added *.m files to repository

README.txt

+####################################################################
+#                                                                  #
+#   ------------------------------------------------------------   #
+#   A COMPARISON OF THE ATLANTIC AND PACIFIC BJERKNES FEEDBACKS:   #
+#   SEASONALITY, SYMMETRY, AND STATIONARITY                        #
+#   ------------------------------------------------------------   #
+#                                                                  #
+#   T. DIPPE, J. F. LÜBBECKE, R. J. GREATBATCH                     #
+#                                                                  #
+#   in                                                             #
+#                                                                  #
+#   JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS                        #
+#                                                                  #
+#                                                                  #
+#   Readme for using the Matlab scripts                            #
+#                                                                  #
+####################################################################
+
+# --------- #
+# TECHNICAL #
+# --------- #
+
+Matlab version used for all analysis: Matlab 2018
+
+
+# ------------- #
+# USED DATASETS #
+# ------------- #
+
+- AVISO-SSH:        https://www.aviso.altimetry.fr/en/home.html
+
+- ERSST:            https://www.ncdc.noaa.gov/data-access/marineocean-data/extended-reconstructed-sea-surface-temperature-ersst-v5
+
+- ERA-Interim USTR: https://www.ecmwf.int/en/forecasts/datasets/archive-datasets/reanalysis-datasets/era-interim
+
+- ERA-40 USTR:      https://apps.ecmwf.int/datasets/data/era40-moda/
+
+- ORAS4 data:       http://icdc.cen.uni-hamburg.de/projekte/easy-init/easy-init-ocean.html
+
+
+# ------- #
+# GENERAL #
+# ------- #
+
+# ANALYSIS USING A BUNDLE OF SCRIPTS
+# ++++++++++++++++++++++++++++++++++
+
+Many scripts will be made up of a group of three to four scripts. These are:
+
+- <name>.m: The main script that does the principal calculations
+
+- <name>_settings.m: Prescribing all kinds of settings, including paths and
+  various plotting options
+
+- <name>_plots.m or similar: Plots
+
+- <name>_wrapper.m: A wrapper around the main script that allows looping over,
+  for example, feedback elements or basins
+
+For a given script <name>, I will refer to the bundle as <name>*.m
+
+
+# ZONAL ANALYSIS VERSUS INDIVIDUAL INDICES
+# ++++++++++++++++++++++++++++++++++++++++
+
+All analyses are based on indices. However, I distinguish between "zonal
+analyses" and "individual indices". Datasets for the zonal analyses contain a
+matrix that holds time series of indices that correspond to a sliding index
+along the equator. The zonal analysis is set up in
+zonal_analysis_region_definition.m (for the published paper: 4 deg lon x
+4 deg lat boxes that slide along the equator from a fixed western boundary
+towards the eastern boundary), an the collection of sliding indices is
+calculated with calculate_equatorial_indices*.m. These datasets should be stored
+in the <path where data for zonal analysis is stored>.
+
+In contrast, individual indices refer to just a single index. Single indices are
+calculated with the function calcIndexAveraged() and should be stored in the
+<path were individual indices are stored>.
+
+Additionally, raw SST data might be required, such as ERSST. These datasets
+should be stored in the <path where SST data is stored>.
+
+
+# --------------- #
+# LIST OF SCRIPTS #
+# --------------- #
+
+# FUNCTIONS
+# +++++++++
+
+- bootstrapFeedbackStrength() and bootstrapFeedbackStrengthDiff(): Significance
+               test for feedback strengths and their differences.
+
+- calcAnomalies(): Calculates the anomalies, and allows for variable detrending
+
+- calcIndexAveraged(): Calculates an index, requires a file that describes the
+                       grids that the variables are given on, including the
+                       spatial extent of each grid cell to apply the correct
+                       spatial averaging. (The grid files are stored in my case
+                       in the file modelGrids.mat, which contains a structure
+                       for each grid, which in turn stores information such as
+                       box_grid_area.)
+
+- calculateFeedback(): Perform a robust regression to estimate the strength of a
+                       given feedback element.
+
+- diagnoseLag(): Diagnose the lag at which the feedback strength between two
+                 variables is maximum.
+
+- eventCharacteristics(): Identifies events in a time series and returns various
+                          statistical measures about them. This function is the
+                          backbone of the SST event analysis in the Discussion.
+
+- testValue(): Given a distribution, a significance level and a test value,
+               discern whether the test value sits on the "significant" tails of
+               the distribution.
+
+
+# (More or less) PROJECT-WIDE SETTINGS
+# ++++++++++++++++++++++++++++++++++++
+
+- atlantic_asymmetric_bjf_plot_settings.m contains general settings
+  for plots that will be called for a number of analysis scripts. Customize the
+  colorbar handles in this script. However, the script is not used uniformly
+  across all analysis scripts. Sorry for the inconvenience.
+
+- zonal_analysis_region_definition.m defines the properties of the zonal
+  analysis, i.e. the total zonal extent of the analysis region, as well as the
+  width of zonal bins that will be used to calculate the equatorial indices.
+
+
+# PREPARING THE DATA: Binning data into sliding indices along the equator
+# ++++++++++++++++++
+
+- calculate_equatorial_indices*.m: Calculate indices for each zonal bin defined
+  in zonal_analysis_region_definition.m. These datasets are the basis for most
+  of the analysis. They should be stored in the <path where data for zonal
+  analysis is stored>.
+
+Date vectors are expected to be Matlab date vectors (see
+https://de.mathworks.com/help/matlab/ref/datevec.html).
+
+
+# ANALYSIS
+# ++++++++
+
+Fig. 1: compare_oras4_ersst*.m
+
+Fig. 2: diagnose_zonal_feedback_lags.*
+
+<Fig. 3: Created in MacOS's Keynote>
+
+Fig. 4-6: lagged_feedback_strength*.m to diagnose the strengths of the feedback
+          elements, and diagnose_feedback_strength_difference_significance*.m to
+          test the significance
+
+Fig. 7: total_bjerknes_feedback_from_regression*.m
+
+Fig. 8: compare_aviso_oras4_strengths_Atl3_Nino34*.m
+
+Figs. 9-11: decadal_feedback_variations*.m
+
+Fig. 12: zonal_enso_properties*.m
+
+Fig. 13: decadal_sst_event_variations*.m
+
+Figs. A1-A2: calculate_instantaneous_feedback*.m, and
+             compare_lagged_instantaneous_feedback_strengths*.m
+
+Figs. A3-A5: total_bjerknes_feedback_from_regression*.m
+
+
+# ------- #
+# CONTACT #
+# ------- #
+
+Contact me via tina.dippe@gmail.com if you have questions.

atlantic_asymmetric_bjf_plot_settings.m

+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                                    %
+%    COMMON SETTINGS FOR PLOTS OF THE ATLANTIC ASYMMETRY ANALYSIS    %
+%                                                                    %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% AXES POSITION
+% +++++++++++++
+
+    % scaling of the figure?
+    scale_figure_height = 0.8;
+    scale_figure_width  = 1;
+
+    % position of the axes
+    x_axes_offset      = 0.02;
+    y_axes_offset      = 0.05;
+    width_axes_offset  = -0.1;
+    height_axes_offset = -0.06;
+
+    % hard-wire axes position
+    axes_position = [0.13 0.11 0.725 0.7476];
+
+% COLOURS AND COLORBAR
+% ++++++++++++++++++++
+
+    my_white  = [254 254 254]./255;
+    my_left   = [0 76 153]./255;
+    my_middle = [0 102 204]./255;
+    my_right  = [0 255 255]./255;
+
+    my_teal       = [0 149 186]./255;
+    my_light_teal = [153 255 255]./255;
+    my_dark_teal  = [0 47 84]./255;
+
+    my_blue      = [0 102 204]./255;
+    my_dark_blue = [0 51 102]./255;
+    my_red       = [255 51 51]./255;
+    my_yellow    = [255 255 51]./255;
+    my_cyan      = [0 255 255]./255;
+    my_purple    = [153 0 153]./255;
+
+    % colorbar handles
+    sunset   = <custom colorbar handle for absolute values>;
+    plasma   = <custom colorbar handle for absolute values>;
+    centered = <custom colorbar handle for differences>;
+
+    % colours to mark negative lags
+    lag_colour        = [0.35 0.35 0.35];
+    lag_border_colour = my_white;
+    lag_stretch_width        = 6;
+    lag_stretch_border_width = 9;
+
+% HIGHLIGHT REGIONS
+% +++++++++++++++++
+
+    % which background regions to plot? Define longitudinal extent here
+    % i.e., mark WAtl, Atl3 in the Atlantic, and Nino4, Nino34, and Nino12
+    % in the Pacific
+    if strcmp(basin_name,'Pacific')
+
+        % longitudinal boundaries of standard regions
+        highlight_regions = [...
+                160 210; ...
+                190 240; ...
+                270 280];
+
+        % and the names of the regions
+        region_names = {'Nino4','Nino34','Nino12'};
+
+    else
+        highlight_regions = [...
+                -40 -20; ...
+                -20 0];
+        region_names = {'WAtl','Atl3'};
+    end
+
+    % y values for the patches; width: 0.25 months, gap: 0.2 months, maximum y value: 12.5
+    if strcmp(basin_name,'Pacific')
+        highlight_y_values = [11.8 12.05; 12.25 12.5; 11.8 12.05];
+    else
+        highlight_y_values = [12.25 12.5; 12.25 12.5];
+    end
+
+    region_colours = [my_teal; my_light_teal; my_dark_teal];
+
+% MISCELLANEOUS
+% +++++++++++++
+
+    % font size
+    scale_font_size = 2;
+
+    % size of the significance crosses
+    size_significance_marker = 8;
+
+    % line widths for the significance markers
+    line_width_significance_markers = 0.5;
+    line_width_significance_outline = 4.5;
+
+    % month shorts
+    month_ids = {'J','F','M','A','M','J','J','A','S','O','N','D'};
+
+    % mute warning from robust regression
+    % query the last warning, including it's ID with
+    % w = warning('query','last').
+    warn_id = 'stats:statrobustfit:IterationLimit';

bootstrapFeedbackStrength.m

+function strength_values = bootstrapFeedbackStrength(data1,data2,sample_size,n_bootstraps,analysis_type)
+
+% Bootstrap two time series and produce a historgram of
+% slope parameters of a linear regression.
+%
+% USAGE: strength_values = bootstrapRegression(data1,data2,sample_size,n_bootstraps)
+%
+%     OUTPUT
+%         strength_values: bootstrapped slope values
+%
+%     INPUT
+%         data1:         Time series 1, "x-values" or predictors for the regression model
+%         data2:         Time series 2, "y-values" or predictands of the regression model
+%         sample_size:   How many samples should be drawn from the
+%                        full data?
+%         n_bootstraps:  How often should the bootstrapping be repeated?
+%         analysis_type: Which analysis method should be used to diagnose the
+%                        feedback strength? acc (ACC), reg (regular linear regression,
+%                        that regresses >data2< on >data1<), or rreg (robust
+%                        regression that regresses >data2< on >data1<)
+
+% ----------- %
+% PREPARATION %
+% ----------- %
+
+    % assign an ID to the analysis type
+    % for use with switch
+    if strcmp(analysis_type,'acc')
+        analysis_id  = 1;
+    elseif strcmp(analysis_type,'reg')
+        analysis_id  = 2;
+    elseif strcmp(analysis_type,'rreg')
+        analysis_id  = 3;
+    else
+        error_string = sprintf('Analysis type >%s< not known.\nChoose either of acc, reg, or rreg.',analysis_type);
+        error(error_string);
+    end
+
+% --------- %
+% BOOTSTRAP %
+% --------- %
+
+    % total pool of data
+    n_data       = length(data1);
+    all_indices  = 1:n_data;
+
+    % storage
+    strength_values = zeros(1,n_bootstraps);
+
+    % actual bootstrapping
+    for c_strap = 1:n_bootstraps
+
+        % randomly draw samples
+        random_sample = datasample(all_indices,sample_size,'Replace',false);
+
+        sample_data1 = data1(random_sample);
+        sample_data2 = data2(random_sample);
+
+        % calculate feedback strengths
+        switch analysis_id
+
+            % correlation
+            case 1
+
+                % acc
+                current_feedback = corrcoef(sample_data1,sample_data2);
+                current_feedback = current_feedback(1,2);
+
+            % normal linear regression
+            case 2
+
+                regression_parameters = polyfit(sample_data1,sample_data2,1);
+                current_feedback = regression_parameters(1);
+
+            % robust regression
+            case 3
+
+                rregression_parameters = robustfit(sample_data1,sample_data2);
+                current_feedback = rregression_parameters(2);  % yes, the order is different from polyfit ...
+
+        % switch: calculate feedback strength
+        end
+
+        % assign regression value
+        strength_values(c_strap) = current_feedback;
+
+    % for: repeat bootstrapping
+    end 

bootstrapFeedbackStrengthDiff.m

+function strength_diffs = bootstrapFeedbackStrengthDiff(data1,data2,sample_size,n_bootstraps,analysis_type)
+
+% Bootstrap tuples of two time series two time series and produce a historgram of
+% of differences of the feedback strength diagnosed from either ACC, linear regression
+% or robust regression. The differences are calculated
+% as follows: Randly sample m tuples from the time series and calculate the slope
+% parameter; then use the remaining n-m tuples, again calculate the slope parameter,
+% and save the difference between the two. n is total length of the time dataset,
+% and m is equivalent with the parameter sample_size.
+%
+% USAGE: strength_diffs = bootstrapRegression(data1,data2,sample_size,n_bootstraps)
+%
+%     OUTPUT
+%         strength_diffs: bootstrapped slope difference values
+%
+%     INPUT
+%         data1:         Time series 1, "x-values" or predictors for the regression model
+%         data2:         Time series 2, "y-values" or predictands of the regression model
+%         sample_size:   How many samples should be drawn from the
+%                        full data?
+%         n_bootstraps:  How often should the bootstrapping be repeated?
+%         analysis_type: Which analysis method should be used to diagnose the
+%                        feedback strength? acc (ACC), reg (regular linear regression,
+%                        that regresses >data2< on >data1<), or rreg (robust
+%                        regression that regresses >data2< on >data1<)
+
+% ----------- %
+% PREPARATION %
+% ----------- %
+
+    % assign an ID to the analysis type
+    % for use with switch
+    if strcmp(analysis_type,'acc')
+        analysis_id  = 1;
+    elseif strcmp(analysis_type,'reg')
+        analysis_id  = 2;
+    elseif strcmp(analysis_type,'rreg')
+        analysis_id  = 3;
+    else
+        error_string = sprintf('Analysis type >%s< not known.\nChoose either of acc, reg, or rreg.',analysis_type);
+        error(error_string);
+    end
+
+% --------- %
+% BOOTSTRAP %
+% --------- %
+
+    % total pool of data
+    n_data       = length(data1);
+    all_indices  = 1:n_data;
+
+    % storage
+    strength_diffs = zeros(1,n_bootstraps);
+
+    % actual bootstrapping
+    for c_strap = 1:n_bootstraps
+
+        % randomly draw samples, no replacement
+        random_sample = datasample(all_indices,sample_size,'Replace',false);
+
+        % opposite sample
+        opposite_sample = setdiff(all_indices,random_sample);
+
+        % calculate feedback strength differences
+        switch analysis_id
+
+            % correlation
+            case 1
+
+                % acc
+                random_feedback   = corrcoef(data1(random_sample),    data2(random_sample));
+                opposite_feedback = corrcoef(data1(opposite_feedback),data2(opposite_feedback));
+
+                feedback_difference = random_feedback(1,2)-opposite_feedback(1,2);
+
+            % normal linear regression
+            case 2
+
+                random_pp   = polyfit(data1(random_sample),data2(random_sample),1);
+                opposite_pp = polyfit(data1(opposite_sample),data2(opposite_sample),1);
+
+                feedback_difference = random_pp(1)-opposite_pp(1);
+
+            % robust regression
+            case 3
+
+                random_rreg   = robustfit(data1(random_sample),data2(random_sample));
+                opposite_rreg = robustfit(data1(opposite_sample),data2(opposite_sample));
+
+                feedback_difference = random_rreg(2)-opposite_rreg(2);
+
+        % switch: calculate feedback strength
+        end
+
+        % assign regression value
+        strength_diffs(c_strap) = feedback_difference;
+
+    % for: repeat bootstrapping
+    end

calcAnomalies.m

+function [anomalies,cropped_dates] = calcAnomalies(data,date_vector,varargin)
+
+% Calculates anomalies relative to a user-specified trend
+% and to the climatological seasonal cycle.
+%
+% USAGE: [anomalies,cropped_dates] = calcAnomalies(data,date_vector)
+%        [anomalies,cropped_dates] = calcAnomalies(__,trend)
+%        [anomalies,cropped_dates] = calcAnomalies(__,start_year,stop_year);
+%        [anomalies,cropped_dates] = calcAnomalies(__,trend,start_year,stop_year);
+%
+%        data and anomalies are vectors. date_vector is a Matlab date vector.
+%        cropped_dates is the cropped date vector.
+%
+% Optional parameter are
+%
+%        trend:      trend that is to be subtracted from the data
+%                    prior to the removal of the seasonal cycle.
+%                    Vector that has the same length as data.
+%                    Default: When no trend is provided, the linear
+%                    trend is calculated and subtracted from
+%                    the data.
+%
+%        start_year: When should anomaly calculation begin?
+%
+%        stop_year:  When should it stop?
+%
+% IF YOU DON'T WHISH TO CALCULATE A TREND,
+% specify a "dummy trend" that consists of zeros and
+% has the same size as the data.
+
+% ----------- %
+% PARSE INPUT %
+% ----------- %
+
+    n_additional = length(varargin);
+
+    % define defaults:
+        trend_data = [];
+        start_year = min(date_vector(:,1));
+        stop_year  = max(date_vector(:,1));
+
+    switch n_additional
+        case 0
+        case 1
+            trend_data = varargin{1};
+        case 2
+            start_year = varargin{1};
+            stop_year  = varargin{2};
+        case 3
+            trend_data = varargin{1};
+            start_year = varargin{2};
+            stop_year  = varargin{3};
+        otherwise
+            error('Wrong amount of input variables specified.');
+    end
+
+% -------------- %
+% CONSTRAIN TIME %
+% -------------- %
+
+    is_time =  ( date_vector(:,1) >= start_year ) & ( date_vector(:,1) <= stop_year );
+
+    % cropping
+    date_vector = date_vector(is_time,:);
+    data        = data(is_time);
+
+    % need to crop the trend data as well if it is not empty
+    if ~isempty(trend_data)
+        trend_data = trend_data(is_time);
+    end
+
+    % for returning
+    cropped_dates = date_vector;
+
+    % use datenums as x-axis
+    x_values = datenum(date_vector);
+
+% ------------------ %
+% DATA QUALITY CHECK %
+% ------------------ %
+
+    is_okay  = ~(isnan(data));
+
+    % anything else but NaNs?
+    if ( isempty(data(is_okay)) )
+        anomalies = nan(size(data));
+        return
+    end
+
+% ------------ %
+% DETREND DATA %
+% ------------ %
+
+    if isempty(trend_data)
+
+%          disp('calculating linear trend');
+
+        % need to have NaN-free data for regression
+        valid_data  = data(is_okay);
+        valid_times = x_values(is_okay);
+
+        % fitting: use only good values
+        vals_poly = polyfit(valid_times,valid_data,1);
+
+        % evaluation: use ALL values
+        trend_data = polyval(vals_poly,x_values);
+
+    % trend data compatible with data?
+    else
+        if ( length(data) ~= length(trend_data) )
+            error('Data and trend data have different sizes.');
+        end
+    end
+
+    % assign anomalies relative to the trend to
+    % the correct piece of monthlyAnomalies
+    detrended = data - trend_data;
+
+% ------------------------------------ %
+% REMOVE CLIMATOLOGICAL SEASONAL CYCLE %
+% ------------------------------------ %
+
+    anomalies = zeros(size(data));
+    seasonal_cycle = zeros(1,12);
+
+    for month = 1:12
+
+        % timing
+        is_month = ( date_vector(:,2) == month );
+
+
+        % climatology
+        climatology = nanmean(detrended(is_month));
+
+        % assign anomalies
+        anomalies(is_month)   = detrended(is_month)-climatology;
+        seasonal_cycle(month) = nanmean(data(is_month));
+
+    end

calcIndexAveraged.m

+function index = calcIndexAveraged(monthlyAnomalies,latGrid,lonGrid,gridArea,latBoundaries,lonBoundaries)
+
+% Calculates a climate index as area average over an area with given boundaries.
+%
+% Usage: index = calcIndexAveraged(monthlyAnomalies,latGrid,lonGrid,gridArea,latBoundaries,lonBoundaries)
+%        index:            Time series of area averages (the "climate index").
+%                          Same length as time dimension of monthlyAnomalies.
+%        monthlyAnomalies: Raw data. Monthly anomalies.
+%                          Dimensions: lon x lat x time
+%        latGrid:          Latitude specification for monthlyAnomalies.
+%                          Dimensions: lon x lat
+%        lonGrid:          Same as latGrid, but for longitude.
+%        gridArea:         Indicates the area of the individual grid boxes.
+%                          Dimensions: lon x lat
+%        latBoundaries:    Vector of length 2 that specifies the latitude boundaries of the area.
+%                          latBoundaries(1): Minimum latitude
+%                          latBoundaries(2): Maximum latitude
+%        lonBoundaries:    Same as latBoundaries but for longitude.
+
+% -------- %
+% CHECKING %
+% -------- %
+
+    % Grid Sizes
+    if ( ( size(monthlyAnomalies,1) ~= size(latGrid,1) ) | ...
+         ( size(monthlyAnomalies,1) ~= size(lonGrid,1) ) | ...
+         ( size(monthlyAnomalies,2) ~= size(latGrid,2) ) | ...
+         ( size(monthlyAnomalies,2) ~= size(lonGrid,2) ) )
+        error('Dimension between either of latGrid, lonGrid, and monthlyAnomalies!');
+    end
+
+    % Longitude format: grid
+    if ( max(max(lonGrid)) > 180 )
+        % disp('Reformatting: Maximum grid longitude > 180');
+        lonGrid(lonGrid > 180) = lonGrid(lonGrid > 180) - 360;
+    end
+
+    % Longitude format: boundaries
+    if ( max(lonBoundaries) > 180 )
+        % disp('Reformatting: Maximum boundary longitude > 180');
+        lonBoundaries(lonBoundaries > 180) = lonBoundaries(lonBoundaries > 180) - 360;
+    end
+
+% ------------------------------------------------ %
+% FIND GRID POINTS CORRESPONDING TO THE GIVEN AREA %
+% ------------------------------------------------ %
+
+    % work with logical arrays the sime size as the data
+    isLat = ( ( latGrid >= latBoundaries(1) ) & ( latGrid <= latBoundaries(2) ) );
+
+    % does the longitudinal specification cross the date line?
+    if ( ( lonBoundaries(1) > lonBoundaries(2) ) & ...
+         ( sign(lonBoundaries(1)) == 1 ) & ( sign(lonBoundaries(2)) == -1 ) )
+        % warning('Specified longitude boundaries cross the date line.');
+
+        isLon_west = ( ( lonGrid >= lonBoundaries(1) ) & ( lonGrid <= 180 ) );
+        isLon_east = ( ( lonGrid >= -180 )             & ( lonGrid <= lonBoundaries(2) ) );
+        isLon      = ( isLon_west | isLon_east );
+
+    % no crossing: first entry is smaller than the second one
+    else
+        isLon = ( ( lonGrid >= lonBoundaries(1) ) & ( lonGrid <= lonBoundaries(2) ) );
+    end
+
+% --------------- %
+% CALCULATE INDEX %
+% --------------- %
+
+    % AREA MASK
+        % initialize the mask:
+        mask = ones(size(monthlyAnomalies));
+
+        % multiply the (3D) mask with the logical array for the area:
+        mask = bsxfun(@times,mask,(isLat & isLon));
+
+        % set zeros to NaN:
+        mask(mask == 0) = NaN;
+
+    % mask anomalies:
+    maskedAnomalies = monthlyAnomalies.*mask;
+
+    % THE INDEX
+        % total area of the region: Not a scalar but already of the same length as the
+        % resulting time series --> can calculate the index time series
+        % in one calculation step
+        totalArea = ones(size(monthlyAnomalies,3),1).*sum(gridArea(isLat & isLon));
+
+        % multiply anomalies with grid box area:
+        weighted = bsxfun(@times,maskedAnomalies,gridArea);
+
+        % THE INDEX:
+        % area average: sum of the weighted anomalies divided by the total area
+        index = squeeze(nansum(nansum(weighted,1),2))./totalArea;

calculateFeedback.m

+function feedback_strength = calculateFeedback(forcing,response,analysis_type)
+
+% Calculate the "feedback strength" (co-variability) between two variables
+%
+% SYNTAX:
+%
+%     feedback_strength = calculateFeedback(forcing,response,analysis_type)
+%
+%     OUTPUT:
+%         feedback_strength: Scalar, "feedback strength" between the >forcing< and
+%                            and >response< datasets, based on the chosen >analysis_type<.
+%
+%
+%     INPUT:
+%         forcing:         Vector, forcing dataset ("forcing" of the "feedback").
+%         response:               Vector of the same size as >forcing<, "response" of the "feedback"