Session Four
============

In our final session we will concentrate on color images and
perspective views of gridded data sets.  Before we start that
discussion we need to cover three important aspects of plotting
that must be understood.  These are

#. Color tables and pseudo-colors in GMT.
#. Artificial illumination and how it affects colors.
#. Multi-dimensional grids.

CPTs
----

The CPT is discussed in detail in the GMT Technical Reference.
Please review the format before experimenting further.


CPTs can be created in any number of ways.  GMT provides
two mechanisms:

#. Create simple, linear color tables given a master color table
   (several are built-in) and the desired *z*-values at color boundaries
   (:doc:`/makecpt`)

#. Create color tables based on a master CPT color table and the
   histogram-equalized distribution of *z*-values in a gridded data file (:doc:`/grd2cpt`)

One can also make these files manually or with awk
or other tools.  Here we will limit our discussion to :doc:`/makecpt`.
Its main argument is the name of the master color table (a list is
shown if you run the module with no arguments) and the equidistant
*z*-values to go with it.  The main options are given below.

======= =============================================
Option  Purpose
======= =============================================
**-C**  Set the name of the master CPT to use
**-I**  Reverse the sense of the color progression
**-V**  Run in verbose mode
**-Z**  Make a continuous rather than discrete table
======= =============================================

To make discrete and continuous color CPTs for data that ranges
from -20 to 60, with color changes at every 10, try these two variants:

   ::

    gmt makecpt -Crainbow -T-20/60/10 > disc.cpt
    gmt makecpt -Crainbow -T-20/60/10 -Z > cont.cpt

We can plot these color tables with :doc:`/colorbar`; the options
worth mentioning here are listed below.  The placement of the
color bar is particularly important and we refer you to the
:ref:`Plot embellishments <GMT_Embellishments>` section for all
the details.
In addition, the **-B** option can be used to set the title
and unit label (and optionally to set the annotation-, tick-,
and grid-line intervals for the color bars.).  Note that the makecpt commands
above are done in classic mode.  If you run :doc:`/makecpt` in modern mode
then you usually do not specify an output file via standard output since
modern mode maintains what is known as the current CPT.  However,
if you must explicitly name an output CPT then you will need to
add the **-H** option for modern mode to allow output to standard output.

======================================================= ==================================================================================
Option                                                  Purpose
======================================================= ==================================================================================
**-C**\ *cpt*                                           The required CPT
**-Dx**\ *xpos/ypos*\ **+w**\ *length/width*\ [**+h**]  Sets the position and dimensions of scale bar. Append **+h** to get horizontal bar
**-I**\ *max\_intensity*                                Add illumination effects
======================================================= ==================================================================================

Here is an example of four different ways of presenting the color bar:

.. literalinclude:: /_verbatim/GMT_tut_14.txt

Your plot should look like :ref:`our example 14 below <gmt_tut_14>`

.. _gmt_tut_14:

.. figure:: /_images/GMT_tut_14.*
   :width: 400 px
   :align: center

   Result of GMT Tutorial example 14

Exercises:

#. Redo the :doc:`/makecpt` exercise using the master table
   *hot* and redo the bar plot.

#. Try specifying **-B**\ 10g5.

Illumination and intensities
----------------------------

GMT allows for artificial illumination and shading.  What this
means is that we imagine an artificial sun placed at infinity in
some azimuth and elevation position illuminating our surface.
The parts of the surface that slope toward the sun should brighten
while those sides facing away should become darker; no shadows are
cast as a result of topographic undulations.

While it is clear that the actual slopes of the surface and the
orientation of the sun enter into these calculations, there is
clearly an arbitrary element when the surface is not topographic
relief but some other quantity.  For instance, what does the slope
toward the sun mean if we are plotting a grid of heat flow anomalies?
While there are many ways to accomplish what we want, GMT offers
a relatively simple way:  We may calculate the gradient of the surface
in the direction of the sun and normalize these values to fall in
the ±1 range; +1 means maximum sun exposure and -1 means complete
shade. Although we will not show it here, it should be added that
GMT treats the intensities as a separate data set.  Thus, while
these values are often derived from the relief surface we want to
image they could be separately observed quantities such as back-scatter
information.

Colors in GMT are specified in the RGB system used for computer
screens; it mixes red, green, and blue light to achieve other colors.
The RGB system is a Cartesian coordinate system and produces a color cube.
For reasons better explained in Appendix I in the Reference book it is
difficult to darken and brighten a color based on its RGB values and an
alternative coordinate system is used instead; here we use the HSV system.
If you hold the color cube so that the black and white corners are along
a vertical axis, then the other 6 corners project onto the horizontal plane to
form a hexagon; the corners of this hexagon are the primary colors Red,
Yellow, Green, Cyan, Blue, and Magenta.
The CMY colors are the complimentary colors and are used when paints are
mixed to produce a new color (this is how printers operate; they also add
pure black (K) to avoid making gray from CMY).  In this coordinate system the
angle 0-360° is the hue (H); the Saturation and Value are harder to
explain.  Suffice it to say here that we intend to darken any pure color
(on the cube facets) by keeping H fixed and adding black and brighten it by adding white; for
interior points in the cube we will add or remove gray.
This operation is efficiently done in the HSV coordinate system; hence all
GMT shading operations involve translating from RGB to HSV, do the
illumination effect, and transform back the modified RGB values.

Color images
------------

Once a CPT has been made it is relatively straightforward to generate
a color image of a gridded data.  Here, we will extract a subset of the
global 30" DEM called SRTM30+:

   ::

    gmt grdcut @earth_relief_30s -R-108/-103/35/40 -Gtut_relief.nc

Using :doc:`/grdinfo` we find that the data ranges from about 1000m to
about 4300m so we need to make a CPT with that range.

Color images are made with :doc:`/grdimage` which takes the usual
common command options (by default the **-R** is taken from the data set)
and a CPT; the main other options are:

==================== ======================================================================
Option               Purpose
==================== ======================================================================
**-E**\ *dpi*        Sets the desired resolution of the image [Default is data resolution]
**-I**\ *intenfile*  Use artificial illumination using intensities from *intensfile*
**-M**               Force gray shade using the (television) YIQ conversion
==================== ======================================================================

We want to make a plain color map with a color bar superimposed above
the plot.  We try

.. literalinclude:: /_verbatim/GMT_tut_15.txt

Your plot should look like :ref:`our example 15 below <gmt_tut_15>`

.. _gmt_tut_15:

.. figure:: /_images/GMT_tut_15.*
   :width: 400 px
   :align: center

   Result of GMT Tutorial example 15

The plain color map lacks detail and fails to reveal the topographic
complexity of this Rocky Mountain region.  What it needs is artificial
illumination.  We want to simulate shading by a sun source in the east,
hence we derive the required intensities from the gradients of the
topography in the N90°E direction using :doc:`/grdgradient`.  Other than the
required input and output filenames, the available options are

  +------------------------------------------------------------------+-------------------------------------------------------------------+
  | Option                                                           | Purpose                                                           |
  | **-A**\ *azimuth*                                                | Azimuthal direction for gradients                                 |
  +------------------------------------------------------------------+-------------------------------------------------------------------+
  | **-fg**                                                          | Indicates that this is a geographic grid                          |
  +------------------------------------------------------------------+-------------------------------------------------------------------+
  | **-N**\ [**t**\|\ **e**][**+s**\ *norm*][**+o**\ *offset*]       | Normalize gradients by *norm/offset* [= 1/0 by default].          |
  +------------------------------------------------------------------+-------------------------------------------------------------------+
  |                                                                  | Insert **t** to normalize by the inverse tangent transformation.  |
  +------------------------------------------------------------------+-------------------------------------------------------------------+
  |                                                                  | Insert **e** to normalize by the cumulative Laplace distribution. |
  +------------------------------------------------------------------+-------------------------------------------------------------------+

The :ref:`GMT inverse tangent transformation <gmt_atan>`  shows that raw slopes from bathymetry tend to be
far from normally distributed (left).  By using the inverse tangent
transformation we can ensure a more uniform distribution (right).
The inverse tangent transform simply takes the raw slope estimate
(the *x* value at the arrow) and returns the corresponding inverse
tangent value (normalized to fall in the plus/minus 1 range; horizontal
arrow pointing to the *y*-value).

.. _gmt_atan:

.. figure:: /_images/GMT_atan.*
   :width: 600 px
   :align: center

   How the inverse tangent operation works.  Raw slope values (left) are processed
   via the inverse tangent operator, turning tan(x) into x and thus compressing
   the data range.  The transformed slopes are more normally distributed (right).

**-Ne** and **-Nt** yield well behaved gradients.  Personally,
we prefer to use the **-Ne** option; the value of
*norm* is subjective and you may experiment somewhat in the
0.5-5 range.  For our case we choose

    ::

     gmt grdgradient @tut_relief.nc -Ne0.8 -A100 -fg -Gus_i.nc

However, for most maps relying on the remote data sets we do not actually
need to extract subsets and run :doc:`/grdgradient` manually.  Instead, we let :doc:`/grdimage`
create the gradients directly from the subset of the global grid, passing the
arguments to :doc:`/grdgradient` via the **-I** option of :doc:`/grdimage`.  
Given the previous CPT and our chosen :doc:`/grdgradient` arguments we can
create the shaded relief image:

.. literalinclude:: /_verbatim/GMT_tut_16.txt

Your plot should look like :ref:`our example 16 below <gmt_tut_16>`

.. _gmt_tut_16:

.. figure:: /_images/GMT_tut_16.*
   :width: 400 px
   :align: center

   Result of GMT Tutorial example 16.


Exercises:

#. Force a gray-shade image.

#. Rerun the example with **-I+a**\ 30\ **+n**\ 1.

Multi-dimensional maps
----------------------

Climate data, like ocean temperatures or atmospheric pressure, are often provided as
multi-dimensional (3-D, 4-D or 5-D) grids in netCDF format. This section will demonstrate
that GMT is able to plot "horizontal"
slices (spanning latitude and longitude) of such grids without much effort.

As an example we will download the Seasonal Analysed Mean Temperature from the
`World Ocean Atlas 1998 <https://psl.noaa.gov/data/gridded/data.nodc.woa98.html>`_
The file in question is named
otemp.anal1deg.nc (ftp://ftp.cdc.noaa.gov/Datasets/nodc.woa98/temperat/seasonal/otemp.anal1deg.nc).

You can look at the information pertained in this file using the program ncdump and
notice that the variable that we want to plot (otemp) is a four-dimensional variable of time,
level (i.e., depth), latitude and longitude.

   ::

    ncdump -h otemp.anal1deg.nc

We will need to make an appropriate color scale, running from -2°C (freezing temperature of salt
water) to 30°C (highest likely ocean temperature).
Let us focus on the temperatures in Summer (that is the third season, July through
September) at sea level (that is the first level). To plot these in a Mollweide projection we
use:

.. literalinclude:: /_verbatim/GMT_tut_17.txt

The addition "?otemp[2,0]" indicates which variable to retrieve from the netCDF
file (otemp) and that we need the third time step and first level. The numbering of the
time steps and levels starts at zero, therefore "[2,0]". Make sure to put the
whole file name within quotes since the characters ?, [ and ] have
special meaning in Unix.
Your plot should look like :ref:`our example 17 below <gmt_tut_17>`

.. _gmt_tut_17:

.. figure:: /_images/GMT_tut_17.*
   :width: 400 px
   :align: center

   Result of GMT Tutorial example 17


Exercises:

#. Plot the temperatures for Spring at 5000 m depth. (Hint: use ncdump -v level to
   figure out what level number that is).

#. Include a color scale at the bottom of the plot.

Perspective views
-----------------

Our final undertaking in this tutorial is to examine three-dimensional
perspective views.  The
GMT module that produces perspective views of gridded data files is
:doc:`/grdview`.  It can make two kinds of plots:

#. Mesh or wire-frame plot (with or without superimposed contours)

#. Color-coded surface (with optional shading, contours, or draping).

Regardless of plot type, some arguments must be specified; these are

#. *relief\_file*; a gridded data set of the surface.

#. **-J** for the desired map projection.

#. **-JZ**\ *height* for the vertical scaling.

#. **-p**\ *azimuth/elevation* for the vantage point.


In addition, some options may be required:

========================= =============================================================================================================
Option                    Purpose
========================= =============================================================================================================
**-C**\ *cpt*             The *cpt* is required for color-coded surfaces and for contoured mesh plots
**-G**\ *drape\_file*     Assign colors using *drape\_file* instead of *relief\_file*
**-I**\ *intens\_file*    File with illumination intensities or arguments to :doc:`/grdgradient`
**-Qm**                   Selects mesh plot
**-Qs**\ [**+m**]         Surface plot using polygons; append **+m** to show mesh.  This option allows for **-W**
**-Qi**\ *dpi*\ [**g**]   Image by scan-line conversion.  Specify *dpi*; append **g** to force gray-shade image.  **-B** is disabled.
**-W**\ *pen*             Draw contours on top of surface (except with **-Qi**)
========================= =============================================================================================================

Mesh-plot
~~~~~~~~~

Mesh plots work best on smaller data sets.  We again use the small
subset of the ETOPO5 data over Bermuda and will use the ocean CPT.
A simple mesh plot can therefore be obtained with

.. literalinclude:: /_verbatim/GMT_tut_18.txt

Your plot should look like :ref:`our example 18 below <gmt_tut_18>`

.. _gmt_tut_18:

.. figure:: /_images/GMT_tut_18.*
   :width: 400 px
   :align: center

   Result of GMT Tutorial example 18

Exercises:

#. Select another vantage point and vertical height.

Color-coded view
~~~~~~~~~~~~~~~~

We will make a perspective, color-coded view of the US Rockies
from the southeast.  Similar to the :doc:`/grdimage` examples, this is done using

.. literalinclude:: /_verbatim/GMT_tut_19.txt

Your plot should look like :ref:`our example 19 below <gmt_tut_19>`

.. _gmt_tut_19:

.. figure:: /_images/GMT_tut_19.*
   :width: 400 px
   :align: center

   Result of GMT Tutorial example 19.

This plot is pretty crude since we selected 50 dpi but it is fast
to render and allows us to try alternate values for vantage point
and scaling.  When we settle on the final values we select the
appropriate *dpi* for the final output device and let it rip.

Exercises:

#. Choose another vantage point and scaling.

#. Examine the :doc:`/grdgradient` options and select another illumination direction in **-I** and plot again.

#. Select a higher *dpi*, e.g., 200.
