Modeling Nutrient and Plankton Processes in the California Coastal Transition Zone : 3 . Lagrangian Drifters

Two types of numerica,1 Lagrangian drifter experiments were conducted, using a, set of increa, singly complex and sophisticated models, to investigate the processes associa, ted with the plankton distributions in the California coastal transition zone (CTZ). The first experiment used a one-dimensional (l-D; vertical) time-dependent physical-bio-optical model, which contained a nine-component food web. Vertical velocities, along the track of simulated Lagrangian drifters, derived from a three-dimensional (3-D), primitive equation circulation model developed to simulate the flow observed within the CTZ, were used to parameterize the upwelling a, nd downwelling processes. The second experiment used 880 simulated Lagrangian drifters from a 3-D primitive equation circulation model which was coupled to the same food web a, nd bio-optical model used in the first experiment. Para, meterization of the biologica,1 processes in both experiments were based upon data, obtained during the CTZ field experiments. Comparison of simulations with da,ta, provided insight into the role of the biological and physical processes in determining the development of the subsurface chlorophyll maximum and other rela, ted features. In both studies, the vertical velocities experienced by a simulated La, gra, ngian drifter as it wa, s advected offshore while entrained within a filament played a mador role in determining the depth to which the euphotic zone and the chlorophyll maximum developed. Also, as the drifters moved offshore, the food web changed from a coastal, nefftic food web to an offshore, oligotrophic food web due to the decrease in nutrient availability. The temporal development of the food web constituents following the simulated drifters was dependent upon the environment to which the drifter was exposed. For example, the amount of time upwelled or downwelled and the initial location in the CTZ region greatly affected the development of the food web.


Introduction
The coastal transition zone (CTZ) is a region off the coast of California which is characterized by the presence of cross-shelf jets or filaments [Brink and Cowles, 1991].As these filaments develop, they entrain recently upwelled water near the coast and transport it offshore.As a result, the circulation processes within the CTZ de- This paper is the third of a series of three studies that were conducted using a set of increasingly complex and sophisticated physical-bio-optical models.This third paper presents the results from two types of simulated The primary objective of this paper is to simulate the plankton dynamics observed while following a Lagrangian drifter as it becomes advected within the filament from nearshore to offshore.The resulting simulations are then used to determine which processes are responsible for creating the chemical and biological distributions observed while following a Lagrangian drifter as it is advected offshore within the CTZ.
The second section presents the methods used to calculate the velocities and resulting chemical and biological concentrations experienced by each of the two types of Lagrangian drifter experiments.The resulting values of the biological and chemical fields that the Lagrangian drifters experienced as they were advected offshore in a filament are presented in section 3. Finally, section 4 presents a discussion of the results and some conclusions.In using this 1-D model for Lagraglan drifter simulations, we assumed that the effects of horizontal gradients were negligible.The approach further assumed that the nutrient and biological distributions along the drifter trajectory resulted from in situ processes and vertical advection only and that horizontal advective and diffusive processes were negligible.

One-Dimensional Lagrangian
The 1-D Lagrangian drifter model simulations were designed to investigate the vertical biological distributions that would be encountered along the trajectory of a Lagrangian drifter released in the CTZ at a point where it would be entrained in the offshore flowing filament.The simulated distributions obtained in this way can be compared to observations of nitrate, chlorophyll, and zooplankton concentrations made while following for 6 days a drifter that had been released as part of the 1988 CTZ field studies [Hofmann et al., 1991].
Two separate simulations were carried out.In the first, the time-and depth-dependent vertical velocities were obtained from a simulated Lagrangian drifter.The chosen drifter used in the first simulation was one of 880 simulated Lagrangian drifters which were generated by a regional primitive equation circulation model that has been configured to simulate circulation conditions in the CTZ (Figure 1) [Hofmann et al., 1991;Haidvo9el et al., 1991a].The specific simulated Lagrangian drifter chosen was initially released in a region where an offshoreflowing filament was observed to form in the model.The path of the simulated Lagrangian drifter, after remapping to the drifter path, is shown in Figure 2a.
The vertical velocities experienced by the chosen simulated Lagrangian drifter were negative (downwelling) throughout the simulation (Figure 2b), and therefore the drifter was displaced vertically from its initial depth drifter in a time interval was calculated using a fourthorder Runge-Kutta scheme' ffn+l : • q-q-q-q-6 (5) where •n+l represents the new location of a particle that is advected from its previous position •n by the velocity ¾ in a time interval At, and ki represents the Runge-Kutta coefficients.These tracers were c,q•amc of moving within the grid boxes, and so the fluid velocities, •, at points not represented by grid points were required for use in the Runga-Kurta scheme.The model obtained these velocities by using a horizontal, bicubic interpolation algorithm of the form The final results obtained from the 3-D physicalbio-optical model consisted of extracting the biological and chemical distributions along trajectories followed by drifters released in the simulated circulation fields.Such an approach allows quantification of the changes in the biological and chemical fields while the water parcel moves from the nearshore neritic environment to offshore waters.

One-Dimensional Lagrangian
region of the nearshore end of a filament that was observed to have developed off the California coast.The drifter was tracked for 8 days as it moved offshore while being advected within the offshore flowing portion of the observed filament.The results from this study characterize the time development of a typical upwelling ecosystem.At the beginning of the study, the water mass that the drifter sampled contained model [Moisan et al., this issue].In this model, a nine-component food web model has been coupled with a wavelength-dependent subsurface irradiance model and a three-dimensional, primitive equation, regional circulation model.This model was developed for the CTZ with the overall objective of quantifying and understanding the physical and biological processes associated with the across-shore transport of nutrients and biomass.
Figure 1.The CTg study region.The region included in the CTg circulation domain is indicated by the box.Within this domain, the release points for the Lagrangian drifter experiments are indicated by crosses.The dots indicate the stations at which nutrient, phytoplankton, and •ooplankton measurements were made during the 1988 CTZ field sampling period.These stations follow along the track of a drifter that was deployed in an offshore flowing filament.The dashed line represents the actual coastal topography; the solid line represents the idealized coastal topography used in the circulation model.
where (xf, y.t) is the position of the Lagrangian driRer and (xi, yi) are the positions of the 16 neighboring grid points.The magnitudes of the chemical and biological fields encountered along the path of the drifter were also calculated using the above bicubic interpolation scheme.Simulated Lagrangian drifter experiments were carried out between model day 140 and 160.A total of 880 drifters were released in the model domain at points which surrounded the location at which a filament was observed to form (Figure 1).Three sets of drifters were released at each location at depths of 30, 60, and 90 m and were followed for 20 days.The position of these drifters varied over time as a result of the vertical and horizontal velocities that they experienced.A fourth drifter set was released at each location; however, this drifter set was constrained to remain at 30 m.The position of this set of drifters varied over time only as a result of horizontal velocities.The resulting paths taken by the simulated drifters also allow for vertical sampling of the 3-D fields as the drifters were advected through the model domain.This form of numerical data sarnpling was similar to the field sampling scheme used byAbbott et al. [1990] andMackas et al. [1991], and thus the results from these are compared.

Figure 3 .(Figure 7 .
Figure 3.Time evolution of the simulated vertical nitrate distributions for conditions of (a) no vertical advection and (b) vertical advective field obtained from a circulation simulation for the CTZ, with (c) observed nitrate fields measured while following a drifter released during the 1988 CTZ field studies shown for comparison.Triangles at the top of Figure 3c indicate the times at which measurements were made.Values were obtained at intervening times by linear interpolation.Contour levels are 2.5 mg N m -a for all panels.Note scale change in the time axis between Figures 3a and 3b, and 3c.