Description
Objective
The purpose of this tutorial is to exercise your ability to read, correlate, and interpolate data
sets. By the end of this tutorial, you will be able to integrate two different datasets, one of
temperature vs. time and one of altitude vs. time, to create an interpolated dataset of
temperatures vs. altitude for a high altitude balloon flight.
Prerequisites: Assignments 1, 2 and 3
Introduction
Experiments produce data, and sometimes the interpretation of that data depends on other
measurements from other experiments. For example, the High Altitude Ballooning Team,
HARBOR flies a helium balloon to over 100,000 ft taking measurements of Earth’s atmosphere
along the way. At the same time, a GPS receiver onboard charts the balloon payload’s location
in real time and broadcasts that to a receiving computer on the ground so that the launch team
can chase, locate, and recover the payload after flight. Each measurement records what
scientists call a time series, that is a table of data and the associated time that measurement
was recorded. A temperature sensor on the payload records the temperature over time – say
every few seconds – and the GPS receiver records the balloon’s altitude over time. If we can
combine these two data sets, we’d have an interesting measurement of the temperature at each
altitude during the balloon’s flight.
But there is a problem. The temperature measurements are regular, but because the GPS
receiver is broadcasting the altitude to the ground, it is not only less frequently measured, but
the timing isn’t regular due to broadcasting issues with the transmitter involved. So we can’t just
simply match up the data from one and the data from another and make a nice plot of
temperature vs. altitude. Instead, we must use the time of the temperature measurement to
interpolate the altitude from the more sparsely sampled GPS data.
A note about interpolation
Interpolation is the process we use to determine an estimate of the value of a measured
quantity between two known values. For example, in the figure below, we have made two
measurements, y0, y1 at two different
values of x0, x1.
We can determine an estimate for any
value of y at any value of x anywhere
between x0,x1 by finding the slope
and intercept of the line connecting
the two points and using that to
compute the value we are interested
in. This is known as linear
interpolation, and, for most well
sampled, smoothly varying
measurements, like our altitude data,
this is an excellent way to
approximate the interpolated value.
And it is the one we will use in this
tutorial. Recalling the equation for a line, y = mx + b, take a moment to work out expressions for
m and b in terms of y0,y1 and x0,x1. You’ll need those later.
Designing your code
1. Develop our problem statement: “We need a code that will read in temperature time
series, read in a GPS time series, and use an interpolation algorithm to produce a plot of
temperature vs. altitude.”
2. Define the inputs and outputs: We will use the following input data files (see the Canvas
assignment page):
o Atmospheric data – Data from the HARBOR PASCAL instrument that logs the
temperature as a function of time.
o GPS data – The transmission log file from the inflight telemetry data
Go ahead and download these. The output will be a plot of temperature vs. altitude, one
panel for the ascent stage of the flight, and the other for the descent stage. Note the first
file contains three columns of temperature data. We will be using the first temperature
column, as this was the sensor taped to the outside of the payload.
3. Develop the algorithm: The algorithm will build on your skills manipulating files from the
last tutorial, and add in the interpolation scheme above. As we read in each temperature
measurement, we’ll need to compare that to the altitude data, located the GPS times that
bound the temperature data, and perform the interpolation. The interpolated altitude will
be stored as a pair with that temperature to create a dataset we can plot. We’ll refer to
this as the “correlated” data, as compared to the “raw” data. We do this because any
interpolation is merely an estimate of the data, not an actual measurement itself.
4. Translate the algorithm into pseudocode and, ultimately, python: By now, you are getting
a pretty good hang of how to get these things going: you write a completely working
python shell that does nothing but list the things you need to do. However, I am going to
go a bit further this time, and instead of just writing a comment line for what I want the
code to do, I will specify a function that will perform that action. So, looking at the
following:
#—————————————————————————-
# G e n e r a l I n f o r m a t i o n
#—————————————————————————
# Name: harbor.py
#
# Usage: python harbor.py
#
# Description: Code to correlate and interpolate temperature vs. time with
altitude vs. time
#
# Inputs: Wxfile: contains the HARBOR weather data (WX)
# GPSfile: contains the HARBOR GPS track data
# DisplayOption: either “show” to screen or “save” to file
#
# Outputs: plots and analysis
#
# Auxiliary Files: None
#
# Special Instructions: None
#
#—————————————————————————-
# C o d e H i s t o r y
#—————————————————————————-
# Version: 1.0
#
# Author(s): John Armstrong (jca)
# jcarmstrong@weber.edu
#
# Modifications:
# 5 JUL 2012 – First Light (jca)
#
#—————————————————————————-
#—————————————————————————-
# I m p o r t L i b r a r i e s
#—————————————————————————-
import sys
import matplotlib
import matplotlib.pylab as plot
import math as m
import numpy as np
#—————————————————————————-
# D e f i n e f u n c t i o n s
#—————————————————————————-
def readWxData(wxFileName):
# Do Stuff
def readGPSData(gpsFileName):
# Do Stuff
def interpolateWxFromGPS(wxTimes,gpsTimes,gpsAltitudes):
# Do Stuff
def plotAllFigs(display):
# Do Stuff
#—————————————————————————-
# M a i n P r o g r a m
#—————————————————————————-
# parse the name of the data file
try:
wxFileName = ‘TempAndPressure.tx’
gpsFileName =‘gpsData.txt’
display = ‘show’ # or save
except (ValueError, IndexError), e:
print e
sys.exit()
# read in temperature and time data
wxTimes, wxTemperatures = readWxData(wxFileName)
gpsTimes, gpsAltitudes = readGPSData(gpsFileName)
# compute wx alts by interpolating from gps alts
wxCorrelatedAltitudesUp, wxCorrelatedTemperaturesUp,
wxCorrelatedAltitudesDown, wxCorrelatedTemperaturesDown = \
interpolateWxFromGPS(wxTimes,gpsTimes,gpsAltitudes)
# plot and quit
plotAllFigs(display)
This is a perfectly functional python code that does absolutely nothing useful, except it
does give us a good guide for how to proceed:
o After my standard header, I write down the shells of a few functions I think I’ll
need, along with very descriptive names, so their name tells me exactly what I
want them to do.
o Next, in the main program, I have a block for reading in the names of the two files
plus a keyword I call display. I want to use this to tell the program whether to
show the graph in the screen or save the graph to a file.
o Finally, I write the rest of the program in terms of the functions that will perform
the duties. This gives me a clean, modular code that I can now proceed to flesh
out one piece at a time.
Now the difficult part. You need to write functions for each of those shells that perform
the proper tasks. Some tips:
1. Don’t forget your top down design! For each function of the program, take a moment to
write down a clear statement of what the code will do, what the inputs and outputs are,
etc. This will save you a lot of time.
2. Reuse your old code! You’ve already got some code that reads in files. Cannibalize it, rewrite it, and re-use it for this purpose. In fact, if you took a little time now, you could
generalize your file reader to work with nearly any file, and would always have that in
your toolkit!
3. Web references – and your textbook – are your friends. For example, note that one of
your files is a comma separated value
(csv) file rather than space delimited.
You can still use the split method from
before, but you will have to change it. I
would guess it is as simple and using
split(“,”) instead of split() but don’t take
my word for it, look it up!
4. Recall the way python returns values
from functions. You can return more
than one value at a time, so the way
these functions are used should give
you some clues as to what values you
have to return.
5. Note that I am separating the “Up” and
“Down” portions of the flight. How will
you do that? Keep in mind that the
balloon goes up until it doesn’t.
6. Make frequent checks of your progress.
For example, an excellent way to see if
your first two functions work is to plot that data right away. It will look something like the
figure above.
7. Finally, just to give you a hand, I went ahead and wrote the plotting algorithm for the final
data. I did this because when atmospheric scientists plot temperature vs. altitude, they
do it in a very unique way, switching the x and y axes, and will look like the figure here:
The following code may help.
def plotAllFigs(display):
plot.figure()
plot.subplot(2,1,1)
plot.plot(wxTimes, wxTemperatures,linewidth=2.0)
plot.xlim(0,2.25)
plot.title(“Harbor Flight Data”)
plot.ylabel(“Temperature, F”)
plot.subplot(2,1,2)
plot.plot(gpsTimes, gpsAltitudes,linewidth=2.0)
plot.xlim(0,2.25)
plot.ylabel(“Altitude, ft”)
plot.xlabel(“Mission Elapsed Time, Hours”)
if display == “save”:
plot.savefig(“fig2.2.1.png”)
elif display == “show”:
plot.show()
else:
print “Unrecognized output, “, display
plot.figure()
plot.subplot(1,2,1)
plot.title(“Harbor Ascent”)
plot.plot(wxCorrelatedTemperaturesUp,
wxCorrelatedAltitudesUp,linewidth=2.0)
plot.ylabel(“Altitude, feet”)
plot.xlabel(“Temperature, F”)
plot.ylim([0,100000])
plot.subplot(1,2,2).set_yticklabels([])
plot.title(“Harbor Descent”)
plot.plot(wxCorrelatedTemperaturesDown,
wxCorrelatedAltitudesDown,linewidth=2.0)
plot.xlabel(“Temperature, F”)
plot.ylim([0,100000])
if display == “save”:
plot.savefig(“fig2.2.2.png”)
elif display == “show”:
plot.show()
else:
print “Unrecognized output, “, display
8. Test and refine: As always.
What to hand in:
1. Generate a complete code that saves the plots above as “raw.png” for the raw data, and
“correlated.png” for the correlated data.
2. In your submission, comment on the differences between the ascent and descent
temperatures. What could have caused these differences? Hint: and examination of the
raw data, especially the GPS data, may help.
3. Also, generate and examine plots for the 2nd and 3rd temperature measurements.
When you email me the code, comment on any anomalies. What possible causes –
location of sensors, sensor performance, environmental conditions – could cause such
differences.
4. Extra Credit – Do you see those little data dropouts on the right hand plot (the spikes
that go to zero)? Those are bad data. Without editing the text file design a way to get rid
of those types of data dropouts to clean up the output. 25% extra credit if you do so!
