extensive mixing also has a counteractive effect on the fall-winter bloom as phytoplankton are carried below the euphotic layer. A three-dimensional (3-D) experiment is then conducted to validate the key conclusions drawn from 1-D simulations from which we find that results from the 3-D experiment are qualitatively in agreement with those from the 1-D experiments.


Abstract
A numerical simulation using the Regional Ocean Modeling System (ROMS) indicates that there is significant interannual-to-decadal variability of along-shelf transport and water properties over the Middle Atlantic Bight (MAB) from 2004-2013.
To examine the relative contribution from local atmospheric forcing versus remote, oceanic open boundary forcing to such low-frequency variability, we implement a suite of process oriented numerical experiments. Results show that the interannual variability is dominated by remote forcing from the open boundaries of the region rather than by local atmospheric forcing. The penetration of the Labrador Current into the region contributes to a significant increase of along-shelf transport in the winters of 2009 and 2010. By contrast, the anticyclonic mesoscale eddies associated with the Gulf Stream decrease the background along-shelf jet and, in certain cases, even reverse the along-shelf transport. In addition, the along-shelf transport appears to have a decadal transition, i.e., weaker during 2004-2008 but stronger during 2009-2013.

Introduction
The Northeast U.S. continental shelf/slope region encompasses an area of approximately 260,000 km 2 from the Scotia Shelf in the north to Cape Hatteras in the south, covering the Gulf of Maine/Georges Bank (GoM/GB) and the entire Middle Atlantic Bight (MAB). The MAB shelf is widest off southern New England, extending over 200 km seaward from shore, and is relatively narrower off Cape Hatteras where the shelfbreak is approximately 30 km from shore (Figure 1-1).
The primary water masses of this region are the relatively cold and fresh Shelf Water and the warm and saline Slope Water. The boundary between these two water masses occurs in a narrow transition region referred to as the shelf/slope front (Mountain, 2003). Associated with this front is a narrow, southwestward flowing baroclinic jet that, to leading order, is in geostrophic balance. The front/jet system itself is part of the basinscale, buoyancy-driven coastal current system originating as the East Greenland Current from the north, and ultimately being entrained into the Gulf Stream near Cape Hatteras.
Along its path, the front/jet system is modified by various factors, including freshwater runoff and offshore recirculation, and experiences a substantial decrease in volume transport (Loder et al., 1998).
Quantifying the along-shelf transports and cross-shelf exchanges of the shelfbreak region have been long-standing research topics (e.g., Beardsley et al., 1981). A mass and salinity balance in the MAB indicates that approximately three quarters of the water that passes south of Nantucket leaves the shelf by the time it reaches Delaware and a third of the water that is lost is replaced by the more saline waters of the upper slope (Biscaye et al., 1994). Clearly, these transport change must involve a considerable amount of cross-shelf exchanges of mass, heat, freshwater, and nutrients. But how these transport changes are accomplished and which processes are responsible for various portions of the exchange has not yet been satisfactorily documented. Intensive in-situ studies since the 1970s have been carried out using moorings and hydrographic surveys at various locations during different time periods (NESDE, Beardsley and Flagg, 1976;NSFE, Beardsley et al., 1985;SEEP-I, Walsh et al., 1988;SEEP-II, Biscaye et al., 1994;and CMO/PRIMER, Dickey and Williams, 2001), all with the common goal of understanding the dynamics of the front and the critical shelf and slope exchange processes. The hydrography of the shelfbreak region has been described in a number of syntheses, the latest of which is produced by Linder and Gawarkiewicz (1998) and Linder et al. (2006).
A difficulty common to all these efforts is how to interpret the episodic and discontinuous observations to form a statistically significant description of the frontal structure accounting for the influence of onshore and offshore front fluctuations.
High spatial resolution and temporally continuous numerical simulations of ocean state variables have become important additional tools for obtaining a better understanding of the shelf/slope circulation and for quantifying its variations. Chen et al. (2001) employed the Finite-Volume Community Ocean Model (FVCOM), configured as a three-dimensional model covering the region from New Jersey to the Nova Scotia shelf, to examine the climatological circulation and its seasonal transition over the GoM/GB. Chen and He (2009) employed the Regional Ocean Modeling System (ROMS) to produce a three-dimensional hindcast of the MAB and GoM during 2004-2008. A more detailed study focusing on the mean state of shelfbreak circulation and the total water transport across the 200 m isobath over the MAB was reported in their succeeding paper 5 (Chen and He, 2010). However, neither the abovementioned climatology or the four-year numerical simulations are sufficient for addressing the interannual variability of the shelfbreak front/jet system that might occur in response to local forcing and/or basinscale natural climate variability.
There is growing evidence that interannual variations in the Northeast U.S. continental shelf/slope region must be linked to processes on a much larger scale, since the entire area is located within a western boundary 'confluence zone', with the subpolar gyre and Labrador Current/Scotia Shelf waters moving southwestward, and the subtropical gyre and the Gulf Stream moving northeastward .
A revealing view of the variability in the region suggests that the Gulf Stream, the slope sea, as well as the GoM/GB and MAB shelf are all impacted by variations in the atmospheric circulation over the subpolar regions (Flagg, 2006), dominated by the North Atlantic Oscillation (NAO). One of the more striking periods in the recent record is the 1990s; Drinkwater et al. (2002), Pershing et al. (2001), and Greene and Pershing (2003) all have posited that the large drop in the winter NAO index in 1996, and the associated changes in atmospheric forcing over the Labrador Sea, were responsible for a cold/fresh Labrador Slope Water flux into the slope sea, up onto the Scotian Shelf and through the Northeast Channel into the Gulf of Maine in 1998. Rossby and Benway (2000) suggested that the behavior of the Gulf Stream south of New England was linked to the Labrador Slope Water that flowed into the slope sea around the Tail of the Grand Bank, and Rossby et al. (2005) illustrated an ~100 km southward shift of the Gulf Stream axis beginning in mid-1995, peaking in 1998 before recovering to a more northerly position in 2000. In addition, recent studies reveal that there is a significant correlation between 6 near-surface transport in the Gulf Stream and the NAO index (Rossby et al., 2010), as well as between Gulf Stream associated warm-core rings and the state of the NAO . The only study of the correlation between the local along-shelf transport off southern New England and the NAO was conducted by  using a regional circulation model that was focused on the period 2004-2009. This study found that the along-shelf transport near the shelfbreak is negatively correlated with the NAO index, with a lag of 13 months. However, their 6-year simulation resulted in a less than compelling statistical argument.
In this study, we aim to advance our understanding of the interannual variability of the MAB shelf/slope circulation and water properties by extending the numerical modeling approach employed by . Specifically, we extend the regional model domain in  to include the influence of the Gulf Stream as well as increasing the length of the simulation to a decade. With this, our objective is to further investigate the interannual variability of along-shelf transport and water properties of the MAB, and to better understand the underlying physical mechanisms controlling such interannual variability.
The rest of this chapter is organized as follows. The numerical model configuration, a realistic simulation from 2004-2013 and a suite of process-oriented numerical experiments are described in Section 2, followed by model verification in Section 3. The mean state of the shelf/slope system during the decade under investigation is discussed in Section 4. Analyses of the interannual variability of the along-shelf transport and its origins are presented in Section 5, and the underlying physical mechanisms are presented in Sections 6. The decadal variation of along-shelf transport during the 10-year simulation and plausible mechanisms are explored in Section 7. Finally, Section 8 summarizes the results and the important findings of this study.

Experiment REAL
Our numerical simulations use the Regional Ocean Modeling System (ROMS).
ROMS is a free-surface, hydrostatic, terrain-following, primitive equations ocean model widely used by the scientific communities for estuarine, coastal and basin-scale ocean applications. The algorithms that comprise ROMS computational nonlinear kernel are described in detail in . Our regional-scale ROMS implementation is bounded by Cape Hatteras to the south and the Scotia Shelf to the north, covering the GoM/GB and the entire MAB (black box in Figure  Free surface and depth-averaged velocities are specified using the method of Flather (1976) with external sub-tidal values taken from HYCOM/NCODA plus five tidal constituents (M 2 , N 2 , S 2 , O 1 , K 1 ) from the global ocean tides model TPXO7.2 (http://volkov.oce.orst.edu/tides/TPXO7.2.html). The tidal input provides needed tidal mixing, hypothesized as an important element of the regional circulation. In addition, a quadratic drag formulation is employed for bottom stress with the value of the quadratic bottom drag coefficient as 7.5×10 -3 , and the Mellor-Yamada Level 2.5 turbulence closure scheme is chosen for vertical mixing .
The local surface forcing is derived from the National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Prediction North America Regional Reanalysis (NCEP/NARR), which has spatial and temporal resolutions of 32 km and 3 hours, respectively. All of the atmospheric components (winds, air temperature, air pressure, relative humidity, rainfall rate, short and long wave radiations) are averaged into daily intervals, spanning from January 01, 2004 to December 31, 2013. Bulk formulae are used for the computation of the surface momentum, sensible and latent heat fluxes. To further constrain the spatial pattern of the net surface heat flux, a thermal relaxation term is implemented following He and Weisberg (2002): where ! is a vertical diffusivity coefficient, Q is the net heat flux, and ρ and ! are the seawater density and specific heat capacity, respectively. The relaxation coefficient c is set as 0.8 m day -1 , and the model simulated sea surface temperature T mod is subtracted from T obs , which is the daily blended cloud-free sea surface temperature obtained from

Experiment Hierarchy
In addition to the above-described REAL experiment, we have also performed five parallel sets of experiments with ROMS to examine the response of the oceanic circulation and along-shelf front/jet system to various external forces, including local surface forcing and remote forcing both from upstream and offshore open boundaries (

Model Validation
For the purpose of model validations we compare our most realistic results (experiment REAL) with three different observational datasets.

11
A direct comparison of mean depth-averaged shelf currents at 27 locations over the MAB between the model and the observations is presented in Figure 1-2. The observations are from Lentz (2008a)  Next, the model simulated along-shelf volume transport is compared at six crossshelf transects with those reported by Lentz (2008a) (Table 1-2). The volume transports are obtained by numerically integrating each cross-shelf transect, which is indicated by the thick light-grey lines in Figure 1-2. Overall, the along-shelf transport estimates decrease from Cape Cod to North Carolina, consistent with the idea that shelf water is continually entrained into the offshore shelfbreak frontal jet from north to south over the MAB, characterized as a so-called 'leaky pipe' by Lozier and Gawarkiewicz (2001). The relatively low along-shelf volume transport off Georges Bank is mainly due to the Gulf Stream warm-core rings that induce shelf-water entrainment, and the higher transport off southern Cape Cod is caused by the outflow from the Gulf of Maine through the Great South Channel. This occurs more frequently here than over the MAB ).
We next sampled the mid-depth (40-55 m) model temperature and salinity to obtain their seasonal cycle over the entire MAB plus the Georges Bank continental shelf/slope region, and compared that with the climatologies constructed by Linder and Gawarkiewicz (1998) and Linder et al. (2006). This comparison is presented for four Surface heating starts to warm shelf water during the spring and leads to the development of a shallow seasonal thermocline over the mid-depth. During summer, cross-shelf thermal gradients are found in two regions with cold water located on the shelf. One is located to the southeast of Georges Bank, resulting from the intensified anti-cyclonic circulation around the bank transporting relatively cold, fresh water from the western Gulf of Maine and across the Northeast Channel. The other region spreads from the southern New England shelf over the Delaware/ Maryland shelf, and is the residual cold winter water that remains under the shallow seasonal thermocline, the so-called 'cold pool', that persists from May through October (Houghton et al., 1982;Lentz, 2008b). The mid-depth temperature of the cold pool area is higher from model simulations than it 13 from the historical climatology produced by Linder et al. (2006), in which the majority of stations were collected during a longer period of 1990-2002.
In contrast to the temperature, seasonal variations in both salinity (Manning, 1991;Mountain, 2003) and cross-shelf salinity gradient (Shearman and Lentz, 2003) tend to be small, except over the inner shelf (depth<60m) where there can be an enhanced crossshelf salinity gradient due to spring runoff (Ullman and Codiga, 2004). The plan view maps (Figure 1-3b) clearly show the proximity of the 34.5 isohaline, which defines the core of the shelfbreak front at mid-depth to the bathymetry offshore of the 100 m isobath throughout the MAB. There also exists a slight freshening over Georges Bank to New Jersey during the summer season. Mountain (2003) observed that the volume and salinity of MAB shelf water exhibited larger interannual variability than its seasonal cycle, depending on the seasonal input of fresh water advected from the St. Lawrence River.
Therefore in the following section salinity will be used to track the interannual variability of the shelf/slope front. Labrador Current transport. This assumption will be examined with our model experiment hierarchy in the following section.
In summary, the abovementioned model-observation comparisons suggest that our model performs reasonably well and is reliable for understanding the mean state, seasonal and interannual variability over the MAB shelf and slope regions.

Mean State
Even though the focus of this study is the interannual variability of the MAB shelf/slope front and jet system, it is still necessary to examine its mean state and climatological seasonal variations to gain an understanding of the fundamental dynamics.
In this section we will present an analysis based on the model results from experiment REAL.

Annual mean
The principal circulation features of the modeled mean surface circulation are shown in Figure  surface. Unlike the temperature, which exhibits a strong seasonal thermocline, the shelfbreak salinity front is a persistent feature throughout the year, with a gradient of about 1 PSU over 10-40 km. In previous studies, more often than not, the 34.5 isohaline is used as a distinct separation in properties between the shelf and slope water and to indicate the shelfbreak front Linder and Gawarkiewicz, 1998;Linder et al., 2006;Chen and He, 2010). It is worth-noting that, over the outer shelf and shelfbreak, the contributions of the cross-shelf temperature and salinity gradient to the density gradients cancel each other ( Figure 1-6 b, c). It is the salinity front that creates a strong density gradient that is primarily responsible for the strong shelfbreak jet.
The momentum budget analysis provides further insights into the shelf/slope flow. Here we focus on the momentum budget in the cross-shelf direction in order to identify the fundamental dynamical balances dominating the along-shelf jet. Figure 1-7 illustrates the cross-shelf distributions of the Coriolis force, the horizontal pressuregradient force (PGF), the viscosity term (horizontal and vertical diffusion combined), and nonlinear advection term (horizontal and vertical advection combined), and these terms are all along-shelf averaged within the shaded area in Figure 1-5. As expected, the Coriolis force and pressure-gradient force are dominant terms and they nearly balance each other. The viscosity term is relatively strong on the shelf near the bottom boundary, while the nonlinear advection term is relatively strong over the shelfbreak due to the energetic currents. But both viscosity and nonlinear advection terms are one order of magnitude weaker than the leading geostrophic terms. This indicates that the along-shelf jet is in geostrophic balance to leading order, which is consistent with previous observational studies (Shearman and Lentz, 2003).

Seasonal means
The seasonal means of the along-shelf velocity are illustrated in Figure 1-8.
Henceforth, four typical months (February, May, August and November) are used to represent the four seasons. The shelfbreak jet accelerates in the fall and is strongest in winter with a maximum mean speed of over 0.35 m s -1 and a width of 30 km. This is also the time when the jet core shifts offshore within a thin surface-trapped layer (shallower than 60 m). In May, the jet core starts to move onshore and the poleward current is intensified as a subsurface feature seaward of the shelfbreak. The intensity of the shelfbreak jet is significantly reduced in August with mean speeds less than 0.2 m s -1 , and the reduced southwestward flow expands to a width of 50 to 60 km, consistent with the observation of Flagg et al. (2006). As discussed earlier, the along-shelf jet is nearly in thermal wind balance. The seasonal variability of the along-shelf jet can largely be attributed to the seasonal changes in the cross-shelf density gradient. Several sources of seasonal variation in the cross-shelf density structure, like the tidal mixing front over Georges Bank (Flagg, 1987), surface heat flux (Shearman and Lentz, 2003), and spring runoff near the MAB coast (e.g., Zhang et al. 2009), could be identified and have been studied in detail within different sub-regions over the MAB. Therefore, in the following, we will primarily focus on the interannual variability of the along-shelf jet.

Along-shelf Transport
Our 10-year-long numerical simulations provide a unique opportunity to investigate the interannual variability in both circulation and hydrography field. A straightforward way to identify interannual variability is through a time series of alongshelf transport. For this we select a cross-shelf section that represents the upper bound of the northern MAB, marked as T 1 in Figure  Two questions naturally arise. 1) What is the origin of this response of the circulation, i.e., is it the direct influence of local surface forcing or of remote forcing? 2) If it is the latter, then how does an upstream influence, where the southwestward Labrador Current from Scotia Shelf flow into the region, compete with any offshore influence, where the subtropical gyre and the Gulf Stream interact in this region? These two questions will be addressed in the following section.

Origins of Interannual Variability
We now focus on the comparisons of the along-shelf transport along the T 1 transect between the REAL experiment and the other five experiments described in Section 2. In Figure 1-9a, there is hardly a discernible difference of along-shelf transport after controlling the surface wind with climatology, and only subtle distinctions after replacing both surface wind and buoyancy forcing with their climatologies. We can therefore confidently conclude that the interannual variability along transect T 1 does not appear to be caused by local atmospheric momentum or buoyancy forcing but rather must be due to processes on a much larger scale.
Focusing now on the impact of remote forcing we compare experiments REAL and OBCs (Figure 1-9b). Unsurprisingly, the interannual variability of the along-shelf transport across T 1 (REAL) disappears in OBCs (which only retains the climatological fluxes; see Table 1-2). The seasonal cycle remains in OBCs with a regular range of 0.8 Sv between its winter maximum and summer minimum. This further supports our previous conclusion that it is the variability of the remote forcing that accounts for the interannual variability of the along-shelf front/jet system along this transect.
We next seek to determine whether this signal derives from upstream or offshore influence by comparing the time series of T 1 along-shelf transport among experiments REAL, UPSTREAM and OFFSHORE. In Figure 1-9c, the red line represents the results after we control the upstream forcing with its climatology. It shows a high correlation with REAL, especially with respect to the minimum values in 2004, 2005, and 2007.
After 2010, the transport of experiment UPSTREAM is generally higher than REAL. We conclude that the upstream influence from the Labrador Current is mainly contributing to the rise of the along-shelf transport.
The magenta line in Figure 1 where Gulf Stream eddies interact closely with the shelfbreak jet during this period. Next, we will try to understand the underlying mechanism and seek a physical explanation using both observations and our model results.

Influence of Remote Processes
In the previous section, based on the numerical experiments, we have made the preliminary conclusion that it's the upstream Labrador Current transport that mainly contributes to the rise of along-shelf transport in the MAB, especially with respect to the high value in 2009/2010 winter as compared with other years. Meanwhile, the drop in transport is due to the offshore influence of the changes in the position of the Gulf Stream.
In particular, the averaged along-shelf transport of 2004-2008 is 1 Sv lower than 2009-2013. In this section, we will better detail the upstream influence from the Labrador Current and the offshore effects from the energetic Gulf Stream.

The Labrador Current
In order to isolate the influence from local sources of coastal runoff and precipitation, the 10-year averaged winter temperature and salinity fields are obtained at 50 m depth from experiment REAL for the entire region (Figure 1-10a (Figure 1-11). The basic structure of the wintertime hydrography ( Figure 1-11 a, c) shows that temperature and salinity values generally increase with depth and distance offshore, with the largest horizontal gradients occurring on the inner shelf and at the shelf edge. This is consistent with the long-term observations of hydrographic properties on the Halifax section by Loder et al. (2003).
Over the upper continental slope, a wedge of relatively fresh and cold upper-layer shelf water overlie two types of slope waters, which are identified by Pershing et al. (2001) (Smethie et al., 2000). The dominant features of the velocity fields along the northeast boundary are surface-intensified southwestward flows on both the inner shelf (the Nova Scotia Current described by Drinkwater et al., 1979) and near the shelf edge over the upper slope, which is part of the downstream remnant of the shelf-edge Labrador Current (Loder et al., 1998). The subsurface northeastward flows are identified as the slope current that is strongly influenced by Gulf Stream meanders and anti-cyclonic warm-core rings (Joyce 1991).
The most striking feature in the 2009 winter that is different from the climatology is the strong southwestward velocity. Even though this could not be easily identified by the hydrography (especially when it comes to salinity due to its coarse representation in HYCOM) the velocity field ( Figure 1-11 e, f) does reveal the spreading of cLSW along the entire slope, replacing the slope current. We will have more to say about this figure in the next section.

The Gulf Stream
The close proximity of the Gulf Stream in southern New England results in a large number of meanders and anti-cyclonic warm core rings (WCRs) each year that, from time to time, impinge upon the continental slope in the MAB. These rings could generate significant temporal and spatial variability in the currents, i.e. reversing the flow at the shelfbreak (Beardsley et al., 1985), pulling streamers of shelf water into the interior (Joyce et al., 1991), or stimulating shear instabilities due to the enhanced horizontal velocity gradients of the shelfbreak jet (Ramp et al., 1983).
During our 10-year numerical simulation, there are three significant reversals of southwestward along-shelf transport on the shelf/slope: 2004 October, 2005 September and 2007 July. For each reversal, we plot the latitude/longitude structure of the surface speed and velocity in Figure 1-12 a-c. An anti-cyclonic ring circulation occurred during each period between 37.5 and 40.5 °N in the vicinity of the 1000 m isobath just south of Georges Bank, which has been well documented as a place with maximum ring activity , and impacted the circulation further to the north by interacting with the shelf/slope front. To support this, we also retrieve daily snapshots of satellite altimetry observed sea level anomalies (SLA) as a more reliable proxy for the presence and duration of warm core rings (WCRs). The gridded SLA fields with spatial resolution of 1/4° × 1/4° are obtained from AVISO based on the Jason-1 and Jason-2 missions. In accordance with the numerical simulations, the daily snapshots reveal notable WCRs with a diameter of more than 150 km in the same location ( Figure 1-12, d-f). Actually, the similarity of these three periods is that the WCRs features are present almost without change for longer than 10 days; a time-longitude plot (not shown) indicates their westward propagation speed is very slow at ~3 km day -1 .
The along-shelf velocity and isopycnals across the T 1 transect during the abovementioned three reversal periods are presented in Figure 1-13 a-c. As expected, the southwestward jet is fully replaced by northeastward currents over the entire water column at the shelfbreak. The result is consistent with previous studies, i.e. the currents in the northern MAB appear to strengthen southwestward when the Gulf Stream shifts southward in winter-spring but are weak or even reversed in summer-fall when the Gulf Stream shifts northward (Peña-Molino and Joyce, 2008). The dynamics of how these fluctuations could temporarily break down the jet were the focus of our analysis. We find that, to leading order, the geostrophic and hydrostatic along-shelf flow obeys the thermal-24 wind balance; the frontal density gradient is in balance with the vertical shear of alongshelf velocity. In wintertime the density front is more sloped than it is in summer and fall, when a strong seasonal pycnocline develops isolating much of the front from the surface ( Figure 1-13 a-c, black lines). Therefore the model shelfbreak jet is weaker in summer than in winter. The presence of offshore eddies from the shelfbreak to the slope affects the magnitude of the along-shelf velocity by completely eliminating the cross-shelf density gradient so that the spatial structure of the velocity field is primarily set by the slope eddy and not the shelfbreak frontal structure.
Observations suggest that the interaction of Gulf Stream rings with the shelfbreak jet may transport significant volumes of shelf water into the slope region (Joyce et al., 1991). Flagg et al. (2006) found that total along-shelf transport for the shelfbreak and upper slope is just less than 3 Sv, and  estimated that the annul shelf-wide WCRs could advect 0.75 Sv of shelf water, accounting for more than 25% of the total transport in the slope sea region. Moreover,  also found that the offshore transport of shelf water by WCRs in Georges Bank is approximately 0.23 Sv, with its maximum reaching as high as 1.9 Sv in certain years co-varying with maximum WCRs occurrence. Therefore, our model results together with the observational evidence suggest that the decrease of the along-shelf transport is due to Gulf Stream WCRs impinging onto the continental slope in the MAB.

Decadal Variability
In this section we focus on the decadal variability of the along-shelf transport in our model simulations. It should be noted that 'decadal variability' here refers to the transition of the averaged state from the first 5-year period to the second 5-year period 25 during the entire length of simulation. Besides the T 1 transect discussed earlier, we select two more cross-shelf sections in the model domain, noted as T 2 and T 3 , respectively, in Figure 1-1; T 2 is located in the southern MAB area, which is characterized as another distinct region along the U.S. east coast continental margin (Linder et al., 2006), and T 3 is close to the northern boundary of the regional model domain. Using the same analysis as the T 1 transect, we calculate the monthly averaged transports cross T 2 and T 3 from experiment REAL (black heavy lines in the three panels of Figure  One should exercise caution in any attempt to identify 'normal' or 'standard' NAO patterns of behavior, and the associated ocean response will necessarily be oversimplified and difficult to associate with the NAO (Visbeck et al., 2001), not to mention the wintertime NAO itself also exhibits significant decadal to multi-decadal variability (Hurrell, 1995). Therefore, we put our effort on identifying short-term NAO 'events' that could be related to ocean climate changes. For instance, it has been found that when the winter NAO shifted from persistent and strong positive to strong single-year negative in 1996 (Figure 1-15), the Gulf Stream front retreated southward, which allows the 27 penetration of the Labrador Current onto the Scotia Shelf and Slope (Han, 2007).
Afterwards, the Labrador Slope Water was observed to steadily advance along the shelfbreak during this transition, penetrating to the southwest as far as the MAB (Drinkwater et al., 1999;Pershing et al., 2001).

Summary
This study sets out to better understand the origin of the interannual-to-decadal variability of along-shelf transport and water properties of the MAB. ROMS is employed to simulate the front/jet system along the U.S. Northeast continental shelf/slope region for winter, which also featured the largest negative NAO index in the 190-year record. Such a return to climatology persisted for several years, which could lead to a change of coastal water environment, especially with respect to the significant regional responses of marine ecosystems, e.g. primary productivity and the biological export of carbon (Drinkwater et al., 2003). An extensive observational/modeling effort will be required for further understanding the long-term variability of the front/jet system in the MAB shelf/slope and its impacts on the coastal environment.   Table 1-2.
Black dashed lines are the two satellite tracks, along which the SSHA data are sampled.

Introduction
With its direct connection to the Southern New England continental shelf, the Rhode Island (RI) coastal area is referred to as a 'mixing-basin' (Beardsley et al., 1985) because of the diversity of water types and ecological species that were observed during the past several decades. The ecosystem is nourished by high concentrations of phytoplankton and has been identified as providing significant economic value through commercial fishing (Sherman et al., 1996a).  et al., 2002). With the exception of a few areas influenced by large river discharge, the significant seasonality and spatial distribution of phytoplankton biomass are maintained by nutrients supplied from the deep water determined by vertical mixing (Nixon et al., 1983), which itself is associated with the stratification and de-stratification of the water column.
There have been several studies of this physical mechanism regulating the biological processes. For example, Chen et al. (1988) formulated a two-mixed-layer model in Long Island Sound including the effects of wind forcing, surface cooling in the upper layer and the spring tide in the lower layer to show that the combination of these physical mechanisms supported an upward nutrient transport that led to the phytoplankton bloom that is typically observed in early fall. Xu et al. (2013) found that the upper mixed layer over the entire MAB shelf is dynamically dominated by wind and surface buoyant plumes, and they influence mixing which have both positive and negative impacts on the evolution of a phytoplankton bloom, i.e. an increase of mixing will increase nutrients availability but decrease light availability. Fields et al. (2015) measured surface chlorophyll-a in Rhode Island Sound and Block Island Sound and, when accounting for hydrographic observations, found that the significant regional heterogeneity in both the timing and magnitude of the seasonal bloom was due to strong tidal mixing variability.
However, several issues remain from these previous studies. For example, the spatially scattered and short-term in-situ observations might be insufficient for drawing any further, detailed conclusions. In addition, ocean color satellite remote sensing does provide both spatial and temporal continuity, but it has limitations in coastal waters due to extensive cloud cover especially during winter, and the presence of sediment and colored dissolved organic matter (CDOM) (Harding et al., 2004). Also, those numerical simulations that so far have been applied to these issues, while facilitating the study of temporal and spatial variability, treat the entire shelf as if it were a dynamically homogenous region, neglecting the fact that shelf processes are inherently nonlinear and exhibit variations over a broad range of spatial and temporal scales. Most importantly, analyses of previous model results of this region are usually statistical, with a lack of fundamental dynamical explanation. With all of this, the physical controls of much of the ecosystem dynamics in RI coastal waters are still not understood.
This study aims to understand the dominant features, and the underlying physical mechanisms, that help to shape both the temporal and spatial variation of phytoplankton in RI coastal waters. The rest of this paper is organized as follows. Section 2 presents the analyses of satellite observations. Section 3 describes the physical-biological model used in this study and the experiment design. Section 4 discusses the model results and Section 5 presents a summary of the key findings of this study.

MODIS observations
The seasonal and spatial variations of sea surface chlorophyll-a in RI costal at each pixel. Considering the bio-optical complexity and the high heterogeneity in the near shore waters, we exclude waters shallower than 10 m. We also exclude data for water deeper than 1000 m, as our focus is on the continental shelf.
The distribution of surface chlorophyll-a concentrations throughout the study area during the nine-year average is presented in Figure 2-1, which shows a general pattern of onshore-offshore decrease from the coast to the shelf edge. Regional differences are evident, particularly on Nantucket Shoals, inside of the Long Island Sound and in the immediate near-shore of the New Jersey shelf, which are all featured by high concentrations. However, the limitations of ocean color algorithms in coastal waters, due to the extensive presence of suspended sediment and colored dissolved organic matter (CDOM), can influence the accuracy of observed chlorophyll-a with errors as large as 100% (Harding et al., 2004). Therefore, in the following we will focus on the area indicated by the black frame in Figure 2-1, mainly covering the entire RI coastal waters and southern New England shelf.
An Empirical Orthogonal Function (EOF) approach is used to identify the dominant temporal signal in the nine-year chlorophyll-a dataset. This method of data reduction is well suited for analyzing ocean color images, which possess long time series and significant spatial variability (e.g. Yoder et al., 2001;Yoder et al., 2002;Xu et al., 2011). While the statistical EOF modes do not necessarily correspond to direct physical forcing mechanisms, partitioning the spatial and temporal variance of a dataset into modes are beneficial to reveal spatial functions having time-varying amplitudes that can be interpreted in relation to physical processes.
Here we apply the computationally efficient, singular value decomposition (SVD) method to calculate eigenvectors, eigenvalues and time-varying amplitudes. Considering N monthly composites, the spatial and temporal variance of a dataset, ! , can be partitioned into modes, i, that result in spatial functions, ϕ ! ( ), having time-varying amplitudes, ! (also known as principal components) such that This means that the time variation of chlorophyll-a for each pixel is the summation of the spatial functions, ϕ ! , whose amplitudes, ! , indicate how the spatial modes vary with time. Prior to performing an EOF analysis, we fill any gaps in the data by running a three-by-three pixel median filter to replace missing values over small gaps. Moreover, the temporal mean, i.e. the black frame in Figure 2-1, is subtracted from each pixel so as to emphasize the anomalies from the general mean pattern.
The first mode explains 44.1% of the anomalous variability of the chlorophyll-a datasets (Figure 2-2 Yoder et al., 2001) with specific, triggering physical factors varying by region (e.g. Xu et al., 2011;Siedlecki et al., 2011). In our focused region, vertical mixing plays the dominant role in bringing the nutrient-rich bottom water to the surface to support phytoplankton growth (Fields et al., 2015), whereas the specific mixing mechanism remains under debate. This will be detailed later. Based on the abovementioned analyses, we raise two questions: i) Does the seasonal variation of vertical mixing associated with surface forcing control the fall-winter bloom in RI costal waters?
ii) Can the decrease of chlorophyll-a with distance offshore be explained by the change in the physical environment that is affected by the depth of the water column?
To answer these two questions, we use a hierarchal numerical modeling approach with both one-dimensional and three-dimensional configurations.

Model description
The numerical model used in this study is the Regional Ocean Modeling System (ROMS) version 3.7. ROMS is a split-explicit and free-surface model that assumes a Boussinesq and hydrostatic fluid when solving the primitive equations . (A more detailed description of this model can be found in Chapter 1 of this thesis). There are also several ecological models included in ROMS for biogeochemical and bio-optical applications.
We choose a relatively simple, four-compartment nutrient-phytoplanktonzooplankton-detritus (hereafter referred to as NPZD) model to represent lower trophic level dynamics. The primary reason for choosing this model type is that it captures the biological food web at its most fundamental level and is relatively straightforward for analyzing physical vs. non-physical processes as these affect the temporal and spatial evolution of the ecology. Despite its relative simplicity, the NPZD model that is embedded in the ROMS circulation model can offer important insights on the issues we aim to address in this study. The governing equations for the four state variables are as follows (the state variables are all in the nitrogen-based unit of mmol N m -3 and the governing equations mostly follow Powell et al., 2006): !" (4) (Please refer to  (1), which restores the near-bottom nutrient fields towards the observed value (N o ) on a time scale (τ). This term is added for better representing sediment re-suspension processes, which are not well represented in this particular NPZD model. In practice, this term is only considered in the deep layers z > D, where D is a threshold depth that requires specification. In our study, D is set to 25 m and the time scale τ is set to 1 day.
The photosynthetic growth and uptake of nitrogen by phytoplankton (U), grazing on phytoplankton by zooplankton (G), and irradiance (I) are formulated as follows: Here T is temperature and I 0 is surface irradiance. According to equation (5), the phytoplankton growth rate U depends on nutrient concentrations, the photosynthetically active radiation I and temperature, and is calculated as a multiplication of three functions: f(N) adopts the Michaelis-Menten curve to describe the change in uptake rate as a function of nutrient; f(I) represents the photosynthesis-irradiance (P-I) relationship; and f(T) reflects the impacts of temperature on the growth rate (Eppley, 1972).
The modifications of equations (1)-(7) from the original NPZD model of Powell et al. (2006) that we adopt (because they are better suited for the continental shelf to shelfbreak region) have been described by Zhang et al. (2013). In brief, there are three important modifications. First, phytoplankton growth and zooplankton grazing rates are assumed to be temperature dependent (through the Q 10 terms; Eppley, 1972). Since the annual temperature in coastal water varies within a range of 20°C, this dependency is necessary to account for seasonal variations in maximal growth rates. Second, the linear zooplankton mortality is replaced with a quadratic functional dependence, which is a more effective way of parameterizing the predation of zooplankton by higher trophic levels (Steele and Henderson, 1981;Fasham, 1995). And third, the nudging term ℎ ! ! !! ! is used to restore the near-bottom nutrient fields towards the observed climatology. In our study we further adjust this near-bottom nutrient restoration value and initial slope of the P-I curve due to local water type in order to better represent the sediment re-suspension processes in RI coastal waters.
The turbulence closure scheme adopted in this study is the Mellor-Yamada Level 2.5 scheme . This scheme is widely used in coastal ocean modeling and has reasonable skill in depicting coastal mixing processes, with the advantage of explicitly solving the bulk characteristics of the turbulent motions (Allen et al. 1995). The turbulent diffusivity ! is written as in which is the turbulent length scale that physically reflects the size of turbulent eddies, is the turbulent velocity scale, ! ! ! is the turbulent kinetic energy, is a nondimensional stability coefficient, and !"#$ is the background turbulent diffusivity that is set to a constant value 1×10 !! m ! s !! . The turbulent kinetic energy (TKE) and can be obtained by solving two prognostics equations (see Allen et al. (1995) for the detailed formulations). inputs of dissolved and particulate biological constituents are derived from the total nitrogen in the nitrate pool based on Howarth et al., (1996), multiplied by the freshwater transport to give discharge rates. The 3-D ROMS-NPZD model is also run for two years to achieve a quasi-periodic state.

Biological seasonal variability a) Surface chlorophyll
The seasonal variations of surface chlorophyll from the 1-D experiments are presented here in order to show that the 1-D model is capable of reproducing the key features of the satellite observations as identified in Section 2. We assume the chlorophyll content per phytoplankton cell is constant (C:Chl = 60 mgC (mg Chl) -1 ) by multiplying by the carbon to nitrogen ratio (C:N= 6.6). This assumption is commonly used in ecosystem models to reduce the number of unconstrained parameters. We do not account for the fact that the relationship between chlorophyll and phytoplankton biomass is nonlinear due to the photosynthetic apparatus of the cell as it acclimates to changes in light and nutrient conditions (Falkowski, 1980). We therefore rate this assumption as common and necessary.
Time series of the surface chlorophyll concentration in the five experiments are shown in Figure 2-6. In all five experiments, the phytoplankton bloom begins in mid-October and then continues into the winter months, which is consistent with the MODIS observations. The moderate broad peak in Nov-Dec attenuates slightly during Dec-Feb owing to solar radiation being lowest during this time of year. This is followed by a more discernable increase in late-March when both sufficient light and nutrients are present.
After that peak the high chlorophyll concentrations decrease rapidly; minimum surface chlorophyll concentrations occur during the summer months. Moreover, Figure 2-6 suggests that the surface chlorophyll concentrations decrease as the water depth increases, which is also in agreement with the satellite observations. These experiments give us confidence in using the numerical simulations to understand in more detail the processes responsible for this seasonal signal in the water column. We next focus on the depth dependence evident in Figure  Simulated zooplankton (Z) concentrations also show strong seasonal variability, featuring two periods of high concentrations: one at subsurface in late summer and the other is vertically uniform in the mixed layer during the fall-winter. Given that our lower trophic level model represents all zooplankton losses mathematically, rather than biologically, by justified closure functions (Steele and Henderson, 1992), it is beyond the scope of this study to investigate the detailed biological dynamics regulating zooplankton seasonality. We do, however, present a detailed parameter sensitivity study (Appendix A) to address some of these issues. Instead, we evaluate the importance of zooplankton grazing on phytoplankton. and dissolved organic nitrogen (DON) that is not explicitly included in the model (Spitz et al, 2003). The importance of detritus remineralization will also be estimated in our sensitivity study (Appendix A).
In summary, the 1-D simulations reproduced two of the key features identified in the MODIS observations: i) the annual cycle of phytoplankton in all experiments is characterized by a distinct fall-winter bloom and, ii) the water column depth is a key parameter in affecting the magnitude of the phytoplankton biomass. In the following, we will further analyze the model results to answer the two questions raised in Section 2.2.

Mechanisms responsible for the fall-winter phytoplankton bloom
Since the seasonal variations of the phytoplankton in all 1-D experiments (H40-H80) are qualitatively similar, we only show the analyses of the results from experiment H40 as an example.
We start by analyzing the processes contributing to the growth of phytoplankton.
As identified in equation (2) (Figure 2-9(b)). This means that the growth of phytoplankton exceed its loss terms due to either mortality or zooplankton grazing, and vice versa. The DIF term demonstrates an opposite distribution to the BIO term, which suggests that the physics of turbulent diffusion acts to reduce the gradient of concentrations in the water column (Figure2-9(c)).
Next we examine the seasonal variations of phytoplankton growth rate, U, and the important components affecting U, as shown in equation (5)  The mechanism for the fall-winter phytoplankton bloom in the RI coastal waters can thus be summarized as follows. Starting from late September, the surface wind turns 76 from a weaker southwestward wind to a stronger northwestward wind and, concurrently, the ocean turns from gaining heat to losing heat. These combine to intensify the turbulent mixing in the water column, which breaks down the stratification and brings nutrients from the bottom up into the euphotic zone. As a result, a phytoplankton bloom is initiated under this favorable environment.

Impacts of water depth
This section aims to investigate the second question, i.e., whether the decrease of chlorophyll offshore is due to the change of water depth. Results from experiments H40 and H80 are presented, which represent shallow and deep water conditions, respectively.
According to the discussion in the previous section, both turbulent mixing and phytoplankton biomass are enhanced during fall-winter months. With that, the results shown here will be all time-averaged during fall-winter months (November to March).
We start with analyzing the impacts of the water depth on the physical environment, particularly the turbulent mixing process. indicating that the spatial scale of turbulent eddies is the main physical factor causing the variation of ! with water depth. In the shallow water environment as described in our study (water depth is generally less than 100 m), the spatial scale of the turbulence is strongly affected by the presence of the ocean bottom. If the water depth is larger, the turbulence can achieve a greater magnitude. This is essentially the reason that the turbulent length scale l, which physically represents the vertical extent of the turbulent eddies, increases with water depth. The main source of this TKE in the fall-winter months, when the stratification is nearly neutral, is the vertical current shear. As shown in Figure 2-14, the differences between the currents and the shear in H40 and those in H80 are small, which explains the small difference of TKE between the two cases.
With the above diagnoses of the physical environment we are now in position to discuss the impact of water depth on phytoplankton biomass.

Results from the three-dimensional experiment
Our focus here is to test that the mechanisms controlling the seasonal and spatial variations of the phytoplankton bloom based on the 1-D experiments are robust and also exist in a more realistic 3-D simulation of RI coastal waters.
We first compare the model simulated surface chlorophyll fields with the MODIS monthly climatology to validate the 3-D simulation (Figure 2-16). The 4-km resolution MODIS dataset is mapped onto the northern Middle Atlantic Bight. Four typical months (February, May, August and November) are selected to represent winter, spring, summer and fall, respectively. Before we go any further, one thing needs to be clarified: the atmospheric correction technique for the MODIS data used in this study potentially produces considerable errors in estuaries and some optically complex coastal environments (Werdell et. al., 2007). For the U.S northeast coast this is a common issue for Chesapeake Bay, Gulf of Maine, New York-New Jersey Bight and Long Island Sound (NOAA Coast Watch East Coast Node), where the latter two areas are included in our model domain. Therefore, even though all of the available MODIS chlorophyll-a concentrations are presented, these two areas as well as those with water depth shallower than 10 m should not be considered in this inter-comparison. In winter, the simulated phytoplankton bloom gradually spreads over the entire coastal region, with a surface chlorophyll concentration of ~ 3 mg m −3 , slightly decreasing in the offshore direction. This is consistent with previous studies (e.g., Ryan et al., 1999a;Yoder et al., 2001) showing the occurrence of a shelf-wide chlorophyll enhancement during the fall-winter season. As time progresses, the seasonal stratification starts to develop in spring, leading to a depletion of nutrients so that the surface biomass consequently diminishes in the upper water column. There is a biological front encompassing the Block Island Sound in the model results that is less obvious in the relatively coarse resolution (4 km) satellite images. This feature has been recognized by Stegmann and Ullman (2004) as a result of strong spring run-off supplying nutrients to phytoplankton but constrained by tidal mixing fronts. In summer, the surface chlorophyll disappears over the entire study domain except for the Block Island Sound and Nantucket Shoals regions, which both feature strong tidal currents. Actually, the higher chlorophyll concentrations are found on Nantucket Shoals in all seasons due to nutrient supply induced by strong tidal mixing (He and Wilkin, 2006). The breakdown of stratification in the fall allows deep-ocean nutrients to reappear in the upper water column, initiating a fall bloom that varies from the coast to outer shelf. In summary, the above comparisons of seasonal maps show that the model is generally able to reproduce the seasonal evolution and major spatial characteristics of the surface chlorophyll fields in RI coastal region.
The monthly mean surface chlorophyll derived from the 3-D experiment is further spatially averaged in RI coastal waters (black rectangle in Figure 2-5). The time series thus obtained, with its standard deviation, are shown in Figure 2-17(a). The temporal evolution shows a relatively pronounced peak in March and a smaller peak in November.
The timing of the phytoplankton bloom in the 3-D simulation agrees well with that of the 80 1-D simulations (Figure 2-6), indicating that the dominant mechanisms responsible for this distribution does not change. Admittedly, the surface chlorophyll concentration in the 3-D experiment is higher than that in the 1-D experiments from April to July. This discrepancy is likely due to the contribution of horizontal advection in the 3-D experiment. According to , there is a branch of flows that occur around the periphery of Rhode Island Sound owing to tidal mixing and local stratification during spring to summer, which inevitably carries phytoplankton from the higher chlorophyll concentrations of Nantucket Shoals.

Summary
To obtain a fundamental understanding of the mechanisms controlling the seasonal variation and spatial distributions of the phytoplankton biomass in Rhode Island (RI) coastal waters, we analyzed satellite chlorophyll-a observations and also performed one-and three-dimensional numerical simulations. We first applied an EOF analysis to a nine-year monthly chlorophyll-a dataset from MODIS. The first EOF mode, which accounts for 44.1% of the total variability, shows that the spatial variation of chlorophylla is in phase from the RI coast to the outer shelf, with the temporal variability dominated by the strong seasonal cycle as characterized by a broad peak during the fall-winter months. The spatial distribution of chlorophyll-a indicates that the phytoplankton biomass decreases with distance offshore as the water depth increases.
A set of idealized, 1-D numerical experiments were conducted using a physicalbiological model (ROMS-NPZD) that was designed to understand the mechanisms controlling the key features of the temporal and spatial variations of phytoplankton biomass. The key findings are as follows. 1) Enhanced vertical turbulent mixing initiates 82 the fall-winter bloom by bringing nutrients from depth into the euphotic zone. The enhanced vertical turbulent mixing is due to the combined effects of increased surface momentum (wind) forcing and surface cooling.
2) The extensive mixing also has a counteractive effect on phytoplankton biomass in the fall-winter months as phytoplankton are carried below the euphotic layer. In deeper waters, turbulent eddies are less affected by the presence of the ocean bottom and thus cause stronger mixing; the stronger turbulent transport of phytoplankton to greater water depths causes a reduction of the surface phytoplankton biomass. We also performed a 3-D NPZD-ROMS simulation to validate the key conclusions drawn from 1-D simulation. It was found that results from the 3-D experiment were qualitatively in agreement with those from the 1-D experiments.
This study indicates that vertical mixing plays a central role in affecting the dominant features of the temporal variations and spatial distributions of the phytoplankton in RI coastal water. However, it is necessary to point out that other physical and biological processes may also be important in affecting the variability of the phytoplankton due to the complexity of the coastal environment. Such processes include spatially-variant, benthic-pelagic coupling processes, the potential impacts from neighboring water bodies (e.g. Long Island Sound and Narragansett Bay), and the potentially considerable influence of a changing and varying climate. Future studies using more sophisticated physical-biological models are recommended to understand the effects of these complex factors.   The parameter used in the Ivlev (1955) formulation (Λ) describes a saturation of the ingestion rate with high prey concentration (Holling, 1959), and a smaller value of Λ indicates a slower approach to saturation. Our sensitivity experiments show that decreasing Λ results in more fluctuations as compared with the control case.
The relative insensitivity of the model results to the variations of detritus remineralization (δ) and sinking rate (w d ) could be attributed to the nitrate nudging that we imposed in the lower water column. The purpose of adding a detritus pool to the simplest three-component NPZ model takes into account the fact that remineralization is not instantaneous; in the control simulation w d = 8 m day -1 and δ= 0.1 day -1 yielding a remineralization length scale of 80 m. Decreasing either w d or δ corresponds to a smaller remineralization length scale and removal of less detritus from the surface layer, however, a physical environment of strong mixing in coastal waters in relative shallow water depth diminishes this effect which requires a supplemental, near bottom nitrate source. This further justifies our imposing a nitrate nudging term.
So far, we have found the dynamics of the model are relatively sensitive to the parameters α, σ d , R m and ξ d among the ten biological parameters. We also present results of surface chlorophyll seasonality after varying each of those parameters (Figure 2-A2).
Consistent with the above discussions, changing these four parameters (α, σ d , R m and ξ d ) produces rather marked variations in the seasonal cycle of surface chlorophyll. The results are detailed below.
Increasing the initial slope of the photosynthesis versus irradiance (P-I) curve (α) results in increasing the efficiency of light utilization at a time when production is controlled by light-limitation. As a consequence, phytoplankton concentrations also increase in fall and winter. In the nutrient-limited conditions of the spring and summer, increasing α deepens the euphotic zone, which does not result in any surface variation.
Nevertheless chlorophyll would accumulate in the subsurface, thereby enhancing the vertically integrated annual productivity.
Varying phytoplankton mortality rate (σ d ) alters chlorophyll concentration in all seasons, while the variations, in terms of peak abundance respond to decreasing σ d by 50%, e.g. the amplitude in March almost doubles compared with the control experiment.
Due to the nonlinear predator-prey relationship in the biological process function, the weakened mortality contributes to an increase of phytoplankton biomass.
Increasing the zooplankton-grazing coefficient (R m ) by 50% leads to an asymmetric variation compared with decreasing it by 50%. Interestingly, this only happens during the fall-winter bloom, while the March peak is not altered. A similar asymmetry, but in the opposite sense, occurs when changing the coefficient of quadratic zooplankton mortality ξ d . The cause is an accumulation of zooplankton during the fallwinter period in the case of increasing R m /decreasing ξ d (not shown here). This biological means that the phytoplankton bloom is consequently influenced by the abundance of a predator. Admittedly, in a lower trophic level model, zooplankton population has been the subject of some controversy especially when it comes to the zooplankton mortality function which behaves as a so-called closure term that maintains the stability of the model (Williams, 2006). The histogram represents maximum normalized RMSD for each parameter with respect to the control simulation (experiment H40 in the main text; see Table 2-1 for parameter names, units and control values). For a given parameter, the blue/red bars indicate the maximum normalized RMSD after decreasing/increasing the control value by 50%, respectively.