`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.

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## Contents

## 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.