Name __________________________
Oceanographic & Meteorological Quantitative Methods – SO335 Lab 3 – (100 pts)
*All code written for this lab should be contained in an appropriately commented script file that
is handed in upon completion of the lab.
Objectives:
At the conclusion of this lab, you should be able to:
(1) Better understand uses of the del operator 
(2) Calculate gradient, divergence, and vorticity using  applied to both scalars (for gradient)
and vectors (for divergence and curl)
(3) Use MATLAB to accomplish objectives (1) and (2).
I. Gradient of a scalar
In Lab 1, you analyzed gridded pressure data for two dates of interest: 28 Jun 2012 and 25 Dec
2013. In this lab, we will return to the pressure fields (so you should load lab1.mat and lab3.mat).
1. Use the gradient function in MATLAB to plot filled contours of pressure gradient for both
dates. In addition to the standard expectations for your figure (appropriate title and axis labels),
add labels to the contours by modifying the following syntax template (replace “….” as
appropriate):
[dpdx,dpdy] = gradient (….);
presgrad_magnitude = sqrt(….);
[c,h] = contourf(….);
clabel(c,h); %clabel will label the contour lines
For hints at how to correctly use gradient and clabel, you should look at the help files for both
(type help gradient and help clabel at the command prompt). Usage examples appear at the top of
the help file. Often there are multiple ways to use each function; the most common uses will
appear first. For the dx and dy spacing, instead of converting to km (or to m), we will continue
with degrees. The spacing is thus 2.5° by -2.5° in the x- and y-direction. (Note the y-spacing is
negative: look at the variable “lat”: point 1 is 90, point 2 is 87.5, point 3 is 85, etc… so the
latitudes count down by 2.5 degrees).
2. Use the quiver function in MATLAB to plot the iˆ and ĵ pressure gradient components
(calculated above using the gradient function) overlaid on contour-filled magnitudes of pressure
gradient and simple, green contour lines of the pressure field. The result is a figure with three
data pieces: contour-filled pressure gradient magnitude, pressure curves (in mb), and quivered
pressure gradient vector.
1
“Pretty up” each figure using the following: make the pressure gradient vector arrows red to help
us see them. Scale the vectors by 2 (see the quiver help command for an example). Standardize
the color ranges using caxis (suggest 0 to 5 as one possible range that shows enough detail to be
useful). Add coastlines. Add a colorbar. Add appropriate titles and axis labels.
You should complete these two tasks for both 28 Jun 2012 and 25 Dec 2013, resulting in four
figures. Only print and attach to the lab deliverable the two figures created in #2 (10 pts
each).
You should also type a one-paragraph description (double-spaced) of the results. In this
paragraph, analyze the relationship between the pressure gradient vectors, the pressure gradient
magnitude, and the pressure lines themselves. Also comment on any important differences
between the two dates. (10 pts).
II. Divergence of a vector
In addition to pressure, the NCEP–DOE Reanalysis II product http://www.esrl.noaa.gov/psd/
data/gridded/data.ncep.reanalysis2.html also contains the u and v wind components, for the
surface (10 m) and also multiple pressure levels (1000 mb up to 10 mb). NOAA provides those
reanalysis files in NetCDF format. For simplicity, the 10-m wind observations from those
NetCDF files have already been extracted for you (using “nc_varget” command) and are hosted
at: http://www.usna.edu/Users/oceano/barrett/SO335/lab3.mat. Once you load lab3.mat, you
should see six variables: uwind_28jun2012, vwind_28jun2012, uwind_25dec2013,
vwind_25dec2013, lon, lat. These files should be the same shape as the pressure fields from Lab
1 and part I of Lab 3.
1. Using the divergence function in MATLAB, calculate the divergence of the vector fields on
both 28 Jun 2012 and 25 Dec 2013. Create two figures (with appropriate titles and axis labels)
that display: magnitude of the divergence field in labeled, filled contours, and the quivered wind
field.
“Pretty” up each figure with the following: Use the command “axis tight” to bring the figure
edges closer to the data. Scale the quivered vector field using the scale factor of 2. Add
coastlines (use linewidth 2). Add a colorbar. Center the color range using the command
caxis([min max]), replacing “min” and “max” with values (center them around zero: for
example, [-1 1], not [-1.2 1.0]). You should have two figures to add to the lab deliverable (10 pts
each).
Similar to the task in Part I of this lab, type a paragraph analyzing the relationship between the
surface wind vectors and the magnitude and sign of the divergence field. (10 pts).
2
III. Vorticity of a vector
1. Using the curl command in MATLAB, calculate the relative vorticity of the surface wind field
for both 28 Jun 2014 and 25 Dec 2013. Similar to the task in Part II of this lab, create figures
with labeled, filled relative vorticity contours, then overlay the surface wind field (add
appropriate titles and axis labels). You should have two more figures to add to the lab
deliverable (10 pts each).
“Pretty up” each figure using similar techniques as in Part II.
Type a double-spaced paragraph analyzing the relationship between the surface wind field and
the magnitude and sign of the relative vorticity field. (10 pts).
Turn in your annotate MATLAB code with the lab deliverable.
Summary of deliverables
2 figures, 1 paragraph from Gradient section (30 points)
2 figures, 1 paragraph from Divergence section (30 points)
2 figures, 1 paragraph from Vorticity section (30 points)
Annotated code (10 points)
3