Forecast Step
#background trajectory [without correction]
ub[:,k+1] = RK4(Lorenz63,ub[:,k],dt,sigma,beta,rho)
#EKF trajectory [with correction at observation times]
ua[:,k+1] = RK4(Lorenz63,ua[:,k],dt,sigma,beta,rho)
#compute model Jacobian at t_k
DM = JRK4(Lorenz63,JLorenz63,ua[:,k],dt,sigma,beta,rho)
#propagate the background covariance matrix
B = DM @ B @ DM.T + Q
if (km<nt_m) and (k+1==ind_m[km]):