#
`measures_interp` documentation

The `measures_interp` interpolates MEaSUREs ice surface velocity data at any location(s), along a path, or onto a new grid.

## Contents

## Before you use this function:

This function requires the MEaSUREs InSAR-Based Antarctica Ice Velocity Map, Version 2 netcdf dataset which can be downloaded here: https://nsidc.org/data/NSIDC-0484.

## Syntax

speedi = measures_interp('speed',lati_or_xi,loni_or_yi) [vxi,vyi] = measures_interp('velocity',lati_or_xi,loni_or_yi) err = measures_interp('error',lati_or_xi,loni_or_yi) count = measures_interp('count',lati_or_xi,loni_or_yi) [u,v] = measures_interp('uv',lati_or_xi,loni_or_yi) [along,across] = measures_interp('track',lati_or_xi,loni_or_yi) [...] = measures_interp(...,'method',interpMethod) [...] = measures_interp(...,'fill')

## Description

`speedi = measures_interp('speed',lati_or_xi,loni_or_yi)` returns local surface velocity at the location(s) given by `lati,loni` or `xi,yi`. Input coordinates are determined as geographic or polar stereographic automatically by the `islatlon` function.

`[vxi,vyi] = measures_interp('velocity',lati_or_xi,loni_or_yi)` returns the polar stereographic (true latitude 71S) x and y components of velocity.

`err = measures_interp('error',lati_or_xi,loni_or_yi)` returns a scalar value of uncertainty estimates presented with the dataset.

`count = measures_interp('count',lati_or_xi,loni_or_yi)` returns the count of scenes used per pixel.

`[u,v] = measures_interp('uv',lati_or_xi,loni_or_yi)` returns the geographic zonal (positive eastward) and meridional (positive northward) components of velocity.

`[along,across] = measures_interp('track',lati_or_xi,loni_or_yi)` returns velocity components along or across a specified track. This can be used to estimate flow through (the across component) a flux gate or grounding line. For the across-track component, positive values are to the right.

`[...] = measures_interp(...,'method',interpMethod)` specifies any interpolation supported by interp2. Default `interpMethod` is `'linear'`.

## Example 1: South Pole station drift

For a single location, interpolation is easy:

```
measures_interp('speed',-90,0)
```

ans = 7.32

which of course is exactly the same as

```
measures_interp('speed',-90,100)
```

ans = 7.32

and is very similar to

measures_interp('speed',-90,0,'method','cubic')

ans = 7.25

But differences in interpolation methods are tiny compared to the uncertainty of InSAR or any satellite-based surface velocity measurements. The self-reported uncertainty at the South Pole is about 11 m/yr, see:

```
measures_interp('error',-90,100)
```

ans = 11.01

## Example 2: Ice speed on a custom grid

You may be working with some other data set that has its own lat/lon grid. Here we consider a 500 km wide grid at 300 m resolution centered on the Siple Coast:

% Create a grid: [x,y] = psgrid('siple coast',500,0.3,'xy'); % Get speed data at each grid point: speed = measures_interp('speed',x,y); % Plot: pcolor(x,y,log10(speed)) shading interp axis equal hold on

It might also be nice to overlay some velocity vectors. Simply use Matlab's built-in `quiver` function. But before we call `quiver`, let's downsample the dataset because 1667x1667 little arrows would just end up looking like a big black square, as each arrow would have to be less than a pixel wide. There are a few ways to downsample. You can simply create a much more coarse grid with `psgrid`, however there would be one tiny problem with that, which is aliasing--probably not much of an issue, but a proper way to deal with aliasing is to perform a low-pass filter before sampling. If you have Matlab's Image Processing Toolbox, the `imresize` function automatically performs antialiasing that way, so we'll use `imresize` and to scale the 300 m grid to 2% of its resolution, or 15 km resolution. Like this:

% Get velocity components: [vx,vy] = measures_interp('velocity',x,y); % Plot quiver arrows on a 15 km grid: quiver(imresize(x,0.02),imresize(y,0.02),imresize(vx,0.02),imresize(vy,0.02),'k');

## Example 3: Flux gate calculation of Thwaites Glacier mass loss

To calculate mass flux across a grounding line, we first define a grounding line. Here we use the grounding line from the Bedmap2 Toolbox and clip the data to include only the region of Thwaites Glacier:

```
load bedmap2gl
gllat = flipud(gllat{1});
gllon = flipud(gllon{1});
gllat = gllat(gllon>-108.5&gllon<-104.5);
gllon = gllon(gllon>-108.5&gllon<-104.5);
```

For context, we can plot this grounding line on a `lima` image with velocity vectors overlaid.

% Initialize a base map: figure lima('thwaites glacier',150,'xy') hold on % Overlay black velocity vectors: measuresps('vel','k') % Plot the segment of grounding line we're using: plotps(gllat,gllon,'g','linewidth',2) % Add text labels: textps(gllat(1),gllon(1),'start','color','g',... 'fontweight','bold','backgroundcolor','w') textps(gllat(end),gllon(end),'end','color','r',... 'fontweight','bold','backgroundcolor','w')

If we think of the grounding line as a path along which you might walk, the only component of ice flow that contributes to continental mass loss is the cross-path component. To estimate the volume of ice crossing the grounding line, interpolate the cross-track component of ice velocity along the entire path of the grounding line, then multiply velocity by thickness for each unit length along the grounding line.

First we define `x` as the distance you'd walk along the grounding line and `dx` is the approximate distance between points along the grounding line. Here we use the `pathdistps` function to calculate the distance traveled along the grounding line.

% Distance along grounding line: d = pathdistps(gllat,gllon); % Distance between each grounding line data point: dx = gradient(d); crossTrackVelocity = measures_interp('cross',gllat,gllon); thickness = bedmap2_interp(gllat,gllon,'thickness'); thickness(isnan(thickness))=0; % zero thickness where undefined flowAcrossGL = crossTrackVelocity.*thickness; figure plot(d/1000,flowAcrossGL) xlabel('distance along grounding line (km)') ylabel('flow across gl (m^3/yr per meter along grounding line)') box off; axis tight;

Above, we see that sometimes ice flow is negative--that happens where a sinuous grounding line lets ice go over the ocean, then reground, then cross the grounding line again. We can easily distill all this rich information down to a single value of mass loss if we ignore firn density and say that everything flowing across the grounding line is pure ice. `massBalanceGT` is taken as the negative to indicate mass loss and multiplied by `1e-12` to convert from kg to GT.

```
totalVolFlow = sum(flowAcrossGL.*dx);
iceDensity = 917; % kg/m3
massBalanceGT = totalVolFlow*iceDensity*1e-12
```

massBalanceGT = 113.97

This value is in close agreement with 113.5 GT/yr found by Rignot et al., 2013.

## Citing these datasets

VELOCITY DATA: Rignot, E., J. Mouginot, and B. Scheuchl. 2017. MEaSUREs InSAR-Based Antarctica Ice Velocity Map, Version 2. [Indicate subset used]. Boulder, Colorado USA. NASA National Snow and Ice Data Center Distributed Active Archive Center. doi: http://dx.doi.org/10.5067/D7GK8F5J8M8R.

A LITERARY REFERENCE FOR THE VELOCITY DATA: Rignot, E., J. Mouginot, and B. Scheuchl. 2011.Ice Flow of the Antarctic Ice Sheet, Science, Vol. 333(6048): 1427-1430. doi:10.1126/science.1208336.

ANTARCTIC MAPPING TOOLS: Greene, C.A., Gwyther, D.E. and Blankenship, D.D., 2016. Antarctic Mapping Tools for Matlab. Computers & Geosciences. http://dx.doi.org/10.1016/j.cageo.2016.08.003

## File history

July 2014: First version written.

August 2014: Updated as a plugin for Antarctic Mapping Tools.

October 2016: Fully rewritten--Now reads data from the new measures_data function, which reads the .nc file directly.

May 2017: Updated for data version 2.

## Author Info

This function was written by Chad A. Greene of the University of Texas Institute for Geophysics (UTIG), July 2014. Rewritten October 2016 for efficiency and usability.