An ideal procedure for routine ionogram analysis should give consistently good results without operator intervention. This requires some built-in "intelligence" and adaptability. With high quality data we want the highest attainable accuracy. With normal data the procedure should have criteria for judging the acceptability of each individual point or profile parameter. It should be able to test, impose and remove physical constraints, and to smooth, de-weight, or reject bad data. Where a section of the profile cannot be calculated directly (such as the underlying, peak or valley regions) the procedure should use a defined physically-based model. Thus it should automatically do the "best" thing, in a consistent fashion, with widely varying types of data; if a normal best is not possible it should explain why and do the next-best.

The **POL**ynomial **AN**alysis program POLAN is an attempt to meet some
of these requirements. It provides an accurate and flexible procedure with
adjustable resolution and the ability to mix physically desirable conditions
with observed data in a weighted least-squares solution. The analysis can
adapt readily to changes in the density and quality of data points, and
respond in different ways to different situations. For routine work POLAN may
be used as a "black box" with only the virtual height data, the magnetic dip
angle and the gyrofrequency as required inputs. Optimised default procedures
are then used in the analysis. If the input data is not self-consistent, and
implies some physically unacceptable feature in the profile, this is noted and
corrected. All results are obtained in a fully automatic, one-pass analysis.

POLAN is designed to reproduce current techniques (using linear laminations,
parabolic laminations, single polynomials or fourth-order overlapping
polynomials) by selection of a single parameter. It also provides a wide range
of high order procedures, which are preferable for most work. When
extraordinary ray data are not available, clearly defined and physically
reasonable models are used for the start and valley regions. This allows
direct comparison of results obtained under different conditions. When
extraordinary ray data are available these are combined with the ordinary data
in optimised procedures to resolve the starting and valley ambiguities. The
physical models are included in the least-squares solutions for these regions,
so that ill-defined data will give reasonable results (based primarily on the
models). Peak parameters are determined by a least squares Chapman-layer fit
to avoid the systematic scale height error inherent in a parabolic-peak
approximation. Observed ordinary and extraordinary ray critical frequencies
may be included in the peak calculation, to obtain best estimates of the
critical frequency **FC**, the probable error in FC, the peak height and
the scale height at the peak. With this careful combination of extraordinary
ray data and physical constraints, POLAN is well suited to studies of the
ionospheric scale height, the size of the valley between the **E**,
**F1** and **F2** layers, and of ionisation below the night F layer.

For a given set of virtual-height data, real-height analysis using POLAN takes roughly twice as long as a simple lamination analysis. For a given overall accuracy, however, POLAN requires only about half as many data points. Thus there is little final difference in computing time, and there can be a worthwhile saving in the time required for scaling the ionograms.

In normal operation results are obtained using a polynomial representation of
the real-height profile, fitted to several points each side of the section
being calculated. This provides an accurate interpolation between scaled
frequencies, which is necessary for an accurate analysis. Virtual height data
define primarily the real-height gradients at the scaled frequencies. Real
heights are therefore defined most accurately between the scaled frequencies
(*Titheridge, 1979*). Thus when an accurate analysis is used to obtain
real heights at the scaled frequencies, it is dealing directly with the most
difficult points. Tests have shown that direct second difference interpolation
is then sufficient to reproduce the profile between scaled frequencies with
little or no increase in the mean error. Results obtained by POLAN are
therefore normally stored as arrays giving the scaled frequencies and
corresponding real heights. Some extrapolated points are added above the layer
peaks, for simpler calculation of mean profiles and to give smooth plots with
second or third order parametric interpolation (which is necessary to cope
with non-monotonic profiles).

Copies of this report can be obtained from WDC-C1 STP or the National Geophysical Data, Solar-Terrestrial Physics Division (E/GC2), 325 Broadway, Boulder, Colorado 80303, USA.

*Increased accuracy with simple methods of ionogram analysis*. Titheridge,
J.E. (1979), J. Atmosph. Terr. Phys., 41, 243--350

Ionosondes | WDC

3-DEC-1997 Matthew Wild