**POLAN** lists errors in the calculated peak parameters **FC, HMAX**
and **SH**. These errors correspond to about an 80% confidence range, in
the least-squares fit of a Chapman layer peak to calculated profile gradients.
They can appreciably underestimate the true errors when the peak is defined by
only a small number of data points which just happen to be a close fit to the
Chapman expression. Also the listed errors make no allowance for real-height
errors introduced at lower heights, which will considerably increase the
overall uncertainty in the height of the layer peak (**HMAX**).

The main errors in a calculated real-height profile arise from uncertainties
in the start region (at night), and in the valley between the E and F layers
(during the day). Lack of data at frequencies below fmin requires the use of
some model for the low-density ionisation. This is best based on the use of a
"starting height" which is passed to **POLAN** as the input parameter
**START**. Suitable mean values for the starting height can be calculated,
as a function of local time, season and latitude, from equations given in
*J. Atmosph. Terr. Phys. 48 (5), 435-446, 1986*.
Note that some previous versions of **POLAN** had an error [the 'additional
height' **ht(30)** was extrapolated and not limited] which produced some
over-large fluctuations in start calculations.

The valley model built in to **POLAN** uses a valley width proportional to
the neutral scale height, which is taken as a simple function of the real
height (with, in the present version, a small bias towards the calculated
scale height of the underlying peak). This seems about the best that can be
done at present.

Most ionograms are continuous across the **F1** cusp. When there is a
discontinuity in virtual height, indicating a separate peak for the **F1**
layer, it may be best to assume only a small following valley. This is
obtained by setting the virtual height at the critical frequency (a scaled or
zero value) equal to 0.2. **POLAN** then assumes a value of 0.2 for the
parameter **VALLEY** at this point, giving a valley width of 0.2 times the
normal default value.

When suitable extraordinary ray data is available, an allowance for the ionisation in the unobserved regions is calculated directly within POLAN. With good data this allowance is accurate to about 10 to 30%. Thus real- height errors are typically about one fifth as large as they would be if no allowance was made for underlying or valley ionisation. Note that calculated heights in the unobserved regions serve only to reproduce the total amount of the unobserved ionisation, and should not be taken to indicate a true profile shape.

Good results for the start and valley calculations require good extraordinary ray measurements at low frequencies (where the x trace is curling up, showing increasing group retardation at decreasing frequencies). Results obtained can vary considerably from one ionogram to another, depending on the availability and quality of low-frequency data and the presence or absence of extraordinary ray measurements. To minimise these variations the model start parameters are included, with a small weight, in all least-squares start calculations. Data of decreasing quality then tends to give results which are increasingly biased towards the model. Thus to increase the consistency of start calculations it is recommended that a standardised model value for START is always provided.

Extraordinary-ray data is useful only to help in start or valley calculations.
It is not employed at other points since horizontal variations in the
ionosphere give varying results from the ordinary and extraordinary
components. Extraordinary ray measurements at frequencies greater than about
1.0 MHz above the lowest ordinary ray frequency fmin (for the start), or more
than 1.0 MHz above the critical frequency of a lower layer (for the valley
calculation) provide little useful information about the unseen regions. If
such data is provided it will be ignored by **POLAN** in most cases.

**POLAN** is now being used by many different groups, under many different
conditions, so we can expect new problems to surface. Please keep me informed
of your experiences with POLAN, so that I can circulate updates as required to
improve operation under different conditions.

With best wishes,

John E. TitheridgePhysics Department

University of Auckland

Private Bag, Auckland

New Zealand.

True height analysis | Ionosondes | WDC

4-DEC-1997 Chris Davis