Arakawa, A. and Lamb, V. R.: Computational design of the basic dynamical processes of the UCLA general circulation model, edited by: Arakawa, A. and Lamb, V. R., in: General circulation models of the atmosphere, methods in computational physics: Advances in research and application, vol. 17, 173–265, Elsevier, Amsterdam, https://doi.org/10.1016/B978-0-12-460817-7.50009-4, 1977.
Banas, N. S., Conway-Cranos, L., Sutherland, D. A., MacCready, P., Kiffney, P., and Plummer, M.: Patterns of river influence and connectivity among subbasins of Puget Sound, with application to bacterial and nutrient loading, Estuar. Coast., 38, 735–753, https://doi.org/10.1007/s12237-014-9853-y, 2015.
Blanke, B. and Raynaud, S.: Kinematics of the Pacific equatorial undercurrent: An Eulerian and Lagrangian approach from GCM results, J. Phys. Oceanogr., 27, 1038–1053, 1997.
Brasseale, E., Grason, E. W., McDonald, P. S., Adams, J., and MacCready, P.: Larval transport modeling support for identifying population sources of European green crab in the Salish Sea, Estuar. Coast., 42, 1586–1599, https://doi.org/10.1007/s12237-019-00586-2, 2019.
Brickman, D. and Smith, P. C.: Lagrangian stochastic modeling in coastal oceanography, J. Atmos. Ocean. Tech., 19, 83–99, https://doi.org/10.1175/1520-0426(2002)019<0083:LSMICO>2.0.CO;2, 2002.
Broatch, E. M. and MacCready, P.: Mixing in a Salinity Variance Budget of the Salish Sea is Controlled by River Flow, J. Phys. Oceanogr., 52, 2305–2323, https://doi.org/10.1175/JPO-D-21-0227.1, 2022.
Burchard, H. and Rennau, H.: Comparative quantification of physically and numerically induced mixing in ocean models, Ocean Model., 20, 293–311, https://doi.org/10.1016/j.ocemod.2007.10.003, 2008.
Chen, C., Limeburner, R., Gao, G., Xu, Q., Qi, J., Xue, P., Lai, Z., Lin, H., Beardsley, R., Owens, B., and Carlson, B.: FVCOM model estimate of the location of Air France 447, Ocean Dynam., 62, 943–952, https://doi.org/10.1007/s10236-012-0537-5, 2012.
Daher, H., Beal, L. M., and Schwarzkopf, F. U.: A new improved estimation of Agulhas leakage using observations and simulations of Lagrangian floats and drifters, J. Geophys. Res.-Oceans, 125, e2019JC015753, https://doi.org/10.1029/2019JC015753, 2020.
Dagestad, K.-F., Röhrs, J., Breivik, Ø., and Ådlandsvik, B.: OpenDrift v1.0: a generic framework for trajectory modelling, Geosci. Model Dev., 11, 1405–1420, https://doi.org/10.5194/gmd-11-1405-2018, 2018.
Davis, K. A., Banas, N. S., Giddings, S. N., Siedlecki, S. A., MacCready, P., Lessard, E. J., Kudela, R. M., and Hickey, B. M.: Estuary-enhanced upwelling of marine nutrients fuels coastal productivity in the US Pacific Northwest, J. Geophys. Res.-Oceans, 119, 8778–8799, 2014.
Deltares, D.: Delft3D-FLOW user manual, Deltares Delft, The Netherlands, 330,
https://content.oss.deltares.nl/delft3d4/Delft3D-FLOW_User_Manual.pdf (last access: 20 April 2024), 2022.
Döös, K., Kjellsson, J., and Jönsson, B.: TRACMASS – A Lagrangian trajectory model. In Preventive methods for coastal protection, 225–249, Springer, Heidelberg, https://doi.org/10.1007/978-3-319-00440-2_7, 2013.
Fredj, E., Carlson, D. F., Amitai, Y., Gozolchiani, A., and Gildor, H.: The particle tracking and analysis toolbox (PaTATO) for Matlab, Limnol. Oceanogr.-Meth., 14, 586–599, https://doi.org/10.1002/lom3.10114, 2016.
Garwood, J. C., Fuchs, H. L., Gerbi, G. P., Hunter, E. J., Chant, R. J., and Wilkin, J. L.: Estuarine retention of larvae: Contrasting effects of behavioral responses to turbulence and waves, Limnol. Oceanogr., 67, 992–1005, https://doi.org/10.1002/lno.12052, 2022.
Giddings, S. N., MacCready, P., Hickey, B. M., Banas, N. S., Davis, K. A., Siedlecki, S. A., Trainer, V. L., Kudela, R. M., Pelland, N. A., and Connolly, T. P.: Hindcasts of potential harmful algal bloom transport pathways on the Pacific Northwest coast, J. Geophys. Res.-Oceans, 119, 2439–2461, https://doi.org/10.1002/2013JC009622, 2014.
Havens, H., Luther, M. E., and Meyers, S. D.: A coastal prediction system as an event response tool: Particle tracking simulation of an anhydrous ammonia spill in Tampa Bay, Mar. Pollut. Bull., 58, 1202–1209, https://doi.org/10.1016/j.marpolbul.2009.03.012, 2009.
Hoyer, S. and Hamman, J.: xarray: ND labeled arrays and datasets in Python, J. Open Res. Softw., 5, 10, https://doi.org/10.5334/jors.148, 2017.
Hunter, E. J., Fuchs, H. L., Wilkin, J. L., Gerbi, G. P., Chant, R. J., and Garwood, J. C.: ROMSPath v1.0: offline particle tracking for the Regional Ocean Modeling System (ROMS), Geosci. Model Dev., 15, 4297–4311, https://doi.org/10.5194/gmd-15-4297-2022, 2022.
Jalón-Rojas, I., Wang, X. H., and Fredj, E.: A 3D numerical model to track marine plastic debris (TrackMPD): sensitivity of microplastic trajectories and fates to particle dynamical properties and physical processes, Mar. Pollut. Bull., 141, 256–272, https://doi.org/10.1016/j.marpolbul.2019.02.052, 2019.
Klocker, A. and Abernathey, R.: Global patterns of mesoscale eddy properties and diffusivities, J. Phys. Oceanogr., 44, 1030–1046, https://doi.org/10.1175/JPO-D-13-0159.1, 2014.
Lange, M. and van Sebille, E.: Parcels v0.9: prototyping a Lagrangian ocean analysis framework for the petascale age, Geosci. Model Dev., 10, 4175–4186, https://doi.org/10.5194/gmd-10-4175-2017, 2017.
Lett, C., Verley, P., Mullon, C., Parada, C., Brochier, T., Penven, P., and Blanke, B.: A Lagrangian tool for modelling ichthyoplankton dynamics, Environ. Model. Softw., 23, 1210–1214, https://doi.org/10.1016/j.envsoft.2008.02.005, 2008.
Li, Y., He, R., and Manning, J. P.: Coastal connectivity in the Gulf of Maine in spring and summer of 2004–2009, Deep Sea Res. Pt. II, 103, 199–209, https://doi.org/10.1016/j.dsr2.2013.01.037, 2014.
Liang, J. H., Liu, J., Benfield, M., Justic, D., Holstein, D., Liu, B., Hetland, R., Kobashi, D., Dong, C., and Dong, W.: Including the effects of subsurface currents on buoyant particles in Lagrangian particle tracking models: Model development and its application to the study of riverborne plastics over the Louisiana/Texas shelf, Ocean Model., 167, 101879, https://doi.org/10.1016/j.ocemod.2021.101879, 2021.
MacCready, P., McCabe, R. M., Siedlecki, S. A., Lorenz, M., Giddings, S. N., Bos, J., Albertson, S., Banas, N. S., and Garnier, S.: Estuarine circulation, mixing, and residence times in the Salish Sea, J. Geophys. Res.-Oceans, 126, e2020JC016738, https://doi.org/10.1029/2020JC016738, 2021.
McKinney, W.: Data structures for statistical computing in python, in: Proceedings of the 9th Python in Science Conference, vol. 445, No. 1, 51–56, https://doi.org/10.25080/Majora-92bf1922-00a, 2010.
Melsom, A., Kvile, K. Ø., Dagestad, K. F., Broström, G., and Langangen, Ø.: Exploring drift simulations from ocean circulation experiments: application to cod eggs and larval drift, Clim. Res., 86, 145–162, https://doi.org/10.3354/cr01652, 2022.
Nepstad, R., Nordam, T., Ellingsen, I. H., Eisenhauer, L., Litzler, E., and Kotzakoulakis, K.: Impact of flow field resolution on produced water transport in Lagrangian and Eulerian models, Mar. Pollut. Bull., 182, 113928, https://doi.org/10.1016/j.marpolbul.2022.113928, 2022.
Nordam, T. and Duran, R.: Numerical integrators for Lagrangian oceanography, Geosci. Model Dev., 13, 5935–5957, https://doi.org/10.5194/gmd-13-5935-2020, 2020.
Nordam, T., Nepstad, R., Litzler, E., and Röhrs, J.: On the use of random walk schemes in oil spill modelling, Mar. Pollut. Bull., 146, 631–638, https://doi.org/10.1016/j.marpolbul.2019.07.002, 2019.
North, E. W., Hood, R. R., Chao, S. Y., and Sanford, L. P.: Using a random displacement model to simulate turbulent particle motion in a baroclinic frontal zone: A new implementation scheme and model performance tests, J. Mar. Syst., 60, 365–380, https://doi.org/10.1016/j.jmarsys.2005.08.003, 2006.
North, E. W., Schlag, Z., Hood, R. R., Li, M., Zhong, L., Gross, T., and Kennedy, V. S.: Vertical swimming behavior influences the dispersal of simulated oyster larvae in a coupled particle-tracking and hydrodynamic model of Chesapeake Bay, Mar. Ecol. Progr. Ser., 359, 99–115, https://doi.org/10.3354/meps07317, 2008.
North, E. W., Adams, E. E. E., Schlag, Z. Z., Sherwood, C. R., He, R. R., Hyun, K. H. K., Socolofsky, S. A.: Simulating oil droplet dispersal from the Deepwater Horizon spill with a Lagrangian approach, edited by: Liu, Y., Macfadyen, A., Ji, Z-.G., and Weisberg, R. H., in: Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record‐Breaking Enterprise, 195, 217–226, American Geophysical Union, United States, https://doi.org/10.1029/2011GM001102, 2011.
Onink, V., Jongedijk, C. E., Hoffman, M. J., van Sebille, E., and Laufkötter, C.: Global simulations of marine plastic transport show plastic trapping in coastal zones, Environ. Res. Lett., 16, 064053, https://doi.org/10.1088/1748-9326/abecbd, 2021.
Paris, C. B., Helgers, J., Van Sebille, E., and Srinivasan, A.: Connectivity Modeling System: A probabilistic modeling tool for the multi-scale tracking of biotic and abiotic variability in the ocean, Environ. Model. Softw, 42, 47–54, https://doi.org/10.1016/j.envsoft.2012.12.006, 2013.
Ralston, D. K., Cowles, G. W., Geyer, W. R., and Holleman, R. C.: Turbulent and numerical mixing in a salt wedge estuary: Dependence on grid resolution, bottom roughness, and turbulence closure, J. Geophys. Res.-Oceans, 122, 692–712, https://doi.org/10.1002/2016JC011738, 2017.
Ricker, M. and Stanev, E. V.: Circulation of the European northwest shelf: a Lagrangian perspective, Ocean Sci., 16, 637–655, https://doi.org/10.5194/os-16-637-2020, 2020.
Rowe, M. D., Anderson, E. J., Wynne, T. T., Stumpf, R. P., Fanslow, D. L., Kijanka, K., Vanderploeg, H. A., Strickler, J. R., and Davis, T. W.: Vertical distribution of buoyant Microcystis blooms in a Lagrangian particle tracking model for short-term forecasts in Lake Erie, J. Geophys. Res.-Ocean, 121, 5296–5314, https://doi.org/10.1002/2016JC011720, 2016.
Schlag, Z. R. and North, E. W.: Lagrangian TRANSport model (LTRANS v.2) User's Guide, University of Maryland Center for Environmental Science, Horn Point Laboratory, Cambridge, MD, USA, Tech. rep., 183 pp.,
https://northweb.hpl.umces.edu/LTRANS/LTRANSv2/LTRANSv2_UsersGuide_6Jan12.pdf (last access: 20 April 2024), 2012.
Shchepetkin, A. F. and McWilliams, J. C.: The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model, Ocean Model., 9, 347–404, https://doi.org/10.1016/j.ocemod.2004.08.002, 2005.
Siedlecki, S. A., Banas, N. S., Davis, K. A., Giddings, S., Hickey, B. M., MacCready, P., Connolly, T., and Geier, S.: Seasonal and interannual oxygen variability on the Washington and Oregon continental shelves, J. Geophys. Res.-Oceans, 120, 608–633, 2015.
Smolarkiewicz, P. K.: A fully multidimensional positive definite advection transport algorithm with small implicit diffusion, J. Comput. Phys., 54, 325–362, https://doi.org/10.1016/0021-9991(84)90121-9, 1984.
Stone, H. B., Banas, N. S., and MacCready, P.: The effect of alongcoast advection on Pacific Northwest shelf and slope water properties in relation to upwelling variability, J. Geophys. Res.-Oceans, 123, 265–286, https://doi.org/10.1002/2017JC013174, 2018.
Stone, H. B., Banas, N. S., MacCready, P., Trainer, V. L., Ayres, D. L., and Hunter, M. V.: Assessing a model of Pacific Northwest harmful algal bloom transport as a decision-support tool, Harmful Algae, 119, 102334, https://doi.org/10.1016/j.hal.2022.102334, 2022.
Sutherland, D. A., MacCready, P., Banas, N. S., and Smedstad, L. F.: A model study of the Salish Sea estuarine circulation, J. Phys. Oceanogr., 41, 1125–1143, 2011.
Testa, J. M., Eric Adams, E., North, E. W., and He, R.: Modeling the influence of deep water application of dispersants on the surface expression of oil: A sensitivity study, J. Geophys. Res.-Oceans, 121, 5995–6008, https://doi.org/10.1002/2015JC011571, 2016.
Vennell, R., Scheel, M., Weppe, S., Knight, B., and Smeaton, M.: Fast lagrangian particle tracking in unstructured ocean model grids, Ocean Dynam., 71, 423–437, https://doi.org/10.1007/s10236-020-01436-7, 2021.
Visser, A. W.: Using random walk models to simulate the vertical distribution of particles in a turbulent water column, Mar. Ecol. Prog. Ser., 158, 275–281, https://doi.org/10.3354/meps158275, 1997.
Wagner, P., Rühs, S., Schwarzkopf, F. U., Koszalka, I. M., and Biastoch, A.: Can Lagrangian tracking simulate tracer spreading in a high-resolution Ocean General Circulation Model?, J. Phys. Oceanogr., 49, 1141–1157, https://doi.org/10.1175/JPO-D-18-0152.1, 2019.
Wang, S., Zhao, L., Wang, Y., Zhang, H., Li, F., and Zhang, Y.: Distribution characteristics of green tides and its impact on environment in the Yellow Sea, Mar. Environ. Res., 181, 105756, https://doi.org/10.1016/j.marenvres.2022.105756, 2022.
Xiong, J. and MacCready, P.: Model hydrodynamic outputs and example codes for running different Lagrangian particle tracking packages, Zenodo [code], https://doi.org/10.5281/zenodo.10810102, 2024.
Xiong, J., Shen, J., Qin, Q., Tomlinson, M. C., Zhang, Y. J., Cai, X., Fei, Y., Lin, C., and Mulholland, M.: Biophysical interactions control the progression of harmful algal blooms in Chesapeake Bay: A novel Lagrangian particle tracking model with mixotrophic growth and vertical migration, Limnol. Oceanogr. Lett., 8, 498–508, https://doi.org/10.1002/lol2.10308, 2023.
