Numerical modeling the development and transport of lobster larvae (Homarus americanus) in the Coastal Gulf of Maine

Danya Xu, Huijie Xue, Steve Cousins

School of Marine Sciences, University of Maine, Orono, ME 04469-5741, USA

1.Introduction

Pelagic marine organisms may be transported considerable distances away from their original spawning or hatching locations by the ocean currents. In the Gulf of Maine, zooplankton and larvae may experience a long journey before they settle down due to strong surface currents. Incze and Naimie (2000) used a coupled physical biological, individual-based model (IBM) to calculate the trajectories of larval and postlarval lobsters in the Gulf of Maine. Their model results show that the local population is supplied by upstream sources.

Lagrangian stochastic modeling of the advection and dispersion of clusters of particles has been a common technique both in atmospheric boundary layer study and in oceanography. Few studies (e.g., Visser,1997, Brickman et al,2002, Proehl et al., 2004) have been done to simulate the distribution of planktonic cells and larvae development. Most of these studies focus on dispersion in the vertical instead of horizontal direction in the ocean. In this study, a robust Lagrangian particle-tracking model is embedded within a 3-D coastal ocean model to study the transport and development of pelagic lobster larvae in the coastal region of the Gulf of Maine. The ocean model calculates the circulation in the Gulf of Maine and its variability in response to wind, surface heat flux, river discharge, and tides. Particles can be tracked in the 3-D, time-dependent Eulerian flow field to examine their Lagrangian trajectories. The particle trajectory model has been extended to include the random walk mechanism that simulates transport processes by sub-grid scale turbulence. Multiple tracers can be released at any given position, specific time and be tracked in different trajectories. After some time, the tracers of the same group may end at totally different places due to random walk associated with turbulence diffusion. This process is very hard to be conducted in drifter experiment in reality but could be simulated in the model.

The model is used to simulate the life history of lobster larvae released at the potential spawning sites near the coast of the Gulf of Maine. In the model, larvae are restricted at the depth of 5m and develop to the postlarvae stage depending on the ambient temperature. Model results showed that larvae hatched at different times around the Gulf result in a great deal of spatial and temporal differences in life history since both the flow field and the surface temperature change seasonally and spatially.

2. Method

2.1 Ocean circulation model

First of all, we have been successfully simulating the seasonal circulation of the Gulf of Maine using the Princeton Ocean Model (POM). Our study region covered the entire Gulf of Maine area. The model has 180 x 120 horizontal grid points and 22 vertical levels to map the Gulf of Maine, Georges Bank, Scotian Shelf and the adjacent slope region with realistic topography to 3000 meter isobath. The model resolution varies from 3-5 km. At the surface, The gulf of Maine nowcast/forecast system is driven at the surface with the heat, moisture, and momentum fluxes from the National Center for Environmental Prediction (NECP) ’s Eta mesoscale atmospheric forecast model with a spatial resolution of 32 km and a temporal resolution of 3h. Boundary forcing includes daily river outflows from St. John, Penobscot, Kennebec, Androscoggin, Saco, and Merrimack, tidal (M2,S2,N2,K1,O1,P1) and subtidal forcing from the open ocean, which is interpolated from the daily nowcast of the NCEP regional Ocean Forecast System (ROFS). This version also includes SST assimilation. The model results are on the web as a part of the Gulf of Maine Ocean Observing System (GoMOOS) effort.

Detailed discussions of the Gulf of Maine circulation model can be found in Xue et al, 2005: The GoMOOS Nowcast/forecast System (Continental Shelf Research, 25(2005), 2122-2146).

2.2 Particle-tracking algorithm

The tracer model is based on Jarle Berntsen (1994). The original model only had the advection term, and particles could move freely in all 6 directions. A random walk term has been added to this tracer algorithm. As we do not know details of the biological behavior and vertical migration of lobster larvae, in our model, larvae move at a fixed depth of 5m.

Random walk formulations are based on the same assumptions as the advection-dispersion equation in which the overall transport of particles during a time interval Dt results from an advection component (model resolved flows) and a dispersive component that accounts for the unresolved flow processes. The advection component is calculated for each particle by interpolating the 3D current velocity, V(t), to the particle¡¯s position and transporting it to a new position at the next time step. Furthermore, particles tend to disperse with time in turbulent flows due to small-scale fluctuations in the field. Since the gridded mean current velocity cannot resolve these smaller scale turbulence, a numerical technique must be employed to simulate particle dispersion. In a Lagrangian framework, this is idealized by superimposing a random walk for each particle, equivalent to an approximate solution to the diffusion term in an Eulerian frame. The equation that describes the particle position can thus be written as

where X_i (t) is the position vector of the i^th particle at time t, V(t) is the local current velocity, Z(t) is a vector representing turbulent dispersion (random walk term), which contains three component Gaussian random numbers with zero mean and a standard deviation related to the rate of diffusion. It could be explained as: the position of a particular particle at next time step is calculated based on the position of the current time step plus the advection distance by the local currents and the diffusion effect.

In order to keep all of the terms’ units in the above formula uniform, we do the dimensional analysis. The dimension of the random walk term is kinematic viscosity (m²s^-1) divided by spatial interval of our model grid.

In the model, the random walk term is calculated from kinematic viscosity (m²s^-1) divided by the spatial interval of our model grid instead of the length scale of eddy diffusion because this term represents an averaged effect of sub-grid scale processes. Another widely used parameterization of the random walk term is (A_m^.Dt)^1/2. More sophisticated methods of including the gradient of the kinematic viscosity (Visser,1997) have also been tested and compared with observed drifter trajectories, which will soon be incorporated in this study in the near future. The kinematic viscosity in the horizontal is calculated by using the Smagorinski (1963) mixing scheme. Using this algorithm, a series of random walk numerical simulation tests have been finished. The model tracer trajectories are consistent with drifter observations.

2.3 Lobster larvae development formula

The development of Homarus americanus larvae can be divided into 5 stages. Spawning takes place offshore and planktonic stages migrate inshore towards the end of larval development (Incze and Naimie, 2000). Larvae are considered to be neutrally buoyant. The biological component of our model consists of temperature-dependent development rates modified from the polynomial equations of MacKenzie (1988) for different larval stages. The lobster larvae duration time is given in table 1. When the lobster larvae become postlarvae, they are ready to settle.

Table 1. Lobster larvae stages development eq. (MacKenzie,1988)

Stage I	Dev I=(851(T-0.84)^-1.91)/2.5
Stage II	Dev II=(200(T-4.88)^-1.47)/2.5
Stage III	Dev III=(252(T-5.3)^-1.54)/2.5
Stage IV	Dev IV=(0.358833T²-14.316T+156.895)/5.

where T is the temperature in ^oC , Numerical lobster larvae develop depending on the local temperature.

In the process of the transportation of the lobster larvae, when larvae hit land, we think the larvae are dead and just remove from the ocean.

3. Results

The lobster eggs are released in the regions along the coast where water depth less than 100m, include part of South of Scotian shelf, German Bank area and Browns Banks. There are 10 larvae released in each model grid (a total of 2,174 x10 larvae) in the entire spawing area. All larvae begin with a same initial stage equal to 1. Larvae are released every 10 days from June 1 to September 21 and are carried through time in each case for 2 months. We have 12 cases. The initial larvae are released at 15m (near the upper thermocline) and transported at this fixed depth till stage IV. After developing to stage IV, the larvae rise up to 1m beneath the surface.

From the circulation and temperature distribution, it is easy to find that Maine Coastal Currents (MCC) has different pattern and this annual variability of the circulation of GOM is thought due to many different factors such as atmospheric forcing, slop/shelf water intrusion. The annual variability of MCC would affect the larval development and transportation. For example: In 2003, maybe because the former colder winter, the Scotia Shelf water intruded into GOM is colder than normal year. The MCC is very strong, it extent to west coast of Maine and New Hampshire. But in 2002, the main branch of MCC turned back into inner Gulf at southwest of Penobscot Bay, only a weak branch of MCC goes to west. In 2004, the situation is in the middle of these two different patterns. We run 2002,2003,2003 total 3 years to examine the variation of the lobster larval development and transportation.

Till now we already finished experiments of 2002,2003,2004. The lobster larvae development and distribution show annual variability due to different circulation pattern.

1) Plots of lobster larval trajectories

Model results of lobster larval development (2002)

Model results of lobster larval development (2003)

Model results of lobster larval development (2004)

2) Time series of larvae number variability (chart 1-7 represent zone A-G)

Time series of number of larvae in different stages for Zone A-G are shown in this table.

2002

2003

2004

3) Stage 4.5

When larvae reach stage IV, they are float up to surface layer (1m). We count the number of stage4.5 larvae in different LMZ.

2002	stage 4.5
2003	stage 4.5
2004	stage 4.5

4) Connection Matrix

The entire coastal region of the Gulf of Maine is divided into 16 different zones (including Browns Bank, German Bank, West Nova Scotia Shelf, Bay of Fundy, Grand Manan Island, 7 Maine lobster manage zone A-G, New Hampshire, Massachusetts Bay, outer Cape Cod)

2002

2003

2003

5) Average duration time

2002	06/01- 09/21
2003	06/01- 09/11
2003	06/01– 09/21

4. Discussion

Development of lobster larvae depends on the initial release position and ambient temperature. Model results show that larvae hatched at different times around the Gulf result in a great deal of spatial and temporal differences in life history since both the flow field and the surface temperature change seasonally and spatially.

In future work, vertical immigration, grazing, prey and mortality will be considered in the lobster larval transport model.

Acknowledgements

We thank Dr. Lewis S. Incze for lobster larvae development formula and helpful suggestions. This research was funded by NOAA.

References

Berntsen, J., Skagen, D.W. and Svendsen, E., 1994, Modeling the drift of particles in the North Sea with reference to sandeel larvae, Fisheries Oceanography, 3, 81-91.

Brickman D. and Smith P.C., 2002, Lagrangian Stochastic model in coastal oceanography, Journal of Atmospheric And Ocean Technology, 19, 83-99.

Incze L.S. and C. Naimie, 2000, Modelling the transport of lobster (homarus americanus) larvae and postlarvae in the Gulf of Maine, Fisheries Oceanography, 9, 99-113.

Proehl, J.A., D.R.Lynch, D.J.McGillicuddy Jr., 2004, Modeling turbulent dispersion on the North flank of Georges Bank using Lagrangian Particle Methods, Continental Shelf Research.

Visser A. W., 1997, Using random walk models to simulate the vertical distribution of particles in a turbulent water column. Mar. Ecol. Prog. Ser., 158: 275-281.

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