Interpolating a velocity field between time steps

Hi! I am a relatively new user of Matlab, working on a project of particle advection in a hydodynamic environment. In order to simulate the advection I have to interpolate current velocities between time steps. I have a field of mean current velocities for each day. I want to split the day into 4 hour intervals, hence I would need to interpolate the velocities at 5 extra time steps. My velocity matrix is named MER.u (92x100x15), where the third dimension represents each day (15 in total). When trying to interpolate I am returned with an error ("The grid vectors do not define a grid of points that match the given values.").

I am struggling to construct a sentence where I would tell Matlab to treat MER.u(:,:,it), to be the corresponding value of MER.mt(1). I am aware that a date giving a field of velocities is not exactly a function but I was assuming linear 1D interpolation is the correct method for this (of course I could and likely am wrong). Can you please help with this, it should be fairly easy.

The code I am using is given bellow.

%MER.mt is a vector of 15 dates in datenum format
%MER:u is a grid 92x100x15 of velocities for 15 days

tn= [MER.mt(1):1/6:MER.mt(end)] ;
interp1(MER.mt, MER.u, tn);

[KSSV]

You have a grid of 92X100. There is spatial variation as well as temporal variation. How you can use interp1? Give more information about the problem and data you have.

[Timotej Turk Dermastia]

Yes I'm aware of this and as I said I don't know whether this is the right approach however My x in interp1(x,v,xq) is a 15x1 vector of times and my xq is a 85x1 vector of new times. My disiried output would be a grid of velocities 92x100x85 where 5 new fields would be calculated between the current time steps.

Answer 1

[KSSV]

u = rand(92,100,15) ;           % random xcomponent of veclocity 
v = rand(92,100,15) ;           % random ycomponent of velocity 
t = linspace(1,150,15) ;        % time steps
ti = [5,20,70] ;                % time where velocities are to be interpolated 
% Initialize interpolated components
ui = zeros(92,100,length(ti)) ;
vi = zeros(92,100,length(ti)) ;
for i = 1:92
   for j = 1:100
       % u comp interpolation
       uij = squeeze(u(i,j,:)) ;
       ui(i,j,:) = interp1(t,uij,ti) ;
       % v comp interpolation
       vij = squeeze(v(i,j,:)) ;
       vi(i,j,:) = interp1(t,uij,ti) ;
  end
end

[Timotej Turk Dermastia]

This worked. Thanks!