Part_4_Ex_1.m

%% DA with covariance localization
% As we saw in previous DA exercises, the EnKF uses the information contained 
% in ensemble statistics to disaggregate TWS vertically and horizontally. However, 
% these ensemble statistics might sometimes lead to spurious correlations, especially 
% when small ensemble sizes are used (Hamil et al., 2001). For example, grid cells 
% located far away from each other might appear to be correlated, when in reality 
% we would expect no correlations between them. 
% 
% Covariance localization aims to avoid this problem by dampening correlations 
% between grid cells located far away. 
%% Setting up of DA
% For this model run, we will use the similar settings as the previous DA experiment. 
% Additionally, we will only perform a processing for 2007-2008 so that the process 
% is quicker.

clc, clear all;
addpath(genpath('./Codes/')); dbstop if error;
load("Config_DA.mat");
config.run.todate = '2008-12-31'
%% 
% We will turn on the switch for covariance localization and provide the filename 
% of the localization matrix

config.DAOptions.Localization = 1;
config.DAOptions.OtherData.rhoLocalization = 'Data/03_DA_Files_50km/OPTIONAL_rho_localization/Rho_localization_matrix_300_km.mat';
%% 
% Let us also create a new folder to store the results. *Copy-paste the missing 
% code from previous exercises.*

config.states.directory = 'Model_States_Output/03_DA_States_Loc/ens%n/';
config.summary.directory = 'Model_States_Output/03_DA_States_Loc/Summary/';
% Make new directory and copy initialization files
%%%%%%%%%%% TO BE FILLED %%%%%%%%%%%%%%%

%% DA run
% The DA is now run exactly as the non-localized EnKF. Functions integrated 
% in |Main06_performDA| will be in charge of applying covariance localization.  
% *Please copy-paste the DA scripts from exercise 3.*

% Define start and end dates
%%%%%%%%%%% TO BE FILLED %%%%%%%%%%%%%%%
% Create array of epochs were DA should be performed
%%%%%%%%%%% TO BE FILLED %%%%%%%%%%%%%%%

for i = 1:(length(t_array)-1)
    fprintf('Processing month number %d out of %d\n',i,length(t_array)-1)
    % Set beginning and ending time for monthly run
    %%%%%%%%%%% TO BE FILLED %%%%%%%%%%%%%%%
    % Perform run for each ensemble member
    %%%%%%%%%%% TO BE FILLED %%%%%%%%%%%%%%%
    
    % DA update step
    %%%%%%%%%%% TO BE FILLED %%%%%%%%%%%%%%%
%% Monthly EnKF

    %%%%%%%%%%% TO BE FILLED %%%%%%%%%%%%%%%
end
%% Result extraction
% *Copy-paste the missing code from previous exercises.*

% Result extraction
%%%%%%%%%%% TO BE FILLED %%%%%%%%%%%%%%%

%% Visualization

F_visualizeEx6(config);
%% Reflection questions
%% 
% # How does covariance localization modify the ensemble covariance matrix?
%% 
%% 
% # Why are TWS time series different when covariance localization is used?
%% 
%% 
% # What can be the benefits and drawbacks of implementing localization? 
%%