What is the difference between these two scripts; and which one is more appropriate to use

% the dataset is *u = squeeze(tdata(1,:,:)./10); v = squeeze(tdata(2,:,:)./10);*

%1st

                    nu = u.*cos(rlong) + v.*sin(rlong);
                    nv = -u.*sin(rlong) + v.*cos(rlong);
                    R = sqrt(nu.*nu + nv.*nv);

% 2nd

                    [TH,R] = cart2pol(v,u);
                     D = rad2deg(TH);

Answer 1

[Roger Stafford]

In "u = squeeze(tdata(1,:,:)./10);" the first level of the first dimension of three-dimensional 'tdata' is divided by 10 and converted into a two dimensional matrix. The 'v' is the same for the second level of that first dimension.

In the second pair, the coordinate axes for the point (u,v), (or rather the matrices of points,) is rotated counterclockwise by radian angle 'rlong' and (nu,nv) are the coordinates with respect to these new axes. The third equation gives the euclidean distance of the points from the origin.

In the third pair the first of the pair converts each of those original cartesian coordinates into polar coordinates. The second changes each of the angles in the polar coordinates from radian measure to degree measure. (It would appear the cartesian coordinates here are in reverse order.)

Asking which is the more appropriate is a meaningless question in this context. They all act together as a unified whole.

An alternate interpretation of the second pair is that all the points have been rotated clockwise by radian angle 'rlong' and (nu,nv) are their rotated cartesian coordinates with respect to the original axes.

[Sophia]

Here v and u are velocity vectors, so when i am taking the magnitude of u and v so by first rotating and then calculating the magnitude by using sqrt((nu.*nu)+(nv.*nv)) to my assumption it would be same as the R in this equation [TH,R] = cart2pol(v,u);

That's what the question is.

[Roger Stafford]

Your equations only make sense if u and v are cartesian components of velocity vectors, not vectors themselves. But if all you want is the magnitude of each velocity vector, why not just do this:

R = sqrt(u.^2+v.^2);

It would give you a matrix of magnitudes. Why bother with rotations and 'cart2pol'?

[Sophia]

The dataset i am using says in its description, here is the link

https://nsidc.org/data/docs/daac/nsidc0116_icemotion.gd.html

Here are the details of the projection-

https://nsidc.org/data/ease/ease_grid.html

The reason why i need to do this, because u and v values change with the change in hemisphere. i.e. from W to E, cuz of the EASE Grid Projection