Geoscientific Model Development www.geosci-model-dev.net 1991-959X 1991-9603 2 2 2009 10.5194/gmd-2-113-2009 http://www.geosci-model-dev.net/2/113/2009/ http://www.geosci-model-dev.net/2/113/2009/gmd-2-113-2009.html http://www.geosci-model-dev.net/2/113/2009/gmd-2-113-2009.pdf 113 122 2009-07-29 LANL* V1.0: a radiation belt drift shell model suitable for real-time and reanalysis applications J. Koller jkoller@lanl.gov G. D. Reeves R. H. W. Friedel Space Science and Applications, ISR-1, Los Alamos National Lab, USA We describe here a new method for calculating the magnetic drift invariant, L*, that is used for modeling radiation belt dynamics and for other space weather applications. L* (pronounced L-star) is directly proportional to the integral of the magnetic flux contained within the surface defined by a charged particle moving in the Earth's geomagnetic field. Under adiabatic changes to the geomagnetic field L* is a conserved quantity, while under quasi-adiabatic fluctuations diffusion (with respect to a particle's L*) is the primary term in equations of particle dynamics. In particular the equations of motion for the very energetic particles that populate the Earth's radiation belts are most commonly expressed by diffusion in three dimensions: L*, energy (or momentum), and pitch angle (the dot product of velocity and the magnetic field vector). Expressing dynamics in these coordinates reduces the dimensionality of the problem by referencing the particle distribution functions to values at the magnetic equatorial point of a magnetic "drift shell" (or L-shell) irrespective of local time (or longitude). While the use of L* aids in simplifying the equations of motion, practical applications such as space weather forecasting using realistic geomagnetic fields require sophisticated magnetic field models that, in turn, require computationally intensive numerical integration. Typically a single L* calculation can require on the order of 105 calls to a magnetic field model and each point in the simulation domain and each calculated pitch angle has a different value of L*. We describe here the development and validation of a neural network surrogate model for calculating L* in sophisticated geomagnetic field models with a high degree of fidelity at computational speeds that are millions of times faster than direct numerical field line mapping and integration. This new surrogate model has applications to real-time radiation belt forecasting, analysis of data sets involving tens of satellite-years of observations, and other problems in space weather. Barron, A.: Approximation Bounds For Superpositions Of A Sigmoidal Function, Information Theory, IEEE Transactions on, 85–85, 1991. Barron, A.: Universal approximation bounds for superpositions of a sigmoidal function, Information Theory, IEEE Transactions on, 39, 930–945, 1993. Barron, A R.: Approximation and estimation bounds for artificial neural networks, Mach. Learn., 14, 115–133, doi:10.1007/BF00993164, 1994. Beutier, T. and D. Boscher: A three-dimensional analysis of the electron radiation belt by the Salammbô code, J. Geophys. Res., 100, 14853–14862, 1995. Bishop, C M.: Neural networks for pattern recognition, Clarendon Press, Oxford University Press, Oxford, New York, 1995. Boscher, D., Bourdarie, S., O'Brien, P., and Guild, T.: ONERA-DESP library V4.1, http://irbem.sourceforge.net/, 2007. Chen, Y., Friedel, R. H W., Reeves, G D., Cayton, T E., and Christensen, R.: Multisatellite determination of the relativistic electron phase space density at geosynchronous orbit: An integrated investigation during geomagnetic storm times, J. Geophys. Res., 112, 1–16, 2007. Cybenko, G.: Approximation by superpositions of a sigmoidal function, Math. Control Signal., 2, 303–314, doi:10.1007/BF02551274, 1989. Dolenko, S., Orlov, Y., Persiantsev, I., and Shugai, Y.: Neural Network Analysis of Solar Wind Data, Applied Problems in Systems of Patttern Recognition and Image Analysis, 11, 296–299, 2001. Huang, C.-L., Spence, H E., Singer, H J., and Tsyganenko, N A.: A quantitative assessment of empirical magnetic field models at geosynchronous orbit during magnetic storms, J. Geophys. Res. (Space Physics), 113, A04208, doi:10.1029/2007JA012623, 2008. Kim, H.-J. and Chan, A A.: Fully adiabatic changes in storm time relativistic electron fluxes, J. Geophys. Res., 102, 22107–22116, 1997. Kleijnen, J. P C.: Design and analysis of simulation experiments, International series in operations research and management science, 111, Springer, New York, 2008. Koons, H C. and Gorney, D J.: A neural network model of the relativistic electron flux at geosynchronous orbit, J. Geophys. Res., 96, 5549–5556, 1991. Lundstedt, H.: Neural networks and predictions of solar-terrestrial effects, Planet. Space Sci., 40, 457–464, 1992. McCollough, J P., Gannon, J L., Baker, D N., and Gehmeyr, M.: A statistical comparison of commonly used external magnetic field models, Space Weather, 6, S10001, doi:10.1029/2008SW000391, 2008. Myers, R H. and Montgomery, D C.: Response surface methodology process and product optimization using designed experiments, Wiley, New York, Chichester, 2002. Olson, W P. and Pfitzer, K A.: Magenetospheric magnetic field modeling, Annual Scientific Report, 1977. Queipo, N V., Haftka, R T., Shyy, W., Goel, T., Vaidyanathan, R., and Kevin~Tucker, P.: Surrogate-based analysis and optimization, Prog. Aerosp. Sci., 41, 1–28, 2005. Reed, R D. and Marks, R J.: Neural smithing: supervised learning in feedforward artificial neural networks, The MIT Press, Cambridge, Mass., 1999. Reeves, G., Friedel, R., Chen, Y., Koller, J., and Henderson, M.: The Los Alamos Radiation Environment Assimilation Model (DREAM) for Space Weather Specification and Forecasting, in Advanced Maui Optical and Space Surveillance Technologies Conference. 2008. Roederer, J G.: Dynamics of geomagnetically trapped radiation, Physics and chemistry in space, Vol 2, Springer-Verlag, Berlin, New York, 1970. Rumelhart, D E., Hinton, G E., and Williams, R J.: Learning representations by back-propagating errors, Nature, 323, 533–536, doi:10.1038/323533a0, 1986. Schulz, M.: The magnetosphere, Geomagnetism, 4, 87–293, 1991. Schulz, M. and Lanzerotti, L J.: Particle diffusion in the radiation belts, Physics and chemistry in space, Vol 7, Springer-Verlag, Berlin, New York, 1974. Tsyganenko, N A.: A model of the near magnetosphere with a dawn-dusk asymmetry 1. Mathematical structure, J. Geophys. Res. (Space Physics), 107, 1179, doi:10.1029/2001JA000219, 2002a. Tsyganenko, N A.: A model of the near magnetosphere with a dawn-dusk asymmetry 2. Parameterization and fitting to observations, J. Geophys. Res. (Space Physics), 107, 1176, doi:10.1029/2001JA000220, 2002b. Tsyganenko, N A. and Sitnov, M I.: Modeling the dynamics of the inner magnetosphere during strong geomagnetic storms, J. Geophys. Res. (Space Physics), 110, A03208, doi:10.1029/2004JA010798, 2005. Tsyganenko, N A., Singer, H J., and Kasper, J C.: Storm-time distortion of the inner magnetosphere: How severe can it get?, J. Geophys. Res. (Space Physics), 108, 1209, doi:10.1029/2002JA009808, 2003. Wojciechowski, M.: ffnet: Feed-forward neural network for python, http://ffnet.sourceforge.net/, 2007. Zaharia, S., Jordanova, V K., Thomsen, M F., and Reeves, G D.: Self-consistent modeling of magnetic fields and plasmas in the inner magnetosphere: Application to a geomagnetic storm, J. Geophys. Res. (Space Physics), 111, A11S14, doi:10.1029/2006JA011619, 2006.