Metos3D: the Marine Ecosystem Toolkit for Optimization and Simulation in 3-D – Part 1: Simulation Package v0.3.2

Abstract. We designed and implemented a modular software framework for the offline simulation of steady cycles of 3-D marine ecosystem models based on the transport matrix approach. It is intended for parameter optimization and model assessment experiments. We defined a software interface for the coupling of a general class of water column-based biogeochemical models, with six models being part of the package. The framework offers both spin-up/fixed-point iteration and a Jacobian-free Newton method for the computation of steady states. The simulation package has been tested with all six models. The Newton method converged for four models when using standard settings, and for two more complex models after alteration of a solver parameter or the initial guess. Both methods delivered the same steady states (within a reasonable precision) on convergence for all models employed, with the Newton iteration generally operating 6 times faster. The effects on performance of both the biogeochemical and the Newton solver parameters were investigated for one model. A profiling analysis was performed for all models used in this work, demonstrating that the number of tracers had a dominant impact on overall performance. We also implemented a geometry-adapted load balancing procedure which showed close to optimal scalability up to a high number of parallel processors.

[1]  C. Kelley Solving Nonlinear Equations with Newton's Method , 1987 .

[2]  James C. McWilliams,et al.  Approach to Equilibrium in Accelerated Global Oceanic Models. , 1996 .

[3]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[4]  S. Khatiwala,et al.  Accelerated simulation of passive tracers in ocean circulation models , 2003 .

[5]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[6]  Homer F. Walker,et al.  Choosing the Forcing Terms in an Inexact Newton Method , 1996, SIAM J. Sci. Comput..

[7]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[8]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[9]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[10]  L. Ciric,et al.  A generalization of Banach’s contraction principle , 1974 .

[11]  Dailin Wang,et al.  A note on using the accelerated convergence method in climate models , 2001 .

[12]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

[13]  Gerhard W. Zumbusch Dynamic Load Balancing in a Lightweight Adaptive Parallel Multigrid PDE Solver , 1999, PPSC.

[14]  M. Levasseur,et al.  Ocean Biogeochemical Dynamics , 2007 .

[15]  Timothy M. Merlis,et al.  Fast Dynamical Spin up of Ocean General Circulation Models , 2006 .

[16]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[17]  Jens Schröter,et al.  Testing a marine ecosystem model: Sensitivity analysis and parameter optimization , 2001 .

[18]  L. Perelman,et al.  A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers , 1997 .

[19]  Fred Wubs,et al.  A method to reduce the spin-up time of ocean models , 2008 .

[20]  Andrei P. Sokolov,et al.  A Three-Dimensional Ocean-Seaice-Carbon Cycle Model and its Coupling to a Two-Dimensional Atmospheric Model: Uses in Climate Change Studies , 2005 .

[21]  G. Paltridge,et al.  Radiative processes in meteorology and climatology , 1976 .

[22]  Andreas Oschlies,et al.  Towards an assessment of simple global marine biogeochemical models of different complexity , 2010 .

[23]  G. D. Robinson Radiative processes in meteorology and climatology. By G. W. Paltridge and C. M. R. Platt. Amsterdam‐Oxford‐New York, Elsevier Scientific Publishing Company, 1976. Pp. 318+xvii. 103.00 Dfl , 1977 .

[24]  Matthew G. Knepley,et al.  PETSc Users Manual (Rev. 3.3) , 2013 .

[25]  Samar Khatiwala,et al.  A computational framework for simulation of biogeochemical tracers in the ocean , 2007 .

[26]  William Gropp,et al.  Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries , 1997, SciTools.

[27]  K. Bryan Accelerating the Convergence to Equilibrium of Ocean-Climate Models , 1984 .

[28]  Andreas Oschlies,et al.  Simultaneous data-based optimization of a 1D-ecosystem model at three locations in the North Atlantic: Part I— Method and parameter estimates , 2003 .

[29]  M. Fasham,et al.  Ocean biogeochemistry: the role of the ocean carbon cycle in global change , 2003 .

[30]  D. Keyes,et al.  Jacobian-free Newton-Krylov methods: a survey of approaches and applications , 2004 .

[31]  E. Siewertsen,et al.  Porting marine ecosystem model spin-up using transport matrices to GPUs , 2012 .

[32]  Samar Khatiwala,et al.  Fast spin up of Ocean biogeochemical models using matrix-free Newton–Krylov , 2008 .