# bottom documentation

bottom returns the lowermost finite values in a 3D matrix. This function is useful for getting the seafloor temperature or atmospheric surface temperature in the presence of topography.

## Syntax

```Zb = bottom(Z)
[Zb,ind] = bottom(Z)```

## Description

Zb = bottom(Z) returns a 2D matrix containing the lowermost finite values in the 3D matrix Z.

[Zb,ind] = bottom(Z) also returns 2D matrix ind which contains the indices along the third dimension of Z corresponding to the lowermost finite values in Z.

## Example: Drake Passage

This example uses some gridded ocean temperature data from the Southern Ocean Database (described below). Begin by loading the example data:

```load sodb_example

whos % displays the names and sizes of variables
```
```  Name         Size                 Bytes  Class     Attributes

d           44x1                    352  double
lat          1x61                   488  double
lon          1x91                   728  double
ptm         61x91x44            1953952  double
readme       1x79                   158  char

```

The 61x91x44 matrix ptm contains potential temperatures at latitudes lat, longitudes lon, and depths d. Here's the potential temperature at the deepest depth, d(44)

```imagescn(lon,lat,ptm(:,:,44))

cmocean thermal
cb = colorbar;
ylabel(cb,'potential temperature (\circC)')
xlabel 'longitude'
ylabel 'latitude'
``` That's not much information! That's because throughout most of the domain the seafloor is shallower than d(44) = 5500 m deep, so we just get NaN values wherever the the 5500 m layer is deeper than the bathymetry.

So instead, plot the lowermost finite values with the bottom function:

```figure
imagescn(lon,lat,bottom(ptm))

cmocean thermal
caxis([-2 12])
cb = colorbar;
ylabel(cb,'bottom temperature (\circC)')
xlabel 'longitude'
ylabel 'latitude'
``` Since we have a depth array d and indices ind corresponding to the deepest finite values at each grid cell, we can get a 2D grid of bottom depths simply from d(ind). Add them to the map as contours:

```% Get bottom temperature and corresponding indices:
[T_bot,ind] = bottom(ptm);

% Make a 2D bottom depth matrix:
D = d(ind);

% Overlay bathymetry contours:
hold on
contour(lon,lat,D,0:1000:5500,'k')

% Underlay a silly-looking earth image:
h = earthimage;
uistack(h,'bottom');
``` On a mildly interesting note, the bottom temperature seems to have some relationship to the bottom depth. Compare the two in profile like this:

```figure
plot(T_bot(:),D(:),'.')
axis tight ij % flips y direction
box off
xlabel 'bottom temperature \circC'
ylabel 'bottom depth (m)'
``` ## How the sodb_example data were acquired

The sodb_example.mat data come from the Southern Ocean Database and were saved using Antarctic Mapping Tools for Matlab (Greene et al., 2017) via the following code:

```lon = -180:2:0;
lat = -75:0.5:-45;
[Lon,Lat] = meshgrid(lon,lat);
[ptm,d] = sodb_interp('ptm',Lat,Lon);
readme = 'potential temperature data from the Southern Ocean Database (Orsi and Whitorth)';
save('sodb_example.mat','lat','lon','ptm','d','readme');```

## Author Info

This function is part of the Climate Data Toolbox for Matlab. The function and supporting documentation were written by Chad A. Greene of the University of Texas at Austin.