Interpolation of time series of data at X and Y coordinates

Hi, I have a set of, X and Y coordinates, i have the time series of temperature data (not a single value) corresponding to these coordinates. I need to get the time series of temperatures at other required coordinates in the domain by interpolating the existing data. Could you please give some logic here? Thank you.

Answer 1

[Matt J]

Use scatteredInterpolant or griddedInterpolant depending on whether your (X,Y,t) data is scattered or gridded.

[Teja Reddy]

Hi Matt J, thanks for your response to my query. But, I have set of data points (many values at a coordinate) at each coordinate. I need to get the same number of data points (not one value) at my required coordinate after interpolation.

Thanks.

[Matt J]

That shouldn't affect my answer. You can interpolate at multiple points using gridded- or scattered -Interpolant. Example:

[X,Y,Time]=ndgrid(1:4,1:4,1:5); 
Temp=rand(size(X));

F=griddedInterpolant(X,Y,Time,Temp);

xq=1.1; yq=2.3; tq=F.GridVectors{3}; %query at xq,yq, and all times tq

TempQ(1:5)= F({xq,yq,tq})  %Interpolated temperatures

TempQ = 1×5

0.4724 0.4795 0.6473 0.2859 0.4701

[Teja Reddy]

Hi Matt J,

Thank you so much for your answer and your patience. I am still confusing, I am very sorry for the poor understandin. I am attaching the query, I hope it will be understandable. Thank you so much.

[Matt J]

I suggest attaching your (x,y,time,temp) data in a .mat file so we can more easily study the data structure and demonstrate solutions.

[Teja Reddy]

Hi Matt.J,

Thank you so much.

Please find the .mat file attached. In this file, we can see the temperature data at 21 locations and corresponding x and y coordinates.

I need to have the "Temperature data" at the below given coordinates with the same size at the existing coordinates.

Each column in the "Temperature" data is corresponding to one x and y coordinate.

(x,y) = (20, 360)

(x,y) = (20, 340)

(x,y) = (20, 390)

Thank you so much.

[Matt J]

load data

Temperature=Temperature.';
N=width(Temperature);

F=scatteredInterpolant([x,y],Temperature(:,1));

[xq,yq]=deal(15,380);  %query coordinates

T=nan(N,1);
for i=1:N
    
    F.Values=Temperature(:,i);
    
    T(i)=F(xq,yq);
    
end

plot(T);
xlabel 'Time'; ylabel 'Temperature'
title 'Temperature v Time @(xq,yq)'

[Teja Reddy]

Hi Matt J,

It is very nice that you have solved so quickly.

When I run the same programs as you have given, it is giving the error that "Unrecognized function or variable 'Temperature'." I am using R2020B of MATLAB.

Thanks

[Matt J]

When I run the same programs as you have given

It can't be the same. At the very least, it seems your data.mat does not contain a Temperature variable.

[Teja Reddy]

Hi Matt J, It is there when i load the data.mat file. Can you send you me the data.mat file when you run your program? I am sorry for the longer discussion on this.

Thanks.

[Teja Reddy]

Hi Matt J, it is also throwing an error "Undefined function 'width' for input arguments of type 'double'

Thanks

[Teja Reddy]

Hi Matt J, it is working fine. Thank you so much for your solution and patience.

[Matt J]

You're welcome, but please Accept-click the answer to indicate that it worked.

[Teja Reddy]

Hi Matt J,

I have a question about the same query.

Why you considered only first column of Temperature while calculating "F" as shown below.?

F=scatteredInterpolant([x,y],Temperature(:,1));

The program should consider all the data points corresponding to all coordinates to get the data at the query point.

Is my question correct?

Thanks

[Matt J]

Why you considered only first column of Temperature while calculating "F" as shown below.?

It was just a way of intializing F. The v argument in scatteredInterpolant([x,y],v) needs to have the same number of rows as [x,y]. I could just as easily have done,

F=scatteredInterpolant([x,y],zeros(size(x)));

The program should consider all the data points corresponding to all coordinates to get the data at the query point.

What I've posted does compute the Temperature T(xq,yq,tq), where tq is a fixed time point, from all (x,y,tq). For each fixed (x,y) we've assumed that the temperatures are all sampled at the same set of times t. That being the case, we don't need to consider Temperatures at times other than tq to get T(xq,yq,tq).

[Teja Reddy]

Thank you Matt for your explanation.