Previous page: Measuring temperatures
and composition in the ionoshere

### How to Get the Temperatures and Ion Composition from
the Spectra

If the actual spectra that the radar measures from the ionosphere
consisted of continuous smooth curves, and if it was necessary
to measure only two quantities, say the width and the total power,
then one could use a ruler and get pretty good answers. However,
the measured spectra are noisy data points like the red circles
on the graph below, and the idea is to get all of the temperatures
and ion compositions "right". Two ideal, or theoretical,
spectra are shown in purple and blue. They have different electron
temperatures and number of electrons. There is no simple way to
get from the data points to the best answers, but one would say
that one spectrum is much better than the other. How does one
find the best match? The method has several steps and illustrates
how a lot of work is done in science.

- The first step is to make a model. In this case the model
is a mathematical function on the computer. It takes temperatures
and composition and produces a spectrum. The model is provided
by the theoretical scientist to the experimental scientist. The
model is really backwards; we would like to put in the spectrum
and get out the temperatures and composition, but this is not
possible, and so the other steps below are necessary.

- The next step is to put a good guess of what the right answers
might be into the model compare the data to the model and get
a number which tells us how good the first guess is. The idea
is to look for better guesses by trying again and again. We can
evaluate the comparison for each guess. If we had only one parameter
(say one temperature only in the model) then all possible evaluations
would form a curve. We find the bottom of the curve, as in the
graph below. Since we have many parameters, the curve is really
a surface with many dimensions, but the computer can handle it.

- The last step is to determine how big the errors in our parameters
are, and to determine if our final evaluation of the comparison
is good enough given the amount of noise on the data points.
This is very important because it determines whether the model
is good enough or we need a new one.

First of the four pages: How does a radar
work?