% Integrate the Lorenz '95 equations. % Lorenz, E. and K. Emanuel, 1998. Optimal Sites for Supplementary % Weather Observations: Simulation with a Small Model, JAS, 55, 399-414. % Equations % \dot{x}_i = -x_{i-2}*x_{i-1} + x_{i-1}*x_{i+1} - x_{i} + f % Written by Jim Hansen, Feb 2003 for 12.990 students % Specify the dimension of the system dim = 10; % Specify the parameter values (f) par(1:dim)=8; % Specify the initial conditions for i=1:dim;x(i)=par(i)+randn;end % Specify the integration step size h = 0.05; % Specify the length of integration steps = 2^12; % Integrate the equations over length steps to remove any transient behavior for i=1:steps xout=step_it('derivsL95',x,par,h,dim); x=xout; end % Integrate the equations over length steps and record state for plotting for i=1:steps time(i)=i*h; xout=step_it('derivsL95',x,par,h,dim); state(i,:)=xout; x=xout; end % Make a pretty picture figure;plot(time(1:1000),state(1:1000,1)) title('A 1D trajectory from the Lorenz 95 attractor'); xlabel('time');ylabel('x(1)'); print -djpeg90 L95.jpg