Shading below y=c in a semilogy plot

I am working with this code for two adjacent semilog subplots (y axis is in log-scale, x axis is a time series). I would like the region of the plots below y = 10^-3 to be shaded in gray, but I am having trouble doing this with functions such as patch, fill, and area. I feel like it should not be complicated, but I think I am blocked by the fact that they are semilogy plots, and that the x axis has specific time formatting.

Thank you in advance for the support. I am using MATLAB 2019a

%% Wells

optW=detectImportOptions('wells');
optW.Sheet='Sheet7';
optW.DataRange='A3';
optW.VariableNamesRange='A2';
optW.VariableTypes(2:10)={'double'};
tW=readtable('20211110_longtermanalysis_wells_PA_ML',optW,'ReadVariableNames',1);

tW.Properties.VariableNames(1)={'WellID'};
tW=tW(strlength(tW.WellID)>0,:);   % was extraneous stuff at bottom from the max() formula added...
tW=stack(tW,2:10,'NewDataVariableName',{'Response'},'IndexVariableName','Date'); % recast to put date into table
tW.Date=datetime(replace(string(tW.Date),'x',''),'InputFormat','dd_MMM_uuuu','Format','MMMyyyy'); % convert to datetime

tW.Response(tW.Response==0)=3*0.0001;         % reset zeros to a minimal value

tW=convertvars(tW,vartype('cellstr'),'categorical');    % use categorical variables where appropriate

hAxw=subplot(1, 2, 1) % it is the use of hold that stops semilogy() from setting yscale
hAxw.YScale='log'; % so, create the axes handle and set the log axis first

fnColor_w=@(t)char('b'*(t=='Gas')+'r'*(t~='Gas'));                % a lookup table for the color

hLw=rowfun(@(x,y,t)semilogy(x(isfinite(y)),y(isfinite(y)),strcat('o--',fnColor_w(t(1)))),tW,'GroupingVariables','WellID','InputVariables',{'Date','Response','WellType'},'NumOutputs',1,'OutputFormat',"uniform");

isPlugged_W=rowfun(@(s)all(s=='Plugged'),tW,'GroupingVariables','WellID', ...
            'InputVariables','PluggingStatus','OutputFormat','uniform'); % which lines are plugged
set(hLw(isPlugged_W),{'MarkerFaceColor'},num2cell(reshape([hLw(isPlugged_W).Color],3,[]).',2)) % set those markers

xlim([datetime(2013,1,1) datetime(2021,1,1)]);
ylim([1E-4, 1]);

box on;


%% Controls

optC=detectImportOptions('wells');
optC.Sheet='Sheet8';
optC.DataRange='A3';
optC.VariableNamesRange='A2';
optC.VariableTypes(2:10)={'double'};
tC=readtable('20211110_longtermanalysis_wells_PA_ML',optC,'ReadVariableNames',1);

tC.Properties.VariableNames(1)={'ControlID'};
t=tC(strlength(tC.ControlID)>0,:);   % was extraneous stuff at bottom from the max() formula added...
tC=stack(tC,2:10,'NewDataVariableName',{'Response'},'IndexVariableName','Date'); % recast to put date into table
tC.Date=datetime(replace(string(tC.Date),'x',''),'InputFormat','dd_MMM_uuuu','Format','MMMyyyy'); % convert to datetime

tC.Response(tC.Response==0)=3*0.0001;         % reset zeros to a minimal value

tC=convertvars(tC,vartype('cellstr'),'categorical');    % use categorical variables where appropriate


hAxc=subplot(1, 2, 2); hold on  % it is the use of hold that stops semilogy() from setting yscale
hAxc.YScale='log'; % so, create the axes handle and set the log axis first

fnColor_c=@(t)char('b'*(t=='Gas')+'r'*(t~='Gas'));                % a lookup table for the color

hLc=rowfun(@(x,y,t)semilogy(x(isfinite(y)),y(isfinite(y)),strcat('o--',fnColor_c(t(1)))),tC,'GroupingVariables','ControlID','InputVariables',{'Date','Response','WellType'},'NumOutputs',1,'OutputFormat',"uniform");

isPlugged_C=rowfun(@(s)all(s=='Plugged'),tC,'GroupingVariables','ControlID', ...
            'InputVariables','PluggingStatus','OutputFormat','uniform'); % which lines are plugged
        
set(hLc(isPlugged_C),{'MarkerFaceColor'},num2cell(reshape([hLc(isPlugged_C).Color],3,[]).',2)) % set those markers

xlim([datetime(2013,1,1) datetime(2021,1,1)]);
ylim([1E-4, 1]);

set(0, 'defaultLineMarkerSize', 11) % increase marker size
% xes = [735235 738157 738157 735235]; yes = [5E-4 5E-4 0.2 0.2];
% patch(xes,yes,'red')
box on

[Star Strider]

In general, all of those functions work on logarithmically-scaled plots and datetime scaled plots, although the most robust (over several releases) in my experience is fill. The correct approach is to first plot them using linear scaling, then do the logarithmic transformation (this of course requires that the coordinates exist under logarithmic transformation, so they must all be finite and greater than zero, since the patch objects will not work with non-finite values).

That aside, I cannot make any of them work with your code, at least in part because it is so difficult to figure out what you’re doing.

Example —

x = datetime(2023,01,01) + calmonths(0:6).';                % Assume Column Vectors
y = 2 + sin((0:numel(x)-1)*2*pi*1.2/numel(x)).';


figure
patch([x; flip(x)], [zeros(size(y))+1; flip(y)], 'b')
Ax = gca;
Ax.YScale = 'log';

.