References
This page lists key references for the numerical methods and software frameworks used in Cocoa.
ADCIRC and GWCE
Luettich, R.A., Westerink, J.J., and Scheffner, N.W. (1992). ADCIRC: An Advanced Three-Dimensional Circulation Model for Shelves, Coasts, and Estuaries. Technical Report DRP-92-6, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.
Kolar, R.L., Gray, W.G., Westerink, J.J., and Luettich, R.A. (1994). Shallow water modeling in spherical coordinates: equation formulation, numerical implementation, and application. Journal of Hydraulic Research, 32(1), 3-24.
Dawson, C., Westerink, J.J., Feyen, J.C., and Pothina, D. (2006). Continuous, discontinuous and coupled discontinuous-continuous Galerkin finite element methods for the shallow water equations. International Journal for Numerical Methods in Fluids, 52(1), 63-88.
Luettich, R.A. and Westerink, J.J. (1999). Elemental Wetting and Drying in the ADCIRC Hydrodynamic Model: Upgrades and Documentation for ADCIRC Version 34.XX. Contractors Report, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.
Luettich, R.A. and Westerink, J.J. (2004). Formulation and Numerical Implementation of the 2D/3D ADCIRC Finite Element Model Version 44.XX. Technical report, University of North Carolina at Chapel Hill and University of Notre Dame.
Dietrich, J.C., Kolar, R.L., and Luettich, R.A. (2004). Assessment of ADCIRC’s wetting and drying algorithm. In Proceedings of the XV International Conference on Computational Methods in Water Resources, Developments in Water Science 55, Elsevier, 1767-1778.
Finite Element Methods
Hughes, T.J.R. (2000). The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications.
Zienkiewicz, O.C., Taylor, R.L., and Zhu, J.Z. (2013). The Finite Element Method: Its Basis and Fundamentals (7th ed.). Butterworth-Heinemann.
Flanagan, D.P. and Belytschko, T. (1981). A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. International Journal for Numerical Methods in Engineering, 17(5), 679-706.
Bochev, P., Edwards, H.C., Kirby, R.C., Peterson, K., and Ridzal, D. (2012). Solving PDEs with Intrepid. Scientific Programming, 20(2), 151-180.
Kokkos
Edwards, H.C., Trott, C.R., and Sunderland, D. (2014). Kokkos: Enabling manycore performance portability through polymorphic memory access patterns. Journal of Parallel and Distributed Computing, 74(12), 3202-3216.
Trott, C.R., Lebrun-Grandié, D., Arndt, D., et al. (2022). Kokkos 3: Programming Model Extensions for the Exascale Era. IEEE Transactions on Parallel and Distributed Systems, 33(4), 805-817.
Trilinos
Heroux, M.A., Bartlett, R.A., Howle, V.E., et al. (2005). An overview of the Trilinos project. ACM Transactions on Mathematical Software, 31(3), 397-423.
Bavier, E., Hoemmen, M., Rajamanickam, S., and Thornquist, H. (2012). Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems. Scientific Programming, 20(3), 241-255.
Wind Stress and Atmospheric Forcing
Garratt, J.R. (1977). Review of drag coefficients over oceans and continents. Monthly Weather Review, 105, 915-929.
Wu, J. (1982). Wind-stress coefficients over sea surface from breeze to hurricane. Journal of Geophysical Research, 87(C12), 9704-9706.
Zijlema, M., van Vledder, G.Ph., and Holthuijsen, L.H. (2012). Bottom friction and wind drag for wave models. Coastal Engineering, 65, 19-26.
Sea Ice Drag
Lupkes, C., Gryanik, V.M., Hartmann, J., and Andreas, E.L. (2012). A parametrization, based on sea ice morphology, of the neutral atmospheric drag coefficients for weather prediction and climate models. Journal of Geophysical Research: Atmospheres, 117, D13112. doi:10.1029/2012JD017630.
Joyce, B.R., Pringle, W.J., Wirasaet, D., Westerink, J.J., Van der Westhuysen, A.J., Grumbine, R., and Feyen, J. (2019). High resolution modeling of western Alaska tides and storm surge under varying sea ice conditions. Ocean Modelling, 141, 101421. doi:10.1016/j.ocemod.2019.101421.
Shallow Water Equations
Vreugdenhil, C.B. (1994). Numerical Methods for Shallow-Water Flow. Springer.
Toro, E.F. (2001). Shock-Capturing Methods for Free-Surface Shallow Flows. Wiley.
Smagorinsky, J. (1963). General circulation experiments with the primitive equations. I. The basic experiment. Monthly Weather Review, 91(3), 99-164.
Dean, R.G. and Dalrymple, R.A. (1991). Water Wave Mechanics for Engineers and Scientists. World Scientific, Singapore.
Chow, V.T. (1959). Open-Channel Hydraulics. McGraw-Hill, New York.
Langbein, W.B. and Leopold, L.B. (1966). River Meanders: Theory of Minimum Variance. U.S. Geological Survey Professional Paper 422-H.
Wetting and Drying
Medeiros, S.C. and Hagen, S.C. (2012). Review of wetting and drying algorithms for numerical tidal flow models. International Journal for Numerical Methods in Fluids, 71(4), 473-487.
Carrier, G.F. and Greenspan, H.P. (1958). Water waves of finite amplitude on a sloping beach. Journal of Fluid Mechanics, 4(1), 97-109.
Balzano, A. (1998). Evaluation of methods for numerical simulation of wetting and drying in shallow water flow models. Coastal Engineering, 34(1-2), 83-107.
Parametric Tropical Cyclone Vortex
Gao, J. (2013). On the Surface Wind Stress for Storm Surge Modelling. Ph.D. dissertation, University of North Carolina at Chapel Hill. (Generalized Asymmetric Holland Model, GAHM.)
Luettich, R.A. (2026). GAHM2026: Updated Generalized Asymmetric Holland Model formulation. (Reference MATLAB implementation for the environmental-wind, boundary-layer, and consistency-scan conventions.)
Lin, N., and Chavez, D. (2012). On hurricane parametric wind and applications in storm surge modeling. Journal of Geophysical Research: Atmospheres, 117, D09120. (Referenced as “Lin & Chavez” in the GAHM2026 formulation; supplies the constant-background environmental-wind option.)
Holland, G.J. (1980). An Analytic Model of the Wind and Pressure Profiles in Hurricanes. Monthly Weather Review, 108(8), 1212-1218.
Holland, G.J., Belanger, J.I., and Fritz, A. (2010). A Revised Model for Radial Profiles of Hurricane Winds. Monthly Weather Review, 138(12), 4393-4401.
Tropical Cyclone Wind-Pressure Relationships
Atkinson, G.D., and Holliday, C.R. (1977). Tropical Cyclone Minimum Sea Level Pressure / Maximum Sustained Wind Relationship for the Western North Pacific. Monthly Weather Review, 105(4), 421-427.
Dvorak, V.F. (1984). Tropical Cyclone Intensity Analysis Using Satellite Data. NOAA Technical Report NESDIS 11, 47 pp.
Knaff, J.A., and Zehr, R.M. (2007). Reexamination of Tropical Cyclone Wind-Pressure Relationships. Weather and Forecasting, 22(1), 71-88.
Courtney, J., and Knaff, J.A. (2009). Adapting the Knaff and Zehr Wind-Pressure Relationship for Operational Use in Tropical Cyclone Warning Centres. Australian Meteorological and Oceanographic Journal, 58(3), 167-179.
Baroclinic Coupling
Pringle, W.J., Gonzalez-Lopez, J., Joyce, B.R., Westerink, J.J., and van der Westhuysen, A.J. (2019). Baroclinic Coupling Improves Depth-Integrated Modeling of Coastal Sea Level Variations Around Puerto Rico and the U.S. Virgin Islands. Journal of Geophysical Research: Oceans, 124(3), 2196-2217. https://doi.org/10.1029/2018JC014682
Pringle, W.J., Wirasaet, D., Roberts, K.J., and Westerink, J.J. (2021). Global Storm Tide Modeling with ADCIRC v55: Unstructured Mesh Design and Performance. Geoscientific Model Development, 14, 1125-1145. https://doi.org/10.5194/gmd-14-1125-2021
Blakely, C.P., Ling, G., Pringle, W.J., Contreras, M.T., Wirasaet, D., Westerink, J.J., et al. (2022). Dissipation and Bathymetric Sensitivities in an Unstructured Mesh Global Tidal Model. Journal of Geophysical Research: Oceans, 127(5), e2021JC018178. https://doi.org/10.1029/2021JC018178
Nycander, J. (2005). Generation of internal waves in the deep ocean by tides. Journal of Geophysical Research, 110, C10028. https://doi.org/10.1029/2004JC002487
Lyard, F., Lefevre, F., Letellier, T., and Francis, O. (2004). Modelling the global ocean tides: modern insights from FES2004. Ocean Dynamics, 56, 394-415. https://doi.org/10.1007/s10236-006-0086-x
Zaron, E.D., and Egbert, G.D. (2006). Estimating open-ocean barotropic tidal dissipation: The Hawaiian Ridge. Journal of Physical Oceanography, 36(6), 1019-1035. https://doi.org/10.1175/JPO2878.1
de Boyer Montegut, C., Madec, G., Fischer, A.S., Lazar, A., and Iudicone, D. (2004). Mixed layer depth over the global ocean: An examination of profile data and a profile-based climatology. Journal of Geophysical Research, 109, C12003. https://doi.org/10.1029/2004JC002378