Interpolation of non monotonic data.

Hello, I need to interpolate two data. One is temperature and other is CO2. I need to interpolate it on same time interval and want to see the value of both (whose value is higher than other). I have tried interp1 function and I have been through many questions and answers here but couldn't find related. I have attached my code here. I always got the error of non monotonic increasing. I have a data from last thousand of years till 2010. In that temperature and CO2 has increased and decreased in some intervals and I can't reshape as it affects on final result. If anyone can help I would say please. I

clear all

load CO2data % Historical CO2 data from Harris

ageCO2=CO2data.years;
fCO2=CO2data.fCO2;
timeCO2=1950-ageCO2;
size(timeCO2)

figure(101)
plot(timeCO2/1000,fCO2)
xlabel('time (1000 years)')
ylabel('CO2 level (ppm)')
title('Historical CO2 level in the atmosphere (ppm)')


load Tdata % Historical temp data from Harris


ageT=Tdata.years;
Temp=Tdata.T;
timeT=1950-ageT;
size(timeT)

figure(102)
plot(timeT/1000,Temp)
xlabel('time (1000 years)')
ylabel('Temperature anomaly (C)')
title('Historical temperature anomaly (C)')

figure(103)
T=plotyy(timeCO2/1000,fCO2,timeT/1000,Temp);
xlabel('time ( 1000 years)')
ylabel(T(1),'CO2 level (ppm)')
ylabel(T(2),'historic temperature level(c)')
title('Atmospheric CO2 vs Temperature level')


u=interp1(fCO2,timeCO2/1000,280);

new_fCO2=linspace(280,191,length(fCO2));
new_timeCO2=interp1(fCO2,timeCO2/1000,new_fCO2,'spline');

figure(102)
plot(fCO2,timeCO2/1000,new_fCO2,new_timeCO2,'-o')

[KSSV]

What problem you are facing now?

[TEJASHKUMAR PATEL]

Error in interp1 (line 161)

F = griddedInterpolant(X,V,method);

Error in CO2interpolation (line 16)

u=interp1(fCO2,timeCO2/1000,280);

[TEJASHKUMAR PATEL]

Is there any way or any function I can interpolate CO2 and temperature with respect to time? Any command or function syntax?

Answer 1

[Bjorn Gustavsson]

The interpolation-function does something else than what you seem to try. It takes one data-vector, D, taken at a discrete set of monotously (sp?) varying points, t, and calculates interpolatevalues of D at another set of points, ti. In your case you have your t as years, if I understand correctly, and some corresponding measure of CO2. you might reinterpolate that data to a regular "montly" value like this:

ti = linspace(min(timeCO2),max(timeCO2),12*round(max(timeCO2)-min(timeCO2)));
fCO2_new = interp1(timeCO2,fCO2,ti,'pchip');

That is how the interpolation-function works. If that is the operation you need is not clear from the code you posted.

HTH

[TEJASHKUMAR PATEL]

Let me try as you have suggest.

[TEJASHKUMAR PATEL]

I got new error like this. I tried by my way but I do not know why it showing like this I am using 2015b version.

Expression or statement is incorrect--possibly unbalanced (, {, or [.

[Bjorn Gustavsson]

Fixed copy-and-paste typo.

[TEJASHKUMAR PATEL]

Thanks for your time. After some manipulation I get the new error of "attemp to execute script name as a file" 
but somehow I solved it but again I am where I was. Got the new error like this,

Error using griddedInterpolant
The grid vectors are not strictly monotonic increasing.

Error in interp1 (line 161)
        F = griddedInterpolant(X,V,method);

Error in nobealo (line 32)
fCO2_new = interp1(timeCO2,fCO2,ti,'pchip');

[Bjorn Gustavsson]

Bah, fixed another typo...

[TEJASHKUMAR PATEL]

Still same. I have attached both temperature and CO2 data with that you can help me more precisly. Thanks a lot

Error using griddedInterpolant

The grid vectors are not strictly monotonic increasing.

Error in interp1 (line 161)

F = griddedInterpolant(X,V,method);

Error in nobealo (line 32)

fCO2_new = interp1(timeCO2,fCO2,ti,'pchip');

[Bjorn Gustavsson]

If you do:

timeCO2=1950-ageCO2;                                      
subplot(2,2,1),plot(diff(timeT),'.')     
subplot(2,2,2),plot(diff(timeT)==0,'.')
subplot(2,2,4),plot(diff(timeCO2)==0,'.')
subplot(2,2,3),plot(diff(timeCO2),'.')

You will see that two consecutive points in your CO2-data are from the same time. That has to be resolved somehow. This way you get the average CO2-value:

timeCO2=1950-ageCO2;                                      
idtCO2 = find(diff(timeCO2)==0);
timeCO2(idtCO2) = timeCO2(idtCO2)/2 + timeCO2(idtCO2+1)/2; % Average
timeCO2(idtCO2+1) = [];                                    % remove the second point from the data
fCO2=CO2data.fCO2;                                % Same procedure for fCO2:
fCO2(idtCO2) = fCO2(idtCO2)/2 + fCO2(idtCO2+1)/2; % Average
fCO2(idtCO2+1) = [];                              % Remove second point

That is then possible to re-interpolate, here to 100000-timesteps between the first and last time in either data-set:

fCO2_reinterpolated = interp1(timeCO2,fCO2,linspace(min(min(timeCO2),min(timeT)),max(max(timeCO2),max(timeT)),1e5),'pchip');

HTH

[TEJASHKUMAR PATEL]

Hey, above solution almost solved all of my problem regarding interpolation of non monotonic incresing data. Thank you very much. Now I will look into this little bit more in deep...