Advancing the West Coast Ocean Forecasting System
Project Team
Project Lead/Scientific PI: Christopher A. Edwards, University of California, Santa Cruz
Transition PI: Clarissa Anderson, SCCOOS
Other Investigators (alphabetically): Eric Bayler (NOAA NESDIS), Jerome Fiechter, Raphael Kudela, Andrew Moore (UC Santa Cruz), Elliott Hazen, Michael Jacox (NOAA NMFS), Alexander Kurapov (OSU/NOAA CSDL), Parker MacCready, Jan Newton (University of Washington/NANOOS), Henry Ruhl (CeNCOOS)
Partners: SCCOOS, CeNCOOS, NANOOS
NOAA/NOS Technical Points of Contact: Edward Myers, Audra Luscher, Carolyn Lindley, Jiangtao Xu
Project Overview and Results
Along the U.S. West Coast, in support of the U.S. Integrated Ocean Observing System, three Regional Associations (RAs; NANOOS, CeNCOOS, and SCCOOS) maintain a mosaic of ocean modeling activities, run as quasi-operational systems at academic institutions and private organizations, that provide numerous products designed to benefit local end-users. NOAA’s National Ocean Service, Coast Survey Development Laboratory (CSDL) is developing the West Coast Ocean Forecasting System (WCOFS), a high-resolution ocean model spanning coastal and offshore waters relevant to all three RAs. The WCOF’s first implementation is presently in transition to operations within the National Ocean Service Center for Operational Oceanographic Products and Services. The goals of this project are (1) to advance coastal ocean modeling, analysis, and prediction through enhancements to the WCOFS model and (2) to transition established products relevant to NOAA’s Ecological Forecasting Roadmap to using WCOFS output. The vision is an advanced, operational, federal ocean model for the U.S. West Coast that supports locally generated, regionally relevant derivative ocean products required by end-users.
We propose several objectives for achieving these goals and contributing to this overall vision. This project will:
(a) assess WCOFS output using RA-developed metrics,
b) contribute specific technical developments to the WCOFS data assimilation implementation,
(c) couple WCOFS to a lower-trophic level, biogeochemical model with phytoplankton and zooplankton diversity and oxygen as state variables, transition a mature Harmful Algal Bloom (HAB) probability model to produce 3-day forecasts using WCOFS output, and
(d) evaluate WCOFS output for use in a fast, efficient habitat model for swordfish and protected species bycatch.
To facilitate transition to operations, around the end of each Project Year we will hold workshops with key CSDL personnel to communicate technical details and assist in issues arising from implementation. To maximize product value (research to applications), we will organize a stakeholder outreach meeting early in the project to discuss WCOFS-related products with end-users, receive feedback, and enable modifications to implementation plans.
Specific benefits of the improved WCOFS implementation include short-term operational HAB predictions across large swaths of the U.S. west coast and dynamic swordfish species and bycatch maps. These products benefit stakeholders within three IOOS RAs, including marine mammal rescue organizations, shellfish growers, and fisheries and coastal resource managers. The improved ocean state estimates will have potentially broad future impacts for a host of other societal needs, including navigation, search and rescue, and environmental hazard response.
Connecting Stakeholders to Ecosystem Change with Ecological Forecast Models
Model Descriptions
WCOFS:
The objective of the WCOFS project is to develop a state-of-the-science operational coastal ocean circulation data assimilation (DA) and forecast system for the entire U.S. West Coast, providing daily updates of 3-day forecasts of shelf currents, temperature, sea level and other variables in support of many societally-relevant needs, including navigation, search and rescue, environmental hazard response, fisheries, and public health. The model, based on the Regional Ocean Modeling System (ROMS), spans coastal waters to about 1,000 km offshore of the Pacific coast of North America, from 24N (mid Baja California, Mexico) to 55N (north of Vancouver Island, Canada). The model’s horizontal resolution is 2 km. Atmospheric forcing is obtained from the 12-km resolution NOAA North American Model (NAM) forecast model. Boundary conditions are provided by the 1/12th-degree NOAA Real-Time Ocean Forecast System (RTOFS) global model, with tides added along open boundaries. The model includes freshwater discharge from several major rivers in the Pacific Northwest (PNW). The skill of the non-DA model has been assessed using a 6-year run and observations of sea level from coastal gauges, HF RADAR surface currents, ARGO float temperature (T) and salinity (S) profiles, surface T from buoys, satellite sea-surface temperature (SST), and glider T and S sections (Kurapov et al., 2017a,b). The non-DA model has been transitioned to operational implementation at the NOAA/NOS/CO-OPS and is being run on a supercomputer at NOAA’s National Center for Environmental Prediction (NOAA/NCEP). The WCOFS’ DA component, currently in operational implementation testing at NOS/CO-OPS, uses a coarser 4-km resolution grid, with interpolation to the model’s 2-km grid, due to the heavy computational burden of DA. The WCOFS DA system will utilize ROMS 4D-Var and assimilate observations of HF RADAR surface currents, sea-level anomaly from satellite altimeters, and SST to improve forecast accuracy of currents and SST fronts. The goals are (a) to enhance the WCOFS system and (b) to evaluate and use WCOFS output for established needs of three adjacent RAs.
Data Assimilation
DA, a critical component of analysis and forecast systems in operational numerical weather prediction (NWP), is now a mainstay in many operational centers for the ocean as well. Most operational centers that run global ocean analysis and forecast systems, including federal agencies and intergovernmental organizations, employ a variety of DA approaches: ensemble optimal interpolation, ensemble Kalman filters (EnKF), and 3-dimensional variational (3D-Var) methods (Martin et al., 2015). Ocean analysis and forecast systems are also run at regional scales (Edwards et al., 2015) with many near real-time examples run routinely by IOOS RAs (Kourafalou et al., 2015; Oke et al., 2015). With computational demands for regional systems typically being less than for global systems, employed DA methods range from 3D-Var, to EnKF to 4D-Var methods.
DA is also a critical component of WCOFS, in terms of 1) producing the best possible analyses as a synthesis of the model and all available observations and 2) producing the best starting point for forecasts. During the last decade Team Member Moore has led development of a state-of-the-science 4D-Var DA system for the ROMS community (Moore et al., 2011a,b,c). The ROMS 4D-Var system has been used in many regions of the world’s oceans (e.g., the Indian Ocean, the Philippine Sea, the Santos Basin, the Tyrrhenian Sea, the Gulf of Alaska, the Intra-Americas Sea, the entire North Atlantic, the Norwegian Sea, the East Australia Current) and, perhaps most extensively, along the U.S. West Coast (e.g., Broquet et al., 2009, 2010; Moore et al., 2013; Neveu et al., 2016). In addition, ROMS 4D-Var is currently run within three RAs (CeNCOOS, MARACOOS, and PacIOOS) in near-real time in support of IOOS. Because WCOFS employs the community version of ROMS, it too uses this advanced 4D-Var system.
At U.C. Santa Cruz (UCSC), a regional ocean analysis and forecast system has been developed and, since 2011, has run every day in support of CeNCOOS to produce near real-time, publicly available ocean state estimates (http://oceanmodeling.ucsc.edu). Though spanning a smaller geographic domain than WCOFS and run at significantly lower horizontal resolution (~10 km), analyses (1980 to the present), produced by the CeNCOOS 4D-Var system have proved to be a very valuable community resource. These analyses are used in a wide variety of studies, ranging from climate variability (Crawford et al., 2017), to juvenile rockfish recruitment (Schroeder et al., 2015), and to marine mammal migration patterns (Becker et al., 2017). As part of this project, technical advances that exist within the CeNCOOS 4D-Var system (UCSC ROMS) but not in the WCOFS 4D-Var system will be transitioned to WCOFS.
Biogeochemical Modeling
Although physical ocean models provide critical information for temperature, salinity, transport and mixing, there exists considerable demand for non-physical oceanographic information as well. Expert panels within the Global Ocean Observing System have defined one useful set of Essential Ocean Variables (EOVs; www.goosocean.org/eov) that include phytoplankton and zooplankton biomass and diversity, nutrients, inorganic carbon, particulate matter, and oxygen. In other advanced regional and global ocean analyses, lower trophic level BGC models are used to provide this complementary ecological information (Ciavatta et al., 2016; Jones et al., 2016; Ford et al., 2017).
For several years, CeNCOOS has supported BGC modeling within UCSC ROMS described above, first using a simple NPZD model then, more recently, the NEMURO ecosystem model (Kishi et al., 2007). The latter model performed well in the evaluation studies (Mattern et al., 2017a) and in those performed as part of the now expiring COMT 2013-2018 project. In its base form, NEMURO has 11-components, including nitrogen- and silicon-based nutrients, two phytoplankton size classes, and three zooplankton size classes. Plankton diversity allows representation of different communities, which vary in nature from diatom-dominated nearshore waters to predominantly smaller organisms found in more-oligotrophic offshore zones. Team Member Fiechter has enhanced the base NEMURO model to include dissolved inorganic carbon, alkalinity, and calcium carbonate (Fiechter et al., 2014) and, more recently, oxygen, based on the formulation in Fennel et al. (2006).
While considerable research effort has been spent over decades constructing and improving biogeochemical models (these efforts should and will continue), it is important to recognize that all models are necessarily imperfect, due to many unavoidable factors: uncertainties in initial conditions, boundary conditions, surface forcing, and model parameterizations. Consequently, unconstrained model output deviates from nature. As with physical fields, DA provides a rigorous approach to constrain biogeochemical model output using observations. Over the last five years, Team Member Edwards has led development of a ROMS 4D-Var DA system for BGC models (Song et al., 2012, 2016a,b,c), and our ability to perform BGC ocean state estimation constrained by satellite-derived chlorophyll using NEMURO is quite mature within the CeNCOOS domain (Mattern et al., 2017a, b). Furthermore, our procedure is robust, ready to assimilate other BGC variables as new data types (e.g., oxygen) become available.
The WCOFS project has long envisioned incorporating a BGC modeling capability to further support ecological forecasting applications, but, at present, does not have a BGC component. As part of this project, we will develop a WCOFS NEMURO system that produces multiple water column EOVs and make progress toward a WCOFS 4D-Var BGC ocean state estimate.
California-Harmful Algae Risk Mapping (C-HARM)
Domoic acid poisoning in marine mammal and bird populations, along with the threat of Amnesic Shellfish Poisoning in humans, is considered to be the leading harmful algal bloom (HAB) issue for much of the U.S. West Coast. A coherent approach to developing predictive capabilities for integrated environmental assessments, early warning systems, action plans, and mitigation strategies for these toxigenic Pseudo-nitzschia blooms was established at the West Coast Governors Alliance Harmful Algal Bloom Summit in 2009 (Lewitus et al., 2012) and then re-energized as part of NOAA’s Ecological Forecasting Roadmap.
In response to the call for a predictive HAB capability in California to better inform management decisions, Team Members Anderson and Kudela developed the C-HARM System to inform when and where toxic blooms occur. During Phase 1 of the NASA-funded C-HARM project, the team successfully generated and validated routine nowcast and forecast products in a pre-transitional demonstration of predictions of toxigenic Pseudo-nitzschia blooms and domoic acid along the central California coast. Statistical ecological models are driven by information from ocean model simulations, enhanced satellite imagery, and community (Cal-HABMAP)/marine mammal observations (Anderson et al. 2016). In the present C-HARM implementation, physical oceanographic information derives from a 3-km resolution, quasi-operational, 3D-Var DA model developed by Dr. Yi Chao that spans the entire California coast (CA ROMS; Li et al., 2008; Chao et al. 2017) and is provided, with support from CeNCOOS and SCCOOS, by a commercial operations provider (Remote Sensing Solutions, Inc.). Optical parameters required by the ecological models are retrieved and processed from satellite data (presently daily 1-km MODIS-Aqua data).
CeNCOOS has served as the C-HARM pre-operational decision-making environment, with everything from satellite data processing to product distribution implemented in-house. A close partnership has been established with NOAA’s NOS National Centers for Coastal Ocean Science (NCCOS) to test the new data product on developmental computers. The C-HARM application has now transitioned to a demonstration readiness level within the end-user domain, hosted on NOAA’s high-performance computing (HPC) cluster, the Supercomputer for Satellite Simulations and Data Assimilation Studies (SSEC). The C-HARM capability is currently migrating to operational implementation at the NOAA CoastWatch West Coast Regional Node in partnership with NOAA/NOS/NCCOS.
As part of this project, we will initially evaluate C-HARM using historical WCOFS output and, if promising, will transition the end-to-end system at NOAA CoastWatch to using the operational WCOFS for its forecast product (See DiGiacomo LOS and Garfield LOS).
Habitat Modeling Background
NOAA’s National Marine Fisheries Service West Coast Regional Office (NMFS/WCRO), which is responsible for implementing U.S. West Coast fisheries management, is tasked with simultaneously maintaining target species catch at sustainable levels, reducing bycatch of protected and non-target species, and supporting the economic health of a fishery. Balancing these multiple and often opposing objectives is a complex management problem. For example, the California Drift Gillnet fishery (DGN) primarily targets broadbill swordfish (Xiphias gladius) in Federal waters off California, but bycatch of endangered species, such as the North Pacific loggerhead (Caretta caretta) and leatherback (Dermochelys coriacea) turtles, have resulted in large-scale fishery closures that are enacted seasonally (leatherback turtles) and for June-August when an El Niño event is occurring or forecast to occur (loggerhead turtles). In making these decisions, the Pacific Fisheries Management Council (PFMC) and the NOAA/NMFS Southwest Regional Office are currently forced to consider coarse, often single-species, management approaches, without considering why interactions occurred where they did or where interactions are likely to occur in the future. Additionally, they are unable to consider whether this closure would increase bycatch of other species due to relocated fishing effort or the effects of the closure on fishers’ livelihoods. These missing considerations are not a result of the PFMC or NMFS lack of desire to explicitly consider these components; rather, they lack the tools to consider all of these pieces holistically.
Through projects previously and currently funded by NOAA and NASA, Team Member Hazen and collaborators have been developing a tool (EcoCast) to inform decision-makers for improved management strategies for the DGN fishery. EcoCast is based on statistical species distribution models (SDMs) developed for a number of swordfish fishery target and bycatch species of interest. These models, constructed using boosted regression trees (BRTs; Redfern et al. 2006, Wood 2008), describe the preferred habitats of target and bycatch species by statistically relating fisheries data (observer, satellite tracking, and logbook data) to concurrent oceanographic data. Target catch and bycatch SDMs are then normalized according to management risk and merged to create a single EcoCast product that predicts the relative probability of target catch and bycatch across the fishery landscape. A swordfish SDM has already been developed using the above approach (Scales et al., 2017) and a manuscript describing the EcoCast tool is now in review (Hazen et al., in review).
At present, EcoCast statistical models use either remotely-sensed data or output from the CeNCOOS-supported UCSC 4D-Var system. As part of this project, we will evaluate EcoCast’s relative performance when using WCOFS output versus the other sources presently in use.
References
Anderson C.R., R.M. Kudela, M. Kahru, Y. Chao, F. Bahr, L. Rosenfeld, D. Anderson, and T. Norris, 2016: Initial skill assessment of the California Harmful Algae Risk Mapping (C-HARM system, Harmful Algae, 59, 1-18, doi: 10.106/j.hal.2016.08.006.
Becker, E.A., K.A. Forney, P. C. Fiedler, J. Barlow, S. J. Chivers, C.A. Edwards, A.M. Moore, and J.V. Redfern, 2016: Moving Towards Dynamic Ocean Management: How Well Do Modeled Ocean Products Predict Species Distributions?, Remote Sens. 8(2), 149; doi:10.3390/rs8020149.
Broquet G., C. A. Edwards, A. M. Moore, B. S. Powell, M. Veneziani and J. D. Doyle, 2009: Application of 4D-Variational data assimilation to the California Current System, Dyn. Atmos. Oceans, doi:10.1016/j.dynatmoce.2009.03.001.
Broquet, G., A. M. Moore, H. G. Arango, and C.A. Edwards, 2010: Corrections to ocean surface forcing in the California Current System using 4D variational data assimilation, Ocean Mod. 36, doi:10.1016/j.ocemod.2010.10.005.
Chao, Y., J. D. Farrara, H. Zhang, K. J. Armenta, L. Centurioni, F. Chavez, J. B. Girton, D. Rudnick, R. K. Walter, 2017: Development, implementation, and validation of a California coastal ocean modeling, data assimilation, and forecasting system, Deep Sea Research Part II: Topical Studies in Oceanography, ISSN 0967-0645.
Ciavatta, S., S. Kay, S. Saux-Picart, M. Butenschön, and J. I. Allen, 2016: Decadal reanalysis of biogeochemical indicators and fluxes in the North West European shelf-sea ecosystem, J. Geophys. Res. Oceans, 121, 1824–1845, doi:10.1002/2015JC011496.
Crawford, W., A.M. Moore, M.G. Jacox, J. Fiechter, E. Neveu, and C.A. Edwards, 2017: A resonant response of the California Current circulation to forcing by low frequency climate variability. Deep Sea Research Part II: Topical Studies in Oceanography, doi: 10.1016/j.dsr2.2017.07.016.
Edwards, C. A., A. M. Moore, B. D. Cornuelle, and I. Hoteit, 2015: Regional Data Assimilation, Ann. Rev. Mar. Sci., Annu. Rev. Mar. Sci. 2015. 7:6.1–6.22, 10.1146/annurev-marine-010814-015821
Fennel, K., J. Wilkin, M. Previdi, and R. Najjar, 2008: Denitrification effects on air-sea CO2 flux in the coastal ocean: Simulations for the northwest North Atlantic. Geophys. Res. Lett., 35, L24608, doi:10.1029/2008GL036147.
Fiechter, J., E. N. Curchitser, C. A. Edwards, F. Chai, N. L. Goebel, F. P. Chavez, 2014: Air-sea CO2 fluxes in the California Current: Impacts of model resolution and coastal topography. Global Biogeochem. Cy., 28, 371–385, doi: 10.1002/2013GB004683.
Jones, E. M., Baird, M. E., Mongin, M., Parslow, J., Skerratt, J., Lovell, J., Margvelashvili, N., Matear, R. J., Wild-Allen, K., Robson, B., Rizwi, F., Oke, P., King, E., Schroeder, T., Steven, A., and Taylor, J., 2016: Use of remote-sensing reflectance to constrain a data assimilating marine biogeochemical model of the Great Barrier Reef, Biogeosciences, 13, 6441-6469, https://doi.org/10.5194/bg-13-6441-2016.
Kishi, M. J., et al., 2007: NEMURO – A lower trophic level model for the North Pacific marine ecosystem, Ecol. Modell., 202, 12–25, doi:10.1016/j.ecolmodel.2006.08.021.
Kourafalou V.H., P. De Mey, M. Le Hénaff, G. Charria, C.A. Edwards, R. He, M. Herzfeld, A. Pasqual, E.V. Stanev, J. Tintoré, N. Usui, A.J. Van Der Westhuysen, J. Wilkin and X. Zhu, 2015: Coastal Ocean Forecasting: system integration and validation. Journal of Operational Oceanography, doi:10.1080/1755876X.2015.1022336.
Kurapov, A. L., S. Y. Erofeeva, and E. Myers, 2017a: Coastal sea level variability in the US West Coast Ocean Forecast System (WCOFS), Ocean Dynamics, 67: 23. doi:10.1007/s10236-016- 1013-4.
Kurapov, A. L., N. Pelland, and D. L. Rudnick, 2017b: Seasonal and interannual variability in oceanic properties along the US West Coast continental slope: inferences from a high-resolution regional model, J. Geophys. Res., 122(7), 5237–5259; doi: 10.1002/2017JC012721.
Lewitus, A.J., Horner, R. A., Caron, D. A., Garcia-Mendoza, E., Hickey, B.M., Hunter, M., Tweddle, J.F., 2012: Harmful algal blooms along the North American west coast region: history, trends, causes, and impacts. Harmful Algae, 19, 133-159. DOI: 10.1016/j.hal.2012.06.009.
Mattern, J.P., H. Song, C.A. Edwards, A.M. Moore, J. Fiechter, 2017a: Data assimilation of physical and chlorophyll observations in the California Current System using two biogeochemical models, Ocean Modelling, 109, 55-71, doi: 10.1016/j.ocemod.2016.12.002.
Mattern, J. P., and C. A. Edwards, and A. M. Moore, 2017b: Improving variational data assimilation through background and observation error adjustments, Mon. Weather Rev., https://doi.org/10.1175/MWR-D-17-0263.1.
Moore, A.M., Arango, H.G., Broquet, G., Powell, B.S., Zavala-Garay, J., Weaver, A.T., 2011a: The regional ocean modeling system (ROMS) 4-dimensional variational data assimilation systems. I: System overview and formulation. Progress in Oceanography 91, 34–49.
Moore, A. M., H. G. Arango, G. Broquet, C. A. Edwards, M. Veneziani, B. S. Powell, D. Foley, J. D. Doyle, D. Costa, P. Robinson, 2011b: The regional ocean modeling system (ROMS) 4-dimensional variational data assimilation systems. II: Performance and application to the California current system. Prog. Oceanogr.doi:10.1016/j.pocean.2011.05.003.
Moore, A. M., H. G. Arango, G. Broquet, C. A. Edwards, M. Veneziani, B. S. Powell, D. Foley, J. D. Doyle, D. Costa, P. Robinson (2011c). The regional ocean modeling system (ROMS) 4-dimensional variational data assimilation systems: III Observation impact and observation sensitivity in the California Current system. Prog. Oceanogr. doi:10.1016/j.pocean.2011.05.005.
Moore, A.M., C. A. Edwards, J. Fiechter, P. Drake, H.G. Arango, E. Neveu, S. Gurol and A.T. Weaver, 2013: A 4D-Var Analysis System for the California Current: A Prototype for an Operational Regional Ocean Data Assimilation System. In ‘Data Assimilation for Atmospheric, Oceanic and Hydrological Applications, Vol. II,’ Liang Xu and Seon Park, Eds. Springer, Chapter 14, 345-366.
Neveu, E., A.M. Moore, C.A. Edwards, J. Fiechter, P.T. Drake, M.G. Jacox, and E. Nuss, 2016: A historical analysis of the California Current using ROMS 4D-Var. Part I: System configuration and diagnostics, Ocean Modelling, doi:10.1016/j.ocemod.2015.11.012.
Oke P. R., Larnicol G., Jones E.M., Kourafalou V., Sperrevik A.K., Carse F., Tanajura C.A.S., Mourre B., Tonani M., Brassington G.B., Le Henaff M., Halliwell G.R., Atlas R., Moore A.M., Edwards C.A., Martin M.J., Sellar A.A., Alvarez A., De Mey P., Iskandarani M., 2015: Assessing the impact of observations on ocean forecasts and reanalyses: Part 2, Regional applications. J Oper. Oceanogr. doi:10.1080/1755876X.2015.1022080.
Redfern, J.V., Ferguson, M.C., Becker, E.A., Hyrenbach, K.D., Good, C., Barlow, J., Kaschner, K., Baumgartner, M.F., Forney, K.A., Ballance, L.T. and Fauchald, P., 2006: Techniques for cetacean–habitat modeling. Marine Ecology Progress Series, 310, pp.271-295.
Scales, K., E. Hazen, S. Maxwell, H. Dewar, S. Kohin, M. Jacox; C.A. Edwards, D. Briscoe, L. Crowder, R. Lewison, S. Bograd, 2017: Fit to predict? Ecoinformatics for modeling dynamic habitat suitability for highly migratory marine species. Ecol. Appl., doi: 10.1002/eap.1610.
Schroeder, I.D., J. A. Santora, A.M. Moore, C.A. Edwards, J. Fiechter, E. Hazen, S.J. Bograd, J.C. Field and B. K. Wells, 2014: Application of a data-assimilative regional ocean modeling system for assessing California Current System ocean conditions, krill, and juvenile rockfish interannual variability. Geophys. Res. Lett., 10.1002/2014GL061045.
Song H., C. A. Edwards, A. M. Moore, J. Fiechter, 2012: Incremental four-dimensional variational data assimilation of positive-definite oceanic variables using a logarithm transformation, Ocean Modelling, 54–55, pp. 1-17, 10.1016/j.ocemod.2012.06.001.
Song, H., C.A. Edwards, A.M. Moore, J. Fiechter, 2016: Data assimilation in a coupled physical-biogeochemical model of the California current system using an incremental lognormal 4-dimensional variational approach: Part 3—Assimilation in a realistic context using satellite and in situ observations, Ocean Modelling, 106, 159-172, doi:10.1016/j.ocemod.2016.06.005.
Song, H., C.A. Edwards, A.M. Moore, J. Fiechter, 2016: Data assimilation in a coupled physical-biogeochemical model of the California Current System using an incremental lognormal 4-dimensional variational approach: Part 2—Joint physical and biological data assimilation twin experiments, Ocean Modelling, 106, 146-158, doi:10.1016/j.ocemod.2016.09.003.
Song, H., C.A. Edwards, A.M. Moore, J. Fiechter, 2016: Data assimilation in a coupled physical–biogeochemical model of the California Current System using an incremental lognormal 4-dimensional variational approach: Part 1—Model formulation and biological data assimilation twin experiments, Ocean Modelling, 106, 131-145, doi:10.1016/j.ocemod.2016.04.001.
Wood, S.N., 2008: Fast stable direct fitting and smoothness selection for generalized additive models. J. R. Statis. Soc. B, 70, 495–518, 10.1111/j.1467-9868.2007.00646.