Diel vertical migration (DVM) of zooplankton and micronekton is widespread in the ocean and forms a fundamental component of the biological pump, but is generally overlooked in global models of the Earth system. We develop a parameterization of DVM in the ocean and integrate it with a size-structured NPZD model. We assess the model's ability to recreate ecosystem and DVM patterns at three well-observed Pacific sites, ALOHA, K2, and EQPAC, and use it to estimate the impact of DVM on marine ecosystems and biogeochemical dynamics. Our model includes the following: (1) a representation of migration dynamics in response to food availability and light intensity; (2) a representation of the digestive and metabolic processes that decouple zooplankton feeding from excretion, egestion, and respiration; and (3) a light-dependent parameterization of visual predation on zooplankton. The model captures the first-order patterns in plankton biomass and productivity across the biomes, including the biomass of migrating organisms. We estimate that realistic migratory populations sustain active fluxes to the mesopelagic zone equivalent to between 15% and 40% of the particle export and contribute up to half of the total respiration within the layers affected by migration. The localized active transport has important consequences for the cycling of oxygen, nutrients, and carbon. We highlight the importance of decoupling zooplankton feeding and respiration and excretion with depth for capturing the impact of migration on the redistribution of carbon and nutrients in the upper ocean.
 Zooplankton and micronekton diel vertical migration (DVM) is ubiquitous in the marine environment. In the most common DVM pattern, the nocturnal migration, organisms descend to depth before sunrise and ascend to the surface at sunset. A wealth of observations, ranging from in situ net captures to remote acoustic data, show regular DVM across a wide range of oceanographic provinces [e.g., Banse, 1964; Longhurst, 1976; Heywood, 1996; Luo et al., 2000; Steinberg et al., 2008a].
 The widespread occurrence of DVM influences the ecology of the upper ocean, modifying the patterns of grazing, predation, and ecological interactions. DVM also alters biogeochemical fluxes of nutrients, carbon, and oxygen in the water column. Excretion, fecal pellet production, and mortality at depth transfer nutrients from the surface to the deep layers, thus enhancing the efficiency of the biological pump [Longhurst and Harrison, 1988; Buesseler and Boyd, 2009]. Many studies have estimated the contributions of DVM to the biological pump in a variety of oceanographic regimes [e.g., Longhurst and Harrison, 1988; Steinberg et al., 2000]. Taken together, these studies suggest that DVM can support active fluxes equivalent to up to 10–30% of particle export.
 Active transport by DVM plays an important role in sustaining the metabolic requirements of mesopelagic communities [Buesseler et al., 2008; Robinson et al., 2010]. Recent budget analyses suggest that the energy demand of the mesopelagic ecosystem cannot be maintained by particle influxes alone. This demand can be partially met by DVM active transport [Steinberg et al. 2008b; Burd et al., 2010].
 In contrast with respiration of sinking particles, which decreases monotonically with depth, DVM respiration is enhanced within the layers where migrating organisms reside during daytime. Therefore, DVM affects the gradients of nutrients and carbon in a different way from the remineralization of particles. The effect of localized respiration could be particularly important for oxygen. In some regions, the migration depth is associated with oxygen minima. It has been suggested that reduced oxygen provides a refuge from predators [Wishner et al., 1998; Steinberg et al., 2008a]. However, it is not clear to what extent respiration by migrating organisms further exacerbates low-oxygen conditions. It is intriguing to consider the possibility that respiration by migrating organisms contributes to establishing environmental conditions that favor migratory behavior.
 Some pioneering studies modeled the distribution of vertically migrating organisms as a direct response to proximate stimuli such as light and food [e.g., Andersen and Nival, 1991; Richards et al., 1996; Han and Straškraba, 1998]. These modeling studies focused on DVM controls and patterns in an idealized setting rather than on the effects on biogeochemistry and ecology across vastly different ocean environments. The importance of DVM calls for detailed investigations of DVM impacts on the marine food web and the cycling of nutrients, oxygen, and carbon. Understanding these interactions requires the integration of a DVM model with a planktonic ecosystem model capable of capturing broad-scale biogeochemical patterns across diverse systems.
 Here, we develop a general framework to include DVM in ocean ecosystem models, and we implement it in a size-structured NPZD model that shares a common structure with more complex models currently run at broad regional and global scales. For the purpose of this work, we simply refer to the diverse assemblage of small diel vertically migrating organisms, including micronekton, as migrating “zooplankton”. The numerical simulations shown here are made in a one-dimensional physical model, although the model can easily be adapted to a three-dimensional general circulation model.
 Our objectives are as follows: (1) to assess the robustness of the modeling framework relative to observation taken in three contrasting ocean biomes, (2) to elucidate the factors that control the viability of migrating versus nonmigrating strategies across these settings, (3) to assess the biogeochemical impacts of DVM across these settings, and (4) to determine the importance of resolving the digestive and metabolic processes to estimate the biogeochemical impact of DVM.
 To address these objectives, we implement a parameterization of predatory losses consistent with existing models of visual predation in the ocean, and a representation of the processes that decouple feeding from egestion, respiration, and excretion in the water column. We test the robustness of the model by evaluating it against data from three major biomes in the Pacific Ocean for which observations are available.
 The rest of the paper is organized as follows: Section 2 describes the modeling framework, with emphasis on the formulation of vertical migration, the dynamics of zooplankton internal nutrient pools, and visual predation. Sections 3 and 4 describe the study sites and model setup. Section 5 describes the results of the simulations, focusing on ecosystem structure, DVM patterns, and water column biogeochemistry. Section 6 concludes the paper.
2 Modeling Framework
 We couple a size-structured model of the marine ecosystem that includes a representation of diel vertical migration to a one-dimensional model of the water column.
 We maintain a relatively simple representation of basic ecosystem functions across a range of oceanographic conditions, and we focus on a realistic simulation of DVM processes.
 We modify the marine ecosystem model developed by Stock and Dunne  to include vertically migrating organisms. The model by Stock and Dunne  captures the partitioning of productivity and biomass across trophic levels in response to different temperatures, nutrient supply, and euphotic zone depths and has been optimized against observations. A schematic of the model is shown in Figure 1. There are 10 state variables representing major functional groups: a generic limiting nutrient (N, expressed in nitrogen units); small and large phytoplankton (SP, LP); small, large, and large migrating zooplankton (SZ, LZ, LMZ); free-living bacteria (B); and three classes of detritus (small labile, small semilabile, and large detritus (SDL, SDS, LD, respectively); where small pools are nonsinking and equivalent to dissolved organic pools. All state variables are subject to advection and diffusion from the physical model.
 Phytoplankton mortality, zooplankton grazing, and bacterial and detritus dynamics follow the formulation of Stock and Dunne . Large detritus, representing an average over the continuous spectrum of sinking particles, sinks with a constant velocity of 20 m d−1 and decays at a temperature-dependent rate of 0.1 d−1. This gives an e-folding length scale of 200 m, which is consistent with the Martin remineralization curve in the upper ocean [Martin et al., 1987]. The decay timescales of the semilabile pool were decreased from the values in Stock and Dunne  and the partitioning between labile and semilabile pools recalibrated for consistency with observations across the ocean regions of interest for this study [Abell et al., 2000].
 The large zooplankton in Stock and Dunne  is parameterized using data from Hansen et al. , with basal metabolic rates adjusted downward relative to the estimates of Buskey , which were derived for copepods in mangrove swamps. Lower basal rates (0.02 d−1 at 20°C) were found to be essential to maintain populations in oligotrophic conditions. The large migrating zooplankton has been added in this study, and aside from the migratory behavior described in section 2.1, it follows the formulation of the nonmigrating large zooplankton.
 In order to simulate DVM in a realistic way, we introduce three major changes to the model by Stock and Dunne . First, we develop a parameterization of migration behavior in response to light intensity (section 2.1). Second, we develop a parameterization to explicitly model internal gut content and metabolite dynamics for large zooplankton and to include the metabolic costs of swimming. To this end, we subdivide LZ and LMZ into three internal nutrient pools (Figure 2), as described in section 2.2. Third, we develop a parameterization for large zooplankton mortality due to visual predation, as described in section 2.3.
2.1 Diel Vertical Migration
 It is generally agreed that DVM originates as a trade-off between the advantage of feeding in phytoplankton-rich surface layers and the advantage of residing in the deeper, darker layers during daytime, where visual predation is inhibited [e.g., Hays, 2003]. Light is considered the most important external control on DVM. However, migration patterns are also influenced by physical and chemical environmental factors, food availability, and cues from predators [Cohen and Forward, 2009]. This results in substantial variability in the timing, depths, and velocity of migrations. Realistic migration patterns can be achieved by different responses to light stimuli. Here, we assume that DVM is controlled by the absolute intensity of light, and migrating organisms cluster around a preferred isolume during daytime. The isolume hypothesis allows for a simple and realistic control on the migration patterns and is supported by experimental evidence [Cohen and Forward, 2009].
 The behavior of daily vertical migrators follows a simple set of rules that dictate the direction and velocity of migration. During daytime, zooplankton migrate toward the preferred isolume (irrDVM). For the control simulation, we choose irrDVM = 10− 3 W m− 2, a value that produces a migration depth in line with observations. At night, when light is below the preferred irradiance everywhere, zooplankton migrate toward the surface food maximum. The migration velocity (wswim) is constant everywhere except around the preferred light level and around the food maximum, where it is reduced linearly toward zero, with scales of 50 and 20 m, respectively. The choice of a smaller scale for the reduction of the swimming velocity around the food maximum compared to the preferred isolume is somewhat arbitrary and reflects the existence of sharper gradients in prey concentrations compared to the length scale of light attenuation in the water column. We set the maximum migration velocity to 3 cm s−1, comparable to the average velocity of migrating scattering layers [Heywood, 1996; Luo et al., 2000; Jiang et al., 2007].
 To prevent unrealistic model-dependent behavior, we include a biological diffusion term () for the migrating organisms. This biological diffusion is a crude way of parameterizing the effects of variations in the swimming velocities of migrating organisms, related to behavioral and physiological differences between individuals, and acts to spread the stationary daytime zooplankton layer above and below the preferred isolume depth. We estimate the magnitude of the biological diffusion from observations. Assuming a thickness for the migrating layer on the order of 10 to 100 m and a migration velocity on the order of 10−2 to 10−1 m s−1, a random swimming diffusion on the order of 10−1 to 10 m2 s−1 is required. Here we adopt m2 s− 1.
 This simple set of rules allows the formation of a localized coherent layer of migrating organisms that compares realistically with Acoustic Doppler Current Profiler (ADCP) observations of migrating scattering layers [e.g., Heywood, 1996; Luo et al., 2000]. An example of a diel migration cycle from the model is shown in Figure 3.
2.2 Zooplankton Internal Pools and Costs of Swimming
 Feeding by migrating organisms at the surface and egestion, respiration, and excretion at depth decouple particle production and nutrient regeneration from photosynthesis [Buesseler and Boyd, 2009; Robinson et al., 2010]. For vertical migration to be effective in altering the flux of particles with depth, the time associated with the gut clearance of migrating organisms must be comparable to or longer than the duration of the vertical migration (approximately 3 h). Relatively long gut clearance times have been suggested for the larger components of mesozooplankton and micronekton communities [e.g., Mackas and Bohrer, 1976]. Similar considerations apply for respiratory and excretory fluxes. Observational evidence shows high levels of respiration extending for up to 24 h following food ingestion [Hernandez-Leon and Ikeda, 2005]. The increase in respiration after feeding originates from biosynthesis processes associated with the incorporation of nutrients and carbon into organism biomass.
 We decouple egestion and metabolism from feeding by partitioning large zooplankton biomass (indicated with Z hereafter for both LZ and LMZ) into three pools (Figure 2): the gut content (Zgut), the metabolic pool (Zmetab), and the body biomass (Zbody). These pools resolve the following fluxes (Figure 2): (1) ingestion, (2) egestion, (3) assimilation, (4) catabolism, and (5) anabolism. Gut clearing is partitioned into egestion and assimilation, and metabolism is partitioned into anabolic biomass buildup and catabolic losses.
 The resulting biomass conservation equations (omitting predatory losses) are as follows:
 Details on how each term is parameterized are shown in Appendix A.
 For vertically migrating organisms (LMZ), we add an explicit catabolic loss term associated with migratory swimming (catabolismswim). We base the formulation on the linear relationship between respiration and swimming velocity proposed by Torres and Childress  to describe respiration rates in euphausiids:
 Here, wswim is the average vertical migration velocity, and wref is a reference velocity used to scale the cost of swimming with respect to basal losses (catabolismbasal). When wref is equal to wswim, active swimming doubles the respiration rate compared to basal activity. The numerical value of wref is relatively unconstrained but can be inferred from observations of zooplankton respiratory rates under different levels of swimming activity. For example, the study by Torres and Childress  suggests values for wref between approximately 1 and 3 cm s−1. This spans routine swimming velocities (approximately 1 cm s−1) and active swimming velocities (approximately 3 cm s−1). In this study we adopt wref = 7 cm s−1 for the control simulations, as we found that a relatively high wref (low swimming cost) is required to maintain realistic populations of migrating organisms. This was particularly true for oligotrophic subtropical regions and will be discussed further in section 4.2.
2.3 Visual Predation
 We implement a parameterization of visual predation to represent the advantage of daytime migration to the deep dark layers and test the sensitivity of the model to the parameter choice. In Appendix B, we derive a functional response for predatory losses based on existing models of visual feeding in the marine environment. The functional response combines the effects of prey density and light availability on predator feeding rates and is based on the ability of visual predators to encounter, recognize, and harvest their prey. The resulting functional form for the rate of ingestion of LZ and LMZ per unit biomass of visual and nonvisual higher trophic-level predators (IHP, d− 1) is as follows:
 Here, (d−1) is the maximum feeding rate of all predators, Z (mmol −3) is the combined biomass of LZ and LMZ, KZ (mmol −3) is the half saturation constant for prey density dependence, αv is the maximum fraction of predation due to visual predators, irr (W m−2) is the in situ irradiance, and Kirr (W m−2) is the half saturation constant for the light response of visual predators (see Appendix B for details).
 For this study, we adopt and KZ values from Stock and Dunne , where was derived by extrapolating the allometric relationship of Hansen et al. , and Kz was calibrated to match global-scale patterns in observed plankton biomass and turnover rates. Limited data exist to constrain the numerical values for Kirr and αv in the open ocean. Measurements of the feeding rate of the coastal fish Gobiusculus flavescens indicate a half saturation constant for the light response , or approximately 1.7 × 10−1 W m−2 [Sornes and Aksnes, 2004]. For the model control runs, we adopt αv = 0.9, to reflect the advantage of visual predation in well-lit waters [Sornes and Aksnes, 2004], and Kirr = 10− 1 W m− 2. The sensitivity of the model to changes in the visual predation parameters αv and Kirr is discussed in section 4.2.
 A plot of the dependence of the limitation factor on local irradiance and prey concentration is shown in Figure 4. At low prey concentrations, the ingestion decreases to zero regardless of light levels. At low irradiances (irr << Kirr), the light-dependent term decreases and nonvisual predation dominates. At high irradiances, the light-dependent term quickly saturates to 1, and the response reduces to a Holling type II dependence with half-saturation constant Kz.
 Converting the higher predator ingestion rate in Figure 4 to an overall loss rate requires an estimate of the biomass of higher trophic-level predators. For the simulations herein, we assume that the biomass of higher predators adjusts in proportion to the biomass of the available prey. This assumption is consistent with widely applied quadratic zooplankton mortality closures [e.g., Steele and Henderson, 1992] as well as the observed tendency for roughly equal biomass of marine organisms in logarithmically spaced size bins [Sheldon et al., 1972].
3 Study Sites
 We couple the ecosystem model to a one-dimensional physical model implemented for a variety of oceanographic conditions. We choose three sites with a range of temperatures and productivities, for which numerous observations are available: station K2 (161°E, 47°N) [Buesseler et al., 2008], station ALOHA (158°W, 22.5°N) [Karl et al., 1996], and one of the EQPAC sites of the U.S. JGOFS process study (140°W, 0°N) [Murray et al., 1995]. Table 2 summarizes the observed ecosystem properties for the three sites.
 Station K2, a productive cold-water site with strong seasonality, shows a phytoplankton bloom associated with incomplete nutrient drawdown as the mixed layer shallows from winter values (80–120 m) to spring/summer values (20–40 m). Picoplankton (size class < 2 µm) dominate biomass and productivity. However, in contrast with the two other sites of this study, large diatoms (> 20 µm) become important during blooms and contribute to the high levels of particle export both directly and by sustaining abundant mesozooplankton populations [Boyd et al., 2008]. Migrating organisms comprise approximately 60% of the mesozooplankton population and reach depths between 200 and 400 m [Steinberg et al., 2008a].
 Ocean station ALOHA is characterized by warm-water oligotrophic conditions. Wintertime mixed layers as deep as 80–100 m fail to reach the nutricline, and nutrients are strongly depleted near the surface. Measurements show low chlorophyll and limited seasonality [Brix et al., 2006]. Picophytoplankton dominate over larger autotrophs; low productivities sustain a microbial loop with high nutrient recycling and limited export [Brix et al., 2006; Buesseler et al., 2007]. Approximately 40% of mesozooplankton migrate diurnally to depths between 400 and 700 m [Al-Mutahiri and Landry, 2001; Steinberg et al. 2008a]. The proportion of migrating zooplankton increases to more than 70% for size classes larger than 2000 µm.
 In the warm-water high-productivity EQPAC site, surface nutrients are never completely depleted, and little seasonality is observed [Lindley et al., 1995]. Most variability is associated with the passage of equatorial waves and with ENSO dynamics [Murray et al., 1995]. Contrary to other productive regions, small phytoplankton assemblages (pico and nanoplankton) dominate [Lindley et al., 1995]. This favors the regeneration loop and reduces particle export [Buesseler et al., 1995]. Approximately 40% of mesozooplankton migrate daily to depths between 300 and 400 m. The proportion increases to more than 70% for size classes larger than 2000 µm [Decima et al., 2011].
4 Model Implementation
 The physical model is a one-dimensional mixed layer/ocean interior model based on a Mellor-Yamada turbulence closure scheme [Kearney et al., 2012]. The model is forced with surface winds, air temperatures, and short-wave irradiances from a reanalysis-based climatology (CORE) [Griffies et al., 2009]. We modulate the mean climatological short-wave irradiance by imposing a seasonally varying diurnal light cycle. Light penetration in the water column follows the two-band, chlorophyll-dependent light absorption scheme of Manizza et al. , using the model-predicted chlorophyll. The interior background diffusivity () at each site was adjusted slightly to improve the fidelity of the physical simulations with the observed seasonal evolution of the mixed layer. We set to 3.0 ⋅ 10− 5, 8.0 ⋅ 10− 5, and 5.0 ⋅ 10− 5 m2s− 1 at K2, ALOHA, and EQPAC, respectively, and add a small uniform upwelling velocity (1.0 ⋅ 10− 7 m s− 1) at EQPAC. In order to prevent long-term drifts in the physical variables and subsurface nutrient trapping, we include a restoring term for temperature and salinity (90 days timescale) and dissolved nutrients (5 year timescale) to monthly climatologies from the World Ocean Atlas.
 The numerical values of the parameters controlling DVM are shown in Table 1. The remaining ecosystem parameters have been taken from the optimization study by Stock and Dunne  as described above (see also Appendixes A and B). We solve the model equations with 5 m vertical resolution, using a forward integration with a time step of 1 h, sufficient to resolve the details of vertical migrations. Additional tests showed good agreement between solutions obtained with finer vertical grids and smaller time steps.
Table 1. Parameters Controlling the Processes Associated With DVM in the Modela
References: (1) Mean irradiance at the DVM depth, estimated from the maximum subsurface backscatter amplitude from a global compilation of ADCP observations (D. Bianchi et al., manuscript in preparation, 2013); (2) Heywood ; (3) Luo et al. ; (4) see section 2.1; (5) Mackas and Bohrer ; (6) Hernandez-Leon and Ikeda ; (7) relatively unconstrained parameters, see the references and discussion in sections 2.2 and 2.3, and the sensitivity analysis in section 4.2.
10− 3 W m− 2
3 cm s− 1
Zooplankton biological diffusion
10− 1 m2 s− 1
Gut clearance rate
3 h− 1
Assimilated pool utilization rate
24 h− 1
Reference velocity to scale the costs of swimming
7 cm s− 1
Visual predation fraction
Half saturation response for light limitation
10− 1 W m− 2
5 Model Results
 The model captures the primary cross-ecosystem differences of water column hydrography, seasonal mixing dynamics, and plankton biomass and productivity across the three study sites (Figure 5 and Table 2). At K2, net primary production (NPP) and particle export are in the range suggested by observations. Depth-integrated chlorophyll and phytoplankton biomass are on the higher end of observations. This might reflect a deeper euphotic zone in the simulation compared to observations (Figure 5). Large phytoplankton account on average for 30–40% of primary producers and dominate during the spring bloom.
Table 2. Ecosystem Diagnostics for theThree Model Implementation Sitesa
For each site, the first column shows observational values, and the second column shows model results. The variables shown are as follows: ZEUPH = euphotic zone depth; NPP = net primary production; CHL = chlorophyll; SP + LP = total phytoplankton biomass; LP:SP + LP = fraction of large phytoplankton; C:CHL = carbon to chlorophyll ratio; SZ = microzooplankton biomass; LZ + LMZ = mesozooplankton and micronekton biomass; LMZ = migratory zooplankton and micronekton biomass; LMZ:LZ + LMZ = fraction of diel vertical migrating mesozooplantkon and micronekton; POC FLUX = particulate organic carbon export from the euphotic zone; PE-RATIO = ratio between POC export and NPP at the base of the euphotic zone; DVM depth = depth of the relative maximum in annual mean subsurface LMZ biomass. Biomass values are integrals over the euphotic zone. Numbers in parentheses and italics represent the following references:
(1) Harrison et al. . Summertime euphotic zone depth and chlorophyll in the western subarctic gyre of the Pacific Ocean.
(2) Boyd et al. . Euphotic zone depths defined by NPP > 0. K2 productivity is the annual range in the WSG from several studies. LP:LP + SP values between 0.1 and 0.3 at ALOHA are taken from Figure 1.
(3) Dunne et al. . Annual means from satellite-based estimates. Values at K2 assume a euphotic zone depth of 55 m for integrated chlorophyll.
(4) Honda et al. . Annual mean NPP from satellite-based estimates.
(5) Elsksens et al. . NPP values after a summer bloom at K2.
(6) Shiomoto et al. . Summertime NPP for the western subarctic gyre of the Pacific Ocean.
(7) Annual average chlorophyll concentrations from the World Ocean Atlas [O'Brien et al., 2002] integrated over the euphotic zone.
(8) Biomasses estimates from the annual mean Chl, assuming an average Chl:C of 60 (see the supplementary material in Stock and Dunne ).
(9) The lower value is calculated from the SP biomass estimate from Zhan et al. , 55 mmol C m− 2, assuming LP:LP + SP fraction equal to 0.3 (references 10 and 11).
(10) Liu et al. . Fraction of SP (picophytoplankton) from a compilation of studies for the western subarctic gyre of the Pacific Ocean. Note that nanoplankton contributes substantially—therefore, the SP fraction could be larger than that accounted by picophytoplankton alone.
(11) Stock and Dunne . Supplementary information. The LP:LP + SP fraction from line P in the eastern subarctic gyre is reported instead of K2. This is likely to be an underestimate for K2.
(12) Steinberg et al. [2008a]. Total mesozooplankton biomass (size > 330 µm) from 0 to 150 m at night. Migratory fraction was estimated from night-day biomass difference.
(13) Buesseler et al. . Two summer surveys at both K2 and ALOHA.
(14) Brix et al. . Annual climatological NPP and clorophyll.
(15) Karl et al. . The study reports total phytoplanktonic biomass. Partitioning between LP and SP is estimated by assuming that 20% of biomass is in the LP size range following references (2) and (11).
(16) Al-Mutahiri and Landry . Mesozooplankton biomass in the upper 150 m. DVM fraction increases to more than 0.6 for size classes larger than 2000 µm.
(17) Taylor et al. . Chlorophyll and biomasses integrated over the euphotic zone. SP includes both nano and picophytoplankton. SZ includes all heterotrophic flagellates and ciliates.
(18) Landry et al. . Biomasses averaged between 4°N–4°S and 110°W–140°W from two 2004–2005 cruises.
(19) Barber et al. . NPP between 1°S and 1°N from two 1992 surveys during and after a major El Nino event.
(20) Chavez et al. . NPP average between 5°S–5°N from two 1992 surveys between 95°W–170°W. Photosynthetic biomass and chlorophyll are the average of climatological values and the two 1992 surveys, assuming a euphotic zone depth of 110 m.
(21) Decima et al. . Total mesozooplankton biomass (size > 500 µm) in the euphotic zone. The migratory fraction is estimated as night-day difference.
(22) Buesseler et al. . POC fluxes at the equator from two 1992 surveys. Values decrease to approximately 2 mmol C m− 2d− 1for the region between 4°N and 4°S.
(23) Buesseler and Boyd . Compilation and review of existing estimates of NPP and POC fluxes.
(24) Depth of maximum subsurface backscatter amplitude from a global compilation of ADCP observations (D. Bianchi et al., unpublished data, 2013).
NPP (mmol C m− 2d− 1)
72 ± 8 (18)
95 ± 7 (19)
77 ± 27 (20)
CHL (mg m− 2)
29 ± 3 (1)
24 ± 6 (17)
SP + LP (mmol C m− 2d− 1)
114 ± 25 (17)
164 ± 36 (20)
LP:SP + LP
0.19 ± 0.7 (17)
64 ± 15 (17)
SZ (mmol C m− 2d− 1)
31 ± 10 (17)
LZ + LMZ (mmol C m− 2d− 1)
25–29.5 (12, 16)
83 ± 7 (21)
LMZ (mmol C m− 2d− 1)
LMZ:LZ + LMZ
POC FLUX mmol C m− 2d− 1)
0.11–0.25 (13, 23)
0.07 (14, 23)
DVM depth (m)
380 ± 40 (24)
310 ± 20 (24)
500 ± 50 (24)
 At ALOHA, euphotic zone depth, net primary production, particle export, chlorophyll, and biomasses are close to observations. Little seasonality is present. The fraction of large phytoplankton, 21%, is similar to observations.
 At EQPAC, euphotic zone depth chlorophyll, biomasses, and particle export are close to the observed range. NPP is less than that observed at the equator, but similar to the productivity of the surrounding region [e.g., Landry et al., 2011]. The proportion of phytoplankton in the large size classes, 16%, is in the range of existing estimates (e.g., 9–23%) [Taylor et al., 2011).
5.1 DVM Patterns
 The differences in zooplankton biomass are captured reasonably well by the model (Table 2). The fractions of vertically migrating zooplankton at K2 and ALOHA are similar to observations (63% and 31% relative to 60% and 40% found by Steinberg et al. [2008a]). The migratory biomass at EQPAC is consistent with observations in falling between the high biomass at K2 and low biomass at ALOHA; however, the migratory fraction (68%) is larger than that suggested by some studies (e.g., 40 %) [Decima et al., 2011]. It should be noted that measurements of migrating biomass are scarce and limited in time. Additionally, the inclusion of micronekton, relatively unconstrained due to sampling difficulties, could substantially increase the proportion of migrating organisms [e.g., Hidaka et al., 2001]. Therefore, studies that focus on zooplankton probably underestimate the total migratory biomass.
 The isolume hypothesis explains first-order differences in the migration patterns. Observations show that migrating organisms cluster at approximately 200–400 m depth at K2, 400–600 m depth at ALOHA, and approximately 340–420 m at EQPAC [e.g., Steinberg et al., 2008a] (see also Table 2). The model migration depths at K2 (340 m), ALOHA (440 m), and EQPAC (410 m) are close to the observed range. This suggests that the isolume hypothesis is adequate to explain the first-order patterns of migration.
5.2 Sensitivity of DVM to the Model Parameters
 We run a set of simulations to explore the model sensitivity to the parameters that control DVM. We focus the analysis on the visual predation fraction (αv), the costs of swimming (wref), the preferred isolume (irrDVM), and the half saturation constant for the light response (Kirr). Substantial uncertainty exists regarding these parameters. The values adopted for the control runs (summarized in Table 1) are chosen based on both published studies and from analysis of the sensitivity studies. The fraction of zooplankton and micronekton undergoing migration was the primary ecosystem property affected by changes in these parameters, and discussion is limited to this property.
 The results of the sensitivity studies are shown in Figure 6. As the fraction of predation from visual predators (αv) increases, DVM becomes an increasingly important mechanism to reduce predatory losses. This increases the proportion of migrating organisms. The response is similar at the three model locations. When all predatory losses are due to visual grazing, migratory zooplankton account for nearly 90% of large zooplankton at K2 and EQPAC and 40% at ALOHA. On the opposite side of the spectrum, at lower levels of visual predation, a non-negligible fraction of migrating organisms remains. When most predatory losses are due to nonvisual predators, the proportion of migrating zooplankton decreases to 30–40% at K2 and EQPAC and around 20% at ALOHA.
 The study by Torres and Childress , based on measurements of respiration in euphausiids, suggests wref values around 2–3 cm s−1. We find that this range supports a realistic migrating population at EQPAC and K2, where the costs of swimming become negligible above wref ≈ 4 cm s−1. This is not the case at ALOHA, where wref values around 7 cm s−1 or larger are required to sustain migratory organisms. At ALOHA, basal metabolic rates are close in value to ingestion rates, due to the low availability of food sources and the higher mesopelagic water temperatures. Therefore, even a small relative increase in metabolism, for example, due to migratory costs, can induce the collapse of the migratory population. This result mirrors the reduction in basal metabolic rates that Stock and Dunne  found necessary to capture mesozooplankton patterns in extremely low-productivity environments.
 The preferred isolume (irrDVM) has a moderate effect on the proportion of migrating zooplankton. Isolumes between 10− 4 and 10− 2 W m−2 produce the largest migrating populations. Deepening of the isolumes results in modest changes in the migrating fractions perhaps due to the low costs of migration (wref = 7 cm s−1) in the control runs. Higher migratory costs lead to a sharper reduction in the migratory fraction for preferred isolumes of very low light intensity (not shown). This reduction occurs as the preferred isolumes rise into the surface layers where visual predation is stronger.
 A substantial uncertainty exists in the value of the half saturation constant for the light response of visual predators (Kirr). Fortunately, we find a limited sensitivity of the migrating biomass to this parameter, suggesting that emergent patterns in migrating fraction provide minimal additional constraints for this parameter.
 It is notable that there is no single parameter change that can reduce the modeled fractions of zooplankton that are migrating to 40% at EQPAC while also maintaining fractions near 60% at K2. Indeed, the migratory fraction at EQPAC is equal to or slightly larger than that at K2 for nearly all the parameter choices considered. While a complete multidimensional search was beyond the scope of this paper, the tendency of the model to overestimate the migratory fraction at EQPAC suggests that an additional significant factor may be missing from either the migration model structure or the environmental forcing included in the 1D modeling framework at this site.
5.3 Biogeochemical Impacts of DVM
 The model fidelity with the overall productivity, particle export, migratory biomass, and depth of migration supports further diagnosis of the biogeochemical impacts of DVM. We thus quantify the relevance of the different export pathways at the three model sites. We define net community production (NCP) as the difference between the primary production and the total respiration within the euphotic zone. At steady state, over the course of a seasonal cycle, the NCP is equal to the total organic matter exported from the euphotic zone. We further break down NCP into contributions from sinking particles, DVM active transport, and mixing of nonsinking detritus and other functional groups out of the euphotic zone. The DVM active transport flux is calculated from the time-averaged advective and diffusive fluxes of LMZ biomass:
 When averaged over a full migration cycle, the residual between the downward and upward migratory fluxes reflects the combined effect of respiration, egestion, and mortality of migrating organisms below the depth horizon considered.
 From these fluxes, we calculate classical ratios such as the e-ratio and pe-ratio (the ratios between total export and particle export and NPP, respectively) and define a dvm-ratio (the ratio between active transport and export of nonsinking organic matter and NPP). We also include an analog for the export of nonsinking organic matter, the dom-ratio, defined as the ratio between the downward flux of dissolved detritus and other nonsinking organic matter by mixing and the NPP. The export results are summarized in Table 3. High levels of export characterize the subarctic ecosystem, with approximately 40% of NPP leaving the euphotic zone over the course of the year. In comparison, the two warm-water sites show high levels of nutrient recycling, with exports limited to approximately 9–14% of the net primary production. At the three sites, sinking particles are the largest source of export. Active transport by DVM and detrainment/diffusion of nonsinking detritus show similar contributions, with values of 1% and 3% of NPP at ALOHA and EQPAC to 7% and 10%, respectively, at K2.
Table 3. Net Primary Production (NPP), Net Community Production (NCP), Export due to Sinking Organic Matter, Export due to Downward Mixing of Nonsinking Organic Matter, Export due to DVM, e-ratio (NCP/NPP), pe-ratio (POC FLUX/NPP), dom-ratio (Export of Nonsinking Organic Matter/NPP), dvm-ratio (DVM Flux/NPP), and Ratio Between DVM and POC Fluxesa
Productivities represent integrals over the euphotic zone; exports are calculated at the euphotic zone boundary. Unit for production and fluxes is mmol C m− 2d− 1.
DVM flux:POC flux
 Ultimately, the majority of export is respired in the mesopelagic zone. However, the distribution of respiratory and excretory fluxes in the water column changes with the process considered. Figure 7 shows the sources of organic and inorganic carbon in the mesopelagic zone, including the production of detritus by migrating organisms. Figure 8 shows the relative contribution of each of these sources to the total export in the mesopelagic zone. Remineralization of sinking particles represents the largest term at all depths. However, around the migration depth, excretion and respiration become major sources of dissolved nutrients and carbon. Here, DVM export is returned to the dissolved pools within a relatively narrow layer (150–200 m thick), where migratory respiration contributes 24%, 25%, and 44% of the total respiration at K2, ALOHA, and EQPAC, respectively. In addition to respiration, DVM locally increases particulate detritus via fecal pellet production and mortality.
 A variety of sources contribute to the “other” respiration and detrital production in Figures 7 and 8. Among these, respiration of nonsinking detritus (i.e., “dissolved” material) represents the largest term. As shown in Figure 7, these respiration terms are limited to the upper layers and become small below ~150 m depth.
 Filter feeding by migrating zooplankton at depth was not included in the control simulations and can transfer additional nutrients and carbon from sinking particles to the dissolved pools. A number of taxa are known to feed on particles at depth [Steinberg et al., 2008a]. However, it is not clear to what extent migrating zooplankton adopt this feeding strategy. Evidence exists suggesting that migrating zooplankton mostly feed in the surface layers at night and leave the mesopelagic zone with nearly empty guts [Longhurst and Harrison, 1988], suggesting limited filter feeding at depth by migrating organisms. We tested the sensitivity of model results to filter feeding behavior by increasing the availability of sinking particles for consumption by large zooplankton from 0% to 50%. This change has minor effects on ecosystem structure and euphotic zone fluxes and increases respiration by approximately 10% around the migration depth.
5.3.1 Mesopelagic Export and Sensitivity to Internal Nutrient Pool Dynamics
 We evaluate the importance of active (DVM) versus passive (sinking POM) export in the mesopelagic zone by considering the ratios between these fluxes at 150 m depth, adopted here as upper boundary of the mesopelagic domain. These ratios are summarized in Table 4. Active transports amount to 15–40% of the export due to particles alone. This is similar to the proportion of export by DVM versus particles from the euphotic zone. The caveat to this result is that the potential overestimation of the migratory fraction at EQPAC establishes the upper bound of 40%.
Table 4. Ratio Between DVM and POC Exports at 150 m Deptha
First row: full model, including gut and metabolic pool dynamics; second row: model without gut and metabolic pool dynamics; third row: model with gut pool dynamics only; fourth row: model with metabolic pool dynamics only. The gut dynamics represents the partitioning of ingested food to egestion and assimilation, with a timescale of 3 h. The metabolic pool dynamics represents the metabolic utilization of the assimilated food, which is partitioned into respiration and biomass buildup, with a timescale of 24 h.
Control runs: gut and metabolic pool dynamics
No internal dynamics
Gut pool dynamics only
Metabolic pool dynamics only
 We conducted a set of sensitivity experiments to determine the importance of decoupling zooplankton feeding, egestion, and excretion on the relative contributions of active to passive exports. Three sets of simulations were run where we turned off gut content and metabolic pool dynamics (Table 4). When no internal pools are considered, egestion and excretion occur at the same time as feeding. In this case, the only losses at depth are basal metabolic activity and predatory losses. This leads to a reduction of active fluxes by a factor of between 2.5 to 4 compared to the full internal pool dynamics. The inclusion of either gut content or metabolic pools decouples feeding and losses and results in a substantial increase in the deep export. Somewhat unexpectedly, gut passage and assimilated pool dynamics have similar individual impacts on export, despite the fact that the gut passage time is comparable to the migration timescale, while the assimilation timescale is longer. The results are similar for depth horizons deeper than 150 m, and emphasize the importance of delayed egestion and metabolism for determining the magnitude of export due to migrations.
6 Discussion and Conclusions
 We have developed a framework to represent explicit diel vertical migrations and integrated this framework with a size-structured model of the marine food web with a similar structure to those presently used in global ecosystem and biogeochemical studies. The model includes vertically migrating organisms and captures basic observed ecological patterns, including planktonic biomass, productivity, and export fluxes and biomasses across a gradient of oceanographic conditions. A single set of parameters captures major differences in the biomass of migrating versus nonmigrating organisms across the systems considered. The migratory biomass fraction is well captured at two sites (K2 and ALOHA) but may be overestimated at EQPAC.
 Sensitivity studies within the existing model structure did not reveal any simple adjustments which are able to address the EQPAC discrepancy without degrading the fit in other areas. It is possible that factors not considered in this study play a significant role in controlling migratory patterns. These could include regional adaptations as well as additional environmental variables. For example, low subsurface oxygen concentration at EQPAC can have both positive and negative impacts on the favorability of migration. In some cases, low oxygen appears to serve as a barrier to migrants attaining preferred depths and make predator avoidance less effective. It has been postulated that extremely shallow oxyclines may help concentrate zooplankton prey for rapid consumption by small pelagic fish [e.g., Chavez and Messié, 2009]. Alternatively, low oxygen may provide additional refuge from predation to zooplankton species that are more tolerant of these conditions than their predators. A net negative effect of low subsurface oxygen could help reduce the migratory fraction in the equatorial region while not effecting fractions at K2 and ALOHA.
 In the model, the fraction of migrating organisms increases with ecosystem productivity. This is surprising given that visual predation should be stronger in light-replete oligotrophic regions (e.g., station ALOHA), thus favoring predator avoidance strategies. However, we find that the benefits of a reduced visual predation are compensated in the model by the metabolic costs of DVM. Among the parameters controlling DVM, the proportion of grazing due to visual predation and the metabolic costs of swimming have the largest influence on the proportion of migrating zooplankton. The energy requirements of DVM have a stronger impact in the oligotrophic gyre compared to more productive sites. Matching the migratory biomass at the oligotrophic site requires a reduction of the costs of swimming compared to the values suggested by some observational estimates [Torres and Childress, 1983]. The results of the sensitivity studies illustrate that the trend of increasing DVM with increasing productivity can be explained based on the magnitude of consumption relative to metabolic needs. In cases where consumption is low and basal and swimming metabolic costs are high (i.e., station ALOHA), the cost of diurnal migration is not profitable relative to the advantage of increased time spent scavenging for sparse food resources.
 Realistic representations of both the planktonic ecosystem structure and DVM patterns allow us to investigate the impacts of DVM on water column biogeochemistry. Active transport by migrating zooplankton in our model contributes approximately 10–20% of total export from the euphotic zone. This proportion increases when considering the export to the mesopelagic zone. Here, realistic migratory populations sustain active fluxes equivalent to between 15% and 40% of the particle export.
 The impact of active transport on vertical profiles of respiration, excretion, and POC production is significant. Whereas the respiration of sinking detritus decreases with depth, respiration by migrating organisms is concentrated in a 100–200 m thick layer around the daytime migration depth. In these layers, DVM respiratory fluxes account for up to one half of the total respiration. Filter feeding at depth, a largely unconstrained process, can increase this proportion.
 In order to capture the full impact of active transport in the mesopelagic zone, it is important to decouple zooplankton egestion and excretion from feeding in the water column. We addressed this process by including gut passage and assimilated nutrient dynamics. The inclusion of these mechanisms increases respiration at depth by up to four times compared to the case where no decoupling is considered.
 Our results indicate that active transport has a strong influence on the local patterns of nutrient regeneration and oxygen consumption in the mesopelagic zone. Due to the oxygen sensitivity of several migrating taxa [e.g., Wishner et al., 1998], changes in oxygen could feedback onto the migration patterns themselves. Large predators are often characterized as having low tolerance to reduced oxygen concentrations compared to migrating organisms, and daytime migration depths could be modulated in several regions by the presence of oxygen minima [Steinberg et al., 2008a]. The possibility that respiratory fluxes by DVM organisms may contribute to the formation and maintenance of oxygen minima is under investigation. Modeling studies have highlighted the dependence of air-sea carbon partitioning on the strength of the biological carbon pump and on the distribution of respiratory processes in the water column [e.g., Kwon et al., 2009]. DVM active transport is different from particle export in that it focuses its effect in a localized and relatively shallow region of the water column. A shallow remineralization favors the recycling of nutrients and carbon in the upper ocean. It is important to establish the global effect of DVM on the global nutrient and carbon cycles and to what extent it differs from other export mechanisms.
 DVM patterns are potentially susceptible to natural and human-induced changes. These responses need to be investigated in a qualitative and quantitative way. Fully coupled three-dimensional simulations of the ocean ecosystem and biogeochemistry including explicit or implicit representations of DVM can be used to address these questions. Our study highlights the importance of resolving processes usually overlooked in global simulations and serves as a foundation for developing DVM parameterizations in Earth system models.
Zooplankton Internal Pool Dynamics
 The conservation equations for large zooplankton biomass (LZ and LMZ) described in section 2.2 (omitting predatory losses for clarity) are as follows:
 We parameterize gut clearing as a first-order process, equivalent to an exponential decay of gut content in the absence of ingestion [Mackas and Bohrer, 1976]. We partition clearing into egestion and assimilation components:
 Here kclear is the temperature-dependent gut clearance rate, and γegest is the fraction of gut clearing that is egested. We choose a value for kclear of 8.0 d−1, corresponding to an e-folding timescale for gut content of 3 h at 20°C [Mackas and Bohrer, 1976], and we set γegest = 0.35 to give an overall assimilation efficiency (0.65) in the typical observed range [Carlotti et al., 2000].
 We divide catabolism into a basal component assumed to be proportional to biomass and a component related to the feeding activity [Flynn, 2005]:
 Here kmetab is the temperature-dependent rate for the utilization of metabolites. We assume a value for kmetab equal to 1.0 d−1, implying an e-folding timescale for the metabolic pool of 24 h, compatible with the results reported by Hernandez-Leon and Ikeda .
 Similar to Stock and Dunne , we divide catabolism into a basal component, assumed to be proportional to biomass, and a component related to the feeding activity:
 Here, μbasal is a temperature-dependent basal rate, 0.02 d−1 as in Stock and Dunne , and γcatab (here 0.54) is the fraction of metabolism that is lost to the processes associated with grazing, digesting, and assimilating food. The catabolic costs are set to allow a gross growth efficiency of 0.30 when the basal metabolic cost is small relative to the food intake [e.g., Hansen et al., 1997], resulting in γcatab= 0.54.
 At steady state, clearing and metabolism are both proportional to the ingestion rate. This allows us to choose the values of γegest and γcatab (0.35 and 0.54, respectively) to maintain, in a steady state sense, the same partitioning of ingestion into egestion and respiration as in Stock and Dunne .
 Vertically migrating organisms (LMZ) include additional respiratory losses due to active swimming, as detailed in section 2.2:
 Therefore, the cost of swimming is represented by the factor .
 Anabolism, corresponding to biomass buildup, is calculated as the difference between metabolism and the three catabolic components:
Derivation of the Visual Predation Model
 We start with the theoretical model of Aksnes and Giske , based on the Holling disk equation. The Holling disk equation relates the maximum feeding rate of a predator to the prey encounter rate and the time spent on searching and handling prey. Here we consider the case of a population of high-order visual predators (HPv) feeding on large zooplankton (Z = LZ + LMZ). Following the model of Aksnes and Giske , the specific ingestion rate of a visual predator (prey s− 1 predator− 1) on preys can be expressed as:
 Here h (s predator prey− 1) is the handling time, and a (m3 s− 1 predator− 1) is the prey encounter rate for predators. The encounter rate can be related to the volume of water cruised by the predator as a function of the cruising velocity v (m s− 1), the predator visual range r (m), and the reactive field angle (θ) to obtain
 The visual range is generally a function of the predator visual system, prey size, and contrast and of ambient light levels. Aksens and Utne  developed a prey detection criterion that relates the visual range to the ambient irradiance irr (W m− 2) based on the neural response of the predators to visual stimuli. The resulting nonlinear equation can be expressed as follows:
where c is the beam attenuation coefficient; T1 is a predator and prey-specific sensitivity parameter, proportional to the prey cross-sectional area and contrast; and Kirr (W m− 2) is the half saturation constant for the light response of predators. For the parameter range encountered in the ocean, a good approximation to the equation is obtained by ignoring the exponential term [Huse and Fiksen, 2010]:
 This approximation overestimates the true visual range, and its validity depends on the magnitude of the sensitivity parameter T1. However, over a wide set of values for T1, the approximate visual range is less than 10% which is larger than the true visual range, suggesting that the approximation is good for predator-prey interactions in the marine environment. By using the approximate visual range, the encounter rate can be related to ambient irradiance:
where amax = π T1 sin 2θ v.
 We can now combine the equation for the ingestion rate with the equation for the encounter rate a to obtain:
 By setting and and converting the units from predator and prey number to biomass, the equation can be rewritten as follows:
where now the units are d−1 and mmol N m−3 for , and Z and , respectively. This equation combines the dependence of the feeding rate on irradiance and prey density in a single expression controlled by three parameters (, Kirr, and ). The same equation can describe nonvisual predation when the light dependence is dropped (Kirr = 0), giving a classical Holling disk equation for nonvisual predators (HPnv):
 We implement visual and nonvisual predatory losses for both large zooplankton and migrating organisms. Following Stock and Dunne , we assume that the biomass of high-order predators (HP) is proportional to the prey biomass, and we allow for two separate contributions from visual and nonvisual predators. The ingestion rate of HPon the available prey (Z) is given by the following equation:
 Here and are the maximum ingestion rates of visual and nonvisual predators. Handling times and encounter rates for a variety of visual and tactile predators suggest feeding rates for visual predators of at least one order of magnitude larger than those for nonvisual predators, and similar half saturation constants [Sørnes and Aksnes, 2004]. Therefore, as a further simplification, we assume that the half saturation constants for prey density dependence are of the same magnitude, that is, . Under this approximation, the feeding rate of high-order predators can be simplified to
 Here, is the maximum feeding rate of all high-order predators, and is the relative contribution from visual predators. Following Stock and Dunne , we adopt KZ = 1.0 mmol N m− 3.
 The authors would like to thank John Dunne for insightful comments on this work. Daniele Bianchi and Eric Galbraith acknowledge funding from the Canadian Institute for Advanced Research. Daniele Bianchi was supported by the U.S. Department of Energy grant DE-FG02-07ER64467 while at Princeton. Jorge Sarmiento was sponsored by BP Carbon Mitigation Initiative project at Princeton University.