# vxvy2uv documentation

vxvy2uv is part of Antarctic Mapping Tools for Matlab (Greene et al., 2017). Click here for a complete list of functions in AMT.

This function transforms polar stereographic vector components to georeferenced (zonal and meridional) vector components.

## Syntax

```[U,V] = vxvy2uv(lat,lon,vx,vy)
[U,V] = vxvy2uv(x,y,vx,vy)```

## Description

[U,V] = vxvy2uv(lat,lon,vx,vy) transforms polar stereographic vector components vx, vy referenced to the geographic locations in lat and lon to geographic zonal and meridional components.

[U,V] = vxvy2uv(x,y,vx,vy) transforms polar stereographic vector components vx, vy referenced to the polar stereographic locations in x and y to geographic zonal and meridional components. Polar stereographic coordinates are automatically determined if any value in the first two inputs of vxvy2uv exceed normal geographic coordinate values.

## Example 1: Continental scale motion

Consider a vector field depicting motion from left to right on a standard polar stereographic map projection. Make its x component 1.5 magnitude everywhere, and we'll add a slight downward-dipping y component too, just to make things interesting. To set up the grid, us psgrid to create a 6000 km wide grid at 250 km resolution, centered on the South Pole:

```[x,y] = psgrid('south pole',6000,250,'xy');
vx = 1.5*ones(size(x));
vy = -0.3*ones(size(x));
```

In cartesian coordinates this is what the vector field looks like. We'll overlay a Bedmap2 grounding line for context:

```quiver(x,y,vx,vy)
hold on
bedmap2('gl','xy')
``` ```close
```

We can convert this vector field to zonal and meridional components like this:

```[u,v] = vxvy2uv(x,y,vx,vy);
```

Let's show the zonal and meridional components on a map. We'll have to use ps2ll to get the georeferenced coordinates of our xy grid first. Initialize a map with antmap, plot a filled coast line as a patch object for context, and plot the vector field with the AMT function quivermc:

```[lat,lon] = ps2ll(x,y);

antmap
bedmap2 'patchcoast'
quivermc(lat,lon,u,v)
``` That looks about right. There's one funny vector close to the South Pole because that's where small errors in angles go haywire.

```close
```

## Example 2: Glacier motion

Let's use the MEaSUREs toolbox to look at ice motion around Recovery Glacier. Start by defining a 500 km wide grid centered on Recovery Glacier. Make the grid 3 km resolution.

```[lat,lon] = psgrid('recovery glacier',500,3);
```

The measures_interp function can return ice velocity components for at each of our lat,lon grid points:

```vx = measures_interp('vx',lat,lon);
vy = measures_interp('vy',lat,lon);
```

In cartesian coordinates, the vector field looks like this:

```[x,y] = ll2ps(lat,lon);
quiver(x,y,vx,vy)
``` That's a bit hard to parse using Matlab's quiver function, but if you zoom in the arrows are there. For example,

```axis([-640322 -553225 758771 839473])
``` ```close
```

You might want zonal and meridional components of ice motion. Let's do that and show vectors atop a ramp image. When calling quivermc below I'm color-scaling the arrows using one of my favorite colormap generators, brewermap, and I don't want to show too many little arrows, so I'll downsample the field to 20% with the 'density',20 option:

```[u,v] = vxvy2uv(lat,lon,vx,vy);

mapzoom('recovery glacier')
ramp
quivermc(lat,lon,u,v,'colormap',brewermap(256,'reds'),'density',20)
``` ## Citing AMT

If this function or any other part of Antarctic Mapping Tools is useful for you, please cite the paper that describes AMT.

Greene, C. A., Gwyther, D. E., & Blankenship, D. D. Antarctic Mapping Tools for Matlab. Computers & Geosciences. 104 (2017) pp.151-157. doi:10.1016/j.cageo.2016.08.003.

## Author Info

The vxvy2uv function and supporting documentation were written by Chad A. Greene of the University of Texas at Austin's Institute for Geophysics (UTIG), September 2015.