ERROR IN C A L C U L A T I N G THE P R O P A G A T I O N

OF S H O R T W A V E R A D I O S I G N A L S

A. I . T o v b i n a

T I M E

UDC 621.391.812.8:529.781

It is known that the determination of the shortwave signals' propagation time is reduced to evaluating the parameters of their trajectories, namely, of the effective reflection height h and the number of reflections n from the ionosphere. In precise-t ime signals the minimum number of reflections is taken into consideration.

Below we provide the results of calculating the signals' propagation time by this method and compare them with regular propagat ion- t ime measurements on the route between Tashkent and Novosibirsk (1850 kin) during the period of 1970-71.

Por this route R -~ 1850 km and nmi n = 1. Since this path has a single hop, it is necessary to take into con- sideration, in addition to the regular layers E, F 1 and F2, also the probability of reflection from the sporadic layerE s.

The effective heights of reflection from the P region are calculated by means of graphs for the diurnal varia- tions of the effective heights of the layers F 1 and Fz. These graphs are forecasts for the given month of median values which correspond to the given ratio of the vertical incidence to the cri t ical frequency of the layer f_t / fo [1]. We can then calculate frequency from the formula

several working frequency values which correspond to the effective height shown on the graph. The secant of the in- cident-wave angle sec~Ocr t corrected for the curvature of the earth and of the ionosphere is obtained from the cor- responding graph according to the given dispersion of signals and the effective reflection height h. The sought-for value of h for the given secant is found from the carrier frequency of 5 or 10 MHz by interpolation between the two nearest values of fwrk" If the carrier frequency should lie outside the obtained working-frequency range, it means that according to the forecast, the probability of reflection from the given layer at that time of the day is small or altogether absent. The t ime of the layer E operation at the reflection points of the above-mentioned path is deter- mined from the graph of the maximum useable frequencies. In the majority of cases the forecast indicates foreach specific instance the possibility of reflection from a single regular layer only. The instances when more than one possible reflection from regular layers (normally two) occurs refer to transition periods when the path passes through a penumbra. The effective height is then calculated as the arithmetic mean of the two effective layer heights.

Since the basic reflecting layer of that path in the daytime is, according to the forecast, layer E and the re- flecting heights from E and Es are assumed to be the same, the problem of accounting for the reflections from Es is thus eliminated in daytime. A different picture is observable at night when the basic reflecting layer is F2 whose effective height differs considerably from that of E s.* The method of accounting for the reflections from the E s layer at night depends on the conditions of the reception of signals whose field strength in Novosibirsk is considerab- ly weaker than that of such shortwave radio stations as RKM and RVM. The signal-to-noise ratio in the majority of cases does not exceed 10. In order to determine the possibility of the reflection of signals radiated at a low power [2], it is recommended to take into account the probability Pbg s of a complete reflection from the screening Iayer Es and not the probability of any reflections.

*The effective height of the E and E s layers was assumed for our calculations to be 120 km.

Translated from Izmefitel 'naya Tekhnika, No. 10, p. 93, October, 1973.

�9 1974 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, No Y. 10011~ No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, me- chanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.

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TABLE 1

Month i !

I >" I "=

Winter Summer Equinox

50 50 50

50 70 60

O'~:J

40 30 50

Charts and nomograms [2] serve to compute PbE s for the given path. In the winter and solstice months the values of PbEs are smal l and amount to 20 and 15% for the carrier frequencies of 5 and 10 MHz respect ively. However, in the summer PbE s increases, at taining at night 55% for 5 MHz and 40% for 10 MHz.

It is obvious that, during the period when the screening layer Esexists, signals are ref lec ted from it and not from the F 2 layer. Thus, for night trans- mission the number of reflections from E s in the course of a month wil l be proportional to PbEs% and from the F2.1ayer to (100-PbE)%. Therefore, the

mean monthly value of the effect ive ref lect ion height for night transmissions was ca lcu la ted as the mean-weighted value of the ref lec t ion heights from Es and F2, with the weights of PbEs and (100- pbEs) respect ively assigned to them.

In order to evaluate the errors in computing the propagation t ime rc lc we have compared these computations with measurements carried out according to the method of simultaneous double-s ided transmissions and receptions

which were averaged out over a month for each exper iment O[Tms ]. The root -mean-square error O[rms], which de- pends on the signal recept ion error, the error in locking-on the t ime scales of the radio station and the receiving point, and the error due to the dispersion of the ref lect ion height v a n e s during a month did not exceed for the path in question 20 gsec in dayt ime and 40 ~sec at night. The differences Ar = r c l c - T m s were grouped for each exper i - ment according to the t ime of the day, month, and season. For each of these groups the root -mean-square v a n e s o l a f ] of the differences were ca lcula ted , thus providing, with O~ms] taken into consideration, an idea of the order of the error incurred in using forecasts for ca lcula t ing the mean monthly v a n e s of propagation t ime.

It wilI be seen from Table 1 (O[AT] = 70 ~sec) that the largest error in forecasting the propagation t ime occurs in summer at night, and this is due to a rise, as compared with other seasons, in the effect of the E s layer on the

nature of signal propagation.

Of part icular interest for locking- in separated clocks is the midday period, when the 10 MHz signals are pro- pagated by ref lect ion from the E layer. These reflections appear approximate ly 2 h after daylight has covered the

entire path and disappear with the coming of night. During this period the forecast errors are at a minimum.

L I T E R A T U R E C I T E D

1. Monthly Forecast of Radiowave Propagation, IZMIR Acad. Nauk SSSR, Nauka, Moscow (1970-71). 2. Instructions for Computing Frequencies of Shortwave Radio Transmissions Which Are Reflected f romthe Es

Layer, Nauka, Moscow (1964).

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