An empirical model of Mercury's magnetospheric cusp activity

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% An empirical model of Mercury's magnetospheric cusp activity
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% Version 1.0
% An cusp indicator as a function of solar wind variables and Mercury solar orbital phase is derived from MESSENGER magnetometer data and proton flux data collected between 23 March 2011 and 17 March 2014.
% Details are documented in http://doi.wiley.com/10.1002/2016JA023687
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% Reference
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% He, M., J. Vogt, D. Heyner, and J. Zhong (2017), Solar wind controls on Mercury's magnetospheric cusp, J. Geophys. Res. Space Physics, 122, doi:10.1002/ 2016JA023687
% He M., Vogt J. (2018) Empirical Modeling of Planetary Magnetospheres in Response to Solar Wind Dynamics Using EOF Analysis and Multivariate Linear Regression. In: L¨?hr H., Wicht J., Gilder S.A., Holschneider M. (eds) Magnetic Fields in the Solar System. Astrophysics and Space Science Library, vol 448. Springer, Cham, http://link.springer.com/10.1007/978-3-319-64292-5_7
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%Contents
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% Mercury_cusp.m : the model code v1.0
% CuspDistCoef.mat : coefficients for the model contained in one variable CuspDist:
% CuspDist.coor.lat and CuspDist.coor.LT, each of which sizes 250x1, define latitude and local time of 250 discrete points in Mercury solar orbital (MSO) coordinates system.
% The other coordinates are define as,
% >> CuspDist.coor.xy_comp =cosd(CuspDist.coor.lat).*exp(1i*mod((CuspDist.coor.LT+12)/24,1)*360/180*pi);
% >> CuspDist.coor.y=real(CuspDist.coor.xy_comp );
% >> CuspDist.coor.x=imag(CuspDist.coor.xy_comp );
% CuspDist.Coef_1BxByBzObitObbxObbyObbz sizes 8x250, whoes first dimension corresponds to are the eight coefficients (two scales pluse two 3d vectors) defined in Equation (2) in http://doi.wiley.com/10.1002/2016JA023687, in the oder:
% in oder to,
% 1) \beta_0
% 2) \beta_IMFx
% 3) \beta_IMFy
% 4) \beta_IMFz
% 5) \tilde{\beta_t0}
% 6) \tilde{\beta_t0}_IMFx
% 7) \tilde{\beta_t0}_IMFy
% 8) \tilde{\beta_t0}_IMFz
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%Communication to:
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% Maosheng He
% Schlossstrasse 6
% 18225, Kuehlungsborn, Germany
% +49 (0) 38293 68 240
% hmq512@gmail.com /he@iap-kborn.de
% July, 01, 2019
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% Syntax
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% [Bstd Coor]=Mercury_cusp(IMFxyzT) returns the cusp activity index Bstd on the grid Coor
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% Inputs
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% IMFxyzT: sizes nx4, whos 2nd dimension corresponds to IMF Bx, By, Bz components and the number of days since January 0, 0000
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% Outputs
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% Bstd: activity index (nT);sizes nx250,
% Coor: the coordinates of the 250 points
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%Examples
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% [x,y,z,t]=ndgrid(-20:5:20,-20:5:20,-20:5:20,0:8:85);
% IMFxyzT=[x(:),y(:),z(:),t(:)];
% [Bstd Coor]=Mercury_cusp(IMFxyzT);
% scatter(Coor.x,Coor.y,500,Bstd(1,:),'.');axis equal;axis ij
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% Copyright (c) 2017, Jacobs University Bremen
% All rights reserved.
% Redistribution and use in source and binary forms, with or without modification, are permitted provided that the
% following conditions are met:
% 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the
% following disclaimer.
% 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the
% following disclaimer in the documentation and/or other materials provided with the distribution.
%
% THIS SOFTWARE IS PROVIDED BY JACOBS UNIVERSITY BREMEN "AS IS" AND ANY EXPRESS
% OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
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