MA5232-Project 4
ASSIGNMENT 4 - due 21 April, 2017
Consider the Lorenz 96 model with dimension d, and F = 8
dxi(t) = (xi+1 xi 2)xi 1dt xidt+Fdt+ 2dWi(t); i = 1; ;d
The initial condition should be generated randomly:
xi(0) N(0;1)
Pick h = 0:005, and consider the process realization at discrete time points:
Xn = xnh:
Suppose one observation is made at every p coordinate, so
[Yn]i = [Xn]p(i 1)+1 + 0:5 n;i; n;i N(0;1)
Use Matlab to implement data assimilation methods, and produce sequential estima-
tionZn ofXn forn 100=h = 20000. In IVLE, a simulation of the signal-observation
system using Euler’s method is provided. A trivial estimator Zn 8 is used to create
benchmark performance.
Use proper data assimilation method to replace Zn. Implement your algorithms
in the following scenarios
1. d = 5, p = 1;
2. d = 10, p = 2;
3. d = 10, p = 5;
4. d = 40, p = 2;
5. d = 100, p = 5.
Submit a numerical report on your results. For each scenario, report the following
three items
The method you are using.
The mean square error, print out by the program.
The snapshot made by the algorithm.
Submit also the MATLAB code you are using, with proper comments.