Surface Mixed Layer

Tianyu Zhou, 11/03/2021, at UDel

Quality Control and Binning

Load data located within Nares Strait (pre-selected and stored in a '.mat' file) and perform quality control procedures.

clc;
clear;
load('../data/OMG_data_Nares')
profi_num = size(output,1);
depth = cell(profi_num,1);
T = cell(profi_num,1);
S = cell(profi_num,1);
rho = cell(profi_num,1);
for n = 1:profi_num
    
    data = output{n,5};
    
    % NOTE: a small percentage of probes do not have salinity or density data!    
    if size(data,2) == 8
        % for these who have salinity or density data
        % Quality control (step1): remove -99 data values
        depth_vec = data(:,2);
        T_vec = data(:,3);
        S_vec = data(:,5);
        rho_vec = data(:,7);
        flag = find(T_vec==-99|S_vec==-99|rho_vec==-99);
        depth_vec(flag) = [];
        T_vec(flag) = [];
        S_vec(flag) = [];
        rho_vec(flag) = [];
        
        % Quality control (step2): binning
        % binning is performed by fun_binning (see the appendix)
        [T_vec,S_vec,rho_vec,depth_vec] = fun_binning(T_vec,S_vec,rho_vec,depth_vec);
        
        depth{n} = depth_vec;   % m
        T{n} = T_vec;       % oC
        S{n} = S_vec;       % ppt
        rho{n} = rho_vec;     % kg/m3
    else
        % for these who do not have salinity or density data
        % Quality control (step1): remove -99 data values
        depth_vec = data(:,3);
        T_vec = data(:,4);
        S_vec = nan;
        rho_vec = nan;
        flag = find(T_vec==-99);
        depth_vec(flag) = [];
        T_vec(flag) = [];
        
        % Quality control (step2): binning
        % binning is performed by fun_binning (see the appendix)
        [T_vec,S_vec,rho_vec,depth_vec] = fun_binning(T_vec,S_vec,rho_vec,depth_vec);
        
        depth{n} = depth_vec;
        T{n} = T_vec;
        S{n} = S_vec;
        rho{n} = rho_vec;
  
    end
    
end
depth = cell2mat(depth);
T = cell2mat(T);
S = cell2mat(S);
rho = cell2mat(rho);

Calculate the Mixed Layer Depth (MLD) for One Cast

Use the definition of Martin (1985): SST+0.1 (note that -0.1 is modified to be +0.1)

% select one cast and find SST

cast = 5;

SST = T(cast,1);

% find MLD

MLD_index = find(T(cast,:)>=SST+0.1,1,'first');

MLD = depth(cast,MLD_index)

MLD = 51

% calculate absolute salinity and potential temperature

lat = output{cast,4};

lon = -output{cast,3};

P = gsw_p_from_z(-depth(cast,:),lat); %pressure

SA = gsw_SA_from_SP(S(cast,:),P,lat,lon); %absolute salinity

pT = gsw_pt_from_t(SA,T(cast,:),P,0); %potential temperature

% calculate the mean and sd of SA and pT within the SML

mean_pT_SML = mean(pT(1:MLD_index),'omitnan')

mean_pT_SML = -1.6160

sd_pT_SML = std(pT(1:MLD_index),'omitnan')

sd_pT_SML = 0.0176

mean_SA_SML = mean(SA(1:MLD_index),'omitnan')

mean_SA_SML = 29.7687

sd_SA_SML = std(SA(1:MLD_index),'omitnan')

sd_SA_SML = 0.2551

% plotting surface values: Potential Temperature

f = figure;

set(f,'units','centimeters','position',[1,1,9*1.2,12*1.2],'color','w')

FontSize = 15;

plot(pT(1:MLD_index+105),-depth(cast,1:MLD_index+105),'linewidth',1.5)

hold on

plot([pT(MLD_index),pT(MLD_index)],[-depth(cast,1),-depth(cast,MLD_index+105)],'--k','linewidth',1.5)

plot([-2 -0.3],[-MLD,-MLD],'--k','linewidth',1.5)

plot(pT(MLD_index),-depth(cast,MLD_index),'r.','MarkerSize',20)

xlim([-2 -0.3])

box on

grid on

xlabel('Potential Temperature (^{o}C)','FontWeight','bold')

ylabel('Depth (m)','FontWeight','bold')

set(gca,'FontSize',FontSize,'tickdir','out','xaxislocation','top')

% plotting surface values: Absolute Salinity

f = figure;

set(f,'units','centimeters','position',[1,1,9*1.2,12*1.2],'color','w')

FontSize = 15;

plot(SA(1:MLD_index+105),-depth(cast,1:MLD_index+105),'linewidth',1.5)

hold on

plot([SA(MLD_index),SA(MLD_index)],[-depth(cast,1),-depth(cast,MLD_index+105)],'--k','linewidth',1.5)

plot([28 35],[-MLD,-MLD],'--k','linewidth',1.5)

plot(SA(MLD_index),-depth(cast,MLD_index),'r.','MarkerSize',20)

xlim([28 35])

box on

grid on

xlabel('Absolute Salinity (ppt)','FontWeight','bold')

ylabel('Depth (m)','FontWeight','bold')

set(gca,'FontSize',FontSize,'tickdir','out','xaxislocation','top')

% plotting surface values: Density

f = figure;

set(f,'units','centimeters','position',[1,1,9*1.2,12*1.2],'color','w')

FontSize = 15;

plot(rho(cast,1:MLD_index+105),-depth(cast,1:MLD_index+105),'linewidth',1.5)

hold on

plot([rho(cast,MLD_index),rho(cast,MLD_index)],[-depth(cast,1),-depth(cast,MLD_index+105)],'--k','linewidth',1.5)

plot([1023 1028.6],[-MLD,-MLD],'--k','linewidth',1.5)

plot(rho(cast,MLD_index),-depth(cast,MLD_index),'r.','MarkerSize',20)

xlim([1023 1028.6])

box on

grid on

xlabel('Density (kg/m^{3})','FontWeight','bold')

ylabel('Depth (m)','FontWeight','bold')

set(gca,'FontSize',FontSize,'tickdir','out','xaxislocation','top')

% calculate and plot the stability frequency

CT = gsw_CT_from_t(SA,T(cast,:),P); %conservative temperature

[N2, p_mid] = gsw_Nsquared(SA,CT,P,lat);

f = figure;

set(f,'units','centimeters','position',[1,1,9*1.2,12*1.2],'color','w')

FontSize = 15;

plot(N2(1:MLD_index+105),-depth(cast,1:MLD_index+105),'linewidth',1.5)

hold on

plot(10^-3*[0 2],[-MLD,-MLD],'--k','linewidth',1.5)

box on

grid on

xlim(10^-3*[0 2])

xlabel('N^{2} (s^{-2})','FontWeight','bold')

ylabel('Depth (m)','FontWeight','bold')

set(gca,'FontSize',FontSize,'tickdir','out','xaxislocation','top')

Calculate the Mixed Layer Depth (MLD) for All Casts

Use the definition of Martin (1985): SST+0.1 (note that -0.1 is modified to be +0.1)

MLD = ones(profi_num,1);

mean_SA_SML = ones(profi_num,1);

mean_pT_SML = ones(profi_num,1);

mean_rho = ones(profi_num,1);

for cast = 1:profi_num

SST = T(cast,1);

% find MLD

MLD_index = find(T(cast,:)>=SST+0.1,1,'first');

if isempty(MLD_index) || MLD_index == 999

MLD(cast) = nan;

mean_SA_SML(cast) = nan;

mean_pT_SML(cast) = nan;

else

MLD(cast) = depth(cast,MLD_index);

% calculate absolute salinity and potential temperature

lat = output{cast,4};

lon = -output{cast,3};

P = gsw_p_from_z(-depth(cast,:),lat); %pressure

SA = gsw_SA_from_SP(S(cast,:),P,lat,lon); %absolute salinity

pT = gsw_pt_from_t(SA,T(cast,:),P,0); %potential temperature

mean_SA_SML(cast) = mean(SA(1:MLD_index),'omitnan');

mean_pT_SML(cast) = mean(pT(1:MLD_index),'omitnan');

mean_rho(cast) = mean(rho(1:MLD_index),'omitnan');

end

mean_pT_SML(isnan(MLD)) = [];

mean_SA_SML(isnan(MLD)) = [];

mean_rho(isnan(MLD)) = [];

MLD(isnan(MLD)) = [];

% make scatterplots: T-S

f = figure;

set(f,'units','centimeters','position',[1,1,15.5*1.5,10*1.5],'color','w')

FontSize = 20;

color = jet(300);

for n = 1:size(MLD,1)

plot(mean_SA_SML(n),mean_pT_SML(n),'.','color',color(MLD(n),:),'MarkerSize',15)

hold on

end

colormap("jet")

colorbar

caxis([1 300])

xlabel('Mean Absolute Salinity (ppt)','FontWeight','bold')

ylabel('Mean Potential Temperature (^{o}C)','FontWeight','bold')

title('MLD (m) and Averaged Water Properties','FontWeight','bold')

set(gca,'FontSize',FontSize,'tickdir','out')

% make scatterplots: rho vs MLD

f = figure;

set(f,'units','centimeters','position',[1,1,15.5*1.5,10*1.5],'color','w')

FontSize = 20;

plot(MLD,mean_rho,'.','MarkerSize',15)

xlabel('Mixed Layer Depth (m)','FontWeight','bold')

ylabel('Mean Density (kg/m^{3})','FontWeight','bold')

set(gca,'FontSize',FontSize,'tickdir','out')