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Mazloff, MR, Cornuelle BD, Gille ST, Verdy A.  2018.  Correlation lengths for estimating the large-scale carbon and heat content of the Southern Ocean. Journal of Geophysical Research-Oceans. 123:883-901.   10.1002/2017jc013408   AbstractWebsite

The spatial correlation scales of oceanic dissolved inorganic carbon, heat content, and carbon and heat exchanges with the atmosphere are estimated from a realistic numerical simulation of the Southern Ocean. Biases in the model are assessed by comparing the simulated sea surface height and temperature scales to those derived from optimally interpolated satellite measurements. While these products do not resolve all ocean scales, they are representative of the climate scale variability we aim to estimate. Results show that constraining the carbon and heat inventory between 35 degrees S and 70 degrees S on time-scales longer than 90 days requires approximately 100 optimally spaced measurement platforms: approximately one platform every 20 degrees longitude by 6 degrees latitude. Carbon flux has slightly longer zonal scales, and requires a coverage of approximately 30 degrees by 6 degrees. Heat flux has much longer scales, and thus a platform distribution of approximately 90 degrees by 10 degrees would be sufficient. Fluxes, however, have significant subseasonal variability. For all fields, and especially fluxes, sustained measurements in time are required to prevent aliasing of the eddy signals into the longer climate scale signals. Our results imply a minimum of 100 biogeochemical-Argo floats are required to monitor the Southern Ocean carbon and heat content and air-sea exchanges on time-scales longer than 90 days. However, an estimate of formal mapping error using the current Argo array implies that in practice even an array of 600 floats (a nominal float density of about 1 every 7 degrees longitude by 3 degrees latitude) will result in nonnegligible uncertainty in estimating climate signals.

Verdy, A, Mazloff MR, Cornuelle BD, Rudnick DL.  2016.  Estimation of the Tropical Pacific Ocean state 2010-2013. Journal of Atmospheric and Oceanic Technology. 34(7):1501-1517.   DOI: 10.1175/JTECH-D-16-0223.1   Abstract

A data-assimilating ⅓° regional dynamical ocean model is evaluated on its ability to synthesize components of the Tropical Pacific Ocean Observing System. The four-dimensional variational data assimilation (4DVAR) method adjusts initial conditions and atmospheric forcing for overlapping 4-month model runs, or hindcasts, that are then combined to give an ocean state estimate for the period 2010–13. Consistency within uncertainty with satellite SSH and Argo profiles is achieved. Comparison to independent observations from Tropical Atmosphere Ocean (TAO) moorings shows that for time scales shorter than 100 days, the state estimate improves estimates of TAO temperature relative to an optimally interpolated Argo product. The improvement is greater at time scales shorter than 20 days, although unpredicted variability in the TAO temperatures implies that TAO observations provide significant information in that band. Larger discrepancies between the state estimate and independent observations from Spray gliders deployed near the Galápagos, Palau, and Solomon Islands are attributed to insufficient model resolution to capture the dynamics in strong current regions and near coasts. The sea surface height forecast skill of the model is assessed. Model forecasts using climatological forcing and boundary conditions are more skillful than climatology out to 50 days compared to persistence, which is a more skillful forecast than climatology out to approximately 20 days. Hindcasts using reanalysis products for atmospheric forcing and open boundary conditions are more skillful than climatology for approximately 120 days or longer, with the exact time scale depending on the accuracy of the state estimate used for initializing and on the reanalysis forcing. Estimating the model representational error is a goal of these experiments.

Verdy, A, Mazloff MR, Cornuelle BD, Kim SY.  2014.  Wind-driven sea level variability on the California coast: An adjoint sensitivity analysis. Journal of Physical Oceanography. 44:297-318.   10.1175/jpo-d-13-018.1   AbstractWebsite

Effects of atmospheric forcing on coastal sea surface height near Port San Luis, central California, are investigated using a regional state estimate and its adjoint. The physical pathways for the propagation of nonlocal [O(100 km)] wind stress effects are identified through adjoint sensitivity analyses, with a cost function that is localized in space so that the adjoint shows details of the propagation of sensitivities. Transfer functions between wind stress and SSH response are calculated and compared to previous work. It is found that (i) the response to local alongshore wind stress dominates on short time scales of O(1 day); (ii) the effect of nonlocal winds dominates on longer time scales and is carried by coastally trapped waves, as well as inertia-gravity waves for offshore wind stress; and (iii) there are significant seasonal variations in the sensitivity of SSH to wind stress due to changes in stratification. In a more stratified ocean, the damping of sensitivities to local and offshore winds is reduced, allowing for a larger and longer-lasting SSH response to wind stress.

Verdy, A, Amarasekare P.  2010.  Alternative stable states in communities with intraguild predation. Journal of Theoretical Biology. 262:116-128.   10.1016/j.jtbi.2009.09.011   AbstractWebsite

Intraguild predation (IGP) is a widespread ecological phenomenon in which two consumers that share a resource also engage in a predator-prey interaction. Theory on IGP predicts the occurrence of alternative stable states, but empirical evidence of such states is scarce. This raises the question of whether alternative states are a rare phenomenon that is unlikely to be observed in nature. Here we analyze a model in which the resource exhibits logistic or chemostat dynamics and consumers have saturating (Type II) functional responses. We show that alternative states can arise for a wide range of biological scenarios and that environmental constraints can make their detection difficult. Our analysis identifies three possible combinations of alternative states: (i) IG prey or IG predator, (ii) coexistence or IG predator, and (iii) coexistence or IG prey. Bifurcation diagrams reveal that alternative states are possible over large regions of the parameter space. However. they can be limited to narrow ranges along the resource productivity axis, which may make it difficult to observe the occurrence of alternative states in communities with IGP. Microcosm experiments provide a promising avenue for detecting combinations of asymptotically stable states along a productivity gradient. (C) 2009 Elsevier Ltd. All rights reserved.

Verdy, A.  2010.  Modulation of predator-prey interactions by the Allee effect. Ecological Modelling. 221:1098-1107.   10.1016/j.ecolmodel.2010.01.005   AbstractWebsite

An Allee effect arising from density-dependent mating success can have significant impacts at the ecosystem level when considered in the context of predator-prey interactions. These are captured by a mathematical model for the exchange of biomass between a structured predator population (continuous weight distribution) and a resource. Because the predator's mating success affects the amount of resources required for the production of offsprings and their future growth into mature organisms, it influences the flux of biomass between trophic levels. Under simple assumptions, the equations can be reduced to an equivalent unstructured predator-prey model in which the Allee effect modulates the predation rate: the mating probability multiplies the rate of predator growth as well as the rate of resource depletion. Implications of the Allee effect for the bifurcation structure and equilibrium densities are examined. The model is compared to a modified version in which the Allee effect instead modulates the assimilation efficiency, hence the mating probability does not appear in the dynamical equation for the resource density. Both models exhibit qualitatively similar dynamics. However, compared to the model in which the Allee effect modulates predation, the model in which the Allee effect modulates assimilation efficiency predicts (i) unrealistically inefficient resource assimilation when predator density is low, (ii) a higher risk of catastrophic extinction resulting from a change in the parameter controlling the strength of the Allee effect, and (iii) no possibility of an increase in population size when the density dependence is enhanced. (C) 2010 Elsevier B.V. All rights reserved.

Verdy, A, Follows M, Flierl G.  2009.  Optimal phytoplankton cell size in an allometric model. Marine Ecology-Progress Series. 379:1-12.   10.3354/meps07909   AbstractWebsite

The competitive ability of phytoplankton cells is simulated in a model chemostat in which cell size is considered to be an adaptive trait. Parameters describing nutrient uptake kinetics are constrained by empirically derived allometric rules. With a steady input of a single nutrient, the evolutionarily stable cell size is selected through competition among phytoplankton. We find that large cells may be favored when (1) phytoplankton growth is limited by the rate at which internally stored inorganic nutrients can be converted into biomass, and (2) maximum quotas increase with size faster than minimum quotas. Increased internal quotas then accelerate the rate of biomass production in large cells, despite their enhanced requirements for resources. The evolutionarily stable strategy is set by the allometric relationships for nutrient uptake kinetics and by metabolism.

Verdy, A, Caswell H.  2008.  Sensitivity analysis of reactive ecological dynamics. Bulletin of Mathematical Biology. 70:1634-1659.   10.1007/s11538-008-9312-7   AbstractWebsite

Ecological systems with asymptotically stable equilibria may exhibit significant transient dynamics following perturbations. In some cases, these transient dynamics include the possibility of excursions away from the equilibrium before the eventual return; systems that exhibit such amplification of perturbations are called reactive. Reactivity is a common property of ecological systems, and the amplification can be large and long-lasting. The transient response of a reactive ecosystem depends on the parameters of the underlying model. To investigate this dependence, we develop sensitivity analyses for indices of transient dynamics (reactivity, the amplification envelope, and the optimal perturbation) in both continuous- and discrete-time models written in matrix form. The sensitivity calculations require expressions, some of them new, for the derivatives of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix calculus. Sensitivity analysis provides a quantitative framework for investigating the mechanisms leading to transient growth. We apply the methodology to a predator-prey model and a size-structured food web model. The results suggest predator-driven and prey-driven mechanisms for transient amplification resulting from multispecies interactions.

Verdy, A, Flierl G.  2008.  Evolution and social behavior in krill. Deep-Sea Research Part Ii-Topical Studies in Oceanography. 55:472-484.   10.1016/j.dsr2.2007.11.001   AbstractWebsite

We simulate the formation of social aggregations in a turbulent fluid environment. The theoretical framework is employed to investigate the ecological consequences of spatial patchiness in the density distribution of krill, which often assemble in swarms or schools. We first describe the formation of aggregations resulting from the interplay of social forces and population dynamics, and then consider an idealized ecosystem model of zooplankton with social behavior who feed on phytoplankton; this is solved analytically for the initial growth of patches and numerically for the steady-state distributions of predator and prey biomass. Environmental variability changes the linear instability criterion for spontaneous aggregation. The second part of the paper addresses the evolution of social behavior in a population with density-dependent mating success. The model simulates the transmission of a gene controlling social behavior; natural selection determines whether the grouping or non-grouping type becomes dominant. It is found that the behavior can evolve when mixing occurs rapidly enough for resources to remain available to the clustered organisms. Turbulent advection prevents the grouping type from becoming dominant if the shear of the flow is strong enough to disrupt the patches; otherwise the aggregated zooplankton benefit from enhanced diffusion of resources by the turbulent flow. (C) 2008 Elsevier Ltd. All rights reserved.

Verdy, A, Dutkiewicz S, Follows MJ, Marshall J, Czaja A.  2007.  Carbon dioxide and oxygen fluxes in the Southern Ocean: Mechanisms of interannual variability. Global Biogeochemical Cycles. 21   10.1029/2006gb002916   AbstractWebsite

[1] We analyze the variability of air-sea fluxes of carbon dioxide and oxygen in the Southern Ocean during the period 1993 - 2003 in a biogeochemical and physical simulation of the global ocean. Our results suggest that the nonseasonal variability is primarily driven by changes in entrainment of carbon-rich, oxygen-poor waters into the mixed layer during winter convection episodes. The Southern Annular Mode (SAM), known to impact the variability of air-sea fluxes of carbon dioxide, is also found to affect oxygen fluxes. We find that El Nino-Southern Oscillation (ENSO) also plays an important role in generating interannual variability in air-sea fluxes of carbon and oxygen. Anomalies driven by SAM and ENSO constitute a significant fraction of the simulated variability; the two climate indices are associated with surface heat fluxes, which control the modeled mixed layer depth variability. We adopt a Lagrangian view of tracers advected along the Antarctic Circumpolar Current (ACC) to highlight the importance of convective mixing in inducing anomalous air-sea fluxes of carbon dioxide and oxygen. The idealized Lagrangian model captures the principal features of the variability simulated by the more complex model, suggesting that knowledge of entrainment, temperature, and mean geostrophic flow in the mixed layer is sufficient to obtain a first-order description of the large-scale variability in air-sea transfer of soluble gases. Distinct spatial and temporal patterns arise from the different equilibration timescales of the two gases.

Verdy, A, Marshall J, Czaja A.  2006.  Sea surface temperature variability along the path of the antarctic circumpolar current. Journal of Physical Oceanography. 36:1317-1331.   10.1175/jpo2913.1   AbstractWebsite

The spatial and temporal distributions of sea surface temperature (SST) anomalies in the Antarctic Circumpolar Current (ACC) are investigated, using monthly data from the NCEP-NCAR reanalysis for the period 1980-2004. Patterns of atmospheric forcing are identified in observations of sea level pressure and air-sea heat fluxes. It is found that a significant fraction of SST variability in the ACC can be understood as a linear response to surface forcing by the Southern Annular Mode (SAM) and remote forcing by ENSO. The physical mechanisms rely on the interplay between atmospheric variability and mean advection by the ACC. SAM and ENSO drive a low-level anomalous circulation pattern localized over the South Pacific Ocean, inducing surface heat fluxes and Ekman heat advection anomalies. A simple model of SST propagating in the ACC, forced with heat fluxes estimated from the reanalysis, suggests that surface heat fluxes and Ekman heat advection are equally important in driving the observed SST variability. Further diagnostics indicate that SST anomalies, generated mainly upstream of Drake Passage, are subsequently advected by the ACC and damped after a couple of years. It is suggested that SST variability along the path of the ACC is largely a passive response of the oceanic mixed layer to atmospheric forcing.

Verdy, A, Jochum M.  2005.  A note on the validity of the Sverdrup balance in the Atlantic North Equatorial Countercurrent. Deep-Sea Research Part I-Oceanographic Research Papers. 52:179-188.   10.1016/j.dsr.2004.05.014   AbstractWebsite

An ocean general circulation model of the tropical Atlantic Ocean is used to study the vertically integrated vorticity equation for the annual mean flow in the Atlantic North Equatorial Countercurrent (NECC). It is found that the nonlinear terms play an important role in the vorticity budget, in the western part of the basin. Sverdrup balance does not hold in the region of the North Brazil Current retroflection, where advection of relative vorticity by the mean flow and by the eddies is important. In the eastern part of the basin, these nonlinearities are negligible and the flow appears to be in Sverdrup balance. In the model, the cut-off location occurs at 32degreesW. The results suggest that in the western part of the basin, observations relying on hydrographic data neglect two important contributions to the vorticity balance: advection of planetary vorticity by the deep meridional flow and advection of relative vorticity. (C) 2004 Elsevier Ltd. All rights reserved.