## 1. Introduction

[2] Radio waves reflected from a time varying ionosphere experience a Doppler shift. A variety of methods have been used over the years to measure Doppler shift. A common technique has involved transmitting on a single frequency and Fourier analyzing the signal returned from the ionosphere. Fourier analysis is desirable because the returned signal normally contains a spectrum of frequencies resulting from multiple reflections between the ground and the ionosphere as well as from separate layers within the ionosphere. As well, the Earth's magnetic field causes the ionosphere to be birefringent so that a single linearly polarized radio wave on entering the ionosphere separates into o and X-ray modal components which each traverse a slightly different path within the ionosphere. The resultant Doppler spectrum can range from a number of sharply defined Doppler-shifted frequencies under quiet conditions to a spread spectrum when the ionosphere is highly disturbed such as may occur during spread F.

[3] From a practical point of view, the multiplicity of Doppler shifted returns from the ionosphere produces signal fading and associated rapid phase shifts which can be highly deleterious in a number of HF engineering applications. Such applications may require the modeling of ionospheric propagation conditions using archival or real time measurements. An inability to measure ionospheric Doppler shift and Doppler spread simultaneously over the full range of ionospheric HF propagation has resulted in the development of statistically based mathematical models of propagation used by engineers for equipment design. Such models often fail to reflect the physical reality of ionospheric propagation and consequently the equipment so designed may not work in practice as well as theoretically expected. The Doppler measurements and calculations presented in this paper provide a physical picture of ionospheric characteristics on which improved ionospheric physical models could be based.

[4] A previous paper [*Lynn*, 2007] has described the application of a time-interleaving technique to the development of a Doppler ionosonde capable of making high-resolution Doppler measurements at every frequency of an ionosonde sweep. The resultant Doppler ionogram can be completed in less than 3 min. This technique was commercialized in the IPS KEL 71 ionosonde. Examples of the output of such an ionosonde when observing a range of ionospheric phenomena are given in that paper. Of particular interest was the discovery that in daytime, the maximum Doppler value near the critical frequency of the ionosphere could be proportional to the rate of change of critical frequency. This relationship deteriorated at night. Further investigation suggested that such a relationship could be explained theoretically in terms of a simple parabolic layer model of the F2 region.

[5] This paper describes in detail the derivation of Doppler shift using a time-varying parabolic layer model of the F2 region in which the parabolic layer parameters are derived from standard non-Doppler ionosonde measurements converted into true height profiles by the readily available software program POLAN. The Doppler measurements thus synthesized are then compared with the observed values obtained from a KEL IPS 71 ionosonde. Apart from the theoretical and scientific interest, a capability to derive accurate Doppler information from the many standard non-Doppler ionosondes already deployed around the world is of particular significance to both HF communications and over-the-horizon (OTH) radar.