Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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Quantifying the effects of Langmuir circulation and photoinhibition on phytoplankton
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productivity in the Ross Sea Polynya with Large Eddy Simulation
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Robyn L. Smyth1,3, Cigdem Akan2,4, Andrés Tejada-Martínez2, Patrick J. Neale1
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Smithsonian Environmental Research Center, Edgewater, Maryland
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2
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Florida
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Center for Environmental Policy, Bard College, Annandale-on-Hudson, New York
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Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los
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Angeles, California
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Department of Civil and Environmental Engineering, University of South Florida, Tampa,
Corresponding author: Robyn Smyth (
[email protected])
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Key Points:
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Depth-integrated productivity was 230 mmol C m-2 d-1 during the spring bloom in the Ross Sea Polynya on a clear sky day with 6-7% reduction due to photoinhibition.
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Deep vertical mixing beyond the euphotic zone mitigates the effects of photoinhibition on depth-integrated primary production.
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Light variation resulting from turbulent motions should be accounted for when estimating the effects of vertical mixing on depth-integrated productivity.
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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Abstract
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Southern Ocean phytoplankton assemblages acclimated to low-light environments that result
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from deep mixing are often sensitive to ultraviolet and high photosynthetically available
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radiation. In such assemblages, exposures to inhibitory irradiance near the surface result in loss
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of photosynthetic capacity that is not rapidly recovered and can depress photosynthesis even
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after transport below depths penetrated by inhibitory irradiance. We used a coupled biophysical
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modeling approach to quantify the reduction in primary productivity due to photoinhibition
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based upon experiments and observations made during the spring bloom in Ross Sea Polynya
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(RSP). Large eddy simulation (LES) was used to generate depth trajectories representative of
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observed Langmuir circulation that were passed through an underwater light field to yield time
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series of spectral irradiance representative of what phytoplankton would have experienced in
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situ. These were used to drive the Rmax model, a time-dependent photosynthesis-irradiance model
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with inhibition determined from a biological weighting function and repair rate estimated from
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shipboard experiments on the local assemblage. We estimate the daily depth-integrated
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productivity was 230 mmol C m-2. This estimate includes a 6-7% reduction in daily depth-
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integrated productivity over potential productivity (i.e., effects of photoinhibition excluded).
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When depth was fixed (no vertical transport), the reduction in productivity was nearly double.
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Relative to LES estimates, there was slightly less depth-integrated photoinhibition with random
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walk trajectories and nearly twice as much with circular rotations. This suggests it’s important to
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account for turbulence when simulating the effects of vertical mixing on photoinhibition due to
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the kinetics of photodamage and repair.
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1 Introduction
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Photosynthesis by Southern Ocean phytoplankton can be both limited and inhibited by natural irradiance. In open ocean regions where mixing is deep, phytoplankton acclimate to
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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overall low light conditions by maximizing light harvesting capacity (i.e., photosynthetic
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efficiency). This photoacclimation, however, leaves them vulnerable to high irradiance
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encountered near the surface [Helbling et al., 1992, Neale et al., 2003]. Many Antarctic
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assemblages from deeply mixed layers are inhibited by near-surface ultraviolet (UV) and
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photosynthetically active radiation (PAR) [e.g., Helbling et al., 1994; Fritz et al., 2008;
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Alderkamp et al., 2011]. Photodamage results in nonlinear loss of photosynthetic capacity [Neale
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et al., 1998a, Hiriart-Baer and Smith 2005] that tends to be slowly recovered in Antarctic
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assemblages adapted to low light [Fritz et al., 2008, Alderkamp et al., 2011, Smyth, et al., 2012].
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How do intermittent exposures to inhibitory irradiance in the actively mixing ocean impact
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depth-integrated water column productivity (PT)? Decades of experimental and modeling studies
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collectively demonstrate that the net effect of photoinhibition and mixing on PT is context-
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dependent with outcomes influenced by response kinetic of the assemblage (rates of
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photoinhibition and repair) and the depth of mixing relative to the depth of the euphotic zone
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[Franks and Marra 1994, Neale et al., 1998b, Hiriart-Baer and Smith 2005]. This understanding
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results largely from “sensitivity analyses” of key variables that do not allow for quantification of
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inhibitory losses in a specific assemblage. Assemblage-specific assessments of the net effect of
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photoinhibition require simultaneous knowledge of incident irradiance and attenuation, mixing
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conditions, and photoresponse of the assemblage that is not generally available.
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We estimated PT and the percent reduction due to photoinhibition during the spring
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bloom in the Ross Sea Polynya (RSP) with deep mixing by Langmuir circulation with a coupled
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bio-physical model parameterized and forced by simultaneous oceanographic measurements and
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shipboard experiments to determine the photoresponse of the assemblage. The Ross Sea is one of
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the most productive regions of the Southern Ocean [Comiso, et al., 1993; Smith and Comiso
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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2009], accounting for 25-30% of the total annual primary production south of 50°S [Arrigo, et
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al., 2008]. Triggered by increasing surface irradiance, shoaling surface layer, and abundant iron,
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the spring bloom is the most productive time of year in Ross Sea [Smith, et al., 2000; Peloquin
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and Smith 2007; Smith et al. 2014]. During the bloom, the south central portion of the RSP tends
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to be dominated by Phaeocystis antarctica, a colonial haptophyte that is easily inhibited, slow to
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recover, and often found in deeply mixed waters with low but variable irradiance [Kropuenske et
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al., 2009, Kropuenske et al., 2010, Mills et al., 2010]. Under dynamic light conditions, P.
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antarctica appears to maximize photosynthetic efficiency under low and moderate irradiance,
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even though this also increases sensitivity to photodamage under very high irradiance
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[Kropuenske et al., 2009]. There is evidence that the spring phytoplankton bloom in the Ross Sea
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is both light limited [Smith et al., 2000] and inhibited by near surface irradiance [Neale et al.,
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2009]. Concurrent incubations in a spectral incubator showed that most of the inhibition was
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caused by exposure to UV radiation [Smyth et al., 2012]. Although not the case in 2005 when the
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field data for this study was collected, the austral spring bloom in the Ross Sea often overlaps
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with the period of maximum ozone depletion over Antarctica [Neale, et al., 2009]. The ozone
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hole allows for transmission of the most damaging wavelengths in the UV-B (290-320 nm)
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range. It is important to understand how UVR influences productivity in the Ross Sea, a key
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region for the productivity of the Southern Ocean, which in turn plays an important role in the
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global carbon cycle [Arrigo et al., 2008, Smith et al., 2012].
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The Rmax model is a time-dependent photosynthesis-irradiance (P-E) model fit to the 2005
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RSP spring assemblage and it predicts the biomass-normalized photosynthetic rate, including
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photoinhibition and repair, from time series of spectral irradiance [Smyth et al., 2012]. It uses a
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biological weighting function (BWF) to characterize the spectrally-dependent photodamage from
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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UV and PAR exposure. BWFs describe the collective, wavelength-dependent response of a
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phytoplankton assemblage to UVR [Neale 2000; Hiriart-Baer and Smith 2004; Fritz, et al.,
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2008]. They are experimentally determined and reflect the photoacclimation of the assemblage to
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the underwater light regime at the time they were assessed [Neale et al. 1998a]. When the mean
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irradiance in the water column shifts due to changes in vertical mixing or water clarity,
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photoacclimation processes occur that alter the spectral response and therefore the shape of the
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BWF. When the photoresponse of the Ross Sea assemblage was determined, productivity was
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high with chlorophyll biomass averaging 6.5 mg m-3 in the surface layer [Neale et al., 2009]. The
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euphotic zone was restricted to the upper 20 m and in situ incubations showed reductions in
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productivity (photoinhibition) in the upper 5 m [Neale et al., 2009] and active fluorometry from
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the ship showed light stress below the depth penetrated by inhibitory irradiance [Neale, et al.
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2012].
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During frequent windy episodes, there was evidence of deep and rapid mixing by
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Langmuir circulation [Neale, et al., 2012]. Langmuir circulation (LC) is an energetic form of
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mixing that results from an interaction between wind shear and surface waves under sustained
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wind forcing [Leibovich 1983; Thorpe 2004]. It produces quasi-coherent vortices that create a
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highly variable light environment for entrained phytoplankton [Denman and Gargett 1983]. For
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the LC events observed in the RSP, mixing depths exceeded 40 m with vertical transit times in
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downwelling regions of 3-7 minutes [Neale et al., 2012]. With the depth of 1% surface PAR at
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18 m, the mixing depth was more than twice the euphotic zone depth. Thus, the RSP assemblage
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experienced intermittent exposure to inhibitory irradiance in near-surface photoactive zone,
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optimal light for photosynthesis and repair in the lower euphotic zone, and periods of extended
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darkness in the aphotic zone where PAR was too low to support photosynthesis. We used a large
Confid dential manuscrript submitted to Journal of G Geophysical Reesearch: Oceaans
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eddy sim mulation (LES S) of Langm muir turbulen nce [Tejada-M Martinez, ett al., 2009] pparameterized
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and forceed by observ vations from the RSP [Neeale, et al., 22012] to deriive 24 h of sspectrally-
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resolved light histories representaative of physical and opttical conditions in the R RSP when thee
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assemblaage was assessed for the Rmax model. A conceptuual diagram oof the modell is presentedd in
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Figure 1..
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Figure 1. Con nceptual diag gram of LES S domain andd underwateer irradiance.. The LES domain lengths are 150 m in the horizontal and a 120 m inn the verticall with a 30 m sponge layyer at the bottom. The LES S was initialized with a density d profille ( and fforced by buuoyancy fluxx (Jb), water fricction velocitty ( ), and Stokes S drift velocity ( ) from ship observationss. Underwatter irradiance regimes arre determineed from meassurements off spectral irrradiance ( ) and attenuatio on. Irradiancce is inhibito ory in the ph hotoactive zoone (purple),, optimal forr photosyntheesis and repaiir in the lower euphotic zone z (green)), and insuffi ficient for phhotosynthesiss in the aphootic zone (graay).
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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LES is used to model turbulent flow in the upper ocean by numerically resolving
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spatially- and temporally-averaged Navier-Stokes equations [Li et al., 2005]. It has been widely
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used in studies concerning processes in the upper ocean mixed layer such as Langmuir
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circulation [e.g., McWilliams et al., 1997; Tejada-Martinez et al., 2009], mixing [e.g., Kukulka et
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al, 2009], and surface wave breaking [e.g., Li et al, 2013]. When parameterized with the Craik-
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Leibovich vortex force to account for wind-wave interactions, LES simulates deep, energetic
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Langmuir turbulence [McWilliams et al., 1997]. There are only a few studies that have used LES
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to investigate biological questions. Lewis [2005] incorporated a nitrate-phytoplankton-
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zooplankton (NPZ) model into a LES to examine the effects of turbulent mixing on
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phytoplankton distribution and found physical mixing dominated biological processes under
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strong wind forcing. LES was also used to examine the relative importance of decreasing mixing
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depth and intensity in triggering spring phytoplankton blooms [Taylor and Ferrari 2011;
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Enriquez and Taylor 2015; Taylor 2016]. They found that weakening turbulence associated with
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the end of winter cooling can trigger the bloom by increasing residence time in the euphotic zone
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prior to notable decreases in mixed layer depth. In these Eulerian simulations, phytoplankton
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growth was a simple function of mean exposure to PAR at depth. The light history-dependent
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variation in photosynthetic capacity that results from photoinhibition and vertical mixing in
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natural water columns requires a Lagrangian approach.
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We used LES to derive neutrally-buoyant Lagrangian particle trajectories that, when
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coupled with observations of irradiance and attenuation, yield the spectrally-resolved light
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histories needed for input into the Rmax photosynthesis model (Table 1). With the resulting LES-
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Rmax model, we predict photosynthesis, inhibition, and repair for 1600 trajectories representing
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phytoplankton cells/colonies entrained in Langmuir turbulence. The results are grid averaged to
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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Table 1: Symbols and units model input and output variables. PT Depth-integrated water column productivity Langmuir number Lat Water friction velocity uτ Stokes drift velocity us Surface buoyancy flux Jb Water density σT Depth of trajectory i zi Surface spectral irradiance Wavelength-specific diffuse attenuation coefficients Spectral irradiance for trajectory i PAR adjusted for pigment absorption at depth of trajectory i Biomass-normalized productivity of trajectory i Biomass-normalized potential photosynthetic rate (no inhibition) Photosynthetic capacity scaling factor (ranges 0-1) Light-saturated rate of photosynthesis Characteristic irradiance for light saturation Maximum repair rate ∗ Weighted irradiance for inhibition ∆ Model time step Biological weights of the inhibitory effect of UV at λ=293-400 nm Biological weight of the inhibitory effect of PAR Vertical eddy diffusivity
mmol C m-2 d-1 nondimensional m s-1 m s-1 W kg-1 kg m-3 m W m-2 nm-1 m-1 W m-2 nm-1 W m-2 g C g Chl-1 h-1 g C g Chl-1 h-1 nondimensional g C g Chl-1 h-1 W m-2 s-1 s-1 s m2 J-1 m2 J-1 m2s-1
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hindcast vertical mean productivity, daily PT, and the reduction in PT owing to photoinhibition.
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We compared results from LES trajectories to productivity estimates from fixed-depth
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trajectories to determine whether PT is over- or underestimated by fixed-depth incubation under
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the observed conditions of high irradiance, high biomass and deep mixing. We also compare
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LES runs with static and variable surface forcing. The latter shows the decay in Langmuir
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turbulence with observed surface heating and declining wind forcing over the course of the day.
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Because mixing deeper than the euphotic zone provides both a sink for inhibited cells and a
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source of uninhibited cells [Neale et al., 1998a], we expect to find greater PT (less inhibition)
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with deep mixing than is predicted by the fixed-depth case.
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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LES provides the best available representation of vertical mixing by LC [Skyllingstad and
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Denbo 1995; McWilliams et al., 1997; Kukulka et al., 2009] but is so computationally intensive
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that its use to address biological questions is limited [McWilliams and Sullivan 2000; Ross and
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Sharples 2004; Enriquez and Taylor 2015]. More commonly, Lagrangian random walk models
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[e.g., Franks and Marra 1994; Neale et al., 1998b; MacIntyre et al., 2000; Ross et al., 2011] or
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simple circular rotations [e.g. Helbling et al., 1994; Hiriart-Baer and Smith 2004] are used to
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account for the effects of vertical mixing on photosynthesis when estimating integrated water
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column productivity. Do estimates of PT produced by the LES trajectories differ from estimates
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made with simpler models of vertical mixing? We compared vertical mean productivity and
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daily PT from light histories generated by a 1-D Lagrangian random walk model [Visser 1997;
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Ross and Sharples 2004] and simple circular rotations to LES-based estimates to evaluate these
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alternative models of vertical mixing.
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2. Observations and modeling
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2.1 Large eddy simulation of Langmuir turbulence - The LES model used is that of Tejada-
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Martinez et al. [2009], consisting of continuity and momentum equations to solve for pressure
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and velocity components and an advection-diffusion equation for density,
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was used to generate particle trajectories representative of Langmuir circulation observed in the
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RSP following steady, overnight winds in excess of 12 m s-1 on 26-27 November 2005 [Neale, et
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al., 2012]. LES of LC are characterized by the turbulent Langmuir number,
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is the water friction velocity and the wind shear stress and
is the surface Stokes drift velocity.
is water density and
, where
. This LES model
where
where is is the acceleration of
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
is the surface wavenumber and is wave amplitude.
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gravity,
represents wind forcing
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relative to wave forcing. Langmuir turbulence is expected to be active and thus important when 0.7 [Li et al. 2005]. Meteorological and oceanographic observations were used to estimate
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wind stress and surface energy fluxes with standard air-sea flux equations from Fairall, et al.
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[2003] as described in Neale et al. [2012] to parameterize and force the LES. The surface wave
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conditions necessary for calculating
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approximated from the air friction velocity using the approach described in Resio, et al. [2008].
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Given the proximity of the ship to the ice shelf (~30 km), observed wind speeds (12-15 m s-1)
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and duration (10 h),
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m, respectively. The time series of observations and model inputs are in Fig. 2 which shows the
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buoyancy flux, Jb (Fig. 2a), water friction velocity,
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and turbulent Langmuir number,
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(LESs) and time-variable (LESv) forcing. LESs was forced with a neutral surface buoyancy flux
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(Jb=0) and wind/wave parameters held constant at values representative of high, steady winds
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overnight with
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buoyancy flux and observed decline in wind forcing (blue lines in Fig. 2 a&b respectively), the
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observations were smoothed with a 2.5 h moving average filter and used to force the time-
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variable LESv (see red lines in Fig 2). Over the day there was a corresponding decline in
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and
were not recorded during the cruise and were
were estimated for fetch-limited conditions to be 0.24 m-1 and 0.6
(Fig. 2b), Stokes drift velocity,
(Fig. 2c)
(Fig. 2d). The LC in the RSP was simulated with static
of 0.39 (see black dashed lines in Fig. 2). To account for the stabilizing
such that
remained less than 0.4 throughout the simulation.
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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Figure 2. Parameters used to force LES forcing parameters (a) surface buoyancy flux (Jb), (b) water friction velocity (u ) (c) Stokes drift velocity (u ) and, (d) turbulent Langmuir number (Lat) from ship observations (blue), averaged during a stationary high wind period to force LESS (black dashed) and moving average filtered to force LESV (red). Vertical lines indicate timing of CTD profiles used to initialize and assess the LES. Black arrow indicates timing of acoustic backscatter measurements of LC presented in Neale, et al. (2012). J b (W kg -1 )
10-7 1
a)
0 -1 -2
u (m s-1 )
0.025
b)
0.02 0.015 0.01
uS (m s-1 )
0.15
c)
0.1 0.05
La t
0.4
d)
0.39 0.38
27Nov
28Nov
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All LES runs were initialized with a smooth density (
profile averaged from a 4 drop
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CTD cast at 06:00 local time on 27 November (Fig. 3a). The LES domain lengths were 150 m in
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the horizontal (x,y) and 120 m in the vertical (z). A sponge layer was placed in the lower third of
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the domain (Fig.1) in order to absorb incoming internal waves and thus avoid their erroneous
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reflection. Horizontal grid spacing was 4.6875 m and vertical grid spacing ranged from 0.2494 to
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0.9355 m with coarsest spacing at the bottom of the domain (pycnocline) and finest at the top of
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the domain (surface). The LES was also run with vertical domain sizes ranging from 90-180 m
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and results were similar to the 120 m domain runs presented here. The LES time step was 0.1 s.
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After a spin up period of 1 hour at the end of which the turbulence had reached approximately 55
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meters depth, 1600 neutrally-buoyant particles were entrained in simulated Langmuir turbulence
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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following McWilliams et al. [1997]. According to Denman and Gargett [1983], the effect of cell
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sinking on light history can be ignored in turbulent Langmuir conditions. In LESs, 1400 particles
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were evenly distributed in the upper 40 m of the domain and 200 particles were seeded from 40
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to 60 m. For LESv, 1550 particles were evenly distributed in the upper 60 m and 50 particles
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were released from 60 to 120 m. Particle locations defined by xi, yi, zi coordinates were output
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every 30 s for 24 hours. LES particle positions in the vertical (zi) direction were used with
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modeled underwater spectral irradiance to define light histories for the time-dependent Rmax
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model. LESs was also used to define the eddy diffusivity profile for a Lagrangian random walk
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model described further below as an alternative to the more expensive LES particle tracks.
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Following McWilliams and Sullivan [2000], eddy diffusivity is defined as 〈
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〉
〈
〉⁄
⁄ 〈
〉⁄
〈
where
〉 is the turbulent vertical buoyancy
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flux calculated from the LES and
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buoyancy flux boundary condition mentioned earlier, implying zero mean density vertical
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gradient ( 〈
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the surface (Fig. 3b). In order to bypass this difficulty, we considered an alternate approach using
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the eddy viscosity defined as
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where
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momentum calculated from the LES and
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of the net mean shear with
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respectively. Figure 3b presents a comparison between
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quantities are nearly equal throughout most of the water column, except for near the surface
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where
〉⁄
is molecular diffusivity. However, the zero surface
= 0) at the surface, leads to an eddy diffusivity that grows unboundedly at
〈
〉 ∙ 〈 〉⁄
is the LES horizontal velocity vector, 〈
and
〈 〉⁄
⁄
〈 〉⁄
(McWilliams et al., 1997)
〉 is the turbulent vertical flux of horizontal =
〈 〉⁄
〈 〉⁄
is the square
the LES downwind and crosswind velocity components, and
where it can be seen that both
grows unboundedly as explained earlier. Thus, the eddy diffusivity in the Lagrangian
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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random walk model is taken as
, implying a turbulent Prandtl number (
) equal to one,
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which is consistent with studies of unstratified and weakly stratified turbulence
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[Venayagamoorthy and Stretch 2010].
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Figure 3. Vertical profiles of density (σ ) and vertical eddy diffusivity (Kz) for the RSP, (a) average σ from 4 CTD drops at 06:00 on 27 November (blue), smoothed to initialize LES (black dashed), and at the end of LES spin up period (red). (b) Mean eddy diffusivity (black dots) and viscosity (red) from LESs. Mean eddy viscosity profile was used to define Kz in the random walk model. 0
20
Depth (m)
40
60
80
100
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b)
a)
120 27.7
27.75 t
(kg m -3 )
27.8
0
0.2
0.4
0.6
2 -1
K z (m s )
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2.2 Spectral irradiance – Incident UV irradiance was measured with a Smithsonian Institution
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multichannel scanning radiometer (SR-19) mounted on the ship science mast. This instrument
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has eighteen 2 nm bandwidth filters ranging from 290-324 nm and an additional 330 nm filter
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with a 10 nm bandwidth [Neale et al., 2005]. The surface spectral irradiance
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700 nm was determined by combining SR-19 measurements with output from the STAR
for λ= 293-
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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radiative transfer model [Ruggaber et al., 1994] using the protocol of Neale, et al. [2005].
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Integrated model output at PAR wavelengths was checked for consistency against an
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independent set of PAR measurements by a Biospherical Instruments GUV-2511 collocated with
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SR-19 (data not shown). UVR at wavelengths < 293 nm were too low to be resolved and were
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thus omitted from the model calculations. Diffuse attenuation coefficients were determined from
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underwater irradiance profiles with the Biospherical Instruments PUV-2500 and PRR-600
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radiometers at 12 wavelengths between 305 and 665 nm (details in Kieber et al. [2009]).
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Attenuation observations from 27 November 2005 were used for the model calculations
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presented here and they ranged from 0.5 m-1 at 305 nm to 0.2 m-1 at 550 nm. From these
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measured wavelengths, wavelength-specific diffuse attenuation coefficients at 1 nm intervals
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(
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linearly to shorter wavelengths (305 nm to 293 nm) and linearly to longer wavelengths (665 nm
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to 700 nm) in Matlab (v. R2012b).
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were interpolated with a piecewise cubic spline (305 nm to 665 nm) and extrapolated log-
With spectral irradiance from the 27 November 2005 and wavelength-specific diffuse
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attenuation, we used LES depth trajectories (zi[t], 1600 per run) to define individual time courses
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of spectral irradiance
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to Fresnel’s equation to account for the greater reflectance from low solar angles at high latitudes
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[Cogley 1979]. For photosynthesis calculations, we found
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differences in pigment absorption of in situ PAR at the depth of the particle at each time relative
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to the xenon lamp used in experiments to derive biological weighting functions [Neale, et al.,
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2014]. To determine the effect of vertical mixing and compare to observations from the RSP, we
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also determined
1
and
, where
is albedo estimated according
which accounts for
for constant depth trajectories in the same underwater light
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field. These light histories reflect only the changes in surface irradiance and approximate light
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exposure during fixed depth incubations used to measure productivity in situ.
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2.3 Rmax photosynthesis model – With light exposure determined for each trajectory, the Rmax
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model predicted time courses of biomass-normalized photosynthesis (1)
287 288
where
is the potential biomass-normalized photosynthetic rate at time [t] defined as 1
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(2)
is the light-saturated rate of photosynthesis (g C g Chl a-1 h-1) and
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where
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characteristic PAR irradiance for light saturation (W m-2). Shipboard experiments on the RSP
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bloom assemblage found
= 2.0 g C g Chl a-1 h-1 and
is the
= 6.3 W m-2 [Smyth et al. 2012].
is a nondimensional scaling factor (0-1) for photosynthetic capacity, i.e. the proportion of
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the potential photosynthetic rate realized given the light history of the particle. Photosynthetic
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capacity decreases due to inhibition and is restored by subsequent repair: 1 1
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subject to the constraint that
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step (30 s) and
∗
∆
(3)
is the repair rate (s-1), ∆ is the model time
∑
(4)
(m2 J-1) are the biological weights of the inhibitory effect of irradiance at each
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where
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wavelength in the modeled UV band (λ = 293-400 nm) and of broadband PAR, respectively.
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and
≤ 1 and where
∆
(s-1) is weighted irradiance for inhibition, ∗
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∗
A fixed repair rate of
3.2 x 10-4 s-1 was determined from experimental treatments
described in Smyth et al. [2012]. Because the previous analysis could only resolve a single
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estimate for
305
information on the variability of
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were run with ±50%
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Additionally, little is known about the light dependence of photosynthetic repair rates in
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Antarctic phytoplankton, but based on the energetic requirements [Raven 1991], little or no
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repair is expected to occur in the dark [cf. Gao et al., 2007]. Because the mixing depth in the
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RSP was much deeper than the euphotic zone depth, vertically circulating phytoplankton
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experienced extended periods of darkness. The photosynthesis model was run with continuous,
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fixed repair at the experimentally-determined rate as well as with light-dependent repair with the
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rate reduced for
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for the Ross Sea assemblage based upon time constraints, we presently have no . To account for this uncertainty, all sets of trajectories
to explore the sensitivity of the results to the specification of
less than
such that
/
.
.
Vertical profiles of mean biomass-normalized productivity for all trajectory sets were
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obtained by grid averaging instantaneous photosynthesis rates (
) of all particles within 0.5
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m depth bins over 15 min and 1 hour time increments. Daily PT for each set of depth trajectories
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was estimated by integrating over 15 min mean profiles using the trapz function in Matlab 2016b
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and multiplying by the mean chlorophyll concentration in the surface layer, 6.5 mg Chl a m-3. PT
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is daily gross productivity in mmol C m-2 d-1 under the assumption of constant Chl a with depth
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and over the modeled time period which is consistent with field observations (data not shown, cf.
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Neale et al. [2012]).
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2.4. Additional models of vertical mixing – Given the computational effort required to produce
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particle trajectories with LES (weeks of supercomputing time for 24 h simulation), we also
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generated depth trajectories with two approaches more commonly used in studies of the effects
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of vertical mixing on photosynthesis, Lagrangian random walk and circular rotations. Lagrangian
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random walk models have been used extensively to investigate the effects of vertical mixing on
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photosynthesis [e.g., Franks and Marra 1994; Neale et al., 1998b; Cianelli, et al., 2004]. We
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used the 1-D Lagrangian particle-tracking model suggested by Visser [1997] and improved by
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Ross and Sharples [2004] to generate sets of random walk (RW) trajectories that represent LC in
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the RSP. This model takes a vertical eddy diffusivity
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includes a deterministic component that leads to a net displacement of particles to regions of
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high diffusivity thus preventing accumulation of particles in low diffusivity regions [Ross and
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Sharples 2004]. Because vertical eddy diffusivity could not be estimated directly from available
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ship data, we ran the Ross and Sharples [2004] model with the mean eddy viscosity profile from
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LESs (see Methods section 2.1). In this profile,
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approximately linearly to 0 at the bottom of the mixing layer (Fig. 3b). 1600 neutrally buoyant
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particles were evenly distributed over a 60 m surface mixing layer (SML). Due to the high
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diffusivities of energetic mixing by LC (
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with a 0.1 s timestep to avoid particle accumulations. The first 10,000 timesteps were discarded
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as a spin-up period. Particle depths were output every 30 sec for 24 hours.
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profile that varies with depth and
peaked at 5.5 m at 0.2 m2s-1 and declined
>0.1 m2s-1), the random walk model had to be run
Variations on circular rotations have been used to represent the quasi-coherent structure
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of LC, and vertical mixing more generally, in both experimental simulations and modeling
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studies of pelagic productivity [e.g., Helbling et al., 1994; Kohler et al., 2001; Hiriart-Baer and
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Smith 2005]. We used the Langmuir cell circulation time of 75 min and mixing depth of 44 m
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estimated from ship observations using Thorpe scales [Neale, et al., 2012] following the
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procedure described in Gargett and Garner [2008]. Although the downwelling velocity is
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typically faster than horizontal or upwelling velocities in a Langmuir circulation cell [Denman
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and Gargett 1983], we used a constant velocity for simple circular trajectories in order to avoid
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the accumulation of particles in slow regions that would occur otherwise [e.g., Hiriart-Baer and
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Smith 2005]. 1600 particles were evenly distributed from 0 to 44 m and circulated through the
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mixing layer in 75 minutes for 19 rotations per day. As with LES trajectories, random walk and
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circular depth trajectories were used to define time courses of spectral irradiance that were used
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to force the Rmax model and estimate for comparison to results with LES trajectories.
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3. Results
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3.1.1 Large Eddy Simulation of Langmuir turbulence - Parameterized and forced with
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observations from the RSP (Figs. 2 & 3), the LES runs yielded turbulent LC that persisted under
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static forcing (LESs) and decayed under time variable forcing (LESv) (see supporting Movie S1
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for dynamic visualization). Figure 4 shows the turbulence structure generated in our simulations
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in terms of the downwind velocity fluctuations on the surface (left panels) and the vertical
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velocity fluctuations (right panels) over a cross-stream and vertical plane, respectively, for
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constant and variable forcing at different hours. During the spin-up period of the simulation,
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Craik-Leibovich vortex forcing generates smooth downwind-elongated Langmuir circulations
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(e.g. see Fig. 16 of Tejada-Martinez et. al., [2009]). As the flow transitions to Langmuir
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turbulence, these initial Langmuir cells grow and interact non-linearly coexisting with smaller
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cells near the surface. An instantaneous snapshot of these coexisting cells can be observed in
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terms of vertical velocity fluctuations in Figure 4 (Hour 1), exhibiting the
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downwelling/upwelling limbs of the cells. Here the cells are no longer smooth appearing
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irregular with the larger cells extending approximately 60 meters deep and embedded smaller
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cells at the surface. In LESs, these larger cells persist throughout the entire simulation, while in
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LESv the intensity of the cells decreases with depth as the wind and wave forcing decays over
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time.
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Figure 4. Results of the Large Eddy Simulation (LES) of the Ross Sea Polyna surface mixing layer. Panels show snapshots of the velocity field at six hour intervals through the 24 h simulations. The panels on the left show the instantaneous velocity in the x-direction ( ′) in the horizontal plane at the surface and the right are cross-stream sections showing vertical velocity fluctuations ( ′). Two panels are shown at each time point comparing the results for LES with static and variable forcing. The units on all panels are m s .
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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Neutrally buoyant particle trajectories output by the LES to represent the motion of
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entrained cells and colonies “behave” as expected for Langmuir turbulence. All trajectories show
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rapid upwelling and downwelling as well as extended periods in the near surface and at depth
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(examples shown below). With the decline in surface forcing and mixing intensity, particles from
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LESv shoaled over time (not shown). Some particles (5% in LESv and 6% in LESs) were “lost” to
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the productivity computation when they were initialized or passed below 80 m and did not reach
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or return to the euphotic zone. This happened at a greater rate in LESs because higher intensity
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mixing created more encounters with the pycnocline.
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3.1.2. Comparing LES results to RSP observations - There are limited data available for
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verifying the turbulent Langmuir circulation predicted by the LES. Qualitatively, acoustic
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backscatter measurements collected at 09:00 h (timing indicated by arrow in Fig. 2a) show
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downwelling bubble plumes that indicate the presence of LC (see Fig. 4 in Neale et al. [2012])
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but not the depth or intensity of mixing. The decline in mixing predicted by LESv is consistent
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with Thorpe scale analysis presented in Neale et al [2012] that found SML conditions were in
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transition from LC to internal waves by 21:00 h following the observed decline in wind forcing
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over the day.
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CTD casts during the LC event enable a comparison of observed and predicted density
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structure, a reflection of vertical mixing, over the course of the modeled day. All LES runs were
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initialized with the same density (
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time when there was a nearly neutral buoyancy flux and steady wind forcing (Fig. 3a). Later that
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morning, density remained uniform to 30 m with weak stratification that increased with depth,
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particularly beyond 60 m (Fig. 5a). Over the afternoon, observed profiles show a sharpening of
) profile averaged from a yo-yo CTD cast at 06:00 h local
Confid dential manuscrript submitted to Journal of G Geophysical Reesearch: Oceaans
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Figure 5. Obsserved densitty profiles (b blue) at (a) 008:34 h, (b) 12:11 h, (c) 15:15 h, andd (d) 20:55 h (LT) ( on Nov vember 27, 2005 2 comparred to densityy profiles froom LESs (bllack dashed)) and LESv (reed) with the correspondin c ng observed temperaturee (cyan) andd salinity (blaack) profiless shown beelow (e-h). Black B arrowss show mixin ng layer deppth based on Thorpe scalle analysis ggiven in Table 2 of Neale et e al. (2012).
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
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the pycnocline that was not reproduced by the LES (Fig. 5b-d). Subsequent
profiles from both
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LESs and LESv did not deviate much from the initialized density structure, showing only a slight
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(20
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m) in as little as 8 minutes, i.e. well before full recovery of photosynthetic capacity has occurred.
456
) from
and a
) due to inhibition.
is
occur when trajectories encounter inhibitory
remained at 1. However, from 4 to 20
) remains reduced
Confidential manuscript submitted to Journal of Geophysical Research: Oceans
457 458 459 460
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a)
UV PAR
200 100 0 0 20 40 60
PB (g C g Chl -1 h-1 ) pot
Depth (m)
Eo (W m-2 )
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Figure 6. Rmax model predictions based upon (a) observed broadband surface PAR (green) and UVR (purple) and (b) example depth trajectories generated by LESs (black) and LESv (red) in relation to the photoactive zone (purple dashed) and the euphotic zone (green dashed). (c) Time courses of potential productivity ( and the (d) photosynthetic capacity scaling factor (Pinh) for phytoplankton on the depth trajectories shown in (b). Decreases in Pinh occur when irradiance exposure is sufficient to inhibit photosynthesis based on the BWF used in the Rmax model.
b)
2
c)
1 0
Pinh
1 LES v
0.5
LES s
d)
0 0
5
10
15
20
24
Hour
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Rapid mixing and slow repair result in high variability in the instantaneous rates of
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photosynthesis at a given depth/PAR and hysteresis in the response of individual cells/colonies
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to PAR exposure (Fig. 7). Persistent reductions in photosynthesis resulting in hysteresis in the
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photosynthesis-irradiance (P-E) response are particularly evident for particles experiencing > 70
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W m-2
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covered the entire range from
